THE BUILDING TRADES POCKETBOOK A HANDY MANUAL OF REFERENCE ON BUILDING CONSTRUCTION INCLUDING Structural Design, Masonry, Bricklaying, Carpentry, Joinery, Roofing, Plastering, Painting, Plumbing, Lighting, Heating, and Ventilation BY The International Correspondence Schools SCRANTON, PA. 1st Edition , 70th Thousand, 7th Impression Scranton, Pa. THE COLLIERY ENGINEER CO. 7 H j *■ . / T If mixed numbers are to be multiplied, reduce them to frac* tions, and proceed as above shown; thus, 1£ in. X 3£ in. — f X = - 3 g- = 4| sq. in. To divide fractions. Invert the divisor (i. e., exchange places of numerator and denominator) and multiply the dividend by it, reducing the result, if necessary; thus, | -r- f | X I = IS = 5 = li- If there are mixed numbers, reduce them to fractions, and then divide as just shown; thus, If 3* = ¥ y, or J# X A = -Nt = i- DECIMAL FRACTIONS. In decimals, whole numbers are divided into tenths, hun* dredths, etc.; thus, A I s written .1; .08 is read T f c , the value of the number being indicated by the position of the decimal point; that is, one figure after the decimal point is read as so many tenths; two figures as so many hundredths; etc. Moving the decimal point to the right multiplies the number by 10 for every place the point is moved; moving it to the left divides the number by 10 for every place the point is moved. Thus, in 125.78 (read 125 and As)> if the decimal point is moved one place to the right, the result is 1,257.8, which is 10 times the first number; or, if the point is moved to the left one place, the result is 12.578 which is A the first num¬ ber, moving the point being equivalent to dividing 125.78 by 10. Annexing a cipher to the right of a decimal does not change its value; but each cipher inserted between the deci¬ mal point and the decimal divides the decimal by 10; thus, in 125.078, the decimal part is A °f -78. 201 257 To add decimals. Place the numbers so that 12.965 the decimal points are in a vertical line, and 43.005 add in the ordinary way, placing the decimal 920.600 point of the sum under the other points. 1,077.827 To subtract decimals. Place the number to be subtracted with its decimal point under 917.678 that of the other number, and subtract in the 482 .710 ordinary way. 434.968 FRACTIONS. 5 To multiply decimals. Multiply in the ordinary way, and point off from the right of the result as many figures as there are figures to the right of the decimal points in both numbers multiplied; thus, in the example here given, there are three figures to the right of the points, and that many are pointed off in the result. If either number contains no deci¬ mal, point off as many places as are in the number that does. If a result has not as many figures as the sum of the deci- _ mal places in the numbers multiplied, prefix enough ciphers before the figures to make up the required number of places, and place the decimal point before the ciphers. Thus, in .002 X .002, the product of 2 X 2 = 4; but there are three places in each number; hence, the product must have six places, and five ciphers must be prefixed to the 4, which gives .000004. To divide decimals. Divide in the usual way. If the divi¬ dend has more decimal places than the divisor, point off, from the right of the quotient, the number of places in excess. If it has less than the divisor, annex as many ciphers to the decimal as are necessary to give the dividend as many places as there are in the divisor; the quotient will then have 21.72 34.1 2172 8688 6516 740.652 no decimal places. = 3. For example, 2.5 10.3; 82.5 2.75 82.50 2.75 To carry a division to any number of decimal places. Annex ciphers to the dividend, and divide, until the desired number of figures in the quotient is reached, which are pointed off as above shown. Thus, 36.5 -v- 18.1 to three decimal places = = 2.016+. (The sign + thus placed after a lo.l number indicates that the exact result would be more than the one given if the division were carried further.) To reduce a decimal to a common fraction. Place the decimal as the numerator; and for the denominator put 1 with as many ciphers as there are figures to the right of the decimal point; thus, .375 has three figures to the right of the point; hence, .375 in. = = f in. 6 ARITHMETIC. To reduce a common fraction to a decimal. Divide the numerator by the denominator, and point off as many places as there have been ciphers annexed ; thus, X 3 S in. = 3.0000 -5- 16 — .1875 in. DUODECIMALS, The duodecimal system of numerals is that in which the base is 12, instead of 10, as in the common decimal system. As a method of calculation it has fallen into almost entire disuse, and it is only in calculation of areas that duodecimals are now used. When the work becomes familiar, the work is practically as rapid as by using feet and decimals, and has the advantage of being absolutely accurate, which the decimal system is not, as inches cannot be expressed exactly in deci¬ mals of a foot. The principles upon which the work is based are as follows: When feet are multiplied by feet, or inches by inches, the product is, of course, square feet or square inches, respectively; but, when feet are multiplied by inches, or vice versa, the results may, for want of a better name, be termed parts (although this name was given originally to the 144th part of a square foot). Suppose a square foot to be divided into 144 sq. in.; then a strip 12 in., or 1 ft., long, and 1 in. wide will correspond to 1 part. A strip 5 ft. long and 7 in. wide will contain 7 X 5, or 35 parts, which, divided by 12 (parts to a square foot), equals 2 sq.ft, and 11 parts, or 2 sq. ft. + (11 X 12) sq. in. Square inches may be reduced to parts by dividing by 12; thus, 54 sq. in. = 4 parts 6 sq. in. To illustrate these principles, let it be required to find the area of a room 18 ft. 10 in. long, and 16 ft. 7 in. wide. Place feet under feet, and inches under inches, thus: Feet. Inches. 10 _7 4 11 18 JL6 301 10 10 312 sq. ft. 3 parts 10 sq. in., 312 sq. ft. 46 sq. in. or, INVOLUTION. . 7 Begin by multiplying 10 in. by 16 ft., which equals 160 parts, or 13 sq. ft. 4 parts. Place the 4 parts in the inches column, and carry the 13 sq. ft. Then 18 ft. X 16 ft. = 288 sq. ft. + 13 sq. ft. = 301 sq.ft. Next, multiply 10 in. by 7 in. = 70 sq. in., or 5 parts 10 sq. in. Set the 10 sq. in. to the right of the column ot parts, as shown. Then, 18 ft. X 7 in. = 126 parts + 5 parts car¬ ried = 131 parts; dividing by 12, 131 parts = 10 sq. ft. 11 parts. Set these down in the proper columns and add, begin¬ ning at the right; 4 parts -f 11 parts = 1 sq. ft. 3 parts. Expressed in square feet and square inches, the result is 312 sq. ft. 46 sq. in., which can be verified by reducing the given numbers to inches, multiplying them, and dividing by 144. INVOLUTION. Involution is the process of multiplying a number by itself one or more times, the product obtained being called a certain power of the number. If the number is multiplied by itself, the result is called the square of the number; thus, 9 is the square of 3, since 3X3 = 9. If the square of a number is multiplied by the number, the result is called the cube of the number ; thus, 27 is the cube of 3, since 3X3X3 = 27. The power to which a number is to be raised is indicated by a small figure, called an exponent, placed to the right and a lit¬ tle above the number ; thus, 7 2 means that 7 is to be squared ; 27' ! means that 27 is to be cubed, etc. The operations of involution present no difficulty, as nothing but multiplication is involved, the number of times the number is to be taken as a factor being shown by the exponent. If the number is a fraction, raise both numerator and denominator to the power indicated. A valuable little rule to memorize for finding the square of a mixed number in which the fraction is £, as 3£, 10£, etc., is as follows: Multiply the next less whole number by the next greater, and add For example, the square of 6i is 6 (the next less number) X 7 (the next greater) + | = 42£; (19i) 2 = 19 X 20 + i = 380i ; (8i) ? = 8 X 9 + i = 72£; etc. 8 ARITHMETIC . EVOLUTION. Evolution is the reverse of involution and is the process of finding one of the equal factors of a number, termed a root, which, multiplied by itself a certain number of times, will give a product equal to the given number. When the number is to be resolved into two equal factors, either on is called the square root; when there are to be three equal fac¬ tors, each one is called the cube root; etc. The operate ns to be performed are indicated by the radical sign y and vin culum , and by an index figure ; for square root, the index is omitted. For example, i/64 is read the square root of 64 which is 8, since 8X8 = 64; y 64 means cube root of 64, which is 4, as 4 X 4 X 4 = 64. A number is said to be a perfect square, or a perfect cube, etc. when the root consists only of a whole number ; thus, 64 is a perfect cube, since the cube root is 4, without any decimal. SQUARE ROOT. In extracting the square root of a number, the first step is to find how many figures there are in the root. This is done by pointing off periods of two figures each, beginning with the unit figure; or, if the number is partly decimal, begin at the decimal point, and point off each way. Thus, in the square root of 625 there are two figures (6'25); in 105.0625, there are four figures (1'05'.06'25) in the root. To extract the square root, having pointed off the number into periods, proceed as follows : Let it be required to find the square root of 217. There are two figures in the whole- number part of the root; thus, 2'17. Find the number whose square is nearest in value to the first period; in this case it is 1. Divide the first period (or trial dividend) by twice this number (which call the trial root), and to the quo¬ tient add ,j the same number; thus, 2 1X2 = 1.5. Disre¬ garding the decimal point, and retaining two figures of the first trial root, the new trial root is 15. Add the second period of the number to the first trial dividend, and then repeat the E VOL UTION. 9 operations shown; thus, + — = 7.23 + 7.5 = 14.73, or 10 /\ 2 2 the correct root to two decimal places. If it is desired to carry the work further, the same operations would be gone through; the next trial root would be 147 (retaining three figures, and increasing the last by 1 if the fourth figure is 5 or over), disregarding the decimal point; thus, 2'17'00 147 147X2 + 2 = 73.809 + 73.50 = 147.309. The position of the decimal point is found by knowing that there are two figures in the whole- number or integral part of the root, or the root is 14.7309, correct to four decimal places. For the next trial root, four figures (as 1,473) would be retained, and another period would be annexed to the trial dividend, etc. The process may be remembered by help of this simple formula, T> , D R R00t = 2R + 2’ in which D is the trial dividend and R the trial root. (The method of using formulas is explained in a succeeding article.) If the first period is a perfect square, as 1, 4, etc., use the first two periods as a trial dividend, add a cipher to the trial root, and proceed as before shown. If the number contains a decimal, pay no attention to the point till necessary to point off the result. The following example illustrates the last named princi¬ ples : What is the square root of 427.75 ? There are two figures in the integral part of the root; thus, 4'27. Since 4 is the square of 2, 4'27 is used as the first trial dividend, and 20 as 4/97 20 the trial divisor; then ~ ■ + — = 10.67 + 10 == 20.7. Next, ZU y\ 2 2 4'27'75 207 disregarding the decimal poin ^ - -f —- = 103.3 + 103.5 = 206.8. Pointing off the two figures in the integral part 01 the root, the root is 20.68, to two decimal places. If a number is wholly decimal, the root will also be wholly decimal. If there arc ciphers immediately following the decimal point in the number, divide the number of ciphers 10 ARITHMETIC. by 2, and, disregarding any remainder ,' the result will be tho number of ciphers between the decimal point and the first significant figure; thus, in the root of .00049, there will be 3 ciphers 2 = 1 cipher in the root, which is .022+. If there is no, or but one, cipher between the point and the first significant figure of the number, there will be none immedi¬ ately after the decimal point in the root. The roots of num¬ bers having ciphers immediately after the decimal point are found in the usual way, disregarding the ciphers (after pointing off the periods) until the position of the decimal point is to be found. If any decimal period consists of but one figure, annex a cipher to it. Thus, j/.5 = j/.50 = .7071; ■j/,00'00'9 = j/'OO'OO^JO = .0094+. If a number is a perfect square, it will be known by a result being obtained which is the same as the trial root used as divisor; thus, in y 40 / 96, it will be found that the third trial root is 64, and the quotient obtained is also 64, which is, therefore, i/ / 4,096. The square root of a fraction is found by finding the square roots of the numerator and the denominator, and dividing the former square root by the latter; thus, \4 t/ 1 1 l/ 4 ^ Otherwise, the fraction may be reduced to a decimal, and the square root of this found. CUBE ROOT The first step in extracting cube root is to point off the number into periods of three figures each, beginning At the right, for whole numbers; begin at the decimal point if the number is partly decimal; and, if the number is wholly decimal, point off towards the right from the decimal point. The cube root of a whole number will contain as many figures as there are periods and parts of periods in the number. If the number is wholly decimal, and has less than EVOLUTION. 11 three ciphers between the decimal point and the first signifi¬ cant figure, there will be no cipher immediately after the decimal point in the root; thus, 1^.125 = .5; i^.OOS = .2. If there are ciphers immediately following the decimal point in a wholly decimal number, the number of ciphers in the root will be found by dividing the number of ciphers in the num¬ ber by 3, neglecting any remainder; thus, in ; :l .000008 there are § = 1 cipher, and the root is .02. If the last period of a decimal number has less than three figures, annex enough figures to make a full period; thus, j^.3 — f^.300. The method of extracting cube root is quite similar to that followed for square root, and may be expressed by the formula: ^ , D , 2R R ° 0t 3 IP + 3 ’ in which D is the trial dividend and R the trial root. The following example shows the process in detail: What is the cube root of 20'796.875? Pointing off from the decimal point to the left, it is seen that there are two figures in the whole-number part of the root. The number whose cube is nearest 20 is 3; then applying the formula, since D — 20, and R = 3, the next trial root is 20 2X3 3 X 3 2 + 3 .74 + 2 = 2.74. Retain two figures, increasing the second if the third is 5 or over; then the second trial root is 27. Annexing another period to the trial dividend, and repeating the above process: 20'796 2X27 3 X 27 2 + 3 = 9.51 + 18 = 27.51. For the third trial root, retain three figures, and as before neglect the decimal point. Annex the next period for the new trial dividend, and repeat the process; thus, 20'796'875 2X275 3X275 2 + 3 91.G7 + 183.33 = 275.00; or, pointing off as above shown, the root is 27.5. If the opera¬ tion is repeated one step further, a root is obtained which is the same as the trial root used, which result shows that the given number is a perfect cube. If the first period is a perfect cube, use two periods as the 12 ' ARITHMETIC. trial dividend, and annex a cipher to the number whose cu is equal to the first period ; this number will then be the fi trial root. Thus, in y 1'728, the trial root will be 10, the fi approximation giving 1'72S + 2 X 10 = 5.76 + 6.67 = 12.43; 3 X 10 2 ' 3 and the operations being continued will give 12 as the exs root. The cube root of a fraction may be found by extracth the cube root of the numerator and that of the denon nator, and dividing the former result by the latter; thus, 3 f27 _ #"~27 _ 3 8 /1 _ fJ: _ 1 V 64 — ^34 4’\8 2' Otherwise, the fraction may be reduced to a decimal, ai the cube root of this found. The general method of extracting cube root is so similar that for extracting square root, which was quite fully show that no further explanation is necessary. HIGHER ROOTS. The fourth root of a number may be found by ext’.actii the square root of the square root of the number; thus, I 4 / 256 = V V 256 = l/l6 = 4. The sixth root of a number maybe found by extracting tl square root of the cube root, or the cube root of the squai root; thus, y 64 — l/ -]/ 64 = 8 = 2. The general formula for extracting any root is Root = I) + n 1 R, n X R n ~ l n in which n is the index of the root sought, D the trial div dend, and R the trial root. For example, I) . 3 „„„ . I) Fourth root = + fifth root - + 1 B. These roots are to be found by the same general metho< explained for square and cube roots. SQUARE ROOTS AND CUBE ROOTS. 13 SQUARE ROOTS AND CUBE ROOTS. Table of Square Roots and Cube Roots, of Numbers . From 1 to 1,005. Note. —Wherever the effect of a fourth decimal in the following roots would be to add 1 to the third and final deci¬ mal in the table, the addition has been made. No. Sq. Rt. C. Rt. NO. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. 1 1.000 1.000 31 5.568 3.141 61 7.810 3.936 * 2 1.414 1.260 32 5.657 3.175 62 7.874 3.958 3 1.732 1.442 33 5.745 3.207 63 7.937 3.979 4 2.000 1.587 34 5.831 3.240 64 8.000 4.000 5 2.236 1.710 35 5.916 3.271 65 8.062 4.021 6 2.449 1.817 36 6.000 8.302 66 8.124 4.041 7 2.646 1.913 37 6.083 3.332 67 8.185 4.061 8 2.828 2.000 38 6.164 3.362 68 8.246 4.082 9 3.000 2.080 39 6.245 3.391 69 8.307 4.102 10 3.162 2.154 40 6.325 3.420 70 8.367 4.121 11 3.317 2.224 41 6.403 3.448 71 8.426 4.141 12 3.464 2.289 42 6.481 3.476 72 8.485 4.160 13 3.606 2.351 43 6.557 3.503 73 8.544 4.179 14 3.742 2.410 44 6.633 3.530 74 8.602 4.198 15 3.873 2.466 45 6.708 3.557 75 8.660 4.217 16 4.000 2.520 46 6.782 3.583 76 8.718 4.236 17 4.123 2.571 47 6.856 3.609 77 8.775 4.254 18 4.243 2.621 48 6.928 3.634 78 8.832 4.273 19 4.359 2.668 49 7.000 3.659 79 8.888 4.291 20 4.472 2.714 50 7.071 3.684 80 8.944 4.309 21 4.583 2.759 51 7.141 3.708 81 9.000 4,327 22 4.690 2.802 52 7.211 3.732 82 9.055 4.344 23 4.796 2.844 53 7.280 3.756 83 9.110 4.362 24 4.899 2.884 54 7.348 3.780 84 9.165 4.379 25 5.000 2.924 55 7.416 3.803 85 9.219 4.397 26 5.099 2.962 56 7.483 3.826 86 9.274 4.414 27 5.196 3.000 57 7.550 3.848 87 9.327 4.431 28 5.291 3.037 58 7.616 3.871 88 9.381 4.448 29 5.385 3.072 59 7.681 3.893 89 9.434 4.465 30 5.477 3.107 60 7.746 3.915 90 9.487 4.481 B 14 ARITHMETIC. Table— ( Continued). No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. No. Sq. Rt, C. Rt. 91 9.539 4.498 131 11.445 5.079 171 13.077 5.550 92 9.592 4.514 132 11.489 5.092 172 13.115 5.561 93 9.644 4.531 133 11.533 5.104 173 13.153 5.572 94 9.695 4.547 134 11.576 5.117 174 13.191 5.583 95 9.747 4.563 135 11.619 5.130 175 13.229 5.593 96 9.798 4.579 136 11.662 5.143 176 13.266 5.604 97 9.849 4.595 137 11.705 5.155 177 13.304 5.615 98 9.899 4.610 138 11.747 5.168 178 13.342 5.625 99 9.950 4.626 139 11.790 5.180 179 13.379 5.636 100 10.000 4.642 140 11.832 5.192 180 13.416 5.646 101 10.050 4.657 141 11.874 5.205 181 13.454 5.657 102 10.099 4.672 142 11.916 5.217 182 13.491 5.667 103 10.149 4.687 143 11.958 5.229 183 13.528 5.677 104 10.198 4.703 144 12.000 5.241 184 13.565 5.688 105 10.247 4.718 145 12.042 5.254 185 13.601 5.698 106 10.296 4.733 146 12.083 5.266 186 13.638 5.708 107 10.344 4.747 147 12.124 5.278 187 13.675 5.718 108 10.392 4.762 148 12.165 5.290 188 13.711 5.729 109 10.440 4,777 149 12.207 5.301 189 13.748 5.739 110 10.488 4.791 150 12.247 5.313 190 13.784 5.749 111 10.536 4.806 151 12.288 5.325 191 13.820 5.759 112 10.583 4.820 152 12.329 5.337 192 13.856 5.769 113 10.630 4.835 153 12.369 5.348 193 13.892 5.779 114 10.677 4.849 154 12.410 5.360 194 13.928 5.789 115 10.724 4.863 155 12.450 5.372 195 13.964 5.799 116 10.770 4.877 156 12.490 5.383 196 14.000 5.809 117 10.817 4.891 157 12.530 5.395 197 14.036 5.819 118 10.863 4.905 158 12.570 5.406 198 14.071 5.828 119 10.909 4.919 159 12.609 5.417 199 14.107 5.838 120 10.954 4.932 160 12.649 5.429 200 14.142 5.848 121 11.000 4.946 161 12.689 5.440 201 14.177 5.858 122 11.045 4.9(50 162 12.728 5.451 202 14.213 5.867 123 11.090 4.973 163 12.767 5.463 203 14.248 5.877 124 11.135 4.987 164 12.806 5.474 201 14.283 5.887 125 11.180 5.000 165 12.8-15 5.485 205 14.318 5.896 126 11.225 5.013 166 12.884 5.496 206 14.353 5.906 127 11.269 5.026 167 12.923 5.507 207 14.387 5.915 128 11.314 5.040 168 12.961 5.518 208 14.422 5.925 129 11.358 5.053 169 13.000 5.529 209 14.457 5.934 130 11.402 5.066 170 13.038 5.540 210 14.491 5.944 SQUARE ROOTS AND CURE ROOTS. 15 Table —( Continued). No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. 211 14.526 5.953 251 15.843 6.308 291 17.059 6.627 212 14.560 5.963 252 15.874 6.316 292 17.088 6.634 213 14.594 5.972 253 15.906 6.325 293 17.117 6.642 214 14.629 5.981 254 15.937 6.333 294 17.146 6.649 215 14.663 5.991 255 15.969 6.341 295 17.176 6.657 216 14.697 6 . tioo 256 16.000 6.350 296 17.205 6.664 217 14.731 6.009 257 16.031 6.358 297 17.234 6.672 218 14.765 6.018 258 16.062 6.366 298 17.263 6.679 219 14.799 6.028 259 16.093 6.374 299 17.292 6.687 220 14.832 6.037 260 16.124 6.382 300 17.320 6.694 221 14.866 6.046 261 16.155 6.391 301 17.349 6.702 222 14.900 6.055 262 16.186 6.399 302 17.378 6.709 223 14.933 6.064 263 16.217 6.407 303 17.407 6.717 224 14.967 6.073 264 16.248: 6.415 304 17.436 6.724 225 15.000 6.082 265 16.279 6.423 305 17.464 6.731 226 15.033 6.091 266 .16.309 6.431 306 17.493 6.739 227 15.066 6.100 267 16.340 6.439 307 17.521 6.746 228 15.100 6.109 268 16.371 6.447 308 17.550 6.753 229 15.138 6.118 269 16.401 6.455 309 17.578 6.761 230 15.166 6.127 270 16.432 6.463 310 17.607 6.768 231 15.199 6.136 271 16.462 6.471 311 17.635 6.775 232 15.231 6.145 272 16.492 6.479 312 17.663 6.782 233 15.264 6.153 273 16.523 6.487 313 17.692 6.790 234 15.297 6.162 274 16.553 6.495 314 17.720 6.797 235 15.330 6.171 275 16.583 6.503 315 17.748 6.804 236 15.362 6.180 276 16.613 6.511 316 17.776 6.811 237 15.395 6.188 277 16.643 6.519 317 17.804 6.818 238 15.427 6.197. 278 16.673 6.526 318 17.833 6.826 239 15.460 6.206 279 16.703 6.534 319 17.861 6.833 240 15.492 6.214 280 16.733 6.542 320 17.888 6.840 241 15.524 6.223 281 16.763 6.550 321 17.916 6.847 242 15.556 6.232 282 16.793 6.558 322 17.944 6.854 243 15.588 6.240 283 16.823 6.565 323 17.972 6.861 244 15.620 6.249 284 16.852 6.573 324 18.000 6.868 245 15.652 6.257 285 16.882 6.581 325 18.028 6.875 246 15.684 6.266 286 16.911 6.588 326 18.055 6.882 247 15.716 6.274 287 16.941 6.596 327 18.083 6.889 248 15.748 6.283 288 16.971 6.604 328 18.111 6.896 249 15.780 6.291 289 17.000 6.611 329 18.138 6.903 250 15.811 6.300 290 17.029 6.619 330 18.166 6.910 16 ARITHMETIC. Table—( Continued ). No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. 331 18.193 6.917 371 19.261 7.185 411 20.273 7.435 332 18.221 6.924 372 19.287 7.192 412 20.298 7.441 333 18.248 6.931 373 19.313 7.198 413 20.322 7.447 334 18.276 6.938 374 19.339 7.205 414 20.347 7.453 335 18.303 6.945 375 19.365 7.211 415 20.371 7.459 336 18.330 6.952 376 19.391 7.218 416 20.396 7.465 337 18.358 6.959 377 19.416 7.224 417 20.421 7.471 338 18.385 6.966 378 19.442 7.230 418 20.4-15 7.477 339 18.412 6.973 379 19.468 7.237 419 20.469 7.483 340 18.439 6.979 380 19.494 7.243 420 20.494 7.489 341 18.466 6.986 381 19.519 7.249 421 20.518 7.495 342 18.493 6.993 382 19.545 7.256 422 20.543 7.501 343 18.520 7.000 383 19.570 7.262 423 20.567 7.507 344 18.547 7.007 384 19.596 7.268 424 20.591 7.513 345 18.574 7.014 385 19.621 7.275 425 20.615 7.518 346 18.601 7.020 386 19.647 7.281 426 20.640 7.524 347 18.628 7.027 387 19.672 7.287 427 20.664 7.530 348 18.655 7.034 388 19.698 7.294 428 20.688 7.536 349 18.681 7.041 389 19.723 7.300 429 20.712 7.542 350 18.708 7.047 390 19.748 7.306 430 20.736 7.548 351 18.735 7.054 391 19.774 7.312 431 20.760 7.554 352 18.762 7.061 392 19.799 7.319 432 20.785 7.559 353 18.788 7.067 393 19.824 7.325 433 20.809 7.565 354 18.815 7.074 394 19.849 7.331 434 20.833 7.571 355 18.841 7.081 395 19.875 7.337 435 20.857 7.577 356 18.868 7.087 396 19.900 7.343 436 20.881 7.583 357 18.89-1 7.094 397 19.925 7.350 437 20.904 7.589 358 18.921 7.101 398 19.950 7.356 438 20.928 7.594 359 18.947 7.107 399 19.975 7.362 439 20.952 7.600 360 18.974 7.114 400 20.000 7.368 440 20.976 7.606 361 19.000 7.120 401 20.025 7.374 441 21.000 7.612 362 19.026 7.127 402 20.050 7.380 442 21.024 7.617 363 19.053 7.133 403 20.075 7.386 443 21.048 7.623 364 19.079 7.140 404 20.100 7 392 444 21.071 7.629 365 19.105 7.147 405 20.125 7.399 445 21.095 7.635 366 19.131 7.153 406 20.149 7.405 446 21.119 7.640 367 • 19.157 7.160 407 20.174 7.411 447 21.142 7.646 368 , 19.183 7.166 408 20.199 7.417 44S 21.166 7.652 369 , 19.209 7.173 409 20.224 7.428 119 21.190 7.657 370 ‘ 19.235 7.179 410 20.248 7.429 450 21.213 7.663 No. 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 SQUARE ROOTS AND CUBE ROOTS. 17 Table— ( Continued).. C. Rt. No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. 7.669 491 22.158 7.889 531 23.043 8.098 7.674 492 22.181 7.894 532 23.065 8.103 7.680 493 22.204 7.900 533 23.087 8.108 7.686 494 22.226 7.905 534 23.108 8.113 7.691 495 22.249 7.910 536 23.130 8.118 7.697 496 22.271 7.916 536 23.152 8.123 7.703 497 22.293 7.921 537 23.173 8.128 7.708 498 22.316 7.926 538 23.195 8.133 7.714 499 22.338 7.932 539 23.216 8.138 7.719 500 22.361 7.937 540 23.238 8.143 7.725 501 22.383 7.942 541 23.259 8.148 7.731 502 22.405 7.948 542 23.281 8.153 7.736 503 22.428 7.953 543 23.302 8.158 7.742 504 22.450 7.958 544 23.324 8.163 7.747 505 22.472 7.963 545 23.345 8.168 7.753 506 22.494 7.969 546 23.367 8.173 7.758 507 22.517 7.974 547 23.388 8.178 7.764 508 22.539 7.979 548 23.409 8.183 7.769 509 22.561 7.984 549 23.431 8.188 7.775 510 22.583 7.990 550 23.452 8.193 7.780 511 22.605 7.995 551 23.473 8.198 7.786 512 22.627 8.000 552 23.495 8.203 7.791 513 22.649 8.005 553 23.516 8.208 7.797 514 22.672 8.010 554 23.537 8.213 7.802 515 22.694 8.016 555 23.558 8.218 7.808 516 22.716 8.021 556 23.580 8.223 7.813 517 22.738 8.026 557 23.601 8.228 7.819 518 22.760 8.031 558 23.622 8.233 7.824 519 22.782 8.036 559 23.643 8.238 7.830 520 22.803 8.041 560 23.664 8.243 7.835 521 22.825 8.047 561 23.685 8.247 7.841 622 22.847 8.052 562 23.706 8.252 7.846 523 22.869 8.057 563 23.728 8.257 7.851 524 22.891 8.062 564 23.749 8.262 7.857 525 22.913 8.067 565 23.770 8.267 7.862 526 22.935 8.072 566 23.791 8.272 7.868 527 22.956 8.077 567 23.812 8.277 7.873 528 22.978 8.082 568 23.833 8.282 7.878 529 23.000 8.088 569 23.854 8.286 7.884 530 23.022 8.093 570 23.875 8.291 18 ARITHMETIC. Table —( Continued). No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. 571 23.896 8.296 611 24.718 8.486 651 25.515 8.667 572 23.916 8.301 612 24.739 8.490 652 25.534 8.671 573 23.937 8.306 613 24.759 8.495 653 25.554 8.676 574 23.958 8.311 614 24.779 8.499 654 25.573 8.680 575 23.979 8.315 615 24.799 8.504 655 25.593 8.684 576 24.000 8.320 616 24.819 8.509 656 25.612 8.689 577 24.021 8.325 617 24.839 8.513 657 25.632 8.693 578 24.042 8.330 618 24.860 8.518 658 25.651 8.698 579 24.062 8.335 619 24.880 8.522 659 25.671 8.702 580 24.083 8.340 620 24.900 8.527 660 25.690 8.707 581 24.104 8.344 621 24.920 8.532 661 25.710 8.711 582 24.125 8.349 622 24.940 8.536 662 25.729 8.715 583 24.145 8,354 623 24.960 8.541 663 25.749 8.720 584 24.166 8.359 624 24.980 8.545 664 25.768 8.724 585 24.187 8.363 625 25.000 8.550 665 25.788 8.728 586 24.207 8.368 626 25.020 8.554 666 25.807 8.733 587 24.228 8.373 627 25.040 8.559 667 25.826 8.737 588 24.249 8.378 628 25.060 8.563 668 25.846 8.742 589 24.269 8.382 629 25.080 8.568 669 25.865 8.746 590 24.290 8.387 630 25.100 8.573 670 25.884 8.750 591 24.310 8.392 631 25.120 8.577 671 25.904 8.755 592 24.331 8.397 632 25.140 8.582 672 25.923 8.759 593 24.352 8.401 633 25.159 8.586 673 25.942 8.763 594 24.372 8.406 634 25.179 8.591 674 25.961 8.768 595 24.393 8.411 635 25.199 8.595 675 25.981 8.772 596 24.413 8.415 636 25.219 8.600 676 26.000 8.776 597 24.434 8.420 637 25.239 8.604 677 26.019 8.781 598 24.454 8.425 638 25.259 8.609 678 26.038 8.785 599 24.474 8.430 639 25.278 8.613 679 26.058 8.789 600 24.495 8.434 640 25.298 8.618 680 26.077 8.794 601 24.515 8.439 641 25.318 8.622 681 26.096 8.798 602 24.536 8.444 642 25.338 8.627 682 26.115 8.802 603 24.556 8.448 643 25.357 8.631 683 26.134 8.807 604 24.576 8.453 644 25.377 8.636 684 26.153 8.811 605 24.597 8.458 645 25.397 8.640 685 26.172 8.815 606 24.617 8.462 646 25.416 8.645 686 26.192 8.819 607 24.637 8.467 647 25.436 8.(549 687 26.211 8.824 608 24.658 8.472 648 25.456 8.653 688 26.230 8.828 609 24.678 8.476 649 25.475 8.658 689 26.249 8.832 610 24.698 8.481 650 25.495 8.662 690 26.268 8.837 SQUARE ROOTS AND CUBE ROOTS. IS Table —( Continued). No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. 691 26.287 8.841 731 27.037 9.008 771 27.767 9.170 692 26.306 8.845 732 27.055 9.012 772 27.785 9.174 693 26.325 8.849 733 27.074 9.016 773 27.803 9.177 694 26.344 8.854 734 27.092 9.020 774 27.821 9.181 695 26.363 8.858 735 27.111 9.025 775 27.839 9.185 696 26.382 8.862 736 27.129 9.029 776 27.857 9.189 697 26.401 8.866 737 27.148 9.033 777 27.875 9.193 698 26.420 8.871 738 27.166 9.037 778 27.893 9.197 699 26.439 8.875 739 27.185 9.041 779 27.911 9.201 700 26.457 8.879 740 27.203 9.045 780 27.928 9.205 701 26.476 8.883 741 27.221 9.049 781 27.946 9.209 702 26.495 8.887 742 27.240 9.053 782 27.964 9.213 703 26.514 8.892 743 27.258 9.057 783 27.982 9.217 704 26.533 8.896 744 27.276 9.061 784 28.000 9.221 705 26.552 8.900 745 27.295 9.065 785 28.018 9.225 706 26.571 8.904 746 27.313 9.069 786 28.036 9.229 707 26.589 8.908 747 27.331 9.073 787 28.053 9.233 708 26.608 8.913 748 27.350 9.077 788 28.071 9.236 709 26.627 8.917 749 27.368 9.082 789 28.089 9.240 710 26.646 8.921 750 27.386 9.086 790 28.107 9.244 711 26.665 8.925 751 27.404 9.090 791 28.125 9.248 712 26.683 8.929 752 27.423 9.094 792 28.142 9.252 713 26.702 8.934 753 27.441 9.098 793 28.160 9.256 714 26.721 8.938 754 27.459 9.102 794 28.178 9.260 715 26.739 8.942 755 27.477 9.106 795 28.196 9.264 716 26.758 8.946 756 27.495 9.110 796 28.213 9.268 717 26.777 8.950 757 27.514 9.114 797 28.231 9.272 718 26.795 8.954 758 27.532 9.118 798 28.249 9.275 719 26.814 8.959 759 27.550 9.122 799 28.267 9.279 720 26.833 8.963 760 27.568 9.126 800 28.284 9.283 721 26.851 8.967 761 27.586 9.130 801 28.302 9.287 722 26.870 8.971 762 27.604 9.134 802 28.320 9.291 723 26.889 8.975 763 27.622 9.138 803 28.337 9.295 724 26.907 8.979 764 27.640 9.142 804 28.355 9.299 725 26.926 8.983 765 27.659 9.146 805 28.372 9.302 726 26.944 8.988 766 27.677 9.150 806 28.390 9.306 727 26.963 8.992 767 27.695 9.154 807 28.408 9.310 728 26.981 8.996 768 27.713 9.158 808 28.425 9.314 729 27.000 9.000 769 27.731 9.162 809 28.443 9.318 730 27.018 9.004 770 27.749 9.166 810 28.460 9.322 20 ARITHMETIC. Table —( Continued ). No. Sq. Rt. C. Rt. NO. Sq. Rt. C. Rt. No. Sq. Rt. 1 C. Rt. 811 28.478 9.325 851 29.172 9.476 891 29.850 9.623 812 28.496 9.329 852 29.189 9.480 892 29.866 9.626 813 28.513 9.333 853 29.206 9.484 893 29.883 9.630 814 28.531 9.337 an 29.223 9.487 894 29.900 9.633 815 28.548 9.341 855 29.240 9.491 895 29.917 9.637 816 28.566 9.345 856 29.257 9.495 896 29.933 9.641 817 28.583 9.348 857 29.275 9.499 897 29.950 9.644 818 28.601 9.352 858 29.292 9.502 898 29.967 9.648 819 28.618 9.356 859 29.309 9.506 899 29.983 9.651 820 28.636 9.360 860 29.326 9.510 900 30.000 9.655 821 28.653 9.364 861 29.343 9.513 901 30.017 9.658 822 28.670 9.367 862 29.360 9.517 902 30.033 9.662 823 28.688 9.371 863 29.377 9.521 903 30.050 9.666 824 28.705 9.375 864 29.394 9.524 904 30.067 9.669 825 28.723 9.379 865 29.411 9.528 905 30.083 9.673 826 28.740 9.383 866 29.428 9.532 906 30.100 9.676 827 28.758 9.386 867 29.445 9.535 907 30.116 9.680 828 28.775 9.390 868 29.462 9.539 908 30.133 9.683 829 28.792 9.394 869 29.479 9.543 909 30.150 9.687 830 28.810 9.398 870 29.496 9.546 910 30.166 9.690 831 28.827 9.402 871 29.513 9.550 911 30.183 9.694 832 28.844 9.405 872 29.530 9.554 912 30.199 9.698 833 28.862 9.409 873 29.547 9.557 913 30.216 9.701 834 28.879 9.413 874 29.563 9.561 914 30.232 9.705 835 28.896 9.417 875 29.580 9.565 915 30.249 9.708 836 28.914 9.420 876 29.597 9.568 916. 30.265 9.712 837 28.931 9.424 877 29.614 9.572 917 30.282 9.715 838 28.948 9.428 878 29.631 9.576 918 30.298 9.719 839 28.965 9.432 879 29.648 9.579 919 30.315 9.722 840 28.983 9.435 880 29.665 9.583 920 30.331 9.726 841 29.000 9.439 881 29.682 9.586 921 30.348 9.729 842 29.017 9.443 882 29.698 9.590 922 30.364 9.733 843 29.034 9.447 883 29.715 9.594 923 30.381 9.736 844 29.052 9.450 884 29.732 9.597 924 30.397 9.740 845 29.069 9.454 885 29.749 9.601 925 30.414 9.743 846 29.086 9.458 886 29.766 9.605 926 30.430 9.747 847 29.103 9.461 887 29.782 9.608 927 30.447 9.750 848 29.120 9.465 888 29.7*9 9.612 928 30.463 9.754 849 29.138 9.469 889 29.816 9.615 929 30.479 9.757 850 29.155 1 9.473 890 29.833 9.619 930 30.496 9.761 SQUARE ROOTS AND CUBE ROOTS. 21 Table— ( Continued). No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. 931 30.512 9.764 956 30.919 9.851 981 31.321 9.936 932 30.529 9.768 957 30.935 9.855 982 31.337 9.940 933 30.545 9.771 958 30.952 9.858 983 31.353 9.943 934 30.561 9.775 959 3(1968 9.861 984 31.369 9.946 935 30.578 9 778 960 30.984 9.865 985 31.385 9.950 936 30.594 9.782 961 31.000 9.868 986 31.401 9.953 937 30.610 9.785 962 31.016 9.872 987 31.417 9.956 938 30.627 9.789 963 31.032 9.875 988 31.432 9.960 939 30.643 9.792 964 31.048 9.878 989 31.448 9.963 940 30.659 9.796 965 31.064 9.882 990 31.464 9.967 941 30.676 9.799 966 31.080 9.885 991 31.480 9.970 942 30.692 9.803 967 31.097 9.889 992 31.496 9.973 943 30.708 9.806 968 31.113 9.892 993 31.512 9.977 944 30.725 9.810 969 31.129 9.896 994 31.528 9.980 945 30.741 9.813 970 31.145 9.899 995 31.544 9.983 946 30.757 9.817 971 31.161 9.902 996 31.559 9.987 947 30.773 9.820 972 31.177 9.906 997 31.575 9.990 948 30.790 9.824 973 31.193 9.909 998 31.591 9.993 949 30.806 9.827 974 31.209 9.913 999 31.607 9.997 950 30.822 9.830 975 31.225 9.916 1000 31.623 10.000 951 30.838 9.834 976 31.241 9.919 1001 31.639 10.003 952 30.854 9.837 977 31.257 9.923 1002 31.654 10.006 953 30.871 9.841 978 31.273 9.926 1003 31.670 10.010 954 30.887 9.844 979 31.289 9.929 1004 31.686 10.013 955 30.903 9.848 980 31.305 9.933 1005 31.702 10.017 The square root of any number from .01 to 10.05, advan¬ cing by .01, may be found by moving the decimal place in the Sq. Rt. column one place to the left; thus, ~/ 9.48 = 3.079. The cube root of any number from .001 to 1.005, advancing by .001, may be found by moving the decimal point in the C. Rt. column one place to the left; thus, 1^.816 = .9345. The approximate squares of numbers from 1 to 31.7, and cubes from 1 to 10, may be found, also. Required, the square of 30.53 : In the Sq. Rt. column, find 30.529 ; 932 is, then, the approximate square of 30.53. Required, the cube of 9.8: Find in theC. Rt. column 9.799 ; then, the approximate cube is 941, 22 WEIGHTS AND MEASURES. WEIGHTS AND MEASURES. LINEAR MEASURE. 12 inches (in.). ... = 1 foot . .ft. 3 feet . .... = 1 yard. .yd. 5.5 yards . ... == l rod . .rd. 40 rods. .... = 1 furlong. .fur. 8 furlongs. ... = 1 mile . .mi. in. ft. yd. rd. fur. mi. 36 = 3 = 1 198 = 16.5 = 5.5 = 1 7,920 = 660 = 220 = 40 = 1 63,360 = 5,280 = 1,760 = 320 8 = 1 SURVEYOR'S MEASURE. 7.92 inches. .... = 1 link . .li. 25 links. .... = 1 rod. .rd. 4 rods 4 100 links > . .... = 1 chain . ch. 66 feet j 80 chains. .... - 1 mile. 1 mi. - 80 ch. = 320 rd. = 8,000 li. = 63,360 in. SQUARE MEASURE. 144 square inches (sq. in.). 9 square feet. 30y square yards. 160 square rods .. 640 acres. sq. mi. A. sq. rd. 1 = 640 = 102,400 = 1 square foot.sq. ft. = 1 square yard.sq. yd. = 1 square rod.sq. rd. = 1 acre .A. = ^square mile.sq. mi. sq. yd. sq. ft. sq. in. = 3,097,600 = 27,878,400 = 4,014,489,600 TABLES. 23 SURVEYOR’S SQUARE MEASURE. 625 square links (sq. li.) .= 1 square rod.sq. rd. 16 square rods. = 1 square chain .sq. ch. 10 square chains. = 1 acre.A. 640 acres. = 1 square mile.sq. mi. 36 square miles (6 mi. square) = 1 township.Tp. 1 sq. mi. = 640 A. = 6,400 sq. ch. = 102,400 sq. rd. = 64,000,000 sq. li. The acre contains 4,840 sq. yd., or 43,560 sq. ft., and in form of a square is 208.71 ft. on a side. CUBIC MEASURE. 1,728 cubic inches (cu. in.).= 1 cubic foot ... 27 cubic feet . = 1 cubic yard.... 128 cubic feet .= 1 cord. 24$ cubic feet. = 1 perch . 1 cu. yd. = 27 cu. ft. = 46,656 cu. in. cu. ft. cu.yd. .cd. .P. MEASURE OF ANGLES OR ARCS. 60 seconds (").= 1 minute .' 60 minutes .= 1 degree . 0 90 degrees.= 1 rt. angle or quadrant □ 360 degrees.= 1 circle.cir. 1 cir. = 360° = 21,600' = 1,296,000" AVOIRDUPOIS WEIGHT. 437.5 grains (gr.).= 1 ounce.oz. 16 ounces . = 1 pound .lb. 100 pounds.= 1 hundredweight .cwt. 20 cwt., or 2,0001b.— 1 ton.T. IT. = 20 cwt. = 2,000 1b. = 32,000 oz. = 14,000,000gr. The avoirdupois pound contains 7,000 grains. LONG TON TABLE. 16 ounces .. = 1 pound. 112 pounds. = 1 hundredweight 20 cwt., or 2,240 lb. = 1 ton. ...lb. cwt. ...T. 24 WEIGHTS AND MEASURES. TROY WEIGHT. 24 grains (gr.) . = 1 pennyweight .pwt. 20 pennyweights.= 1 ounce.oz. 12 ounces. = l pound.lb. 1 lb. = 12 oz. = 240 pwt. = 5,760 gr. DRY MEASURE. 2 pints (pt.) . = 1 quart .qt. 8 quarts .= 1 peck .pk. 4 peeks.= 1 bushel .bu 1 bu. = 4 pk. = 32 qt.= 64 pt. The U. S. struck bushel contains 2,150.42 cu. in. = 1.2444 cu. ft. Its dimensions are, by law, 18£ in. in diameter and 8 in. deep. The heaped bushel is equal to if struck bushels, the cone being 6 in. high. The dry gallon contains 268.8 cu. in., being \ bu. For approximations, the bushel may be taken at If cu. ft.; or a cubic foot may be considered £ of a bushel. The British bushel contains 2,218.19 cu. in. = 1.2837 cu. ft. ■= 1.032 U. S. bushels. LIQUID MEASURE. 4 gills (gi.) . = 1 pint.pt. 2 pints ....... = 1 quart .qt, 4 quarts. = 1 gallon .gal. 31 i gallons . = 1 barrel .bbl. . 2 barrels, or 63 gallons . = 1 hogshead .hhd. 1 hhd. = 2 bbl. = 63 gal. = 252 qt. = 504 pt. = 2,016 gi. The U. S. gallon contains 231 cu. in. = .134 cu. ft., nearly or 1 cu. ft. contains 7.480 gal. The following cylinders con¬ tain the given measures very closely : Diam. Height Diam. Height Gill.. If in. 3 in. Gallon . 7 in. 6 in. Pint . 3£in. 3 in. 8 gallons 14 in. 12 in. Quart . 3fin. 6 in. 10 gallons 14 in. 15 in. With water at its maximum density (weighing 62.425 lb. per cu. ft.), a gallon of pure water weighs 8.345 lb. THE METRIC SYSTEM. 25 For approximations, 1 cu. ft. of water is considered equal to gal., and 1 gal. as weighing 8} lb. The British imperial gallon, both liquid and dry, con¬ tains 277.274 cu. in. = .16046 cu. ft., and is equivalent to the volume of 10 lb. of pure water at 62° F. To reduce U. S. to British liquid gallons, divide by 1.2. Conversely, to convert British into U. S. liquid gallons, multiply by 1.2; or, increase the number of gallons §. 12 articles = 12 dozen = 12 gross = 2 articles = 20 articles = 24 sheets = 1 knot (U 1 meter MISCELLANEOUS TABLE 1 1 1 1 1 1 S.) 20 quires = 1 ream. 1 league = 3 miles. 1 fathom = 6 feet. 1 hand = 4 inches. 1 palm = 3 inches. 1 span = 9 inches. = 6,086.07 ft. = 1| miles (roughly). — 3 feet 3f inches (nearly). dozen. gross. great gross, pair, score, quire. THE METRIC SYSTEM. The metric system is based on the meter, which, according to the U. S. Coast and Geodetic Survey Report of 1884, is equal to 39.370432 inches. The value commonly used is 39.37 inches, and is authorized by the U. S. government. The meter is defined as one ten-millionth the distance from the pole to the equator, measured on a meridian passing near Paris. There are three principal units—the meter, the liter (pro¬ nounced lee-ter), and the gram, the units of length, capacity, and weight, respectively. Multiples of these units are obtained by prefixing to the names of the principal units the Greek words deca (10), hecto (100), and kilo (1,000); the submulti¬ ples, or divisions, are obtained by prefixing the Latin words deci ( T V), centi ( T ^), and milli (nsW)- These prefixes form the key to the entire system. In the following tables, the abbreviations of the princi pal units of these submultiples begin with a small letter, while those of the multiples begin with a capital letter; they should always be written as here printed. 26 WEIGHTS AND MEASURES. MEASURES OF LENGTH. Name. Meters. U. S. In. Feet. Millimeter (mm.) = .001 = .039370 = .003281 Centimeter (cm.) = .010 = .393704 = .032809 Decimeter (dm.) = .100 = 3.937043 = .328087 Meter (m.) = 1.000 = 39.370432 = 3.280869 Decameter (Dm.) = 10.000 = 32.808690 Hectometer (Hm.) = 100.000 = 328.086900 Kilometer (Km.) = 1,000.000 = .621 mi. = 3,280.869000 Myriameter (Mm.) 6.214 mi. = 32,808.690000 = 100.000 = = 1,000.000 = .621 mi. = = 10,000.000 The centimeter, meter, and kilometer are the units in practical use, and may he said to occupy the same position in the metric system as do inches, yards, and miles in the U. S. and English system of measurement. MEASURES OF AREA. Name. Sq. Met. Sq. In. Sq. Ft. Acres. Sq. millimeter (mm. 2 ) = .0000010=.001550 Sq. centimeter (cm. 2 ) = .0001000=.155003 ==.00107641 Sq. decimeter (dm. 2 ) = .0100000=15.5003 =.10764100 Sq. meter, or centare (in. 2 , or ca.) = 1.000000=1,550.03= 10.764100=.000247 Sq. decameter, or are (Dm. 2 , or A.) = 100.0000= 155,003=1,076.4101= .024710 Hectare =10,000.00 =107,641.01= 2.47110 Sq. kilometer = .3861099 sq. mi. =10,764,101= 247.110 Sq. myriameter = 38.61090 sq. mi. =24,711.0 MEASURES OF VOLUME. Name. Cu. Met. Cu. In. Cu. Ft. Cu. Yd. Cu. centimeter (cm. 3 ) = .000001= .061025 Cu. decimeter (dm. 3 ) = .001000= 61.0254 Centistere = .010000 = 610.2540 = .35316 Decistere = .100000 = 3.53156 Stere [= cu.m, (m. 3 )] = 1.000000 = 35.3156 = 1.308 Decastere =10.000000 =353.156 =13.080 THE METRIC SYSTEM. 27 MEASURES OF CAPACITY. Name. Milliliter (ml.) | (=cu. centimeter) { Centiliter (cl.) Deciliter (dl.) Liter (1.) (= cubic ) decimeter) j Decaliter (Dl.) ) (= centistere) J Hectoliter (HI.) ) (= decistere) j Kiloliter (Kl.) (= cu. m., or stere) Myrialiter (Ml ) = = (= decastere) j The milliliter (or cubic centimeter) and the liter are the units most commonly used. A liter of pure water at 4° C., or 39.2° F., weighs 1 kilogram. Liters. Liq. Meas. Dry Meas. = .00100 = .008454 gill = .001816 pint = .01000 = .081537 gill = .018162 pint = .10000 = .845370 gill = .18162 pint = 1.0000 = ( 1.05671 qt. ( .264179 gal. = .11351 peck = 10.000 = 2.64179 gal. = 1.1351 peck = 100.00 = 26.4179 gal. = 2.83783 bu. = 1,000.0 = 264.179 gal. = 28.3783 bu. = 10,000 = 2641.79 gal. = 283.783 bu. METRIC WEIGHTS. The gram is the basis of metric weights, and is the weight of a cubic centimeter of distilled water at its maximum density, at sea level, Paris, barometer 29.922 inches. Name . Milligram(mg.)= Centigram (eg.) = Decigram (dg.) = Gram (g.) = Decagram (Dg.)= Hectogr’m (Hg)= Kilogram (Kg.) = My riogr’ m (Mg)= Quintal (Q.) = Grams. Grains. Av. Oz .001= .01543 .010= .15432 .100= 1.54323 1.000=15.43235= 10.000 = 100.000 1,000.000 10,000.000 100,000.000 Av. Lb. .03527= = .35274= = 3.52739= =35.27395= .0022046 .0220462 .2204622 2.2046223 = 22.0462234 = 220.4622341 Tonneau (T.) =1,000,000.000 =2,204.6223410 The gram and the kilogram (called kilo ) are the units in common use. 28 WEIGHTS AND MEASURES. FACTORS FOR CONVERSION. For approximations, it may be useful to remember tne ml- lowing : 1 centimeter = .4 in. (nearly). 1 meter = 40 in. (roughly). 1 kilometer == £ mile (nearly). 1 liter = 1 liquid quart (nearly). 1 liter = | peck (nearly). 1 gram = 15.4 grains. 1 kilogram = 2£ pounds. To convert metric measures into U. S. measures , by use of the preceding tables, find the desired equivalent in U. S. measure of a metric unit of the denomination given, and multiply this equivalent by the metric number. For ex¬ ample, it is desired to find the equivalent in pounds of 19.6 kilos. From the table of weights, 1 kilo = 2.2046 lb.; hence, 19.6 kilos = 2.2046 X 19.6 = 43.21 lb. In similar man¬ ner, 8 liters expressed in U. S. gallons = .264179X8 = 2.113432 gal. To convert U. S. measures into metric measures, find how much a metric unit of the desired denomination is equal to in U. S. measure, and divide the given number by this equiv¬ alent. For example, it is desired to convert 4^ miles into kilometers. From the table of lengths, it is found that a kilometer is .621 mi.; hence, dividing 4.5 by .621, the result is 7.24 kilometers. Other useful conversion factors are as follows: Length.— 1 in. = .0254 meter; 1 ft. = .3048 meter; 1 yd. = .9144 meter; 1 mi. = 1,609.34 meters = 1.609 kilometers. Area.— 1 sq. in. = .000645 square meter; 1 sq. ft. = .0929 square meter; 1 sq. yd. = .836 square meter; 1 acre = 4,047. square meters. Capacity.— 1 cu. in. = .0164 liter; 1 U. S. bushel = 35.24 liters; 1 U. S. dry quart = 1.101 liters; 1 U. S. peck = 8.81 liters; 1 cu. yd. = 765 liters; 1 U. S. liquid quart = .9463 liters; 1 U. S. gallon = 3.785 liters. Weight.—1 grain = .0648 gram; 1 avoirdupois ounce = 28.349 grams; 1 Troy ounce = 31.103 grams; 1 avoirdupois pound = 453.59 grams. SPECIFIC GRA VITIES AND WEIGHTS. 29 SPECIFIC GRAVITIES AND WEIGHTS. The specific gravity of a solid or liquid body is the ratio between its weight and that of a like volume of distilled water. If the solid is of irregular shape, its specific gravity may he found by weighing it in air and in water; the loss of weight in water is the weight of an equal volume of water; hence, if This the weight in air, and W' the weight in water, W the specific gravity is •===— iv — w The weight of water in various conditions is as follows: Water, pure at 32° F. weighs 62.417 lb. per cu. ft. Water, pure at 39° F. weighs 62.425 lb. per cu. ft Water, pure at 62° F. weighs 62.355 lb. per cu. ft. Water, pure at 212° F. weighs 59.700 lb. per cu. ft. Water, sea.weighs 64.080 lb. per cu. ft. Ice .weighs 57.400 lb. per cu. ft. Snow, fresh.weighs 5 to 12 lb. per cu. ft. Snow, wet.weighs 15 to 50 lb. per cu. ft. Metals. Name of Metal. Weight per Cu. In. Pounds. Weight per Cu. Ft. Pounds. Specific Gravity. Aluminufa. .096 166 2.66 Antimony. .242 418 6.70 Bismuth. .350 607 9.74 Brass, cast. .292 504 8.10 Brass, rolled. .303 524 8.40 Bronze (gun metal) . .305 529 8.50 Copper, cast. .314 542 8.70 Copper, rolled. Gold, 24 carat . .321 555 8.90 .694 1,204 19.26 Iron, cast . .260 450 7.21 Iron, wrought. .277 480 7.66 Lead, commercial. .410 710 11.38 Mercurv, 60° F. .489 846 13.58 Platinum . .779 1,342 21.50 Silver . .378 655 10.50 Steel. .283 490 7.85 Tin, cast. .265 459 7.35 Zinc... .253 437 7.00 c 30 WEIGHTS AND MEASURES. Building Materials, Etc. Name of Material. Weight per Cu. Ft. Pounds. Specific Gravity. Bluestone . 1G0 2.56 Brick, pressed . 150 2.40 Brick, common. 125 2.00 Chalk . 156 2.50 Charcoal. 15-30 ' .24-.48 Clay, compact . 119 1.90 Coke, loose.. 23-32 •37-.51 Coal, hard, solid . 93.5 1.50 Coal, hard, broken. 54 .865 Coal, soft, solid. 84 1.35 Coal, soft, broken. 50 .80 Concrete, cement . 140 2.25 Cement, Portland . 80-100 1.4( Cement, Rosendale. 56 .89 Earth, dry, shaken. 82-92 1.36 Earth, rammed. 90-100 1.52 Earth, moist, shaken. 75-100 1.31 Glass, average . 186 2.98 Glass, common window . ;i57 2.52 Granite.. ‘170 2.72 Gravel (see sand) . Limestones and marbles. 168 2.70 Lime, quick . 53 .85 Marble (see limestone). Plaster of Paris. 141.6 2.27 Porphyry . 170.0 2.73 Quartz... 165 2.65 Sand. 90-106 2.65 Sandstone .. 151 2.41 Shales . 162 2.60 Slate . 175 2.80 Trap rock . 187 3.00 Masonry. Common brickwork, cement mortar 130 2.10 Common brickwork, lime mortar. 120 1.90 Granite or limestone rubble, dry. 138 2.21 Granite or limestone rubble. 154 2.45 Granite or limestone, well dressed 165 2.65 Mortar, hardened . 103 1.65 Pressed brickwork. 140 ' 2.25 Sandstone rubble . 145 2.32 FORMULAS. 31 Woods (Dry). Name of Material. Weight per Foot. B. M. Weight per Cu. Ft. Pounds. Specific Gravity. Ash . 3.9 47.0 .752 Ash, American white... 3.2 38.0 .610 Boxwood . 5.0 60.0 .960 Cherry. 3.5 42.0 .672 Chestnut. 3.4 41.0 .660 Cork. 1.3 15.6 .250- Elm.. 2.9 35. Q .560 Ebony. 6.3 76.1 1.220 Hemlock . 2.1 25.0 .400 Hickory . 4.4 53.0 .850 1 agnum vitae . 6.9 83.0 1.330 Mahogany, Spanish. 4.4 53.0 .850 Mahogany, Honduras ... 2.9 35.0 .560 Maple. 4.1 49.0 .790 Oak, live. 4.9 59.3 .950 Oak, white. 4.0 48.0 .770 Oak. red. 3.3 40.0 .640 Pine, white .. 2.1 25.0 .400 Pine, yellmv. 2.8 34.3 .550 Pine, Southern. 3.7 45.0 .720 Sycamore . 3.1 37.0 .590 Spruce. 2.1 25.0 .400 Walnut . 3.2 38.0 .610 FORMULAS. Formulas are simply short methods of indicating opera¬ tions otherwise expressed by rules, by using letters and signs in place of words. The letters are usually those of the English alphabet, and the signs are those previously given. Besides showing at a glance the various steps, formulas are much more convenient than rules to memorize. Many people are unnecessarily deterred from using a formula, because a few letters are used instead of many words; but a formula can really be more readily followed than a rule. We 32 FORMULAS. shall confine our attention to explanations of some simple formulas, and to showing how a formula may be transposed so as to obtain any required term. To show the similarity between a rule and a formula, let it be required to find the area of footing necessary to sustain a certain load, having given the safe load per square foot. The rule is: Divide the total load in pounds by the safe load in pounds per square foot; the quotient is the required area in square feet. Not much space can be saved by expressing such a simple rule in a formula, but the operation is more quickly comprehended. Let the total load in pounds be represented by’the letter P, the safe load per square foot by the letter S, and the required area by the letter A. Then the rule is p expressed by the formula A = -- A formula is used by substituting for the letters the quan¬ tities known in the problem, and finding the unknown by performing the indicated operations. Sometimes the formula as written does not give the desired quantity directly, but must be rearranged so as to enable it to be found. This is done by simple operations, the aim being to obtain the desired qiiantity by itself on one side of the equality sign. Thus, in the above formula, suppose it is desired to find the value of P, A and S being given. By multiplying A and p by S (such operation being called clearing of fractions) there results A X S = P, in which the desired quantity P is by itself and is found to be equal to the product of A and S. The formula is further shortened by omitting the X sign, and writing A S = P. When two or more letters are thus written, it means that they are to be multiplied together. In a similar manner, S may be obtained, by dividing the last found formula through by A ; thus, S = ~ • Example.— The safe bearing power of a soil is 1,500 lb. per sq. ft. What area of footing is required to sustain a load of 30,000 lb.? Here A is wanted, and P and S are given. Hence, A *= P c , FORMULAS. 36 30,000 = 20 sq. ft. Again, suppose it was desired to ascer- 1,500 tain how much per sq. ft. a footing 20 ft. in area carried, the total load, 30,000 lb., being known. Then, A and P are given to find S ; or S = = = 30,000 20 1,500 lb. The following formula shows how to determine the safe load that a stone beam or liptel will carry, if uniformly loaded: 2 bdlA = w, in which b = d = A f L = W = JL breadth in inches; depth in inches; number from a table; factor of safety; length in feet; safe distributed load, in pounds. Suppose any other quantity than W is wanted ; it may be found by transposing the formula ; thus, if the depth to sustain a certain load is required, the formula is thus arranged: Multiplying through by / L, 2 b d 2 A = WfL. Arranging so as to have d 2 alone on one side of the = sign, WfL 2b A Extracting the square root, d d 2 - \ 2bA Example.— It is desired to carry a distributed load of 3,840 lb. on a piece of bluestone flagging 4 ft. wide and 6 ft. span, using a factor of safety of 10. How thick must the stone beam be? Here, W = 3,840 lb.; 5 = 4 ft. X 12 = 48 in.; L = 6 ft.; / = 10 ; A is found from a table to be 150 for blue- stone ; then d is the required term. Substituting the values, there results d 3,840 X 10 X 6 = V 16 = 4 i in. 2 X 48 X 150 A rule for finding the strength of a wooden column is •. From the ultimate compressive strength of the material in pounds per square inch, subtract the fraction: the ultimate strength 34 FORMULAS. multiplied by the length of column in inches , and divided by 100 times the least side in inches. The difference is the ultimate strength of the column in pounds per square inch. This rule is rendered much more intelligible by using a formula ; thus: Let S = ultimate strength of column in lb. per sq. in.; ultimate compressive strength of material in lb. per sq. in. ; length of column, in inches; least side of column, in inches. Ul U l = d Then, S = U- 100 d' The values of U for different woods are found in tables. Example.—T he ultimate compressive stress of white pine, parallel to the grain, is 8,500 lb. per sq. in. What is the ulti¬ mate load a 10" X 10" column 20 ft. long will carry? Looking through the problem, it is found that all the quan¬ tities in the formula are given except S'; the length expressed in inches = 240 in.; and the least side is 10 in., as the col¬ umn is square. Substituting these values in the formula Ul S = 3,500 - S 3,500 X 240 U — 100 d’ = 3,500 — 840 = 2,660 lb. 100 x 10 Suppose it is desired to find the side of a square wooden column to carry a known load. The preceding formula con¬ tains the required term d, but as it also involves S, which depends on d, that term must be eliminated. Let P represent the total load on the column; then, since the sectional area is dA, P = d- S ; or, substituting for £ its value, Ul ' 100 d. d 2 U- p = at ^ u- Multiplying by 100 and dividing by U, dl. d U l 100 * ,0 °4 = ,oo d* V Such a quantity must be added to both sides of this equa¬ tion (so as not to change its value) as will make the right side l- a perfect square. This quantity is found by trial to be Then, 100 r- -* + U ^ 400 100 d*-dl + ^ or 400 ' LINES AND PLANE SURFACES. 35 Extracting the square root of both members, placing : 20 on the left of the equality sign, and dividing by 10, l l = d. /loop P 1A , l ,1 ;100P , P \ U + 400 0 20 ’ and lo\ u + 400 1 200 = y xb multiplying the expression under the radical by it, *\u l !P P - -a -- = d* r T 40,000 ^ 200 In using any formula , care must be taken to have all dimen¬ sionsweights , etc. expressed in the units required by the for mula. MENSURATION. LINES AND PLANE SURFACES. TRIANGLE. Right Triangle. Hypotenuse c = ]/ a 2 + b-. Side a = | /c 2 — b 2 . Side b = ]/ c 2 — a 2 . Area — i a b. Oblique Triangle. If altitude or height h and base known : Area =’ | b li. If the three sides are known : Let s = £(a + b + c). Area = i/ s(s — a)(s — b){s — c). *This formula, while given as an exercise in formulas, is also useful in calculating directly the size of a square wooden column, instead of ascertaining it by trial, as is usual. 36 MENSURATION. TRAPEZIUM. Divide into two triangles and a trapezoid. Area = £b h'+ $a(h'+ h)+ %ch ; or, area = h[bh'+ch-\-a(h'+h)]. REGULAR POLYGONS. Divide the polygon into equal triangles and find the sum of the partial areas. Otherwise, square the length of one side and multiply by proper number from the following table: Name. No. Sides. Multiplier. Triangle 3 .433 Square 4 1.000 Pentagon 5 1.720 Hexagon 6 2.598 Heptagon 7 3.634 Octagon 8 4.828 Nonagon 9 6.182 Decagon 10 7.694 IRREGULAR AREAS. Divide the area into trapezoids, triangles, parts of circles, etc., and find the sum of the partial areas. If the figure is very irregular, the approximate area may be found as follows: Divide the figure into trapezoids by equidistant parallel lines b, c , d, etc. The lengths of these lines being measured, then, calling a the first and n the last length, and y the width of strips, Area = + & + c -f etc. + m^. LINES AND PLANE SURFACES. 37 CIRCLE. A = area. 7 r {pi) = 3.1416. Z - .7854. 4 p = perimeter or circumference. p = n cl = 3.1416 d. p = tyd (approximately). p — 2 7 r r = 6.2832 r. 77 3.1416 d — 2 7 5 p (approximately). d = 1.128]/A. r -Jt- 2 77 6.2832' r = .5642j/ A. A — ~~ = .7854 d 1 . 4 A «= 77 r 2 = 3.1416 1 *. Side of square of area equal to circle = .8862 d. Diameter of circle of area equal to a given square = 1.128 X side. RING. Area = .7854(D 2 - d 2 ). SECTOR. If radius r and rise h are known, chord c = 2]/2hr — h 2 . If chord c and rise h are known, c 2 + 4 /i 2 radius r = • c 2 Approximately, r = Subchord e = ^i/c 2 + 4/t 2 . 38 MENSURATION. g g_ c If h is not more than .4 c, length of arc l — —-—, nearly. O If l and r are known, Angle E* = 57.296 ^ = 57. 3p nearly. Area = ilr. If r and angle E* are known, Ie ngtli ( = ^ = E, nearly. ■-= ,0175 Er. Area = .0087 r 2 E. SEGM ENT. - Area of segment = area of sector — area of triangle. xV Height of triangle = r — h. If l, r, c, and h are known, Area = ilr — ic (r — h). If c, h, r, and E are known, find l as shown under Sector; the area may then be found by the preceding formula. ELLI PSE. t V 7T-* l D2 + & {D- d)* \ 2 8.8 ’ Area = .7854 I) d. * If the angle E contains minutes and seconds, these must be expressed in decimals of a degree. Divide the minutes by 60, and the seconds (if any) by 3,600, and add the sum of the decimals to the degrees; thus, 30°45'36" = 30° + U + = 30.76°. If E is given in degrees and decimals, it may be reduced to minutes and seconds thus, .76° = .76° X 60' — 45.6'; .6' x 60" = 36"; hence, 30.76° = 30° 45' 36". t The perimeter of an ellipse cannot be exactly determined, and this formula is merely an approximation'giving fairly close results. SOLIDS AND CURVED SURFACES. 39 H ELIX. d — diameter of helix ; l = length of 1 turn of helix ; t = pitch, or rise in 1 turn ; n = number of turns; it 2 = 9.8696. I = j/^d^M 2 . t = V F — vSd*. Total length = nl = n\/ F 1 d' 2 -f t-. SOLIDS AND CURVED SURFACES. C — convex surface ; S — whole surface; — C + area of end or ends; A = area larger base or end ; a = area smaller base or end; P = perimeter of larger base ; p — perimeter qf smaller base; D = larger diameter ; d — smaller diameter; V = volume of solid. In a cylinder or prism, A = a, P = p, and D — d. CYLINDER. c = Ph = 3.1416 d h ; S = 3.1416 d h + 1.5708 d -; V = Ah = .7854 d- h. FRUSTUM OF CYLINDER. h = i sum of greatest and least heights; C = Ph = 3.1416 d h; S — 3.1416 dli + .7854 d- + area of elliptical top; V = A h = .78M d 2 h. 40 MENSURATION. PRISM OR PARALLELOPIPED. C = Eh] S =Eh +2 A; V = Ah. For prisms with regular polygon as bases, F = length of one side X number of sides. To obtain area of base, if it is a polygon, divide it into tri¬ angles, and find sum of partial areas. FRUSTUM OF PRISM. If a section perpendicular to the edges is a triangle, square, parallelogram, or regular polygon, sum of lengths of edges V = tion. number of edges Xarea of right sec- CON E. c c= ipz = 1.5708 d l ; S = 1.5708 dl + . 7854d 2 * * S 6 * 8 ; V = ~ = .2618 d 2 h. 6 FRUSTUM OF CONE. c a iZ(P + p)= 1.5708 l(D + d); S = 1.5708 1 (D + d) + .7854 (D°- + cZ2); V = .2618 h (D 2 + Dd + (E). PYRAM ID. C = hPl] S = ±El + A; V = Ah 8 ' To obtain area of base, divide it into tri¬ angles, and find their sum. SOLIDS AND CURVED SURFACES. 41 FRUSTUM OF PYRAMID. C = U(P + p)i S = 5 1 (P + p) A A + Q> j V = | h ( A + a + -]/ A a). PRISMOID. A prismoid is a solid having two parallel plane ends, the edges of which are connected hy plane triangular or quadri¬ lateral surfaces. A = area one end ; a = area of other end ; m — areaof section midway between ends; l — perpendicular distance between ends; V = ^(4 + a + 4m). The area m is not in general a mean between the areas of the two ends, hut its sides are means between the correspond¬ ing lengths of the ends. ^ ^ Approximately, V = —~— l. 42 MENSURATION. CALCULATING THE WEIGHT OF CASTINGS, ETC. The first step is to ascertain the number of cubic inches in the casting. To illustrate the method, consider the column shown in the figure to be divided into several parts, as given below. With irregular shapes, as at e, follow the principle of “give and take,” reducing the shape to an equivalent one, easy to calcu¬ late. The operations are then as follows: Cu. In. Cylinder a, excluding cap. Net height = 12 ft. — (14 in. + 1 in.) = 141.5 in.; net area = 10” circle — 84” circle = 21.8 sq. in. Contents == 21.8 sq. in. X 141.5 in. = 3,084.7 Base b — 19 in. X 19 in. X 14 iu. = 541.5 cu. in.; deduct area of 10” circle X Is” — H7.8 cu. in.; also, for corners (5” square—5” circle) X 14” — 8.1 cu. in. Net contents Triangular ribs c = 4 (44 in. X 7 in.) X 14 in. X 4 = Brackets d. Horizontal part d is, very nearly, 5 in. X 5 in. X 14 in. = 374 cu. in. Vertical part e: To-com- pensate for swelled portion next cylinder (see e'), con¬ sider vertical portion as triangular, with sides 5 in. X 7 in.; its contents are 4 (5 in. X 7 in.) X 14in. — 19.7 cu. in. Each bracket — 57.2 cu. in.; 4 brackets = 57.2 X 4 » Lugs f — 11 in. X 5 in. X 1 in. = 55 cu. in.; deduct 4 (4” square — 4” circle) X 1” = 1.7 cu. in.; also, two f” holes — .9 cu. in. Net contents of each lug, 52.4 cu. in.; 4 lugs = 52.4 X 4 = Cap g — (16” X 16” — 4” circle) X 14” = 415.6 70.9 228.8 209.6 365.2 Carried forward 4,374.8 SOLIDS AND CUE VED SURFACES. 43 Brought forward, ' 4,374.8 Upper part of cap li = (16" square — 12" square) X 1" thick — deduction for bevel; 256 cu. in. — 144 cu. in. = 112 cu. in. Portion to he deducted consists of 4 wedges, each 16 in. X 1 in. at the back, 13 in. at the edge, which is 1| in. from back; by rule for wedges, deduction is [J X (16 in. + 16 in. -f 13 in.) X 1 in. X li in.] X 4 = 45 cu. in. Net contents of part li — 112 — 45 = 67.0 Total contents of column = 4,441.8 One cu. ft. of cast iron weighs 450 lb., or 1 cu. in. weighs .26 lb.—called i lb., roughly. Hence the weight is 4,442 X >26 = 1,155 lb. This calculation is much more detailed than is usual; generally, no account is taken of rounded corners, small fillets, holes, etc. When a casting or a rolled shape of steel, etc. is of uniform cross-section throughout—as a rail, I beam, or channel—the weight may be very expeditiously determined after calcu¬ lating the sectional area. A cubic foot of wrought iron weighs 480 lb.; hence, a piece 1 yd. long and 1 in. square contains 36 cu. in., and weighs of 480 lb. = 10 lb.; or, if 1 ft. long and 1 in. square, weighs ^ = 3^ lb. Therefore, if the sectional area be known or calculated, the weight per foot may be found by taking the area, or by multiplying the latter by 3£. This result will be in pounds, and, if multi¬ plied by the total length in feet of the member, will give the whole weight. If the member is made of steel, which weighs 490 lb. per cu. ft., the weight per foot may be determined by multiplying the sectional area by 3.4. For cast iron the multiplier is 3j. Example.— What is the weight per foot of a 20" steel I beam, having a sectional area of 26.4 sq. in.? 26.4 X 3.4 = 89.76 lb., or, practically, 90 lb. By reference to Table XIX, page90, it will be seen that this is the weight given. If the weight per foot is given, and it is desired to find the sectional area, the former, divided by or multiplied by .3. will give the required area. For steel, the multiplier is .294, and for cast iron .32. 44 MENSURATION. CIRCUMFERENCES AND AREAS OF CIRCLES FROM 1-64 TO 100. Diam. Circum. Area. ISt .0491 .0002 3*2 .0982 .0008 1 T5 .1963 .0031 .3927 .0123 3 .5890 .0276 l .7854 .0491 5 TS .9817 .0767 JL 1.1781 .1104 7 T5 1.3744 .1503 i 5 1.5708 .1963 9 T5 1.7671 .2485 1 1.9635 .3068 H 2.1598 .3712 1 2.3562 .4418 13 T5 2.5525 .5185 7 8 2.7489 .6013 1 5 T5 2.9452 .6903 l 3.1416 .7854 n 3.5343 .9940 H 3.9270 1.2272 u 4.3197 1.4849 H 4.7124 1.7671 11 5.1051 2.0739 If 5.4978 2.4053 H 5.8905 2.7612 2 6.2832 3.1416 2| 6.6759 3.5466 2f 7.0686 3.9761 2f 7.4613 4.4301 2| 7.8.540 4.9087 2| 8.2467 5.4119 2f 8.6394 5.9396 2f 9.0321 6.4918 3 9.4248 7.0686 3| 9.8175 7.6699 3f 10.2102 8.2958 31 10.6029 8.9462 31 10.9956 9.6211 31 11.3883 10.3206 3f 11.7810 11.0447 31 12.1737 11.7933 4 12.5664 12.5664 4 t 12.9591 13.3641 4i 13.3518 14.1863 Diam. Circum. Area. 4| 13.7445 15.0330 AX 14.1372 15.9043 4f 14.5299 16.8002 4f 14.9226 17.7206 15.3153 18.6555 5 15.7080 19.6350 6* 5f 16.1007 20.6290 16.4934 21.6476 5* 16.8861 22.6907 5i 17.2788 23.7583 51 17.6715 24.8505 5f 18.0642 25.9673 18.4569 27.1086 6 18.8496 28.2744 19.2423 29.4648 6y 19.6350 30.6797 6f 20.0277 31.9191 6i 20.4204 33.1831 6| 20.8131 34.4717 Of 21.2058 35.7848 21.5985 37.1224 7 21.9912 38.4846 7i h 7| 22.3839 39.8713 22.7766 41.2826 23.1693 42.7184 7£ 23.5620 44.1787 7* 23.9547 45.6636 7f 24.3474 47.1731 7f 24.7401 48.7071 8 25.1328 50.2656 81- 25.5255 51.8487 8| 25.9182 53.4563 8f 26.3109 55.0884 8^ 26.7036 56.7451 8f 27.0963 58.4264 8f 27.4890 60 1322 81 27.8817 61.8625 9 28.27-44 63.6174 9 t 28.6671 65.3968 29.0598 67.2008 9f 29.4525 69.0293 9i 29.8452 70.8823 9| 30.2379 72.7599 9f 30.6306 74.6621 TABLE OF CIRCLES. 45 Table —( Continued). Diam. Circum. Area. % 31.0233 76.589 10 31.4160 78.540 10} 31.8087 80.516 lol 32.2014 82.516 lot 32.5941 84.541 10} 32.9868 86.590 lot 33.3795 88.664 lot 33.7722 90.763 lot 34.1649 92.886 11 34.5576 95.033 Ilf 34.9503 97.205 111 35.3430 99.402 lit 35.7357 101.623 111 36.1284 103.869 lit 36.5211 106.139 lit 36.9138 108.434 lit 37.3065 110.754 12 37.6992 113.098 12* 38.0919 115.466 12| 38.4846 117.859 12f 38.8773 120.277 12} 39.2700 122.719 12* 39.6627 125.185 12t 40.0554 127.677 12* 40.4481 130.192 13 40.8408 132.733 13} 41.2335 135.297 13} 41.6262 137.887 13| 42.0189 140.501 13} 42.4116 143.139 13| 42.8043 145.802 13t 43.1970 148.490 13} 43.5897 151.202 14 43.9824 153.938 14} 44.3751 156.700 14} 44.7678 159.485 14* 45.1605 162.296 14} 45.5532 165.130 14| 45.9459 167.990 14t 46.3386 170.874 14} 46.7313 173.782 15 47.1240 176.715 15} 47.5167 179.673 15} 47.9094 182.655 16* 48.3021 185.661 15} 48.6948 188.692 D Diam. Circum. Area. 15* 49.0875 191.748 15t 49.4802 194.828 15} 49.8729 1 197.933 16 50.2656 201.062 16} 50.6583 204.216 16} 51.0510 207.395 16* 51.4437 210.598 16} 51.8364 213.825 16* 52.2291 217.077 16t 52.6218 220.354 16} 53.0145 223.655 17 53.4072 226.981 17} 53.7999 230.331 17} 54.1926 233.706 17* 54.5853 237.105 17} 54.9780 240.529 17* 55.3707 , 243.977 17* 55.7634 247.450 17} 56.1561 250.948 18 56.5488 254.470 18} 56.9415 258.016 18} 57.3342 261.587 18* 57.7269 265.183 18} 58.1196 268.803 18* 58.5123 272.448 18* 58.9050 276.117 18} 59.2977 279.811 19 59.6904 283.529 19} 60.0831 287.272 19t 60.4758 291.040 19* 60.8685 294.832 19} 61.2612 298.648 19* 61.6539 302.489 19* 62.0466 306.355 19} 62.4393 310.245 20 62.8320 314.160 20} 63.2247 318.099 20} 63.6174 322.063 20* 64.0101 326.051 20} 64.4028 330.064 20* 64.7955 334.102 20* 65.1882 338.164 20} 65.5809 342.250 21 65.9736 346.361 21} 66.3663 350.497 21} 66.7590 354.657 46 MENSURATION. Table —( Continued). Diam. Circura. Area. 211 67.1517 358.842 21} 67.5444 363.051 21} 67.9371 367.285 21} 68.3298 371.543 21} 68.7225 375.826 22 69.1152 380.134 221 69.5079 384.466 22} 69.9006 388.822 221 70.2933 393.203 22} 70.6860 397.609 22} 71.0787 402.038 22} 71.4714 406.494 221- 71.8641 410.973 23 72.2568 415.477 23} 72.6495 420.004 23} 73.0422 424.558 231 73.4349 429.135 231 73.8276 433.737 231 74.2203 438.364 23} 74.6130 443.015 231 75.0057 447.690 24 75.3984 452.390 241 75.7911 457.115 24} 76.1838 461.864 241 76.5765 466.638 24} 76.9692 471.436 24} 77.3619 476.259 24} 77.7546 481.107 24 } 78.1473 485.979 25 78.5400 490.875 25} 78.9327 495.796 25} 79.3254 500.742 251 79.7181 505.712 25} 80.1108 510.706 25} 80.5035 515.726 25} 80.8962 520.769 25} 81.2889 525.838 26 81.6816 530.930 26} 82.0743 536.048 26} 82.4670 541.190 26} 82.8597 546.356 26} 83.2524 551.§47 26} 83.6451 556.763 26} 84.0378 562.003 26} 84.4305 567.267 27 8-1.8232 572.557 Diam. Circum. Area. 27} 85.2159 577.870 27} 85.6086 583.209 27} 86.0013 588.571 27} 86.3940 593.959 27} 86.7867 599.371 27} 87.1794 604.807 27} 87.5721 610.268 28 87.9648 615.754 28} 88.3575 621.264 28} 88.7502 626.798 28} 89.1429 632.357 28} 89.5356 637.941 28} 89.9283 643.549 28} 90.3210 649.182 28} 90.7137 654.840 29 91.1064 660.521 29} 91.4991 666.228 29} 91.8918 671.959 29} 92.2845 677.714 29} 92.6772 683.494 29} 93.0699 689.299 29} 93.4626 695.128 29} 93.8553 700.982 30 94.2480 706.860 30} 94.6407 712.763 30} 95.0334 718.690 30} 95.4261 724.642 30} 95.8188 730.618 30} 96.2115 736.619 30} 96.6042 742.645 30} 96.9969 748.695 31 97.3896 754.769 3H 97.7823 760.869 311 98.1750 766.992 31} 98.5677 773.140 31} 98.9604 779.313 31} 99.3531 785.510 31} 99.7458 791.732 31} 100.1385 797.979 32 100.5312 804.250 32} 100.9239 810.545 32y 101.3166 816.865 32} 101.7093 823.210 32} 102.1020 829.579 32} 102.4947 835.972 32} 102.8874 842.391 \ TABLE OF CIRCLES. 47 Table—( Continued ). Diam. Circum. Area. Diam. Circum. 32f 103.280 848.833 38* 121.344 33 103.673 855.301 38* 121.737 331 104.065 861.792 38} 122.130 331 104.458 868.309 39 122.522 33f 104.851 874.850 39} 122.915 331 105.244 881.415 39} 123.308 33| 105.636 888.005 39* 123.700 33* 106.029 894.620 39} 124.093 331 106.422 901.259 39} 124.486 34 106.814 907.922 39* 124.879 341 107.207 914.611 39} 125.271 341 107.600 921.323 40 125.664 34f 107.992 928.061 40} 126.057 341 108.385 934.822 40} 126.449 341 108.778 941.609 40* 126.842 341 109.171 948.420 40} 127.235 341 109.563 955.255 40* 127.627 35 109.956 962.115 40* 128.020 351 110.349 969.000 40} 128.413 351 110.741 975.909 41 128.806 35f 111.134 982.842 41} 129.198 351 111.527 989.800 41} 129.591 351 111.919 996.783 41* 129.984 351 112.312 1,003.790 41} 130.376 351 112.705 1,010.822 41* 130.769 36 113.098 1,017.878 41* 131.162 361 113.490 1,024.960 41} 131.554 361 113.883 1,032.065 42 131.947 36f 114.276 1,039.195 42} 132.340 361 114.668 1,046.349 42} 132.733 361 115.061 1,053.528 42* 133.125 361 115.454 1,060.732 42} 133.518 361 115.846 1,067.960 42* 133.911 37 116.239 1,075.213 42* 134.303 371 116.632 1,082.490 42} 134.696 371 117.025 1,089.792 43 135.089 371 117.417 1,097.118 43} 135.481 371 117.810 1,104.469 43} 135.874 37f 118.203 1,111.844 43* 136.267 371 118.595 1,119.244 43} 136.660 371 118.988 1,126.669 43* 137.052 38 119.381 1,134.118 43* 137.445 381 119.773 1,141.591 43} 137.838 381 120.166 1,149.089 44 138.230 381 120.559 1.156.612 44} 138.623 381 120.952 1,164.159 44} 139.016 Area. 1,171.731 1,179.327 1,186.948 1,194.593 1,202.263 1,209.958 1,217.677 1,225.420 1,233.188 1,240.981 1.248.798 1.256.640 1,264.510 1,272.400 1,280.310 1,288.250 1.296.220 1.304.210 1.312.220 1,320.260 1,328.320 1,336.410 1,344.520 1.352.660 1,360.820 1,369.000 1.377.210 1,385.450 1,393.700 1.401.990 1.410.300 1,418.630 1.426.990 1,435.370 1,443.770 1,452.200 1.460.660 1,469.140 1.477.640 1,486.170 1,494.730 1.503.300 1,511.910 1,520.530 1,529.190 1,537.860 48 MENSURATION. Table— ( Continued). Diam. Circuru. Area. Diam. Circum. 44f 139.408 1,546.56 50* 157.473 44 * 139.801 1,555.29 50* 157.865 441 140.194 1,564.04 50* 158.258 44* 140.587 1,572.81 50* 158.651 44* 140.979 1,581.61 50| 159.043 45 141.372 1,590.43 50* 159.436 451 141.765 1,599.28 50* 159.829 45| 142.157 1,608.16 51 160.222 45* 142.550 1,617.05 51* 160.614 45| 142.943 1,625.97 51* 161.007 45| 143.335 1,634.92 51* 161.400 45* 143.728 1,643.89 51* 161.792 45* 144.121 1,652.89 51* 162.185 46 144.514 1,661.91 51* 162.578 46* 144.906 1,670.95 51* 162.970 462 145.299 1,680.02 52 163.363 46| 145.692 1,689.11 52* 163.756 46| 146.084 1,698.23 52* 164.149 46| 146.477 1,707.37 52* 164.541 462 146.870 1,716.54 52* 164.934 46* 147.262 1,725.73 52* 165.327 47 147.655 1,734.95 52* 165.719 47 * 148.048 1,744.19 52* 166.112 47} 148.441 1,753.45 53 166.505 47* 148.833 1,762.74 53* 166.897 47* 149.226 1,772.06 53* 167.290 47* 149.619 1,781.40 53* 167.6S3 472 150.011 1,790.76 53* 168.076 47* 150.404 1,800.15 53* 168.468 48 150.797 1,809.56 53* 168.861 48* 151.189 1,819.00 53* 169.251 48* 151.582 1,828.46 54 169.646 48* 151.975 1,837.95 54* 170.039 48* 152.368 1,847.46 54* 170.432 48'| 152.760 1,856.99 54* 170.824 482 153.153 1,866.55 54* 171.217 48* 153.546 1,876.14 54* 171.610 49 153.938 1,885.75 54* 172.003 49* 154.331 1,895.38 54* 172.395 49* 154.724 1,905.04 55 172.788 49* 155.116 1,914.72 55* 173.181 49* 155.509 1,924.43 55* 173.573 49* 155.902 1,934.16 55* 173.966 492 156.295 1,943.91 55* 174.359 49* 156.687 1,953.69 55* 174.751 50 157.080 1,963.50 55* 175.144 Area. 1.973.33 1.983.18 1,993.06 2,002.97 2,012.89 2,022.85 2,032.82 2,042.83 2,052.85 2,062.90 2,072.98 2,083.08 2,093.20 2,103.35 2.113.52 2,123.72 2,133.94 2.144.19 2,154.46 2,164.76 2,175.08 2,185.42 2,195.79 2.206.19 2,216.61 2,227.05 2.237.52 2,248.01 2.258.53 2,269.07 2.279.64 2.290.23 2.300.84 2.311.48 2,322.15 2.332.83 2,343.55 2,354.29 2,365.05 2.375.83 2.386.65 2.397.48 2.408.34 2.419.23 2,430.14 2,441.07 TABLE OF CIRCLES. 49 Table —( Continued). )iam. Circum. Area. 55} 175.537 2,452.03 56 175.930 2,463.01 56} 176.322 2,474.02 56} 176.715 2,485.05 56} 177.108 2,496.11 56} 177.500 2,507.19 56} 177.893 2,518.30 56^ 178.286 2,529.43 56} 178.678 2,540.58 57 179.071 2,551.76 57} 179.464 2,562.97 57} 179.857 2,574.20 57 f 180.249 2,585.45 57} 180.642 2,596.73 57} 181.035 2,608.03 57} 181.427 2,619.36 57} 181.820 2,630.71 58 182.213 2,642.09 58} 182.605 2,653.49 58} 182.998 2,664.91 58} 183.391 2,676.36 58} 183.784 2,687.84 58} 184.176 2,699.33 58} 184.569 2,710.86 58} 184.962 2,722.41 59 185.354 2,733.98 59} 185.747 2,745.57 59} 186.140 2,757.20 59} 186.532 2,768.84 59} 186.925 2,780.51 59} 187.318 2,792.21 59} 187.711 2,803.93 59} 188.103 2,815.67 60 188.496 2,827.44 60} 188.889 2,839.23 60} 189.281 2,851.05 60} 189.674 2,862.89 60} 190.067 2,874.76 60} 190.459 2,886.65 60} 190.852 2,898.57 60} 191.245 2,910.51 61 191.638 2,922.47 61} 192.030 2,934.46 61} 192.423 2,946.48 61} 192.816 2,958.52 61} 193.208 2,970.58 iam. Circum. Area. 61} 193.601 2,982.67 61} 193.994 2,994.78 61} 194.386 3,006.92 62 194.779 3,019.08 62} 195.172 3,031.26 62} 195.565 3,043.47 62} 195.957 3,055.71 62} 196.350 3,067.97 62} 196.743 3,080.25 62} 197.135 3,092.56 62} 197.528 3,104.89 63 197.921 3,117.25 63} 198.313 3,129.64 63} 198.706 3,142.04 63} 199.099 3,154.47 63} 199.492 3,166.93 63} 199.884 3,179.41 63} 200.277 3,191.91 63} 200.670 3,204.44 64 201.062 3,217.00 64} 201.455 3,229.58 64} 201.848 3,242.18 64} 202.240 3,254.81 64} 202.633 3,267.46 64} 203.026 3,280.14 64} 203.419 3,292.84 64} 203.811 3,305.56 65 204.204 3,318.31 65} 204.597 3,331.09 65} 204.989 3,343.89 65} 205.382 3,356.71 65} 205.775 3,369.56 65} 206.167 3,382.44 65} 206.560 3,395.33 65} 206.953 3,408.26 66 207.346 3,421.20 66} 207.738 3,434.17 66} 208.131 3,447.17 66} 208.524 3,460.19 66} 208.916 3,473.24 66} 209.309 3,486.30 66} 209.702 3,499.40 66} 210.094 3,512.52 67 210.487 3,525.66 67} 210.880 3,538.83 67} 211.273 3,552.02 50 MENSURATION. Table —{Continued). Diam. Circum. 4 Area. Diam. Circum. Area. 67} 211.665 3.565.24 73} 229.729 4,199.74 67} 212.058 3,578.48 73} 230.122 4,214.11 67| 212.451 3,591.74 73} 230.515 4,228.51 67} 212.843 3,605.04 73} 230.908 4,242.93 67} 213.236 3,618.35 73} 231.300 4,257.37 68 213.629 3,631.69 73} 231.693 4,271.84 68} 214.021 3,645.05 73} 232.086 4,286.33 m „ 214.414 3,658.44 74 232.478 4,300.85 68} 214.807 3,671.86 74} 232.871 4,315.39 68} 215.200 3,685.29 74 233.264 4,329.96 68| 215.592 3,698.76 74} 233.656 4,344.55 68} 215.985 3,712.24 74} 234.049 4,359.17 68} 216.378 3,725.75 74} 234.442 4,373.81 69 216.770 3,739.29 74} 234.835 4,388.47 69} 217.163 3,752.85 74} 235.227 4,403.16 69} 217.556 3,766.43 75 235.620 4,417.87 69} 217.948 3,780.04 75} 236.013 4,432.61 69} 218.341 3;793.68 75} 236.405 4,447.38 69} 218.734 3,807.34 75} 236.798 4,462.16 69} 219.127 3,821.02 75} 237.191 4,476.98 69} 219.519 3,834.73 75} 237.583 4,491.81 70 219.912 3,848.46 75} 237.976 4,506.67 70} 220.305 3,862.22 75} 238.369 4,521.56 70} 220.697 3,876.00 76 238.762 4,536.47 70} 221.090 3,889.80 76} 239.154 4,551.41 70} 221.483 3,903.63 76} 239.547 4,566.36 70} 221.875 3,917.49 76} 239.940 4,581.35 70} 222.268 3,931.37 76} 240.332 4,596.36 70} 222.661 3,945.27 76} 240.725 4,611.39 71 223.054 3,959.20 76} 241.118 4,626.45 71} 223.446 3,973.15 76} 241.510 4,641.53 71} 223.839 3,987.13 77 241.903 4,656.64 71} 224.232 4,001.13 77} 242.296 4,671.77 71} 224.624 4,015.16 77| 242.689 4,686.92 71} 225.017 4,029.21 77} 243.081 4,702.10 71} 225.410 4,043.29 77} 243.474 4,717.31 71} 225.802 4,057.39 77} 243.867 4,732.54 72 226.195 4,071.51 77} 244.259 4,747.79 72} 226.588 4,085.66 77} 244.652 4,763.07 72} 226.981 4,099.84 78 245.(115 4,778.37 72} 227.373 4,114.04 78} 245.437 4,793.70 72} 227.766 4,128.26 78} 245.830 4,809.05 72} 228.159 4,142.51 78} 246.223 4,824.43 72} 228.551 4,156.78 78} 246.616 4,839.83 72} 228.944 4,171.08 78} 247.008 4,855.26 73 229.337 4,185.40 78} 247.401 4,870.71 TABLE OF CIRCLES. 51 Table— ( Continued) Diam. Circum. Area. Diam. Circum. Area. 78} 247.794 4,886.18 84} 265.858 5,624.56 79 248.186 4,901.68 84} 266.251 5,641.18 79} 248.579 4,917.21 84} 266.643 5,657.84 79} 248.972 4,932.75 85 267.036 5,674.51 79* 249.364 4,948.33 85} 267.429 5,691.22 79} 249.757 4,963.92 85} 267.821 5,707.94 79* 250.150 4,979.55 85} 268.214 5,724.69 79} 250.543 4,995.19 85} 268.607 5,741.47 79} 250.935 5,010.86 85} 268.999 5,758.27 80 * 251.328 5,026.56 85} 269.392 5,775.10 80} 251.721 5,042.28 85} 269.785 5,791.94 80} 252.113 5,058.03 86 270.178 5,808.82 80} 252.506 5,073.79 86} 270.570 5,825.72 80} 252.899 5,089.59 86} 270.963 5,842.64 80} 253.291 5,105.41 86} 271.356 5,859.59 80} 253.684 5,121.25 86} 271.748 5,876.56 80} 254.077 5,137.12 86} 272.141 5,893.55 81 254.470 5,153.01 86} 272.534 5,910.58 81} 254.862 5,168.93 86} 272.926 5,927.62 81} 255.255 5,184.87 87 273.319 5,944.69 81} * 255.648 5,200.83 87} 273.712 5,961.79 81} 256.040 5,216.82 87} 274.105 5,978.91 81} 256.433 5,232.84 87} 274.497 5,996.05 81} 256.826 5,248.88 87} 274.890 6,013.22 81} 257.218 5,264.94 87} 275.283 6,030.41 82 257.611 5,281.03 87} 275.675 6,047.63 82} 258.004 5,297.14 87} 276.068 6,064.87 82} 258.397 5,313.28 88 276.461 6,082.14 82} 258.789 5,329.44 88} 276.853 6,099.43 82} 259.182 5,345.63 88} 277.246 6,116.74 82} 259.575 5,361.84 88} 277.629 6,134.08 82} 259.967 5,378.08 88} 278.032 6,151.45 82} 260.360 5,394.34 88} 278.424 6.168.84 83 250.753 5,410.62 88} 278.817 6,186.25 83} 261.145 5,426.93 88} 279.210 6,203.69 83} 261.538 5,443.26 89 279.602 6,221.15 83} 261.931 5,459.62 89} 279.995 6,238.64 83} 262.324 5,476.01 89} 280.388 6,256.15 83} 262.716 5,492.41 89} 280.780 6,273.69 83} 263.109 5,508.84 89} 281.173 6,291.25 83} 263.502 5,525.30 89} 281.566 6,308.84 84 263.894 5,541.78 89} 281.959 6,326.45 84} 264.287 5,558.29 89} 282.351 6,344.08 84 264.680 5,574.82 90 282.744 6,361.74 84} 265.072 5,591.37 90} 283.137 6,379.42 84} 265.465 5,607.95 90} 283.529 6,397.13 52 MENSURATION. Table — ( Continued ). Diam. Circum. Area. Diam. Circum. Area. 90| 283.922 6,414.86 95} 299.237 7,125.59 90} 284.315 6,432.62 95} 299.630 7,144.31 90| 284.707 6,450.40 95} 300.023 7,163.04 90| 285.100 6,468.21 95} 300.415 7,181.81 90| 285.493 6,486.04 95} 300.808 7,200.60 91 285.886 6,503.90 95} 301.201 7,219.41 91} 286.278 6,521.78 96 301.594 7,238.25 91} 286.671 6,539.68 96} 301.986 7,257.11 91} 287.064 6,557.61 96} 302.379 7,275.99 91} 287.456 6,575.56 96} 302.772 7,294.91 91| 287.849 6,593.54 96} 303.164 7,313.84 91} 288.242 6,611.55 96} 303.557 7,332.80 91} 288.634 6,629.57 96} 303.950 7,351.79 92 289.027 6,647.63 96} 304.342 7,370.79 92} 289.420 6,665.70 97 304.735 7,389.83 92} 289.813 6,683.80 97} 305.128 7,408.89 92} 290.205 6,701.93 97} 305.521 7,427.97 92} 290.598 6,720.08 97} 305.913 7,447.08 92} 290.991 6,738.25 97} 306.306 7,466.21 92} 291.383 6,756.45 97} 306.699 7,485.37 92} 291.776 6,774.68 97} 307.091 7,504.55 93 292.169 6,792.92 97} 307.484 7,523.75 93} 292.562 6,811.20 98 307.877 7.542.98 93} 292.954 6,829.49 98} 308.270 7,562.24 93} 293.347 6,847.82 98} 308.662 7,581.52 93} 293.740 6,866.16 98} 309.055 7,600.82 93} 294.132 6,884.53 98} 309.448 7,620.15 93} 294.525 6,902.93 98} 309.840 7,639.50 93} 294.918 6,921.35 98} 310.233 7,658.88 94 295.310 6,939.79 98} 310.626 7,678.28 94} 295.703 6,958.26 99 311.018 7,697.71 94} 296.096 6,976.76 99} 311.411 7,717.16 94} 296.488 6,995.28 99} 311.804 7,736.63 94} 296.881 7,013.82 99} 312.196 7,756.13 94} 297.274 7,032.39 99} 312.589 7,775.66 94} 297.667 7,050.98 99} 312.982 7,795.21 94} 298.059 7,069.59 99} 313.375 7,814.78 95 298.452 7,088.24 99} 313.767 7,834.38 95} 298.845 7,106.90 100 314.160 7,854.00 The preceding table may be used to determine the diameter when the circumference or area is known. Thus, the diameter of a circle having an area of 7,200 sq. in. is, approximately, 95} in. TABLES OF DECIMALS. 53 DECIMAL EQUIVALENTS OF PARTS OF ONE INCH. 1-64 .015625 17-64 .265625 33-64 .515625 49-64 .765625 1-32 .031250 9-32 .281250 17-32 .531250 25-32 .781250 3-64 .046875 19-64 .296875 35-64 .546875 51-64 .796875 1-16 .062500 5-16 .312500 9-16 .562500 13-16 .812500 5-64 .078125 21-64 .328125 37-64 .578125 53-64 .828125 3-32 .093750 11-32 .343750 19-32 .593750 27-32 .843750 7-64 .109375 23-64 .359375 39-64 .609375 55-64 .859375 1-8 .125000 3-8 .375000 5-8 .625000 7-8 .875000 9-64 .140625 25-64 .390625 41-64 .640625 57-64 .890625 5-32 .156250 13-32 .406250 21-32 .656250 29-32 .906250 11-64 .171875 27-64 .421875 43-64 .671875 59-64 .921875 3-16 .187500 7-16 .437500 11-16 .687500 15-16 .937500 13-64 .203125 29-64 .453125 45-64 .703125 61-64 .953125 7-32 .218750 15-32 .468750 23-32 .718750 31-32 .968750 15-64 .234375 31-64 .484375 47-64 .734375 63-64 .984375 1-4 .250000 1-2 .500000 3-4 .750000 1 1 DECIMALS OF A FOOT FOR EACH 1-32 OF AN INCH. Inch. 0" 1" 2" 3" 4" 5" 0 0 .0833 .1667 .2500 .3333 .4167 .0026 .0859 .1693 .2526 .3359 .4193 "Tfc .0052 .0885 .1719 .2552 .3385 .4219 5^ .0078 .0911 .1745 .2578 .3411 .4245 .0104 .0937 .1771 .2604 .3437 .4271 .0130 .0964 .1797 .2630 -.3464 .4297 .0156 .0990 .1823 .2656 .3490 .4323 .0182 .1016 .1849 .2682 .3516 .4349 * .0208 .1042 .1875 .2708 .3542 .4375 32 .0234 .1068 .1901 .2734 .3568 .4401 TS .0260 .1094 .1927 .2760 .3594 .4427 if .0286 .1120 .1953 .2786 .3620 .4453 JL .0312 .1146 .1979 .2812 .3646 .4479 if .0339 .1172 .2005 .2839 .3672 .4505 TS .0365 .1198 .2031 .2865 .3698 .4531 if .0391 .1224 .2057 .2891 .3724 .4557 l .0417 .1250 .2083 .2917 .3750 .4583 if .0443 .1276 .2109 .2943 .3776 .4609 .0469 .1302 .2135 .2969 .3802 .4635 if .0495 .1328 .2161 .2995 .3828 .4661 .0521 .1354 .2188 .3021 .3854 .4688 if .0547 .1380 .2214 .3047 .3880 .4714 \h .0573 .1406 .2240 .3073 .3906 .4740 U .0599 .1432 .2266 .3099 .3932 .4766 54 MENSURATION. Table —( Continued). Inch. 0" 1" 2" 3" 4" 5" 1 .0625 .1458 .2292 .3125 .3958 .4792 ft .0651 .1484 .2318 .3151 .3984 .4818 if .0677 .1510 .2344 .3177 .4010 .4844 U .0703 .1536 .2370 .3203 .4036 .4870 7 T .0729 .1562 .2396 .3229 .4062 .4896 M .0755 .1589 .2422 .3255 .4089 .4922 it .0781 .1615 .2448 .3281 .4115 .4948 u .0807 .1641 .2474 .3307 .4141 .4974 DECIMALS OF A FOOT FOR EACH 1-32 OF AN INCH, Inch. 6" 7" 8" 9" 10" 11" 0 .5000 .5833 .6667 .7500 .8333 .9167 3*5 .5026 .5859 .6693 .7526 .8359 .9193 1*5 .5052 .5885 .6719 .7552 .8385 .9219 3% .5078 .5911 .6745 .7578 .8411 .9245 .5104 .5937 .6771 .7604 .8437 .9271 3% .5130 .5964 .6797 .7630 .8464 .9297 T5 .5156 .5990 .6823 .7656 .8490 .9323 35 .5182 .6016 .6849 .7682 .8516 .9349 i_ .5208 .6042 .6875 .7708 .8542 .9375 & .5234 .6068 .6901 .7734 .8568 .9401 TU .5260 .6094 .6927 .7760 .8594 .9427 32 .5286 .6120 .6953 .7786 .8620 .9453 § .5312 .6146 .6979 .7812 .8646 .9479 if .5339 .6172 .7005 .7839 .8672 .9505 T ? 3 .5365 .6198 .7031 .7865 .8698 .9531 if .5391 .6224 .7057 .7891 .8724 .9557 2 .5417 .6250 .7083 .7917 .8750 .9583 tf .5443 .6276 .7109 .7943 .8776 .9609 T 9 5 .5469 .6302 .7135 .7969 .8802 .9635 if .5495 .6328 .7161 .7995 .8828 .9661 i .5521 .6354 .7188 .8021 .8854 .9688 3* .5547 .6380 .7214 .8047 .8880 .9714 if .5573 .6406 .7240 .8073 .8906 .9740 33 .5599 .6432 .7266 .8099 .8932 .9766 * .5625 .6458 .7292 .8125 .8958 .9792 if .5651 .6484 .7318 .8151 .8984 .9818 if .5677 .6510 .7344 .8177 .9010 .9844 §5 .5703 .6536 .7370 .8203 .9036 .9870 7 e .5729 .6562 .7396 .8229 .9062 .9896 if .5755 .6)589 .7422 .8255 .9089 .9922 if .5781 .6615 .7448 .8281 .9115 .9948 33 .5807 .6641 .7474 .8307 .9141 .9974 GEOMETRICAL DRAWING. 55 GEOMETRICAL DRAWING. > 4 - To erect a perpendicular to the line b c at the point a. With a as a center, and any radius, as ab, strike arcs cutting the line at b and c. From b and c as centers, and any radius greater than b a, strike arcs intersecting at d. Draw d a, which will be perpendicular to b c at a. To draw a line parallel to a b. At any points a and 5, with a radius equal to the required distance between thelines.draw _ _ - arcs at c and d. The line c d , tangent to . the arcs, will be the required parallel. To bisect the angle b a c. With a as a center, strike an arc cutting the sides of i the angle in b and c. With b and c as centers, and any radius, strike arcs inter¬ secting, as at d. Draw d a, the bisector. To erect a perpendicular at the end of a line. d\ Take a center anywhere above the line, as at ^ b. Strike an arc passing through a and j cutting the given line at c. Draw a line ji through c and b, cutting the arc at d. Draw the line ad, which will be the required perpendicular. To divide a line into any number of equal parts. Let it be required to divide the line ab into 5 equal j>arts. Draw any line a d, and point off 5 equal divisions, as shown. From 5 draw a line to b and draw 4-4', 5-3', etc. parallel to 5 b. To divide a space between two parallel lines or surfaces (for example, the spa¬ cing of risers in a stairway). Draw a b andce the given distance apart. Then move a scale along them, until as many spaces are included along a d as there are number of divisions required. Mark the points 1 , 5,3, etc., and draw lines through them parallel to ab and ce. / 56 GEOMETRICAL DR A WING. The magnitude of an angle depends not upon the length of its sides, hut upon the number of degrees contained in the arc of a circle drawn with the vertex as a center. The circle is divided into 360 equal parts, called degrees. To divide a quadrant as shown in the fig’ ure, first divide it into 3 parts by the arcs at e and d, chords e d and a e being equal to the radius. Then subdivide with dividers. An inscribed angle has its vertex (as c or d) in the circumference of a circle. Any angle inscribed in a semicircle is a right angle, as a c b, or a d b. To draw a circle through three points not in a straight line , as a, b, and c. Bisect a b and also b c. The two bisectors will intersect in a point d, which will be the center of the required circle. To find the center of a circular arc, as abc, take a point, as b on the curve, and draw ba and be. Bisect these lines by perpendiculars; the intersec¬ tion d will be the required center. To find a straight line nearly equal to a semi-circumference, as abc. On the diameter construct the equilateral tri¬ angle a c li. Through a and c draw h e and hf. Then ef is the length of the semi-circumference. Draw any line, as hkl; then If is almost exactly the length of arc k c, and b l that of arc b k. To construct a hexagon from a given side . Describe a circle with a radius a b equal to the given side. Draw a diameter as cb. From c and b as centers, and a radius equal to the given side, draw arcs cutting the circle at k,d,f and e. Connect c, k,f, b, e, and d. GEOMETRICAL ERA WING. 57 To inscribe an octagon in a square. Draw the diagonals ac and bd. With a as a center, and ae as a radius, strike an arc cutting the sides of the square at / and h. Repeat the operation at b, c, and d, and draw lines connecting the eight points thus found to form the figure required. To draw any regular polygon in a circle. Divide 360° by the number of sides; the quotient will be the angle aob. Lay off this angle at the center with a protractor, and draw its chord, a side of the required polygon. Step this side around on the cir¬ cumference, and connect the points found. To draw a segment of a circle, having given the chord a b and height cd. Draw ef, through d, parallel to ah ; also, ad and db. Draw ae and bf perpendicular to e k d k f a d and d b ; also a h and b k perpendic- \ / ular to ab. Divide ed, df, ac, cb, ah, ' ffx \ \ i / / yki /' and 6 & into the same number of equal ° c 6 parts. Draw lines connecting the points as shown, and trace the curve through the intersections. To draw a segment of a circle by means of a fixed triangle. Let a 5 be the required chord, and d c the rise. Drive nails at a and b. Make a triangle, as shown, from thin strips, so that the vertex comes at c, and stiffen it with the cross- biace. Now, by moving the triangle, always keeping the sides touching the nails at a and b, the arc may be traced by a pencil held at c. To draw an ellipse, having given the axes. Draw concentric circles whose diameters are equal to the axes ab and cd. From o draw any radius, as oe. From g, where oe cuts the inner circle, draw gf parallel to the major axis ab. From e, draw ef parallel to the minor axis d c. The intersection / gives a point on the ellipse. Other points are similarly found. 58 GEOMETRICAL DR A WING. To draw an ellipse with a string, having given the axes ab and c d. With c as a center, and a radius equal to o b, strike arcs cutting the major axis at e and /, the foci of the ellipse. Stick pins at e and /, and attach a string as shown, the length of the string being equal to the length of the major axis. Keep the string stretched with a pencil point, and sweep around the ellipse. To draw a parabola. Having given the coordinates a b and b c, to draw a parabola, complete the rectangle abed. Divide bc and cd into the same number of equal parts. From 1', 2', S', etc., draw lines through a. Through 1, 2, 3, etc., draw lines parallel to a b. The intersections of 1' a and 1-1", of 2' a and 2-2", etc. are points on the required parabola. To draiv a hyperbola. Hating given the coordinates a b and b c, to draw the curve. Complete the rectangle abed, and divide bc and c d into the same number of equal parts. Select any point e on the line b a prolonged ; as e is taken farther from a, the hyperbola will approach a parabola in form. Connect 1, 2, S to e, and 1', 2', S' to a. The intersec¬ tions of le and l'a, of 2e and 2'a, etc. are points on the required hyperbola. To draw a spiral. From a point, as o, draw radiating lines, oa,ob,o c, etc., making equal angles with each other. At any point, as d, on oa, start the spiral by drawing de perpendicular to o a ; from e where d e intersects o b, draw ef perpendicular to ob; etc. By making the angle between the lines smaller, the spiral may be made to make more turns, and the broken line will approach more nearly to a curve. GEOMETRICAL DRAWING. 59 To draw a spiral, second method. Draw a small circle, as bfa. Divide the circumference into any number of equal parts, eight or more. Draw tangents at the points of division, as be, de, etc. With b as a center, and ba as a radius, strike the arc ac. With d as a center, and d c as a radius, strike the arc ce, etc. This method is a very close approximation, though not mathe¬ matically correct. The Roman Ionic volute. For the eye, draw the small circle, taking \ the distance between ab and cd, in ( b ), as its diameter. In (a) is shown the eye en¬ larged. Mark points 1 and 2, at the middle of /c and/ d. Divide 2-12 "into three parts b y points 6 and 10. At a distance below cd equal to 2k times the space between 2-1 and 6-5, draw 3- 4. Draw 1-12, 10-9, 2-3, and 5-4. Draw 45° lines from 3 and 4; draw 6-7, 10-11, 9-8, 11-12, and 7-8. Use the points thus found as centers, 1 being the center for arc ae; 2 for arc eg; 3 for arc gf\ etc. To draw a helix. A helix is the curve assumed by a straight line, as d f, drawn on a plane, when the plane is wrapped around a cylin¬ drical surface. To draw a helix, having given the plan of the cylinder a be and the rise c' c", divide the arc a be into any number of equal parts, as at 1, 2, b, etc. Di\ ide c' c" into the same number of equal parts. Draw verticals through the divisions of the arc abc, and horizontals through the divisions of ~rr i/ iw 60 GEOMETRICAL ERA WING. c’ c", intersecting in points 1 ', 2', b", etc. Other points may be similarly found and the curv.e drawn. To develop the surface of a cylinder cut by a plane oblique to ,, the axis. Let abc be the f plan of the cylinder, and a' c" the inclination of the cutting plane. Divide the arc abc into a n y number of equal etc. Draw d e equal to the 3, and mark the same divi- e, as dl", l"-2", etc. Draw ;lirough points 1', 2', etc., intersecting verticals drawn through 1 ", 2", etc., as shown. Trace a curve through the points d, 1"', 2"', etc., and the figure dfe will be the development of the half cylinder abc. LAYING OUT ANGLES. By Two-Foot Rule. —To lay off any angle given in the table, open the rule at the middle until the distance between the inside corners at the knuckle joints (6-inches’ mark) is equal to the distance given for that angle under Chord. Degrees. Chord. Inches. Degrees. Chord. Inches. 5 hi 50 10 1 35 55 bhl 15 la 9 5 60 6 20 O 3 ^33 65 6/, 65 25 9 9 ~33 70 30 35 3 35 351 75 80 7 t 6 8 7§f 40 4& 85 85 45 451 90 85 To lay off an angle greater than 90°, subtract the angle from 180°; lay out the latter angle, extending one side, so that the greater angle formed will be the one required. GEOMETRICAL ERA WING. 61 By Steel Square.— To lay off* any angle given in the table, set either blade or tongue of the square along the line a b, mark¬ ing the 12" point at a. Mark c at a distance from b equal to that given in the table for the required angle, and draw a c ; then the angle bac will be the angle sought, approximately correct. For example, to find an angle of 30°, the distance b c is 611 in. Angle. Degrees. Distance. Inches. Angle. Degrees. Distance. Inches. 5 1ft 33° 42' Q 10 2ft (1 pitch) 15 q 7 ^32 35 m 18° 25' A 40 loft (1 pitch roof) 45 12 20 41 (1 pitch) 221 50 14ft 25 £19 °32 53° 7' 16 26° 33' a (f pitch) (1 pitch) D 55 171 30 t M 5 60 20 if Taking a at the 3" Mark. 65 6ft 75 lift 671 71 80 17 (Octagon Cut) Angle 70 81 90 abc £ 62 STRUCTURAL DESIGN. STRUCTURAL DESIGN. LOADS ON STRUCTURES. Loads on buildings may be classed under three general divisions: dead loads, live loads, and snow and wind loads. DEAD LOADS. The dead loads consist of the weight of the materials com¬ posing the structure. For instance, the brickwork in the walls forms a portion of the dead load upon the footings; the materials in the floors impose a dead load upon the columns, etc. In order to figure the amount of the dead loads on structures and the members therein, the weight of the various materials used must be known, and the following tables will be found useful. (For weights of metals, masonry, woods, etc., see pages 29, 30, and 31.) TABLE I. Approximate Weight of Building Materials. Material. Average Weight. Lb. per Sq. Ft. Corrugated galvanized iron, No. 20, unboarded Copper, 16 oz., standing seam . Felt and asphalt, without sheathing. Glass, £ in. thick. Hemlock sheathing, 1 in. thick . Lead, about } in. thick....,. Lath-and-plaster ceiling (ordinary). Mackite, 1 in. thick, with plaster *. Neponset roofing felt, 2 layers. Spruce sheathing, 1 in. thick . Slate, t 3 g in. thick, 3 in. double lap. a . Slate, £ in. thick, 3 in. double lap.*. Shingles, 6" X 18", 4 to weather. Skylight of glass, T 3 5 to £ in., including frame... Slag roof, 4-ply... Tin, IX . Tiles (plain), 104" X 6i" X I" — 51" to weather Tiles (Spanish), 144" x 104" — 74" to weather... White-pine sheathing, 1 in. thick . Yellow-pine sheathing, 1 in. thick . “4 H 2 If 2 6 to 8 6 to 8 10 * 2 * 6f 44 2 4 to 10 4 f 18 84 24 4 LOADS ON STRUCTURES. 63 Where only the approximate dead load due to the weight of floor, partition, or roof construction is desired, the follow- ing table will be of use. In this table the wooden floors and roof sheathing are taken as 1 in. thick. TABLE II. Weight of Floors, Partitions, and Roofs. Material. Weight. Lb. per Sq. Ft. Floors, including weight of beams — Wooden, in dwellings. Wooden, office buildings .. Hollow-tile arch. Brick and concrete (broken stone) . Partitions — Wooden . Hollow tile. . Roofs, including f raming — Shingle . .. Tin . 10-15 25-30 70-90 100-130 15-20 15-30 6-10 6- 8 Sla.te . - . 12-15 Tnr fmrl crrnvpl . 10-12 P!nrrii P’fl.t.pd iron . 8-10 Tile . 20-30 Note. —If roofs are plastered underneath, add 6 pounds per square foot to the weight given. In calculating the dead loads, there are certain weights which must be assumed. For instance, the weight of the floorbeams and girders are not known, because their size has not as yet been determined; likewise, the dimensions of the columns and many other structural details are unknown. The assumed weights are obtained by approximating the dimensions of the parts of the structure and estimating their weights. After the structure has been designed, the actual dead loads should be checked, to make sure they approxi¬ mate closely to those assumed. If any considerable variation is found, it can be taken care of by increasing or diminishing the sizes already determined. 64 STRUCTURAL DESIGN. Weight of Fireproof Floors.— In figuring the dead load for any system of floor construction, it is necessary to carefully calculate the total weight of the elements composing the system, which are the arches, filling, flooring, ceiling, and the steel construction. The weight of fixed or permanent parti¬ tions should always be taken into account, and the beams, etc. carrying them, proportioned accordingly. Where the parti¬ tions are movable, an additional weight of, say, 20 lb. per sq. ft., should be added to the dead load on the entire floor area. The finished floor line is usually considered as being 3 in. above the top of the I beams, and the ceiling line as 2 in. below the bottom of them. Cinder concrete filling, which is the usual backing for fireproof arch construction, averages in weight, when dry, 72 lb. per cu. ft., but is sometimes assumed to weigh only 48 lb. per cu. ft. The weight of the various systems of fireproof floors vary from 60 lb. to 125 lb. per sq. ft. of floor surface, including the steel used; generally, however, a load of 80 lb. per sq. ft. will be sufficient for all economical fireproof floors. TABLE III. Approximate Weight of Fireproof Floors. (Exclusive of Partitions.) Depth of I Beams. Weight. Lb. per Sq.Ft. Including Beams. Brick Arch. Hollow Tile. 8 74 63- 74 9 74 65— 80 10 81 68- 81 12 94 71- 93 15 113 91-113 Semi-fireproof floors, supported upon I beams placed 5 ft. apart crossed every 4 ft. with heavy T’s, constructed of buckled plates i in. thick and covered with 6 in. of concrete composed of broken stone and cement, imbedding sleepers to which l in. finished floor is secured, weigh, approximately 95 lb. per sq. ft. LOADS ON STRUCTURES. 6d TABLE IV. Weight of Fireproofing Materials. Kind. Span. Ft. Thickness. In. Weight. Lb. per Sq. Ft. Dense-tile flat arch . 4- 7 6-12 22-42 Porous-tile flat arch. 3-10 6-15 21-43 Dense-tile partition. 3- 6 15-28 Porous-tile partition. 3- 6 14-27 Porous-tile ceiling. 2- 4 12-20 Porous-tile roofing. 2- 4 12-20 LIVE LOADS. The live load is variable, and consists of the weight of people, furniture, stocks of goods, machinery, etc. The amount of this load, which should be added to the dead load, depends upon the use to which the building is to be put. Where the floor is required to support a considerable live load, concentrated at a particular place, such as a heavy safe or piece of machinery, special provision should he made in the floor construction for it. Table V gives the live loads per square foot recommended as good practice in conservative building construction. TABLE V. Live Loads. Lb. per Sq. Ft. Dwellings, offices, hotels, and apart¬ ment houses . Theaters, churches, ballrooms, and drill halls. Factories . Warehouses. From 40 to 70 From 80 to 120 From 150 up From 150 to 250 A live load of 70 lb. per sq. ft. will seldom be attained in dwellings; hut, as city houses are liable to be used for other than dwelling purposes, it is not generally advisable to 66 STRUCTURAL DESIGN. use a lighter load. In country houses, hotels, etc., where economy demands it, and the intended use for a long time is certain, a live load of 40 lb. per sq. ft. of floor surface is ample for all rooms not used for public assembly. For such rooms, a live load of 80 lb. per sq. ft. will usually be sufficient, as experience shows that a floor cannot be crowded more than this. If the desks and chairs are fixed, as in a schoolroom or church, a live load over 40 to 50 lb. will never be attained. Office-building floors have been designed for a live load ranging from 20 to 150 lb. per sq. ft., but a conservative prac¬ tice is to use about 70 lb. per sq. ft. An investigation of the live loads in over 200 office buildings in Boston showed that the greatest live load in any office was 40 lb. per sq. ft., while the 10 heaviest loaded offices averaged 33 lb. per sq. ft., the average live load for the entire number of offices being about 17 lb. per sq. ft. Retail stores should have floors proportioned for a live load of 100 lb. and upwards; while, for wholesale stores, machine shops, etc., a live load of at least 150 lb. per sq. ft. should be figured on. The static load in factories seldom exceeds 40 to 50 lb. per sq. ft. of floor surface, and usually a live load of 100 lb., including the effect of vibrations due to moving machinery, is ample. The conservative rule is, in general, to assume loads not less than the above, and to be sure that the beams are proportioned to avoid excessive deflection. Stiffness is a factor as important as mere strength. In designing the floors of office or buildings of like char¬ acter, it is good practice to figure the full live load on the floor joists or beams, but to consider only a certain percentage as coming upon the girders, columns, and foundations, on the assumption that all of the floors will not be fully loaded at the same time. This percentage should be carefully considered in each case ; and the amounts will depend upon the height of the building in question and the judgment of the designer. In proportioning the foundations of hotels, office buildings, etc., the live load may be neglected, but should be considered in heavy warehouses. In buildings carrying heavy machin¬ ery causing much vibration, it is good practice to double the estimated live load. LOADS ON STRUCTURES. 67 SNOW AND WIND LOADS. Data in regard to snow and wind loads are necessary in connection with the design of roof trusses. Snow Load.-— When the slope of a roof is over 12 in. rise per foot of horizontal run, a snow and accidental load of 8 lb. per sq. ft. is ample. When the slope is under 12 in.-rise per foot of run, a snow and accidental load of 12 lb. per sq. ft. should be used. The snow load acts vertically, and therefore should be added to the dead load in designing roof trusses. The snow load may be neglected when a high wind pressure has been considered, as a great wind storm would very likely remove all the snow from the roof. Wind Load. —The wind is considered as blowing in a hori¬ zontal direction, but the resulting pressure upon the roof is always taken normal (at right angles) to the slope. The wind pressure against a vertical plane depends on the velocity of the wind, and, as ascertained by the U. S. Signal Service at Mt. Washington, N. H., is as follows: TABLE VI. Velocity. Pressure. (Mi. per Hr.) (Lb. per Sq. Ft.) 10. . 0.4. .Fresh breeze. 20. . 1.6. .Stiff breeze. 30. . 3.6. ....Strong wind. 40. . 6.4. .... High wind. 50. .10.0. .Storm. 60. .14.4. .Violent storm. 80. .25.6. .Hurricane. 100. .40.0. ... Violent hurricane. The wind pressure upon a cylindrical surface is one-half that upon a flat surface of the same height and width. Since the wind is considered as traveling in a horizontal direction, it is evident that the more nearly vertical the slope of the roof, the greater will be the pressure, and the more nearly horizontal the slope, the less will be the pressure. Table VII gives the pressure exerted upon roofs of different slopes, by a wind pressure of 40 lb. per sq. ft. on a vertical plane, which is equivalent in intensity to a violent hurricane, 68 STRUCTURAL DESIGN. TABLE VII. Wind Pressure on Roofs. Pounds per Square Foot. Rise. In. per Foot of Run. Angle With Horizontal. Pitch. Proportion of Rise to Span. Wind Pressure Normal to Slope. 4 18° 25' h 16.8 6 26° 33' I 23.7 8 33° 41' 1 3 i 29.1 12 45° O' 36.1 16 53° 7' 1 38.7 18 56° 20' i 39.3 24 63° 27' 1 40.0 In addition to wind and snow loads upon roofs, the weight of the principals or roof trusses, including the other features of the construction, should be figured in the estimate. For light roofs having a span of not over 50 ft., and not required to support any ceiling, the weight of the steel construction may be taken at 5 lb. per sq. ft.; for greater spans, 1 lb. pel sq. ft. should be added for each 10 ft. increase in the span. STRENGTH OF MATERIALS. DEFINITIONS OF TERMS. Stress. —This is the cohesive force by which the particles of a body resist the external load that tends to produce an altera¬ tion in the form of the body. Stress is always equal to the effective external force acting upon the body; thus, a bar subjected to a direct pulling force of 1,000 lb. endures a stress of 1,000 lb. Unit stress is the stress or load per square inch of section. For instance, if the bar mentioned above is 1 in. X 2 in. in section, the unit stress of the bar would be 1,000 lb. -v-2sq. in. (sectional area) = 5001b. Tensile stress is produced when the external forces tend to Stretch 9 body, or pull the particles away from one another. STRENGTH OF MATERIALS. 61 * A rope by which a weight is suspended is an example of a. body subjected to tensile stress. Compressive stress is produced when the forces tend to compress the body, or push the par¬ ticles closer together. A post or column of a building is sub¬ jected to compressive stress. Shearing stress is produced when the forces tend to cause the particles in one section of a body to slide over those of the adjacent section. A steel plate acted on by the knives of a shear, or a beam carrying a load, are subjected to shearing stress. Transverse or bending stress is produced by loads acting on a beam tending to bend it, and is a combination of tensile, compressive, and shearing stresses. The ultimate strength of any material is that unit stress which is just sufficient to break it. The ultimate elongation is the total elongation produced in a unit of length of the material of a unit area, by a stress equal to the ultimate strength of the material. Strain.—The amount of alteration in form of a body pro¬ duced by a stress is called strain. If a steel wire is subjected to a pulling stress, and is elongated of an in., this alteration is the strain. Unit strain is the strain per unit of length or of area. It is usually taken per unit of length, and is called the elongation per unit of length. If an iron bar 6 ft. long is sub¬ jected to a pulling or tensile force which elongates it 1 in., the unit strain will be 1 in. -r- 72 (length of the bar in inches) = .0139 in. Modulus of Elasticity.—The modulus or coefficient of elasticity is the ratio between the stresses and corresponding strains for a given material, which may have a somewhat different modulus of elasticity for tension, compression, and shear. If l be the strain or increase per unit length of a material subjected to tensile stress, and p the unit stress producing this elonga- tion, the modulus of elasticity E — -• For example, a wrought-iron bar, 80 in. long, subjected to a unit tensile stress p of 10,000 lb., stretched .029 in. The unit strain l, or stretch per inch of length, is .029 in. -f- 80 in. = .0003625 in. Then, 10,000 ,0003625 27,586,200, 70 STRUCTURAL DESIGN. The relation E — y is true only when equal additions of stress cause equal increases of strain. Previous to rupture, this condition ceases to exist, and the material is said to be strained beyond the elastic limit , which, therefore, is that degree of stress within which the modulus of elasticity is nearly constant and equal to stress divided by strain. Modulus of Rupture.—The fibers in a beam subjected to transverse stresses are either in compression or tension, but the strength of the extreme fibers agrees neither with their compressive nor tensile strength; hence, in beams of uniform cross-section above and below the neutral axis, a constant determined by actual tests is used. This is called the modulus of rupture, and is generally expressed in pounds per square inch. Factor of Safety.—This is the ratio of the breaking strength of the material to the load imposed upon it, under usual condi¬ tions. For instance, if the ultimate strength of an iron tension bar is 50,000 lb., and the load it sustains is 10,000 lb., the factor of safety is 50,000 lb. h- 10,000 lb. — 5. TABLE VIII. Strength of Metals in Pounds per Square Inch. £5 4-i 4-1 Material. o . -+-• O) s| c A A"! ia i-O Ultimate Shearing. mimo oi aiq -noipuodjOci 4,000 2,000 5,000 4,000 3,000 2.500 1.500 1,500 •hirjo OJ p’ll'BI'BJ oooo o oooo oo O O O' O O iCOOlO o o OOrrOO COTfTj^cO O ^ •uirj£) oj ‘(Liaj •moo eppmopY oooo ooo oooooo OiOOO lO LO lO OtOiOiOiOO 1^(NC^ CO CM CM CO CM CM CM CO CO CO •uirjO o; pquTBj ubissaad -moo ojsmptfi OOOO oooooooooooo OOOO OOO O'oooo oooo iCiCCO 0-0 0 O O 0^0 o oooo Tf CO LO o' Tf rf lO iO ^ Tf Tf 1C ^ CM •UITUf) qipw opsu’ex ojumijui oooooooooooooooo oooooooooooooooo OOOOOOOOOO OO^OO 0^0 o' ^ d cf o' cT Ci cc o' o' cc o o' od ^ r-l r—1 H T—1 ri H o o3 •G 0) -4~> a a o> a> 2"p -e ti 5 bc-S 73 ^ & ci ci ft £ r; >>.5 .5 pp £ O © O d 03 tPl Cl - 0> -M 03 w T) fi J 05 © CO ffl O “ „ rt d f-i ei co S g PflS « p-l 2 >>©ft ccMooo ft CO C5 03 • r—i •»—I P P ^ Jh 0.0 <*-1 «»-H «rH 'd’si oo 72 STRUCTURAL DESIGN. The values for different woods in Table IX are aver¬ age values for commercial timber. Column 3 in the table shows the ultimate compressive strength parallel to the grain, which values are used in figuring the ultimate strength of columns. Column 4 gives the allowable compressive strength perpendicular to the grain, the values given being the load per square inch of section required to produce an Fig. 1. indenture of of an inch. Reference to Fig. 1 will explain this more clearly. The left-hand portion of column 5 will be found of use in calculating the resistance of the timber at the heel of a roof truss. For instance, in Fig. 2, to calculate with what force the piece c of the tie member b opposes the thrust of the rafter mem¬ ber a. The sectional area of the surface dcf is 10 in. X 18 in. = 180 sq. in. The ultimate shearing strength of Georgia yellow pine, parallel with the grain, according to Table IX, is 600 lb.; then, 180 X 600 = 108,000 lb., the ultimate strength of the timber. If the safe strength is desired, divide by the required factor of safety ; if 4 is used the safe strength will be 108,000 -i- 4 = 27,000 lb. Column 6, giving the modulus of rupture for different woods, is used in figuring the strength of beams (see page 106). From recent tests to determine the physical properties of timber, made by the Forestry Division U. S. Dept, of Agri¬ culture, the following conclusions are deduced: That the bleeding of long-leaf yellow pine, for sap products, is not detrimental to its durability and strength; that moisture reduces the strength of timber, whether that moisture be the sap or that absorbed after seasoning; also, that large timbers are equal in strength to small, provided they are sound and contain the same percentage of moisture. STRENGTH OF MATERIALS. 73 TABLE X. Average Ultimate Strength of Masonry Materials. Material. Compression. Lb. per Sq. In. Tension. Lb. per Sq. In. Modulus of Rupture. Building Stone. Bluestone. 13,500 1,400 2,700 Granite, average. Connecticut. 15,000 12,000 600 1,800 New Hampshire. 15,000 1,500 Massachusetts. New York. 16,000 15,000 1,800 Limestone, average . Hudson River, N. Y. 7,000 17,000 1,000 1,500 Ohio. 12,000 1,500 Marble, Vermont . 8,000 700 1,200 Sandstone, average. 5,000 150 1,200 New Jersey . 12,000 650 New York. 10,000 1,700 Ohio... 9,000 100 700 Slate. 10,000 4,000 5,000 Stonework (strength of stone) . 4 TS 4 1T5 TS Brick. 40 Brick, light red. 1,000 600 Good common. 10,000 200 Best hard. 12,000 400 800 Philadelphia pressed . 6,000 200 600 Brickwork, common lime mortar 1,000 50 Good cement-and-lime mortar. 1,500 100 Best cement mortar. Terra cotta . Terra-cotta work'. 2,000 5,000 2,000 300 Cements, etc. 200 200 Cement, Rosendale, 1 mo. old. 1,200 Portland, 1 mo. old . 2,000 400 400 Rosendale, 1 yr. old. 2,000 300 400 Portland, 1 yr. old . 3,000 500 800 Mortar, lime, 1 yr. old. 400 50 100 Lime and Rosendale, 1 yr. old. 600 75 200 Rosendale cement, 1 yr. old. 1,000 125 300 Portland cement, 1 yr. old. 2,000 250 600 Concrete, Portland, 1 mo. old. 1,000 200 100 Rosendale, 1 mo. old. 500 100 50 Portland, 1 vr. old . 2,000 400 150 Rosendale, 1 yr. old . 1,000 200 75 74 STRUCTURAL DESIGN. The values in the preceding table are ultimate, and from ts to sV of these values is used as the safe working strength of the materials. The following table gives the safe working loads allowable in good practice for brickwork, masonry, and foundation soils: TABLE XI. Safe Bearing Loads. Brick and Stone Masonry. Lb. per Sq. In. Brickwork. Bricks, hard, laid in lime mortar . 100 Hard, laid in Portland cement mortar. 200 Hard, laid inRosendale cement mortar. 150 Masonry. Granite, capstone. 700 Squared stonework . 350 Sandstone, capstone. 350 Squared stonework . 175 Rubble stonework, laid in lime mortar . 80 Rubble stonework, laid in cement mortar 150 Limestone, capstone. 500 Squared stonework . 250 Rubbl$, laid in lime mortar. 80 Rubble, laid in cement mortar. 150 Concrete, 1 Portland, 2 sand, 5 broken stone 150 Foundation Soils. Tons per Sq. Ft. Rock, hardest in native bed. Equal to best ashlar masonry. Equal to best brick . Clay, dry, in thick beds. Moderately dry, in thick beds. Soft .. Gravel and coarse sand, well cemented Sand, compact and well cemented . Clean, dry. Quicksand, alluvial soils, etc. 100 — 25—10 15-20 4- 6 2- 4 1 - 2 8-10 4- 6 2- 4 .5- 1 PROPERTIES OF SECTIONS. 75 PROPERTIES OF SECTIONS. CENTER OF GRAVITY. The center of gravity of a figure or body is that point upon Which the figure or body will balance in whatever position it may be placed, provided it is acted upon by no other force than gravity. If a plane figure is alike or symmetrical on both sides of a center line, the latter line is termed an axis of symmetry , and the center of gravity lies in this line. If the figure is symmet¬ rical about any other axis, the intersection of the two axes will he the center of gravity of the section. Thus, the center of gravity of a square, rectangle, or other parallelogram is at the inter¬ section of the diagonals; of a circle or ellipse, at the center of figure; etc. The center of gravity of a triangle is found at the intersection of lines drawn from the middle of each side to the opposite apex ; or, it is § the distance from any apex to the middle of the opposite side. For any section, the center of gravity may be found by the principles explained in the following article on Neutral Axis. It may be deter¬ mined approximately, but simply, by drawing to scale upon cardboard the outline of the section ; then, by cutting out the figure, and balancing it in different directions on a knife edge, the center of gravity will be at the intersection of the lines on which the section balances. NEUTRAL AXIS., When a simple beam is loaded, there is always compres¬ sion in the topmost fibers and tension in the bottommost fibers. There must, therefore, be a certain position in the cross-section at which the fibers are neither in compression nor tension—that is, they are neutral; hence the position of these neutral fibers is called the neutral axis of the section. The neutral axis of a beam section passes through the center of graxnty of the section, and at right angles to the direction in which the loads act. If the section of the beam is sym¬ metrical its axis of symmetry will be a neutral axis, provided 76 STRUCTURAL DESIGN. it is "perpendicular to the line of action of the loads. By finding the center of gravity of a cardboard pattern, the neutral axis of any section may be located. For simple sections, such as rect¬ angles, triangles, etc., the required neutral axis is found by the fore¬ going principles. When, however, the section is made up of combi¬ nations of rectangles, etc., as in Fig. 3, the distance c of the neutral axis from any line or origin of moments (usually taken at an edge of the section) may be cal¬ culated as follows: Rule .—Find the sum of the products of the area of each elementary section multiplied by the perpendicular distance between its center of gravity and the line or origin of moments; divide this sum by the total area of the figure; the result will give the required distance c. Example. —The distance c, in Fig. 4, is thus found; the line »r origin of moments being taken at the line a b : ; j 1 2 3 4 5 Elementary Section. Dimensions. Inches. Area. Sq. In. Distance From a b to Center of Gravity. Inches. Prod¬ ucts. Col. 3 X Col. 4. Upper plate . 2 upper angles— Web-plate. 2 lower angles... Lower plate. 8" X * 3" X 3" X f" 18" X ¥' 3 h" X 3i" X i" 12" X i" 4.00 3.56 X 2 9.00 3.98 X 2 6.00 .25 f 1.53 9.50 17.40 18.75 1.00 10.89 85.50 138.50 112.50 Totals . 34.08 348.39 , * For areas, see4able, page 85. For decimal equivalents of fractions of inches, see page 53. f See table, page 85. PROPERTIES OF SECTIONS. 77 Therefore, distance c of neutral axis (and center of gravity) from ab = 348.39-T-34.08 = 10.22 in. By finding another neutral axis in similar manner, the intersection of the two axes will be the center of gravity of the section. If the section, as in Fig. 4, is symmetrical about a vertical axis, the intersec¬ tion of this axis and the neutral axis will be the center of gravity. J I i , y/t% Fig. 4. MOMENT OF INERTIA When a beam is subjected to loading, as in Fig. 5, the fibers of the beam tend to resist the compression at the top and the tension at the bottom, each fiber exerting a force or moment directly proportional to the distance it is located from the neutral axis (pro* vided the elastic limit of the mate¬ rial is not ex- Support Support Fig. 5. ceeded); hence, the topmost and bottommost fibers are of considerably more value than those located near the neutral axis. It is therefore necessary, before the strength of any section can be obtained, to ascertain the average value of all the fibers in the section; this value is called the moment of inertia. The moment of inertia (usually designated by the letter I) of any body or figure is the sum of the products of each particle of the body or elementary area of the figure multi¬ plied by the square of its distance from the axis around which the body would rotate. This axis is the neutral axis. For example, assuming that the section shown in Fig. 6 is 3 in. X 12 in., and that it is divided into 36 equal parts, each having an area of 1 sq. in., the approximate moment of inertia may be calculated as follows: 78 STRUCTURAL DESIGN. Fibers b, b, b, b, b, b Fibers c, c, c, c, c, c Fibers d, d, d, d, d, d Fibers e, e, e, e, e, e Fibers /, /, /, /, /, / Fibers g, g, g, g, g, g 6 sq. in. X 5.5 X 5.5 — 181.50 6 sq. in. X 4.5 X 4.5 = 121.50 6 sq. in. X 3.5 X 3.5 = 73.50 6 sq. in. X 2.5 X 2.5 = 37.50 6 sq. in. X 1.5 X 1.5 = 13.50 6 sq. in. X .5 X .5 = 1.50 . 1 ; I, or moment of inertia = 429.00 In this manner the approximate moment of inertia for any section may be obtained. Table XII, page 83, gives con¬ venient formulas by which the moment of inertia for usual sections may be de¬ termined. For instance, according to this table, the formula for the moment of inertia of any rectangular section is I — in which b is the breadth of the beam, and d the depth. Thus, the moment of inertia for the section shown in Fig. 6 may be found as follows: y 3 x 12 X 12 X 12 b b b- c c c- d a A - e c e — f t /- a a 9— V a V f f f C e e d <1 A c c c V b — i ** I «5 >0 L a 12 432, Fig. 6. which is nearly the same as the approxi¬ mate result, 429, obtained in the previous calculation. Tables XIII to XIX, on pages 84 to 90, give the moment of inertia for rolled steel sections, and will be found useful in designing structural steel work. As beam or column sections are often made up of several elementary sections, the moment of inertia is then found thus: Rule.— The moment of inertia is equal to the sum of the prod¬ ucts of each elementary area multiplied by the square of its distance from the neutral axis, plus its moment of inertia about a parallel axis through its center of gravity. PROPERTIES OF SECTIONS. 79 a/8 P/afe If i represents the moment of inertia of each elementary figure, a the area of each, d 2 the square of the perpendicular distance from the center of gravity of each elementary section to the neutral axis a 6, Fig. 7, and I the required moment of iner¬ tia, the rule may be expressed thus: 1= 2 (ad 2 + i). Example. —The moment of iner¬ tia of the section shown in Fig. 4 may he found as follows, the figure being redrawn with the neutral axis located by the distance c, obtained from calculations on page 77, and shown in Fig. 7. Solution. —First work out the for- Fig. 7. mula ad' 2 + i for each elementary section, as in the follow¬ ing table. T 3X3X §id % I iX/8P/atl \3£3£rf\ii £X/2pZfe Elementary Section. Area a. Sq. In. d. In. dK i. ad- + i. Upper plate . 4.00 9.97 99.4 *.0833 397.68 2 upper angles. f3.56X2 8.69 75.51 13.20X2 544.03 Web-plate . 9.00 .72 .5184 243.00 247.66 2 lower angles. 3.98X2 7.18 51.55 4.33X2 418.99 Lower plate ... 6.00 8.53 72.76 .125 436.68 Moment of inertia of section, I = 2 (a d- + i) = 2,015.04. Graphical Method. —The location of the neutral axis and the moment of inertia of any section may be obtained by the following graphical method, which is sufficiently accurate for all practical purposes. Example. —Locate the neutral axis, and find the moment of inertia of the section shown at (a), Fig. 8. Solution.— First, draw the section, either full size or to any scale, as at (a). * Figured by formula -vx-, on page 83. f See page 85, 80 STRUCTURAL DESIGN. Second , divide this section by horizontal lines into strips of equal or unequal height; find the area in square inches and the center of gravity of each strip; since the strips in this case are rectangles, the centers of gravity will be at the cen¬ ters of the strips, through which points dot-and-dash lines have been drawn. Third, on any horizontal line lay off, from left to right, to any scale, distances proportional to the area of the strips, talcing them in order from top to bottom of the section. This horizontal line may be called the load or area line. Thus, at (b ), the distances A B, B C, CD, etc. are measured to a scale of, say, in. to 1 sq. in. area, and represent the areas of the sections P, Q, R, etc., respectively, in (a). Fourth, from the ends A and M of this line, draw lines inclined 45° to it, and intersecting at a point N called the pole. Draw lines from N to points B, C, D, etc. Fifth, commencing anywhere on a horizontal line through the top of the section, draw the line 1-2 parallel with the 45° line A N ; from the intersection of this line with one through the center of gravity of slice P, draw 2-3 parallel with B N ; from the intersection of 2-3 with the horizontal line passing through the center of gravity of slice Q, draw the line 3 -4 parallel to CN. Continue in this manner, drawing the remaining lines A-5, 5-6, etc., parallel, respectively, to DN, EN, etc. Sixth, draw, from the points 1 and 11 at the end of the curve, 45° lines intersecting at the point 12, through which PROPERTIES OF SECTIONS. 81 draw a horizontal line, cutting the section as shown at (a), Fig. 8; this line will he the neutral axis of the figure. Seventh, the moment of inertia I may he found hy multi¬ plying the area * in square inches of the section-lined figure by the entire area of the section. Thus, if in this case the area of the former is 4.67 sq. in., and that of the section at (a) is 16.25 sq. in., the moment of inertia will be equal to 16.25 sq. in. X 4.67 sq. in. = 75.88, the value of I for this section. RADIUS OF GYRATION. This term, like moment of inertia, is the expression of a certain value ot any section, and is one of the factors in the principal column formulas for determining the strength of cast-iron and steel columns. Rule. —The radius of gyration ( R ) of any section is equal to the square root of the quotient obtained by dividing the moment of inertia f of the section (I) by the area of the section {A). The rule may be thus expressed by formula: R For convenient formulas to obtain the radius of gyration of usual sections, see Table XII, page 83. For the radius of gyration of rolled shapes, see tables on pages 84 to 93. Example.— What is the least radius of gyration of the structural steel- column section shown in Fig. 9? Solution.— The value of J, or moment of inertia (found by one of the methods given on pages 78 to 80), on the axis XX, is while on the axis Y Y it is equal to 366.1. area is 41.44 sq. in. Using the least value of I, R = a ! 55, or 2.97. Fig. 9. equal to 1,129, The sectional there results, 41.44’ *To find area of irregular figures, see page 36. In obtain¬ ing dimensions necessary for determining^ the area, the same scale should be adopted as used in laying out the sec¬ tion at (a), Fig. 8. f See pages 77 to 81. 82 STRUCTURAL DESIGN. SECTION MODULUS, OR RESISTING INCHES. The section modulus , or, as it is sometimes called, resisting inches, of a section is equal to the moment of inertia divided by the greatest distance of the neutral axis from the outside fibers of the figure or section. This rule expressed in formula would be, where, Q — section modulus; I — moment of inertia * of the section ; c = greatest distance from the outside fiber to the neutral axis f. Example. —What is the section modulus for the cross-sec¬ tion of a 3" X 12" joist ? Solution. —Since the cross-section is rectangular, the neutral axis must pass through the center of the section, and the distance c is in this case equal to one-half the depth, that is, 6 in. The moment of inertia may be found by the method given on page 77 ; or more easily by the formula for rectangular sections given in Table XII, on page 83. This bd 3 formula is I — —--, where b = the breadth, and d = the depth JLZ of the joist. Then, I = 3 X 12 X 12 X 12 12 or 432. Having found the value of c and I, they may be substi¬ tuted in the formula for obtaining the section modulus, and which is the section modulus, or resisting inches, for a 3" X 12" joist. Formulas for obtaining directly the section modulus of the usual sections are given in Table XII, page 83. The section modulus is given for the usual rolled structural sections in the tables on pages 84 to 90. These latter are especially convenient as by them sections of different dimensions can be readily compared, and the most economical selected. * See page 77. f See page 76. PROPERTIES OF SECTIONS. 83 TABLE XII. Shape of Section. Moment of Inertia. I. Section Modulus. Q- Sq. Least Radius of Gyration. R 2 . d 4 d 3 d 2 12 6 12 bd 3 bd 2 62 12 6 12 6 4 - b ' 4 I &2 -f&'2 12 .56 12 b d 3 — b'd' 3 I I 12 .5 d A 7T 1 4 “ , or .0491 d 4 64 IT ——, or .0982 d s oA d 2 16 .0491 (d 4 - d' 4 ) /7/4\ .0982(d 3 -^ » d 2 +d'2 16 & d 3 _ 2 6' d' 3 I I 12 0.5 d A ^ (Approx.) 0.00 (Approx.) I A A (72 (Approx.) ^J< Approx -> I A Note — 4. = total area of section. In calculating the least radius of gyration be sure to use the least moment of inertia. xx' denotes the neutral axis, and the value of I given is that about this axis, 84 STRUCTURAL DESIGN. TABLE XIII. Properties of Steel Channels. Depth of Channel. Weight per Foot. Area. Thickness of Web. Width of Flange. Neutral Axis Perpendicular to Web at Center. Neutral Axis Parallel to Back of Channel. Moment of Inertia. Section Modulus. Radius of Gyration. Inches. Moment of Inertia. Radius of Gyration. Inches. Center of Gravity From Back. In. Lb. Sq. In. In. In. I. Q. R. r. S'. In. 15 50 14.71 .72 3.72 402.70 53.70 5.23 11.220 .87 .80 15 40 11.80 .47 3.63 371.60 49.50 5.62 11.500 .99 .89 15 33 9.70 .40 3.38 304.20 40.50 5.64 7.900 .92 .79 12 40 11.76 .76 3.42 197.00 32.80 4.09 6.630 .75 .72 12 27 7.90 .38 3.13 161.00 26.80 4.54 5.730 .86 .78 12 20 5.90 .28 2.88 124.70 20.80 4.59 3.690 .79 .69 10 30 8.82 .68 3.04 103.20 20.60 3.42 3.990 .67 .65 10 20 5.90 .31 2.88 85.50 17.10 3.81 3.750 .80 .74 10 15 4.40 .25 2.60 66.82 13.40 3.89 2.490 .74 .66 9 16 4.70 .28 2.56 57.09 12.70 3.48 2.590 .74 .66 9 13 3.80 .23 2.36 45.48 10.10 3.46 1.640 .64 .57 8 13 3.80 .25 2.22 35.56 8.89 3.07 1.470 .62 .58 8 10 3.00 .20 2.08 28.20 7.05 3.08 1.000 .58 .52 7 13 3.80 .28 2.22 27.35 7.81 2.69 1.890 .71 .62 7 9 2.61 .20 2.00 19.05 5.43 2.70 .814 .56 .51 6 17 4.85 .38 2.41 25.43 8.48 2.28 2.390 .70 .78 6 12 3.48 .28 2.19 18.70 6.23 2.32 1.380 .63 .65 6 8 2.35 .20 1.94 12.75 4.25 2.33 .710 .55 .52 5 9 2.59 .25 1.91 9.67 3.87 1.93 .810 .55 .57 5 6 1.76 .18 1.66 6.53 2.61 1.93 .390 .47 .45 4 8 2.31 .27 1.86 5.47 2.73 1.54 .685 .55 .59 4 5 1.46 .17 1.59 3.59 1.80 1.57 .293 .45 .46 3 6 1.76 .36 1.60 2.10 1.40 1.08 .310 .42 .46 3 5 1.47 .26 1.50 1.80 1.20 1.12 .250 .41 .44 3 4 1.19 .17 1.41 1.60 1.10 1.17 .200 .41 .44 PROPERTIES OF SECTIONS. 85 TABLE XIV. Properties op Steel Angles—Equal Legs. Size of Angles. Thickness. Weight per Foot. Area of Section. Distance from Cen¬ ter of Gravity to Back of Flange. Moment of Inertia, Axis Parallel to Flange. Section Modulus, Axis as Before. Radius of Gyration, Axis as Before. In. In. Lb. Sq. In. In. I. Q. R. 6 X 6 _7 34.00 10.03 1.87 35.300 8.170 1.87 6 X 6 7 17.20 5.06 1.66 17.680 4.070 1.87 6 X6 3. 14.80 4.36 1.64 15.400 3.520 1.88 5 X 5 f 24.20 7.11 1.56 17.000 4.780 1.55 5 X5 i 12.30 3.61 1.39 8.740 2.420 1.56 4 X 4 1 3 1 20.80 6.11 1.35 9.450 3.320 1.24 4 X 4 5 1(5 8.16 2.40 1.12 3.720 1.290 1.24 3£X3i 1 13.50 3.98 1.10 4.330 1.810 1.04 3£X3i 7.11 2.09 .99 2.450 .9S0 1.08 3 X 3 12.10 3.56 1.03 3.200 1.480 .94 3 X 3 i 4.90 1.44 .84 1.240 .580 .93 2£X2i 1 7.85 2.31 .82 1.330 .760 .76 2£X2i l. 4.05 1.19 .72 .700 .400 .77 2iX2i 1 7.17 2.11 .78 1.040 .650 .70 2iX2| X 3.70 1.06 .66 .510 .320 .69 2iX2i A 2.75 .81 .63 .390 .240 .69 2 X 2 i 6.32 1.86 .72 .720 .510 .62 2 X 2 2.41 .71 .57 .280 .190 .62 If XU TB 4.72 1.39 .61 .390 .320 .52 If Xlf A 2.11 .62 .51 .180 .140 .54 UXli t 3.33 .98 .51 .190 .190 .44 HXU 1.80 .53 .44 .110 .104 .46 U X if 5 TB 2.55 .75 .46 .123 .134 .40 UXH 1.02 .30 .35 .044 .049 .38 1 XI 1 1.57 .46 .36 . .045 .064 .31 1 XI i. .78 .23 .30 .022 .031 .31 2. N/ 1 3 Tff .99 .29 .29 .019 .033 .26 7 W 7 •g* A ■§■ .68 .20 .25 .014 .022 .27 fX f 3 .85 .25 .26 .012 .024 .22 fX f 8 .58 .17 .23 .009 .017 .23 86 STRUCTURAL DESIGN. TABLE XV. Properties of Steel Angles—Unequal Legs. Size of Angle. Weight per Foot Area of Section. Neutral Axis Parallel to Shorter Flange. Neutral Axis Parallel to Longer Flange. Center of Gravity.* Moment of Inertia. Section Modulus. Kad. of Gyration. (In.) Center of Gravity.* Moment of Inertia. Section Modulus. d t—i d o •i-H c3 o o 'd aj PS Inches. Lb. Sq. In. In. I. Q- R. In. r. Q'. R' 6X4X1 28.4 8.34 2.2 31.84 7.89 1.9 1.18 11.81 3.85 1.2 6X4X1 12.3 3.61 1.9 13.51 3.32 1.9 .94 4.90 1.60 1.2 5 X 31X i 20.3 5.98 1.8 15.15 4.53 1.6 1.03 6.23 2.39 1.0 5 X3iX % 10.4 3.05 1.6 7.78 2.29 1.6 .86 3.18 1.21 1.0 5X3X1 19.3 5.68 1.9 14.91 4.55 1.6 .88 4.27 1.85 .9 6 X 3 X vb 8.2 2.40 1.7 6.26 1.89 1.6 .68 1.75 .75 .8 41X3 Xi 17.8 5.23 1.7 10.73 3.59 1.4 .91 3.89 1.75 .9 41X3 X ts 7.7 2.25 1.5 4.67 1.54 1.5 .72 1.70 .75 .9 4 X 31X i 17.8 5.23 1.4 8.12 2.95 1.2 1.12 5.83 2.33 1.0 4 X 31X ts 7.7 2.25 1.2 3.57 1.24 1.3 .93 2.55 .99 1.1 4X3X1 13.5 3.98 1.4 6.04 2.31 1.2 .87 2.73 1.28 .8 4 X 3 X tb 7.1 2.09 1.3 3.38 1.23 1.3 .76 1.65 .74 .9 31X3 XI 12.5 3.67 1.2 4.11 1.76 1.1 .92 2.75 1.32 .9 31X3 Xtb 6.6 1.93 1.1 2.33 .96 1.1 .81 1.58 .72 .9 31 X 21X t 9 b 10.6 3.13 1.2 3.76 1.62 1.1 .75 1.61 .89 .7 31 X 21X i 4.9 1.44 1.1 1.80 .75 1.1 .61 .78 .41 .7 3 X 21X tb 9.7 2.84 1.0 2.44 1.21 .9 .79 1.53 .86 .7 3 X21 Xi 4.5 1.31 .9 1.17 .56 .9 .66 .74 .40 .8 3X2X1 7.7 2.25 1.1 1.92 1.00 .9 .58 .67 .47 .6 3 X 2 X I- 4.1 1.19 1.0 1.09 .54 1.0 .49 .39 .26 .6 21X 1? X t 6 b 3.6 1.07 .8 .53 .37 .7 .42 .19 .18 .4 21X U X t 3 b 2.3 .67 .8 .34 .23 .7 .37 .12 .11 .4 2 X 11 X ts 3.6 1.07 .6 .40 .30 .6 .52 .28 .23 .5 2 X 11X i5 2.3 .67 .6 .26 .19 .6 .47 .19 .15 .5 If X 11X t 6 b 2.5 .72 .5 .13 .15 .4 .38 .08 .10 .3 * pjstance measured from outside of flange. PROPERTIES OP SECTIONS. 87 TAbiLE XVI. Properties of Steel T Shapes—Equal Legs. Size of T. Flange by Stem. Thickness. Weight Per Foot. Area of Section. Distance of Center of Gravity From Flange.* Neutral Axis Parallel to Flange. Natural Axis Square to Flange and Coincident With Stem. Moment of Inertia. Section Modulus. Radius of Gyration. Inches. Moment of Inertia. Section Modulus. Radius of Gyrat ion. Inches. In. In. Lb. Sq. In. In. I. Q. R. I'. Q'. R'. 4 X 4 x 13.60 4.00 1.18 5.70 2.02 1.20 2.80 1.40 .84 4X4 A 10.40 3.07 1.15 4.70 1.64 1.23 2.19 1.09 .85 3* X 3* x 11.70 3.45 1.06 3.72 1.52 1.04 1.89 1.08 .74 X 3i 7 T7? 10.40 3.07 1.03 3.35 1.35 1.05 1.65 .94 .73 3? X 3? 5 T?T 6.80 2.04 .98 2.30 .93 1.09 1.07 .61 .73 3 X 3 1 10.00 2.94 .93 2.31 1.10 .88 1.20 .80 .64 3X3 TJJ 9.10 2.67 .92 2.12 1.01 .90 1.08 .72 .64 3 X 3 t 7.80 2.28 .88 1.81 .86 .90 .90 .60 .63 3X3 y 5 s 6.60 1.95 .86 1.60 .74 .90 .75 .50 .62 2* X 2* § 6.40 1.89 .76 1.00 .59 .74 .52 .42 .53 2k X 2k 5 Te> 5.50 1.62 .74 .87 .50 .74 .44 .35 .52 2k X 2k 5 Tff 4.90 1.44 .69 .66 .42 .68 .33 .30 .48 2* X 2k l 4.10 1.20 .66 .51 .32 .67 .25 .22 .47 2X2 5 TR 4.30 1.26 .63 .45 .33 .60 .23 .23 .43 2 X 2 x 3.70 1.08 .59 .36 .25 .60 .18 .18 .42 If X If x 3.10 .90 .54 .23 .19 .51 .12 .14 .37 1? X If 3 T(T 2.25 .66 .52 .17 .14 .51 .09 .10 .37 4 X H 1 2.55 .75 .42 .15 .14 .49 .08 .10 .34 15- X H A 1.85 .54 .44 .11 .11 .45 .06 .07 .31 if XH L 2.04 .60 .40 .08 .10 .36 .05 .07 .27 If X if T 3 5 1.55 .45 .38 .06 .07 ' .37 .03 .05 .26 1 X 1 1.23 .36 .32 .03 .05 .29 .02 .04 .21 1 XI 1 e .90 .26 .29 .02 .03 .29 .01 .02 .21 * Distance measured from outside of flange. 88 STRUCTURAL DESIGN. TABLE XVII. Properties of Steel T Shapes—Unequal Legs. Size of T Flange by Stem. Thickness. Weight per Foot. Area of Section. Distance of Center of Gravity From Flange. * Neutral Axis Parallel to Flange. Neutral Axis Square to Flange and Coincident With Stem. Moment of Inertia. Section Modulus. Radius of Gyration in Inches. Moment of Inertia. Section Modulus. Radius of Gyration in Inches. In. In. Lb. Sq. In. In. I. Q. R. T. Q'. R'. 6 X 4 t 20.6 6.06 1.04 7.66 2.58 1.13 11.50 3.83 1.38 6 X 4 17.0 5.00 .99 6.37 2.11 1.13 9.22 3.07 1.34 5 X 3 JL 13.5 3.97 .75 2.60 1.15 .83 5.23 2.09 1.18 5 X 2k 3. 10.4 3.07 .57 1.24 .64 .64 4.24 1.70 1.18 4* X 3 3. 10.0 3.00 .75 2.10 .94 .86 3.10 1.38 1.04 4i X 3 A 8.5 2.55 .73 1.80 .81 .87 2.60 1.16 1.03 4 X 3k i a 12.5 3.70 1.01 3.97 1.60 1.04 2.88 1.44 .88 4 X3k 1 9.8 2.88 .92 3.20 1.24 1.05 2.18 1.09 .87 4 X 2k 3. 8 8.6 2.52 .63 1.20 .62 .69 2.10 1.05 .92 4 X 2 3. 8 7.9 2.31 .48 .60 .40 .52 2.12 1.06 .96 3k X 4 1 a 12.8 3.75 1.25 5.50 1.98 1.21 1.89 1.08 .72 3k X 4 t 9.9 2.91 1.19 4.30 1.55 1.22 1.42 .81 .70 3 X 4 l a 11.9 3.48 1.32 5.23 1.94 1.23 1.21 .81 .59 3 X 3k l a 10.9 3.21 1.12 3.50 1.49 1.06 1.20 .80 .62 3 X3k TS 9.8 2.88 1.11 3.30 1.37 1.08 1.31 .88 .68 3 X 3k JL 8 8.5 2.49 1.09 2.90 1.21 1.09 .93 .62 .61 p O X 2k f 7.2 2.10 .71 1.10 .60 .72 .89 .60 .66 3 X2k 6.1 1.80 .68 .94 .52 .73 .75 .50 .65 3 X 2 3. 8 6.4 1.88 .55 .53 .37 .56 .85 .57 .71 3 XU .1 8 5.7 1.68 .40 .22 .20 .34 .85 .57 .75 2k X 3 3 8 7.2 2.10 .97 1.80 .87 .92 .54 .43 .51 2k X 3 TS 6.1 1.80 .92 1.60 .76 .94 .44 .35 .51 2k XH 1 4 3.1 .90 .32 .10 .11 .34 .24 .23 .54 * Distance measured from outside of flange. PROPERTIES OF SECTIONS. 89 TABLE XVIII. Properties of Steel Z Bars. Neutral Axis Neutral Axis Perpendicular Coincident to Web. With Web. d d jd hH d •rH 4-> 0) fl hH t-H 4 0 t>C Pi +j ; 0 C ' d 0 •rH H^> +3 *H 0) Cl HH Vh CO d d 'd d 0 •rH CO d d ft d 0 •rH H-» c3 £ fa m u O 0> 0 O >rH £ Vh O O krH H «+H m rt <4_| d d <+H ,d H-> ft O 0) m C d? oj P4 a 0 s O O o» m O 'd c3 P5 In. In. In. Lb. Sq. In. j. Q. .K. p. Q'. 12'. 6 3^ 3. 15.6 ' 4.59 25.32 8.44 2.35 9.11 2.75 1.41 6* 3xs 7 ys 18.3 5.39 29.80 9.83 2.35 10.95 3.27 1.43 6± 3f X. 21.0 6.19 34.36 11.22 2.36 12.87 3.81 1.44 6 3i A 22.7 6.68 34.64 11.55 2.28 12.59 3.91 1.37 6* 6* 3t 9 5 1 25.4 7.46 38.86 12.82 2.28 14.42 4.43 1.39 3* Is 28.0 8.25 43.18 14.10 2.29 16.34 4.98 1.41 6 3* t 29.3 8.63 42.12 14.04 2.21 15.44 4.94 1.34 6* 6| 3 t 9 5 13 TS 7 ■jr 32.0 9.40 46.13 15.22 2.22 17.27 5.47 1.36 3| 34.6 10.17 50.22 16.40 2.22 19.18 6.02 1.37 5 3|- xs t 11.6 3.40 13.36 5.34 1.98 6.18 2.00 1.35 St’s 3x6 13.9 4.10 16.18 6.39 1.99 7.65 2.45 1.37 5p 3f T5 1 040 the ultimate or breaking strength of the column per square inch of cross-section. Then, 3,040 -f- 5 (factor of safety) = 608 lb., the safe strength of the column to compression per square inch of section. The sectional area of the column is 12 in. X 10 in. = 120 sq. in.; hence, the safe load that the column will support is equal to 608 X 120, or 72,960 lb. Details of Design.— For slow-burning construction, the Fire Underwriters’ Association will not allow the use of square wooden columns less than 8 in. on a side; so, although the actual required size of column to safely sustain the load might be much less than 8 in., it is not advisable in first-class buildings of this construction to use wooden columns less than this size. Large timber posts—that is, posts not under 8 or 10 in. least dimension—are considered as offering more resistance to fire than cast-iron columns; hence, they are often used, especially in mill construction, in preference to the latter. Care should be taken in selecting timber for columns or posts to obtain only seasoned wood, without wind or twist, free from defects likely to affect its strength. The ends of the posts should be cut square, so as to take a uniform bearing at the base and cap plates. The timber commonly used for posts is yellow pine, which includes the Northern, Southern, or Georgia pines; white pine, spruce, and Oregon spruce are frequently used, and in some instances, oak. Details of the usual cast-iron caps and bases which are used with wooden columns are given on page 197. TABLE XXIII. API'KOXIMATE LREaKING LOADS FOR NORTHERN YELLOW-PlNE COLUMNS, IN THOUSANDS OF Lb. Calculated by the formula: S = U— U = 4,0001b. COLUMNS. 97 cb rH X CO rH o r-i co iO oo o OOOiXi>l- 05 05 co co co oo Tt« lOCXMNO'MOO X 00 00 l> CO co to Tft CO CO cO CO CO CO cO rH CO (Mt^oeococor^o X 05oooor^cocoi0so »v tOiOiOiOiOOtOiO CO rH *«. Ol COrHrtll^COI^tNCOO X O O 05 00 00 l'— I'- CO CO ■v. tOiOTf^Tf Tf 04 rH •s. rH rH lOO^OOOLOXHO X C4CJHH000500XN V. T^^TTiTtlrfrfCOCOCOCO rH rH *v O rH (MI--04COC0t^C0C0TfC0^ X lO^^COCOWNHHOO •v COCOCOCOCOCOCOCOCOCOCO o rH lOOiOHCOdXCOOCOC^N X CO CO N co co LO lO LO ^ CO 05 CO 10 00HO^(MX'£05COC005 x (M01rrHH0005 0500 00 00N C4 C4 04 04 04 04 04 rH rH rH rH H H 00 s l> O5iO OCCT>OrHC0 d <2 r—ir—inririrHrHHrHHCS 0)&H tJ 0) »—1 rO c3 +-> 0) cr co •< CO m c3 O) a c3 OJ 0) o r-o C3 § co 53 c3 O •H -H> O c3 ?H ft 0) Ph c3 ^3 o o § ^3 *■* £ § 43 £ O 'O c3 T3 O d 1—1 03 £ _ ►> Ai O « 42 5 oj g 4) I £ o O g -l® =L > 42 r—1 P •rH 4H r-H d a aoJS ^ rO co ^ s-i r A £ Pi T3 a, 0 | m .d be P d JO o 43 H 4) s* e '§> s- o •£ -£ - tH tH o o pH f>H s s ro o J.S 8 i n tS * -*0 ^ CO il 5 ’SS ^5 O 85 1: CO 98 STRUCTURAL DESIGN. CAST-IRON COLUMNS. A formula for obtaining the strength of cast-iron columns having flat or square ends is, S = - u 1 + —V V 3,600 R-J in which ,600 R- S = breaking strength of column in lb. per sq. in. of section ; l = length of column in inches; *R 2 = square of the least radius of gyra¬ tion ; f U — ultimate compressive strength of cast iron in lb. per sq. in. Having calculated the value of S, the safe strength per square inch may be obtained by dividing by the factor of safety. The safe load on the column is then found by multi¬ plying this value by the sectional area of the column in square inches. Example. —Find the proper working load for a 10-in. square cast-iron column, 20 ft. long, using a factor of safety of 6, the thickness of the metal being 1 in. Solution.— The ultimate compressive strength U of cast iron in lb. per sq. in., according to Table VIII, page 70, is 81,000; the length l equals 20 ft. X 12 in. = 240 in.; and the formula for determining A 2 for a hollow square column is, according to Table XII, page 83, b 2 + b' 2 R 2 = Substituting figures, jgj = 10 2 + 8 2 12 * 100 + 64 = 13.6. 12 12 Upon substituting these values in the formula, there results, 81,000 _ 81,00 0 2.17 S / 24 0 X 240 \ \3,600 X 13.6/ 37,327 lb. per sq. in. ,600 X 13. Using a factor of safety of 6, the safe load per sq. in. of sec¬ tion is 37,327 -T- 6 == 6,221 lb. Since the net area section is * For values of R 2 , see page 83. f See page 70. COLUMNS. 99 100 sq. in. — 64 sq. in. = 36 sq. in., the entire load that the column will safely sustain is equal to 6,221 lb. X 36 sq. in. = 223,956 lb. Design of Cast-Iron Columns.— Since cast-iron columns are usually more or less in a state of internal strain, due to the unequal cooling of the metal in the molds, and also because of the uncertain nature of the casting, a factor of safety of from 6 to 8 should be used in designing them. Fig. 10 shows a design for a circular cast-iron column. A shows the elevation for the cap and brackets supporting steel floorbeams. Special care ... , , , , , , . i Wood Column should be exercised m the design of the bracket a, the web being made, as shown at A, to extend to the edge of the plate m, and with the general out¬ line of its front edge forming an angle of about 60° with m. If the web is made as shown by full line at a in B, and the beam takes a bearing upon the edge of the plate m, the tendency will be to fracture the edge of the bracket. It is well to have at least fillets in all the corners of the casting, and also to thicken the metal in the column adjacent to the brackets, as shown at b. The bolt holes / should be always drilled, either in the casting or in the steel beams after the latter are in place, because, if the holes are cored in the casting and the holes punched in the beams at the mill, it is likely that the beams will be supported entirely by the shear of the bolts, without bearing upon the bracket at all. The bolts should tit the bolt holes / closely, and it is best, if practicable, to drill the holes in both beams and cast-iron flange ; this will insure as rigid a connection as is possible with this form of construction. The strengthening webs of the base should be placed in the most effective position, that is, on the diagonals, as shown in Fig. 10; ifiplaced on t}ie diameters, the corners will hav? Plan of Baje Fig. 10. 100 STRUCTURAL DESIGN. a tendency to break off, thus reducing the bearing surface of the base. In designing cast-iron columns a good rule to observe is to have the thickness of the metal in the body of the column not under f in. If made less than this, the difficulty of obtain¬ ing sound castings is increased, because the metal, in flowing into the mold, is liable to cool before completely filling it, and thus weak spots and dangerous flaws are formed. Inspection of Cast-Iron Columns.— All building castings, and especially columns, should be carefully inspected before being placed in the building. Air bubbles and blowholes are a common and dangerous source of weakness, and should be searched for by tapping the casting with a hammer. Bubbles or flaws filled in with sand from the mold, or purposely stopped with loam, cause a dullness in the sound. The cast¬ ing should be free from flaws of any kind, with the exterior surface smooth and clean, and the edges sharp and perfect. An uneven or wavy surface indicates unequal shrinkage. Cast-iron columns should be straight, and cored directly through the center, the metal being as nearly as possible of uniform thickness throughout. It is not unusual to find cast- iron columns, designed to be £ in. thick throughout, 1£ in. on one side and i in. on the other. The base and cap of a cast-iron column should be turned accurately, being true and perpendicular to the center line. Fireproofing of Cast-Iron Columns. —Cast-iron columns sub¬ jected to the intense heat of a conflagration are liable to destruction when water is played upon them. In consequence, especially when located in important situations and when their failure in case of fire would practically destroy the build¬ ing, they should be thoroughly fireproofed. There are several means employed to accomplish this. The columns may be incased in a light cast-iron shell, an air space of from 1 to 3 in. being left between the column and the casing; this space is sometimes, but not usually, filled with a incombustible, non- conductive material. Two rough and one finish coats of good hard mortar plaster laid upon an expanded metal casing, sur¬ rounding the column, with an air space between, make a good fireproof protection. Terra-cotta tile is also much used- COLUMNS. 101 TABLE XXIV. Breaking Loads for Square Cast-Iron Columns. In thousand pounds. U — 81,000. Dimen. of Side. In. Thick¬ ness. In. Length of Column in Feet. 8 ft. 10 ft. 12 ft. 14 ft. 16 ft. 18 ft. 20 ft. 6 1 594 6 1 700 584 6 f 820 685 567 6 929 770 638 535 7 1 2 775 664 573 494 430 7 f 840 725 625 532 460 395 7 i 1,090 935 810 688 589 505 440 7 7 8 1,220 1,060 915 770 660 570 491 7 1 1,368 1,180 1,020 860 780 625 540 8 f 1,162 1,040 915 805 708 621 540 8 f 1,380 1,218 1,060 930 815 710 582 8 7 8 1,550 1,370 1,220 1,065 930 814 700 8 1 1,730 1,530 1,340 1,169 1,018 882 770 8 n 1,900 1,660 1,450 1,248 1,098 950 835 9 i 1,391 1,262 1,138 1,013 908 800 715 9 * 1,643 1,473 1,338 1,192 1,060 940 831 9 7 8 1,861 1,678 1,510 1,340 1,180 1,060 938 9 1 2,100 1,880 1,690 1,500 1,320 1,176 1,040 • 9 n 2,300 2,070 1,840 1,630 1,450 1,276 1,135 10 i 1,934 1,784 1,584 1,467 1,328 1,190 1,064 10 n_ 2,184 2,000 1,820 1,643 1,485 1,334 1,200 10 l 2,440 2,250 2,040 1,850 1,660 1,490 1,345 10 H 2,890 2,650 2,400 2,140 1,930 1,730 1,550 10 li 3,040 2,710 2,470 2,225 1,992 1,780 1,600 11 7 2,510 2,340 2,150 1,950 1,783 1,623 1,484 11 l 2,810 2,650 2,430 2,200 2,020 1,821 1,680 11 li 3,100 2,920 2,670 2,440 2,230 2,030 1,840 11 li 3,430 3,180 2,930 2,660 2,440 2,200 1,990 12 l 3,150 2,970 2,770 2,570 2,370 2,180 1,980 12 H 3,520 3,300 3,007 2,850 2,620 2,420 2,230 12 li 3,870 3,620 3,370 3,120 2,870 2,640 2,430 12 H 4,170 3,900 3,600 3,350 3,080 2,820 2,570 13 H 3,890 3,690 3,460 3,250 3,140 2,780 2,560 13 H 4,290 4,070 3,820 3,580 3.340 3,060 2,830 13 H 4,650 4,400 4.130 3.940 3,570 3,000 3,040 13 H 5,000 4,740 4.420 4,130 3.830 3,520 3,240 14 li 4,740 4,530 4,280 4.000 3,760 3,510 3,260 14 If 5,060 4,870 4,620 4,340 4,050 3,770 3,520 14 5,520 5,270 4,980 4,680 4,870 4,060 3,800 14 if 5,900 5,610 5,300 5,980 4,650 4,330 4,030 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12 13 13 13 13 14 11 1 l 14 STRUCTURAL DESIGN. TABLE XXV. iking Loads for Round Cast-Iron Columns. In thousand pounds. U — 81,000. Thick- Length of Column in Feet. ness. In. 8 ft. 10 ft. 12 ft. 14 ft. 16 ft. 18 ft. 20 ft. 1 a 418 5 8 505 412 i 570 465 374 7 8 651 525 423 347 1 a 560 474 393 332 270 IL 8 655 566 476 402 332 287 f 820 658 544 456 384 324 280 7 8 880 732 610 510 425 360 313 1 971 810 670 559 470 396 339 t 850. 735 631 542 462 400 352 1 1,000 910 743 640 545 468 405 7 8 1,120 960 810 710 620 529 455 1 1,260 1,082 930 785 675 578 502 1,360 1,185 1,005 865 732 625 545 1 1,040 923 810 710 620 535 480 1 1,220 1,073 950 820 720 628 560 7 8 1,360 1,200 1,050 918 805 595 614 1 1,550 1,362 1,192 1,039 900 758 682 If 1,710 1,500 1,300 1,130 958 851 751 f 1,420 1,280 1,141 1,020 900 798 705 i - 1,640 1,495 1,318 1,170 1,036 910 820 i 1,830 1,580 1,460 1,292 1,143 1,010 895 if 2,030 1,810 1,470 1,310 1,160 1,110 980 ! 1,640 1,510 1,363 1,260 1,120 1,000 895 7 8 1,840 1,680 1,540 1,385 1,250 1,113 990 1 2,100 1,923 1,740 1,570 1,420 1,258 1,119 If 2,300 2,110 1,920 1,720 1,550 1,370 1,217 * 1,869 1,740 1,600 1,440 1,310 1,200 1,080 7 8 2,130 1,960 1,800 1,630 1,490 1,360 1,223 1 2,380 2,180 2,020 1,840 1,670 1,500 1,360 If 2,580 2,350 2,180 1,990 1,800 1,620 1,470 f 2,020 1,900 1,740 1,620 1,480 1,363 1,265 7 8 2,400 2,250 2,100 1,920 1.760 1,590 1,465 1 2,660 2,480 2,320 2,120 1,940 1,745 1,610 If 2,920 2,720 2,540 2,310 2,120 1,900 1,750 T 2,600 2,450 2,310 2,160 1,970 1,820 1,670 1 2,930 2,700 2,580 2,390 2,140 2,090 1,880 if 3,250 3,090 2,850 2,670 2,440 2,300 2.070 H 3,560 3,360 3,140 2,910 2,660 2,440 2,250 COLUMNS. 103 STRUCTURAL-STEEL COLUMNS. The method of securing the ends of a column greatly influences its strength. While wooden and cast-iron columns usually occur in building construction with flat or square ends, structural-steel columns are often used, having either hinged, flat or square, and flxed ends. Where the ends are securely fixed, so that the column is likely to fail in the shaft, before the end connections are ruptured, greater strength is developed than with columns having hinged or pinned ends. Columns having flat or square ends are somewhat stronger than hinged-end columns, hut not so strong as those having their ends firmly secured. The strength of structural-steel columns may he determined hy the following formulas: S = For Fixed Ends. U 1 + / J 2 V V 36,000 R n -J S For Square Ends. U 1 + Y V 24,000 Ii- ) For Pin Ends. 1 + ( 18,000 R* ) in which & = ultimate strength of column in pounds per square inch ; U — ultimate compressive strength of the material in pounds per square inch ; l — length of column in inches; *R = least radius of gyration. The value of U for structural steel is usually taken at from 52,000 to 54,000 lb. for soft steel, and as high as 60,000 for medium steel. Having determined S, the safe load per square inch is found by dividing S by the factor of safety. This quotient, multiplied by the area of the section, will give the safe load the column will sustain. * See page 81. I 104 STRUCTURAL DESIGN. Example. —What safe load will a square-end structural- ■y steel column, 20 ft. long, having the sec¬ tion shown in Fig. 11, support, taking the ultimate compressive strength at 52,000 lb. per sq. in., and using a factor of safety of 5 ? Solution.— First calculate the radius of gyration about both the axes XX and Y Y, by the method given on page 81. This will determine the least radius of gyration, which in this case is around Fig. 11. the axes Y Y, and is approximately 2.13 in. The value of R 2 will then be 2.13 X 2.13 = 4.53. The value of l, the length of the column in inches, is 20 (ft.) X 12 (in.) = 240 in.; andf 2 = 240X240 = 57,600. Substituting the above values in the formula, U „ '52,000 rp "V-- ej r -r!r—A" - e* U F ■ ' S = s = 1 + (24,000#“) 1+ ( 57,600 = 34,000, ,000i? 2 / ' V 24,000 x 4.53/ Which is the ultimate strength of the column in pounds per square inch of section. The total sectional area is as follows: * Area of 4 — 5" X 3"X rs" angles = 2.40 X 4 = 9.60 sq. in. f Area of T B S " X 10" web-plate = 10 X .3125 = 3.125 sq. in. Total area of section = 12.725 sq. in. Then 34,000 (ultimate strength of the column in pounds per square inch of section) X 12.72 (sq. in.) = 432,480 lb. The factor of safety required being 5, the safe load that the column will support is 432,480 -4- 5 = 86,496 lb. The formulas above given being somewhat awkward to use, more convenient ones have been deduced, and while they give somewhat different values for S than those obtained by the previously stated formulas, the differences are on the side of safety. These formulas may be applied to columns whose lengths are between 50 and 150 least radii of gyration ; * See table, page 86. f For table of decimal equivalents, see page 53. COL UMNS. 105 that is, if the radius of gyration of a column is 2 in., these formulas will apply to columns whose lengths are between 100 and 300 in. Fixed ends, Square ends, Pin ends, Medium Steel. S = 60,000 — 210 4 JX S = 60,000 - 230 4 JX S = 60,000 — 260 4 Soft Steel. S = 54,000 — 185 4 JX S = 54,000 — 200 4 JX S = 54,000 - 225 4 In these formulas, S = ultimate or breaking strength of the column in pounds per square inch of sectional area; l = length of the column in inches; R — least radius of gyration in inches. Example. —What is the ultimate strength in pounds, per square inch of section, for a fixed-end column 22 ft. long, the least radius of gyration for the section being 2.5 in. and the material being medium steel ? Solution.— The formula S' 60,000 — 210=, by substitu- JX ting the values for l and R, becomes S = 60,000 - 210 =-= = 37,824 lb., z.o the ultimate strength per square inch of column section. Structural columns are usually considered as having square ends, and a factor of safety of 4 is generally allowed. The fol¬ lowing formulas will give the allowable stress in pounds per square inch which such columns will sustain : Medium Steel. Soft Steel. S = 15,000 — 574 S = 13,500 — 5o4 JX JX The formula for medium-steel columns is for lengths over 50 times the least radius of gyration; that for soft-steel col¬ umns is for lengths over 30 times the least radius of gyration. For columns of dimensions less than these figures, a safe load of 12,000 lb. per sq. in. of section can safely be assumed. No column should be used whose length is greater than 150 least radii of gyration, or whose length exceeds 45 times the least dimension of the column. 106 STRUCTURAL DESIGN. Design of Structural-Steel Columns.— Structural-steel col¬ umns should be so designed that, where several lengths are connected end to end, the splice may be made in a rigid and secure manner; they should also be so constructed as to facilitate connecting floorbeams or girders on all sides. All beam connections to the column should be carefully designed and provided with sufficient rivets, to avoid failure of the connections by shearing of the rivets. Rivets in columns should be so spaced as not to exceed 3 in. center to center, at the ends of the column, for a distance equal to twice the width of the column. The distance between rivets from center to center, in a direction parallel with the line of strain, should not exceed 16 times the least tliickness of metal of the parts joined ; and the distance from center to center between the rivets at right angles to the line of strain should not exceed 32 times the least thickness of metal. Further con¬ siderations in regard to rivets and rivet spacing are given on pages 128 to 133. BEAMS AND GIRDERS. A body resting upon supports and liable to transverse stress is called a beam. Beams are designated by the number and location of the supports, and may be either simple, cantilever, fixed, or continuous. A simple beam js one that is supported at each end, the distance between its supports being the span. A cantilever is a beam that has one or both ends overhanging the support; a beam having one end firmly fixed and the other end free is a cantilever. A fixed beam is one that has both ends firmly secured. A continuous beam is one which rests upon more than two supports. MOM ENTS. The moment of a force around a fixed point is equal to the force multiplied by its lever arm, which is the perpendicular distance from the line of action of the force to the point; this product is called foot-pounds or inch-pounds, according to the unit used. Thus in (a), Fig. 12, the moment about c = 10 lb. BEAMS AND GIRDERS. 107 '10 ft. = 100 ft.-lb. In {b) the moment about c is 10 lb. X 8 ft. = 80 ft.-lb. Likewise in (c) the moment around c is 20 lb. < 24 in. = 480 in.-lb. In (d), the beam is supported at c ; the Dree a has a moment about c of 30 b. X 8 ft. = 240 ft.-lb., acting in a irection contrary to the motion of lock hands. The force b has a mo- aent about c of 20 lb. X 10 ft. = 200 t.-lb., acting in the direction of motion if clock hands. It is evident that the >eam will turn around c in the direction >f the greater moment, with a moment if 240ft.-lb. —200ft.-lb. = 40ft.-lb.; the ieam is, therefore, not in equilibrium. ;fa force of 4 lb. be added to b, creating i moment of 4 lb. X 10 ft. = 40 ft.-lb., n counterbalance the moment of 40 't.-lb. tending to rotate the beam, the atter will then be in equilibrium. Eence, moments tending to produce rotation in the same direction are alike, ind should be added; those acting in opposite directions ire unlike, and the smaller should be deducted from the greater. The total moment of a system of forces about a point is the algebraic sum of the moments of all the forces around that point. If a body is in equilibrium , the algebraic sum of the moments of the forces acting upon that body is zero about any point in that body. 30 t\ ISO Uk - lOftir] c‘ > (d) Fig. 12. I TV SL TV a TV THEORY OF BEAMS. If a beam is loaded as at W W W, Fig. 13, the weights pro¬ duce reactions at the supports. These forces, or reactions, Ri, and _R 2 , oppose the action of the weights and their combined action must equal the total weight. The weights and reactions, constituting the external forces, tend to produce bending in the beam, and are resisted by the internal forces, consisting of the strength of the fibers composing the beam. In a simple Fig. 13. I 108 STRUCTURAL DESIGN. beam, the effect of loading is to shorten the upper fibers, and to lengthen the lower ones. Somewhere between the top and bottom of the cross-section are located fibers which are neither shortened nor lengthened ; this position is called the neutral axis (see page 75). In steel and like material of homogeneous nature, the neutral axis passes through the center of gravity of the section. At any point in the length of a beam, the tendency to produce bending is equal to the algebraic sum of the moments of the external forces at that point; this moment is called the bending moment. A beam resists bending at any point by the resistance of its particles to extension or compression, the sum of the moments of which about the neutral axis of the cross-section is called the moment of resistance, or resisting moment. For a beam to be sufficiently strong to sustain the load, the moment of resistance must equal the bending moment. If the moment of resistance is expressed in inch-pounds, the bending moment must likewise be reduced to inch-pounds. Reactions. —The reactions or supporting forces of any beam or structure must equal the loads upon it. If the load upon a simple beam is uniformly distributed, applied at the center of the span, or symmetrically placed and of equal amount upon each side of the center, the reactions R x and R 2 will each be equal to one-half the load. When the loads are not symmet¬ rically placed, the reactions are found by the principle of moments in the following manner: Fig. 14 represents a simple beam supporting loads W x , W 2 , and W 3 ; Ms the span or distance between the reactions R x and R 2 ; a, b, and c are the distances from the reaction R x to the loads W x , W 2 , JF 3 , respectively. Then, the right-hand reaction, R* = ( W\ X a) + (TF 2 X b) + ( W 3 X c ) l This formula expressed in a general rule is: To find the reaction at either support, multiply each load by its distance from the other support, and divide the sum of these products by the distance between supports. -fr- off d'h”; it, Fig. 14. 1 No BEAMS AND GIRDERS. 109 Since the sum of the reactions must equal the sum of the toads, if one reaction is found, the other can be obtained by sub¬ tracting the known one from the sum of the loads. Example .—What are the reactions at R± and R 2 , Fig. 15 ? Solution.— The lever arm of a uniformly distributed load is always the distance from the center of moments to the center of gravity of the load. The total uniform load a is 3,000 X 10 = 30,000 lb., and the distance of its center of gravity from Ri is 13 ft. The moments of the loads about Ri are as follows: J 4,000 lb. X 4 ft. = 16,000 ft.-lb. 30,000 lb. X 13 ft. = 390,000 ft.-lb. 9,000 lb. X 20 ft. = 180,000 ft.-lb. Total = 586,000 ft.-lb. The distance from R x to R<> is 30 ft.; hence, 586,000 -r- 30 = 19,533} lb., the reaction at i? 2 . As the sum of the loads is 43,000 lb., the reaction at R\ is 43,000— 19,533} = 23,466} lb. Shear.— The loads and reactions, besides causing bending or flexure, create shearing stresses in the beam by their opposing tendency; that is, as the reactions act upwards and the loads downwards, the effect is to shear the fibers of the beam vertically. At any section of a beam, the shear is equal to either reaction minus the sum of the loads between that reaction and the section considered. The maximum shear is always equal to the greatest reaction. For a simple beam with a uniformly distributed load, the maximum shear is at the sup¬ ports, and is equal to one-half the load, or to the reaction; the shear changes at every point of the loaded length, the minimum shear being zero at the center of the span. The maximum shear in a simple beam having a single load con¬ centrated at the center is equal to one-half the load, and is uniform throughout the beam. Where a beam supports © 20 ft. §13 ft. --i dftl © © a V—IO ftr-A - 30 ft~ Fig. 15. 110 STRUCTURAL DESIGN. several concentrated loads, changes in the amount of shear occur only at the points where the loads are applied. For example, in the beam loaded as shown in Fig. 16, the shear on the line a b is equal to the reaction R x of 40 lb. minus the load n of 10 lb., or 30 lb. The shear between o and p, on the line c d, is equal to the reaction R\ of 40 lb. minus the sum of the loads n, m, and o, or zero. Working from the same reaction JSi, the shear on the beam between p and q is equal to Ri — (n + m + o + p), or 40 lb. — 55 lb. = —15 lb. Thus, all the beam to the left of o is in what may be called positive shear, while to the right of p the shear is in the opposite direction, and may be called negative shear. It is evident that there is a section in the beam—for instance, cd— -where the shear changes from positive (+) to negative (—); that is, it passes through zero, or changes sign. Example. —(a) What is the maximum shear on the beam shown in Fig. 15? (5) What is the shear 11 ft. from the right support? (c) Where does the shear change sign? Solution. —(a) Taking the center of moments at R», the reaction at Ri is as follows: 9,000 lb. X 10 ft. = 90,000 ft.-lb. 3,000 lb. X 10 ft. X 17 ft. = 510,000 ft.-lb. 4,000 lb. X 26 ft. = 104,000 ft.-lb. Total = 704,000 ft.-lb. Then, 704,000 ~ 30 — 23,466| lb., the reaction Ri. The total load being 43,000 lb., the reaction R. 2 is 43,000 — 23,466| = 19,5331 lb.; hence the maximum shear is R\. (6) The reac¬ tion Ro being 19,533j lb., and there being but a load of 9,000 lb. between it and a section 11 ft. distant, the shear at the latter point is 19,533? — 9,000 = 10,533? lb. (c) Working from R u the first load is 4,000 lb., and the shear at this point is 23,466f — 3 3 3 3 3 3 $ 3 § 3 3 5 « n m o ! P Q 1 * * * Fig. 16. BEAMS AND GIRDERS. Ill 4,000 = 19,466f lb. Then enough of the uniform load must he taken to equal this amount. It is clear that the shear becomes negative somewhere in the uniform load, since the latter is 30,000 lb., or more than 19,466f lb. Dividing 19,466f by 3,000, the load per foot, the result is 6.48 ft., the distance from left end of uniform load to point where the shear changes sign; hence the distance from R^ is 4 + 4 + 6.48 = 14.48 ft. Bending Moment. —The algebraic sum of the moments of the external forces about any point in a beam is the bending moment at that point; that is, the bending moment at any point is the moment about that point of either reaction minus the sum of the. moments of the intermediate loads about the same point. For example, the bending moments at several points on the beam shown in Fig. 17 are as follows: At Wi = Ri a; at W 2 = R x (a+b) — W x b; at W 3 = R\ (u —(— —j— c) — [ TIT; c -f- TFi ( b c)], or R% d , etc. GFiCFcF -E, Fig. 17. JR, The bending moment varies, depending on the shear, and attains a maximum value at the point where the shear changes sign. If the loads are concentrated at several points, the maximum bending moment will be under the load at which the sum of' all the loads between one support up to and including the load in question first becomes equal to, or greater than, the reaction at the support. Hence, to find the maximum bending moment in any simple beam: Rule .—Compute the re- actions and determine the point where the shear changes sign. Calculate the moment about this point of either reaction, and of each load between the re¬ action and the point, and subtract the sum of the latter a moments from the former. Example. —What is the maximum, bending moment in inch-pounds of the beam loaded as shown in Fig. 18? Solution. —Taking moments about 7?i and remembering 112 STRUCTURAL DESIGN. that a uniform load has the same moment as an equal load concentrated at the center of gravity of the uniform load, the total moment is found to be 358,250 ft.-lb. The span being 25 ft., the reaction R 2 is 358,250 -f- 25 = 14,330 lb. As the sum of the loads is 32,500 lb., the reaction R x is 32,500 — 14,330 = 18,170 lb. This is the greatest reaction and greatest shear. Beginning at R x and adding the loads in succession, it is found that the load of 10,000 lb. plus the uniform load between the reaction and the load d is 10,000 + (500 X 13) = 16,500 lb., which is less than the left reaction, or R x ; when, however, the load d is added, the sum of the loads is greater than the reaction; hence, the shear changes sign under the load d, and the greatest bending moment is also at that point. Tak¬ ing moments about the point under the load d, the moment of R x is 18,170 x 13 = 236,210 ft.-lb. The moments of the loads between d and R x are : 6,500 lb. X 6i ft. = 42,250 ft.-lb. 10,000 lb. X 7 ft, = 70,000 ft.-lb. Total = 112,250 ft.-lb. Then, 236,210 ft.-lb. — 112,250 ft.-lb. = 123,960 ft.-lb., the maximum bending moment. The bending moment in inch- pounds is 123,960 ft.-lb. X 12 = 1,487,520 in.-lb. If W = the load and L — the span, the maximum bend¬ ing moment in a simple beam uniformly loaded is — X £ & WL 8 ' ( ^ is the distance from the center of 4 beam to center of gravity of each half of the uniform load.) The maximum bending moment in a beam with a load con- W L centrated at the center is ——. Thus, a beam uniformly loaded will carry safely twice as much as if the load were concentrated at the center. While, by the preceding principles, the bending moment in any beam supported at one or two supports may be deter^ mined, it is more convenient to use concise formulas. The following table gives formulas for the maximum bending moment, maximum safe loads, and greatest deflections (or sag), for beams loaded and supported in different ways; BEAMS AND GIRDERS. 113 TABLE XXVI. 114 STRUCTURAL DESIGN . Resisting Moment.— The moment of resistance of a beam is the sum of the moments about the neutral axis of all the stresses in the fibers composing the section. The safe resisting moment of any beam section is equal to the product of the safe fiber stress and the moment of inertia divided by the distance from the neutral axis to the extreme fibers. If I is the moment of inertia, c the distance in inches from the neutral axis to the extreme fibers, and S the safe fiber stress in pounds per square IS I inch, the resisting moment M\ = -—; but since - = Q, the c c section modulus (see page 82), Mi — QS; that is, the safe resisting moment is equal to the safe fiber stress multiplied by the section modulus. To obtain the safe unit fiber stress, the modulus of rupture of the material (see Tables VIII, IX, X) is divided by the required factor of safety. Example.—W hat is the safe resisting moment of a Northern yellow-pine beam 10 in. wide X 12 in. deep, using a factor of safety of 4 ? Solution.— In the formula M i = QS , the section modulus b d 2 Q for a rectangular section (by Table XII) is —r-, or, for the O 10 V 19 V 19 given section, Q = — - --= 240. From Table IX, the D modulus of rupture for Northern yellow pine is 6,000 lb.; the desired factor of safety being 4, the safe unit fiber stress S is 6,000 -4- 4 = 1,500 lb. Then QS = 1,500 X 240 = 360,000, the safe resisting moment, or Mi , of the beam section in inch- pounds. A beam will ’safely support a given load when the safe resisting moment M\, in inch-pounds, is equal to, or greater than, the bending moment M also in inch-pounds. Econom¬ ical design requires that the safe resisting moment be but little, if any, in excess of the bending moment, having regard, also, to the nearest commercial, or stock, sizes. Deflection. —Stiffness in beams is as important as strength. Lack of stiffness causes vibrations, springy floors, deflection, or sagging, producing plaster cracks in ceilings. To prevent excessive deflection, shallow beams must be avoided. The deflection of beams carrying plastered ceilings should not exceed 3 -|(j of the span. Usually this limit is not exceeded BEAMS AND GIRDERS. 115 when the depth of wooden beams is at least ^ the span. In dwellings, the full floor load being seldom realized, and as bridging is used between joists, their depth may, with safety, be 14 in. for a span as great as 22 ft. The depth of rolled-steel beams should not be less than & the span, and that of plate girders not less than X V If doubt exists as to the stiffness of a beam, its deflection should be calculated by formulas from Table XXYI, and if found excessive, the load should be diminished, or the size of beam increased. Example.—A 6 " X 10" white-oak beam, uniformly loaded with 5,000 lb., has a span of 16 ft. 8 in. What is the deflection? 5 Wl 3 Solution. —From Table XXVI, the deflection = ^ET from Table IX, E — 1,100,000; I - -yy = Hence deflection = 5 X 5,000 X 8,000,000 = nence, aenecuon 3g4 x 1 100 000 x 500 b d s 6 X 1,000 12 .94 in. = 500. CALCULATION OF BEAMS. Wooden Beams.— These are principally used to support a uniformly distributed load, consequently a convenient for¬ mula for determining directly the safe strength of rectangular beams uniformly loaded is useful, and may be deduced from the foregoing principles as follows: The bending^moment M in foot-pounds is or in inch-pounds, —5 . Placing 8 ’ -" ' 8 this equal to the resisting moment, M\, or Q S, there results 12WL 8 QS 8 = QS,or 12WL = 8 QS; whence W= -yyy 3 5 d 2 QS L For a rectangular beam, the section modulus Q — g > an( ^ r 2 S b d? Sbd\ the above formula may be written II = y jr —y — 9 ^ ’ 0 and d are in inches and L in feet. This formula expressed in words is as follows: Rule. — The safe uniformly distributed load in pounds for a rectangular beam is equal to the safe unit fiber stress multiplied by the breadth in inches and by the square of the depth in in< /j es, and, the prodiict divided by nine time? the span in feet, 116 STRUCTURAL DESIGN. TABLE XXVII. Safe Uniformly Distributed Loads for Rectangular Wooden Beams, 1 Inch Thick. Depth of Beam. in Feet.. 6 " 7" 8 " 9" 10 " 12 " 14" 16" 5 800 1,090 1,420 1,800 2,220 3,200 4,380 5,690 6 665 910 1,190 1,500 1,850 2,670 3,650 4,740 7 570 780 1,020 1,290 1,590 2,290 3,130 4,060 8 500 680 890 1,130 1,390 2,000 2,740 3,560 9 445 610 790 1,000 1,230 1,780 2,430 3,160 10 400 540 710 900 1,110 1,600 2,190 2,840 11 365 495 650 820 1,010 1,450 1,990 2,590 ' 12 335 450 590 750 930 1,330 1,820 2,370 13 310 420 550 690 860 1,230 1,690 2,200 14 285 390 510 640 800 1,150 1,570 2,040 15 265 360 480 600 740 1,070 1,460 1,900 16 250 340 450 560 700 1,000 1,370 1,780 17 235 320 420 530 650 940 1,290 1,680 18 220 300 400 500 620 890 1,220 1,590 19 210 290 380 480 590 840 1,150 1,500 20 200 272 360 450 560 800 1,090 1,420 21 lbo 260 340 430 530 760 1,040 1,360 22 180 248 325 410 510 730 1,000 1,300 23 175 237 310 390 480 700 950 1,240 24 165 228 297 380 460 670 910 1,190 25 160 218 285 360 450 640 880 1,140 26 155 210 275 350 430 620 840 1,100 27 149 202 265 330 410 590 810 1,060 28 143 195 255 315 400 570 780 1,020 29 138 188 246 307 380 550 750 980 30 134 182 237 297 370 530 730 950 Safe load for any thickness = safe load for 1 in. X thick¬ ness in inches. Thickness for any load = lopd a- safe load for l in. BEAMS AND GIRDERS. 117 The Tames given are safe loads for spruce or white-pine beams, with a factor of safety of 4. For oak, or Northern yellow pine, multiply tabular values by 1£, and for Georgia yellow pine, multiply tabular values by 1|. Table XXVII is calculated fora maximum fiber stress of 1,000 lb. per sq. in., but may be used with any fiber stress by dividing that stress by 1,000 and multiplying by the tabular value; thus, for a stress of 800 lb., the safe load is .8 the tabular value. Loads given below the heavy zigzag line produce deflec¬ tions likely to crack plastered ceilings. Example. —What uniformly distributed load will a hem¬ lock joist 3 in. wide X 14 in. deep safely support, the span being 20 ft., and the factor of safety, 5? Solution.—I n the formula W = = 3,500 lb., the modulus of rupture of hemlock (see Table IX), 5, the factor of safety, = 700 lb. per sq. in.; b = 3 in.; d 2 = 14 in. X 14 in. = 196; and L = 20 ft. Then the safe uniformly distributed 700 X 3 X 196 load IF = 9X20 2,287 lb. Otherwise, from Table XXVII, the safe load with a fiber stress of 1,000 lb. per sq. in. for this beam = the load for 1 in. width X the width, or 1,090 X 3 = 3,270 lb.; but for a safe 700 stress of 700 lb. per sq. in., the safe load is = .7 of 3,270 lb. = 2,289 lb. The following example shows how to calculate the size of a rectangular beam necessary to support a given load : Example.— What .size Georgia yel- low-pine joist would be required to support two concentrated loads placed as shown in Fig. 19, using a factor of safety of 4 ? 3 JT-, 1 20 ft- Solution.—T he reaction R» = Ri Fig.19. Ro (3,000 X 3) + (2,000 X 15) 20 = 1,950 lb., and J2i = ( 3,000 + 2,000)—1,950 = 3,050 1b. The greatest bending moment 31 is found, by trial, to be under the 2,000 lb. load, and is equal to 1,950 lb. X 5 ft. = 9,750 ft.-lb., or 117,000 in.-lb. Such a section must be obtained that will ]agve a resisting moment equal to this bending moment of 118 STRUCTURAL DESIGN. 117,000 in.-lb. The modulus of rupture of yellow pine, 7,000 lb., divided by the factor of safety 4, gives a unit fiber stress of 1,750 lb. Then as the resisting moment of any beam section, Mi — QS, by transposition, Q = —, or - 1 ^ -- Q - = 67, the required section modulus. bd 2 By Table XII, for any rectangular section, Q = ——. By O trial, the value of Q for a 3" X10" beam is 50; as this is evidently too small, try a 3" X 12" beam; for this Q is 72, which is ample, and this beam is selected, being the nearest stock size. Rolled-Steel Beams.— In calculating the size of steel beam sections, the greatest bending moment is first calculated; then the section modulus required is equal to the bending moment in inch-pounds divided by the safe unit fiber stress, obtained by dividing the modulus of rupture of the material by the factor of safety. This may be expressed in formula as Q = 2_ > i n which, as before, Q — section modulus, If = bending moment in inch-pounds, and S = safe or allowable unit fiber stress in pounds per square inch. Having found the section modulus, the proper size channel or I beam may be selected from Tables XIII and XIX, the one being chosen which has a section modulus (see column headed Q) nearest to that required, the deepest beam having the required section modulus and lightest weight being preferred. In selecting rolled structural-steel beams the depth of the beam in inches should never be less than one-half the span in feet, in order to avoid excessive deflection, which causes cracks in plastered ceilings. For instance, if the span is 20 ft., a beam should be not less than 10 in. deep. Example.— The brick-and-concrete floor of an office build¬ ing weighs 110 lb. per sq. ft., and is designed for a live load of 40 lb. per sq. ft. The span of the beams is 20 ft., and they are spaced 5 ft. on centers. Using a factor of safety of 4, what size steel I beams are required ? Solution.— Total load is 110 lb. + 40 lb. = 150 lb. per sq. ft; floor surface supported upon one beam is 20 ft. X 5 ft. = 100 sq. ft.; total load on one beam is 100 sq. ft. x 150 lb. = 15,000 lb., BEAMS AND GIRDERS. 119 = IF. The load being uniformly distributed, the bending , nr v mil wttt • WL 15,000 X 20 „„ , nA moment, 3/, by Table XXVI, is— 3 — = — ! —^— = 37,500 O O ft.-lb. or 450,000 in.-lb. The modulus of rupture for struc¬ tural steel being about 60,000 lb. (see Table VIII), and the required factor of safety, 4, the allowable unit fiber stress is 60,000 -f- 4 = 15,000 lb. The section modulus, Q = — ; substituting the values of M and S, Q — 450,000 = 30. From 15,000 Table XIX, page 90, it is found that a 10" beam weighing 33 lb. per ft. has a section modulus of 32.3, and would meet the requirements. It is, however, seen that for a 12" beam, weighing 31£ lb. per ft., Q = 36.7; and on account of its greater strength and less weight, this beam would be by far the most economical. Stone Beams. —The strength of lintels, flagstones, etc. may be calculated as rectangular beams, except that it is usual to use a factor of safety at least of 10. It is, however, more con¬ venient to use the formula, W = ~ X c, in which W = safe uniformly distributed load in tons of 2,000 pounds; b = breadth of beam in inches; d — depth of beam in inches; l — span of beam in inches; c — coefficient taken from the following table : Kind of Stone. Coefficient. Bluestone. .18 Granite. .12 Limestone . .10 Sandstone . .08 Slate . .36 Example.— A limestone lintel 20 in. wide X 14 in. thick spans a 42" opening. What is the safe distributed load ? 120 STRUCTURAL DESIGN. b d 2 Solution.— Substituting values in the formula, — r— X c, W = 20 X lo — " X .10 = 9.33 tons = 18,660 lb. *XjU If the load is concentrated at the center of the span, the safe load will be one-half the safe uniform load. DESIGN OF RIVETED GIRDERS. For heavy loads and long spans, plate girders are substi¬ tuted for rolled beams. A plate girder consists of a web-plate, flange P/arej rLAN&t A A/CL ES. - £nd Stiffeners. Filler — f/ange P/ate^ ^ EEEZEZnML Intermediate Stiffeners. — Web P/ate. l owcr flang. Web Plate. Packing pieces or fillers. e Q Fig. 20. with stitfeners, if required, and of the upper and lower flanges, as shown in Fig. 20. Loads upon a plate girder develop shearing stresses, resisted by the web-plate, and horizontal compres¬ sive and tensile stresses, resisted by the upper and lower flanges. The usual cross-sections of plate girders are shown in Fig. 21. The single-webbed girders (a) are the most economical in material, and the most accessible for painting and inspection. The box girders (6), however, may be used to advantage where a wide top flange is required for lateral stiffness. Proportioning Web.— The width of the web-plate governs the depth of the girder, which, to avoid excessive deflection, BEAMS AND GIRDERS. 121 should not be less than T V the clear span, although some authorities permit £>. If made more shallow, the sectional area of the flanges should he increased, so as to reduce the stress on them, and the deflection in proportion. The thickness of web-plates depends upon the shear, which is greatest at the supports. This thickness must be such that the internal resistance to shear—found by multi¬ plying the area of cross-section of web by the safe unit shear¬ ing stress—shall be equal to the maximum shear on the girder; that is, if A be the area of cross-section, in square inches; s, the safe unit shearing stress; and S, the maximum shear, then As = S; but as A is equal to the thickness (f) in inches multiplied by the net depth (d'), in inches, td's = S, s or t — Hence, the necessary thickness in inches of web is equal to the maximum shear divided by the product of the net depth of the girder in inches times the safe unit shear. The net depth is the width of the web minus the sum of diameters of all rivet holes in a vertical line at the end stiffeners. The safe unit shear is usually taken at about f the safe horizontal stresses; or, for steel gir¬ ders in buildings, about 11,000 lb. per sq. in. In no case should the web be less than x b b in. thick. Example. —Fig. 22 shows the end of a girder, the greatest reaction be¬ ing 120,000 lb.; with an allowable unit shearing stress of 11,000 lb., what should be the thickness of the web-plate? Solution.— The width of plate is 48 in., and there are 13 — rivet holes. Allowing } in. for punching each hole, the net depth is 48 in. — (J X 13) = 36f in. Applying the formula, ‘ = - W x ito o o = ^ in ' As this is 1685 lhan * in - ,he latter thickness is used. * 122 STRUCTURAL DESIGN. Stiffeners.— Web-plates, besides resisting direct vertical shear, must resist buckling. To avoid failure by buckling before the full shearing strength of the plate is realized, stiffeners, composed of angles, as shown in Fig. 20, must be used. Some engineers require the use of stiffeners when the unit shear exceeds the ui at stress allowed by the following formula: . 12,000 s = 1 + d°- in which 3,000 <2 s — allowable unit stress; d = depth of girder, between flanges, in inches; t = thickness of web-plate in inches. A more convenient rule provides that stiffeners he used when the thickness is less than eg the clear distance between vertical legs of flange angles. For example, in a girder with a f" X 36" web and 6" X 6" flange angles, the distance between vertical legs of angles is 36 — (2 X 6) = 24 in.; ^ of 24 in. = .48, say £ in.; the web-plates being but f in. thick, stiffeners must be used. Stiffeners should never be omitted over the end supports, and should be provided under all concentrated loads. The distance between centers of intermediate stiffeners is usually made equal to the depth of girder. Under no condition, however, should stiffeners be placed more than 5 ft. a"part. End stiffeners should be considered as columns transmit¬ ting the entire load upon the web to the supports. The size of intermediate stiffeners is not usually calculated; they are usually made the same size as the end ones, or lighter. Angles used for stiffeners should not be less than 3" X 3" X tb"; on shallow gir¬ ders, however, with light loads, it might be economical to use 2^" X 2j" X re" angles; butsmalleronesshould never be used. Stiffeners should extend over the vertical legs of the flange angles, being either swaged out to fit, as shown at (a) and ( b ), Fig. 23, or, preferably, provided with filling pieces, as shown in Fig. 20. Fig. 28. BEAMS AND GIRDERS. 123 Example.—U sing 4 end stiffeners (2 each side), and a safe unit compressive stress of 13,000 lb., what size angles should be used for stiffeners of the girder shown in Fig. 22. Solution. —The required sectional area is 120,000-^13,000 = 9.23 sq. in.; 9.23 sq. in. -p 4 = 2.31 sq. in., the area required for each angle. From Table XIV, a 4" X 4" X tb" angle has a sectional area of 2.40 sq. in., which is ample. Flanges. —The flanges of a girder—called top and bottom chords in open or lattice girders—include the flange plates and angles, as shown in Fig. 20. Frequently, one-sixth the sectional area of the web plate is included as part of each flange, although, in many cities, the building ordinance will not allow this to be done. If the sixth is so included, the web should never be spliced at the point of greatest bending, and all splices should be so designed that, by proper placing of the rivets, the strength of the web included in the one- sixth be reduced as little as possible. In a simple girder, the top flange is subjected to compres¬ sion, and the bottom one to tension. It is the practice, for economy in construction, to make the flanges alike, only the lower flange being calculated. The bottom flange being in tension, the area of the rivet holes are deducted, so that the net area at the point of least strength may be obtained. The horizontal stresses on the flanges are resisted by the fibers in one flange acting with a moment about the center of gravity of the other. This moment is equal to their total strength multiplied by the distance between centers of gravity of the flanges. Thus, Fig. 24 shows a plate girder pin connected at a, and a chain in tension, representing the lower flange, at b. It is evident that the reactions tend to turn the girder about a, and rupture the chain, which resists 124 STRUCTURAL DESIGN. this tendency with a lever arm d equal to the distance between the centers of gravity of the flanges. The depth is, in practice, however, usually taken to be the depth of the web. To find the net area of the lower flange, let 3I X be the resisting moment in foot-pounds; M, the bending moment in foot-pounds; s, the allowable unit tensile stress; a, the net area of flange in square inches; and d, the depth of girder in feet; then sXaXd — M u which must be equal to M ; from M which a = sXd Rule .—The net sectional area of the lower flange of a plate girder is equal to the greatest bending moment in foot-pounds divided by the product of the allowable unit tensile stress in pounds and the depth of the girder in feet. In proportioning the flanges, the sectional area of the flange plates should equal, approximately, that of the flange angles. This is not possible in heavy work, and the best that can be done is to use the heaviest sections obtainable for the flange angles. Example.—A steel girder is 6 ft. deep, and 80 ft. span, and the load 3,000 lb. per lineal foot, (a) What net flange area is required, using a safe unit tensile stress of 15,000 lb. per sq. in.? (b) Of what size sections should the flange be made? Solution.—( a) The entire load is 80 X 3,000 = 240,000 lb. From Table XXVI, page 113, the bending moment is WL 240,000 X 80 3- /4x£ Hange P/otes. M= Ang/ej. 8 t 8 The net flange area M 2,400,000 = 2,400,000 ft.-lb. a = = 26.6 sq. in. Fig. 25. sXd 15,000 X 6 (5) Assume the section shown in Fig. 25. The area of a 6" X 6" X t" angle being, approximately, 7 sq. in., the sec¬ tional area of the flange is, Two 6" X 6" X i" angles = 7X2 = 14.00 sq. in. Three 14" X T V' plates = 14 X T 7 S X3 = 18.37 sq. in. Total = 32.37 sq. in. From the total area deduct the metal cut out for rivet holes, which, taken as | in. larger than the rivet, are 1 in. in BEAMS AND GIRDERS. 125 diameter. The web is not considered in the flange section. The areas deducted are, therefore, Four 1" holes through \ n metal = 2£ sq. in. Two 1" holes through 1£§" metal = 3£ sq. in. Total = 6| sq. in. The net area of the flange is 32.37 — 6.37 = 26 sq. in., which, although a little less than the net area required, 26.6 sq. in., could be used. Length of Flange Plates. —The bending moment on a simple beam varies throughout the length ; and, to design girders economically, the net flange area should vary with the bend¬ ing moment. This condition is fulfilled by using flange plates of different lengths, each extending only as far as needed to provide the net section required. It is good practice to con¬ tinue the inner plate the entire length of the girder, in order to stiffen it laterally. The lengths of flange plates in girders uniformly loaded may be obtained approximately by the formula: 1^ = 2 + L J-j'x/a’p/ates. H/vetsjdio\ ■jxsyy Angles. L\ being the required length of the plate in feet; L, the length of girder in feet; a, the net sectional area of all plates to and including the plate in question, beginning with outside one ; and A, the total flange area. The 2 ft. is added to allow for riveting. Example. —Fig. 26 shows a flange section of a girder. The span being 60 ft., what should be the length of each flange plate? Solution.— Area of a 5" X 5" X £'"‘angle (see Table XIV, page 85) is 7.11 sq. in. Area of each plate is f in. X 12 in. = 4.5 sq. in.; the rivet holes are £ + £ = £ in., and the area cut out by a hole through a f" plate is .328 sq. in.; hence, the net area of each plate is 4.5 sq. in. — (.328 sq. in. X 2) = 3.844 sq. in.; or, for 3 plates, 3.844 X 3 = 11.532 sq. in. The net area of the two angles is (7.11 sq. in. X 2) — (.656 X 4) = 11.596 sq. in. There¬ fore, the net area of flange will be 11.532 + 11.596 = 23.128 sq. in. Fig. 26. 126 STRUCTURAL DESIGN. By the formula, the leng th of outside plate hi =2 + 60 A / = 26.42, say 26 ft. 6 in. \ 23.128 Similarly, the length of the intermediate plate Lx — 2 + 60 = 36.56 ft., say 36 ft. 6 in. The inner plate is continued the entire length of the girder, so as to stiffen it laterally. Fig. 27 shows a graphical method of finding the lengths of flange plates for a girder carrying any number of concen¬ trated loads. Lay off a b to any scale, equal to the span, and locate on it the point of appli¬ cation of each load, as c, d, and e. Having cal¬ culated the bending moment under each load, lay it off, to a con¬ venient scale, on the corresponding perpendicular to a b, through c, d, and e, as cf, d g, and e h. Draw the lines af,f g, gh, and hb. Divide eh, the line representing the greatest bending moment, into as many equal parts as there are square inches in the net section required. (For a method of dividing a space into equal parts, see Geometrical Draining, page 55.) Take er equal to as many parts as there are square inches in the net sectional area of flange angles; also, rs equal to net area of the first plate, etc. Draw parallels to a b through r, s, t, etc. Make ik equal to ah ; where ik, etc. intersects a f and b li, erect perpendiculars p l and q m, etc. Then l m, measured to same scale as a b, is the length of the first flange plate; n o, that of the second, etc. The lengths thus found should be in¬ creased 1 ft. at each end, to allow for riveting. The lengths of plates for uniformly loaded girders may be similarly found. Having calculated the maximum bending moment, lay it off to scale, perpendicular to the middle of die span. The curve representing the bending moment is in ihis case a parabola, and may he drawn through the point BEAMS AND GIRDERS. 127 just named and the ends of the span, by the method given in Geometrical Drawing on page 58. The remainder of the work is like that shown in Fig. 27. Rivet Spacing.— Enough rivets must be placed in the end stiffeners of girders to transmit the shear to the web. For example, 100,000 lb. is the reaction on a girder constructed as in Fig. 22 ; the web is f in. thick, the rivets £ in. diam. The allowable unit bearing value being 15,000 lb. (by Table XXIX, page 131), the ordinary bearing of a plate on a j" rivet is 4,920 lb.; adding | because the plate is web bearing, gives 6,560 lb. Since the double shearing value of the rivet is greater than the web-bearing value of the plate, 6,560 lb. must be taken as the resistance of one rivet. Then the number of rivets required in the two pairs of angles is 100,000 g- 6,560 = 15.2, say 16, or 8 rivets in each pair. Rivets in intermediate stiffeners are usually spaced the same as in end stiffeners, their spacing not being calculated. No rivets in stiffeners should be spaced more than 6 in. apart, or more than 16 times the thickness of the angle leg. As the shear increases from the point of greatest bending towards the supports, the number of rivets j>laced in the vertical legs of the flange angles, to resist their tendency to slide on the web, must also increase as the supports are approached. The horizontal stress, per inch of length, which is transmitted from the web to the flange at any point, is equal to the maximum shear at any point divided by the depth of the girder in inches. For example, in the girder shown in Fig. 28, the shear at a is Ri, or 100,000 lb.; at 5, it is 100,000 lb. — (5,000 lb. X 4) = 80,000 lb., at c, 60,000 lb., etc. The horizontal stress per inch of length at a is 100,000 (4 X 12) = 2,083lb.; at 6, 80,000 -f- 48 = 1,667 lb.; at c, 60,000 ^48 = 1,2501b.; at d, 833 lb., etc. Using V rivets, the safe bearing value of each is 6,560 lb. At a, the stress being 2,083 lb. per inch of run, the rivets should be placed 6,560 h- 2,083 = 3.14 in. center Uniform Load 5000 lb, per / i'nea/ foot. Fig. 28. 128 STRUCTURAL DESIGN. to center; at b, 6,560^-1,667 = 3.93 in.; at c, 6,560-i-1,250 = 5.24 in.; at d , 6,560-^833 = 7.87 in. In practice, rivets are spaced alike in both flanges; and as 6 in. is the greatest allowable pitch in a compression member, further calcula¬ tion is needless. The rivet spacing from a to b is, then, 3£ in.; b to c, 4 in.; c to d, 5i in.; beyond d, as the theoretical pitch is more than 6 in., the 6-in. pitch should be used. At the ends of each flange plate, sufficient rivets must be used, spaced 2^ to 3 in. on centers, to transmit the allowable stress on the net section of the plate to the adjacent mem¬ bers. The remaining rivets should be spaced the greatest allowable pitch for a compression member, namely, 16 times the thickness of the thinnest outside plate—provided the pitch does not exceed 6 in. For example, in a f" X 12" flange plate, after deducting the area of two 1" holes (£" rivets + i"),the net sectional area is 3f in. Assuming the safe unit fiber stress at 15,000 lb., 3.75 in. X 15,000 = 56,250 lb., strength of plate. The safe value of each rivet in this case will be taken at 5,410 lb.; then the number required in each end of the plate is 56,250 -e- 5,410 — 10, say 5 each side of the web, and they should be spaced from 2\ to 3 in. on centers. In splicing the lower flange angles, which are in tension, enough rivets should be placed therein to equal in resistance that of the net section of the angles. In splicing the top angles, since they are in compression, only enough rivets need be used to securely hold them in abutting position. STRENGTH OF RIVETS AND PINS. RIVETS. In proportioning riveted joints, the friction between the plates cause.d by the clamping effect of the rivets is neglected. Hence, a riveted joint may fail in two ways, namely, by the shearing of the rivets, and by the crippling or crushing of the metal in the member around the rivet hole. It is necessary therefore, in designing a riveted joint, to consider, besides the shearing of the rivets, the bearing value of the plates or rolled sections. STRENGTH OF RIVETS AND PINS. 129 The strength of a riveted joint also depends upon the dis¬ tribution of the members connected, and the location of the rivets; that is, whether the rivets are in single or double shear, and the members connected in ordinary or web bearing. A rivet may be in single shear, as at (a), or in double shear as shown at ( b ), in Fig. 29. At (a) the tendency is to shear the rivet along the line a b, and the strength of the rivet is equal to its sec¬ tional area multiplied by the shearing strength of the material composing it. At (b) the tendency is to shear the rivet along the lines a b and cd ; hence, the strength of the rivet in this case is twice that of the former, and is equal to twice the sectional area of the rivet, midtiplied by the shearing strength of the material in the rivet. The plates or structural sections composing a joint tend to fail or cripple, as at a, Fig. 30. Hence, the bearing strength of a plate is equal to the thickness of the plate multi¬ plied by the diameter of the rivet and this product by the bearing strength of the material compo¬ sing the plates or rolled sec¬ tions. Where the plate is situated, as at (6), Fig. 29, between two outside plates, the central plate is said to be subjected to web bearing, and it is usual to consider the value of this plate, in resisting bearing, to be a third higher than in ordinary bearing, as at (a). The most reliable test of steel and iron is the tensile, and the shearing and bearing values are deduced from it. Com servative practice takes shearing values for high-grade iron and steel at £ of the tensile strength of the material, and the ordinary bearing value at li times the tensile, while web bear¬ ing is taken at twice the tensile strength, On this basis the following table is formed: Fig. 29. 130 STRUCTURAL DESIGN. TABLE XXVIII. Allowable Shear and Bearing Values. Pounds per Square Inch. Character of Rivets. Work. \ Shearing. Ordinary Bearing. Web Bearing. Iron rivets 1 Railroad bridges 6,000 12,000 16,000 Iron rivets Highway bridges and buildings 7,500 15,000 20,000 Steel rivets I Railroad bridges 7,500 15,000 20,000 Steel ' rivets _ Highway bridges and buildings 9,000 18,000 24,000 It is therefore important, in designing riveted joints, to determine whether the shearing strength of the rivets or the bearing values of the plates is the stronger, and to proportion the joint accordingly. Table XXIX gives the shearing and bearing values for the principal sizes of rivets and plates used in steel construction. The greatest economy in material is obtained when the net area of the plates or members joined is the greatest possible; that is, when the percentage or ratio existing between the net section and the gross section is as great as can be. It is usual, in proportioning riveted work, where the rivets are driven by hand in the field, to increase the number of rivets 25 or 50 percent, to allow for faulty riveting. It has previously been said that rivets fail by shearing; they are, however, in rare instances liable to fail by bending. This occurs only when the rivets are long and it is impossible to drive them enough to have them upset sufficiently to fill the holes. In such case the only remedy is to so design the joint as to lessen the grip of the rivet, or increase the number of rivets, and consequently reduce the tendency to bending. Rivets are never proportioned to withstand flexure. STRENGTH OF RIVETS AND PINS. 131 TABLE XXIX. Shearing and Bearing Values of Rivets. Diam¬ eter of Rivet. Inches. A 8 1. 9 A 8 i 2 _ 8 1 Diam¬ eter of Rivet. Inches. _1 9 I x 8 1 Diam¬ eter of Rivet. Inches. I L 9 I I 7 8 1 Single Shear at 6,000 Lb. per Sq. In. Bearing Value at 12,000 Lb. per Sq. In. for Different Thickness of Plate in Inches. 1 4 5 TB A 8 7 16 1 9 9 TB 1 660 1,180 1,840 2,650 8,610 4,710 1,120 1,500 1,860 2,250 2,630 3,000 1,880 2,320 2,810 3,280 3,750 2,250 2,790 3,370 3,940 4,500 3.250 3,940 4,590 5.250 3,720 4,500 5,250 6,000 5,060 5,910 6,750 6,560 7,500 Single Shear at 7,500 Lb. per Sq. In. Bearing Value at 15,000 Lb. per Sq. In. for Different Thickness of Plate in Inches. 1 4 6 «TB A 8 7 IB 1 9 TS 1 830 1,470 2,300 3,310 4,510 5,890 1,410 1,880 2,340 2,810 3,280 3,750 2,340 2,930 3,520 4,100 4,690 2,810 3,520 4,220 4,920 5,620 4,100 4,920 5,740 6,560 5,630 6,560 7,500 6,330 7,380 8,440 8,200 9,380 Single Shear at 9,000 Lb. per Sq. In. Bearing Value at 18,000 Lb. per Sq. In. for Different Thickness of Plate in Inches. 1 4 5 TB A 8 7 1 9 9 TB * 990 1,770 2,760 3,970 5,410 7,060 1,680 2,250 2,790 3,370 3,940 4,500 2,820 3,480 4,210 4,920 5,620 3,370 4,180 5,050 5,910 6,750 4.870 5,910 6,880 7.870 5,580 6,750 7,870 9,000 7,590 8,860 10,120 9,840 11,250 132 STRUCTURAL DESIGN. Example. —Fig. 31 shows the riveted joint for a tension member. The allowable stress for the rivets in single shear is 7,500 lb. per sq. in., and the l‘t 2 fWrtiron Bon safe bearing and tensile values of the wrought-iron bars 15,000 „ ~ -- rer" i 1 « JL Fig. 32. the resisting moment of the section obtained, which may be calculated (see page 114), or obtained from Table XXX, which also gives the shearing and bearing values for differ¬ ent size pins. Example. —What size pin will be required to resist bend¬ ing in the connection shown in Fig. 32? Solution.— The bending moment is 10,000 lb. X 6 in. = 60,000 in.-lb. The proper size pin having the required resisting moment may be obtained from Table XXX, page 137, or calculated thus : The section modulus for a solid cylindrical section is, accord¬ ing to Table XII, page 83, .0982 d 3 . Since d , the diam¬ eter of pin, must be assumed, try 31 in. The section modulus is .0982 X 31 X 31 X 31, or 4.21. Then, as the safe resisting moment of any beam equals the section modulus multiplied by the safe stress of the material (see page 114), and assuming that the safe working stress of the material in the pin is 15,000 lb. per sq. in., the resisting mo¬ ment is 4.21 X 15,000 = 63,150 in.-lb. Since the safe resisting moment must equal or exceed the bending moment (see page 108), a pin 31 in. in diameter will be sufficient to resist the bending'Stresses. Where the lines of action of the stresses, in several mem¬ bers connected at a common joint by a pin, are inclined to one another, as at (a), Fig. 33, the stresses in the oblique members should be resolved into their vertical and horizontal components (see page 141). Having found these forgll the forces acting upon the pih, the greatest bending moment due to all the vertical components, and that due to the horizontal components, should be obtained. Then, by adding the squares of these two amounts together and taking the square root of the result, the greatest resultant bending moment will be found. STRENGTH OF RIVETS AND PINS. 135 Example. —Find the greatest resultant bending moment upon the pin shown at (a), Fig. 33. Solution.— Draw accurately the frame diagram, as at (b), Fig. 33, in which the full lines represent the direction of the members assembled at the joint. Lay off to some convenient 136 STRUCTURAL DESIGN. scale upon c d, a distance that will represent the stress in that member; then, by the principle of the parallelogram of forces, db will be the horizontal, and de the vertical, component of the stress in c d. Likewise, draw the horizontal and vertical components of the stresses in the members c a and c h. Since the member ce is horizontal, it will have no vertical com¬ ponent. The vertical and horizontal components of all the stresses in the oblique members may be obtained by scaling the lines which represent them. Since all the members except the right-hand oblique one are in pairs, one-half of each stress will be carried on each side of the center line. Having obtained the amounts of the horizontal and vertical components, the diagrams (c) and (d) may be drawn. Care must be exercised to see that all the forces upon one side of the pin are equal to those upon the other; otherwise, the joint would not he in equilibrium, and would tend to move in the direction of the greater force. The diagram (c) shows the horizontal components of all the forces, the bend¬ ing moment due to which is obtained as follows: (For bending moment see page 111.) 22,050 lb. X 5 in. = 110,250 in.-lb. deduct, 3,000 lb. X 3 in. = 9,000 in.-lb. 15,000 lb. X 4 in. = 60,000 in.-lb. 69,000 in.-lb. Total horizontal bending moment = 41,250 in.-lb. From the diagram (d) of all the vertical components the bending moment due to them is obtained thus : 1,800 lb. X 5 in. = 9,000 in.-lb. 5,150 lb. X 3 in. = 15,450 in.-lb. Total vertical bending moment = 24,450 in.-lb. The resultant bending moment is, then : ]/ 41,250 2 + 24,450 2 = 47,900 in.-lb. From Table XXX, page 137, using a safe unit stress of 15,000 lb., it will be seen that a pin which is 3 T 3 B in. in diameter has a resisting moment of 47,670 in-lb., which, while scant, will do. If the pin is designed to resist bending, it is seldom neces¬ sary to consider the shear. The bearing values are found the same as for rivets, and are given in Table XXX. Shearing and Bearing Values and Maximum Resisting Moments of Pins. STRENGTH OF RIVETS AND PINS. 137 Shearing Values. At 11,250 Lb. per Sq. In. oooooooooooooooooo OOOOOOOOOIOOOOOOOOO dddCO lO CO CO CC^HOHOOKMOOO oo lo co cf cf co co oT o rd cT aT oT id o' id go H(NCO^iOCOt^COO(NCOCOCOOiOOOOH t— 1 rH i—1 rH i—i Cl d Cl CO CO At 9,000 Lb. per Sq. In. oooooooooooooooooo OOiO^OOOOOOOOOOOOOOO co ci^ 10 co © © ©^ oo io r-^ © cowcqoqo ^ o' CO co" Cl tH r-T r-T CO co" cT i o" r-T I'-" -f -t" HCKMCOO'iOCNCOCOCOiOCOCl^iO HHHHddClCl At 7,500 Lb. per Sq. In. oooooooooooooooooo lOOOOOO>OlOOOlOOOOiOOO'0 iHOOiH 00 c^i> © io" o" Tf^ erf co" cd cf r-T r-T o" ©"cdcdr^f co" r-T id cc" dCOCOCO^^iOiOCOcOI^NCOGOOOOO H H H At 15,000 Lb. Per Sq. In. oooooooooooooooooo oooooooooooooooooo (OCOH«XOMH®fflCOH HHNM^lOt'COO^t'ONHiOW rH rH rH Cl Cl CO CO CO S = 15,000 Lb. Per Sq. In. oooooooooooooooooo NKOOHbHNOHOOOOOOQO COOtr rf MlOCOtO t-^OOCOCO 1> OJ^rH CO^i-q r^jrToiOrH'cQ't^'frOcocyrcoioocoicicocq HHClCICOcJlOt'CCCl^t'CCgrH rH rH rH , and from z to a determines R x . Analyzing each joint as before shown, no diffi¬ culty will be met until the joints CD ON ML and MNQZ are reached; it is found that three un¬ known forces exist at each of these joints, and, as it is impracticable to determine the stresses graphically when more than two forces are unknown, the value of one must be otherwise obtained. Upon inspecting the frame diagram, it will be observed that the joint at B C is 148 STRUCTURAL DESIGN. similar to D E ; and it is reasonable to suppose that L K will have an equal stress with P 0. From this it would appear that there must be an equal and like stress exerted by L M, to retain the foot of L K in position, as is exerted by 0 N to keep P 0 in place. The stresses in ML and L C being known, that in D 0 may be determined by drawing a line from d parallel to D 0, to such a point o that—having drawn on equal in length to Im —the line nm, parallel to NM, will close on to. The polygon of forces will be from to to l, l to c, c to d, dtoo,o to n, and n to to, the starting point. The joint MNQZ now offers no difficulty to solution, as mn has been previously determined. The final joint OP QN may be solved by drawing from p a line parallel to P Q, which will, if the diagrams have been correctly drawn, pass through n, and from this point will coincide with n q. One half the vertical-load diagram being completed, and the loading being symmetrical, it is unnecessary to draw the other half unless as a check. The equality of the triangles l k to and pon, and their resemblance to nmq, greatly assist in drawing diagrams for trusses of this type. Method of Trial for Obtaining Third Unknown—It one unknown stress prevents the solution of the diagram, it may sometimes be found by trial. Thus, assume the amount of unknown stress and proceed with diagram ; if it fails to close, again assume amount of unknown stress and try. Proceed thus until diagram closes. ROOF TR USSES. 149 Wind-Stress Diagrams .—First find the external forces and reactions, as in the Howe truss, page 143, and redraw the frame diagram, as in Fig. 45. The solution of the wind-stress diagram, Fig. 46, offers the same difficulties as in draw¬ ing the vertical-load diagram, and may be ^ similarly solved. The last joint FR QPE is solved by drawing from / a line parallel to FR, and from q, a line par¬ allel to R Q; their inter¬ section is at r, and the polygon of forces is from e to f,J to r, r to q, q to p, and p to e. DETAIL DESIGN OF ROOF TRUSSES. Trusses subjected to wind, acting perpendicular to the gable, should be braced with diagonal braces connecting the several trusses. If, however, the roof sheathing is of planking secured directly to the trusses, and especially if run diagonally, other bracing may not be required. If stone gables protect the roof in a longitudinal direction, lateral bracing may in many cases be omitted. The vertical and wind loads of a truss may be figured from Tables I, VII, pages 62, 68. The weight of the truss is the most uncertain factor, being practically unascertainable until the design is made ; hence, it is well, after designing the truss, to calculate and compare its weight with that assumed. The stresses being determined, the members must be proportioned to sustain them. Roof trusses differ from bridge trusses in that the loads are generally statical and not suddenly applied ; consequently, a smaller factor of safety may be employed. It is the practice, in ordinary construction, to employ for timber members in a roof truss a 150 STRUCTURAL DESIGN. factor of safety of from 4 to 6 ; and for structural steel and wrought iron, 3 to 4 ; cast iron is seldom used in roof trusses, and is never used with a factor of safety less than 10, unless the load creates compressive stress only, in which case a somewhat smaller factor may be used. The factor of safety r-2'py--24' , -~ H*-*--[ o- —24^—?4^\ i ;i ..J—{j—H -ri! li ■—ti—if—1 T-jir—e-&-®v- —r* :! U !: r-4- —t-, ■7^-w io - Detaihf Splice in Tie Mem bet Coffers WrtIron Washer/"ThicK. - Purlins.^ ifdiaPod^ i " < v -> -- -, l • > j, detail of Joints on Tie Member Sphceplate notshotv/i. ,» Yellowfine /A t2-fPait Dowel /i'Rnir <-A\ \ Mns aboutik" /aw$L JMjecfio/iin Sj \ ^^CasrIroniuo^fyT^fl^ ' 'yr fairs Yeiiotvfine/ ^ C ori t Purhn4m m (Lagjcrews /r iv/ ^ IH? \mjnj/e '’''•I <§t|\ Fig. 47. {Strut is much a matter of judgment, and may be altered as the designer’s experience dictates. Tension members are liable to fail at the least cross- section ; therefore, the screw ends of long rods and bolts should be enlarged, so that the cross-section at the root of the threads will be at least as large as elsewhere. Allowance ROOF TRUSSES. 151 'dOfTfsmC&freTvCetirreofMbordoto— 152 STRUCTURAL DESIGN. ROOF TRUSSES. 153 154 STRUCTURAL DESIGN. must be made for diminution of cross-section by bolt or rivet holes. To determine the net section required in any tension member, divide the stress upon the member by the allowable tensile stress of the material. In proportioning compression members, the length of which is not over from 8 to 10 times the diameter or least side, the cross-section may be figured by dividing the stress by the allowable direct unit compressive stress. If, however, the length exceeds these dimensions, the members must be regarded as columns, and figured as such. If a member is subjected alternately to compression and tension, its section should be somewhat increased over that required to sustain either stress. Where the rafter members of a truss support purlins between the panel points, the members are subjected to bending, as well as to direct compressive stress. In design¬ ing them, it is customary, with wooden members, to propor¬ tion them by first determining the proper size of beams to sustain the transverse stress, and adding sufficient sectional area, by increasing the width, to sustain the direct compres¬ sive or tensile stress, as the case may be. Where the direct stress is compressive, it should be also checked by applying the column formulas. Structural-steel or wrought-iron mem¬ bers are usually proportioned for the bending stress, the direct stresses being provided for by increasing the thickness of the rolled section, care being taken that the sum of the extreme transverse-fiber stress and direct-fiber stress is not more than the safe stress of the material. Where members are connected by bolts or pins, the pins are usually prox>ortioned to sustain the transverse stresses, and, if so proportioned, generally have sufficient resistance to shearing. Strength of pins is treated on pages 133-187, and the information given there will be found sufficient. Since the direct stresses in members connected at a common joint by a pin creates bending stresses upon the pin, the members should be packed closely, and those members hav¬ ing opposite stresses brought in juxtaposition if possible. In designing any structure, and especially roof trusses, the following points should be carefully observed: (a) Propor- ARCHES. 155 tion all parts of a joint so that the maximum strength will he realized throughout, in order that one part will not he likely to yield before another. ( b) Weaken as little as possible the pieces connected at a splice, (c) Give sufficient hearing surface to bring the compression on the surface well within the safe l imi ts, so that there will be no danger of crippling plates or crushing the ends of members before their maximum strength is realized. ( d ) Distribute rivets and holts so as to give the greatest resistance with the least cutting away of other parts. ( e ) See that the central axis of every member coincides as nearly as possible with the line of action of the stress. (/) Examine all sections and parts for tensile, compressive, transverse, and shearing stresses. ( g) Finally, hear con¬ stantly in mind that the strength of a structure depends on the strength of its weakest part, and that the failure of a single joint may he as fatal to the life of a structure as though a member were insufficient. A close study of the details of the trusses shown in Figs. 47, 48 and 49, in connection with the foregoing explanations of principles, will give a general idea of how such parts are designed. _ Principles.— Let resultants of all the loads on the left and right halvesof thearch, respectively, and let Pi he equal to P 2 , and located equally distant from the crown. Let Pi and P 2 rep¬ resent the verti¬ cal reactions, which, since the loads are sym¬ metrically placed, are equal ARCHES. and P 2 , in Fit 50 (a), represent the Fig. 50. Let b be the horizontal distance 156 STRUCTURAL DESIGN. between R x and Pi ; also between P 2 and P 2 , or, in other words, the leverage of P x and P 2 with respect to P x and P 2 . Let Q be the horizontal thrust, which is equal at all points; also, let c be the leverage of Q with respect to the crown. Now assume the right-hand half of the arch to be taken away, as in (5). To preserve equilibrium in the left side, the force Qi must be supplied at the crown. The algebraic sum of the vertical forces, and, likewise, the sum of the horizontal forces, must equal zero, or there will not be equilibrium. Then R } must equal Pi, and Qi must equal Q. Also, the sum of the moments about any point must equal zero. Hence, taking moments about the abutments in (a), Qc = Pi b, and P b Q = ; also, since the arch is symmetrically loaded, „ P 2 b , Pi b P 2 b QoC = —— and In this case Pi or P 2 may c c c represent any number of loads, provided they are equal and symmetrically placed. METHODS OF DETERMINING THE LINE OF PRESSURE. Line of Pressure.— If a cord, fastened at each end, supports a number of loads, it will take a position of equilibrium, depending on the amount and loca¬ tion of the loads, as in (o), Fig. 51. In such a case, the cord is in tension. If the system is inverted, it will assume the posi¬ tion shown in (b), in which the forces are still in equilibrium; but, Instead of a cord in tension, the lines op,pq , etc. must be members capable of resisting compression. This latter case ARCHES. 157 represents what exists in an arch, and the broken line inter¬ secting the vertical forces forms the line of pressure; the material in the arch must be of such strength and so disposed as to safely resist the compressive forces acting along this line. To determine the line of pressure for any arch, points at the abutments and crown must be fixed upon ; otherwise, an indefinite number of lines of pressure could be drawn. In metal arches, the abutments and crown are generally hinged, or pin-connected, and the line of pressure necessarily passes through these three points. In masonry arches the abutments and crown are generally not hinged, although there are exceptions; and, therefore, a point must be assumed at each abutment and at the crown, through which the line of pres¬ sure is to pass. The line of pressure should, for a masonry arch, be within the middle third of the arch ring, the depth of keystone of which is first assumed, or made equal to that of some existing arch of about the same span. Thus, with an arch 3 ft. deep, the line of pressure should be within a space 6 in. on either side of the center of the depth. If it lies with¬ out the middle third, the joints tend to open, which result, while the danger of failure of the arch may not be great, would be unsightly. Again, if the line of pressure passes through the middle third, the angle that it makes with any joint will not be such that the voussoirs are likely to slide on their surface of contact. In taking the loads upon arches, all weights must be reduced to the same standard ; that is, in this case, the loads have been made equivalent to masonry weighing 140 lb. per cu. ft. The arch and loads are assumed to be 1 ft. in thickness, so that all superficial measurements also repre¬ sent cubic contents. Analytic Method.— In the arch shown in Fig. 52 (a), the pres¬ sure curve is considered as passing through points at the abutments f the depth of the voussoirs from the intrados, and through the center of depth at the crown. The theoreti¬ cal rise of the arch is 10.75 ft., and the theoretical span, 51.32 ft. The arch and load is divided by dotted lines into sections, which, for convenience, are numbered. 158 STRUCTURAL DESIGN. If w be the width of any section, and h its height, then its area a is w X h. Also, if c is the distance from the crown to the center of gravity of a section, the moment m of any section about the crown is a X c. Call A the sum of all the a’s from the crown up to and including the section considered; thus, A for section 3 is, in the following table, 31.25 + 63.75 + 70. Call M the total of the m’s ; thus, M for section 3 is 78.12 + 478.12 + 875. Then, the distance C from the crown to the center of gravity of the portion between ARCHES. 159 the crown and the section considered is — of that section A (see Neutral Axis, page 75) ; thus, for section 3, the distance C 1 431 24 for the portion including the sections 1, 2, and 3 is ■ * ' — = 8.67 ft. The above .values may be tabulated as follows: Section. w h a = w X h c m = a X c A = 2 a M = 2 m C = M A 1 5 6.25 31.25 2.5 78.12 31.25 78.12 2.50 2 5 12.75 63.75 7.5 478.12 95.00 556.24 5.85 3 5 14.00 70.00 12.5 875.00 165.00 1,431.24 8.67 4 5 16.50 82.50 17.5 1,443.75 247.50 2,874.99 11.61 5 5 14.00 70.00 22.5 1,575.00 317.50 4,449.99 14.01 6 2 14.75 29.50 26.0 767.00 347.00 5,216.99 15.03 cc X -P The horizontal thrust, Q — —^—, in which x is equal to one-half the theoretical span, or 25.66 ft. minus the value of C for the 6th section, which is, in this case, 15.03, giv¬ ing x — 10.63; P is equal to A for the last section, 347; and b equals the theoretical rise of the arch, 10.75 ft. Hence, . i . , . , - x X P 10.63 X 347 b 10.75 cu. ft. Multiplying by 140 lb., the weight of masonry per cubic foot assumed in this case, the horizontal thrust is 48,020 lb. The line of pressure may now be determined as follows: Draw through point p in Fig. 52 (5), the horizontal line yz; lay off to scale from p, in order, the distances C obtained from table. At these points lay off the vertical distance ef, g h', ij, etc., equal respectively to the values 31.25, 95,165, etc., from the column headed A. For instance, if the diagram is drawn to a scale of 1 in. to 100 cu. ft., the distance ef will be .31, or nearly j in. From f h', j, etc., to the same scale, mark off the constant horizontal thrust Q, as at f q, h' r, j s, etc. Thus, i 160 STRUCTURAL DESIGN . the vertical and horizontal forces at each section being given, the resultant of these two forces in each case is eq,g r, i s, etc. Extending each until it intersects the joint beyond e, g, i, etc., the pressure curve may be drawn through these latter points of intersection, as shown by the heavy black line, and the thrust at the joints may be found by measuring e q, gr, is, etc. with the scale to which the diagram was drawn. Since in this case the pressure curve falls well within the middle third of the arch ring, the arch may be consid¬ ered satisfactory, provided the safe crushing strength of the masonry is not exceeded. The influence of the last oblique thrust, which is the resultant thrust of the arch upon the pier, or abutment, will be explained in the following method of determining the pressure curve. This method is somewhat simpler, as it requires practically no calculations. Graphic Method. —Fig. 53 shows the wholly graphic method of finding the line of pressure. It is for a 6-rowlock brick segmental arch, 24 ft. span, 2 ft. 10 in. rise, and 26 ft. radius of intrados. ARCHES. 161 Begin by drawing, to scale, a diagram of one-half the arch. As in the previous example, the arch and its load is con¬ sidered to be 1 ft. thick; and the brickwork weighs 140 lb. per cu. ft. A load of 9,200 lb. upon one-half the arch has been assumed. Lay off, to scale, a height of brickwork whose weight will represent this load. Commencing at the crown, divide the load into, say, sections of 2 ft., as far as possible. The weight of each slice will be its contents mul¬ tiplied by 140 lb., and is marked on the diagram. Next, fix a point at the crown, and one at the spring of the arch, through which the pressure curve is assumed to pass. The points may lie anywhere within the middle third of the width; but the point a at the crown has been taken at the outer edge, and the point u at the spring at the inner edge, of the middle third. Lay off from a, on the vertical a d', the dis¬ tances ab,bc,cd, etc., which represent the weight of the slices from the crown to the spring. Thus, if the scale were 1 in. per 1,000 lb., a b would be 1.1 in. long. Next, draw 45° lines from a and h, intersecting at i; and from i draw i b, i c, i d, etc. Through the center of gravity of each slice, draw a vertical, as o v, p w, q x, etc. Starting from a, draw a v parallel to ai ; from v, draw vw parallel to bi, etc. These lines form a broken line, which changes its direction on the vertical line through the center of gravity of each slice. From the last point k, draw kj parallel to ih, and intersecting ai, extended, at j ; from,/ draw a vertical line./Z, which will pass through the center of gravity of the half arch and load. From l, where the horizontal line al intersects O', layoff a distance Im equal to ah , which represents the weight of all the slices. From l draw a line through the point u ; and from m, a horizontal line intersecting l u, extended, at n. Then m n will be the horizontal thrust at the crown, required to maintain the half arch in equilibrium when the other half is removed; and l n will be the direction and amount of the oblique thrust at the skewback. On l a extc ided, lay off, from a, a distance ab' equal to mn. From b', draw lines to b, c, d, etc., which represent the thrusts at the center of gravity of each slice. From a, draw a o, parallel to b' a ; from o, draw op, parallel to b’ b, etc.; then a, o, p, etc. will be points on the 162 MASONRY. line of pressure. If this line lies within the middle third, the arch will he stable, provided the pressure is within safe limits. The pressure at u is found by measuring b' h with the same scale as for a b, be, etc., and is about 16,000 lb. Hard- burned brick, laid in cement mortar, will safely sustain a compressive stress of from 150 to 200 lb. per sq. in. The area at the skewback, 144 sq. in., multiplied by 200, gives 28,800 lb., which is well within the safe limit. The stability of the abutments may be determined thus: Having calculated the weight of the pier or wall, lay off this weight on the vertical line from h to d', and draw d' b'. Draw a vertical line through the center of gravity of the pier, cutting In at c '; also, a line from c', parallel to b'd'. The latter line will be the resultant thrust of the arch, after being influenced by the weight of the pier. If this line falls beyond the foot of the pier, at the ground line, the pier will be incapable of resisting the thrust of the arch. In order that a pier may be secure, this final or resultant line of thrust should fall on the ground line, well within the middle third of the base. MASONRY. MATERIALS OF CONSTRUCTION. STO N E. Granite is the most valuable stone where strength is required, its crushing strength averaging about 20,000 lb. per sq. in. Owing to its hardness, it is very costly to dress, and its use is limited to the most expensive kinds of buildings. Granite being very dense and compact, absorbs but little water, and hence is valuable in damp situations. Exposed to fire, it disintegrates at a temperature of from 900° to 1,000° F., being less durable in this respect than fine-grained compact sandstones. The average weight of granite is about 167 lb. per cu. ft. Limestone is a very common building stone, and, when compact, is very durable. It is usually quite absorptive, and MATERIALS OF CONSTRUCTION. 163 becomes dirty quickly; while under intense heat, it is con¬ verted into lime. Limestone must be well seasoned before use, to get rid of the quarry water. The strength of lime¬ stone varies from 7,000 to 25,000 lb. per sq. in., the average being about 15,000 lb. The weight of limestone is about 155 to 160 lb. per cu. ft. Sandstone is, in general, an excellent building stone, capable of resisting great heat, and the better kinds absorb only small quantities of water. The dark-brown, flinty sand¬ stones retain their color very well, ranking better than granite. A stone containing much pyrites becomes unevenly discolored, due to formation of rust, and hence the stone should be carefully examined in this respect. The average strength of sandstones is about 11,0001b. per sq. in., varying from 4,000 to 17,000 lb. The weight of sandstone is about 140 lb. per cu. ft. The densest and strongest stones are generally the most durable. A fresh fracture, when examined under a magni¬ fying glass, should be clear and bright, showing well- cemented particles. When a good stone is tapped with a hammer, it gives out a ringing sound. The absorptive quality of a stone may be tested by noting the increase in weight after soaking in water for 24 hours. One that increases 5 per cent, or more should not be used. For ordinary building purposes, tests of crushing strength are unnecessary, as if stone is of good quality the strength is generally very much in excess of any probable loads. BRICK. Brick should be sound, free from cracks or flaws, stones, or lumps. They should be of uniform size, with sharp edges and angles, and true and square surfaces. If two good brick are struck together, they give out a ringing sound; while if the sound is dull, the brick is of inferior quality. A good brick will not absorb more than 10 per cent, of its weight of water; the best will not absorb over 5 per cent., while soft brick will take up from 25 to 85 per cent. The crushing strength of good quality brick should not be 164 MASONRY. less than 4,000 lb. per sq. in. Most good brick will have 2 or 3 times this strength. The weight of a common brick is about 44 lb., or 118 lb. per cu. ft.; pressed brick of the same size will weigh 5 lb. each, or 131 lb. per cu. ft. The size of brick is variable, as shown by the following table. The standard brick, adopted by several associations of builders and makers, is 84" X 4" X 24" for common brick, and 84" X 41" X 24" for face brick. Size of Brick. Name. Thickness. Inches. Width. Inches. Length. Inches. Common brick. 2-24 4 84 Philadelphia pressed. 24 4 8t% Peerless Brick Co. 2f 44 84 Baltimore and Trenton 24 44 84 Croton. 24 4 84 Colabaugh. 24 34 84 Maine common. 24 34 74 North River common. 24 34 8 Milwaukee .. 24 44 84 Stourbridge firebrick. 24 44 94 TERRA COTTA. All pieces of terra cotta for external w T ork should be tested before use. They should emit a metallic sound when struck, and a fracture should show close texture and uniform color. The surface should be hard enough to resist a knife scratch, and the glazing should not be chipped off. Solid terra cotta weighs about 120 lb. per cu. ft., while hollow pieces of ordinary size average from 65 to 85 lb. The safe working strength of terra-cotta blocks in walls is about 5 tons per sq. ft., if unfilled, and 10 tons, if filled solid with concrete. LIME. When properly burned, quicklime should possess the fol¬ lowing qualities: It should be in lumps, free from cinders, . and with little or no dust; it should slake readily in water to MATERIALS OF CONSTRUCTION. 165 a smooth, impalpable paste, without residue; and it should dissolve in soft water if enough is added. Lime weighs about 66 lb. per bu., or about 53 lb. per cu. ft. One barrel of lime, weighing 230 lb., will make about 2| bbl., or .3 cu. yd. of stiff paste. In l-to-3 mortar, 1 bbl. of unslaked lime will make about 6£ bbl. of mortar ; or 1 bbl. of lime paste will make about 3 bbl. of mortar. For a l-to-2 mortar, about 1 bbl. of quicklime to 5 or 5| bbl. of sand are used. CEMENTS. The two kinds of hydraulic cements are termed Portland and natural (often called Rosendale, from a place in .New York where much of it is made). The former is prepared by mixing together suitable proportions of clay and carbonate of lime, finely pulverized, and burning the mixture at a high heat in kilns, after which the mass is ground to a fine powder. Natural cements are so called because they are made from the natural rock, which contain the clay and limestone in the proper proportions. • Portland cements are dark in color, weigh from 90 to 100 lb. per cu. ft., are very slow in setting, and attain great ultimate strength. Natural cements are light in color, weigh from 50 to 60 lb. per cu. ft., are very quick setting, and become from i to | as strong as Portland cement. A barrel of Portland cement weighs about 375 lb. net; one of the Eastern Rosendales, 300 lb., and Western Rosendales (from Wisconsin, Kentucky, Illinois, etc.), about 265 lb. A cubic foot of slightly compacted cement mixed with j cu. ft. of water will make from f to f cu. ft. of paste; or 1 bbl. of cement will make about 3f cu. ft. of stiff paste. Simple Cement Tests. —Mix a handful of the cement to be tested with water, and make it into two cakes about £ in. thick, with thin edges. Let one dry in air for an hour and then put it in water for 24 hours, the other being kept in air. If at the expiration of that tune the latter has become quite hard, and when broken shows considerable tensile strength, with a clean, sharp fracture, without crumbling, and the cake in water retains its shape and has become much harder, such 166 MASONS Y. a cement is probably amply good for all building purposes. If the cake kept in water shows bad checks or cracks on the edges, such cement is unsafe to use under water, for any important work. If the sample in air becomes quite hard, while that under water crumbles, the cement may often be improved by mixing about half as much slaked lime with it. If it then hardens, it may be used in wet situations. The rapidity of setting in air may often be retarded, if required, by the addition of a small quantity of slaked lime. A cement which remains soft in air and does not become hard in water in 24 hours, may be a good cement for some purposes, but is very slow setting and undesirable for use in damp positions. Tensile Strength. —When a testing machine is available, tests of tensile strength of cements are usually made. The following table indicates the average strength of cemenl mortars of various ages and compositions: Tensile Strength of Cement Mortars. Age of Mortar When Tested. Average Tensile Strength. Pounds Per Square Inch. Portland. Rosendale. Clear Cement. Min. Max. Min. Max. 1 day, 1 hour, or until set, in air.. 100 140 40 80 1 week. 250 550 60 100 4 weeks . 350 700 100 150 1 year . 450 800 300 400 1 Part Cement to 1 Part Sand. 1 week. 30 50 4 weeks. 50 80 1 year. 200 300 1 Part Cement to S Parts Sand. 1 week. 80 125 4 weeks. 100 200 1 year. 200 350 All samples, except the first, were kept in air 1 day, and the remainder of the time in water. MATERIALS OF CONSTRUCTION. 167 SAND. The sand should he sharp, free from clay or earthy materials, and should he preferably pit sand. Sea sand should never be used unless thoroughly washed, as the salt in the sand causes efflorescence, and the cementing material does not adhere well to the rounded grains. Pulverized brick, cinders, furnace slag, etc. are sometimes used as sub¬ stitutes for sand with good results. The addition of a small quantity of brick dust to ordinary lime-and-sand mortar seems to give it the property of setting under water, and also prevents disintegration when the mortar is exposed to the elements. _ MORTAR. In mixing lime mortar, a bed of sand is first made in a mortar box, and the lime is distributed as evenly as possible over it, both lime and sand being previously measured. The lime should be slaked by pouring on from 11 to 2 times as much water, and covered with a layer of sand, or preferably, a tarpaulin, to retain the vapor given off. Sufficient water should be used at the start; if more must be added later, it chills the hot lime and makes it lumpy. Too much water makes the paste thin, weak, and slow in drying. Additional sand is then added, if necessary, until the mortar contains the proper proportion, which is usually 3 of sand to 1 of lime, although 2-to-l is much better. The bulk of the mortar will be about \ greater than that of the dry sand alone, so that 20 cu. ft. or 16 bu. of sand, and 4 cu. ft. or 3.2 bu. of quick¬ lime, will make about 221 cu. ft. of mortar. For cement-and-lime mortar, the materials should be well mixed together before water is added, and the mortar should be used before the cement sets. A good method of mixing cement mortar is as follows: One-half the quantity of sand is first spread over the bottom of the mortar box; next, the cement is spread evenly over the sand; and the remainder of the sand is then put on. The dry materials are thoroughly mixed together, either by noe or by shovel; water is then added to so much of the mass as is required for immediate use, and this portion is mixed 168 ' MASONRY. until it has the uniform consistency of a stiff paste. The quantity of water required depends upon the cement used, but it is better to have an excess than a deficiency. Owing to the rapidity of setting, only small lots should be mixed at a time. In winter, a small proportion of lime is sometimes mixed with the cement, the heat generated in slaking being supposed to prevent freezing until the cement has set. Salt is often added for the same purpose, the quantity being about 1 lb. of salt to 18 gal. of water, an additional ounce being added for each degree of temperature below 32° F. Salt is objectionable, however, as it causes efflorescence. CONCRETE. Concrete should be made by spreading the aggregate evenly over a layer of cement mortar (made as described under Mortar) in a box or on a platform, and mixing the materials thoroughly. The aggregate is usually broken stone, not over a specified size; but gravel, broken brick, etc., may be substituted. Whichever is used should be free from dirt, and be well sprinkled before mixing. The pieces should be of different sizes, so that the smaller pieces will fit in the spaces between the larger. The voids in broken stone are one-half the bulk, which space, in good work, is practically just filled by the mortar; hence, in estimating on concrete, it is necessary to figure about as much broken stone as there are to be cubic yards of concrete. The quantity of sand will be about one-half cubic yard per yard of stone—when gravel is not also used ; while the cement will vary according to proportions required. See table on page 170 giving proportions of cement and sand per cubic yard of mortar. Probably the best proportion for a strong concrete is 1 part of cement, 2 parts of sand, and 4 or 5 parts of broken stone, these quantities being sufficient to fill all the voids. A very good concrete may be made by using the follow¬ ing quantities of materials, which when mixed will make 1 cu. yd.: 2 bbl. of Rosendale cement, .5 cu. yd. of sand, and MATERIALS OF CONSTRUCTION. 169 .9 cu. yd. of broken stone. The mortar alone amounts to .55 cu. yd. A concrete nearly as strong and considerably cheaper is made of 1 bbl. of Rosendale cement, 2 bbl. of sand, .5 cu. yd. of gravel, and .9 cu. yd. of stone. These when mixed will make 1 cu. yd. The mortar amounts to .28 cu. yd. In laying, concrete should not be dumped from a consid¬ erable height, as the thoroughness of the mixture would be destroyed. It should be spread in layers of, say, 8 in. in thickness, and tamped enough to compact the mass well, the surface of each layer being left rough, to form a better bond with the succeeding one. The strength of concrete increases considerably with age. For example, a Portland cement concrete 1 month old will crush under a load of about 15 tons per sq. ft., while if it is a year old, it will sustain about 100 tons per sq. ft. These figures, under favorable conditions, may be nearly doubled. Natural cement concretes, with various proportions of mate¬ rials and of ages from 6 months to 4 years, showed crushing strengths of from 70 to 100 tons per sq. ft. QUANTITIES OF MATERIALS. Proportion of Mortar in Masonry. Kind of Masonry. Per Cent, of Mortar. Minimum. Maximum. Brickwork, coarse, ¥' to f" joints ... Brickwork, ordinary, to 1" joints 35 40 25 10 30 Brickwork, pressed, joints . Ashlar, courses 12" to 20" high, joints 15 a" y Ashlar, courses 20" to 32" high, joints 7 8 to |".. 5 6 Rubble, coarse, not dressed . 33 40 Rubble, roughlv dressed. 25 30 Rubble, well dressed, coursed . Concrete, clean stone, without grav- 15 20 el or screenings. 50 55 170 MASONK Y. Quantities of Materials Per Cubic Yard of Cement Mortar. Proportions. Materials. Cement. Sand. Barrels Cement (Packed). Sand. Cu. Yd. Portland or Eastern Rosendale. Western Rosendale. 1 0 7.1 6.4 .0 1 1 4.2 3.7 .6 1 2 2.8 2.6 .8 1 3 2.0 1.8 .9 1 4 1.7 1.5 .95 1 5 1.3 1.1 .97 1 6 1.2 1.0 .98 If brickwork is figured by the thousand brick, the quanti¬ ties of cement and sand obtained by aid of these tables should be multiplied by either 2i, 2, or If, according to whether the brickwork is coarse, ordinary, or pressed. The last given figures are the number of cubic yards which 1,000 standard size brick will lay. As a perch is of a cubic yard, if stonework is thus estimated, the figures in the tables may be used for perch measurement by deducting from the final results. Example.—H ow many barrels of Eastern Rosendale cement and cubic yards of sand will be required for laying 100 cu. yd. of rubble masonry in l-to-3 cement mortar? By the first table, it is seen that the minimum percentage of mor¬ tar in coarse rubble is 33; hence, for each cubic yard of masonry } cu. yd. of mortar is required. According to the second table, a l-to-3 mortar requires, per cubic yard, 2 bbl. of cement and .9 cu. yd. of sand ; or 1 cu. yd. of rubble requires § bbl. of cement and .3 cu. yd. of sand ; and for 100 cu. yd. the quantities are 07 bbl. of cement and 30 cu. yd. of sand. While founded on actual work, the above tables are not intended to furnish more than fairly close approximations, as there are so many uncertainties about mortar and masonry that very accurate estimates cannot be made. FOOTINGS AND FOUNDATIONS. 171 FOOTINGS AND FOUNDATIONS. Before beginning a structure, the character of the soil should be investigated. For ordinary work, this can he done by boring—using a 2" auger—at short intervals, around the site. The auger will bring up samples sufficient to determine the character of the soil. This is a useful precaution, but can be dispensed with for the usual run of buildings, the bearing power being judged by experience of loads in adjacent struc¬ tures, or by examinations of near-by excavations. Soils may be classed as rock, ordinary soil, and made ground. A level bed of rock makes the best possible founda¬ tion ; sand and gravel rank next; clay is safe for moderate loads if kept dry ; quicksand should be removed if possible ; and soft, marshy ground should be piled, or the footings spread enough to reduce the pressure to safe limits. Made ground, usually formed of garbage, waste earth, etc., should not be built on for important structures, without tests as to its bearing power. For small buildings, however, good made ground is safe to build on. Table XI, page 74, gives the loads which different kinds of soils will carry. If water is encountered in excavating foundations, careful provision must be made for its removal by means of suitable drains. The ground water level should be considered also. Thus a building may have a good foundation on wet ground, until the water is drained off, by excavation of deep trenches in the street, which causes settlement in the foundation. The frost line, or depth to which ground becomes frozen, must be taken into account, and founda¬ tions must be started below it; otherwise they may be cracked and heaved out of place. This depth varies from 3 ft. to 6 ft., according to the severity of the climate. Foundations should not be laid on a sloping bed, owing to the lia¬ bility of slipping. Nor should the walls be built partly on rock and partly on earth, as shown in Fig. 1, for the weight causes the Fig. 1. 172 MASONRY. earth to settle, and the wall, being carried by the rock only, would be unstable; or water, flowing between the rock and masonry, and freezing, might force out the thin wall. When a level bed cannot be otherwise obtained, concrete may be advantageously used for this purpose. If the natural surface is rough, the better will concrete adhere to it. In fact, con¬ crete should be used much more than it is for foundation work. For buildings of moderate weight, erected on soft, clayey soils, the bearing power of the latter may often be con¬ siderably improved by spreading layers of sand, gravel, or broken stone, and pounding it into the soil. Or, the soil may be compacted by driving short piles, say 6 ft. long and 6 in. in diameter, as close together as necessary; from 2 to 4 ft. apart is generally close enough. The results will be better if the piles are drawn out and the holes filled with sand, well compacted. Thus the soil is consolidated, and the sand, acting as so many small arches, transmits the load to the sides of the hole, as well as to the bottom. PROPORTIONING FOOTINGS. Footings should be designed for the load they are to carry, with the object of producing a uniform settlement in all parts of the building. They evidently should not be as wide under an opening as under a solid wall, and when the openings form a considerable proportion of the wall area, that part of the footings under them slxmld be omitted, the weight being transmitted by arches or beams to the footings under the FOOTINGS AND FOUNDATIONS. 173 sides of the openings. This caution is very important, as a majority of cracks in masonry are probably due to continuous footings where little or none are needed. If one portion of the foundation, as, for example, that under a tower, carries much more weight than another part, its width should be pro¬ portionately increased. In designing footings, the center of the wall should be placed verti¬ cally over, or, prefer¬ ably, a little inside the center of the base, as sketched in Fig. 2; then the walls will be slightly tilted inwards, but will be kept in place by the floor joists, etc. Where there are interior piers, these should have a some¬ what greater load per square foot — that is, less area per toil of load—than the walls, so that the latter will be pressed together, thus preventing cracks; also, as the piers usually support iron columns, to allow for the compression in the brickwork joints, the iron being practi¬ cally incompressible. Footing courses should be battered or stepped up, making the angle abc in Fig. 3(a), about G0°. The load then becomes well distributed over the base. If the footings are laid as shown at (6), the projections are liable to break off at the edges ot the wall, and the load will be unevenly carried by the soil. L 174 MASONRY. To show the method of proportioning footings (and of figuring loads in structures), the area of the footings for a 45' X 60' brick warehouse, shown in Fig. 4, having five stories and basement, a tar-and-gravel roof, tile arch floors, and without partitions, will be determined. There are two rows of columns, spaced 14£ ft. apart longitudinally and transversely. The walls of the building are 75 ft. high, 25 ft. being 20 in. thick, and 50 ft., 16 in. thick. As the basement floor rests directly on the ground, its load will not be consid¬ ered. The floor loads on the first and second stories will be taken at 200 lb. per sq. ft., and on the others at 150 lb. Assume that brickwork weighs 120 lb. per cu. ft.; the tile floor 80 lb. per sq. ft.; the tar-and-gravel roof 10 lb. per sq. ft.; and the snow load at 12 lb. per sq. ft. Then, for each foot in length of the side walls, the load is: Dead Load. Walls— 1 ft. 8 in. X 1 ft. X 25 ft. = 41.7 cu. ft. 1 ft. 4 in. X 1 ft. X 50 ft. = 66.7 cu. ft. 108.4 cu. ft. X 120 lb. = 13,008 lb. Floors — (80 lb. per sq. ft. X 1 ft. X 7* ft.) X 5 = 2,900 lb Roof- 10 lb. per sq. ft. X 1 ft. X 7* ft. = 72 lb. Live Load. On Floors — (200 lb. per sq. ft. X 1 ft. X 7* ft.) X 2 = 2,900 (150 lb. per sq. ft. X 1 ft. X 7£ ft.) X 3 == 3,262 6,162 lb. Wind, neglected on nearly flat roof 0 lb. Snow — 12 lb. per sq. ft. X 1 ft. X 7£ ft. = _87 lb. Total dead and live load = 22,229 lb. Assume that, upon testing, the soil has been found to be moderately dry clay. By reference to page 74, the average safe load for this soil is found to be 3 tons per sq. ft. Hence, dividing the total load, 22,229 lb., by 6,000 lb., there results 3f ft. as the approximate width of the footings for the side walls. If the foundation walls are made 6 ft. deep, and bat- FOOTINGS AND FOUNDATIONS. 175 tered 1 in. per foot, the top width will he 2f ft. Thus far the weight of the foundation wall has not been considered. Hay¬ ing obtained the approximate width of the footing, its weight can now be computed. The average width of the foundation wall is 3 ft. 2 in., and it is 6 ft. deep; the contents will be 19 cu. ft. per foot of length ; the walls are good limestone rubble, weighing 150 lb. per cu. ft., so that the total weight will be 2,850 lb. Adding this to 22,229 lb. and dividing by 6,000 lb., the unit load, the final result is about 4} ft. as the width of the footing. The footings for the end walls and piers may be similarly figured. Spread Footings. —These are used on compressible soils to bring the load per square foot within the safe bearing power of the soil. They may be made of timber, in wet soils, alter¬ nate courses being laid transversely; of layers of I beams or rails, laid in concrete; or of concrete with several trans¬ verse courses of twisted iron rods (a patented method). These are shown at (a), (5), and (c), Fig. 5. In the first two cases, it is necessary to figure the safe length of the projecting portion. For example, determine the size of the timber footing, Fig. 5 (a), for a wall having a load of 40,000 lb. per ft. in length. The ground is wet and not safe to load over 3,000 lb. per ft.; consequently, the footings must be 13} ft. wide. Ihe stepped-out foundation is 32 in. wide, making the projection L ' 5 ft 4 in. on each side. To find what size timber is required, 176 MAS ONE Y. consider either side as ac, a cantilever beam, 1 ft. wide, uniformly loaded, supported at c, and resisting the upward reaction of the earth w of 3,000 lb. per sq. ft.; for 5 ft. 4 in. it is L w = 16,000 1b.; call this W. According to Table XXVI, page 113, the bending moment is M = —— = ——-- Z Z = 42,667 ft.-lb.; or 512,000 in.-lb. The resisting moment (see page 114) M\ = QS, S being the safe unit fiber stress, and Q the section modulus, which for a b d 2 rectangular beam is, from Table XII, page 83, — — ; b is the width and d the depth. Suppose that the timber is spruce and that the safe bending stress is 1,000 lb. per sq. in.; let the beam be 12 in. wide; its depth remains to be determined. 1,000 X 12 X d 2 . ... , Then, Mi = ---. Since the safe resisting moment 6 should equal the bending moment, Mi = M , or 1,000 X 12 X d 2 6 = 512,000; whence, d -]/ 256 = 16 in. 1512,00 0 X 6 \ 1,000 X 12 Hence, 12" X 16" timbers, set side by side, with cross-layers of planks above and below, shown in Fig. 5 (a), would be used. The principles are the same when the footing consists of I beams, or rails, but other values are used for Q and S, on account of the different cross-sections and material. (See page 118 for rolled-steel beams.) The safe offsets for stone footings may also be figured in the same manner. In general, it is best to make the offset in each course of stonework or brickwork not greater than the depth of the course. For cal¬ culation of stone beams, as flagstones, lintels, etc., see page 119. PILES. When piles are driven closely to confine puddle in a coffer dam, or for preventing the fall of an earth bank, they are called shed piles, and consist of planking from 2 to 6 in. thick, the bottoms being cut at an angle which forms a driving toe, that tends to keep the pile close up to the FOOTINGS AND FOUNDATIONS. 177 adjacent one. The heads are kept in line by securing longi¬ tudinal stringers, or wales, to them by spiking or bolting. Piles which sustain loads are called bearing piles. They may be square or round in section, but are usually round, and are from 9 to 18 in. in diameter at the top. They may be used either with or without the bark. White pine or spruce is suitable where the ground is soft; where it is firmer, Georgia pine may be used to advantage. Where the soil is very compact, hard woods, such as oak, hickory, ash, elm, beech, etc., are used. Piles are usually driven at intervals of from 2i to 4 ft. between centers, according to the nature of the soil and the weight to be sustained. The following formula gives the safe load for a pile: in which W — safe load in pounds; io == weight of hammer in pounds; h = fall of hammer in feet; k = penetration of pile in inches at the last blow (head of pile in good condition, not split or broomed). This formula gives a factor of safety of 6. Assuming t hat the fall of the hammer is 30 ft., its weight 2,000 lb., and its penetration at the last blow i in., or .5 in., the safe load is 2 X 2,000 X 30 _ 120,000 _ goQOOlb., or 40 tons. .5 + 1 1-5 Where piles are spaced at 3 ft, between centers each way, the foundation area will safely sustain a load of from 3 to 5 tons per sq. ft., and when spaced at 2.) ft. between centers tach way, the load may be increased to from 5 to 7 tons per sq- ft- , , ,, Where the soil is very hard, it is necessary to shoe ie piles with cast or wrought iron, to make them drive more easily. In order to preserve the heads from brooming_anr splitting, wrought-iron hoops, from * to 1 in. thick, and 2 or o in. wide, are used. , When driven, the piles are carefully sawed off to the same level, usually below the water-line, and capped by cross-rows of timbers or planking, forming a grillage upon which the 178 MASONR Y. masonry is laid. Sometimes large flat stones are laid directly on several of the piles. This method is good, provided the stones are set so as to bear evenly on the piles, without much pinning up by spalls, which are liable to be crushed. The heads of the piles may also be embedded in concrete for 2 or 3 ft., which makes a very satisfactory foundation. THICKNESS OF WALLS. Stone foundation walls should be at least 8 in. thicker than the wall above, for a depth of 12 ft. below grade or curb level; for each additional 10 ft. or part thereof in depth, they should be 4 in. thicker. Thus, if the first-story walls are 12 in., the foundation should be 20 in. thick if 12 ft. deep, and 24 in. thick if over 12 ft. Stone foundations should not be less than 16 in. thick; a thinner wall does not bond well; only small stones can be used, and it cannot be carried to any height. The thickness of foundation walls in all the large cities is controlled by the building laws. Where there are no existing laws, the following table will serve as a guide : Thickness of Foundation Walls. Height of Building. Dwellings, Hotels, etc. Warehouses. Brick. Inches. Stone. Inches. Brick. Inches. Stone. Inches. Two stories. 12 or 16 20 16 20 Three stories . 16 20 20 24 Four stories. 20 24 24 28 Five stories. 24 28 24 28 Six stories . 24 28 28 32 The table on page 179 is a tabulated summary of the New York Building Law in regard to walls, and may be safely taken as a standard. It applies only to buildings having solid masonry walls, and not to those of skeleton-construction type, in which the walls are carried on the framework. w p? o £ g «• M C* R 2 w 2 & £ gf-f W tc R) R ◄ cu >o t§ oj CS s R o to CO w 55 M u t-H « H FOOTINGS AND FOUNDATIONS. 179 cj £ 60 fl •rH Fh c3 © w r d a c3 0 r O a o a o • (D-rt to S +- oi g is ^ o «2 a a * a*-i o w ■R 4J 3 . ■tipis -Pr a; a; M WO 0 > O ■§ ^ rH ^ ® ®° ^ ^ n O O kA l-gsj d ® d 0 5> o R a CO 0 5> O R _ C3R ®0 5 » q3P^ ^§§g Cl ^ ^ w OOiOiOOiC QiC?ONOOOH PiA> o o iA ji o ftco io co r- oo © W rH o *+o eo •rO £ o tj £ * o -a o3 V •o xn P d *3 to ^ 5? aJ -a bo O x a r 23 • rH Fh os a c3 0) ^ v w . • O H* P ^ Cl CM "d Cl O ~ a rHrH uo© cj oJ' o> co cj 0 "d O OXX •BS 4-» o o 0 0 cs d a a a o CD O 00 hcioin o lb io o .H(N(MC4 ci (3 a! qj aJ ^ £ £ * £ H o o o o 0.2 »i a a o o.5R o H CO (M O Stiu Cl Cl Cl CO CO M g a * PH o R A o 5 a • ■§P0 ^OifliOO rt'Ol'COO W r- ( Mo h CD I— CO w *If brick is used, width may be 4" less. For foundations over 10' deep, thickness must be increased 4 ior each addi¬ tional 10' or part thereof. . c/ , f Non-bearing partition walls, less than oO high, may be < . j If clear span is over 27, all bearing walls must be 4 thicker for each 12*' over 27 span. 180 MASON 11Y. For heights greater than those given, the lower part must he 4" thicker for each 25' or fraction thereof in height, the upper 115' or 100', respectively, remaining as given in table. MASONRY CONSTRUCTION. NOTES ON STONEWORK. Stone being the stronger material, a wall should have as much stone and as little mortar as possible. Contact of the stones in bed joints is not advisable, as the shrinkage of the mortar may leave them bearing only on the projecting angles. The thickness of joints in stonework is from T 3 S to £ or $ in., depending on the class of work; but for ordinary ashlar, the usual thickness is about | in., and more in rough masonry. Bed joints should be full and square to the face, as if worked slack at the back—to make thin face joints— spalls are likely to break off at the front edges. Good bond¬ ing is essential for a strong wall, and the proper placing of headers should be carefully watched. Long pieces of stone should be well supported and bedded to prevent breaking; pieces more than, say, four times the thickness, should not be used. Stone, especially if stratified, should be laid on its natural or quarry bed, as if set vertically, water easily pene¬ trates between the layers, and, freezing, splits off the outer ones. For damp places, stonework (and brickwork) should be laid in cement mortar or lime-and-cement mortar, while in dry positions good lime mortar may be used. In laying stone, the mortar should be kept back about an inch from the face of the wall; otherwise spalls may be broken off, owing to the outside mortar hardening more rapidly than that in the interior, settlement bringing the pressure on the hard layer. This precaution is very important in the case of lug sills, band courses, etc. The joints may be pointed, after the wall is built, with some non-staining mortar. The value of grouted walls is a much disputed point. A wall grouted with thin lime mortar undoubtedly requires a long time to dry thoroughly, while if the grout is thick, it MASONR Y CONSTR UCTION. 181 does not fill every crevice. With cement grout, however, a wall so filled is very much stronger than one laid with stiff mortar, as has been shown by tests. When using cement grout, the brick or stone should not be wet; they will then absorb the water in the grout, and also some of the cement, thus increas¬ ing the adhesion. Grout is usually made of ordi¬ nary mortar, thinned to the consistency of cream. If an extra strong wall is required, a 1-to-l mortar may be used. Ashlar should be care¬ fully bonded, either by using courses of different p IG g thickness, or, if the ashlar is only from 2 to 4 in. thick, by means of wire ties and anchors, such as are shown in Fig. 11. When the courses are from 4 to 8 in. thick, a good bond to the backing may be had by using each thickness in alternate courses. When the backing 'is brick, the joints in it should be as thin as possible ; and if lime mortar is used, some cement should be added, to prevent shrink¬ age. Very thin ashlar must not be considered in deter¬ mining the strength of walls, but the backing must be made sufficiently strong, in¬ dependent of the ashlar. All projecting courses, such as cornices, lintels, sills, etc., should be beveled on top, and have a drip cut on the under side, as shown at a, Fig. fi, to prevent water from soaking into the joints. Lug sills should only be beveled between the jamb lines, the ends 182 MAS ONE Y. being cut level, as at b, thus keeping out water from the joint between brick and stone, and also forming a more secure bearing for the wall. The top of exposed walls should be covered by coping, in long pieces, and have the vertical joints well filled with good mortar. Gable co¬ pings should be anchored very firmly, either by iron dowels or ties, or by bond stones, the latter method being shown in Fig. 7. CLASSES OF STONE MASONRY. Rubb|e Masonry. —This is used for rough work, such as foundations, backing, etc., and although frequently consist¬ ing of common field stone, quarried stone should be used where possible, as better bonding and bedding can be secured. At (a), Fig. 8, is shown a common- or random-coursed rubble wall, in which the stones are bonded every three or four feet, as at a. The angles are laid with large well-shaped stone, the long sides alternating; in the body of the wall the stones are set irregularly, the interstices in the heart of the wall being filled with spalls and mortar. At ( b ) is shown cobweb rubble, which is used for suburban work. The quoins, or corner stones, are hammer-dressed on top and bottom, but may be rock-faced. All the joints should be hammer-dressed and no spalls should show on the face, while the joints should not be thicker than i in. This class of work is more expensive than common rubble. At (c) is shown a rubble wall with brick quoins. In this work all the horizontal joints have hammer-dressed level beds. This makes a good wall and can be built cheaply when the stone used splits readily. At ( d) is shown regular-coursed rubble. In this work continuous horizontal joints are run at intervals of 15 to 18 in. in the height, as at a b c and d ef. No attention need be paid to uniformity of height in the different courses, but the beds should be made as nearly parallel as possible. Ashlar. —When the outside facing of a wall is of cut stone, it is called ashlar, regardless of the manner in which the stone is finished. MASONR Y CONS TR UCTION. 183 Regular-coursed ashlar, shown at (e), Fig. 8, has pieces uniform in height and the courses continuous. Stones about 12 in. high and from 18 to 24 in. long are the cheapest, both as to first cost and in expense of handling. The illustration shows the stone hush-hammered with tooled draft lines. A good effect is produced by making the courses of two differ ent heights, as shown at (/), the courses a being from 10 to 18 in high and composed of “ facers,” while the courses b are 184 MASONRY. from 5 to 7} in. high and constitute binding courses. The latter should be at least 4 in. wider than the thickest stones used in the facing courses. Random , or broken-range, ashlar consists of blocks truly squared but of different sizes, forming a broken range or course. As this masonry is in itself irregular ; it is well adapted to buildings of irregular plan or of irregular sky line. Random ashlar is finished in various ways. The simplest, though not the least effective, finish is the plain rock face, shown in ( g ). The block must first be cut true and square all around, forming beds and vertical joints, after which straight lines are drawn around the edges, about 2 in. from the face of the block. A wide pitching chisel is then used along these lines, knocking off the surplus material. The smallest stone used should not be less than 4 in. in height, nor the largest greater than 16 in. The bond, or the lap of one stone over another, should be at least 6 in. for the smaller stones and 8 in. for the larger. The length of any block should not be less than 1£, nor more than 4, times its height. The hardest kinds of rock are best suited for masonry of this sort, which is, perhaps, the most common kind of ashlar used in modern building. STONE FINISHES. Some of the tools used in making the finer finishes for stonework are shown in Fig. 9. The crandall (a) consists of a wroxight-iron bar, flattened at one end, with a slot, f in. wide and 3 in. long, in which ten double-headed points, made of square steel about 9 in. long, are fastened by means of a key. It is used to finish the surface of sandstone after it has been worked with the tooth-axe or chisel. The patent hammer (b), made of several thin blades of steel, ground to an edge and held together with bolts, is used for finishing granite or hard limestone. The bush hammer (c), from 4 to 8 in. long and 2 to 4 in. square, has its ends cut in pyramidal points. This hammer is used for finishing limestone and sandstone after the surface has been made nearly even. MASONRY CONSTRUCTION. 185 Fig. 9. 186 MASONRY. At (d) is shown the appearance of rock-faced or pitch¬ faced work. The face of the stone is left rough, just as it comes from the quarry, and the edges are pitched off to a line. Rock-faced finish is cheaper than any other kind, as but little work is required. At (e) are shown two kinds of crandalled work; that on the left shows the appearance when the lines run all one way, while that on the right shows the lines crossing. This finish is very effective for the red Potsdam and Longmeadow sand¬ stones. At (/) is shown broached work, in which continuous grooves are formed over the surface. At ( g ) is shown bush-hammered work, which leaves the surface full of points. This finish is very attractive on bluestone, limestone, and sandstones, but should not be used on softer kinds. At (/i) is shown pointed work ; that on the left half of the stone being rough-pointed, while the right half is fine-pointed. In the rough-pointed work, the point is used at intervals of one inch over the stone, while in the fine-pointed, the i>oint is used at every half inch of the surface. At (i) is shown the patent-hammered finish, generally used on granite, bluestone, and limestone. The stone is first dressed to a fairly smooth surface with the point, and then finished with the patent hammer. The fineness of the work is determined by the number of blades in the hammer. For U. S. government work, 10 cuts per inch are generally specified, but 8 cuts per inch is good work. At (j) is illustrated tooled work. For this finish, a chisel from 3 to 4£ in. wide is used, and the lines are continued across the width of the stone to the draft lines. At (k) is shown vermiculated work, so called from the worm-eaten appearance. Stones so cut are used in quoins and base courses. This dressing is very effective, but expensive. At ( l) is shown droved work, similar to tooled work, except that the lines are broken, owing to the smaller size of the chisel used. It is less expensive than tooled work. When a smooth finish is desired, the surface of the stone is rubbed. This is best done before the stone becomes seasoned. MASONRY CONSTRUCTION. 18 ? BONDS IN BRICKWORK. In Fig. 10 are shown the three principal bonds in brick¬ work. In (a) is shown English bond, consisting of alternate courses of stretchers and headers. The longitudinal bond is obtained by means of either one-quarter bats, as shown, or preferably by three-quarter bats. This bond is probably the strongest and best one, although not much used. In ( b ) is shown Flemish bond, consisting of alternate headers and stretchers in the same course. The lap is obtained by use of three-quarter bats, with quarter, half, and three-quarter inte¬ rior closers. In (c) is shown the ordinary bond, which consists of 5 or 6 courses of stretchers to each course of headers. This bond is not as strong as the first two named, as there is a continuous ver¬ tical joint extending be¬ tween the header courses. From (a) to ( i ), Fig. 11, are shown methods of bonding face brick to the backing in both solid and hollow walls; also of bonding terra-cotta fur¬ ring to walls. At (j), (k), and (l)\ are shown methods of joining old and new walls; ( j ) shows a vertical groove cut in the old wall to form a sliding joint with the new wall; (k), a 2" X 4" piece spiked to the old wall for the same purpose; and ( l ), a steel- tie bond (also adapted for bonding face brick). In Fig. 12 are shown methods of tying face brick to the woodwork in brick-veneered walls by means of steel ties, etc. 188 MASONRY. MASONRY CONSTRUCTION DURING EXTREMES OF TEM PERATU RE. Extremes of heat or cold are both unfavorable to the union of the building material and the mortar. MASONRY CONSTRUCTION. 189 Extreme heat causes quick evaporation of the water in mortar, leaving the mortar in practically the same condition as be¬ fore mixture. This effect is intensified by the very dry condition of the stone or brick, which readily absorbs moisture from the mortar. In hot weather the surfaces of the brick and stone are covered with dust, which is very detri¬ mental to adhesion, and should be removed before using the material. The mortar, whether lime or cement, should be thinner than usual, and the brick and stone should be well sprinkled before laying. When built, the wall should be frequently sprayed with water, to lower its temperature, and prevent excessive evapor¬ ation. In making concrete, the sand and gravel should be well washed, and kept moist by liberal spraying; where practicable, a tem¬ porary cover over the work, to keep off the sun’s rays, should be provided. In plastering, similar points require attention; the openings in the build- in 190 MASONR Y. ing should be closed, to prevent hot-air currents from extracting moisture too rapidly from the plaster. Where patent plaster is used, the dry lathing should be well mois¬ tened before the mortar is applied, and care must be exer¬ cised that the coats do not become dry before the subsequent ones are applied. Hard plasters are not injured by frost after they have begun to set, but should be protected from it for the first 36 hours after application. Extreme cold prevents the setting of mortar by freezing the moisture in it, and also by forming films of ice on the brick or stone. If lime mortar is to be used during freezing weather, rich, newly slaked lime, thoroughly well mixed, gives good results, as it retains much of the heat of slaking. With hydraulic cement the set takes place more rapidly, and, if well begun, frost does not apparently injure the mortar; the particles in combining expel the excess of moisture; a much closer contact is thus secured, and the mortar is denser. Although, in appearance, the work may not have suffered from the action of frost on the cement, many experiments have conclusively shown that cement rnoBtar after freezing loses as much as one-third the tensile strength it possesses when not frozen. In order to lower the freezing point, a solution containing 2 or 3 per cent, of salt is mixed in the mortar, reducing the temperature of freezing about 5°; that is, until the ther¬ mometer registers below, say, 28°, the operations are safe. It has been conclusively proved, however, that the addition of salt to cement is injurious to its strength, as the crystalliza¬ tion of the salt creates a force opposing adhesion, and tends to disintegrate the particles; salt also attracts moisture, thus making the walls constantly wet. The top of the walls should be kept covered when work is stopped, so that rain may not enter and, freezing, sepa¬ rate the constituent parts of the masonry. Sheets of tar¬ paulin or roofing felt are most convenient for the purpose. When the temperature has reached the freezing point, it is unsafe to dress-cut unseasoned stone in the open air, as the quarry sap in the stone freezes, and the stone may be frac¬ tured during the process of cutting. MASONRY CONSTRUCTION. 191 WATERPROOFING WALLS. Damp cellar walls are due either to water soaking through from the outside, or to wet bottoms, from which water rises in the walls by capillary action. The decay of vegetable matter con¬ tained in dirty water generates gases injurious to health, so that the pre¬ vention of dampness in walls is a point of great importance. Provision must be made to convey the water away from the walls, as well as to make the latter damp-proof. No earth should be placed against the wall, a 12" or 18" space next to it being filled with broken stone or gravel, with, if practicable, an open- jointed tile drain laid at the bottom, as shown in Pig. 13. The outside of Hff the walls and footings should be plastered thickly with 1-to-l cement mortar ; or, preferably, with asphalt and coal tar, mixed in the proportion of 9 to 1, and applied, while hot, about f in. thick to the dry walls. The asphalt course should also extend through the walls, as shown at the under side of the concrete floor, which should be 3 or 4 m. thick, and laid on a 6" or 8" bed of broken stone. In place of concrete, a very durable composition, made of 60 parts of hot asphalt, 10 of coal tar, and 30 of sand, may be use . The ascent of moisture in walls may be prevented by inserting on the footing course two courses of roofing sat or very hard brick, laid with broken joints m cement mortar, or a few layers of tarred felt may be used. Efflorescence.— Efflorescence, or the white coating frequently seen on outside of stonework and brickwork, is caused by the deposition of soluble matter in the mortar, whic^be g dissolved in the water used in mixing is deposited u^.n the surface of the wall, as the water evaporates. This efflorescence may be removed by washing the walls With a elution . at muriatic acid in 20 parts of water. When clean and dry the Fig. 13. 192 MASONRY. walls may be coated with a preservative; one of the commonest being boiled linseed oil, which, applied in 2 coats, and, when dry, washed over with weak ammonia, will be effectual for 2 or 3 years before needing renewal. Lead and oil paint is some¬ times used, but is objectionable, as it changes the color of the masonry, and also flakes off. Cabot’s brick preservative is used to waterproof brick and sandstone, and is effectual where the heart of the wall is kept dry. Sylvester’s process, which has proved quite successful, and is simple in preparation and application, consists of two washes, the first being made of Castile soap and water, in the proportion of £ lb. of soap per gallon of water, and the second of $■ lb. of alum per gallon. The soap wash is applied, boiling hot, with a brush, to the clean and dry walls, and allowed to dry 24 hours before the alum wash—which need not be hot— is put on in the same manner. The coats are applied alter¬ nately 2 or 3 times, making the wall practically impervious. All ordinary cements will cause efflorescence, and when such are used in stonework, the face stones should be set entirely with Yicat, Lafarge, or some other non-staining cement mortar, mixed with sand in the proportion of 1 to 2. If this method be too expensive, the joints of the stonework may be raked out to a depth of 1 in., and pointed with a mortar made with one of these cements. Good lime mOrtar is often used in setting ashlar, and by some is claimed to be practically as good for the purpose, and considerably cheaper than the cements named. CHIMNEYS AND FIREPLACES. Chimneys. —In planning chimneys, the points to be consid¬ ered are the height, and the number, size, and arrangement of the flues. Attention must also be given to the location in respect to valleys, etc. on the roof. To make the chimney ‘ draw ” properly, a separate flue should be provided, extend¬ ing from each fireplace to the top of the chimney. For ordi¬ nary stoves and small furnaces, the flues may be 8in. X 8 in.; but if the furnace is large, it is better to make the flue 8 in. X 12 in., and the same size should be used, when possible, for fireplaces having large grates. (See Fireplaces.) Flues MASONE Y CONSTR UCTION. 193 are sometimes only 4 in. wide; but are then easily choked with soot and difficult to clean, so that a flue should not be less than 8 in. wide. Flues should always be lined with some fireproof material; in fact, the building laws of large cities so require. The lining is usually fireclay, tile, or gal- vanized-iron pipe. If the pipe used is round, the space between it and the Avails of the chimneys may be utilized for ventilation. The outer walls of chimney flues should be 8 in. thick, if flue linings are not used. Whenever it is necessary to change the direction of the flue, the diversion should be effected by long curves, and not by sharp turns, which retard the passage of smoke. Chimneys should extend above the highest point of the building or of those adjoining; other¬ wise they are likely to smoke. This may be obAdated, when the chimney is not carried high enough, by using a hood having two open sides; but as hoods are unsightly, their use should be avoided, when possible. The top of a chimney should be covered by a stone slab, either solid, to prevent the entrance of rain—the smoke passing out through holes at the sides near the top—or with a hole the size of the flue cut in it, preventing disintegration of the exposed mortar joints. Fireplaces. —The general construction of a fireplace is shown in Fig. 14. The projection in the room is called the chimney breast, and its width a is generally 5 ft., Avhich is the standard Avidth for ordinary fireplaces, the return b in this case being 17 in. The height of the fireplace opening at c is about 30 in. from the finished floor line to the springing line of the arch, the rise of which may be 3 or 4 in. The width of the opening betAveen the rough bricks, as d, should be 25 or 26 in., and the depth of the niche e, from 12 to 13 in. These measure¬ ments may be adjusted to suit special grates and fittings. The arrangement of the floor framing requires no explana¬ tion, other than that the trimmer joists should be kept 2 in. from the brickAVork. A temporary Avooden center supports the brick trimmer arch during construction. The space above the arch is leA r eled up Avith cement concrete, upon which is laid the slate or tile hearth. With this method of construct¬ ing a fireplace, it is almost impossible for the woodAvork to catch fire. 194 MASONRY. The opening above the fireplace, or throat, is gradually contracted to the size of the flue lining, as shown at l and to. Several courses of brick are corbeled out from the back, as at n ; on the ledge formed is placed a sliding iron damper. A preferable form of construction consists in the insertion, just below the throat l, of a tilting damper, which may be operated by a key placed in the front of the fireplace. A good proportion for flues of fireplaces in which it is intended to burn wood or bituminous coal, is to make the sectional area of the flue that of the fireplace opening, if the flue is rectangular, and T V if the flue is circular ; thus, for a fireplace which is 30 in. wide X 30 in. high, or 900 sq. in. in area, the area of a rectangular flue would be 90 sq. in., which is nearly equivalent to an 8" X 12 " flue ; for a circular flue it would be 75 sq. in., which is equivalent to a 10" flue. When anthracite coal is to he used in the fireplace grates, the flue area may he made that of the fireplace opening for the rectangular form, and for the circular. - a- Fig. 14. MASONRY CONSTRUCTION. 195 CEMENT WALKS AND FLOORS. Where the curb is not already in place, stakes should be set to grade and to aline either edge of the walk, the other being obtained h y leveling over, taking care to allow an out¬ ward pitch on Fig. 15. the surface of about 1 in. per ft. Straight-edged strips should be nailed to the inside of each line of stakes, with top edges level with them, to form the mold for the concrete. The ground should he leveled off about 10 in. below the finished grade of the walk, and well settled by ramming, as at d, Fig. 15. A foundation a, 5 in. thick should then be laid, of either coarse gravel, stone chips, sand, or cinders, well tamped or rolled. The concrete should have the proportions of 1 part of cement, 2 parts of sand, and 5 or 6 parts of gravel, mixed dry ; then a sufficient quantity of water is added to make a stiff mortar. This concrete should he spread in a layer from 3 to 4 in. thick, as at b, and should he well tamped. Before it has set, the finishing coat c should he laid, and only as much concrete should be laid as can he covered with cement the same day, for if the concrete gets dry on top, the finishing coat will not adhere to it. The top coat should consist of equal parts of the best Portland cement and sand, or clean, finely crushed granite or flint rock, mixed dry, water being then added to give the consistency of plastic mortar. It should be applied with a trowel, to the thickness of 1 in., and be carefully smoothed and leveled flush with the tops of the guides. It is best to mark off the Avalk into squares, etc., by grooves } or | in. deep, so that in case it should crack, the fractures will follow the grooves and not disfigure the whole walk. In hot weather, the cement should not be allowed to dry too rapidly, but should be sprinkled occasionally. Usually a walk is ready for use in from 24 to 30 hours after completion, and the forms may then he removed. The same general methods above described apply to cemented cellar floors. 198 MASONRY. Fig. 16 . MASONR Y CONSTR UCTION. 197 198 MAS0NR Y. HANGERS, CAPS, ANCHORS, ETC. The use of joist and girder hangers, etc. simplifies greatly the work of framing both for house and mill construction. With these hangers a good bearing and firm support for the joists, girders, etc. may be had, and in case of fire the timbers may give way without injury to the masonry. At (a), (5), and (c), Fig. 1G, are shown the ordinary forms Fig. 18. of wrought-iron stirrups, or hangers; at (d), (e), and (/) are shown joist hangers for use in frame buildings; at ( g ), ( h), ( i ), and (j) hangers for use in brick walls. At ( k) is repre¬ sented a hanger for heavy girders or joists, adjustable to suit several sizes of timber by changing the bearing plate a, thus serving the same purpose as that shown at (7), which repre¬ sents a hanger made in right and left parts, and fastened MAS ONE Y CONSTRUCTION. 199 together by a bolt. Of the hangers shown, (c£), (g), (k) are the Van Dorn ; (e), (h), (i), (j), (0. the Du P lex 5 and the Goetz, types. At (a), (b), and (c), Fig. 17, are represented 2-member post caps; one is steel and the others are cast iron. At (d) and (e) are shown3-mem- ber post caps; at (/), (flO. and (h) t one steel and two cast-iron 4-mem¬ ber post caps. At (i) and (j) are shown two cast- iron wall-bearing plates; at (k), a steel wall-plate hanger; at (Z), a cast-iron box anchor for use over a 1 edged wall; at (m), (n), and ( o ), cast-iron bar anchors, the latter for I beams. At (p) is shown a steel base plate, and at ( q ) and (r), two forms of cast.-iron base plates. The caps, fa )''and (p), are the Van Dorn ; and those at anchor 1 passes t'hrongh the ’wall, as at (, a cast-iron washer, 0 ^ g h 5ar:"iS e nns of ties for anchoring ! Fig.19. 200 MASONRY. beams, channels, etc.; (a), (b), ( c ), and (d) represent ordi¬ nary wall anchors; (e) is a tie-rod anchor running through the wall, and (/) shows the upper I beams connected by a flsh-plate and secured to the girder by dips. When wall boxes or hangers are not used, templets, or bearing stones, should be placed under the ends of beams and girders, to distribute the weight evenly on the wall. They should be of tough stone, having a thickness of about 1 the least surface dimension, but not less than 4 in. It is weL to place flat stones above the joists, etc., so that any shrinkage in the latter will not affect the wall. The building laws of some cities provide that joists shall be supported on corbels, at least 4 in. wide. This is a good construction, but a cornice is required to conceal the corbel. ARCHES. The general forms of arches are semicircular, segmental, pointed, elliptical, etc., the name being determined by the Voussoir curve of the intra- dos, or inner curve of the arch. The outer curve is termed the extra- dos. The soffit is the concave surface of the arch. Vous¬ soir s or ring stones are the pieces com¬ posing the arch, the center or highest stone being termed the keystone or kcy- block. The first courses at each side are called springers, except in the case of segmental arches, in winch they are termed skewbacks. The voussoirs between the skewbacks or springing stones and the keystone collectively form the flanks or haunches, and t he spandrels are those portions of the wall above the haunches and below a horizontal line through the crown of the extrados. . See Fig. 20. The span is the horizontal distance between jambs, and ARCHES. 201 the perpendicular distance from the springing line to the highest part, or crown, of the soffit is the rise. The joints of circular and segmental arches radiate from a single center. In arches having two or more centers, the 'oints in each arc of the curve radiate from their respective centers. The joints of elliptic arches are found thus: Draw lines from each of the several points (spaced off on the intra- dos or extrados) to the foci, as shown at («), Fig. 21; bisect ihe angles thus formed, and the bisecting lines will give the direction of the joints. The joints in flat arches are drawn from the vertex of an equilateral triangle having the spring¬ ing line as a base. , . , , Examples. —At (a), Fig. 21, is shown a semicircular arch, of which a & is the springing line and c d the rise. At (6) is shown a segmental arch; the center a is taken on the line ab, which bisects the span cd. The radius of this arch equals approximately the square of the span divided by eight times the rise. For exact formula, see Sector, page o7. At (c) is shown a Moorish , or horseshoe, arch, the springing line ab being below the center from which the curve is struck making a sweep of about 230 degrees. A similar form is the pointed Moorish arch, differing from (c) only above the line cd, above which it takes the form of a iwo-centercd or pointed arch. These two arches are called stilted arches, from the fact that the center is raised above the springing me. Another example of stilted arch is shown at (d , m which the arch centers are on the line a 6, and the springing line c d ' S AtWfe shown a fiat arch built of wedge-shaped voussoirs together serving as a lintel; the joints radiate from a center at the vertex of an equilateral triangle of winch the span is 0D An/> is r r e "e abtweTby this construction rheZ^:^ — £ own weight and that of the “£ wstu rs - 202 MASONRY. 1 the same length us the springing line be. At (/;) is shown an arch in which the centers are taken inside the jamb lines, ARCHES. 203 thus flattening the arch ; in this example, the radius is equal to '$ of the span. At ( i) is shown a pointed arch having the span a b, and the height c d, which is greater than the span. To find the centers, proceed as follows: Draw the line a d, and bisect it by ef, which cuts the springing line at /, on JL^- CT f\ \ IT pK &/ 1 « 4 dl \ \\ \v ft b ■0 // (m) -ft c g (nj Fig. 21. (6.) ab produced. Then, with/as cen¬ ter and a radius/ a, one side of the arch may be drawn, the other half . being similarly found. At O') and (k) are shown examples of Jour-centered Gothic, commonly called Tudor, arches. At O') is repre¬ sented an arch in which the given span a b is divided into six equal parts, as at c, d, e, etc. To find the centers for the longer radii, with c and e as centers, and a radius ce, describe arcs intersecting at/; draw Jc and fe, and produce these 204 MASONRY. lines to g , A, i, and j ; the last two points will he the required centers. With c and e as centers, and a radius c a, describe arcs a g and b h ; with i and j as centers, and a radius i A, describe the arcs h k and g k. At ( k) is shown an arch of similar construction, but the span a 6 is divided into four equal parts. The distances a c and b d are each made equal to a b ; lines are then drawn from c and d through e and / and produced to g and A; the arcs are then struck in a manner similar to that shown at (j ). At ( l ) is represented an ogee arch, which is stilted one part in seven of the total height. The span is divided into six equal parts, and the centers for the lower arcs are taken at a and b, at each side of the center line c d ; the arcs are tangent on the outer line of the molded architrave, the posi¬ tion of e and / being determined by the width of the neck at g. At (m) is shown a three-centered arch having the span a b given. To lay out this arch, divide a b into four equal parts, as at cde; from a and b as centers, with a radius ae, describe the arcs ef and e/, intersecting on the center line fg. From c and e as centers, with a radius c a, describe the arcs ah and bi; and from / as a center, with the radius/A, describe the arc A g i, completing the figure. At (o) is shown a three-centered skew arch, which closely approaches an elliptic curve in form. To construct the arch, having given the required span a b and the height c d, proceed as follows: Take any point e on c d, and make aj and g b equal to e d. Draw / e, and bisect this line by the line A i, cutting the center line d c at A. Draw A/A and A gj ; vith/ and g as centers, draw the arcs a k and bj ; and with A as a center, draw the arc k dj. At (p) is represented a form of arch used for egg-shaped sewers. To lay out the curves, draw the springing line a b and the center line d e ; from / and g as centers, with a radius g c, describe arcs cutting the springing line in a and b ; with these points as centers, and a radius af, describe the arcs/A and g i. Divide the span g f into four equal parts by points/ c, and k, and from the points a and b as centers, with a radius a k, describe arcs intersecting the center line d e at the point l ; ARCHES. 205 now, with l as the center, and a radius l h, describe the arc h e i ; draw the upper curve g df, which is a semicircular arc struck from the common center c, thus completing the figure. To construct a rampant arch (such as is used for carry¬ ing a flight of stone steps), as shown in Fig. 22, the base line a b and the angle of inclination being given, draw ab to the required length, and at a lay off the angle of inclination; draw the line a c; bisect it, and at the points a, b J and c erect the lines ad,b e, and f g h, each perpendicular to a b. Now, through h —a point on the under side of the arch determined by the thickness required for the step backing and voussoirs— draw a line d e parallel to a c, completing the rhomboid adec. Divide the line ac into any number of equal parts, and divide a d and c e into one-hal f as many equal parts. From h draw lines to the points on ad and ce just found ; make gf equal to g h, and from/draw lines through the points on the line a c, producing them to intersect those first drawn, as at j, etc. These points then will be on the required curve, which may be readily traced through them. To locate the axes and foci of the ellipse, erect ck perpendic¬ ular to a c at c, and make it equal in length to g h. W itli g as a center, and a radius gk, describe an arc intersecting ec at l, a line drawn from l through the center g will give im as the major axis; and no, perpendicular to it at g, will be. the minor axis. Taking the distance g m as the radius, and with n as the center, describe arcs cutting the major axis at v and p ; these points will be the foci of the ellipse, and, alter maiking the thickness of the joints on the intrados, the joint lines may be drawn as explained for (?i), Fig. 21. N 206 MASONRY. RETAINING WALLS. A retaining wall is a wall built to rebut the pressure of earth, either wet or dry. In designing such a wall it is neces¬ sary to ascertain the character of the material to be retained. If the latter is rock, the wall evidently need not be as thick as if the material were wet clay, and would be merely a face wall. Any granular material, when unconfined, spreads out to its natural slope, termed technically the angle of repose, which varies with the material and also with the quantity of moisture in it. The slope usually taken in engi¬ neering work, as being safe for nearly all kinds of earth, is 1£ ft. horizontal to 1 ft. vertical, corre¬ sponding to an angle of 33° 42'. The pressure, then, which a retain¬ ing wall sustains, is evidently the weight of the prism of earth in¬ cluded between the back face of the wall a b, Fig. 23, and the plane b c, inclined to the hori¬ zontal at the angle of repose of the material—the earth having a level top surface. The amount and direction of this pressure are indeterminate, and so many varying factors enter into the problem that no attempt will be made to explain the theory of retaining walls, and only a few practical points will be touched on respecting their design. There is considerable diversity of practice in the propor¬ tioning of retaining walls. Most authorities, however, agree that the base should be from .3 to .5 of the height, the latter ratio being the greatest required under any but the most unusual conditions. The following proportions represent very safe—but not excessive—construction: In Fig. 24, let a h = 1; then g k *= .4; a b = £; g h — 5 cd, ef, etc. = from 9 to 12 in. each, the distance i k being divided up so as to make steps of about these widths. For example, let ah = 16 ft.; then gk — 16 X .4 = 6.4 ft., say 6 ft. 6 in.; gh = ^ of 16 ft. = 1 ft. 4 in.; ab = £ of 16 ft. = 2ft. 8 in.; cd, etc. = ( gk — gi) -h 3 = lOin. Fig. 23. RETAINING WALLS. 207 The preceding proportions are not intended to apply in their entirety to small walls less than about 6 ft. high, in such cases steps are usually unneces¬ sary, and the top width should not be less than 18 in., so that the wall may be sufficiently thick to withstand the action of frost on the backing. A wall designed as above indicated will be amply strong to retain a considerable surcharge, or bank, of earth sloping back above the top of the wall. Area walls that are supported at short in¬ tervals by cross-walls, beams, etc. do not need to be as thick as retaining walls which have no such bracing. The masonry courses, while usu¬ ally laid horizontally, should prefer¬ ably be laid sloping towards the embankment, to lessen the liability of slipping, and should be started below the frost line. The stones should be as large as possible, bonding and r-iah- -4ah- Fig. 24. breaking joints both longitudinally and transversely, built of brick, the bond should be the same as stone with broken joints, wherever possible, to make the wall a homo¬ geneous mass. The back should be left rough, to increase the friction between the wall and the backing, and the work progresses,'it should be coated thickly with hot cml tar or other waterproof material, as a precaution against tvater soaking in. Above thefrost level, on the upper surface "lIhe emhankment, the back of the wall tered sharply up to ^ “^^Tupon tim backing. T^preventthe^cumulaUorfo^water at the back of the wall, oor^ drain tiles should be laid at proper levels along the k i tiin W all to collect all surface and rift water, and dis f tt lme tough small openings, called weepers, left ^ wallTor ".rpose. The natural drainage of the soil never should be dammed up by a wall. 208 CARPENTRY AND JOINERY. CARPENTRY AND JOINERY. WOODS USED IN BUILDING. White, or Northern, pine is a light, soft, straight-grained wood, and is used in' building principally as a finishing material where a good but inexpensive job is required. Its power of holding glue renders it valuable to the joiner. Georgia pine, also known as hard pitch, or long-leafed, pine, has a dense dark color, and well-marked grain, on account of which it is sometimes used as a finishing material. The wood is heavy, hard, strong, and, under proper conditions, very dura¬ ble, but decays rapidly in damp places. On account of its resinous nature it does not take paint well. Georgia pine is often confused with Carolina, yellow, or Southern pine, which is greatly inferior to it. Loblolly pine, sometimes called Texas pine, has a close resem¬ blance to Georgia pine, but is of coarser grain, softer in fiber, and grows more sap-wood. It is largely used in the Southern states for framework and interior finish. Oregon pine, sometimes called Washington fir, while really belonging to the spruce family, so closely resembles pine that it is so called. While nearly as strong as Georgia pine, it is much lighter in weight, and more easily worked. Owing to the long lengths in which it can be obtained it is in demand for flagstaffs and long framing. Black spruce, growing in the Southern states and Canada, is light in weight, reddish in color, and though easy to work, is very tough in fiber. It is largely used for submerged cribs and piles, as it not only preserves well under water, but also resists the destructive action of parasitic Crustacea. White spruce, scarcely distinguishable from black, is largely used throughout the Eastern states for all classes of lathing, framing, and flooring. Norway spruce has a tough, straight grain which makes it an excellent material for masts of ships, etc. Under the name of white deal it fills the same place in European woodworking shops as white pine does in America. WOODS USED IN BUILDING. 209 Red spruce, growing in the Northeastern portion of the United States and in Canada, is similar to black spruce. Hemlock is like spruce in appearance, but much inferior in quality, is brittle, splits easily, and liable to be shaky. It is only used as a cheap, rough framing timber. White cedar, a soft, light, fine-grained, and very durable wood, lacking strength and toughness, is much used for boat-building, cigar-box manufacture, shingles, and tanks. Red cedar, a smaller tree than white cedar, similar to it in texture but more compact and durable, is of a reddish- brown color, and possesses a strong, pungent odor, which repels moths and other insects, making it extremely valuable as shelving for closets, and linings for chests and trunks. Cypress, a wood very similar to cedar, growing in the Southern part of both Europe and the United States, is one of the most durable woods, and well adapted for outside or inside work. Special care must be taken in seasoning it, as it tends to sliver and become shaky if forced in the drying. Redwood, the name given to one of the species of giant trees of California, grows to a height of from 200 to 300 ft., its trunk being bare and branchless for one-third of its height. The color is a dull red, and the wood, resembling pine, is used in the West the same as pine is in the East. As an interior finish it is capable of taking a high polish, and its color improves with age. White oak is the hardest of the American oaks, and grows in abundance throughout the eastern half of the United States. The wood, heavy, hard, cross-grained, strong, and of a light yellowish-brown color, is used where strength and durability is required, as in cooperage and carriage making. Red oak is darker and redder, coarser, more brittle, and of a more porous texture than white oak. English oak, though similar to American oaks, is superior to them for such structural purposes as ship building and house framing. Oak is especially prized as a material for cabinetwork, when the log is quarter-sawed. In first-class work, it is usually cut into veneers T 3 C in. thick, which are laid on cores of white pine or chestnut. The silver grain and the 210 CARPENTRY AND JOINERY. high polish that the wood is capable of receiving make it one of the most beautiful used in joinery. Hickory is the hardest and toughest of American woods, and, owing to the difficulty in working it, is very little used as a building material. Hickory is also attacked by boring insects. This wood possesses great flexibility, and hence is valuable for carriages, sleighs, and implements requiring bent-wood details. 1 Ash, the wood of a large tree growing in the colder portions of the United States, is heavy, hard, and very elastic. Its grain is coarse, and very much like bastard-sawed oak in appearance. Ash is sometimes used for cabinetwork, but its tendency to become decayed and brittle renders it unfit for structural work. The white ash is exceedingly tough, and is largely used for interior trim. It closely resembles white oak, and when properly filled can be brought to a high polish. Black ash has a brown, cedar-like appearance. Locust is one of the largest forest trees in the United States, and furnishes a wood that is as hard as white oak. It is composed of very wide annual layers, in which the vessels are few but very large and are arranged in rows, giving the wood a peculiar striped grain. Its principal use is in exposed places where great durability is required. As its hardness increases with age, it is used for turned ornaments and occasionally in cabinetwork. Black walnut is heavy, hard, porous, and of a purplish color, marked by a beautiful wavy grain. Strong, durable, and not subject to the attacks of insects, it is used generally for small cabinetwork, gun stocks, and interior decoration. The knotted roots of the tree furnish material with a curly grain, called burl, which is cut up into veneers. Cherry. —The wood of the wild cherry is moderately heavy, hard, very durable, and has a close, fine grain. It is suscep¬ tible of a high polish, and is much used for fine interior trim and cabinetwork. Cherry stained black to imitate ebony cannot be detected, except by scraping the polished surface. It is largely used for piano cases, furniture, etc. Birch strongly resembles cherry in texture, and in some species in color also. Black or cherry birch furnishes the best WOODS UbED IN BUILDING. 211 lumber, but is not as durable, and is more affected by atmos¬ pheric influences. Maple is a light-colored, fine-grained, strong, and heavy wood. The medullary rays are small and distinct, giving a silver grain to the quarter-cut lumber. It is used for flooring and interior trim, but for fine work it is used as veneers. Curly maple is maple in which the waviness of the grain is similar to that obtained from the roots of the walnut tree. Bird's-eye maple is produced in old trees by the circular inflection of the fibers. Though both the curly maple and the bird’s-eye are practically distorted fibers, and reduce the strength of the wood, they are highly prized in the cabinet¬ maker’s art. Chestnut is comparatively soft, close-grained, and, though very brittle, is exceedingly durable when exposed to the weather, and has recently come into use for interior finish. It is not as well suited for sills as locust. Butternut is of a light color and possesses a strongly marked grain. The lumber can be secured only in short lengths, and though soft and easily worked it will not split easily; it resists moisture, and remains unaffected by heat until the wood begins to char. It is not suitable for framing material, but is used in cabinet work on account of its taking a very high polish. Beech is hard and tough, of a close, uniform texture, which renders it desirable for tool handles and plane stocks. It is used but slightly in building, owing to its tendency to rot, but may be used where constantly submerged. Poplar, or whitewood, a lumber of the tulip tree, is a large straight forest tree, abundant in the United States. It is light, soft, very brittle, and shrinks excessively in drying. In color it varies from white to pale yellow. The cheapness and ease of working poplar cause it to be largely used for the cheaper grades of carpentry and joinery work, but it warps and twists exceedingly in even slight atmospheric changes. Buttonwood, also called sycamore, is the wood of a tree gen¬ erally known as the plane tree. It is heavy, hard, of a light- brown color, and very brittle. The grain is fine, close, and susceptible of a high polish. It is very hard to vork, liable 212 CARPENTR Y AND JOINER Y. to decay, and has a strong tendency to warp and twist under variations of temperature. On this account it is best used for veneered work. Apple and pear trees furnish wood to he used for tool handles, plane stocks, and small turned work. Neither is much used in building. Pear wood is sometimes used for carved panels, on account of its yielding so easily to edge tools. Boxwood is close-grained, yellow in color, and on account of its lack of shrinking and warping tendencies, very desir¬ able for small carved and turned work. It is particularly useful in wood engraving. Basswood is the name given to the American linden tree. In general appearance it strongly resembles pine, hut is much more flexible. It has a great tendency to warp, and will shrink both across and parallel to the grain. It is much used for curved panels. Mahogany is a native tree of the West Indies and Central America. The color, grain, and hardness of the wood vary considerably according to its age and locality of growth. It is used for the highest grades of joiner work. The straight- grained varieties do not warp or shrink materially with atmospheric changes, while the cross-grained varieties warp and twist to a remarkable extent, and can, therefore, be used to advantage only when veneered upon some more reliable wood. The soft and inferior grades from Honduras and Mexico are called baywood to distinguish them from the rich deep-red San Domingo or Spanish mahogany. Prima Vera or white mahogany is of a creamy color, very much like the baywood in texture, and makes a beautiful finish for fine work. Rosewood is a heavy, hard, and brittle wood, from several trees native to the tropical countries. It has a beautiful grain, alternating in dark brown and red stripings, which when well polished makes the surface one of the handsomest products of the vegetable world. As a veneer, it is applied to all kinds of cabinet, furniture, and joinery work where richness and durability are required, regardless of expense. Ebony, a dark, almost jet-black wood, native to the East Indies and parts of Africa, is heavy, strong, and exceedingly QUALITIES OF TIMBER. 213 hard, with an almost solid annual growth. It takes a high polish, and is used in cabinetwork ; its veneers are also applied to interior work. Lignum vitae is an exceedingly heavy, hard, and dark- colored wood. It is very resinous, difficult to split, and soapy to the touch ; it is used mostly lor small turned articles, tool handles, and pulley wheels. Sweet- or red-gum, a tree of large growth, is very plentiful in the Southern and Western States. It is soft in texture, but strong and tough, and strongly resembles light-colored walnut. It presents a very handsome appearance when selected and well finished, but has a tendency to warp and shrink, which makes it unreliable, unless used in veneered work. It is largely used for fine interior trim, and cabinet¬ work. Relative Hardness of American Woods. If the hardness of shell-bark hickory is assumed to be 100, other woods will compare with it as follows: Shell-bark hickory Pignut hickory ... White oak . White ash . Dogwood. Scrub oak . White hazel . Red oak . White beach. Black walnut. Black birch . 100 Yellow oak. . 60 . 96 White elm . . 58 . 84 Hard maple . . 77 Red cedar . . 75 Wild cherry . . 73 Yellow pine .— . 72 Chestnut. . 69 Yellow poplar . . 51 . 65 White birch . . 43 .. 65 Butternut . . 43 . 62 White pine. . 30 QUALITIES OF TIMBER. The best timber is obtained from mature trees, the fibers of which have become compact and firm, both by the drying up of the sap and by the compressive action of the bai k. There is a great difference both in appearance and strength between the heart-wood, or duramen , and the sap-wood, or alburnum; in the former, the fibers are firm and dense, and possess a deep color; in the latter, they arc opc n, poroiu, a filled with sap, and are usually of a pale color. The hea 214 CARPENTR Y AND JOINER Y. wood is much stronger, and less liable to decay and to the attacks of insects, than sap-wood. The medullary rays consist of vertical layers or sheets, radiating from the center, and connecting the pith with the bark, as shown at i and,/, Fig. 1. They are not, however, continuous, but are broken by the interweaving of the fibers. Those rays extending from the pith to the bark are called primary rays; those extending through only a portion of the stem are called secondary rays. The medul¬ lary rays are prominent in oak, beech, and sycamore, but are not so well defined in birch, chestnut, and maple. It is the presence of these medullary rays, sometimes called silver grain, that gives so much beauty to quartered oak. Fig. 1 represents a section of an oak or ash tree of 13 years’ growth, the coarse texture formed of the large sap vessels being shown at a, the closer texture at b, the bark at c, the primary medullary rays at i, and the secondary ones at j. Selecting the Stock. —In good lumber for building purposes, the heart-wood should be sound and mature, the sap-wood, or layers next the bark, being entirely removed. The wood should appear uniform in texture, straight in fiber, be free from large or loose knots, flaws, shakes, or any kind of blemish. When the rings are close and narrow, they denote a slowness of growth, and are usually signs of strength. When freshly cut, the wood should smell sweet; a disagreeable smell is a sign of decay. The surface, when sawed, should not appear woolly, but be firm and bright, and it should not be clammy and choke the saw. When planed, the wood should have a silky appearance; the shavings should come off like ribbons and stand twisting around the fingers. When the wood appears dull and chalky, and the shavings are brittle and friable, it is not first-class stock. Good lumber should be uniform in color; when blotchy or discolored it signifies a diseased condition. Fig. 1. QUALITIES OF TIMBER. 215 Imperfections. —There are various defects in timber which may he caused either by the nature of the soil in which it grew or by accidents due to storms, etc. Heart-shakes are cracks or partings of the fibers, radiating from the center of the tree. They are common in nearly all classes of timber, and are caused by the shrinkage of the inner layers incidental to loss of vitality; the cracks are wider towards the heart. Star-shakes are cracks radiating from the center, but differ from heart-shakes in that they are wider towards the bark ; they are caused by the rapid drying of young timber while it is full of sap. Cup-shakes are curved splits which separate the layers, and are caused by severe wind storms. Rind-galls are curved swellings, caused generally by resin¬ ous layers forming over a wound where a branch has been broken off. Foxiness is a yellow or red coloring, signifying the early stages of decay. Dry-rot is a fungus growth, and can be discovered by a black-and-blue tinge; the end wood is crumbly and crisp. Timber thus affected is of no permanent value, as the rot continues until the fiber becomes powder. Twisted fibers are caused by the twist ing tendency of winds blowing generally in one direction; such timber possesses little strength, owing to the oblique direction of the fibers. Knots are either stubs of branches or the gnarly growth formed where the branches are lopped off. Knots may be small and sound, in which condition they are not objection¬ able, or they may be large and loose ; if large, the strength of the timber is very much reduced, and, if loose or dark in color, they will ultimately fall out, loose knots being the stubs of dead branches. _____ QUARTER AND BASTARD SAWING. The term quarter sawed signifies that the log is cut into quarters before being reduced to boards, while the term bastard sawed denotes that all the saw cuts are parallel to the squared side of the log. In genuine quarter sawing (also 216 CARPENTR Y AND JOINER Y. called rift sawing) the cuts should he as nearly-as possible at right angles with the circles of growth, or parallel with the medullary rays a, as shown in Fig. 2; while in bastard sawing, the cuts are nearly parallel with the circles of growth and expose the edges of the medullary rays a and the full- Fig. 2. Fig. 3. face grain of the laminations, as shown at b' and c' in Fig. 3. The advantages in quarter sawing material having well- defined medullary rays are that it wears better, shrinks less, and the silver grain presents a very fine effect. Fig. 4 illustrates four methods of cutting the boards from the “ quarters.” The tree is first quartered by cutting it on lines ab and cd, after which the quar¬ ters may be reduced to boards by any of the methods shown. The best results are secured by the method shown between a and c, as the saw cuts are nearly on radial lines, and the full face of the silver grain will be exhibited. The section between c and b shows the next best method; fewer triangular strips are formed, but the boards will not present as rich an effect, as many of the medullary rays are CARPENTR Y JOINTS. 217 cut obliquely. The result of cutting the section between a and d, while economical in material, will not give as good results as the two former methods. Where thick material is desired, the system of cutting shown on the section between d and b is adopted, the cuts being made in the order in which they are marked. As before stated, the best effects are produced when the saw cuts come parallel, or nearly so, with the medullarj raj s, this is shown in Fig. 2. These rays on the end section are marked a, and are seen to cross the annual rings b and c at nearly right angles, so that the edges of these rings are exposed on the face, and through which the silver gram a' emerges. The value of quarter sawing does not consist merely in the beautiful figuring of the material, but as it places the medullary rays at right angles with the annual rings, it is found that the quartered material shrinks less than one-quarter as much in the width as the common- sawed stock. This is an invaluable virtue, which the joiner and cabinetmaker are not slow to appreciate. Quarter-sawed stock is also less sensitive to changes of temperature, and when once thoroughly seasoned and well put together, it makes an admirable finish both for interior treatment an* furniture, and its beauty is greatly enhanced with age. CARPENTRY JOINTS. A bevel-shoulder joint (a), Fig. 5, is a mortise and tenon used to unite inclined to upright or horizontal pieces. It is made by cutting beveled shoulders on the inclined piece and a corresponding sinking in the cheeks of the mortise o a P ° A Zrd^wuth joint (5) is an angular notch cut in a timber to allow it to fit snugly over the piece on which it rests A bridle joint (c) is one in which the mortise is supplanted by a tongued notch and the tenon by a grooved socket The tongue, called the bridle, is equal to about one-third thickness of the timber. . , ... A cogged joint {d), called also a corked joint, is made wit 218 CARPENTR Y AND JOINER Y. Fig. 5. (a) CARPENTR Y JOINTS. 219 Fig. 5. [b) 220 CARPENTRY AND JOINERY. a cog in the top of the lower timber, and a corresponding notch in the under surface of the upper timber. The cottered joint (e) is used in tightening up tie-beams to king posts, etc., and consists of a steel strap and slip wedges. In a notched joint (/), made by cutting a notch in each piece of timber, the notches are always less in depth than one-half the thickness of the material. The dovetail joint (g), used to obtain a close, rigid union, consists of a wedged-like pin cut in the end of one piece, and a corresponding notch in the other. A fished joint (h), used for joining timbers in the direc¬ tion of their length, is formed by butting the squared ends together and placing short pieces of wood or iron, sailed fish¬ plates, over the faces of the timbers and bolting or spiking the whole firmly together. The fox-wedged joint ( i) is used to secure the tenon in a mortise that is not cut through. Thin wedges of hard wood are placed in saw cuts in the end of the tenon. On driving in the tenon the wedges cause it to expand and fit tightly in the mortise, which is dovetailed or widened out at the back. A halved joint ( j ) is made by notching each piece one- half of its thickness, so that the top and bottom surfaces of both timbers are flush. Beveled or dovetailed halving is shown at ( k ). The scarf joint ( l ) is used where the timber has to be lengthened ; this joint forms a rigid splice. A lap joint (to) is made by laying one end of a timber over another and fastening them together with bent straps, which have screw ends by which they may be tightened. The efficiency of this joint can be increased by inserting hard¬ wood tongues across the faces in contact. The lip joint (n) is furnished with a lip a to make a stronger cross-section. It may also be applied to halved or dovetailed joints. A tusk-tenon joint (o) is formed by inserting a tenon into a corresponding mortise. The tenon is strengthened by a shoulder at the root called a tusk. The tenon is generally one-sixth the thickness of the timber, and is placed midway in the depth. The upper shoulder is beveled so as to avoid BALLOON FRAMING. 221 cutting away the material of beam into which it is inserted. This joint is a common one for uniting tail-beams to headers in floor framing. A checked joint (p) is made when two pieces cross each other, and it is desired to reduce the height occupied by the upper timber. „ The socket joint (q) is formed by inserting the ends of tim¬ bers into an iron casting. It is commonly used at the apex and toes of principal rafters. When used for the latter pur¬ pose, provision must be made to permit the evaporation of the sap. , , ... , , . The strap joint, shown in elevation and plan at (r) and (s), is made by girding the joint by a strong iron band. This joint is an approved method of tying the foot of a principal rafter to a tie-beam composed of two planks. . , I The tie joint (t) is one usually adopted to tie the incline rafter to the tie-beam, and prevent it from spreading. BALLOON FRAMING. In this system of framing, timbers of small section are used to construct a light, skeleton frame, whose rigidity depends entirely on its thin, canvas-like covering. This is the dis tinguishing feature of balloon framing compared with braced fraud,m in which the rigidity depends upon a well-arranged sssssa^ssssx points on good construction wfll be noted. After the wall a is completed, ,ai V n a -t1i°hSrrlouid hi kept°back ‘from L face 0^1, . that the outside Simple and triangles; g „:“c £££ ^ suro 222 CARPENTR Y AND JOINER Y. of the squares of the other two sides. This principle is illus¬ trated at the near corner of the sill in the figure. Lines are drawn on the top of the sill equidistant from the outer edges, and a nail is driven at their intersection. From this point 3 ft. is measured on one line and 4 ft. on the other, and nails are driven at the points marked. Where the pieces are square Fig. 6. to each other, the hypotenuse will measure just 5 ft. Tri¬ angles with sides which are multiples of 3, 4, and 5, such as 6, 8, and 10, 9, 12, and 15, etc., may he used also. The sill having been bedded, leveled, and squared, the cellar posts c are set up on base stones, and the beam d placed in position; the beam may be attached to the tops of the BALLOON FRAMING. 223 posts by toe-nailing, but a more workmanlike method is to secure it by means of iron drift-pins, driven through the beam from above ; or by inserting dowel-pins of wood or iron in the tops of the posts, and boring the beam to suit. In order to reduce the depth of the wood liable to shrink¬ age, the top of the beam is kept up 4 in. higher than the lower edge of floor joists e, gains, or notches /, being cut out of its upper edge, into which seats the joists are fitted ; unless this is done, the joists will be liable to split when loaded, as indicated at 1 and 2. At the wall bearings g the joists are simply checked over the sill, but the heels or bearing of the joists on the wall should be supported by wedging up each one with a piece of slate, after the joist has been spiked to the sill and stud. The space between the joists should be filled in with stone or brick (usually the latter) up to the top of the joists, and 7 in. higher between the studs, as at h ; this prevents the passage ot air-currents and lodgment for rats and mice. To equalize the shrinkage at the bearing beam and wall sill, the joists should rest on top of the sill instead of being checked over it, as shown; but in common work this is seldom done, as 4 in. of effective height of the stud would thus be sacrificed. In order to provide for the inevi¬ table shrinkage, the joists should be kept about £ in. higher at the center of the building. When 4" studs are used, a firm, solid corner post can be made by nailing a 2" X 4" stud to the face of a 4" X 6" scantling. The second tier of joists should be butt-jointed at the cen¬ ter partition i, toe-nailed into the plate j, and further secured from spreading by a fish-plate well nailed to each joist. Sometimes the joists are lapped over one another and spiked, which gives each joist a 4" bearing on the partition ; but this affects the equal spacing, and allows vibration, which may crack the plaster. Also, if hot-air pipes are to pass between the studs, the space thus contracted necessitates a narrower pipe, with less heating capacity. The wall ribbon is shown at k ; over this ribbon are notched the joists l. Where there are continuous partitions, the studs should be toe-nailed to the plate beneath and spiked to the second-floor joists. The plates being lapped and spiked to the plate 224 CARPENTRY AND JOINERY. surmounting the wall studs, tie the building lengthwise, and stiffen the partition. Before the building is sheathed, the corner posts m should be again carefully replumbed and adjusted by means of a plumb-bob suspended from the wall plate and run down to the sill, when the most accurate adjustment can be made. The sheathing n should be placed diagonally at an angle of 45°, and be well nailed to each stud with two or three nails, according to the width of the board. The butt joints should be cut on the center line of the studs. With boarding thus placed, well fitted and nailed, the structure is completely braced in a very simple and effective manner. The outer surface should be covered with a layer of heavy building paper o, lapped at the edges and tacked in place. Paper, being of close texture and a non-conductor of heat, makes an excellent covering material, rendering the building warmer in winter and cooler in summer. The base p should be capped to throw off the rain water, and should project about 1£ in. outside the wall. The corner boards, as at q, 1£ in. thick, should be firmly nailed in place, the inner edges being slightly beveled, so that the siding, when sprung in, will fit tightly. The siding r should be clear, white-pine boards, beveled on section, as shown, from f in. thick at the lower edge to x % in. at the upper edge, and generally from 4 in. to 5 in. wide, according to the weathering, or exposed surface. The siding should have a lap of 1 in. or more, and should be nailed at each stud, the nails being of sufficient length to pass through the boarding and enter the stud; this gives better results than if they are simply driven into the sheathing. The gauge , or exposed width, of the siding varies where it comes in contact with door and window frames, in order that the horizontal lines of the siding will aline with those of the sill and head of the frame. Great care should be exercised in fitting the siding in place; when cut to the required length it should be somewhat longer than the distance between the vertical casings, in order that, when sprung into position, the end fibers will enter the edge wood of the casings, and thus insure a close joint, even after the casings have slightly shrunk. BALLOON FRAMING. 225 Sizes in Inches of Framing in Buildings. Balloon-Frame Braced-Frame u Building. Building. y>p •a ° il coO 1 a> S Area, 1,500 Sq. Ft. or Less. 2 Stories High. Area, Dver 1,500 Sq. Ft. 3 Stories High. Area, 1,500 Sq. Ft. or Less. Area Over ' 1,500 Sq. Ft. Corner posts 2X4 2X6 2X6 2X6 10X10 spiked to 4X0 spiked to 6X8 spiked to 4X8 spiked to 6X8 Sills 4X8 4X10 4X10 4X10 6X10 Plates Two 2X4 Two 2X6 6X8 6X10 6X10 Interties 4X8 6X8 8X10 Girts Studs, 1X4 11X4 2" to 3" bearing 3X6 3X6 4X6 plank partition and 3X4 for parti¬ tions. opening Studs, wall and 2X4 2X6 2X6 3X6 partition 5X8 6X8 Braces 2X4 2X6 4X6 Sheathing 1X9 1X9 1X9 1X9 Two 11" Rough floor 1X6 1X6 1X0 1X6 3-41 Finished floor 1X4 1X4 1X4 1X4 1-1* 2X8 2X 10 3X8 3X10 4X10 Floor to to to to joists 3X10 3X12 3X12 3X12 10X12 Rafters 2X0 to 2X8 2X8 to 2X10 2X8 to 2X10 3X8 to 3X10 4X10 to 8X10 Tie-beam 3 2X6 2X8 2X10 2X12 226 CARPENTRY AND JOINERY. ROOF FRAMING. LENGTHS AND CUTS OF RAFTERS. The first step is to lay out a roof plan on a board or sheet of drawing paper, to a scale of, say, 1£ in. to 1 ft. Fig. 7 (a) represents such a plan of a roof of uniform pitch, the wing being the same width as the main building; one end of the roof is hipped, while the other ends are finished with gables, as may be readily understood by reference to the perspective view ( b). In both views, the same letters refer to the same parts. Length and Cuts of Common Rafters. —At the center of a b in (a), erect a perpendicular cc' equal to the height of the ridge above the wall plates; join c' and b ; then, the angle at b is the foot-cut, and that at e', the plumb-cut of the common ROOF FRAMING. 227 rafters. The length may he found by scaling. The angles are, transferred by means of a bevel to the rafter, as shown in (c), in which b is the foot-cut, and c the plumb-cut. Length and Cuts of Hip Rafters.— On the line that represents the hip on plan—as eg in (a)—erect a perpendicular ee' equal to the height c c' of the ridge ; join e' and g ; the angles at e f and g are the plumb- and foot-cuts, respectively, and the length may be found by scaling. The lengths and cuts for the valley rafter i h are in this case the same as for the hip rafter, and are found in the same way, as shown at h and i' in (a). Both hip and valley rafters have cheek-cuts, which are the same as those of the jack-rafters. Length and Cuts of Jack-Rafters. — Erect a perpendicular m e" at the center of the span / g ; with / as a center, and e' g, the true length of the hip rafter, as a radius, strike an arc cutting m e" at e"\ join / and e"', then the angle at e" is the cheek-cut. The foot- and plumb-cuts will be the same as for the common rafters. The length of any jack-rafter, as o p, is found by prolonging it to cut / e", as at p'; then op', measured by scale, is the length of op. Cheek-Cut for Rafters of Any Pitch.— On the face of the rafter draw the plumb-cut, as at a b, Fig. 8; parallel to a b draw d e at a distance c equal to the thickness of the rafter; square over from d to /, and join / and a, thus obtaining the cheek- cut. 228 CARPENTRY AND JOINERY. fix / i i \ i \ i \ / 1 / 1 £/ « 7 l i / l / \a i i 1 / IN h | 52 \ l X i -iN Lengths of Hip or Valley Rafters; Wall Plates at Right Angles. Having fixed the rise and run by the square for the common rafter, take 17 in. for the run of the hip or valley rafter. Thus, if the roof is -one-third, i. e., 8 in. rise and 12 in. run, the hip or valley rafters will have the same rise, 8 in., and 17 in. run. This rule gives results too great by about T 6 a in. in 10 ft. Lengths of Jack-Rafters. —Having obtained the lengths of the first two adjacent jack-rafters at the toe of the hip rafter, by the graphic or other method, measure the difference between their lengths, and keep adding this difference for the subsequent ones. Miter Cuts for Purlins. On the squared end of the purlin draw a plumb- line, as at a b, Fig. 9. Draw perpendiculars, as c and d, from the corners of the purlin to this line. On the upper edge of the purlin lay off' a distance d' equal to d, and on the lower edge lay off c' equal to c ; from e draw lines to the points marked, thus obtaining the lines for the cut. This is for a cut over a Fig. 10. hip rafter; where the cut is over a valley rafter, the bevel will be the same, but d' is laid off on the lower, and d on the upper, edge. Profiling Hip and Jack Rafters for a Curvilinear Roof.—In Fig. 10 the arrangement of the rafters is shown in plan, e g being a hip rafter, and h l a jack-rafter. In the elevation, b' c' is the span and oe' is the rise. To find the shape of the hip rafter eg, make e"g" equal in length to eg, and lay off e"k", k" h", etc., equal to ek, kh, etc. Erect perpendiculars at e", k", h", etc. At e, k, h, c, etc., drop perpendiculars ROOF FRAMING. 229 cutting the curve e' g' at k', h', etc. horizontals cutting perpen¬ diculars from e", k", h", etc., at the points e"', h"', etc. A curve drawn through these From k' h', etc. draw points gives the required out¬ line of the hip rafter. The shape of the jack-rafter h l is the same as the curve h' g'. PITCHES FOR A GAM¬ BREL ROOF. A method of determining the pitches for a gambrel roof is shown in Fig. 11. The line af is made equal to the width of the front plus the eave projections. On the center < 7 , with a radius equal to one- half of this measurement, describe a semicircle ahf; divide this into five equal parts, as at b, c, d, and e, and erect g h perpendicular to af. Draw ab and fe, the side slopes, and b h and e h, the upper slopes; then abhcf will be the outline of the roof. A PLANK TRUSS- Fig. 12 shows a trussed rafter suitable for a fiat pitch roof of from 30 to 40 ft. span, the rafters being set at from 230 CARPENTRY AND JOINERY. 21 to 3' centers. The rafters and joists are 2 in. X 8 inland of a good quality of spruce or hemlock. The lattice braces are 1 in. X 8 in., and are placed in pairs, one on each side of the main members, to which they are spiked. The spiking should be well done, especially near the supports. The tie-member is spliced at the center of the span by two 1" X 8" fish-plates, well spiked to the ceiling joist; two iron dogs, well driven in, further strengthen the splice. The roof is covered with H" X 6" tongued-and-grooved surfaced spruce, then with a layer of felt, upon which tin is laid. All other necessary details of construction are shown in Fig. 12. MISCELLANEOUS NOTES. SIDING A CIRCULAR TOWER. In covering a circular tower with beveled siding, as shown at (a), Fig. 13, it will be found, on bending the strip of siding around the cylinder, that the edges will creep upwards in the middle, as indi¬ cated at ( b ). This if owing to the slope ol the back of the siding, next the sheathing, caused by its lapping over the upper edge of the strip underneath; so that it really forms part of a conical sur¬ face. It will be neces¬ sary to find the slope length of the cone, to serve as a radius to describe the curvature to which the lower edge of the siding should be cut. Draw a vertical center line a b in (c), representing the center line of MISCELLANEOUS NOTES. 231 the tower, and at a point b draw c b and b d, each equal to one- half the diameter of the tower on the sheathing line, plus the thickness of the upper edge of the siding; from c or d draw a line towards a, having the same inclination as the back of the siding on the wall; the point where the line intersects a b‘ as at a, will be tne vertex of the cone, and a c will be its slope length, and also the radius for describing the curve ced. As the radius will be too long to lay down full size, any chord of the curve, as c e, may be used, from which offsets h, i, and j may be measured and laid down, so that the points can be fixed on the floor. A few wire nails being driven to mark the points, a flexible strip run around them will give a satisfactory curve, and the lower edge of the siding strip will be cut as at c' e'd' in (d), the curve of which is shown greater than it would be in practice, in order to emphasize it. The butt joints of the siding, as at c'd', being radial lines, must be cut square to the curve c' e'd'. Should special siding with a straight back to hug the sheathing, as shown at (e), be used, no curvature will be required for the lower edge, as, in sheathing a cylinder, boards with straight, parallel edges can be used. PROPORTIONS OF ROOMS. Church Dimensions.— In figuring the floor area it is usual to allow from 5 to 7 sq. ft. for each person. This includes space occupied by passages, pulpit, etc. Width between pews, back to back, from 30 to 34 in. Length of seat allowed for adults, from 18 to 24 in.; for children, from 14 to 16in.; height of seat, 18 in.; width, from 13 to 15 in. Schoolrooms— Width, from 16 to 24 ft. Height of level ceiling, 12 ft.; if floor area exceeds 360 sq. ft., 13 ft.; and if over 600 sq. ft., 14 ft. In one-story structures, where ceiling can be raised to tie-beams, the height to wall plate may be 11 ft., and to tie-beams 14 ft. Height of window sills from floor, 4 ft. Length allowed for seats of junior classes, from 14 to 18 in.; for senior classes, from 20 to 24 in. Distance apart for desks, back to back, 30 in. 232 CARPENTRY AND JOINERY. Acoustic Proportion of Rooms. —Height 2, width 3, length 5 or 6; or add height of platform to height of speaker, and half the width of the room for the height. Stable Dimensions. —Width for building with one row of stalls, 18 ft., occupied as follows: Hay rack, 2 ft.; length of horse, 8 ft.; for harness hanging against wall, 2 ft.; gutter, 1 ft.; and passageway, 5 ft. Height from floor to ceiling, from 12 to 16 ft. Width of stalls, from 5 ft. 9 in. to G ft. Loose boxes should he equal to at least two stalls. Stable doors, 4 ft. wide X 8 ft. high. Coach-house doors, from 7 to 8 ft. wide and 10 ft. high. Where practicable dispense with ceiling and place ventilator over each horse’s head. Corn bins should be lined with galvanized sheet iron. Glazed brick make bright and healthful walls; desirable tints are buff, cream, light green, and French gray. Paving should be of concrete or clinker brick. Stalls should have a fall of 4 in. toward gutter. Harness room should be isolated from the stable, and is usually placed between the stable and coach house. FLAGPOLES. For a flagpole extending from 30 to 60 ft. above the roof, the following proportions give satisfactory results : The diameter at the roof should be made fa the height above the roof, and the top diameter | the lower. To profile the pole, divide the height into quarters; make the diameter at the first quarter £§ of the lower diameter ; at the second quarter. I ; and at the third quarter, Thus, if a pole is 41 ft. 8 in. high above a roof, the lower diameter is fa of 41 ft. 8 in., or 10 in.; that of the first quarter, 9f in.; the second, 8£ in.; the third, 7^ in. ; and the top, 5 in. Flagpoles may be made of spruce or pine ; Oregon pine is preferable, and where the entire sap-wood is removed by cutting the pole out of the heart of a large trunk, a durable pole is obtained. The pole should be i>ainted with at least four coats of white lead, and should be capped by a suitable finial, terminating in a gilded ball. Halyards should be at least | in. in diameter, and be of waterproofed, braided cotton, or Italian hemp. MISCELLANEOUS NOTES. 233 PREVENTION OF DECAY. The destructive effect of water in causing rot of woodwork is well known, and precautions must he taken, in the con¬ struction of exposed surfaces, to lessen this result as much as possible. A few of these points are noted below. The decay of veranda posts resting on the floor is due to capillary action; every time there is a shower or the floor is washed, some water finds its way under the post and is absorbed. This can be avoided by the interposition of an iron shoe, to keep the post from contact with the floor. Water running down the faces of projections, as window sills, lintels, etc., at first drops off at the lower angle, but gradually forms a film across the projecting under surfaces; the drops are thus attracted into the stone or brick wall or the woodwork, as the case may be, causing disintegration of the mortar or decay of the wood. A simple preventive for this action is to groove or throat the under side, near the edge, causing the water to drip from the line of the groove. The necessity for this exists where there are horizontal projections exposing an under surface, such as water-tables, sill and lintel courses, copings, cap or drip members, and molded bands or cornices, whether of wood or stone. The lower sash of windows, unless properly constructed and kept well painted, suffers through capillary action. If a film of water is allowed to form be¬ tween the sills of the window frame and sash, it readily follows the vertical grain of the stiles; while the wind forces in rain until the inner sill is also wet. This may be prevented by form¬ ing grooves on the sill of the window frame and on thd lower edge of the sash, as shown in Fig. 14. Water absorbed between slates or shingles rusts the nails securing them, and also rots shingles. For this reason, slates too fine in texture are not as good as rougher ones, as the closer the contact of the surfaces, the better does capillarity Fig. 14. 234 CARPENTRY AND JOINERY. act. Sawed shingles are not as good as split ones, the woolly surfaces retaining moisture, and being more favorable to its ascent. Shingled roofs should neither be close-boarded nor have the shingles underlaid with paper, in order that the air may circulate and dry them more readily. Shingles should be well dipped in creosote before being laid, and afterwards thoroughly coated with it, to render them as impermeable as possible. Metal-roof flashings and valleys present surfaces between which water will creep up, and, unless they are made of sufficient width or height, the roof will not be water¬ tight. STEEL SQUARE. The standard steel square, shown in Fig. 15, is the one known to the trade as No. 100, but catalogued by some dealers as No. 1,000. The square consists of two parts, the blade, gen¬ erally 24 in. long and 2 in. wide, and the tongue, usually 18 in. long and 1| in. wide. The outside edges on one face are divided into inches and sixteenths, and on the other face the inches are divided into twelfths. On the inside edge the graduations are to eighth inches on one side and to thirty- seconds on the other. On the tongue, near its junction with the blade, Fig. 15 ( b ), will be seen a diagonal scale (shown enlarged in Fig. 16), used for taking off hundredths of an inch. The line a 5 is here 1 in. long, and is divided into 10 parts; the line c d being also divided into 10 parts, diagonal lines are drawn connect¬ ing the points of division as shown. For example, to take off .76 in., count off seven spaces from c, eg equaling .70 in.; now count up the diagonal line until the sixth horizontal line ef is reached ; then ef is equal to .76 in. On the same side of the tongue is the brace scale, which may be seen at C, Fig. 15 (5). This scale gives the length of a brace of given rise and run, or, in other words, the length of the hypotenuse of a right-angled triangle with equal sides. For instance, the hypotenuse of a triangle each of whose sides is 57 in., is 80.61 in. The length and end cuts for a brace of any rise and run may be found by using the square in a similar manner. MISCELLANEOUS NOTES. 235 Go the blade, Fig. 15 ( 6 ), is shown the board-measure scale, the use of which will be explained by aid of an example. Let it be required to find the number of board feet in a V X 7" board, 13 ft. long. Under the 12 " mark, find the num¬ ber 13, and follow the horizontal space in which 13 is found to the 7" mark; the answer is there found to be 7/5 ft. B. M. If the board is oyer 1 in. thick, the problem is solved in the same way, the result being multiplied by the thickness in inches. If the length of the board is greater than any num¬ ber given under the figure 13, it should be divided into parts, as in the following example: Required the contents i» board measure of a 2" X 9" plank, 23 ft. long. Divide the length into two parts, 10 ft. and 13 ft.; the contents of the 10' 236 CARPENTRY AND JOINERY. part is found, as before shown, to be 7f^ ft. B. M.; that of the 13' board to be 9 T % ft. B. M. Therefore the total contents (if 1 in. thick) is -f 9 T 9 2 = 17 T 3 2 ft. B. M.; but as the board is 2 in. thick, the contents are 2 X 17^, or 34£ ft. B. M. The octagonal scale, found on the tongue at A B, Fig. 15 (a), is used in inscribing an octa¬ gon in a square. The scale is marked 10, 20,30, etc. To inscribe an octagon in a 12" square (see Fig. 17), b draw the lines a b and c d, bisecting the sides; from d markde and d/, each equal to 12 divisions on the octagonal scale; mark bg, etc., in the same way, and draw eg, a side of the required octagon. The other sides may be similarly found. For a 10" square, make d e equal to 10 divisions; for a 7" square, equal to 7 divisions, etc. In Fig. 18 (a) is shown an adjustable fence, a strip of hard Fig. 18. wood about 2 in. wide, 1£ in. thick, and 2 l s ft. long. A saw kerf, into which the square will slide, is cut from both ends, leaving about 8 in. of solid wood near the middle. The tool is clamped to the square by means of screws at convenient points, as shown. Let it be required to lay out a rafter of 8' JOINER Y. 237 rise and 12' run. Set the fence at the 8" mark on the blade, and at the 12" mark on the tongue, clamping it to the square with li" screws. Applying the square and fence at the upper end of the rafter, we get the plumb-cut d e at once. By apply¬ ing the square, as shown, twelve times successively, the required length of the rafter and the foot-cut c b are obtained. In this case the twelve applications of the square are made between the points c and d. Bun and rise must also be meas¬ ured between these points. If run is measured from the point b, which will be the outer edge of the wall plate, it will be necessary to run a gauge line through b parallel to the edge of the rafter, and subtract a distance eg from the height of the ridge, to give us the correct rise. The square must then be applied to the line b g. A rafter of any desired rise and run may be laid off in this manner by selecting proportional parts of the rise and run for the blade and tongue of the square. For a half-pitch roof, use 12 in. on both tongue and blade; for a quarter-pitch, use 6 in. and 12 in.; for a third-pitch use 8 in. and 12 in., etc. The terms half-pitch, quarter-pitch, etc., refer to the height of the ridge expressed as a fraction of the span. JOINERY. JOINTS IN JOINERY. A beaded joint (a) Fig. 19, is one disguised by a quirked bead which is worked on one edge; this joint is used in matched lining, etc. Butt joints ( b ), (c), and (d), are used for returns, when one piece is fitted to the edge of anothei’, and may be rebated, matched, or plain-butted, as required. The feathered or slip-tongue joint (e), formed by plowing correspoixding grooves in adjacent pieces and filling it with a slip tongue, is generally employed for plank flooring. A grooved, tongued-and-mitered joint (/) possesses the quali¬ ties of strength and effectiveness, and no edge grain is exposed. The half-lap dovetail joint ( g) is a form in which the dove¬ tails appear only on one side, and is the method adopted for drawer fronts. P 238 CARPENTRY AND JOINERY. Fig. 19. JOINERY. 239 The lapped-and-tongucd miter joint ( h ) is somewhat similar to (/), but a slip tongue is inserted instead of being worked out of the solid material. A lapped miter joint (i) is made by rebating and mitering the boards to be joined, and securing them with nails. A miter-and-butt joint (j) is a good form for an angle joint and is simpler than ( i). A miter-keyed joint is a miter strengthened by a slip feather, as at ( k ), or with slips of hard wood fitted into saw kerfs, as at (0- A rabbeted joint (m) is formed by cutting rectangular slips out of the edges of the boards to a depth generally equal to one-half of their thickness, the tongues thus formed being lapped over each other. A rule joint ( n) is a hinged joint used for the leaves of tables, etc. Beveled joints ( o) and (p) are formed to close tightly and exclude the wind and water. The blind dovetail joint (q), used for boxes and cabinets where the dovetails are not to show, is made by dovetailing three-fourths of the thickness of the board and mitering the other fourth. DOORS. Proportions.— The ratio between the width and height of doors at main entrances and in public buildings is usually as 1 to 2; that is, the height is twice the width. For single doors in dwellings and offices, the ratio should be as 1 to 2 \; or the height should be ‘2k times the width ; doors 2' 8" X 6' 8" and 8' X 7' 6", are thus proportioned. The width of a door is regulated by the purpose for which it is intended ; in public buildings provision is made for the passage of several persons at a time, while in private houses and offices a width suitable for one person is sufficient. In the former case, the width may be from 6 to 14 ft., while in the latter, the general rnle makes the minimum width 2 ft. 8 in. for communicating doors, and 2 ft. for closet doors. A hinged door more than 4 ft. wide should be made double; that is, in two folds. As double folding doors take up much 240 CARPENTRY AND JOINERY. wall space when kept open, sliding doors are frequently sub¬ stituted. Where there are several doors of different widths in the same room, to give a better effect to the interior treat¬ ment the height of the principal doors should be fixed by the proportion given, and the others made the same height. If the width of double or sliding doors does not exceed 6 ft., the height may be that of principal doors, but if wider, the height should he one-fourth more than the width. The width of sliding doors, however, is largely regulated by the depth obtainable for the pocket in the partition. Framing. —The width of the stiles and top rail should be about one-seventh the width of the door, the bottom rail about one-tenth the height, and the muntins and lock-rails £ in. less in width than the stiles. The thickness will depend somewhat on the style of finish and the class of lock to be used. If the door framing is solid and rim locks are used, the thickness for chamber doors may be 1\ in.; if mortise locks are used, the thickness should not be less than 1£ in. Solid doors for principal rooms are made from 1£ in. to 2 in., and entrance and vestibule doors from 2£ in. to 2£ in. thick. When doors are veneered, the thickness is usu¬ ally increased £ in. When mortise locks are used, the doors should, for strength, be framed with a lock-panel so that the joints adjacent to the lock will not be injured. Construction. —The mode of con¬ structing a 5-paneled door is shown in Fig. 20, certain parts being re¬ moved to clearly show the joints. The parts marked a are the outer stiles; b, the muntins; c, the bottom rail; d, the lock-rails; e, the top rail; /, the lower panels; g, the lock-panel, and h, the upper panels. The mortises i are made one-third the Ihickness of the framing into, which the JOINERY. 241 tenons j are fitted. The edges of the framing are grooved i in. deep, to receive the panels, the width of the groove being the same as the thickness of the tenon. The upper edge of the tenons of the top rail and the lower edge of the tenons of the bottom rail are haunched, as shown at k. The bottom rail has double tenons with a bridge between the mortises. The muntins are mortised into the rails. The panels should be kept from } to T 3 ^ in. less than the width of the space between grooves, to permit expansion. In putting the door together, only the shoulder, or that portion of the tenon next the panel, should be glued, so that in case of shrinkage or swelling the joints will remain close. When the stiles are driven up and the clamps applied, the wedges l should be well fitted, should have the edges next the tenons brushed with glue, and be driven tightly in. The horns m, or extra lengths of the stiles during construction, are designed to withstand the pressure exerted when the end wedges are driven in, which would otherwise be forced out by shearing the fibers of the wood beyond the mortise, thus destroying the joint. Fitting. —The width of the door should be about T 3 5 in. less than the width between the jambs, allowing a clearance of about 3 3 2 in. on each side, and the opening edge should be slightly beveled. The standard bevel to which locks are made is } in. in 2| in., but where the door is narrow, it may require the lock-face beveled to as much as £ in. in 2 in., or even more. An equal clearance should be left at the upper rail, while the bottom rail may require from | in. to i in., in order that the door may swing clear of the floor covering. Where “saddles” are used—which are not to be recom¬ mended—the door may fit within 3 3 5 in. An appreciable amount of the clearance will be taken up by the layers of paint or varnish. Butts. —A simple rule for finding the width of butt required for any door is: To twice the thickness of the door, less £ in., add the greatest amount of projection of any part of the door casing beyond the face line of the door (which is usually the base block). Thus, if a door is 2 in. thick, and the base block projects 15 in., the width of the butt will be 2 in. + 2 in. 5 in. + 1 j in., 242 CARPENTRY AND JOINERY. or 5f in., in which case a b\" width would be used. The edge of the butt will thus be kept | in. back from the face of the door. One-half of the thickness of the butt should be out out of the door, and one-half out of the jamb of the frame. In locating the butts, it is usual to keep the lower end of the lower butt in line with the upper edge of the lower rail, while the top end of the upper butt may be kept from 6 to 7 in. below the upper edge of the top rail. Where three butts are used, it is well to keep the lower end of the intermediate butt in line with the upper edge of the lock-rail, instead of placing the butt midway between the upper and lower butts, as the butts will then line up with the framing. By keeping the pin of the lower butt slightly in advance of the upper butt, the door, in opening, will rise at the toe and increase the clearance, so that inequalities in the floor level may be overcome. For first-class working doors the following con¬ ditions must be observed: first , the floor must be level in every direction; second , both jambs of the door frame must be accurately plumbed, facewise and edgewise, else the toe of the door will either rise above or fall towards the floor when operated; third , the head-jamb, or transom, as the case may be, must be level; fourth , the butts must be of good quality, well fitted, and the pins kept true to line. , WINDOWS. Area.— The following proportions are given by different authorities for fixing the amount of window surface : (1) One- eighth of the wall surface should be windows. (2) The area of glass should equal at least ^ of floor area. (3) One square foot of glass should be allowed to 100 cu. ft. of interior space to be lighted. It is better to have a surplus than a deficiency of light, as if too bright, it can be regulated by blinds or shades. Design. —The height of the window should be twice its Width. Architraves should be from £ to } the width of the window opening, and where pilasters adjoin architraves their width should equal that of the latter. Where consoles are used their length should not be less than | nor greater than \ the width of the opening. The entablature should JOINERY. 243 oe from i to ^ the height of the opening. Where engaged columns flank windows, at least f of the column should pro¬ ject beyond the face of wall. To obtain a uniform frieze line around rooms in dwell¬ ings, it is well to keep the window and door heads equi¬ distant from the ceiling. Thus, where the walls are 10 or 10i ft. high, and the doors 8 ft. high, the top of the casing is from 18 to 24 in. from the ceiling. This space may he occupied by frieze and cornice, or a picture mold may extend around the room in line with the upper edge of the door and window casings. Where ceilings are not over 14 ft. high, this same effect can be obtained by introducing transom sash over the doors, filling these with either chipped plate or art glass. The glass line of windows in dwellings should be about 30 in. from the floor for principal rooms, and about 36 in. for bedrooms. In all cases, the heads of windows should be as near the ceiling as the construction and interior scheme of treatment will permit, to obtain better light and ventilation. The meeting rails of window sash should be placed not less than 5 ft. 9 in. above the floor; otherwise, the rail will be on a level with the eyes, obstructing the view and detract¬ ing from the effect of the window. On this account the height of the upper sash is sometimes made only i that of the lower, or j the clear height. For buildings of any preten¬ sions, it is a mistake to cut up the sash into small panes. It should be remembered that windows are designed for the purpose of lighting, and all obstructions created by sash bars detract from the desired result. Where the designer prefers to have window sash subdivided, metallic bars of zinc, copper or lead will be found more durable than wood, and will not take up so much of the daylight area. Sashes should slide vertically, counterbalanced by means of cord, chain, and weights, or by spring sash balances Those that are hinged and open inwards cannot be made water-tight, and those opening outwards are likely to be injured by e action of wind, so that for general service the best results are obtained by use of sliding sash. Sash stops should be fastened with screws passing through slotted sockets, thus preventing the sashes from rattling and v arping. 244 : CARPENTRY AND JOINERY. Construction.— In Fig. 21 is shown a view of a window frame with sliding sash, adapted for a frame building. The pulley stile a may be from If- to If in. thick, and should he tongued into the blind stop b and the plaster cas¬ ing c, each of which is \ in. thick. These tongues make the stiles rigid, pre¬ venting them from deflect¬ ing sidewise when the sashes are being operated. An open space of from 2 to 2£ in. is left between the back of the pulley stile and the rough stud, thus form¬ ing a box for the weights. A movable pocket for the insertion of the weights is cut out of the lower portion of each pulley stile on the inside , so that it may be covered by the lower sash. The parting strip d is f or f in. thick, and passes into a groove f in. deep in the pulley stile. The outside casing e, If in. thick X 5 in. w'ide, is firmly nailed through the blind stop into the pulley stile and to the wall sheathing. The inner face of the window frame is finished with a casing, which may be of any style of finish—in this case, by an architrave, the width being sufficient to cover the plaster joint. The sash stop g, from f to f in. thick, is secured with round-headed screws passing through slotted sockets for adjustment. The members g, d, and b should be kept in line, their projection beyond the face of the pulley stile being regulated by the thickness of the sash stop. The sill h, from If to If in. thick, is tongued into the pul¬ ley stiles and well nailed. Sills are sometimes made with a straight inclined surface instead of being worked with two facias, as shown. When water collects on the sill, it is readily drawn under n, the lower rail of the sash, by capillarity, or driven in by wind; by raising the surface under the sash JOINERY. 245 above the level of the outer portion, and running a small rounded groove in the fillet, the effect of the wind is to divert the water outwards. Under h is placed the subsill i, It in. thick which is attached to the pulley stile, and likewise grooved for the reception of the beveled siding j. For dur¬ able work, the window frames should be put together with stiff white-lead paint, particularly adjacent to the sill and subsill. The sashes k are made from If to If in. thick. Strength is added to the upper sash by the elongation of the stile forming a molded horn, as by this device the tenon of the meeting rail m can be made equal to its thickness. The meeting rails, If to If in. thick, according to width of open¬ in'* may be double- or single-beveled, as shown, so that they will come tightly together when closed. The lower rail n may be from 3 to 4| in. wide, and should be accurately fitted to the sill; the outer edge should be clear about | in., but the inner portion should be in contact with it, thus preventing the ready passage of water. The inner face should be rehated and beveled to fit the edge of the stool o. 11ns stool should be rebated to form an air-tight joint, and be bedded m white lead An apron p is fixed to the edge of the sill and to a Blaster ground q, and finished with a bed mold as shown. The length of the apron should be equal to the width from out to out of casings, and have the moldings returned on ^^n Fig. 22 is shown a box-frame window, suitable for a stone orVick wall. The general design and construction of the frame and sash are similar to that shown in F>g. 21 the milv changes being in parts that require to be adapted to a new condition. In brick walls it is usual to set the window frames during the erection of the walls, thus facilitating the plumbing of the brick jambs, particular care being taken o bmce the frames, in order to keep them plumb and level. By keeping the blind-stop casing a 1 m. wider than the back lining the frame can be firmly held in place after the braces have been removed. The sill c, made of 3" plank, is (or should be) bedded in haired lime mortar, or for first-class work stiff white-lead paint and white sand. The groove on the bed permits the formation of a mortar tongue, making it 246 CARPENTRY AND JOINERY. practically air-tight; the slightest shrinking and warping of the sill allows the passage of air and water, unless this device is adopted. A finished casing d may be attached to the inner frame casing e , after the building is ready for trimming, thus covering its marred condi¬ tion. The win¬ dow stool or seat f rests on furring strips, and is tongued into the sill, providing for its expansion and contraction; it is generallyfinished with a molded apron g. The jamb lining h is tongued into the finished casing, and the opening trimmed with a casing, such as i, nailed to the lining h and the rabbeted plaster ground./. The hanging stile k in brick-set frames is attached thereto before setting, but where outside blinds are not used, an angle mold may be substituted. In stone walls, window frames are not usually set until the building is roofed and either prepared for the plastering, or when the plastering has been completed. There are two reasons for this, the principal one being the difficulty experienced in setting jamb stones and lintels while the frame is in position, and the second that, with all due care, the frames are more or less damaged during building opera¬ tions and are never so true to line, level, and plumb as those set in place after the walls are completed. When set in this latter order, it is necessary to encase the masonry openings with screeds or wooden strips, carefully alined and plumbed, JOINERY. 247 and so arranged to allow for a bed of haired mortar iin. thick around the jambs and window head. The frames are secured by means of holdfasts or wall plugs. When set In this manner, the casing d is not required, unless it be that the interior trim is of a material different from that of the window frame. NOTES ON STAIRWAYS. Proportioning Treads and Risers.—1. Take the sum of two risers and subtract it from 2U inches ; the result will be the width of the tread. This rule is based on the assumption that an average step is 2 ft. and that the labor of lifting the foot verti¬ cally is twice that exerted in moving Treads. Risers, horizontally, consequently the width Inches. Inches. of the tread, added to twice the height 6 8£ of the riser, should be equal to 2 ft. 7 8 2. The first column of the accom- 8 7£ panying table gives the width of treads; 9 7 the other gives the corresponding height 10 of risers. 11 6 3. The product of the tread and risers 12 5? should equal 66 inches: thus, with a tread of 11 in. the riser would be 6 in.; with a riser of 7 in., the tread would be 9f in. Miter Bevel for Stringer Cut.—The following method is of service in ob¬ taining the accurate bevel to apply on the edge of a stair stringer, where it is desired that the riser miter with the stringer, as in an open string stairway. By the use of the pitch board, mark on the outside face of the stringer the cuts for the treads and risers, as in Fig. 23. Draw be parallel to ad. 248 CARPENTRY AND JOINERY. and at a distance t from ad equal to the thickness of the stringer. At b, draw be square across the upper edge of the stringer, and connect c and a. Then bac is the miter bevel required. At a' is shown a bevel set to the line obtained, so that it can be used at all the other riser lines. DEVELOPMENT OF A RAKING MOLD. In Fig. 24 is shown a method for determining the cross- section of a raking mold to miter with a given eave mold. This method will apply equally well to any mold¬ ing. The eave mold in this case is a cyma recta, the profile being shown as abfhjc. Divide the out¬ line into any number of equal parts, as at/, h, j, etc. Draw any horizontal line Ik and erect perpendicu¬ lars from /, h,j, etc., cut¬ ting the line Ik. Draw a l" at the required angle and draw be, fg, etc., parallel to al". From any point l', lay off the distance l' k f and subdivisions equal to l k. Drop perpendiculars to al’’ from V, k', etc. intersecting be, fg, etc. Through the intersections thus found, trace the curve V c', which is the profile of the required mold. To find the profile of a vertical cut in the raking mold, at any point, as l", lay off l" k" and subdivisions parallel to l k. Proceed to find points e, g, i, c", etc., as before. HOPPER BEVELS. In making hoppers or boxes with inclined sides, it is necessary to obtain the face and edge bevels; when the sides are mitered, the edge bevel is called the miter bevel, and when they are butted, it is termed the butt bevel. In Fig. 25 the diagrams are assumed to be laid out on a board, as if in bench practice. JOINERY. 249 In (a), let c b be the width of a side of the hopper, and ce the splay ; let c be on the edge k l. Strike the arc pj, and draw cj square to k l ; then cj is the width of the stuff. Lay out the thickness b a ; draw a d parallel to c b ; also, c d parallel to ba ; and cbad will represent a section of the W Fig. 25. board. Project b to b', and draw cb then the angle gb'c will be the face bevel. Make h h’ equal to b a, and draw g' h'; project a to a'; and draw b'a', then gb'a' will be the miter bevel. If the edges are cut off along the line f a, the miter bevel will be 45°. If the hopper is to have butt joints, the face bevel is found as above shown. To obtain the butt bevel, proceed as follows : Draw af through a, parallel to g h ; project / to / on g' h', and draw b'f ; then the angle g b'f will be the butt bevel. In (b) is shown a perspective view of the board kg hi, with the bevels in position, gb'c and g b' a ' being those required for a miter-jointed hopper, and gb'c and gb'f those for a butt-jointed one. At c"f b' c, is shown an outline of the butt joint, and at c c'"a' b' that of the miter joint. DIMENSIONS OF FURNITURE. Chairs and Seats.— Height of the seat above the floor, 18 in.*, depth of the seat, 19 in.; top of the back above the floor, 38 in. Chair arms are 9 in. above the seat. A lounge is 6 ft. long and 30 in. wide. 250 BOOFim. Tables.—Writing and dining tables are made 2 ft. 5 in. high. Dining tables extend from 12 to 16 ft., by means of a sliding frame. There should be 2 ft. clear space between the frame and the floor. Bedsteads. —These are classed as single, 3 to 4 ft. wide; three-quarter, 4 ft. to 4 ft. 6 in.; and double, 5 ft. wide. All bedsteads are from 6 ft. 6 in. to 6 ft. 8 in. long inside. Foot¬ boards are 2 ft. 6 in. to 3 ft. 6 in., and headboards from 5 ft. to 6 ft. 6 in. high. Other Furniture. —For bureaus convenient sizes are; 3 ft. . c in. wide, 1 ft. 6 in. deep, 2 ft. 6 in. high ; or 4 ft. wide, 1 ft. 8 in. deep, 3 ft. high. Commodes, or night stools, are 1 ft. 6 in. square on the top, and 1 ft. 6 in. high. Chiffoniers are 3 ft. wide, 1 ft. 8 in. deep, 4 ft. 4 in. high. Cheval glasses are made about 5 ft. 6 in. high, 2 ft. wide. Washstands of large size for portable bowl and pitcher are 3 ft. long, 1 ft. 6 in. wide, and 2 ft. 7 in. high. Small sizes are 2 ft. 8 in. long. Wardrobes are from 6 ft. 9 in. to 8 ft. high, from 1 ft. 5 in. to 2 ft. deep, and from 3 ft. to 4 ft. 6 in. wide. Sideboards are from 5 to 6 ii. long, about 2 ft. 2 in. deep and 3 ft. 3 in. high. Upright pianos vary from 4 ft. 10 in. to 5 ft. 6 in. in length, from 4 ft. to 4 ft. 9 in. in height, and are about 2 ft. 4 in. deep. Square pianos are about 6 ft. 8 in. long by 3 ft. 4 in. deep. ROOFING. SLATING. A good slate should present a bright, silk-like luster, and should emit a clear metallic ring when tapped; if it is soft, it will present a dull, lead-like surface, and emit a muffled sound. When cut, the edges should show a fibrous-like texture, free from splinters, and the material should not show signs of being either brittle or crumbly. It is this element in slate, which may be called its temper, that largely defines its value; if brittle or too hard, the slate will be liable to fly to pieces when being squared and punched, or to be readily broken when being nailed in place. If the slate ROOFING . 251 is soft, it will, by absorbing moisture, be liable to be attacked by frost, so that the edges will crumble away, and the slates will work loose, owing to the nail holes becoming enlarged. There are many varieties of color in slate, due to the pres¬ ence of iron and mineralized vegetable substances. The pronounced colors are bluish black, blue, red, and green, while many tints of these shades exist, blending into grays and purples. The commercial classification is based on straightness, freedom from curled and warped surfaces, smoothness of surface, and uniformity of color and thickness. The best way of judging the classification is to examine samples of the various grades. First-class slate should be hard and tough, non-absorbent, unfading, straight-grained, free from ribbons and other imperfections, and of uniform color throughout. No better test of the weathering qualities of slate can be contrived than the simple one of examining roofs where it has been in service for several years. The sizes of slate range from 6 in. X 12 in. to 16 in. X 24 in., there being about 25 different sizes. The size to select depends on the character of the edifice and its location; for ordinary dwellings, a common size is 8 in. X 16 in. The thickness of slate is about T 3 g in., or 5 to the inch ; for extra- strong roofs, slates } in. thick are used, while with the larger- sized slates, the thickness is | in. or more. Slate weighs 175 lb. per cu. ft., and if A" slates are used, the weight of the material on the roof will average 6? lb. per sq. ft. of surface covered. Slates are sold by the square, meaning that this quantity will cover 100 sq.ft, of roof surface; an ordinary railroad car has a capacity of between 40 and 50 squares. The roof being devised for protection against the elements, particularly rain and snow, the steeper the pitch, the more effective will be its power to shed them; while the wind will not so readily blow rain under the courses, nor strip them off so easily. Where slates arc small and light, and exposed to violent winds, the greater the necessity for increasing the pitch. Experience shows that the minimum pitch for slate roofs varies with the size of the slate. The pitch may be expressed either by the angle which the roof makes with the 252 ROOFING. horizontal, or by the ratio of the height of the ridge to tne span; the latter expression is the one generally employed. (See Table VII, page 68.) For large sizes of slate the pitch should not be less than 21° 50', or one-fifth; for medium sizes, 26° 33', or one-fourth; and for the smaller sizes, 33° 41', or one-third. Slates are laid on either strips or boarding; the latter costs the most, but the results justify the extra cost. Close boarding makes the roof a better non-conductor of heat, and is required for strength where thin slates are used. In Fig. 1 is shown a sectional view of a roof on a frame build¬ ing, where theslates are nailed to strips a. These strips are usually from 1 to 1£ in. thick and 2y or 3 in. wide, and are well nailed to the rafters; the distance between centers of the strips should be equal to the gauge or ex¬ posed portion of t he slate. The lowest strip is thicker than the others, so as to tilt the first course enough to insure a close-fitting joint between the first two thicknesses. In commencing to slate, the first course is laid double, the lower course being laid with the back or upper surface of the slate downwards. The length of this course will be equal to the gauge plus the lap. The lap is the distance that the upper slate overlaps the head, or upper end of the second slate below it, and should not be less than 3 in., although slaters sometimes use only a 2" lap. The gauge or exposed length of the slate is equal to half its length after deducting the lap. ROOFING. 253 There are several ways of nailing the slate, either near the head or at the shoulder, in which the distance of the holes from the head will he slightly less than the gauge of the slate, to enable them to clear the head of the one underneath. Another method of laying slate, where economy is desired, is that known as half slating , in which a space is left between the edges of the slate in each course equal to one-half the width of the slate. By this method, only two-thirds of the usual number are required to cover a given surface. This class of work is adapted for covering sheds, and while serviceable under ordinary conditions, will not be water¬ tight under the action of driving storms of rain and snow. Slate nails have large flat heads, so as to have a good hold on the slate; their lengths vary with the thickness of the slate, and are usually called 3-penny or 4-penny*, having lengths of 1£ in. and If in., respectively; the proper length should be twice the thickness of the slate plus the thickness of the boarding. To prevent rust, slate nails are usually gal¬ vanized iron or steel; sometimes they are tar-coated. For extra-good work, copper nails are used. For other data on Slating, see page 351. TIN ROOFING. There are two kinds of tin-roof coverings in common use, namely, flat seam and standing seam. In the for¬ mer method the sheets of tin are locked into one an¬ other at the edges, and nailed to the roof-boards as shown in Fig. 2. Six or eight 1" wire nails are Fig. 2. allowed to the ordinary sheet. The seams are flattened with wooden mallets and soldered water-tight. The seams constitute the weakest part * The term penny as applied to nails is a corruption of the original form in which the nails were defined as 3-pound, 4-pound, etc., meaning that 1,000 of the nails weighed 3 pounds, 4 pounds, etc., respectively. Q 254 ROOFING. of a flat tin roof, and should therefore he made and soldered with great care. The tinner should not hurry the soldering, for time is required to properly “sweat” the solder into the seams, Resin is the best flux; chloride of zinc or other acids should not be used. A better method of fastening the sheets to the roof is by means of tin cleats about 1£ in. X 4 in. These are nailed to the roof, and locked over the upper edge of the sheet, about 15 in. apart. Standing-seam roofing is that in which the sloping seams are composed of two upstands in¬ terlocked, and held in place by cleats. They are not soldered, but are simply locked together, as shown in Fig. 3. The sheets of tin are first double-seamed and sol¬ dered together into long strips that reach from eaves to ridge. One edge is turned up about 1£ in. and the other about 1£ in. The cleats are placed about 15 or 18 in. apart. When the upstands and cleats are locked together the standing seam is about 1 in. high. Before laying tin, the uneven edges of the boarding should be smoothed off and the boarding covered with at least one thickness of sheathing paper or dry felt, to form a cushion and otherwise protect the tin. Knot holes in the boarding should be covered with pieces of heavy galvanized iron. Only the best quality of tin should be used, and it should be painted on the under side before it is laid. The outer edges of the tin should be turned over the upper edge of the cornice, and clasped to a strip of hoop iron; or, where it connects with a metal gutter, the two should be locked and soldered. Where a tin roof abuts a chimney or wall, the tin should be turned up sufficiently to prevent water from rising over it. This upstand should be counter- flashed with sheet lead; and abutting a wooden wall it should be turned up against the boarding, and the siding or shingles laid over it. The tin should also be turned up against all balcony posts, and the edges at the angles weu soldered. Fig. 3. ROOFING. 255 The roof should he painted within a few days after it Is laid, either with red lead in linseed oil, or a good asphaltum paint, particular care being taken to scrape off all resin before the paint is applied. There is little or no difference between the methods of laying tin or copper roofing. The most important point to be considered in copper roofing is to have the copper thoroughly tinned before commencing to solder it. For other data on Tin Roofs, see page 353. GRAVEL ROOFS. The rafters should be spaced close enough to make the roof firm, when planked or boarded. For sheathing, tongued- and-grooved lumber is preferable ; and in any case the plank or roof boards should be laid closely—making close joints, both at edges and ends—and should be free from holes or loose knots, and securely nailed to the rafters. Over the sheathing should be laid four layers of roofing felt, the first course, next the eaves, being five layers thick. Each suc¬ cessive layer should be lapped at least f its width over the preceding one, and firmly secured with cleats. The quantity of felt per 100 sq. ft. of roofing should be net less than 70 lb. The surface under the outer layer of the first course, and under each succeeding layer, as far back as the edge of the next lap, should be well covered with a thin coating of cement, in no case applied hot enough to injure the woolly fiber of the felt. Over the entire surface should be spread a good coating of cement, amounting in all (including that used between the layers) to about 10 gal. per 100 sq. ft., heated as before specified. While the cement is hot, it should be completely covered with a coating of dry slag, granulated and bolted for the purpose, no slag being used that will not pass through a (pinch mesh, and none smaller than will be caught by a 1-inch mesh. All chimneys and walls that pro¬ ject above the roof should be flashed and countcrflashed with zinc or copper. Gravel roofs form a very durable and inexpensive covering, but are not suitable for any but practically fiat surfaces. 256 ROOFING. GUTTERS. In Fig. 4 is shown a strong and durable box gutter, suitable for either a frame building or for a brick or stone stru cture, baying a wooden cornice. A series of lookouts are nailed to the wall studs (or built into the brickwork or stonework), forming a solid base for the cornice and gutter. The width of the lookouts may be varied, to obtain the grade for the gutter bed, or it may be uniform, strips being nailed to the upper edges of the pieces. On a gable roof the cover- plate over the crown mold should be kept in line with the sheathing on the Toof slope. In lining this gutter, if a strip of hoop iron is tacked to the fillet of the crown mold, with its lower edge kept £ in. below the mold, the lining maybe tightly clasped over the strip, and face nailing dispensed with, thus making a neat and durable job. The lining should pass behind the eave mold, but need not be carried up the slope. The insertion of a triangular strip at the angle of the gutter bed and the wall is of advantage, as the ROOFING. 257 gutter is more readily cleaned by the wash than with a square corner. The end of the gutter is closed at the gable, so that the crown mold can run up the facia and be continuous; it is usual to leave a space of from 4 to 6 in. between the closed end and the gable facia. Figs. 5 and 6 show methods of forming standing gut¬ ters, the former being adapted for shingled roofs, and the latter for either shingle or slate roofs. It is impor¬ tant to insert the tilting fillet in both cases, for two rea¬ sons: First, to ob¬ tain the tilt for the lower double course so that the bed of the second course will lie close to the back of the lower course; and second, to form a drip at the edge of the lower course, so that water will not Fig. 6. be drawn up by capillary attraction under the shingle or slate and pass over the upper edge of the flashing. These are durable forms of gutters, but they have the disadvantage of acting as guards, retain snow on the roof, and mar to some extent the appear¬ ance of the roof planes. Trough gutters of wood, tin, or copper are frequently used, and where securely fastened in place, below the drip line of the roof covering, give good results. Gutters should have a pitch of in. per lineal foot, wherever practicable, so that the bed of the gutter will be well cleansed during a rain fall. Where the pitch is less than stated, it is difficult to flush the dust out of the pockets formed by the “ kinking’ of the gutter lining. 258 PLASTERING. PLASTERING. Plastering consists in the application of a plastic material called mortar, to the walls and ceilings of a building. The plaster is either laid directly on the face of the wall, or it may be spread oyer a grille base of wood or metal strips calico lath, the edges of which are sufficiently separated to allow the mortar to pass through and fold over on the inner fane thus forming a key, to hold the substance in position. LATHING. On brick or stone walls, lathing is usually attached to vertical furring strips, 1 in. thick by 2 in. wide, set at 12" or 16" centers. By this means there is a clear air space between the plaster slabs and the wall, thus insuring a continually dry surface, which would otherwise be liable to dampness. In the case of walls in frame buildings, the lath is attached directly to the studs forming the framing of the walls. The ceiling lath may be nailed directly to the under edges of tne joists, or attached to cross-furring, similar to that used on the walls, set at right angles to the joists and fixed at 12" centers. By the latter method better results are obtained, as the warp¬ ing of the joists does not affect the lath. Lath may be either split or sawed; the former gives a better wall, as there are no cross-grained fibers to reduce the strength, while in the latter such fibers make the lath curl and warp from the absorp¬ tion of moisture from the mortar; being cheaper, however, sawed lath is generally used. Lath made of pine, spruce, or hemlock, should be straight-grained, well seasoned, free from sap and rot, clear of shakes and large or loose knots, and, to prevent the subsequent discoloration of the plaster, it should be free from live knots and resinous pockets. The regular size of a lath strip is £ in. X 1J in. X 4 ft., the length regulating the spacing of the furring strips, studs, and joists. Lath is nailed in place in parallel rows, the edges being kept a full | in. apart, to enable the soft plaster to be pressed through and form a key. The ends should not lap, PLASTERING. 259 but be butt-jointed and flush ; continuous joints should not occur on one support, but the lathed surface should be divided into panels from 15 in. to 18 in. wide, and the joints be made to break on alternate supports, as shown by the panel abed in Fig. 1, page 262, otherwise continuous cracks will be liable to disfigure the plaster. The lath is usually attached to joists and studs with cut or wire nails, about 1| in. in length and having large flat heads, one nail being used at each support. The nails should be galvanized, to prevent the moisture from attacking the iron and causing them to rust, as well as caus¬ ing large yellow blotches to appear on the surface of the plaster. There are several metallic substitutes for the wood lathing, such as wire netting, crimped, perforated, and expanded metal, all of which possess much merit, and are preferable to wood. The carpenter fixes plaster grounds 2 in. wide, shown at e, e, to the masonry and framework, for the attachment of the joiner work. Plaster casings are also placed around window openings, and false jambs at doonvays. For 3-coat work, the plaster grounds on brick or stone walls that are to be coated on the solid wall should be f in. thick, and those for lathed surfaces l in. ; at no point should the surface of the solid wall or that of the lathing approach the face of the grounds nearer than the regulation thickness for the plaster, which will thus be about 1 in. PLASTERING. Materials.— The substances which enter into the composi¬ tion of mortar depend upon the nature of the surface to be coated, the order in which the layers are applied, and the desired finish. For ordinary work they are lime paste, sand, hair, and plaster of Paris. Lime is the product of the calcination or burning of lime¬ stone. The material is heated in a kiln until it emits a red glow, thus expelling the carbonic acid and moisture; the residue is quicklime, lumps of which, after being removed from the kiln, are called lime shells. In preparing the mortar, the lime shelly arc deposited in a woodeu slaking 260 PLASTERING. box, and are liberally sprayed with water; they soon begin to swell, crackle, and fall into a powdery mass. This process is called slaking and the pow r dered substance is slaked lime ; during the process, the lime increases from two to three times in bulk and much heat is given out, which transforms the excess of moisture into steam. Mortar is usually mixed by manual labor, but on extensive works and in cities it is often prepared by mortar mills, a more thorough incorpora¬ tion of the ingredients and a tougher paste being produced by the machine process. Sand may be procured from the natural deposits in pits or along river shores. It should be clean; this can be deter¬ mined by rubbing a moistened quantity of it between the hands; the grains should be sharp and angular, not round and polished. Where the sand is coarse, it should be screened to the desired fineness, by being passed through a sieve. It should be free of salt, otherwise it v T ill attract and retain moisture; this presence can be detected by tasting. Sand is mixed in the mortar for economy, and to check the exces¬ sive shrinkage of the lime paste. The sand in the mortar increases its bulk, while sufficient strength is retained, if each grain is well enveloped in a film of the paste. Hair is employed to bind the paste together and to render it more tenacious. Cattle or goat hair is used for this purpose, but the latter is considered the best. The hair should be long, free from grease and dirt, of sound quality, and beaten up if matted. Owing to the presence of salt in salted hides, hair taxen therefrom is undesirable. Plaster of Paris is obtained from gypsum, by gentle calcina¬ tion. It is very soluble in water, which renders it unfit for external use, but it is valuable for cornice molds and enrich¬ ments, and is also used in several plastic mixtures. The great value of plaster of Paris is that paste made from it rapidly sets and acquires full strength in a few hours. Its volume expands in setting, making it a good material for fill¬ ing chinks and holes in repair work. Mixing the Materials. —The composition of the successive coats are generally classified as coarse stuff , fine stuff, plasterers' j>utty, gauged stuff , and stucco. For all of them it is esseq- PLASTERING. 261 tial that the lime should he thoroughly slaked. In much of the lime used there are more or less overburnt, hard, obsti¬ nate nodules which resist the permeation of water, and fail to disintegrate; these must be removed from the lime by screen¬ ing, otherwise a pitted appearance of the finished work will invariably ensue from the future slaking of the particles. Coarse stuff, used for the first coat, is composed of from one to two measures of sand to one of slaked lime. The lime paste and hair are well mixed; then, after adding the sand, the mass is worked together with a hoe, until the materials are completely combined. The mixture is then piled in a heap for a week or ten days, to allow it to sour or ferment, the lime expending its heat and becoming effectually slaked. The lime and sand, if mixed while the lime is still hot, pro¬ duces a much tougher mortar, though some authorities hold that the sand should be added last, after the hair, which, to prevent being charred by hot lime, is always mixed in the mortar after the lime has been cooled. One pound of hair is usually added to every 2 or 3 cu. ft. of mortar, according to requirements, it being essential to add more for ceiling stuff than for walls. The consistency of the prepared mortar should be such that when the paste is made to fold over the edge of the trowel it w T ill hang well together. Fine stuff is the pure lime which has been slaked to a paste by the addition of a small quantity of water, after which it is further diluted until it is as thin as cream. When the lime held in suspension has subsided, the excess of water is drained off, and the moisture allowed to evaporate until the stuff is sufficiently stiff for use. When desired, a small quantity of white hair is added. Plasterers’ putty, which is always used without hair, is practically fine stuff, but the creamy paste, having been strained through a fine sieve, has become much more velvety. Gauged stuff consists of about f of the foregoing putty and about j- of plaster of Paris, which causes the mixture to set quickly, so that it must be immediately used, not more than can be applied in 20 or 30 minutes being prepared. An excess of plaster in the mixture will cause the coat to crack. Tin's is used gs a finishing coat for walls and ceilings, and 262 PLASTERING. also for running cornices; for the latter work, equal pro¬ portions of putty and plaster are used. Stucco, for interior work, consists of | fine stuff and j sand, and is used as a finishing coat, the mixture being whipped and reduced, by the addition of water, to a thin paste. Application. —For 3-coat work, the process of applying and finishing the layers will he described in the order in which they are applied. The coarse stuff is taken in batches from the souring pile, tempered to the proper degree of firmness, shov¬ eled into hods, carried to the rooms, and depos¬ ited on the mortar board, as at /, Fig. 1. A quan¬ tity of mortar is placed on the hawk g, by means of the trowel h, then slices of the mortar are spread firmly and evenly over the surface of the lathing. The mortar should he tough, hold well together, and soft enough to be pressed between the lath, bulging out behind and forming the key. The thickness of the layer should be fully £ in.; in cheap work it is often only a skim coat, and it is hot unusual to see the lath through it. After the coat has somewhat hard¬ ened, it is scratched over diagonally by wooden comb-like blades, as i, i ; from this fact the first layer is often called the scratch coat. The grooves fulfil the same function as the spaces between the lath, to allow a good key for the subsequent layer. The second coat, consisting of fine stuff, to which a little hair is sotnqtipaes added, is applied when the scratch cop,t hfts PLASTERING. 263 become sufficiently firm to resist pressure; the second layer is called the brown or floated coat, because its surface is worked by means of boaM-shaped trowels, called floats. It is also known as the straightening coat, since all the wall surfaces are straightened and made true. This is effected by first toiming a series of plaster hands, called screeds, 5 or 6 in. wide, on the surface to be floated. The surfaces adjacent to the angles are carefully plumbed up from the plaster grounds, but kept about i in. back from the face, to allow for the finishing coat. Sim¬ ilar screeds are formed along the ceiling angles; these screeds are made straight, and coincide with those at the opposite angles. Intermediate horizontal and vertical screeds are then formed between the screeds adjacent to the ceiling and the plaster grounds; these are usually placed from 4 to 8 ft. apart, and are gauged to line by means of a straightedge. The screeds thus form a system of framing which has been reduced to a true plane; the panels are then filled in flush with the screeds, and firmly rubbed down with a two-handled float, called the derby. The surface is then worked over with a wooden hand float, the coat being firmly compacted by inces¬ sant rubbing; when the coat becomes dry during the process, it is moistened with water,-applied with a wide brush. A close, firm layer can be obtained only by the thorough, labori¬ ous operation of pressing and rubbing the particles ot the mortar together. The ceiling surfaces are treated m a similar manner, and the screeds are carefully leveled so as to secure true and level planes. In order to form a key for the subse¬ quent coat, the surfaces are scratched over with a broom.. Where cornices are desired, they are run before the finis - ing coat is put on ; where the molded surfaces do not project more than 2 in., the body may be of coarse stuff, but where the projection is in excess of this, a cradling of brackets and lath, made to conform to the general profile, should be arranged for its support. Cornice molds are made of galva¬ nized iron, or zinc, attached to a wooden back, which m urn is secured to guide and brace strips. Longitudinal strips are attached to the wall either by nails or a layer of plaster of Paris, and on this the mold guide runs. The coarse duff is made to conform to the approximate profile with a muffled 264 PLASTERING. mold, that is, by forming a layer of plaster of Paris along the edge of the mold, about } in. in thickness ; or an extended profile can be cut out of zinc and attached, temporarily, to the mold. When the coarse stuff has been properly profiled, the surface is coated with gauged stuff and carefully worked over with the correct mold, until an exact and perfect finish is obtained. The internal and external angles cannot be finished by means of the molds, but require to be carefully molded and mitered by hand, using steel plates called jointing tools. There are several kinds of finishing coats, such as troweled stucco, rough sand finish, hard-finish white coat, etc. In all cases the material is applied to the wall in the form of a stiff paste, by means of a steel trowel, and is spread uniformly over the surface to a thickness of about f- in. Troweled stucco, consisting of fine stuff and sand, to which a little hair may be added, is thoroughly polished to a glazed finish with a trowel, the surface being kept moist by water applied with a brush. Rough sand finish can be produced on the stucco by cover¬ ing the hand float with a piece of carpet or felt, which will cause the sand to raise and present the characteristic sand¬ paper surface. Hard-finish white coat consists of gauged stuff, smoothed and polished with the steel trowel; as this material sets rapidly, care must be taken to observe that the second coat is well dried, otherwise the unequal shrinkage will cause hair cracks to occur all over the finishing coat. A similar finish may be obtained by the use of plasterers’ putty, mixed with a small proportion of white sand, and where desired a little white hair may be added; this will give a more durable finish, but it will not set so quickly, and it requires a more thorough working than the former finish. The space between the plaster grounds and the floor is usually finished with a scratch and a brown coat of plaster, so as to prevent air-currents entering the room from the channels between the furring strips; in cheap work this filling is omitted, the space being covered by the skirting or base. SANITARY MAXIMS. 265 PLUMBING. SANITARY MAXIMS. 1. General water-closet accommodation should never he placed in cellar or basement, but should be located where plenty of daylight and ventilation can be obtained, and should open to the outer atmosphere either direct, or by air-shafts at least 3 ft. square. 2. To prevent damp cellars, subsoil drains should be employed where necessary. They must be effecti\ ely ti apped from sewers or house drains, and some means must be em¬ ployed to maintain a seal. A check-valve, or back-water trap should be used to prevent a back discharge of sewage into them, should the drains become choked. 3. The arrangement of all drainage or vent pipes should be as direct as possible. 4. If there is a sewer in a street, every building should connect to it separately. 5. Where the soil is natural, the house sewer may be of vitrified earthemvare pipe, uniformly bedded and jointed with Portland cement and clean sharp sand. This pipe must run straight, and must have a clear bore. 6. If the soil is filled in or made, the house sewer must be of extra-heavy cast iron, asphalt-coated; of wrought iron, galvanized, and asphalt-coated; or of brass pipes, to avoid leakage by a settlement of the earth. 7. When it is necessary to run a private sewer to connect with a sewer in another street, it should belaid outside the curb of the street which the buildings face, not across lots where buildings may in future be erected. 8. The main house drains should be run above the ce ar floor when possible, and be secured against the cellar walls supported upon piers built under each joint, or suspended from the cellar ceiling by adjustable hangers. 9. If house drains must be run under the cellar floors they should be laid in straight runs, and clean-outs or inspection 266 PLUMBING. fittings should be placed at each branch or change in direction. 10. All changes in direction should be made with curved pipes or Y branches and or £ bends. 11. Old sewers should never be employed for new build¬ ings unless first ex¬ amined and tested by the smoke ma¬ chine. 12. All house- drainage system? should be discon¬ nected from city sewers by means of a. mi 'n disconnect¬ ing crap, as shown in Fig. 1. Fig. 1. If the sewage from a country building delivers into a sea, a river, or open space, the main drain trap may often be advantageously omitted. A fresh-air inlet must always accompany a main drain trap. 13. Fresh-air inlet orifices must be at least 15 ft. from the nearest window or door, and no cold-air box for a furnace should be so placed as to draw air from them. 14. All vent outlets should discharge at least 2 ft. above the highest part of a roof ridge, coping, or light-shaft, and as far as possible away from the light-shaft and all water tanks. 15. Vent pipes above roofs must be 4 in. in diameter or larger, and no cowls or vent caps should be used. 16. Vent pipes passing up through a low roof, and within 30 ft. of any windows in taller adjoining buildings, should be extended to safe points above the higher roofs. 17. All drain, soil, waste, and vent pipes between the main disconnecting trap and the vent outlets must be clear and unobstructed by traps, check-valves, etc. 18. All house-drainage work should be as accessible as possible, being placed either on the faces of walls or in air- shafts. When placed in walls they should be covered by movable pipe boards. SANITARY MAXIMS. 267 19. Every fixture in a building must be separately trapped close to each fixture, except where a sink and washtubs adjoin each other, in which case the waste pipe from the tubs may join the inlet side of the sink trap below the water seal. 20. All fixture and other such traps in a building must be back-vented by a separate pipe which may deliver into a special back-vent stack at a point about 2 or 3 in. below top of fixture, for tenement or apartment buildings, and at much higher points, if desired, for private-residence work, but in no case at points lower than bottoms of fixtures or bowls. 21. Where lead-waste or back-vent branches connect to cast-iron stacks, the connections must be made with heavy brass ferrules and wiped solder joints; if to wrought-iron or brass stacks, by means of brass-screwed solder nipples pro¬ vided with a socket to receive the lead pipe and form a flush internal surface. All solder joints in a plumbing system should be “ wiped.” 22. Special precaution should be taken to secure perfect joints between water-closet traps placed above the floor and the branch soil and vent pipes for same. Brass floor plates should be used for the floor connections. A smoke test is necessary to prove these joints. Back-vent horn or porcelain traps should not be permitted, as they soon break off*. The best modern practice is to back-vent the soil-pipe waste close to the floor connection by means of a wiped or screwed joint. 23. Overflow pipes from all fixtures must connect to traps on house side of their seals. 24. All fixture safes should be properly graded to a special waste pipe which must deliver openly at some point, such as a safe-waste sink in the cellar. The outlets of these pipes should be covered with light flap valves. 25. The sediment pipe from the kitchen boilers should not be connected on the outlet side of the sink or other trap. 26. A separate small tank or cistern should be employed to flush every water closet, and in no case should any water closet or urinal be supplied directly from the street pressure pipes when there is any liability of a drawback in the street mains. 27. One water closet, at least, should be allowed for fifteen 268 PLUMBING . inmates of a building. Every story of a tenement should contain at least one water closet. 28. Drinking water should be drawn directly from the street mains. Tank water may be used for washing and bathing purposes. 29. House tanks should be made of wood, and if placed inside the building should be lined with tinned and planished sheet copper. 30. Outside tanks may be circular and made of cedar staves or wrought iron. Overflow from such tanks should discharge on the roof. 31. Overflow pipes from inside tanks may deliver into an eaves gutter if available, or may be trapped and discharge into an open sink. No pipe connecting to a tank should deliver directly into the drainage system. 32. All rain-water leaders, area water boxes, and subsoil drains, must be trapped from the drainage system, and the seals maintained. 33. In all cases where water comes muddy from the mains, a straining filter should be located in the cellar, to filter all water in the building; muddy water clogs boilers, water- backs, and circulation pipes. 34. A special germ-proof filter is a very valuable addition, and should be placed at a convenient point, to supply water for drinking purposes. 35. Steam-exhaust, blow-off, or drip pipes should not deliver directly into a drainage system. Such water should deliver through a deep seal trap, and at a temperature not higher than 100° F. 36. No privy vaults or cesspools for sewage should be per¬ mitted in any place where water closets can be connected with a city sewer. 37. All privy vaults and cesspools should be frequently treated with small quantities of disinfectant, and should be cleaned out thoroughly and often. 38. All architects should see that every drainage system, when completed, is tested with smoke under a pressure of at least 1 inch water column, because the sanitary arrangements are seldom perfect when this final test is neglected. DRAINAGE SYSTEM. 269 DRAINAGE SYSTEM. PIPES AND FITTINGS. Cast-Iron Soil Pipes.—These should be uniform in thickness and homogeneous throughout. They should be tested with water pressure and then coated with asphaltum before being Used. These pipes come in 5' lengths and are known as extra heavy . The maker’s name should preferably be cast on each piece. Any pipes lighter than the following should be rejected. Weight of Cast-Iron Soil Pipe. Nominal Diameter. Inches. Weight per Foot. Pounds. Nominal Diameter. Inches. Weight per Foot. Pounds. 2 5i 7 27 3 9* 8 33i 4 13 10 45 5 17 12 54 6 20 Cast-iron soil-pipe fittings should correspond with the grade of pipes used. They should have easy curves. No sharp 90° bends or T branches should be used; only obtuse angle fit¬ tings. Fittings are made as staple goods at the following angles: 90°, 45°, 22i°, 11-]°, and are known as quarter, eighth, sixteenth, and thirty-second fittings, respectively. Cast-iron soil-pipe joints are made with picked oakum and molten lead calked solidly home in the sockets; 12 oz. of soft pig lead must be used in each joint for each inch in diameter of the pipe. Wrought-lron and Steel Pipes.— When used for drainage purposes these should be stamped with the maker s name. They should be galvanized and conform to the following table: R 270 PLUMBING. Weight of Wrought-Iron or Steel Drainage Pipe. Nominal Diameter. Inches. Thickness of Metal. Inches. Weight per Foot. Pounds. 1* .14 2.7 2 .15 3.6 2* .20 5.7 3 .21 7.5 3? .22 9.0 4 .23 10.7 4? .24 12.3 5 .25 14.5 6 .28 18.8 7 .30 23.3 8 .32 28.2 9 .34 33.7 10 .36 40.1 11 .37 45.0 12 .37 49.0 Fittings for vent pipes on wrought-iron or steel pipes may be the ordinary cast or malleable steam and water fittings. Fittings for waste or soil pipes must be the special, extra¬ heavy cast-iron, recessed and threaded, drainage fittings, with smooth interior waterway and threads tapped, so as to give a uniform grade to branches of not less than £ in. per ft. All joints must be screwed joints made up with red lead, and the burr formed in cutting must be carefully reamed out. When the male threads are screwed up tightly, the ends should abut each other in the couplings. Short nipples on wrought-iron or steel pipe, where the unthreaded pipe is less than in. long, should be of the thick¬ ness and weight known as extra heavy or extra strong. Brass Soil, Waste, and Vent Pipes, and Solder Nipples. —These should be thoroughly annealed, seamless drawn, brass tubing of standard iron-pipe gauge. Connections on brass pipe and between brass pipe and traps or iron pipe must not be made with slip joints or couplings. Threaded connections on brass pipe should be tapered and of the same size as iron-pipe threads. The following average thicknesses and weights per lineal foot should be employed: DRAINAGE SYSTEM. 271 Weight of Brass Soil, Waste, and Vent Pipe. Nominal Diameter. Inches. Thickness. Inches. Weight per Foot. Pounds. 14 .14 2.8 2 .15 3.8 24 .20 6.1 3 .21 7.9 34 .22 9.5 4 .23 11.3 44 .24 13.1 5 .25 15.4 6 .28 20.0 Brass ferrules should be bell-shaped, extra-heavy cast brass, not less than 4 in. long and 2i in. in diameter. The least weight of cast-brass ferrules and solder nipples should be as follows: Weight of Brass Ferrules and Nipples. Ferrules. Nipples. Inside Weight, Diameter. Each. In. Lb. Oz. 2 * 1 0 34 1 12 44 2 8 Inside Weight, Diameter. Each. In. Lb. Oz. 14 0 8 2 0 14 24 1 6 3 2 0 4 3 8 Particular care should be taken to inspect all cast-brass ferrules before calking them in place, as they are very liable to have sand holes in them, which will cause annoyance u testing the roughing when finished. 272 PLUMBING. Lead Pipes.— The weight of lead pipe should conform to the following table: Weight of Lead Soil, Waste, and Vent Pipe. 1 Nominal Diameter. Inches. Weight per Foot. Pounds. Nominal Diameter. Inches. Weight per Foot. Pounds. 1 £* 2 £ 3 6 H 3 4 8 2 4 8 All lead traps and bends should be of the same weight and thickness as their corresponding pipe branches. This grade is known in commerce as D. SIZES AND GRADE OF SEWERS. Sizes of Pipes.— House sewer and drain pipes must be at least 4 in. in diameter where water closets discharge into them. Where rain water discharges into them, the house sewer and the house drain up to the leader connections should be in accordance with the following table : Size of Pipe for Drainage. Diameter. Drainage Area, Square Feet. Inches. Fall i In. per Ft. Fall i In. per Ft. 6 5,000 7,500 7 6,900 10,300 8 9,100 13,600 9 11,600 17,400 * For flush pipes only. DRAINAGE SYSTEM. 273 Least Sizes of Soil, Waste, and Vent Pipe. Name of Pipe. Diameter. Inches. Main and branch soil pipes.. Main waste pipe. Branch waste pipes for kitchen sinks. Soil pipe for water closets on 5 or more floors Waste pipe for kitchen sinkson 5 or more floors Bath or sink waste pipe.. Basin or urinal waste pipe. Pantry-sink waste pipe . Safe waste pipe . Water-closet trap .. Wash tubs, 13" waste pipe and 2" trap for set of 2 tubs. Waste pipe for a set of 3 or 4 tubs. Main vents and long branches . Water-closet vents on 3 or more floors. Vent pipe for other fixtures on less than 7 floors Vent pipe for fixtures on 8 stories or less . Vent pipe for 9 stories and less than 16 . Vent pipe for 16 stories and less than 21. Vent pipe for 21 stories and over . ; . Branch vents for traps larger than 2 in. Branch vents for traps 2 in. or less . 4 2 2 5 3 13-2 H-H l* 1 -H 33-4 lf-2 2 2 3 2 3 4 5 6 2 13 For fixtures other than water closets and slop sinks and for more than 8 stories, vent pipes may be 1 in. smaller than above stated. All vent pipes that pass out through the roof should be increased one size through and above the roof, to allow for ice accumulations inside. In no case should any of these pipes be less than 4 in. in diameter, except in mild climates. Care should be taken to prevent the use of the old-fashioned cast-iron vent caps. If the open end must be protected, wire baskets may be used. The fresh-air inlet should be of the same size as the drain, up to 4 in.; for and &' drains, it should not be less than 4 in. in diameter ; for 1" and 8" drains, not less than 6 in. in diameter, and for larger drains not less than 8 in. in diameter. The fresh-air inlet orifice should have an area equal to that of the pipe. 274 PLUMBING. Fall for Drain and Waste Pipes.— The fall of a drainage system should be so arranged that the velocity of the flow obtained will be not less than about 275 ft. per ruin. This velocity can be closely approximated by pitching the pipes as follows: Grades for Drain Pipes. Diameter. Inches. Fall. Diameter. Inches. Fall. 2 V fall in 20' run 7 1' fall in 70' run 3 1' fall in 30' run 8 1' fall in 80' run 4 1' fall in 40' run 9 1' fall in 90' run 5 1' fall in 50' run 10 1' fall in 100' run 6 1' fall in 60' run DISPOSAL OF SEWAGE. Sewage from buildings is disposed of chiefly by the follow¬ ing methods: (1) By a connection to the street sewer; (2) by cesspools; (3) by director indirect discharge to sea, or river, in close proximity to the buildings. The first plan is always adopted in well- regulated cities, having a sewer system, and the work is usually done under the supervision of city authori¬ ties. Cesspools are commonly used where the first and third methods cannot be em¬ ployed. They should be built water-tight if within 200 ft. of any buildings or within 100 yd. of any well. Fig. 2 shows common practice in cesspool connections. The main drain from the house is continued through the cellar wall, a trap a and fresh-air inlet b being placed outside; either a vitrified or a cast-iron sewer pipe c connects with the cesspool d ; and a cesspool vent e is run up the trunk of a tree. A tight-fitting manhole cover should be provided for access. DRAINAGE SYSTEM. 275 The size of a cesspool must be determined by the approxi¬ mate amount of discharge. The least size for a 7- or 8-room house is from 6 to 8 ft. in diameter, and from 10 to 12 ft. deep. The following rule is in common use: For a house with G rooms or less, make the cesspool 6 ft. in diameter; for a 7-room house, 7 ft.; increase the diameter 6 in. for each additional room up to 10 rooms; then 3 in. for each additional room up to 20; then 11 in. for each additional room. The general depth is from 10 to 15 ft. The cesspools should be brick-lined, domed over, and, if possible, provided with an overflow. INSPECTION AND TESTING OF DRAINAGE SYSTEMS. Drainage systems in all well-regulated cities are inspected and tested twice before being passed by the authorities as perfectly sanitary. These tests are: (1) A test of the rough¬ ing in , which consists of the iron or brass drains, soil, waste, and vent lines, and sometimes the fixture branches, also, before any pipes are concealed. (2) A test of the entire system when the fixtures are all set, the traps sealed with water, and the work otherwise complete. The first or roughing test is accomplished by closing all branches and filling the system with water (if the weather permits), allowing the water to stand in the pipes for a cer¬ tain time, depending on the inspector’s judgment. Any leaks can be detected by water flowing from them. In applying this test, particular care must be taken to use plugs in the lower openings, which cannot be blown out by the heavy pressures that occur at these points. Should the weather be too cold for the water test, the com¬ pressed-air A est is applied. In this case air is pumped into the system until the pressure is 10 lb. by the gauge, when a valve between the pump and the system is closed. The pres¬ ence of leaks is made manifest by the gauge indicating a decreasing pressure as the test continues. The location of leaks, however, is difficult unless some pungent volatile oil, as ether or oil of peppermint, is allowed to vaporize within the system and thus cause an odor in the vicinity of the leaks; or. the leaks may be located by the bubbles formed 276 PLUMBING. when a soap-and-water solution is applied to the joints with a brush. The final test is the more important one. The chief objects are to positively ascertain (a) if the system when completed is gas-tight; ( b ) if the traps have perfect seals; (c) if every part of the system is trapped that should be trapped; (cl) if any back-vent pipes are run into hollow par¬ titions, attics, or chimneys. The test was formerly made by vaporizing oil of peppermint in the drainage system, without pressure, trusting to a diffusion of a pungent vapor to indi¬ cate any leaks. This form of peppermint test is now aban¬ doned by modern sanitary engineers as untrustworthy, the smoke test being substituted. This is applied by blowing smoke through the system; when the smoke shows at the various vent outlets, they are closed tightly, and the drains are subjected to a smoke pressure of from 1 in. to 1£ in. of water column. This pressure is sufficient to force smoke through the most minute leaks, but is not enough to blow through the seal of a good trap. The best smoke machine for testing house drains consists of a double-action blower, combined with a smoke-generating chamber furnished with a balanced floating cover. Such a blower will force air through the fire in a steady stream, and a uniform efflux of dense smoke is obtained. The advantage of the floating cover is that it will rise in its water seal when the desired pressure is obtained, and the pressure cannot be increased sufficiently to force the seals of traps, because the excess of smoke will escape to the atmosphere from under the cover. The smoke machine may be applied to the fresh- air inlet; or to one of the vent pipes above the roof—prefer¬ ably to the latter, as any smoke that escapes while lighting the fuel, which is oily cotton waste, cannot enter the building and thereby spoil the test. House-drainage systems should be tested once a year, and a report of the sanitary condition should be furnished after each inspection and test. This action is made necessary by the fact that the plumbing is often abused to such an extent as to become dangerous; and settlement of buildings often causes leakage. PLUMBING FIXTURES. 277 PLUMBING FIXTURES. BATHS. The most common materials for baths are (a) porcelain, or earthenware lined with porcelain enamel; ( b ) cast iron, painted or lined with porcelain enamel; (c) tinned sheet- copper lining, inclosed by an iron or steel jacket, commonly called iron-clad baths. Wood-cased tinned copper baths are out of date. Class (a) is used in the very finest of work; class ( b ) in plain substantial work; and class (c) in cheap work. The two kinds of baths which predominate are the Roman shape, which slopes at both ends, and usually has the connections at the back, and the French shape, which slopes at one end only, with connections at the foot. French shapes are adapted to corners; Roman, for placing along a wall, away from corners. The following dimensions are taken from a list of baths made by a reputable firm: Dimensions of Baths. Dimensions. Roman Shape. French Shape. * Porce¬ lain. flron Enameled. t Porce¬ lain. flron Enameled. Ft. In. Ft. In. Ft. In. Ft. ! In. Length . 5 0 4 6 4 6 1 4 i 6 Length, including fittings. 4 10 4 10 Width outside. 2 5 2 5 2 5 2 4 Width, including fittings... 2 9 2 9 Height on legs. Depth. 2 1 1 7 1 1 ■lJ-ll 7 2 1 1 7 2 1 0 8 Width of roll rim ... 0 6 2£ 0 3 2 9 * A 5' 6" bath is the same height, depth, and width of roll rim, but is 1 in. wider. _ . . ., f The sizes of these baths increase by jumps of 6 in., the other dimensions remaining about the same. I A 5' bath has same dimensions excepting length ; a <> f> fl,pd a 6' bath are X in, \\14er, 278 PLUMBING. Porcelain baths are variously classed by different makers, but usually alphabetically; class a means perfect, without flaw, warp, or twist; class b, slightly imperfect, a little warped or rough in the enamel, but hardly perceptible; class c, defective, badly warped, cracked, and blistered. Marble safes for baths are countersunk to a depth of } in. and are H in. thick; they usually project from 3 to 6 in. beyond the outside line of the bath and its trimmings, and should be nearly flush with the floor. Spray baths and shower baths, furnished with hot and cold water, should be provided with a mixing chamber and a thermometer, the bulb of which must be located in the center of the current. Spray and shower combinations are supplied by makers to fit their baths, but special ones are also furnished, independent of baths. A countersunk marble or slate floor slab 3 ft. G in. square, is usually set under a combination, and the bathroom floor is made water-tight. Porcelain receptors, 3 ft. 6 in. square, 9 in. high, 6 in. deep, with 2k in. roll rim, are preferable, however. About 20 ft. of brass tubing, closely per¬ forated with very fine holes, is sufficient for a good spray. A shower should not be less than 8 in. in diameter. The height from the floor to shower should be about 7 ft. 6 in. The combination should be provided with a 3" waste pipe, and a 4" or 5" flush strainer in the center of floor slab or receptor. Seat and foot baths vary in sizes and shapes. The following are dimensions of well-designed roll-rim baths: Dimensions of Seat and Foot Baths. Dimensions. Seat Bath. Foot Bath. Ft. In. Ft. In. Length. 2 3 1 10 Length, including fittings . 2 8 Width . 2 2 1 7 Width, including fittings. 1 11 Height, front. 1 0 1 5 Height, back. 1 9 1 5 Depth. 11 Width of roll rim. 2k Oi *-a PLUMBING FIXTURES. 279 They are connected with a hot and cold supply and waste connections, the same as plunge baths. Rain baths are a kind of shower bath, especially adapted for bathing establishments, and have the advantage over plunge baths for such places, in that they occupy but little floor area, and that they are thoroughly hygienic, as the same water never comes in contact with the body twice. In all spray, needle, shower, bidet, and rain baths, and shampoos, a mixing chamber should be used. Such a chamber is shown in Fig. 3 ; cold water, en¬ tering through (a), and hot water, through (&), are admitted to the chamber (c) in small jets and thoroughly mixed before passing into the discharge pipe (d), the top of which discharges through the show r er, or the shampoo attachment as desired A thermometer (e) has its bulb ex¬ tending into a circuit of mixing water, to indicate the temper¬ ature of the mixture. The difference between shower and rain baths is that a shower falls in large drops at low veloc¬ ity, and the rain comes in minute jets at high \elocit> . Sunken baths are simply large pools sunk below the floor level; they are made of wood, brick, or terra cotta, and are lined with sheet lead or copper, or faced inside with enameled tiie. The dimensions and capacity depend upon the size of the room. The depth varies from 2 to 4 ft. Water is usually d 280 PLUMBING. provided at the end, from a point above the floor level, as from a nozzle attached against the wall. Waste and overflow connections are provided, similar to ordinary baths. WASH BASINS. Wash basins are known as round and oval, and may be had with or without overflow attached. Sizes of round bowls are 10,12,13,14,15,16,17,18, and 20 in. in diameter, measured from the outside of the flange. Oval patterns are 14 in. X17 in., 15 in. X 19 in., 16 in. X 21 in. The 16" round, and the 15" X 19" oval basins are generally used. Wash basins should be set near windows, in a position convenient to put a mirror over them, so placed as to have the light from both sides. Marble basin slabs are 1{ in. thick, countersunk on top, and have molded exposed edges. Large slabs should be 1£ in. thick. Basin slabs are right or left hand, according as they set in a corner at the right or left hand as a person faces the basin. Backs are usually 8, 10, or 12 in. high, aprons 5 in. deep, and the height from top of slab to floor is generally 2 ft. 65 in. Corner basins should be provided with back and end plates; ordinary basins, with back plate only; recess basins, with back and two ends. Safes under basins are the same size as the slabs. WATER CLOSETS. Pan and Plunger Closets.— These have been condemned by health boards and sanitary authorities for the past 20 years or more, and should never be xised; any old ones dis¬ covered should be replaced by closets of modern construction. Hoppers.— Hoppers or washdown closets are designated as short or long hoppers, according as their traps are above or below the floor. Long hoppers are only used where PLUMBING FIXTURES. 281 there is danger of the trap being frozen, in which case the traps are placed below frost level. A long hopper is shown in Fig. 4, while Fig. 5 illustrates a short hopper. They can be had in porcelain, glazed earthenware, or cast iron painted or enameled. Short hoppers are fitted with a flushing tank overhead ; long hoppers are usually fitted with a valve below frost level. Washout Closets. —They consist of a basin and trap, both above the floor. They differ from hopper closets in that the water in the basin is separate from that in the trap, as shown in Fig. 6. They are generally used on good com¬ mon work, and are thor¬ oughly sanitary; but, being somewhat noisy, are not so desirable as siphon closets for dwellings. Siphon Closets.— They have their contents removed by siphonage through a long crooked outlet, the w^ater in the basin being employed as Fig. 7. a trap. They are almost noiseless in operation. There are many kinds of these closets on the market but the most reliable are the simple siphon-jet 282 PLUMBING. arrangements with flushing rim, as shown in accompanying figure. Those having a low-down tank are the most silent in action. Pneumatic siphon-jet closets are too complicated to be reliable. Fig. 7 shows the closet in action; the dotted lines show the water channels for the flush. The dimensions of closets vary considerably; the follow¬ ing, however, is good practice: Width of bowl over all...13 in. Height from seat to floor..17 in. Depth from wall to front of seat.23 in. The distances from the center of the outlet opening to the walls, etc.—or the “ roughing-in ” dimensions, as they are called—vary with nearly every closet. Latrines.— Latrines are used chiefly for prisons, factories, etc., and are set up in ranges of two or more, partitions being placed between each latrine, about 24 in. apart. The waste- pipe section is usually 5 or 6 in. in diameter, and the flush pipe 3 or 4 in. They are flushed by a large tank, located about 6 ft. above the seat, the flush pipe being connected to the bottom of the latrines. i Closet Ranges.— Closet ranges, used in schools, fa Tories, etc., are merely large troughs with one outlet and a flushing arrangement. They should be simple and have no mechanical parts to get out of order. There are many different lands, but the automatic-supply range is probably the best. The combi¬ nations are of 3 lengths, 24, 27, and 30 in. between partitions; height from floor to top of seat, 1 ft. 6 in.; height from floor to top of iron partition, 5 ft. 10 in.; depth of partition, 2 ft. 2 in.; width of range, from front to back, 1 ft. 7 in. They can be had painted or enameled. If a hot chimney is near, it is advisable to use local vent-closet ranges, and in such case allow about 15 in. extra length for a ventilating extension. Closet Seats.— Closet seats should be made of hard wood, and the grain arranged so that the seat will not warp, sliver, or fall to pieces. Quartered oak, in two or three layers crossed, or in one piece with dowels or cross-strips, seems to be the best material. The seat should be secured to the porcelain bowl. The hole should taper from back to front, PL UMBING FIXTURES. 283 and have the shape and dimensions shown in Fig. 8. The upper surface of the seat should be properly counter¬ sunk. Seat Vents. —Many closets are provided with horns above the water-line in the bowl, for the purpose of ven¬ tilating the bowl. These are of no use, however, unless a strong, positive draft is con¬ stantly maintained in the vent lines. The size of vent pipeis preferably 3 in. for each closet, and not less than 2 in. Two or three closets may local vent into a 4" pipe, the size of the pipe increasing with the number of closets con¬ necting to it. All closets having horns attached to them for back-venting traps should be discarded, as these horns easily break off. All connections between metal pipes and porce¬ lain should be bolted flange joints, without horns. Floor Connections.— The ordinary brass-bolted floor flange makes a good connection, but if it is not perfect there is no means of knowing the fact. One of the best floor connec¬ tions for a closet is shown in Fig. 9. This is a water- • sealed floor connection. The pipe a is continued 1| in. above the finished floor, the end being rounded a-nd free from burrs. The floor is countersunk to receive a supporting flange b which is attached to the pipe. A brass flange c compresses the rubber gasket d against the porcelain when the bolts e are drawn up. An annular space is thus formed around the neck of the pipe a, which fills with wmter at the first operation of the closet, thus seal- Fig. 9. 284 PLUMBING. ing the connection. If the connection leaks, this water will run out on the floor; if it does not, gas cannot escape. Closet Cisterns.— There are a variety of kinds of closet cis¬ terns on the market, some being simple and others com¬ plicated. In choosing a closet tank, (1) select for flushing qualities; (2) quietness in action; and (3) simplicity of con¬ struction. Fig. 10 shows a plain valve cistern for wash-down closets and hoppers; its dimen¬ sions are about 23 in. X 12 in. X 10 in. It is provided with a ball-cock a and an outlet valve b which is operated by a lever c bolted to a cross-bar d, the lever being worked by a chain pull. The tube g forms an over¬ flow which discharges into the flush pipe e. A deafening pipe /deadens the noise of the incoming water. The volume of flush from this tank is irregular, depending on the time the valve b is held up. A better arrangement is shown in Fig. 11. This is a siphon cistern particularly adapted for wash-outs as well as wash-downs and hoppers; its di¬ mensions are about 19 in. X 9 in. X 10 in. A momentary retention of the pull opens the valve a and starts the siphon, formed by the shell b suspended over, and attached to, an inner standing tube, which is secured to the valve a. A refill to the bowl is obtained by a slot in the lower end of the siphon tube which causes the siphon to break gradually. PLUMBING FIXTURES. 285 An after-wash cistern, shown in Fig. 12, is suitable for seat action. The lever is attached to the seat in such a manner that when the seat is depressed the valve a is closed, and the valve b opens, causing a flow from chamber c into chamber d. When the seat is re- leased a opens, b closes, and the closet is flushed. A refill float-valve cistern especially suit¬ able for siphon-jet closets, and wash-out closets requiring a refill to bowl, is shown in Fig. 13. When the float a is raised it remains buoyed up until sufficient water has passed through the closet, when it returns gradually to its seat. The pipe b serves as an over¬ flow and at the same time gives an abundant refill to the bowl. These cisterns are re¬ markably quiet in action. They are made in two sizes. Cisterns with valves away from the edges are preferable, for the wood is liable to warp and cause the lock¬ nuts to cut the copper. Water-closet floor slabs Fig. 13. are about 27 in. square, and countersunk around the closet. When ordered in a closet combination the hole is cut, and the countersinking done, by the manufacturer. They can be had in Italian or Tennessee marble, and slate. These slabs are sent with unpolished edges and corners, unless other¬ wise ordered. When the slabs are to be drilled for pipes, a diagram should accompany the order, giving exact distances to centers of openings, s 286 PLUMBING. URINALS. Urinal ranges are lipped troughs with partitions set 2 ft. apart. They are most satisfactory when flushed by an auto¬ matic-siphon tank which discharges through a large jet at the upper end and a spray tube at the back. The tank should be at least 4 ft. above the spray tube. The outlet to trough should be arranged with a siphon which will automatically discharge contents when the supply tank discharges. The period of automatic flushes vary with the water supply; good flushes are obtained if the interval is from 5 to 10 min. Urinal ranges are made of cast iron, either plain, painted, or, preferably, enameled. The usual dimensions of a urinal range are about as follows: Height of partition, 5 ft. 8 in.; width of partition, about 1 ft. 6 in.; width of urinal, from back to front of lip, 11 in.; depth of trough, 6 in.; regular height of lip, 2 ft.; the height for children is 1 ft. 2 in. Individual urinals are made of porcelain and are provided with at least two openings, one for the flush and the other for the discharge. The best class have perforated flushing rims, and overflow openings inside. They are known as flat or corner urinals. The best forms are those in which the trap is combined with the bowl, and arranged to be connected without any metal being exposed. The connection betw r een the porcelain and the metal is usually water-sealed, which is advantageous. The waste pipe is provided with a flange and bolt for making a perfect junction with the earthenw r are. When a flushing tank is used, the combination is simple, efficient, and hygienic. Individual urinals are set in stalls, the height of which stall should be at least 5 ft. 6 in.; width inside, 2 ft.; length of partition, 2 ft. 4 in.; depth of middle partition, 1 ft. 8 in. Middle partitions stand on nickel plated brass legs about 10 in. high. The size of urinal cisterns should be, for 2 urinals, a 2-gal. cistern; 3 urinals, a 3-gal. cistern, etc. SINKS. Sinks are generally classified as kitchen, pantry, slop, and stable sinks, and are made of different materials and in numerous sizes and shapes. PLUMBING FIXTURES. 287 Kitchen sinks are generally rectangular in plan, and are not provided with ping and chain, or overflow openings, Special kitchen sinks are furnished to order with overflow attachments and plugs. Sizes of Cast-Iron Kitchen Sinks. (Depth inside; other dimensions outside.) Length. Inches. Width. Inches. Depth. Inches. Length. Inches. Width. Inches. Depth. Inches. 164 18 124 12 5 6 30 324 20 18 6 6 16 16 6 324 21 6 22 14 6 36 18 6 23 15 6 36 214 6 254 20 154 124 6 6 38 42 20 22 6 6 20 14 6 48 20 6 24 14 6 48 23 6 244 16 6 24 14 8 24 254 27 18 174 15 6 6 6 30 50 50 24 24 26 8 64 64 24 28 28 30 30 20 17 20 16 18 6 6 6 6 6 62 76 56 60 78 22 22 32 28 28 8 7 9 10 10 All sinks should he fitted up open, tnat is, no wooaworn of any description in the form of boxings should be allowed near them, for these boxings become moist and foul, and make breeding places for cockroaches and other vermin. If possible, the walls against which sinks are set should be glazed tile or other material of a non-porous character. Sloping drain boards should be provided at every sink, Ash or oak from H to 2 inches thick are well adapted f<* drain boards. Sinks that are not cast with sloping bottoms should be set so that the bottom will have a fall towards t e, strainer. The faucets should be located, if possible, at the end opposite the strainer. 288 PLUMBING. Sizes op Copper Pantry Sizes of Cast-Iron Slop Sinks. Sinks. Length. Inches. Width. Inches. Depth. Inches. Length. Inches. Width. Inches. Depth. Inches. 16 20 20 24 30 36 36 23 36 48 48 60 16 14 16 20 20 18 21 15 21 20 20 20 10 12 12 12 12 12 12 15 16 12 17 12 12 12 14 14 14 16 16 18 18 20 16 20 24 24 30 30 5-6 5-6 5-6 5-6 5-6 5-6 5-6 5-6 Sizes of Porcelain Sinks. Sizes of Earthenware Length. Inches. Width. Inches. Depth. Inches. Pantry Sinks. Length. Inches. Width. Depth. Inches. 36 23 7 Inches. 42 48 28 30 24 24 18 20 7 7 9 9 20 23 25 14 16 17 41 51 51 Porcelain sinks can be had with a plain top or roll rim. Copper pantry sinks are made in either square or oval pat¬ terns ; the former has a flat, and the latter, a round bottom. Sizes for both patterns are given in the table. Pantry and kitchen sinks should be set 2 ft. 6 in. or 2 ft. 7 in. from the floor to the top of the cap. Slop sinks can be bad with or without overflow and plug. These sinks should be set at such a height that the rim will be not more than 24 in. from the floor. A sink should be located near a window for light, near the pantry or dining room for convenience, and away from the stove for comfort. PLUMBING FIXTURES. 289 LAUNDRY TUBS. Laundry tubs, generally speaking, are made of slate, cement, soapstone, glazed earthenware, or solid porcelain. Wood, cast iron or sheet steel are not suitable materials for wash tubs. Tubs used in tenement and apartment houses should be provided with overflows. The height of wash tubs from floor to top of rim is from 32 to 36 in. The wringer should be set on the right-hand tub. The following tables give the average sizes of slate and cement tubs: Slate Tubs. Cement Tubs. No. In. In. In. No. In. In. In. Parts. Long. Wide. Deep. Parts. Long. Wide. Deep. 1 24 2A 16 2 48 21 or 24 16 2 48 21 16 2 53 24 16 2 54 24 16 2 60 24 16 3 78 24 16 3 72 21 or 24 16 3 80 24 16 3 90 24 16 Earthenware and porcelain tubs come separately, and are connected up singly or in sets of 2, 3, or 4, as required. They arc made in two sizes, Nos. 1 and 2, according to the dimen¬ sions shown in the following table : Dimensions. No. 1. No. 2. Ft. In. Ft. In. Length for each tub . 2 0 2 7£ Length required for 2 tubs. v — 4 1 5 4 Length required for 3 tubs. 6 2 8 0 Length required for 4 tubs. 8 3 10 y Width from front to back. 2 ■1-1? 2 If Depth inside . 1 3 1 3 290 PLUMBING. WATER SUPPLY AND DISTRIBUTION. METHODS OF SUPPLY. The source of supply of water to a building will depend upon prevailing conditions and the location of the building. City buildings are usually supplied from city mains, while country buildings are supplied from wells, lakes, and streams, by means of pumps, hydraulic rams, etc. Street Service.— House pipes should connect to the mains by corporation stops. A stop and waste should always be placed under the sidewalk at the curb, and also a separate stop and waste upon the service pipe just inside the cellar wall. If the street pressure is great enough to force water to the top floor of a building, all fixtures are usually supplied with both hot and cold water, by street pressure. If the pressure is too low, or the supply intermittent, a tank is placed in the attic to supply the building. If the pressure is too high, it is customary to apply a pressure regulator in the cellar. The sizes of street service pipes depend chiefly upon the street pressure and the size of building to be supplied. The following is common practice: Sizes of Street Service Pipes. Class of Building. Size of Pipe. Inches. Single dwellings, two or three stories high Larger dwellings. Tenement buildings and apartment houses Hotels and factories. i or i 1 or li H or 2 2 and up These pipes should be increased one size if pressure is low. Pumps.— The amount of water raised by single-acting pumps is estimated by multiplying the number of strokes whioh the piston travels in one direction per minute by the volume displaced or traversed by the piston in a single stroke, the supposition being that the water flows into the pump barrel WATER SUPPLY AND DISTRIBUTION. 291 only when the piston ascends. It has been found, however, that the column of water does not cease flowing when the piston descends, and that the amount of water delivered is greater than usually supposed; in some cases, it is nearly double the theoretical amount. A column of water 34 ft. high is balanced by the pressure of the atmosphere, but in practice it requires a very good pump to draw to a height of 28 ft. Damping Hot Water .—The height to which hot water can be raised by suction is much less than that of cold water, the height varying with the temperature. This is due to the increased pressure of the vapor. Where possible, the hot water should flow into the pump by gravity. The following table gives the maximum vertical heights of suction pipes for different temperatures: Absolute Pres¬ sure of Vapor. Lb. per Sq. In. Vacuum. Inches of Mercury. Temperature. Degrees, Fahr. Maximum Height of Suction. Feet. 1 27.88 101.4 31.6 2 25.85 126.2 29.3 3 23.81 144.7 27.0 4 21.77 153.3 24.7 5 19.74 162.5 22.4 6 17.70 170.3 20.1 7 15.66 177.0 17.8 8 13.63 183.0 15.5 9 11.59 188.4 13.2 10 9.55 193.2 10.9 11 7.51 197.6 8.5 12 5.48 201.9 6.2 13 3.44 205.8 3.9 14 1.40 209.6 1.6 The Hydraulic Ram.— This machine is employed to raise water to a point higher than the source of supply; it is chiefly used where a large flow of water with a low fall is obtainable, and raises part of the water which operates it. The efficiency varies with the ratio of the rise of the discharge to the fall oj che drive pipe, about as follows; 292 PLUMBING. Ratio of lift to fall, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26. Per cent, efficiency, 72, 61, 52, 44, 37, 31, 25, 19, 14, 9, 4, 0. To obtain the highest efficiency with any fall, the dash valve should be adjusted to close at the instant the water in the drive pipe has attained its maximum velocity. A ram having a discharge pipe 80 or 100 ft. long will deliver about f the quantity supplied to a height about five times the fall; or ^ the quantity supplied to a height of ten times the fall. If the pipes are lead, the drive pipe should be of the A grade, for diameters up to 2 in., and cast or wrought iron for greater diameters. The discharge pipe, if lead, should be of the B grade for rises of 50 ft. or less, and of the A grade for rises between 50 and 100 ft. For falls greater than 10 ft., or rises of more than 100 ft., the pipe must be heavier than just given. The length of drive pipe should be from 25 to 50 ft. If the discharge pipe is very long (say £ mile) a larger size than given in the table should be used. With a given supply of water under a great fall, the ram need not be as large as for the same quantity of water under a less fall. When large quantities of water are to be raised, it is better to increase the number of rams, in preference to having one of very large capacity. Several rams may be set so as to deliver into one discharge pipe, each having a separate drive pipe. Cisterns.—These are used to store rain water under¬ ground, for use in country buildings. For an ordinary house with 8 rooms or less, located in a climate where the rainfall is not less than 30 in. per annum, and where very long droughts do not occur, a brick cistern 5 ft. in diameter and 7 ft. deep will be large enough for a family of 10 people. Larger build¬ ings should be provided with two or more cisterns, Sizes of Pipe for Rams. Water Supply Size of Pipe. to Ram. Gal. per Min. Drive. In. Discharge. In. f- 2 U- 4 1 8 1 * 3-7 li i 6 -14 2 i 12 -25 2i 1 20 -40 2i li 25 -75 4 2 WA TER S UPPL Y AND DIS TRIB UTION. 293 Cistern filters are essential in all cases. Fig. 14 shows an excellent and simple form, which may be built a few feet away from the cistern, and con¬ nected to it by the pipe /. The filter well is built of brick, laid in 1-to-l Portland cement mor¬ tar. and is divided into two compartments by a partition slab a of slate or flagstone. The bottom is inclined so that the sediment will collect at d. The chamber B has a perforated bottom b, upon which is placed Fig. 14. a course of gravel, then clean sand, and is topped with gravel nearly up to the level of the discharge pipe /. Rain water enters A through the pipe c, and deposits any mud that it may contain, at d. Any overflow in A is discharged through pipe e. The water flows upwards through the sand in chamber B, which clarifies it. The filter may be easily cleaned by stop¬ ping up /, pouring water into B, and pumping out the mud and dirty water from A. Renewal of the filtering material is thus seldom necessary. DISTRIBUTION. Sizes of Water Pipes in Building. Supply Branches. To bath cocks . To basin cocks. To water-closet flush tank To water-closet flush valve To water-closet flush pipes To sitz or foot baths. To kitchen sinks. To pantry sinks . To slop sinks. To urinals .. Low High Pressure. Pressure. Inches. Inches. *-l 4- i 1_ 4- 4 _1 JL i -n l-i lf-H i- 1 l a 4- f h~ I i 1- b i-1 1- 4 i- i b- 4 294 PLUMBING. Kitchen Boilers.—Iron boilers, or hot-water storage tanks, should be galvanized both outside and inside, particularly inside. These boilers are commonly made of mild steel, and are not so durable as the old-time wrought-iron boilers. Many of the poorer grades become pitted very rapidly, and are not to be recommended for first-class work. The longi¬ tudinal seams are either single or double riveted; when double riveted, the rivets should be staggered. Copper range boilers are in every case to be preferred, if properly coated inside with block tin. They are classed as light, heavy and extra heavy, the latter being tested to 150 lb. water pressure. The best forms of copper boilers are those which are reinforced inside by stiffeners or braces so that they will not collapse when a partial vacuum is formed within them. Ordinary steel or iron boilers are tested to 150 lb. water pressure, and extra heavy ones to 250 lb. pressure. The latter should always be used when the street pressure is more than 40 lb. by the gauge, or when a water hammer may at any time come upon the plumbing system. Standard Sizes of Galvanized Boilers. Capacity. Gal. Length. Ft. Diameter In. Capacity. Gal. Length. Ft. Diameter. In. 18 3 12 48 6 14 21 3* 12 52 5 16 24 4 12 53 4 18 24 3 14 63 6 16 27 4| 12 66 5 18 28 3* 14 79 6 18 80 5 12 82 5 20 32 4 14 98 6 20 35 5 13 100 5 22 36 6 12 120 6 22 36 4* 14 120 5 24 40 5 14 144 6 24 42 4 16 168 7 24 47 4i 16 182 8 24 The size of boiler which should be employed for any par¬ ticular work depends chiefly upon existing conditions, such, WA TER S UPPL Y AND DISTRIB UTION. 295 for example, as the water supply and the nature of the building. A safe rule is to allow a 35- or 40-gal. boiler for a building having one bathroom, and to add 30 gal. addi¬ tional capacity for every extra bathroom. The size can only be computed by first ascertaining the maximum quantity of hot water which will be drawn off in a given time, and the nature of the heating agents which warm the water. The size of the waterback is another item which cannot be calculated, because it is based on the size of the boiler or tice it is found that about 100 sq. in. of waterback heating surface in actual contact with the fire is sufficient to give good results with a 40-gal. boiler if water is plentiful, and with a 50-gal. boiler if water is scarce. Boiler Connections. —These are made in different ways, but the most common and reliable method is shown at (n) in Fig. 15. The cold supply pipe e has a branch / taken off to 296 PLUMBING. supply the boiler. The return pipe g furnishes a supply to the waterback a, and the sediment cock h is used to empty the boiler when necessary. The hot water enters the boiler through the flow pipe c, and rising to the top, is conveyed to the fixtures through d. The only objection to this arrangement is that it requires a long time for the water in the boiler to become hot, because the hot water continu¬ ally mixes with the cold. To overcome this trouble, c is often connected to d over the boiler, as shown in (b). But the latter method is also objectionable, in that circulation between the range and the boiler will cease when the service pipe is shut off, because the hot water will siphon down to the vent hole in the top of the inner tube. The waterback will then blow steam through c and d. PLUMBERS’ TABLES. Fluxes. Flux. Used With. Metals to be Joined. Resin. Copper bit or blowpipe. Lead, tin. copper, brass, and tinned metals. Tallow, unsalted. Blowpipe or wiping process. Lead, tin, or tinned metals. Sal ammoniac. Copper bit or blowpipe. Copper, brass, and iron. Muriatic acid. Copper bit. Dirty zinc. Chloride of zinc. Copper bit or blowpipe. Clean zinc, copper, brass, tin, and tinned metals. Resin and sweet oil. Copper bit or blowpipe. Lead and tin tubes. Borax. Blowpipe. Iron, steel, copper, and brass. PLUMBERS ’ TABLES. 297 Solders. Variety. Hard. Soft. Fusing Point. Zinc. Copper. Silver. d •rH H Lead. Bismuth. Spelter, hardest .. 1 2 700° Spelter, hard . 2 3 Spelter, soft . 1 1 550° Spelter, fine . 2 2 4 Silver, hard . 1 4 Silver, medium . 1 3 Silver, soft. 1 2 Plumbers’, coarse . 1 3 480° Plumbers’, ordinary. 1 2 440° Plumbers’, fine . 2 3 400° Tinners’ .. 1 1 370° For tin pipe . 3 2 330° For tin pipe . 4 4 1 Weight per Foot of Lead Pipe and Tin-Lined Lead Pipe. Inside Diam. Brooklyn A A Extra Strong. In. Lb. Oz. Lb. Oz. * 1 12 1 8 1*5 £ 3 0 2 0 3 8 2 12 * 4 12 3 8 1 6 0 4 12 H 6 12 5 12 1 £ 8 8 7 8 11 10 0 8 8 2 11 12 9 0 A Strong. cq Medium. C Light. D Extra Light. Lb. Oz. Lb. Oz. Lb. Oz. Lb. Oz. 1 4 1 0 0 12 0 10 1 0 0 13 1 12 1 4 1 0 0 12 2 8 2 0 1 8 1 0 3 0 9 4 1 12 1 4 4 0 3 4 2 8 2 0 4 12 3 12 3 0 2 8 6 8 5 0 4 4 3 8 7 0 6 0 5 0 4 0 8 0 7 0 6 0 4 12 298 PLUMBING. Weight of Sheet Zinc, Copper, and Lead. Zinc. Copper. Lead. Weight, Thick- Weight, Thick- Weight, perSq.Ft. ness. per Sq.Ft. ness. perSq.Ft. Ounces. Inches. Ounces. Inches. Pounds. .031 10 .013 10 3 .046 12 .016 12 YE 4 .053 14 .019 14 YZ 5 .061 16 .022 16 6 .069 18 .025 18 n .076 20 .029 20 15 8 Weight per Foot of Lead Tubing and Waste Pipe. Tubing. Waste Pipe. Diameter Weight Diameter Weight Diameter Weight Inches. Ounces. Inches. Pounds. Inches. Pounds. * H 2 4 5, 6, 8 u 2 3, 4 41 8, 10 6 32 21 21 4, 6 5 8, 10, 12 l 4 5, 6, 8,13 3 41, 5 6 12, up. Weight of Brass Tubing. Nominal Diameter. Inches. Weight per Lineal Foot. Pounds. Nominal Diameter. Inches. Weight per Lineal Foot. Pounds. 2 , .25 2 4.00 I 4 .43 21 5.75 t .62 3 8.30 1 _ .90 31 10.90 i 1.25 4 12.70 l 1.70 41 13.90 U 2.50 5 15.75 H 3.00 6 20.60 N PLUMBERS' TABLES. 299 Weight of Sheet Iron. o U £ « fro 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Thickness. Inches. Black Iron. Weight per Sq. Ft. Pounds. Number of Gauge. - Thickness. Inches. Black Iron. Weight per Sq. Ft. Pounds. Galvanized Iron. Weight per Sq. Ft. Pounds. .300 .284 .259 .238 .220 .203 .180 .165 .148 .134 .120 .109 .095 .083 .072 12.0 11.4 10.4 9.5 8.8 8.1 7.2 6.6 5.9 5.4 4.8 4.4 3.8 3.3 2.9 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 .065 .058 .049 .042 .035 .032 .028 .025 .022 .020 .018 .016 .014 .013 .012 2.6 2.3 2.0 1.7 1.4 1.3 1.1 1.0 0.9 0.8 0.7 0.6 0.6 * 0.5 0.5 3.0 2.7 2.3 2.1 1.7 1.5 1.3 1.2 1.1 1.0 1.0 0.9 0.7 0.7 0.6 Spacing of Lead Pipe Tacks. Size of Pipe. Inches. a. 8 i 9 l H it Vertical Pipe. Hot. Cold. Inches. Inches. 18 24 19 25 20 26 21 27 22 28 23 29 24 30 Horizontal Pipe. Hot. Inches. 12 14 15 16 17 18 18 Cold. Inches. 16 17 18 19 20 21 22 Tacks are spaced ciosei — is much more liable to sag when heated. 300 HEATING AND VENTILATION. Length of Wipe Joints for Lead Pipe. Diameter of Pipe. Inches. Length of Joint. Inches. Diameter of Pipe. Inches. Length of Joint. Inches. Diameter of Pipe. Inches. Length of Joint. Inches. * 2i It water 3 2 waste 2* 2t li waste 2 2j waste 2£ i 2i li water 3i 3 waste 2i 1 2i 1| waste 2i 4 waste 3 HEATING AND VENTILATION. STEAM HEATING. A steam-lieating system, with steam haying a pressure less than 10 lb. by the gauge, is called a low-pressure system. If the steam is at a higher pressure, the system is called high-pres¬ sure system. Wh'en the water of condensation flows back to the boiler by gravity alone, the apparatus is known as a gravity-circulating system. When the boiler is run at a high, and the heating system at a low, pressure, the condensed steam must be returned to the boiler by a pump, steam return trap, or injector. The low-pressure gravity circulating systems considered to be the best are: the two-pipe system with wet returns; the two-pipe system with dry returns ; the one-pipe system , in which all mains, branches, and risers are relieved into a return main below the water-line; and the one-pipe circuit system, in which all pipes are run above the water-line. The choice of any system will depend upon special conditions and requirements. RADIATION. To find the amount of direct radiating surface required to heat a room, basing calculations upon its cubic contents, allow 1 sq. ft. direct radiating surface to the number of cubic feet shown in the following table: STEA M HE A TING. 301 Proportion of Radiating Surface to Volume of Room. Description. Cu. Ft. Bathrooms or living rooms, with 2 or 3 exposures and large amount of glass surface. 40 Living rooms, 1 or 2 exposures with large amount of glass surface . 50 Sleeping rooms . 55- 70 Halls . 50- 70 Schoolrooms . 60- 80 Large churches and auditoriums. 65-100 Lofts, workshops, and factories. 75-150 The above ratios will give reasonably good results on ordi¬ nary work, if the engineer uses proper judgment in allowing for exposures, leakages through building, etc. Proportion of Radiating Surface to Glass Surface: ^Baldwin’s Rule .—Divide the difference in temperature between that at which the room is to be kept and the coldest outside atmosphere, by the difference between the temperature of the steam pipes and ihat at which the room is to be kept. The quotient will be the square feet or fraction thereof of plate or pipe surface to each square foot of glass, or its equivalent in wall surface. Let S = amount of radiating surface required to counter¬ act the cooling effect of the glass and its equiva¬ lent in exposed wall surface in square feet; t = difference in degrees F. between the desired tem¬ perature of the room and that of the external air; t\ = difference in degrees F. between the temperature of heating surface and that of the air in the room; s = number of square feet of glass and its equivalent in exposed wall surface. Then, applying rule, S = - 7 - s. h The heating surface found by this rule only compensates for the heat lost by transmission through windows, walls, and * This rule also applies to hot-water heating. 302 HEATING AND VENTILATION. other cooling surfaces; it does not provide for cold air enter¬ ing the room through loosely fitting doors, windows, etc., for which an ample allowance must be made. Some build¬ ings are so poorly constructed that 50 per cent, or more must be added to the amount of heating surface obtained by the rule in order to counteract the cooling effect of these air leak¬ ages. A common practice is to add 25 per cent, for buildings of ordinary good construction. Ample allowance should be made for rooms exposed to cold winds. It is usual to esti¬ mate about 10 sq. ft. of wall surface as equivalent in cooling power to 1 sq. ft. of glass. PIPING. Sizes of Steam Pipes. Radiating Surface. Sq. Ft. 1-Pipe Work. In. 2-Pipe Work. Radiating Surface. Sq. Ft. 1-Pipe Work. In. 2-Pi Wor e Steam In. Ret. In. Steam In. Ret. In. 40- 50 1 i 3 1,600- 2,000 4£ 4 3£ 100- 125 li 1 i 2,000- 2,500 5 4i 4 125- 250 1 £ li l 2,500- 3,600 6 5 4£ 250- 400 2 H li 3,600- 5,000 7 6 5 400- 600 2 £ 2 n 5,000- 6,500 8 7 6 600- 900 3 21 2 6,500- 8,000 9 8 6 900-1,200 3! 3 2 | 8 ,000-10,000 10 9 6 1,200-1,600 4 3| 3 - If the mains are high above the boiler, and have short, straight runs, small pipes may be used. If they are unusually low or extremely long or crooked, they should be large. The above table will give good r'esults in ordinary systems. To determine approximately the size of steam mains or principal risers, allow 1 sq. in. of sectional area of pipe for each 100 sq. ft. of radiating surface. To determine the amount of radiating surface a pipe will supply, allow 100 sq. ft. for each square inch of sectional area of pipe. STEAM HEATING. 303 Sizes of Tappings for Prime Surface Radiators. Direct Radiators. Indirect Radiators. 1-Pipe Work. 2-Pipe Work. Surface. Size. Surface. Steam. Return. Surf. Steam. Ret. Sq. Ft. In. Sq. Ft. In. In. Sq. Ft. In. In. 25 1 30 2 30 1 * 25- 50 H 30- 50 1 i 30- 50 It 1 50- 90 li 50-100 It l 50-100 1 * H 100-160 2 100-160 U » 1 100-160 2 1* DIRECT RADIATORS. Heat units emitted j>er hour, per square foot of external surface, per degree of difference in temperature. Vertical Tubes, Prime Surface Radiators. Difference in Temper¬ ature. F°. Tubes Massed. Single Row Tubes. Height, 40 Inches. B. T. U. Height, 24 Inches. B. T. U. Height, 40 Inches. B. T. U. Height, 24 Inches. B. T. U. 50 1.29 1.54 1.46 2.01 60 1.33 1.58 1.50 2.06 70 1.36 1.62 1.54 2.12 80 1.39 1.66 1.58 2.17 90 1.41 1.70 1.62 2.22 100 1.46 1.74 1.65 2.27 110 1.49 1.78 1.69 2.32 120 1.52 1.82 1.73 2.38 130 1.56 1.86 1.77 2.43 140 1.59 1.90 1.81 2.48 150 1.63 1.94 1.85 2.53 160 1.66 1.98 1.88 2.59 170 1.69 2.02 1.92 2.64 180 1.73 2.06 1.96 2.70 190 1.76 2.10 2.00 2.75 200 1.80 2.14 2.03 2.80 210 1.83 2.18 2.07 2.85 220 1.86 2.22 2.11 2.90 230 1.90 2.27 2.15 2.96 240 1.93 2.31 2.19 3.01 304 HEATING AND VENTILATION. Flue Radiators—Natural Draft. Radiating Surface. B. T. U. Emitted. Total B. T. U. Emitted. Extended. Sq. Ft. Plain. Sq. Ft. Extended. Sq. Ft. Plain. Sq. Ft. Extended. Plain. 57.80 40.40 1.65 1.97 95.37 79.58 6.40 4.24 2.05 2.39 13.12 10.13 63.10 41.20 1.39 1.85 87.81 76.22 7.18 4.50 1.90 2.24 13.64 10.08 INDIRECT RADIATORS. Heat units emitted per square foot of actual surface per hour, per degree of difference in temperature. Natural Draft, Extended Surfaces. Height of Flue. Feet. Velocity of Air per Second. Feet. * B. T. U. Emitted. Height of Flue. Feet. Velocity of Air per Second. Feet. B. T. U. Emitted. 5 2.90 1.70 30 6.70 2.60 10 4.10 2.00 35 7.14 2.67 15 5.00 2.22 40 7.50 2.72 20 5.70 2.38 45 7.90 2.76 25 6.30 2.52 50 8.20 2.80 Forced Draft, Plain Surfaces. Velocity of Air per Second. Feet. * B. T. U. Emitted. Velocity of Air per Second. Feet. \ B. T. U. Emitted. Velocity of Air per Second. Feet. B. T. U. Emitted. 3 3.42 8 5.71 18 8.50 4 4.00 10 6.33 20 9.00 5 4.50 12 6.93 22 9.42 6 4.94 14 7.50 24 9.79 7 5.33 16 8.06 * A British thermal unit is the quantity of heat necessary to raise the temperature of 1 lb. of water 1° F. STEAM HEATING. 305 SIZE OF CHIMNEYS. Chimneys are proportioned either to the amount of radiating surface in a building, or to the horsepower required for machinery, or to both combined. The draft pressure increases with the height of the chimney. Boilers operating under forced draft from fans or blowers do not require high chimneys, except for the purpose of conveying the gases of combustion above the breathing zone. But in all ordinary buildings the chimneys should be built suffi¬ ciently high and large so that forced draft is not necessary. Size of Chimney for Given Amount of Radiation, or Horsepower. Steam Radiation Sq. Ft. Horse¬ power. Diameter, or Side, of Chimney in Inches. 20 ft. High. 40 ft. High. 60 ft. High. 80 ft. High. 100 ft. High. 250 2.5 7.5 6.8 6.3 6.0 6.0 500 5.0 9.5 8.8 8.0 6.5 7.4 750 7.5 11.4 10.3 9.4 8.8 8.5 1,000 10.0 12.8 11.5 10.5 10.0 9.5 1,500 15.0 15.3 13.5 12.5 11.5 11.3 2,000 20.0 17.3 15.3 14.0 13.3 12.5 3,000 30.0 20.5 18.3 16.5 15.8 15.0 4,000 40.0 23.5 20.8 19.0 17.8 17.0 5,000 50.0 26.0 23.0 21.0 19.5 18.5 6,000 60.0 28.5 25.0 22.8 21.3 20.3 7,000 70.0 30.5 27.0 24.5 ' 23.0 21.5 8 ; 000 80.0 32.5 28.5 26.0 24.3 23.5 SIZE OF BOILERS. No hard-and-fast rules can be employed for determining the heating capacity of boilers or for ascertaining the sizes best adapted for different jobs. The following table is deduced from practical tests and observations by Prof. Carpenter, of Cornell University, and is considered to be within the limits of safety. Two cases are taken: (A) when the rate of coal consumption is 10 lb., and ( B ) when it is 8 lb. per sq. ft. of grate surface per hour. The latter is preferable for hot-water heating. Proportioning Parts of Heating Boilers.— Steam Heaters. 306 HEATING AND VENTILATION. o o o o rH 100 7 19* 10 100 80 300 240 42.5 1 33.3 34.5 26.5* 1430 | 1111* 33.3 41.5 two 4-inch 34 7,500 75 7 1 9* 9.5 95 76 285 ooq 40.5 31.5* 32.7 25.6* 1071 833* 26.5 32.5 two 3-inch 28 5,000 * iCOO lOC^ ^GiOdooGodococo^io O — OJM^HCOCOHHN CM O O o Tt^ Oi to o cd x> tq odGOiOCO^^NOi'oiOaj^CO ^ CO O O O CO Cl GO H H tO lQ -H lO lO OOXO'HO'MOOOMM’iOCOOs CO COO-HOiCOClTf HH rH CM H 2,000 (MOP*h*OC'lCOOMClCOHCOi s * 04 H CO CO rH rH 1,500 tO CM OCOiOCOO^^ iCCDI>OCDHCCOClLOi>OOCOiC rH N tO » to ^ toco^^oo^^: OiOCOiO(MOtOHNNiOCOC4(M rH CO UD rH rH CO CM rH rH 750 tO hH o *> oo *° ^ ^ X> id CO O 00 00 hH CO r^-’ CO ^ id , ~~ lit) TfH rH tH CO M lO rH -H o> © & a o ■H H> c3 • rH *3 cS Ph £ © © © © a, H ci od (T^ H ^ ^ ^ H 2c2<5 ^ - ^MObCb J 3 !-,fH^ t oSg > C^di *2 eH “ »3 § r} «£? -t-» -*j "' fd d 5rJ o' efts td^* P< ^M^bebcggbe - -> & a&oo &&«§§>,© a a g>g*s ° g'c'c^ | g $§•§ ^gw 3 3 » § . c-cc m .a .a a x3 © © © pi a .'V* M h ^ '•H ry* ‘■"“ , rC 1 r>m ’- rKr\ /'*> H^hiHhPh^hhhOv'mH Co Is Ho e $ j§ I I •♦o s rH tO o rH rH CO lO to CO CO CO o to H 00 o o CO to »o rH o CM CO CO rH rH CM CO ~r h CO Tt< o CM CO r-- G> to O CO co rH CO o CO CM ex; rH rH CM CO CO CO IO to CM CO o o 00 CO 00 co 00 o o> rH CO CO a CO CM Oi (M rH rH CO o CO CM CO G* 05 tH lO to 00 CO td tO CO CM CO CM rH rH to to M M oo r- CO CM 00 o CO rH cd -r (M CM CM CO CM rH rH tH o CO CM i> lO tO CO CO 1 - —H CO CO rH cd rH CM CM CO 04 Oi hO lO O CO r- tO 05 tO o CM CM CO CM CO rH CM* rH GO CO to to to a CO —H o CO cd rH CM i—l CO CM CO rH 'drC • . • . . . . oS ® oK ® s ®£ oPh s£ • rH C\ t-H CO jj. ^ 6 1 00 ^ EC EC EC EC EC CO CO CO CO ^EC l 20 H 35 20 1 * 56 40 25 2 116 85 70 50 21 220 150 120 100 90 3 345 240 200 170 150 140 125 110 100 90 31 500 340 280 245 225 205 190 175 162 150 4 700 485 390 340 310 280 260 240 230 220 41 925 640 535 460 410 375 345 325 300 295 5 1,200 830 700 600 540 490 450 420 400 380 6 1,900 1,325 1,100 950 850 775 700 650 620 600 7 2,000 1,600 1,400 1,250 1,140 1,050 975 925 875 8 1,970 1,720 1,550 1,440 1,350 1,300 1,250 9 1,900 1,800 1,700 1,620 Diameter of Radiator Connections. Direct Radiation. Fall of Temperature, 20°. Size of pipe in inches. * 1 H 1* 2 2* Area in square feet . 16 24 40 60 120 240 The sectional area of the mains should approximate the sum of the area of its branches, hut in many cases, particu¬ larly where there is no indirect work, the sizes may be a little less. The fittings used on hot-water mains should all have easy curves and the branches should be Y’s, to reduce resistance to a minimum. Special distributing fittings should be used to induce circulation through radiators op the first floor. HOT-WATER HEATING. 811 Sizes of Mains and Branches. Sizes of Main. Sizes of Branches. 1 " will supply two 11 " will supply two 1"; or one V and two f". Is" will supply two 11"; or one 11" and two 1". 2 " will supply two 11"; or one 11" and two 11". 21 " will supply two 11" and one 11"; or one 2" and one 11". 3" will supply one 21" and one 2"; or two 2" and one 1{". 31" will supply two 21" ; or one 3" and one 2": or three 2". 4" will supply one 31" and one 21"; or two 3"; or four 2". 41" will supply one 31" and one 3"; or one 4" and one 21". 5" will supply one 4" and one 3"; or one 41" and one 21". 6 " will supply two 4" and one 3"; or four 3"; or ten 2". 7" will supply one 6" and one 4"; or three 4" and one 2". • 8" will supply two 6" and one 5"; or five 4" and two 2". All flow and return pipes should be of the same size. All pipes must rise from the boiler to the radiators with a pitch of at least 1 in. in 10 ft. The expansion-tank capacity should be at least ^ that of the entire apparatus, if it is an open tank. Closed tanks are not to be recommended. Radiating Surface Supplied by Hot-Water Risers. Direct Radiation. Fall of Temperature , 20°. Diameter of Story Where Heater is Located. Riser. 1 2 3 4 5 6 Inches. Sq. Ft. Sq. Ft. Sq. Ft. Sq. Ft. Sq. Ft. Sq. Ft. 1 12 17 21 24 1 22 32 40 48 li 38 56 70 80 88 11 66 92 112 132 145 2 140 196 238 2 S0 310 21 240 328 400 470 515 3 350 490 595 700 770 850 31 510 705 860 1,010 1,110 1,215 4 700 980 1,190 1,280 1,540 1,660 312 HEATING AND VENTILATION. There is a practical limit to the advantageous vertical length of risers, especially with the smaller pipes. If a small riser extends to a great height, the friction become: excessive, and the quantity of water delivered will he mucl. . smaller than it would otherwise be. Limiting Height of Risers. Diameter in inches. £ 1 H H 2 Height in feet ... 20 30 45 60 80 The horizontal pipes on the upper floors of a building, and also the risers leading thereto, may be made smaller in diameter than those upon the lower floors, because the force which impels the water increases with the height of the circuits. The proper size of a pipe having been determined for a given service on the first floor, the diameter for equal service on higher floors—the temperatures remaining the- same—may be found by multiplying by the following factors: Story.2d 3d 4th 5th Factor .87 .80 .76 .73 The area of heating surface that may be properly supplied by a pipe of given diameter will increase as the circuit is made higher. If the area which is known to be right for a given size of pipe on the first floor, be taken as 1, the areas on the uppei floors will increase in the following order: Story. 2d 3d 4th 5th Proper area heating surface. 1.40 1.70 1.98 2.20 FURNACE HEATING, It is assumed in the following rules and tables that the average temperature of the hot air in the flues is about 120°, and that the air is moved solely by natural draft. A simple method for proportioning hot-air pipes to deliver a given volume of air to the several floors is to assume that 1 sq. in. of stack, or flue, area will supply 100 cu. ft. of air per hour at the first tLor, 125 at the second floor, and 150 at the third floor. FURNACE HEATING. 313 Ratio of Area of Hot-Air Pipes to Volume of Room. Rooms. Ratio. 1 Sq. In. to Cu. Ft. First-floor rooms, moderate exposure. 30 First-floor rooms, great exposure . 20-25 Second-floor rooms . 25-35 Third-floor rooms. 30-40 A more accurate method is as follows: Rule .—For rooms on the first floor, add together the total glass surface and £ the area of the exposed walls in square feet, and multiply the total by 1.5; the product is the proper area of the pipe in square inches. For second-story rooms, multiply by 1 to 1.25, according to the exposure; and for the third story, by .75 to 1. If leaders are of considerable length, their area should be about x greater than the connecting stacks. Size of Hot-Air Pipes and Registers. First-Floor Rooms. o a$ n oj> •<-h m 12X15 10 X 12 or 10X14 9X12 8 X 12 OH CD • .ss o ° a • 02 ^ O-ri Pi n bx)i—i •H CD 10X14 9X12 8 X 12 8 X 10 U Pi ©M ai cSjr 1 ■ r * P-l <+-1 o 10 - 9- 8 - 7- CO ° a . 8 g£ mp4 16X16 to 18X20 14 X 14 to 16X16 10X10 to 13 X 14 7X12 to 12X12 2 g>. fetes w *53 © 10 9 8 8 314 HEATING AND VENTILATION. Area of Rectangular Registers. Size of Opening. In. 6X10 8X10 8X 12 8X 15 9X12 9X 14 10 X 12 10 X 14 10 X 16 12 X 15 12 X 19 Net Area. Sq. In. 40 53 64 80 72 84 80 93 107 120 152 Size of Opening. In. 14 X 22 15 X 25 16 X 24 20 X 20 20X24 20 X 26 21 X 29 27 X 27 27 X 38 30X30 Net Area Sq. In. 205 250 256 267 320 347 400 486 684 600 Area of Round Registers. Diam of Opening. In. Net Area. Sq. In. Diam. of Opening. In. Net Area. Sq. In. 7 26 16 134 S 33 18 169 9 42 20 209 10 52 24 301 12 75 30 471 14 103 36 679 VENTILATION. Ventilation is a process of moving foul air from any space and replacing it with fresh air. A positive displacement, however, does not take place; the incoming fresh air chiefly dilutes the foul air to a point suitable for healthful respira¬ tion. Pure air, such as exists in the open country, contains about 4 parts of carbonic acid ( C0 2 ) per 10,000 parts of air, while badly ventilated rooms often contain as much as 80. VENTILA TION. 315 parts of CO 2 per 10,000 of air. Hygienists, after careful study, have decided that an increase of 2 parts of C0 2 per 10,000 of air should be accepted as the standard of respirable purity, and any excess of C0 2 above this may be considered as vitiation. Production of C0 2 per Hour. Source. Cu. Ft. Adult man ... .6 One cubic foot of gas, burning. .8 Ordinary lamp . 1.0 Candle .. .3 Taking the figures above given —1 parts of C0 2 per 10,000 parts of fresh air, and 6 parts (= 4 + 2) per 10,000 of vitiated air—as the standard for proper health conditions, it is found that 3,000 cu. ft. of fresh air per hour are necessary for each adult person. If a different standard than 6 is used, the number of cubic feet per person will be found by dividing B,000 by the difference between this standard and 4. If any lights deliver their products of combustion into the room, the amount of CO- 2 given off by them should be con¬ verted into its equivalent in men, thus: One ordinary gas light equals in vitiating effect about 5f men, an ordinary lamp If men, and an ordinary candle about f man. It is considered good practice to allow 2,000 cu. ft. of fresh air per hour for each inmate of a room or auditorium. Hospi¬ tals and such places, where the vitiation is due to exhalations from diseased or sick people, should be provided with at least twice this amount. NATURAL VENTILATION. In natural ventilation systems, the drafts in the flues or ducts are caused by the difference in density between the air in the ducts and the outer atmosphere. The higher the tem¬ perature in the ducts, the more rapid will the draft become. In the following table 50 per cent, (a fair average in good work) has been deducted from the theoretical flow, to offset 316 HEATING AND VENTILATION. all ordinary resistances in the flues, such as friction, change in direction, etc. The difference in temperature given in the table is that existing between the outer atmosphere and the average of the air in the flue. Knowing the velocity per minute, and the cubic feet of air per minute to be removed, the area of the flue in square feet is found by divi¬ ding the volume by the velocity. Flow of Air in Flues per Square Foot of Section. By Natural Draft , in Cubic Feet per Minute. Height of Flue in Feet. a . £ ft a) 10 Cu. Ft. 15 Cu. Ft. 20 Cu. Ft. 30 Cu. Ft. 40 Cu. Ft. 50 Cu. Ft. 60 Cu. Ft. 80 Cu. Ft. 100 Cu. Ft. 10 108 133 153 188 217 242 264 306 342 15 133 162 188 230 265 297 325 375 420 20 153 188 217 265 306 342 373 435 485 25 171 210 242 297 342 383 420 485 530 30 188 230 265 325 375 419 461 530 594 40 216 265 305 374 431 482 529 608 680 50 242 297 342 419 484 541 594 680 768 60 266 327 376 460 532 595 650 747 842 70 288 354 407 498 576 644 703 809 910 80 308 379 435 533 616 688 751 866 972 90 326 401 460 565 652 728 795 918 1,029 100 342 419 484 593 684 765 835 965 1,080 125 384 470 541 664 766 857 939 1,085 1,216 150 419 514 593 726 838 937 1,028 1,185 1,325 FORCED VENTILATION. There are two classes of forced ventilation : (1) The plenum system, in which the air pressure in the building is slightly greater than that of the outer atmosphere; in other words, that system by which air is blown through the building by a fan or other blower placed at the inlet. (2) The vacuum system, or that method of removing foul air, and causing a consequent inrush of fresh air, by an exhaust fan placed at the outlet to the vent flue or stack. In the latter system, the VENTILATION. 317 air pressure in the building is slightly lower than that of the outer atmosphere. The plenum system is the more whole¬ some and preferable method. The capacity of a fan, that is, the amount of air which it will deliver, depends considerably upon the construction of the fan, and upon the resistance to the flow of the air. The following table shows a safe capacity for some leading forms of blowers and exhaust fans, operating against a pres¬ sure of 1 oz. per sq. in., or If in. water, nearly: Diameter of Wheel. Ft. Revolutions per Minute. Horsepower Required. Capacity per Minute. Cu. Ft. 4 350 6.0 10,600 5 325 9.4 17,000 6 275 13.5 29,600 7 230 18.4 42,700 8 200 24.0 46,000 9 175 29.0 56,800 10 160 35.5 70,300 If the resistance is greater than above given, the required capacity may he obtained by increasing the number of revo¬ lutions-, increasing the horsepower correspondingly. Or, if the resistance is less, the required capacity may be obtained by reducing the number of revolutions, with a corresponding decrease of power. In selecting a fan, it is advisable to choose a large one, so that it may run easily, quietly, and economically. A small fan, which must be run at high speed, wastes too much energy, and often makes a disagreeable noise. Fresh-air inlets, if near the floor, should be so-arranged that the velocity of inlet will not exceed 2 ft. per second ; a higher velocity is considered a perceptible draft. Higher velocities, however, are permissible if the inlets are located more than 8 ft. above the flpor. Vent-flue inlets can safely be made to operate with a velocity of 6 or 8 ft. per second, without the air-current being disagreeably perceptible, u 318 GAS AND GAS-FITTING. GAS AN D GAS-FITTING. GAS. KINDS OF GAS. Coal gas is made by heating bituminous coal in air-tight boxes or retorts. The heat breaks up the combinations of hydrogen and carbon in the coal, transforming them into other compounds, most of which are gaseous at ordinary temperatures. Among the new compounds thus made are tar, ammonia, and sulphureted hydrogen. The tar and ammonia are condensed and removed. The gas also undergoes puri¬ fication and scrubbing; in the former process, the gas is forced in thin streams through pans filled with lime, oxide of iron, etc.; and in the latter, through bodies of liquid charged with certain chemicals. Oil gas is made from petroleum in a similar way and from almost any kind of oil, grease, or fat. Producer gas differs from the coal gas commonly used for lighting, in having much less combustible matter, and in having a large percentage of nitrogen. It is made by burning anthracite or bituminous coal in a closed furnace, with a supply of air too small for complete combustion. The average quality of producer gas contains from 10 to 15 per cent, of hydrogen, from 20 to 30 per cent, of carbon monoxide ( CO), and from 40 to 60 per cent, of nitrogen. Producer gas burns with a dull reddish flame, and its heating value is about one- fourth that of good coal gas. Water gas is made from anthracite coal and steam. The coal is placed in an air-tight cylinder, ignited, and raised to an incandescent heat by an air blast; the blast is then shut off, and dry steam is blown through the glowing fuel. The intense heat breaks up the steam into free oxygen and hydro¬ gen. the oxygen combining with the hot carbon, forming CO, and the hydrogen passing along with it, but not com¬ bining. These are then led to a gas holder. The operations of blowing up and making gas alternate at intervals of about GAS. 319 3 minutes, until the fuel is exhausted. The fresh gas burns perfectly in heating burners, but when used for lighting pur¬ poses, is always enriched in carbon, by the vaporization of petroleum before it leaves the generator. The density of pure water gas is .4 that of air. It naturally has very little odor, but some impurities are allowed to remain to give the gas a perceptible odor. Acetylene (chemical symbol, C 2 -H 2 ) is composed of 12 parts of carbon to 1 of hydrogen by weight, or 92.3 per cent, carbon and 7.7 per cent, hydrogen. It is the most brilliant illumi¬ nating gas known. Its density is about .91, and its weight at 32° F. is .073 lb. per cu. ft. It is without color, and has a strong odor, like garlic. It is poisonous to breathe, in about the same degree as ordinary gas. The heat developed by the combustion of 1 cu. ft. is theoretically 1,090 heat units. Acetylene is manufactured by mixing calcium carbide with water. The carbide is a mixture of coke and lime which had been fused in an electric furnace. It is reddish brown, or gray, in color, somewhat crystalline, and decomposes water like ordinary quicklime; the calcium takes oxygen from the water, forming oxide of calcium, or common quicklime, while the carbon combines with the hydrogen of the water, and forms the desired compound, acetylene. Considerable heat is given off during the operation. Pure carbide of calcium will yield 5.4 cu. ft. of acetylene per pound ; but it is hardly safe to reckon upon more than 4.5 cu. ft. from the commercial carbide. Special burners are required for acetylene illumination, provided with small air holes to supply more air to the flame than is obtained by ordinary burners. Acetylene will give a light of about 240 candlepower when burned at the rate of 5 cu. ft. per hoiir, while good coal gas only gives 16 candlepower at the same rate of combustion. Acetylene can be reduced to liquid form, at a temperature of 60°, by a pressure of about oOO lb. per sq. in., but is then unsuitable for use in buildings, owing to the danger of explosion. Acetylene corrodes silver and copper, forming explosive compounds, but does not affect brass, iron, lead, tin, or zinc. These facts should be borne in mind when constructing apparatus for its use. 320 GAS AND GAS-FITTING. Gasoline gas, or carbureted air, sometimes called air gas, is a mixture of gasoline vapor with air, and, when pure, is so rich in carbon that special burners must be employed for lighting purposes. The quantity required to produce 1,000 cu. ft. of gas of from 14 to 16 candlepower is about gal. of the best grade, and more if the gasoline is of a lower grade. The specific gravity of gasoline is about .74 that of water. The temperature of a gasoline-gas machine should range between 40° to 80°. The highest grade of gasoline, that is, the grade that will evaporate most freely at ordinary tem¬ peratures, should be used for winter service. The generators should be located outside the building, in a sheltered place. An air pump is used to pump fresh air through the gen¬ erator, and a mixing device is commonly employed for mixing air with the gas before it reaches the burners. The pump and mixer are usually located in the cellar of the building. PRESSURE OF GAS. If a gas is lighter than air, at the same temperature, the pressure will be greatest at the top of the chamber containing the gas; if heavier, the greatest pressure will be at the bottom of the chamber. The upward pressure of gas having a less density than air is caused by its deficiency in weight, and con¬ sequent inability to balance the pressure of the atmosphere. For illustration, consider a column of gas 1 ft. square and 100 ft. high, having a density of .5, or one-half that of air, the temperature being the same as that of the atmos¬ phere—say 60°. Air at 60° weighs .0764 lb. per cu. ft., and as the column contains 100 cu. ft., it will weigh .0764 X 100 = 7.64 lb. The gas having a density of .5 will weigh only half as much, or 3.82 lb., and is, therefore, unable to balance an equal volume of air. Consequently, it is pressed upwards with a force of 7.64 — 3.82 = 3.82 lb. against the top of the chamber which contains it. Whatever the actual pressure of the gas may be at the bottom of the column, it will, in this case, be increased at the top to the extent of 3.82 lb. per sq. ft. The increase of pressure in each 10 ft. of rise in the pipes, with gas of various densities, is shown ir> the following table: GAS. 321 Rise in pressure (in. of water). 0 . .0147 .0293 .044 .058 .073 .088 .102 Density of gas. 1 . .9 .8 .7 .6 .5 .4 .3 Example. —The pressure in the basement, at the meter, is 1.2 in. of water; what Avill be the pressure on the sixth story, 70 ft. above, the density of the gas being .4? Solution.— The table shows that the increase will be .088 for each 10 ft. of rise; therefore, .088 X 7 = .616 increase. Then pressure at sixth story = 1.2 + .616 = 1.816 in. MEASUREMENT OF PRESSURE AND FLOW. Pressure.—The pressure of gas is measured by the common water gauge, which is shown in Fig. 16. The tubes b and c are glass, and are filled with water up to the zero of the scale, which is graduated in inches and fifths or tenths of an inch. The tube c is opened to the air at the top. When pressure is admitted to a, the water will sink in the tube 6, and will rise in c. The difference in the height of the water in the two tubes, measured in inches, is the measure of the pressure exerted in inches of water. For measuring heavier pres¬ sures, mercury is used instead of water. Pressures measured in inches of water or mercury may be translated into pounds per square inch or square foot, by multiplying the reading by the following figures: 1 in. of water at 62° F. = 5.2020 lb. per sq. ft. 1 in. of water at 62° F. = .0362 lb. per sq. in. 1 in. of mercury 62° F. = .4897 lb. per sq. in. Pressure per square inch or square foot may be converted into inches or feet of water, or inches of mercury, by multiplying the pressures by the following figures: 1 lb. per sq. ft. = .1923 in. of water at 62° F. 1 lb. per sq. in. = 27.70 in. of water at 62° F. 1 lb. per sq. in. = .2042 in. of mercury at 62° F. Fig. 16. 322 GAS AND GAS-FITTING. gas, passing through a pipe in a given time, is computed by multi¬ plying the velocity by the area of the pipe. The velocity may be measured by a Pitot tube, as shown in Fig. 17. This consists of two tubes, a and b , inserted in a plug c, the lower end of a being square, and that of b curved to face the current; the upper ends are con¬ nected to a water gauge d. Gas entering through b depresses the water column as shown ; the veloc¬ ity corresponding to the reading is found from tables which are gen¬ erally furnished with the instrument. The actual quantity of the gas is computed by correcting the volume for temperature and pressure, reducing it to a volume at standard temperature of 32° F. and standard pressure of 1 in. of water. The correction for temperature may be made as follows : Rule I .—Multiply the measured volume by 192 and divide the product by h&O plus the actual temperature. The quotient will be the volume at 82° F. The correction for pressure may be made as follows : Rule 2 .—Multiply the volume at 82° F. by the pressure in inches of water plus 107, and divide the product by 4 08. The quotient will be the volume at 1 inch pressure, and at 32° F. Example.— A pipe passes 1,000 cu. ft. of gas per hour, under a pressure of 8 in. of w r ater and at a temperature of 60°. What will the volume be when the pressure is reduced to 1 in., and the temperature to 32° ? Solution.—B y the first rule, the volume at 32° is Flow.—The volume of 1,000 X 492 = 946.1 cu. ft. 460 + 60 By rule 2, the volume under 1 in. pressure and at 32° is 946.1 X (8+ 407) 408 962.3 cu. ft. If the quantity of gas delivered through a pipe of given GAS. 323 length is known, that supplied through a longer or shorter pipe is to the known volume as the square root of the given length is to the square root of the required length. With pipes of the same length and diameter, the volumes delivered at any proposed pressure is to that supplied at any other pressure as the square root of the proposed pressure is to the square root of the given pressure. GAS METERS AND PRESSURE REGULATORS. Meters.—For ordinary purposes, the volume of gas passing through a pipe is measured by an apparatus called a gas meter. A gas meter measures the volume only, and its indications are not affected by any change that may occur in the pres¬ sure of the gas. The difficulty thus encountered in correctly measuring the volume of gas actually delivered under varying pressures, is overcome by using a governor between the meter and the street main, or service pipe. The governor is a species of reducing valve which will receive gas at any pressure, whether steady or variable, and will discharge it at a steady low pressure. Fig. 18 shows a meter of the ordinary type. To read such a meter, note the lesser of the two figures between which each hand points, or the figure to which it points, beginning at the left-hand dial; then add two ciphers to the right of the three figures, and the number so obtained will be the 324 GAS AND GAS-FITTING. amount of gas in cubic feet which the meter has measured. Thus the pointers in the diagram indicate that 14,200 cu. ft. of gas have passed through the meter. The dial marked two feet may he used to ascertain the quan¬ tity of gas consumed per hour by a burner, by noting the time required for the pointer to make a revolution. Thus, the hand will make revolutions per hour if 5 cu. ft. pass through the meter in that time. This dial may also be used in testing for leaks. Pressure Regulators.— The objects sought in the use of pres¬ sure regulators or governors are economy in the consumption of gas, steadiness of the lights, and most effective opera¬ tion of the burners. It is of great importance that both volume and pressure at the burners should be closely regu¬ lated. The amount of gas wasted by over pressure is much greater than is generally believed. A good new lava-tip burner consuming 5 cu. ft. per hour at .5 in. pressure, will consume about .5 of a cu. ft. more for each increase of .1 in. in the pressure. Thus an over pressure of .1 in. will increase the gas bill about 10 per cent. The variation, in even the best regulated systems, is usually much greater than one- tenth inch, and is freciuently ten-tenths or more. The two systems ot regulation in use are the pressure and the volumetric regulation. In the first system, a governor is attached to the service pipe at. the meter, and the house dis¬ tributing pipes are maintained at constant pressure; in the second system, each burner is supplied with a governor, the pressure in the pipes not being controlled. The proper place for a pressure regulator, if used, is between the meter and the main. The meter should then be adjusted to suit the house pressure instead of the street pressure. The pressure required at the burners, to secure the best results, varies greatly in different forms of apparatus. The following are the pressures generally used: Argand burners..2 in. of water. Common batswing burners... .5 in. of water. Wellsbach incandescent burners.5 or more. Wenham and Lebrun lamps .5 to 1 or more. Atmospheric burners.1.0 or more. 6AS-FITTING. 325 i GAS-FITTING. ILLUMINATION REQUIRED. The number of gas lights required to properly illuminate a room depends on its size, condition of wall surfaces, etc. The reflection from the walls in small rooms is proportion¬ ately greater than in large ones, and hence a less number of burners is required in proportion to the floor space. A 5' (cubic feet per hour) batswing burner is assumed to give a light of 16 candlepower under a pressure of .5 in. of water. For large rooms, such as a church, etc., the proper illumi¬ nation will be furnished by using one burner to each 4 0 sq.ft, of floor. If there are balconies, etc., extra lights must be provided according to the same rule. For smaller rooms, such as are found in ordinary dwellings, the proportion may be 1 light to about 80 sq. ft. of floor. The amount of light required is, therefore, from .4 to .2 candlepower per square foot, according to the size of the room. If incandescent gas lights, such as the Welsbach, are used, the number of lights may be much less, as these lights furnish from 50 to 60 candlepower on a consumption of about 3 cu. ft. of gas per hour, at a pressure of .5 in. SIZE OF PIPES. Each pipe must have enough capacity to suppl\ all its burners when they are in full operation. Allowance must also be made for all heating and cooking apparatus likely to be required. The quantity required for lighting may be reckoned as 5 cu. ft. per hour for each burner, unless other¬ wise given. The actual quantity required by improved burners, however, differs so much that it is impracticable to compute the volume required by merely noting the number of burners. . , Service pipes should never be less than f m. because of liability to chokage, and, if of iron, it is advisable to make the diameter at least 1 in. For small cook stoves, the supply pipe should be at least i in., and for larger stoves, 1 to 1* m. 326 GAS AND GAS-FITTING. Having ascertained the probable maximum quantity required in cubic feet per hour, the diameter of the pipe can be round from the following table. If the length of the pro¬ posed pipe exceeds the maximum length given, the next larger size pipe should be chosen. If the pressure exceeds 2 in., the principal pipes may be reduced one size. If the pressure is less than 1 in., all pipes must be increased one size, and with very long pipes, the diameter will require to be increased still more. When gasoline gas is used, no dis¬ tributing pipe should be less than | in. Capacity op Gas Pipes. Diameter of Pipe. In. Maximum Length. Ft. Capacity per Hour. Coal Gas. Cu. Ft. Gasoline Gas. Cu. Ft. JL 6 10 8 20 15 10 30 30 20 t 50 100 75 1 70 175 125 H 100 300 200 H 150 500 350 2 200 1,000 700 2? 300 1,500 1,100 3 450 2,250 1,500 4 600 3,750 2,500 In this table, the pressure is assumed to be about 2 in. of water. The quantities stated are those which the pipes will deliver at the burners without objectionable fall of pressure. INSTALLATION AND TESTING. The pipes used for the distribution of gas in buildings are standard plain wrought-iron or steel pipe. If the location of the pipes is not shown by the architect, then the gas-fitter must use his own judgment in determining their position. He should be governed by the following con¬ siderations ; GAS-FITTING. 327 1. The pipes should run io the fixtures in the most direct manner practicable. 2. The pipes must be graded to secure proper drainage with¬ out excessive cutting of fioorbeams, or otherwise damaging the building. 3. Pipes which run crossways of fioorbeams should be laid not more than 1 ft. from the wall, to avoid serious injury to the floor. 4. Fixtures should be supplied by risers rather than by drop pipes, as far as practicable. 5. All pipes should be located where they can be got at for repairs, with the least possible damage to the floors or walls. 6. The fittings should be malleable iron galvanized, beaded fittings being preferable to plain ones. Plain black iron fit¬ tings should never be used on important work. Testing. —As soon as the pipes are all in place and are properly secured, the system should be tested to find if it is gas-tight. Air should be forced in the system until the gauge indicates 15 or 20 in. of mercury, or 7 to 10 lb. per sq. in., the pressure being continued for about an hour, and if the gauge shows a falling off in pressure of more than i in. of mercury, or | lb. per sq. in., then the system cannot be passed as perfect. The mercury-column differential proving gauge is well adapted for testing gas pipes, etc., which are to be made air-tight; common spring gauges are unreliable. The extent of a leak may be judged by the rapidity of the fall in pressure, but its location must be found by the sense of smell. For this purpose a small quantity of ether should be introduced into the pipes. The vapor of the ether will diffuse throughout the system and escape from the leak, where it will be detected by its odor. The gauge should be provided with an ether cup especially for testing purposes. In case of large buildings, it is ad visible to test the piping in sections, say one floor at a time, because it is much easier to locate leaks. After each section is tested they may be con¬ nected, and then subjected to a final test. The pipes should not be covered until the tests are com¬ pleted. The owner, architect, or inspector should witness the tests. 328 ESTIMATING. ESTIMATING. APPROXIMATE ESTIMATES. The following table shows the approximate cost per cubic foot of various kinds of structures. In computing the con¬ tents of a building there is no uniformity in practice, but no great error will be made in figuring the solid contents from floor of cellar to ridge of roof. Cost of Buildings per Cubic Foot. Class of Building. Cost per Cu. Ft. Cents. Small frame buildings, costing from $800 to $1,500 . 8 to 9 Frame houses, 8 to 12 rooms, costing from $1,500 to $10,000. 9 to 11 Brick houses, 8 to»10 rooms. 10 to 14 Highly finished city dwellings (brick or stone). 17 to 20 Schoolhouses (brick). 9 to 11 Churches (stone). 20 to 25 Office buildings (well finished). 30 to 40 Hospitals, libraries, and hotels. 32 to 44 STONEWORK. Stone masonry is usually measured by the perch ; in some sections of the country, however, measurement by the cord is preferred, but the best method (as being invariable) is by the cubic yard. In estimating by the perch, it should be stated how much the perch is taken at, whether 24f or 25 cu. ft. Note should also be made in regard to deduction for open¬ ings, as in most localities it is not customary to deduct those under a certain size, and corners are usually measured twice. Rough stone from the quarry is usually sold under two classifications, namely, rubble and dimension stone. Rubble consists of pieces of irregular size, such as are most easily obtained from the quarry, up to 12 in. in thickness by 24 in. STONE WORK. 329 in length. Stone ordered of a certain size, or to square over 24 in. each way and to be of a particular thickness, is called dimension stone. Rubble masonry and stone backing are generally figured by the perch or the cubic yard. Dimension-stone footings are measured by the square foot unless they are built of large irregular stone, in which case they are measured the same as rubble. Ashlar work is always figured by the superficial foot; openings are usually deducted and the jambs are meas¬ ured in with the face work. Flagging and slabs of all kinds, such as hearths, treads for steps, etc., are measured by the square foot; sills, lintels, moldings, belt courses, and cor¬ nices, by the lineal foot, and irregular pieces are generally figured by the cubic foot. All carved work is done at an agreed price by the piece. METHODS OF ESTIMATING MASONRY. The following proportions and cost of materials, and amount of labor required for the classes of work below speci¬ fied, are reasonably accurate, and will serve to give a good idea of how to estimate such work. Cost of Rubble Masonry per Perch. Using l-to-3 Lime Mortar. 1 perch stone (25 cu. ft.) delivered at work.$1.25 1 bu. lime.25 £ load of sand, at $1.50 per load.... .25 l day mason’s labor, at $2.50 per day.83 i day helper’s labor, at $1.50 per day.38 Total. $2.96 Using l-to-3 Portland Cement Mortar. 1 perch stone.$1.25 i bbl. Portland cement, at $2.60 per bbl. 1.30 £ load sand, at $1.50 per load .25 i day mason’s labor, at $2.50 per day.83 | day helper’s labor, at $1.50 per day.38 Total ... $*- 01 330 ESTIMATING. Using l-to-3 Rosendale Cement Mortar. 1 perch stone... $1.25 h bbl. Rosendale cement, at $1.25 per bbl.63 l load sand, at $1.50 per load.25 | day mason’s labor, at $2.50 per day .83 y day helper’s labor, at $1.50 per day.38 Total .$3.34 Cost of 1 Square Foot of Ashlar. \ Cost of stone, bluestone facing.$ .30 Hauling stone, say T V of cost of stone.03 Mortar .01 Labor, estimating 80 sq. ft. per day for two masons and one laborer: 2 masons, at $3.00 per day.08 1 laborer, at $1.50 per day.02 Cost per square foot.$ .44 Cost of 1 Cubic Yard of Concrete. 1 bbl. of Rosendale cement, at $1.25 per bbl. $1.25 3 bbl. of sand, or | load, at $1.50 per load.50 1 cu. yd. (about 6 bbl.) of broken stone, at $1.50 per cu.yd. 1.50 Mason, i day, at $2.50.63 Laborer, 1 day, at $1.50. 1.50 Total. $5.38 Cost of 1 Square Yard of Cellar Floor. Concrete, in. thick, at $5.38 per cu. yd.$ .67 Sand bed, 6 in. thick, approximately 1 bbl.17 Spreading sand. .02 fy bbl. of Portland cement for finishing coat, at $2.60 per bbl.22 rV bbl. of white sand, at $1.00 per bbl. .08 Mixing and spreading surface layer.08 Cost per square yard...$1.24 STONEWORK. 331 DATA ON ASHLAR AND CUT STONE. Cost. —The following figures are average prices of stone when the transportation charges are not excessive; the figures are not given as fixed values, but to show the relative costs. They are based on quarrymen’s wages of $2.25 per day, and stone cutters’ of $3.00 per day. First-class rock-face bluestone ashlar, with from 6" to 10" beds, dressed about 3 in. from face, will cost, ready for lay ing, from 35 to 45 cents per square foot, face measure; while very good work will cost from 25 to 40 cents per square foot. Regular coursed bluestone ashlar, 12 to 18 in. high, with from 8" to 12" beds, will cost about 50 cents per square foot. To this (and the previous figures) must be added the cost of hauling, w r hich on an average will be about 2 cents per square foot. The cost of setting ashlar may be taken at about 10 cents per square foot. The rough stock for dimension stone will cost, at (lie quarry, if Quincy granite, in pieces of a cubic yard, or less, from 50 to 75 cents per cubic foot; if bluestone, about 50 cents; if Ohio sandstone, about 30 cents per cubic foot; if Indiana limestone, about 25 cents per cubic foot; and if Lake Superior red stone, about 40 cents per cubic foot. Flagstones for sidewalks, ordinary stock, natural surface, 3 in. thick, with joints pitched to line, in lengths (along walk) from 3 to 5 ft., will cost, for 3' walk, about 8 cents per square foot (if 2 in. thick. 6 cents); for 4' walk, 9 cents; and for 5' walk, 10 cents per square foot. The cost of laying all sizes will average about 3 cents per square foot. The above figures do not include cost of hauling. Curbing (4" X 24" granite) will cost, at quarry, from 25 to 30 cents per lineal foot; digging and setting will cost from 10 to 12 cents additional; and the cost of freight and hauling must also be added. The following figures show the approximate cost of cut bluestone for various uses: Flagstone, 5", size 8 ft. X 10 ft., edges and top bush- hammered, per sq. ft., face measure .$ -65 Flagstone, 4", size 5 ft. X 5 ft., select stock, edges clean cut, natural top, per sq. ft. .30 332 ESTIMATING. Door sills, 8 in. x 12 in., clean cut, per lineal foot.$1.25 Window sills, 5 in. V 12 in., clean cut, per lineal foot.80 Window sills, 4 in. X 8 in., clean cut, per lineal foot.. .45 Window sills, 5 in. X 8 in., clean cut, per lineal foot.60 Lintels, 4 in. X 10 in., clean cut, per lineal foot._ .60 Lintels, 8 in. X 12 in., clean cut, per lineal foot. 1.10 Water-table, 8 in. X 12 in., clean cut, per lineal foot. 1.25 Coping, 4 in. X 21 in., clean cut, per lineal foot. 1.10 Coping, 4 in. X 21 in., rock-face edges and top, per lin. ft. .45 Coping, 3 in. x 15 in., rock-face edges and top, per lin. ft. .25 Coping, 3 in. X18 in., rock-face edges and top, per lin. ft. .30 Steps, sawed stock, 7 in. X 14 in., per lineal foot.90 Platform, 6 in. thick, per square foot.45 To the prices of cut stone above given must be added the cost of setting, which, for water-tables, steps, etc., will be about 10 cents per lineal foot, and, for window sills, etc., about 5 cents per lineal foot. In addition, allow about 10 cents per cubic foot for fitting, and about 5 cents per cubic foot for trimming the joints after the pieces are set in place. A stone cutter can cut about 6 sq. ft. of granite per day, 8 sq. ft. of bluestone, and about 10 sq. ft. of Ohio sandstone or Indiana limestone. These figures are for 8-cut patent- hammered work. For rock-face ashlar (beds worked about 3 in. from face, the rest pitched), a workman can dress from 25 to 28 sq. ft. of random ashlar per day, and from 18 to 20 sq. ft. of coursed ashlar. In dressing laminated stone, from 2 to 3 times more work in a day can be done on the natural surface than on the edge of layers. In figuring cut stone, an ample allowance should be made for waste, which, on an average, will be 25 per cent. BRICKWORK. Brickwork is generally estimated by the thousand brick laid in the wall, but measurements by the cubic yard and by the perch are also used. The following data will be useful in calculating the number of brick in a wall. For each superficial foot of wall, 4 in. (the width of 1 brick) in thick¬ ness, allow 7h brick; for a 9" (the width of 2 brick) wall, BRICKWORK. 333 allow 15 brick; for a 13" (the width of 3 brick) wall, allow 22i brick ; and so on, estimating 7j brick for each additional 4 in. in thickness of wall. The above figures are for the ordinary Eastern standard brick, which is about 8£ X 4 X 2£ in. in dimensions. If smaller brick are used, the figures will be increased proportionately. As brick vary considerably, a minimum size should be specified, when a large number are bought; otherwise, many more will be required than were figured on. If brickwork is estimated by the cubic yard, allow 500 brick to a yard. This figure is based on the use of the size of brick given above, with mortar joints not over f in. thick. If the joints are | in. thick, as in face brickwork, 1 cu. yd. will require about 575 brick. Iu making calcula¬ tions of the number of brick required, an allowance of, say, 5 per cent, should be made for waste in breakage, etc. The practice in regard to deductions for openings is not uniform throughout the country, but small openings are usually counted solid, as the cost of extra labor and the waste in working around these places balances that of the brick¬ work saved. All large openings, 100 sq. ft. or over in area, should be deducted. When openings are measured solid, it is not usual to allow extra compensation for arches, pilasters, corbels, etc. Rubbed and ornamental brickwork should be measured separately, and charged for at a special rate. Brick footings may be computed by the lineal foot. The following table, based on steps or offsets of one-quarter brick, or 2 in., for each course in the footing, gives the number of brick per lineal foot in footings for brick walls from 9 to 2G in. thick: 9" wall, footing 2 courses, 10£. 18" wall, footing 4 courses, 39. 13" wall, footing 3 courses, 22b 22" wall, footing 5 courses, 60. 26" wall, footing 6 courses, 85£. DATA ON BRICKWORK. The following estimates on the cost of brickwork are very carefully compiled, and will be found trustworthy. It is to be understood that the prices will vary with the cost of materials and labor; but the proportions will be constant. v 384 ESTIMATING. The figures are based on kiln, or actual, count—that is, with deductions for openings. When the work is measured with no deductions for openings, the cost per thousand may be assumed as about 15 per cent, less than the prices given, which are exclusive of builder’s profit. Cost op Common Brickwork per Thousand Brick. Using l-to-8 Lime Mortar. 1,000 brick .$ 6.00 3 bu. lump lime at $.25 per bu.75 £ load sand (£ cubic yard) at $1.50 per load.75 7 hours, bricklayer, at $.35 per hour . 2.45 7 hours, laborer, at $.15 per hour. 1.05 Total.$11.00 Using l-to-8 Portland Cement Mortar. 1,000 brick ...$ 6.00 U bbl. Portland cement, at $2.60 per bbl. 3.90 h load sand, at $1.50 per load.75 7 hours, bricklayer, at $.35 per hour. 2.45 7 hours, laborer, at $.15 per hour. 1.05 Total.$14.15 Using 1-to-U Lime-and- Cement Mortar. 1,000 brick.$ 6.00 3 bu. lime, at $.25 per bu.75 i load sand.75 1 bbl. cement. 2.60 7 hours, bricklayer, at $.35 per hour. 2.45 7 hours, laborer, at $.15 per hour. 1.05 Total.$13.60 Using l-to-8 Rosendale Cement Mortar. 1,000 brick...$ 6.00 U bbl. Rosendale cement, at $1.25 per bbl. 1.87 i load sand.75 7 hours, bricklayer, at $.35 per hour . 2.45 7 hours, laborer, at $.15 per hour. 1.05 Total.$12.12 CARPENTRY. 335 Cost of Pressed Brickwork per Thousand Brick. Using Lime Putty Mortar. 1.000 pressed brick, cost from $20.00 to $40.00, average $30.00 li bu. lime.38 £ load fine sand ..37 30 hours, bricklayer, at $.40 per hour .. 12.00 15 hours, laborer, at $.15 per hour. 2.25 Total.,.$45.00 CARPENTRY. ESTIMATING QUANTITIES. Board Measure.— The rough lumber used in framing is meas¬ ured by the board foot, which means a piece 12 in. square and 1 in. thick. Lumber is always sold on a basis of 1,000 feet board measure; the customary abbreviation for the latter term is B. M., and for thousand is M; thus, 500 ft. board measure, costing $14.00 per thousand, would be written: 500 ft. B. M. at $14.00 per M. To obtain the number of board feet in any piece of timber, the length of the scantling in inches may be multiplied by the end area in sq. in., and the result divided by 144. For example, the number of feet B. M. in a floor joist 20 ft. long, 3 in. thick, and 10 in. deep, will be 240 in. (= 20 ft. X 12) multiplied by 30 sq. in. (the end area), or 7,200 sq. in., 1 in. thick; dividing by 144, the result is 50 ft. B. M. The rule used by most contractors and lumber dealers is as follows: Multiply the length in feet by the thickness and width in inches, and divide the product by 12. Thus, a scantling 26 ft. long, 2 in. thick, and 6 in. wide, contains 26 ft. B. M. 26 X 2 X 6 12 This rule, expressed in a slightly different manner more convenient for mental computation, is: Divide the prod¬ uct of the width and thickness in inches by 12, and multiply the quotient by the length in feet. Thus, a 2" X 10" plank, 18 ft, o v 1 o long, contains — — X 18 — 30 ft. B. M, 336 ESTIMATING. Studs.— To calculate the number of studs, set on 16" cen¬ ters, the following rule may be use#: From the length of the partition deduct one-fourth, and to this result add 1. Count the number of returns, or corners, on the plan, and add two studs for each return. (The reason for adding 1 is to include the stud at the end, which would otherwise be omitted.) The sills, plates, and double studs must be measured separately. For example, the total number of studs required for the lengths of partitions given at the left is as follows: Deducting one-quarter of 60 ft. from it, the 30 ft. 6 in. 10 ft. 6 in. 9 ft. 6 in. 5 ft. 0 in. 4 ft. 6 in. 60 ft. 0 in. remainder is 45; adding 1 stud, the result is 46. If there are, say, 4 returns, at 2 studs each, the total number is 46 + 8 = 54 studs. As a general rule, when (as is usual j the studs are set at 16" centers, 1 stud for each of partition will be a sufficient allowance to plates, and double studs. Thus, if the total foot in length include sills, length of partitions is 75 ft., 75 studs will be sufficient for sills, double studs, etc. If the studs are set at 12" centers, the num¬ ber required will be equal to the number of feet in length of partition plus one-fourth. Thus, if the length of partitions is 72 ft., 72 +18, or 90 studs, will include those required for sills, plates, etc. The same rules may be used for calculating the number of joists, rafters, tie-beams, etc. A good way to estimate bridging is to allow 2 cents apiece, or 4 cents a pair ; this will be sufficient to furnish and set a pair made of 2" X 3" spruce or hemlock stuff. Sheathing.— To calculate sheathing or rough flooring (which is not matched), find the number of feet B. M. required to cover the surface, making no deductions for door or window openings, for what is gained in openings is lost in w’aste. If the sheathing is laid horizontally, only the actual measure¬ ment is necessary, but, if it is laid diagonally, add 8 or 10 per cent, to the actual area. In sheathing roofs where many hips, valleys, roof dormers, etc. occur, there will be a great deal of waste material caused by mitering the boards, fitting around cheeks of dormers CARPENTRY. 337 and forming saddles behind chimneys. This waste is not readily calculated and must be determined by the actual conditions as well as by the care exercised by the men in utilizing the cuttings. In covering large areas a great deal of material can be saved by ordering the lengths of boards to suit the spacing of the rafters. Flooring.— In estimating matched flooring, a square foot of stuff is considered to be 1 ft. B. M. If the flooring is 3 in. or more in width, add one-quarter to the actual number of board feet, to allow for waste of material in forming the tongue and groove; if less than 3 in. wide, add one-third. Flooring of in., finished thickness, is considered to be li in. thick; and for calculating it the following rule may be used : Increase the surface measure 50 per cent. (This consists of 25 per cent, for extra thickness over 1 in., and 25 per cent, for waste in tonguing and grooving.) To this amount add 5 per cent, for waste in handling and fitting. In figuring the area of floors, the openings for stairs, fire¬ places, etc. should be deducted. Siding.—Siding is usually measure^ oj the superficial foot. No deduction should be made for ordinary window or door openings, as these usually balance the waste in cutting and fitting. Careful attention must be given to the allowance for lap. If 6" (nominal width, actual width 5| in.) siding, laid with 1" lap, is used, add one-quarter to the actual area, in order to obtain the number of square feet of siding required. If 4" stuff is used, add one-third to the actual area. When, as above noted, no alloAvance is made for openings, the corner and baseboards need not be figured separately. Cornices. —Cornices may be measured by the running foot, the molded and plain members being taken separately. A good method of figuring cornices is as follows: Measure the girth, or outline, and allow 1 cent for each inch of girth, per lineal foot. This price will pay for material and for setting, the cost of the mill work being estimated at 50 per cent., or j cent. Quantity of Material Set per Day. —It is impossible to esti¬ mate this exactly, as it depends on the skill of the artisan, his rapidity of working, the ease or difficulty of the work, 338 ESTIMATING. besides numerous accidental circumstances. The subjoined figures, while founded on knowledge gained in many years’ experience, are only intended to give an idea of the relative quantities, and not as a standard to be adhered to in all cases. The estimates are based on a 9-hour day, and wages of $2.25 per day. If the hours or pay be less or greater, the results will be correspondingly diminished or increased. Unless other¬ wise noted, the figures represent the labor of two men working together. Quantities of Material Put in Place per Day. Class of Material. Feet B. M. or Number. Remarks. Studding, 2" X 4" or 2" X 6" 600-800 Wall or Partition.- Rafters. Floor joists, 2" X 10" or 500-600 3" X 12". 1,500 Sheathing, unmatched. 1,000 Laid horizontally. Sheathing, unmatched. 800 Laid diagonally. Sheathing, matched . 800 Laid horizontally. Sheathing, matched. 600 Laid diagonally. Sheathing, roof. 1,000 Plain gable roof. Much cut up by Sheathing, roof.. 500 hips, valleys, dor¬ mers, etc. Includes fitting and setting cor- Siding . 700 ner boards, base, trim, and scaf¬ folding. Posts and beams over cel- 400-500 Includes scarfing lars . and doweling. For base and Plaster grounds, lineal feet, 400 wainscot, leveled per man. and straightened in good shape. Bridging, number of pairs, 12 Includes cutting per hour, per man. and setting. False jambs around open¬ ings, per hour, per man 1 Nails.—To calculate the quantity of nails required in executing any portion of the work, the following table, based on the use of cut nails, will be found useful: i CARPENTRY. 33 ^ Table for Estimating Quantity of Nails. Material. Pounds Required. Name of Nail. 1,000 shingles. 5 4d. 1,000 laths . 7 3d. 1,000 sq. ft. of beveled siding... 18 6d. 1,000 sq. ft. of sheathing. 20 8d. 1,000 sq. ft. of sheathing. 25 lOd. 1,000 sq. ft. of flooring . 30 8d. 1,000 sq. ft. of flooring. 40 lOd. 1,000 sq. ft. of studding .. 15 lOd. 1,000 sq. ft. of studding . 5 20d. 1,000 sq. ft. of furring 1" X 2" 10 lOd. 1,000 sq. ft. £" finished flooring 20 8d. to lOd. finish 1,000 sq. ft. 1±" finished flooring 30 lOd. finish ESTIMATING COSTS The character of the work, which must be determined by the spirit and letter of the specifications, will be the control¬ ling factor in fixing costs. In the case of material, where the requirements are exacting and demand a grade of material which can only be obtained by special selection, an extra rate must always be considered. This is best secured by con¬ tracting with the lumber merchants for the supply of the material to strictly accord with the architect’s stipulation. The matter of labor, however, is One on which too much care and forethought cannot be expended. \\ hat may be con¬ sidered satisfactory work by one contractor would be con¬ sidered inferior by another, and this often accounts lor the great differences in estimates. Cost per Square Foot. —For all classes oi materials that enter into the general framing and covering oi a building, a close estimate may be made by analyzing the cost per square foot of surface; that is, the cost of labor and materials—studs and sheathing in Avails, joists and flooring in floors, etc.— required for a definite area should be closely determined, and this cost, divided by the area considered, will give the price per square foot. If the corresponding whole area is multiplied by the figure thus obtained, the result will, of course, be the cost of that portion of the Avork, M bile it is 340 ESTIMATING. usual to adopt a uniform rate for the various grades of work, a careful analysis will show that roof sheathing in place costs more than wall sheathing, owing to its position; and that the studs in walls and partitions cost more than floor joists, as they are lighter and require more handling. The following example shows how to determine the cost per square foot of flooring, and indicates the general method to he pursued in like cases. The area used in calculation is a square of 100 sq. ft. The cost of labor is estimated at 50 per cent, of that of the materials, which experience has shown to be a very close approximation to the actual cost of general carpenter work. Cost of Finished Floor per Square. Joists, hemlock, 8 pieces, 3 in. X 10 in. X 10 ft. = 200 ft. B. M. at $14.00 per M.$ 2.80 Bridging, hemlock, 7 sets, 2 in. X 3 in. X1. ft. 4 in. = 9 ft. B. M. at $14.00 per M.13 Rough flooring, hemlock, £ in. thick, laid diagonally, 100 ft. + 25 ft. + 10 ft. = 135 ft. B. M. at $17.00 per M 2.29 Finished flooring, white pine, £ in. thick, 125 ft. B. M. at $22.00 per M. 2.75 Nails, about 3 lb. at $1.80 per 100 lb.05 Labor, 50 per cent, of cost of materials. 3.99 Total cost for 100 sq. ft.$12.01 Cost per square foot, $12.01 -p 100 = 12 cents. A similar method may be followed in estimating the cost of interior finish, paneling, doors, etc. Cost per Thousand Feet. —The following analysis shows the general method of estimating rough carpenter work: Cost of 1,000 Ft. B. M. of Hemlock. Including Framing. 1,000 ft. of hemlock.$14.00 Nails and spikes, allowing 100 lb. to 3,000 ft. of lumber, at $1.80 per 100 lb.60 Labor, taking 50 per cent, of the cost of material as cost of framing. 7.00 Cost per thousand feet B. M $21.60 JOINERY. 341 Cost of Miscellaneous Items of Carpentry. Class of Work. Cost. Remarks. Setting window frames in $ .30 Each; about 1 hour re- wooden buildings. Furring brick walls 1"X quired. .02* Per sq.ft.; includes labor, 2" strips, 12" centers. material, and nails. Furring brick walls, 1" X Oil Per sq. ft. 2" strips, 16" centers..... Cutting holes and fitting plugs in brick walls, 12" .02 Per sq. ft. centers . Cutting holes and fitting plugs in brick walls, 16" centers .. Setting window frames in brickwork. .01* Per sq. ft. .50 Each ; includes nails and bracing. Door frames in brickwork .50 Each. Window frames in stone- 1.25 Each ; for ordinary work, w T ork . screeded and bedded. Window frames in stone- 2.00 Each; for careful work. work . Door frames in stonework 2.00 Each; for very careful work. Furnishing and setting 1.25 Each. trimmer-arch centers... Arch centers, 3i-ft. span, 8" reveal. 1.00 Each; includes supports and wedges. JOINERY. Joinery includes all the interior and exterior finish put in place after the framing and the covering are completed; as, for example, door and window frames, doors, baseboard, paneling, wainscoting, stairs, etc. Most of these materials are worked at the mill and brought to the building ready to set in place. Frames.— In taking off door and window frames, describe and state sizes. Measure architraves by the running foot, giving width and thickness, whether molded or plain, and state the number of plinth and corner blocks. Sash.— State dimensions (giving the width first); thickness of the material, molded or plain; stylo" of check-rail and sill 342 ESTIMATING. finish; thickness of sash bar, whether plain, single, or double hung; and sizes (giving dimensions in inches) and number of lights. Use standard sizes as much as possible. Doors.—Describe and state the sizes and thickness,whether the framing is stuck-molded, raised-molded, or plain; and number of panels, whether plain or raised. Use stock sizes wherever possible and suitable. Blinds.—Describe size and thickness, whether paneled or slatted (fixed or movable), and w r hether molded or plain. Baseboard and Beam Casings.—Measure by the running foot, stating width and thickness of stuff 1 , and whether molded or plain. Wainscoting.—Measure by the superficial foot. State land of finish, whether paneled or plain, and style of molding and panels. Measure wainscoting cap and base by the running foot. Stairways.—They are generally taken by the contractor at so much per step, including everything complete according to the specifications. In measuring stairways, take off the amount of rough material in carriage timbers, and the planed lumber in treads, risers, and strings. Measure balustrades by the lineal foot. Give the size of newels and the style of treat¬ ment. Measure spandrel and stairway paneling the same as wainscoting. Fixtures.— Kitchen dressers may be taken at a fixed price complete, or at a fixed rate per square foot, or as dressed lumber—drawers and doors being taken separately. Ward¬ robes, bookcases, mantels, and china closets should be treated separately, and a fixed price stated. Porches, exterior balus¬ trades, balconies, porte-cocheres, etc., may be taken at a price per lineal foot, or the actual quantity of material may be measured. DATA AND EXAM PLESOF ESTIMATING JOINERYWORK. For any molded work which goes through the mill, the usual charge is 1 cent per square inch of section per lineal foot of the stuff 1 from which the molding is made, as a base, from which is deducted a percentage, usually 40 to 60 per cent., depending on the grade of the material, For example, a JOINERY. 343 (undressed thickness, 1 in.) door casing, 5 in. wide, will cost 1 cent X 5, less, say 50 per cent., or 2£ cents per lineal foot. Baseboard.—The cost of material and fitting in place may he estimated at 1 cent per square inch of section per lineal foot. This is for pine ; if hardwood is used, double this price. The same rule applies also to chair rails, cap rails, and natural-finish picture molds. Paneling.—This may be estimated at 12 cents per square foot for 1-inch pine stuff; if overt in., add simply for extra material. If the paneling is of hardwood and veneered, add 50 per cent, to price of pine. Wainscoting.—If plain, this may be estimated at cents per square foot, the cap being figured separately by the lineal foot. Door Frames.—The following estimate represents the approximate cost of an ordinary door frame. This and suc¬ ceeding estimates are given more to show how to make systematic and accurate estimates than to give any fixed prices. Cost op Door Frame in Place. Size, 2 ft. S in. X 6 ft. S in. Jambs (rabbeted for doors), 13 ft. G in.; head jamb, 3 ft.; total jambs, 16i ft. of 1}" (1|") X 6" clear face material, at 1 cent per sq. in. per ft., less 50 per cent.$0.62 Casing, 34£ ft. of Y' (1") X 5", with ground edge mold, at same rate.8625 Back-band molding, 34| ft. of (1") X 2" at same rate as casing.845 Plinth blocks, 4 pieces, 9" X If" (2") X 5i" at 1 cent per sq. in. per ft., less 50 per cent...1575 Dadoing and hand-smoothing casing, back band, and plinth blocks .50 Nails.05 Putting together and settingup (2*hours).65 Cost in place. $3.18 D 00rSi _The subjoined estimate gives the cost of a door of moderate price. If the door is veneered with hardwood, the cost is about 50 per cent, additional. A curved door in a curved wall costs about twice as much as straight work. 344 ES TIMA TING. Cost of Door in Place. Size, 2 ft. 8 in. X 6 ft. 8 in. 1| in. thick, 5-panel, double face, flat-paneled, and stuck- or solid-molded door, delivered. $2.00 Fitting hinges and lock, hanging and trimming.. .50 Butts, 1 pair 4" X 4" lacquered steel.40 Mortise lock, brass face and strike, wood knob, bronze escutcheons....80 Cost in place.„. $3.70 A fair workman can hang, trim, and put hardware on, including mortise locks, about 6 ordinary doors per day. For veneered doors, or those requiring extra care, not more than 3 can be put in place. Window Frames.— The following estimate gives approxi¬ mately the cost of a window frame of the size mentioned : Cost of Window Frame in Place. Size, 2 Lights, 28 in. X in. Jambs 12 ft., head jamb 3£ ft., total 15£ ft.; 15? ft. X1?in. (1|) X 5 in., at 1 cent per sq. in. per ft., less 50 per cent. . $0.48 Sill, 3£ ft. X 1? in. X 5£ in., same rate._... .13 Subsill, 4 ft. X 1£ in. X 4 in., same rate..16 Blind stop, 15i ft. X ¥ in. X 2 in.15 Parting strip, 14£ ft. X i in. X 1 in.04 Outside casing, 11 £ ft. x 1£ in. X 5 in.36 Head jambs, 4 ft. X 1£ in. X 7 in.17 Cap, 4 ft. X 1£ in. X 3 in.08 Molding, 4£ ft. of 1£" .03 Sill nosing, 4 ft. X 1£ in. X 4 in.10 Apron, 4 ft. X v in. X 5 in.10 Cove molding, 4 ft. of .02 Casing, 16£ ft. X I in. X 5 in.. .41 Back band, 16£ ft. X 1? in. X 1£ in.12 Sash stop, 14jj ft. X i in. X H in.05 Labor for frame complete, with outside casing attached at mill, and for setting inside casing at building. 1.00 Total cost.$3.40 JOINER Y. 345 Windows.—The cost of an ordinary window may be esti¬ mated as follows: Cost of Sash in Place. Size , 2 Lights , 28 in. X 28 in. Cost of 2 sashes If in. thick, at mill.$1.15 Glass, first-quality double-thick American, and setting 1.75 Sash weights, 35 lb., at 1 cent per lb.35 Cord for weights, 22£ ft., at £ cent per ft.11 Sash lifts, 2.05 Sash lock . - ..25 Hanging sash and putting on stops.50 Cost in place.$4.16 For curved sash in curved walls, the cost is about twice that of straight work. Stairs.— -The cost per step for an ordinary stairway, con¬ structed according to the following specifications, is about $3.00. For a better class of work, add about one-quarter to this price. Length of step, 3 ft.; tread, Georgia pine; riser, white pine; open stringer, white pine; nosing and cove; dovetail balusters, square or turned; rail 2.’ in. X 3 in.; 6" start newel, cherry; two 4" square angle newels, with trimmed caps and pendants; simple easements; furred underneath for plaster¬ ing; treads and risers tongued together, housed into wall stringers, wedged, glued, and blocked. The material of such a stairway will cost about $1.84 per step. This rate includes landing facia and balustrade to finish on upper floor. The labor on the same, millwork, and setting in place, is about $1.16 per step. For example, fora stairs having 17 steps and landing balustrade (including return, about 14 ft.), the entire cost will be 17 X $3.00 = $51.00, of which $31.28 will represent cost of dressed lumber, inclu¬ ding turned balusters and newels and worked rail, and $10.72 will represent cost of labor in housing stringers, cutting, mitering, and dovetailing steps, working easements, fitting and bolting rails, and erecting stairway in building. 346 ESTIMATING. Verandas. —For small dwellings, it has been found by experi¬ ence that a veranda built on the following specifications will cost about §2.25 per lineal foot: Width, 5 ft.; posts, turned, set 6 to 8 ft. on centers; floor timbers, 2 in. X 6 in.; flooring, white pine, sound grade; rafters, 2 in. X 4 in. dressed ; purlins, 2 in. X 4 in., set 2 ft. on centers: rqof sheathing, matched white pine; box frieze and angle mold; angle and face brackets; steps; no balustrade. To include balustrade, with 2" turned balusters, add about fiO cents per lineal foot. For a veranda, built according to the following specifica tions, the cost will be §4.00 per lineal foot: Width, 8 ft.; columns, 9" turned; box pedestals; box cornice and gutter; level ceiling; roof timbers, 2 in. X 6 in.; roof covered with matched boards; a good grade of tin; floor timbers, 2 in. X 8 in.; floor, l\ r ' white pine, second grade, with white-lead joints; no balustrade. Including balustrade, with 2\" turned balusters, rail and base to suit, add 80 cents per lineal foot. Where a portion of the veranda is segmental or semi¬ circular, a close approximation to the cost will result if the girth of the circular part is measured, and a rate fixed at twice that for straight w r ork of the same length. This applies to veranda framing, roofing, casing, and balustrades. ROOFING. / ROOF MENSURATION. While the ordinary principles of mensuration are all that are necessary to calculate any roof area, yet the modern house, with its numerous gables and irregular surfaces, intro¬ duces complications which render some further explanation of roof measurement desirable. The most common error made in figuring roofs, and one which should be carefully guarded against, is t that of using the apparent length of slopes, as shown by the plan or side elevation, instead of the true length, obtaiued from the end elevations. ROOFING. 347 The area of a plain gable roof, as shown in end and side elevations in (a), Fig. 1, is found by multiplying the length gj by the slope length b d, and further multiplying by 2, for both sides. The area of the gable is found by multiplying the width of the gable a d by the altitude c b and dividing by 2. At ( b ) is shown the plan and the elevation of a hip roof, having a deck z. The pitch of the roof being the same on each side, the line c d shows the true length of the common rafter Im, ce being the height of the deck above ad. At (c) is shown the method of determining the true lengths of the hips, and the true size of one side of the roof. Let abed represent the same lines as the corresponding ones in ( b). (b) Fig. 1. From the line a d, through b and c, draw perpendiculars, as g h and ef ; lay off from g and e on these lines the length of the common rafter ab, in (b), and draw the lines ah and df; then the figure ahfd will show the true shape and size of that side of the roof shown in the elevation in (b). The triangle d ef equals in area the triangle ag h or a similar triangle a i h. Hence, the portion of the roof a hfd is equal in area to the rectangle aife , whose length is one-half the sum of the eaves and deck lengths, and whose breadth is the length of a common rafter. A method of obtaining the lengths of valley—applicable also to hip rafters—is shown at (d), which is the plan of a 348 ESTIMATING. hip-and-gable roof. To ascertain the length of the valley rafter a b, draw the line a c perpendicular to a b and equal in length to the altitude of the gable; then draw the line c b, which will be the length required. As an example of roof mensuration, the number of square feet of surface on the roof shown in Fig. 2 will be calculated. The area of the triangular portion acb is equal to one-half the base a b, multiplied by the slope length of c d. The latter "is found by making c c', perpendicular to d c, equal to the height of the ridge (10 ft.) above a b, and drawing c'd, which is the required slope length. Using dimensions, the area of acb is --—— = 158.1 sq. ft. A The area of the trapezoid gfili is one-half the sum of fi and g h, multiplied by the true length of h i, which, by laying offii',8 ft. along/ i, and drawing V h , is found to be 10 ft. 7| in., or, say, 10.6 ft. Then gfi h — 1 X 10.6 = 100.7 sq. ft.; or, ROOFING. 349 for the two slopes of the gable, the area is 201.4 sq. ft. As the opposite gable is the same size, the area of the two is 201.4 X 2 = 402.8 sq. ft. The area of q p n k is equal to the area qpw, minus the area k n w, which is covered by the intersecting gable roof. The area qpw is equal to the area acb, or 158.1 sq. ft. The area of knw is equal to 4 the product of nw and the slope of sk (which, by laying off kk' equal to the height of the gable, 5.5 ft., and drawing sk', is found to be nearly 7.5 ft.). Then area & raw = —£—— = 48.7 sq. ft., which, deducted from- 158.1 sq. ft., shows the area of qp n k to be 109.4 sq. ft. The area of ap q c is multiplied by the true slope length of tv, which is tv', measuring 15.25 ft. Substituting dimensions, the area is found to be ^ X 15.25 = 228.7 sq. ft. From this deduct the area of yzu, which is the portion covered by the intersecting gable roof. The true length of t u along the slope is t u' , which measures 12 ft.; hence, the area of yzu is 14 * ■ 12 U 84 sq. ft. The net area of ap q c is, z therefore, 228.7 — 84 = 144.7 sq. ft,; bcqw being equal to apqc, its area is the same, making the area of both sides 289.4 sq. ft. The area of knml is '’HZL Z x ml', the slope length of m l. Substituting dimensions, the area is —^ X 8.5 — 114.7 sq. ft. As klxw is equal to knml, the area ol both is 229.4 sq. ft. Adding the partial areas thus obtained, the sum is 158.1 + 402.8 + 109.4 + 289.4 + 229.4 = 1,189.1 sq. ft., or 11.9 squares. __ SHINGLES. Measurement.—In measuring shingle roofing, it is necessary to know the exposed length of a shingle, which is found bj deducting 3 inches—the usual cover of the upper shingle over the head of the third shingle below it-from the w 350 ESTIMATING. length; dividing the remainder hy 3, the result will be the exposed length; multiplying this by the average width of a shingle, the product will be the exposed area. Dividing 14,400, the number of square inches in a square, by the exposed area of 1 shingle, will give the number required to cover 100 sq. ft. of roof. For example, it is required to compute the number of shingles, 18 in. X 4 in., necessary to cover 100 sq. ft. of roof. With a shingle of this length, the exposure will be ^ = 5 in.; then the exposed area of O 1 shingle is 4 in. X 5 in., or 20 sq. in., and 1 square requires 14,400 -f- 20 = 720 shingles. In estimating the number of shingles required, an allow¬ ance should always be made for waste. The following table is arranged for shingles from 16 to 27 in. in length, 4 and 6 in. in width, and for various lengths of exposure. Table for Estimating Shingles. Exposure to Weather. Inches. No. of Sq. Ft of Roof Covered by 1,000 Shingles. No. of Shingles Required for 100 Sq. Ft. of Roof. 4 In. Wide. 6 In. Wide. 4 In. Wide. 6 In. Wide. 4 Ill 167 900 600 5 139 208 720 480 6 167 250 600 400 7 194 291 514 343 8 222 333 450 300 Shingles are classed as shaved or breasted, and sawed shingles. The former vary from 18 to 30 in. in length, and are about £ in. thick at the butt and in. at the top; the latter are usually from 14 to 18 in. long, and of various thick¬ nesses, five 18" shingles, placed together, measuring 2$ in. ..t the butt, the thickness of each at the top being ^ in. Strictly first-class shingles are generally given a brand of XXX, and those of a slightly poorer quality are termed ROOFING. 351 No. 2; but in some sections of the country, the brand A is general; thus, “choice A” or “ standard A” are practically equivalent to the XXX shingles. Shaved shingles are usually packed in bundles of 500, or 2 bundles per thousand. Sawed shingles are made up into bundles of 250, and are sold on a basis of 4 in. width for each shingle. If the wider ones are ordered, the cost per thousand is correspondingly increased. For example, if it requires 1,000 of 4" shingles to cover a roof area, and 6" ones were ordered, only two-thirds as many, or 667, would be needed and furnished, while the cost would be that of 1,000 standard- width shingles. Shingles cost from $3.00 to $5.00 per thousand, according to material and grade. Dimension shingles—those cut to a uniform width—of prime cedar, shaved, | in. thick at the butt, and Jg in. at the top, will cost $0.00 to $10.00 per thou¬ sand, but such shingles are usually 6 in. wide and 24 in. long, so that a less number will be required per square than of ordinary shingles. A fairly good workman will lay about 1,500 shingles pel day of 9 hours, on straight, plain work; while, in working around hips and valleys, the average will be about 1,000 pesr day. Cost.—The method of estimating the cost of shingle roofing is as follows: Cost of 1,000 Shingles in Place. Exclusive of Sheathing. 1,000 shingles XXX. $5-00 Labor: 1 man can lay 1,500 shingles per day; wages being $2.25, the cost per thousand is.. 1.50 Nails, about. 25 (Flashing, about 10 cents per sq. ft.) .. . Cost per thousand, about. $6.75 SLATING. Measurement.— In measuring slating, the method of deter¬ mining the number of slates required per square is similar to that given for shingling; but, in slating, each courseo^ erlaps 352 ESTIMATING. only two of the courses below, instead of three, as in shingling. The usual lap, or cover of the lowest course of slate by the uppermost of the three overlapping courses, is 3 in.; hence, to find the exposed length, deduct the lap from the length of the slate, and divide the remainder by 2. The exposed area is the width of the slate multiplied by this exposed length, and the number required per square is found by dividing 14,400 by the exposed area of 1 slate. Thus, if 14" X 20" slates are to be used, the exposed length 20_3 will be —-— = in.; the exposed area will be 14X8i A — 119 sq. in., and the number per square will be 14,400 119 ~ 121 slates. The following rules should be observed in measuring slating: Eaves, hips, valleys, and cuttings against walls are measured extra, 1 ft. wide by their whole length, the extra charge being made for waste of material and the increased labor required in cutting and fitting. Openings less than 3 sq. ft. are not deducted, and all cuttings around them are measured extra. Extra charges are also made for borders, figures, and any change of color of the work, and for steeples, towers, and perpendicular surfaces. The following table, based on 3" lap, gives the sizes of the American slates, and the number of pieces required per square. Number of Slates per Square. Size. Inches. 6X12 7X12 8X12 9X12 7X14 8X14 9X 14 10 X 14 8X16 Number of Pieces. 533 457 400 355 374 327 291 261 277 Size. Inches. 9X 16 10 X 16 9X18 10 X 18 11 X 18 12 X 18 10X20 11 X 20 12X20 Number of Pieces. 246 221 213 192 174 160 169 154 141 Size. Inches. 14X20 11 X 22 12 X 22 13 X 22 14X22 12X24 13X24 14 X 24 16 X 24 Number of Pieces. 121 138 126 116 108 114 105 98 86 ROOFING. 353 Cost.— The cost of slating may he estimated as follows: Cost op 1 Square op Slating. Slates, 8 in. X 12 in..85.00 Labor: 1 slater will average 2 squares per day; wages being 82.00 per day, 1 square will cost. 1.00 Nails, 8" X 12" slates require 5 lb. 9 oz. (5.6 lb.) of galva¬ nized nails per square, which, at $2.20 per 100 lb., cost. .12 Roofing felt, 1 roll.. 2.40 Labor and nails for applying felt...15 Flashing will cost about 10 cents per sq. ft. . Cost per square .$8-67 This figure is exclusive of roof sheathing, the cost of which may be estimated as shown for hemlock framing, on page 340. The cost of slating per square varies from 7 to 13 cents per sq. ft., depending on the class of work. TIN ROOFS. In estimating tin (and also other metal) roofs, hips and valleys are measured extra their entire length by 1 ft. in width, to compensate for increased labor and waste of mate¬ rial in cutting and laying. Gutters and conductor, or leader, pipes are measured by the lineal foot, 1 ft. extra being added for each angle. All flashings and crestings are meas¬ ured by the lineal foot. For seams, addition is made to superficial area, depending on the kind of seam used, whether single-lock, standing, or roll-and-cap. No deduc¬ tions are made for openings (chimneys, skylights, ventilators, or dormer-windows), if less than 50 sq. ft. in area; if between 50 and 100 sq. ft., one-half the area is deducted ; if over 100 sq. ft. the whole opening is deducted. An extra charge is made for labor and waste of material to flash around such openings. A box of roofing tin contains 112 sheets 14 in. X 20 in., and weighs from 110 to 140 lb. per box, according to whether it is IC or IX plate. The IC plate, which is the most used, weighs about 8 oz. per sq. ft,, and the IX, aboutlOoz. As there are con¬ siderable variations in the weights of tin made by different 354 ESTIMATING. manufacturers, a fair average will be obtained by estimating IC tin at 1 lb., and IX tin at 1£ lb., per sheet. Double-size roofing tin can be had 20 in. X 28 in., weighing, if IC, 225 lb. per box. This size is the most economical, as by its use much material and labor are saved, on account of the less number of seams and ribs required. A 14" X 20" sheet will cover about 235 sq in. of surface, using standing joints; or a box will cover about 182 sq. ft. With a flat-lock seam, a sheet will cover 255 sq. in., allowing | in. all around for joints ; or a box will lay 198 sq. ft. These figures make no allowance for waste. Two good workmen can put on, and paint outside, from 250 to 300 sq. ft. of tin roofing per day of 8 hours. Tin roofing will cost from 8 to 10 cents per sq. ft., depending on the quality of material and workmanship. TILE ROOFS. Tile roofs are constructed of so many styles of tile that no general rules of measurement can be given, and every piece of work must be estimated according to the particular kind of tile used and the number of sizes and patterns. Informa¬ tion on all these points are to be found in the catalogues of tile manufacturers. GRAVEL ROOFING. In gravel roofing, the cost per square depends on the num¬ ber of thicknesses of tarred felt and the quantity of pitch used per square. PLASTERING. Plastering on plain surfaces, such as walls and ceilings, is always measured by the square yard; but there are consid¬ erable variations in detail in the methods of measurement in different sections of the country. The following rules, how¬ ever, probably represent the average practice, and are equita¬ ble to both parties concerned: On walls and ceilings, measure the surface actually plas¬ tered, making no deduction for grounds or for openings of less extent than 7 superficial yards. PLASTERING. 355 Returns of chimney breasts, pilasters, and all strips of plastering less than 12 in. in width, measure as 12 in. wide. In closets, add one-half to the actual measurement; if shelves are put up before plastering, charge double measure¬ ment. For raking ceilings or soffits of stairs, add one-half to measurement; for circular or elliptical work, charge two prices; for surfaces of domes or groined ceilings, charge three prices. Round corners and arrises (other than chimney breasts) should be measured by the lineal foot. On interior work, increase the price 5 per cent, for each 12 ft. above the ground after the first. For outside work, add 1 per cent, for each foot above the lower 20 ft. All repairing and patching should be done at agreed prices. Stucco Work.— Cornices composed of plain members and panel work are measured by the square foot. Enriched cor¬ nices, with carved moldings, are measured by the lineal foot. When moldings are less than 12 in. in girth, measurement is taken by the lineal foot; when over 12 in., superficial meas¬ urement is used. For internal angles or miters, add 1 ft. to length of cornice; and for external angles, add 2 ft. to length. Sections of cornices less than 12 in. measure as 12 in. Add one-half for raking cornices. For cornices or moldings abutted against wall or plain surface, add 1 ft. to length of cornice; if against soffit of stairs or other inclined or coved surface, add 2 ft. to length of cornice. Octagonal, hexagonal, and similar cornices, less than 10 ft. in single stretches, measure one and one-half times the length. For circular or elliptical work, charge double prices; for domes and groins, charge three prices. Column and pilaster capitals, frieze enrichments, and work of this character, which require artistic treatment, are either made to conform to the models furnished by the architect, or they are modeled from the architect’s designs and submitted to him for approval. Expense of modeling is large ; prices are usually obtained from specialists in this department. 356 ESTIMATING. ESTIMATES OF QUANTITIES AND COSTS. Plastering. —Two plasterers and one laborer should average from 60 to 70 sq. yd. per day. The cost of labor on 3-coat work, costing about 25 cents per sq. yd., will be about 12 cents. For 2-coat work, costing about 20 cents per sq. yd., the cost of the labor will be about 8 cents. Both of these figures on labor are exclusive of the cost of lathing. The following analyses of cost of 2- and 3-coat plastering are carefully made, and may be relied on as bases for esti¬ mates. Very fine w r ork will cost considerably more. Cost of 100 Sq. Yd. of 3-Coat Plastering. 1,440 laths, 1£ in. wide, f" spacing, at $2.10 per 1,000. $ 3.02 10 lb. 3d. nails, at $2.05 per 100 lb.20 Labor : putting on lath, 1 day.. 2.25 13 bu. of lime, at $.25 per bu.. 3.25 1 bu. of hair, 8 lb., at $.04 per lb.32 11 loads of plastering sand, at $1.50 per load. 2.25 I bbl. of plaster of Paris, at $1.50 per bbl.50 Labor: Plasterer, ot days, at $3.00 per day. 9.75 Helper, 2£ days, at $1.50 per day. 3.75 Cartage . 1.00 Total. $26.29 Cost per sq. yd., $26.29 -r- 100 = 26 cents, approximately. Cost of 100 Sq. Yd., 2-Coat Plastering. Cost of lath and putting on, same as above.$ 5.47 10 bu. of lime, at $.25 per bu... 2.50 3 bu., or 6 lb., of hair, at $.04 per lb.24 1 load of sand . 1.50 | bbl. plaster of Paris, at $1.50 per bbl. .50 Labor: Plasterer, 2\ days, at $3.00 per day. 6.75 Helper, 2\ days, at $1.50 per day. 3.37 Cartage . 1.00 Total. $21.33 Cost per square yard, $21.33 -*- 100 = 21 cents, approxi¬ mately. PAINTING AND PAPERING. 357 Lathing.— This is measured by the superficial yard, no openings under 7 superficial yards being deducted. Plastering laths are about 1£ in. wide, £ in. thick, and usually 4 ft. long, the studding being generally placed 12 or 16 in. on centers, so that the ends of the lath may be nailed to them. The laths are usually set from £ to f in. apart, requiring about 1| or 1£ laths, 4 ft. long, to coyer 1 sq. ft. For a good average grade of work, a man will lay, on an average, about 15 bunches, or 1,500 laths per day, while a rapid workman will put on about 2,000 laths. The cost of nailing up laths will be from 18 to 25 cents per bunch, or $1.80 to $2.50 per thousand, being about equal to the cost of the laths and nails. PAINTING AND PAPERING. PAINTING. Painting is measured by the superficial yard, girting every part of the work that is covered with paint, and allowing additions to the actual surface to compensate for the diffi¬ culty of covering deep quirks of moldings, for carved and enriched surfaces, etc. Ordinary door and window openings are usually measured solid, on account of the extra time taken in working around them, “ cutting in ” the window sash, etc. Porch and stair balustrades, iron railings, and work having numerous thin strips are also figured solid, for a like reason. Allowance is frequently made for distance from ground that the work is to be done, as in cornices, balconies, dormers, etc., and also for the difficulty of access. Charges are usually made for each coat of paint put on, at a certain price per superficial yard and per coat. Graining and marbling (imitations of wood and stone) and varnishing are rated at different prices from plain work. Capitals and columns and other ornamental work, which are difficult to measure, should be enumerated, and a clear description of the amount of work on them should be given. Quantities.— One pound of paint covers from 3^ to 4 sq. yd. of wood first coat, and from 4£ to 6 sq. yd. for each addi- 358 ESTIMATING. tional coat; on brickwork, it will cover about 3 and 4 sq. yd., respectively. Colored paint will cover about one-third more surface than white paint. Using prepared or ready-mixed paint, 1 gal. will cover from 250 to 300 sq. ft. of wood surface, two coats; for covering metallic surfaces, 1 gal. will be sufficient for from 300 to 350 sq. ft., two coats. The weight per gallon of mixed paints varies considerably, but, on an average, may be taken at about1G lb. Prepared shingle stains will cover about 200 sq. ft. of sur¬ face, per gallon, if applied with a brush; or this quantity will be sufficient for dipping about 500 shingles. Rough- sawed shingles will require about 50 per cent, more stain than smooth ones. One pound of cold-mater paint will cover from 50 to 75 sq. ft. for first coat, on wood, according to surface condition, and about 40 sq. ft. of brick and stone. One gallon of liquid pigment filler, hard oil finish or var¬ nish, will generally cover from 350 to 450 sq. ft. of surface for first coat, according to the nature of wood and finish, and from 450 to 550 sq. ft. for the second and subsequent coats. Ten pounds of paste wood filler will cover about 400 sq. ft. One gallon of varnish weighs from 8 to 9 lb.; turpentine, about 7 lb.; and boiled or raw linseed oil, about 7f lb. For puttying, about 5 lb. will be sufficient for 100 sq. yd. of interior and exterior work. For sizing, about £ lb. of glue is used to 1 gal. of water. For mixing paints, the following figures represent the aver¬ age proportions of materials required per 100 lb. of lead : Quantities of Materials. Coat. Lead. Lb. Raw Oil. Gal. Japan Drier. Gal. Priming coat . 100 7 1 Second coat. 100 6 Third coat.. 100 6s-7 The drier is omitted in the second and succeeding coats, PAINTING AND PAPERING. 359 unless the work is to be dried very rapidly, as it is considered injurious to the durability of the paint. On outside work, boiled oil is generally used in about the proportion of 3 gal. of boiled oil to 2 gal. of raw oil. Cost. —The cost of applying paint, on general interior and exterior work, will average about twice the cost of the materials; while for very plain work, done in one color, the cost may be taken at about H times that of the materials. For stippling, the cost will be about the same as for two coats of paint. For varnishing, the cost of labor will be about H times the price of the varnish. The class of work demanded, however, will regulate the actual cost, as the rubbing down of the successive coats requires the expenditure of much time. The following figures represent fair average prices, for various classes of work, and have been adopted by the Builders’ Exchange of a large Eastern City: Interior Work. Cost per Square Yard. 1 coat paint, 1 color.-.$0.12 1 coat paint, 2 colors .15 2 coats paint, 2 colors.20 3 coats paint, 2 colors.25 2 coats paint, 3 colors.25 3 coats paint, 3 colors.32 1 coat shellac.10 Walls, 1 coat size, 2 coats paint.20 Walls, 1 coat size, 3 coats paint, stipple.30 Hardwood Finish. 1 coat paste filler, 1 coat varnish.$0.30 1 coat paste filler, 2 coats varnish. 40 1 coat paste filler, 3 coats varnish.50 Natural Finish. 1 coat liquid filler, 1 coat varnish. $0.20 1 coat liquid filler, 2 coats varnish . 25 1 coat liquid filler, 3 coats varnish, rubbed.40 Floors: filling, shellacing, varnishing, or waxing, 2 coats .35 360 ESTIMATING. Tinting Walls. Distemper Color. Cost per Square Yard. Tinting, 50 yards, or less .. $0.09 Tinting, 50 yards, or more...07 Patching and washing walls .07 Exterior Painting. Woodwork. 1 coat, new work. 2 coats, new work, 2 colors. 2 coats, new work, 3 colors... 3 coats, new work, 2 colors. 3 coats, new work, 3 colors.. Brickwork. 1 coat. $0.12 2 coats .18 3 coats . 25 Sanding. 2 coats paint, 1 coat sand..'.. $0.28 3 coats paint, 1 coat sand.35 3 coats paint, 2 coats sand .50 Miscellaneous. Dipping shingles, per 1,000 . Additional coat, per 1,000. Blinds, per foot, 1 coat . Fence, per foot, 1 coat 4 feet high, wood Iron fence, per foot, 1 coat. Tin roof, per yard, 1 coat. PAPERING. Papering is usually figured per roll, put on the wall. The paper is generally 18 in. wide, and is in either 8-yd. or 16-yd. tolls. On account of waste in matching, etc., it is difficult to estimate very closely the number of rolls required, but an approximate result may be obtained as follows: Divide the perimeter of the room by 1£ (the width of paper in feet); the $3.00 .50 .08 .12 .08 .05 $0.10 .18 .20 .25 .28 MISCELLANEOUS NOTES. 361 result will be the number of strips. Find the number of strips that can be cut from a roll, and divide the first result by the second; the quotient will be the number of rolls required. No openings less than 20 sq. ft. in area should be deducted, in order to compensate for cutting and fitting at such places. Add about 15 per cent, to the area to allow for waste. The border, whether wide or narrow, is usually figured as 1 roll of paper. The cost of paper is extremely variable, ranging from 15 cents to $6.00 per double roll; the average cost is probably 20 to 25 cents per roll for ordinary houses. Paper hanging costs from 30 to 75 cents per double roll, with strips butted, the former figure being for the usual grade of work; with lapped strips, the cost is less, being from 20 to 25 cents per roll. Sometimes an extra charge is made for papering ceilings. MISCELLANEOUS NOTES. Plumbing.— An approximate figure for cost of plumbing is 10 per cent, of the cost of the building. This figure is for good materials and labor, and of course is subject to con¬ siderable variation. For an ordinary house, costing from $1,500 to $3,000, the cost of plumbing may be taken as about 8 per cent, for moderate-priced fixtures and public sewer service. The cost of labor alone will average about | the cost of the materials. Gas-Fitting.— The cost of gas-fitting may be approximately figured as about 3 per cent, of the cost of the building. The cost of labor alone varies from about i to f the cost of materials. The better the grade of fixtures, the lower will be the ratio—provided there is no excessive ornamentation, requiring much time to put in place—as the cost of the labor is about the same for cheap fixtures as for more costly ones. Heating.— The cost of hot-air installation is, approximately, 5 per cent, of the cost of the building; for steam heating, 8 per cent.; for hot-water heating, 10 per cent. In estimating on heating by furnace, the average cost of labor is about | that of materials. In steam and hot-water heating, the ratio is about 5. 362 ELEMENTS OF ARCHITECTURAL DESIGN. Ha dware.—Hardware is best estimated by noting the quan¬ tities required for each portion of the work as it is being measured, afterwards making these items into a separate hardware bill. Many of the articles, as, for example, the number of fixtures for doors or window trimmings, may be readily counted from the plans. Hardware for windows, doors, etc., are sometimes included in estimating the cost per window, door, etc., and are not considered separately. The cost of hardware depends entirely on the class of work and finish desired, and the best way to estimate on it is, after making the schedule, to select suitable designs and figure the prices from a catalogue. An approximate estimate for ordi¬ nary buildings is li per cent, of the cost of the building. From 15 to 20 per cent, of the cost of hardware will pay for the putting in place. ELEMENTS OF ARCHITECTURAL DESIGN. PROPORTIONS OF THE GREEK AND ROMAN ORDERS. In proportioning the Greek and Roman orders, a uniform standard of measurement was adopted, so that the several parts of the order might be arranged in perfect ratio. This standard consists of modules and parts. A module is the semi- diameter of the column, measured at the base, and each module is divided into 30 equal parts. Each diameter, there¬ fore, is equal to 2 modules, or 00 parts. THE GREEK ORDERS. In Fig. 1 is shown a diagram of the Greek orders, aftef measured drawings by acknowledged authorities, drawn to a uniform altitude. A is an example of pure Doric, from the Portico of the Parthenon, at Athens. B is the Ionic, and is taken from the North Porch of the Erechthcum, while C is GREEK AND ROMAN ORDERS. 363 the Corinthian, after the monument of Lysicrates. In each example a is the stylobate or base, b is the column, and c the entablature. The column of the Doric consists of a shaft and capital, the shaft resting directly on the stylobate, while the columns of the Ionic and Corinthian have a base, shaft, and capital. The entablature of each order has three divi¬ sions—the architrave, frieze, and cornice. A comparative statement of the relative values of the divi¬ sions of each of the Greek orders is given in Table I, and is based on the module, or semi-diameter, as the unit of measure¬ ment ; as previously explained, a part is & of this unit. Greek Orders. 364 ELEMENTS OF ARCHITECTURAL DESIGN. •mnnipo omi -T?iqR;na jo ot;Ra O0MC4 (N lO rf* CO OJ tN Height of Entablature. Total. ft ^HS 00 co lO H H (M a COft T* jCornice. i £ «(U3rH|« CO l> co (M rH a * HH Frieze. h ft C5|U5nHf CM 1- ^ rH r—1 rH a r-H rH rH Arch. 9 ft ci|cnoHr ^|c» (M O CM rH CM CM m. J rH rH rH Height of Column. : Total. ft o o o m. rH CO O rH rH C4 ft, <3^ O ft r|*H«Hc« co »o CM rH (M m. O rH CM Shaft. e ft »C|<0rH|«> CM M C l CM rH o >o o rH rH rH Base. d ft io|co-*!» O CO CM CM CM a 'o o o Title. Doric . Ionic . Corinthian . d 2 a ft g o> H O x '<3 d ft 33 rt o o r-H *r-C rH O rH H 3 £ M § a ft _ 03 d 5 oo O ^ ft S3 g 3 03 a Sh O P ,P ‘D P-l 4-1 ft a 3 >* 5 C ft o 3“ * ft ^ a; a> +n ft ft is 3 3 2 P ,o J a> o fH © ps Ml •>H *rH 'S -3 ^ ^6 2 03 - ft rt ^ ft ft _, 0> d 03 O *H O . 3 8 SP a - 3 a ^ bJO T3 P > o o K" p Sh r—< > o p o •>-H r—< 03 ft ft 03 d a ft o *H 03 V? 03 03 8 a Sh +j 8 >> 3 -Q c ft „ 03 CO co 03 r-J r—( ^ ft Q3 ft 03 d'd 03 ft H b (3 t> CO CO d 2 £ !>» gffl n 03 <3 O ft I—I *H * co ^ S 2 rjl 3 d ft 03 a d 3 3 X 03 d >» 03 to p CO p Pi 03 ft fcH o 03 <3 ft x -d ® CO ft OS to ?i 5 *■* O (D rP rg ±3 ^ 3 © kT d 3' <33 d 2 o is CO d 03 ft 03 §3 Pi 03 03 Sh - r8 CO o O 03 te ft H d °'d be d d d •d .o ►i 0-c o •s rP P to o _ *C 5 p 03 M H 03 H ft * EH d 2 -d fid® o-i a o ft CO M O X. o tn 03 co co co 3 ft cj > ft tH a d £ OQ ft <3 d 3 a o o o> Pi co 0> P P of r-H >> to CO 3 -M o co o> Pi n £ 3 C3 X 2 03 ft GREEK AND ROMAN ORDERS. 365 THE ROMAN ORDERS. The Romans adopted the column and beam system of the Greeks, and joined to it the arch and vault. The union of the two elements of arch and beam, is the keynote of the Roman style. In this style the orders were used more for decoration than for construction, and were superposed, or set one upon the other, dividing the buildings into stories. The five Roman orders are shown in Fig. 2. A is the Tuscan; B , the Doric; C, the Ionic; D, the Corinthian; and E, the Composite. In each of these, a', b', and c' represent the pedestal, column, and entablature, respectively. For comparison, the relative values ot the lov er diameters o e shafts, when the orders are profiled to a uniform total heig 1 of 31 ft. 8 in., is given in Table II. x 366 ELEMENTS OF ARCHITECTURAL DESIGN. TABLE II. Roman Oedebs. With Uniform Altitude = Sift. 8 in. Title. Index Letter on Fig. 2. Lower Diameter of Shaft. With Pedestal. Without Pedestal. Tuscan . A to » h- 4 o AH 3 ft. 7/ s in. Doric . B 2 ft. 6 in. 3 ft. 2 in. Ionic . C 2 ft. 2* in. 2 ft. 9| in. Corinthian . D 2 ft. 0 in. 2 ft. 6| in. Composite. E 2 ft. 0 in. 2 ft. Of in. Table III gives the relative measurements, with respect to the module, or semi-diameter of the shaft, for proportioning the Roman orders, and is valuable for consultation when preparing preliminary designs, the reference letters being those shown in Fig. 2. _ NOTES. In connection with the Roman orders it is well to keep in mind that the pedestal is one-third, and the entablature one- fourth, the height of the column in all cases. To find the semi-diameter of the column in any order, divide the height to be occupied by the number of modules in the given order. Thus, if the given height is 23 ft. 9 in. and the order is the Ionic, with the pedestal, the semi¬ diameter, or module, will be 23 ft. 9 in. -4- 28£ — 10 in.; if without the pedestal, the module will be 23 ft. 9 in. -h 22£ = 12f in. The lower one-third of the columns is cylindrical, the upper two-thirds being diminished by a conchoidal curve called the entasis, the reduction of the shaft at the neck in all cases being one-sixth of the lower diameter. In terms of the lower diameter, the Tuscan, Doric, Ionic, Corinthian, and Composite columns are respectively 7, 8, 9, 10, and 10 diameters high. Roman Orders. GREEK AND ROMAN ORDERS. 367 i '53 d W d ■'ll 8Z8I.TJ p lO At) lO lOlO rH rH rH rH a rH rH rH rH rH ■6 *qojy p -*\e» OObOiO CO CO rH H a O O rH rH rH T'Blox p O O O O O | a VOODOO rH rH rH Cd Cl d •/ fl^o p O O O O O CO CO Cl H H o o a O O O CS 39. Specific gravities and weights, 29. Sphere, 41. Spiral, 58. Spread footings, 175. Square and cube roots, 13. cast-iron columns, 101. measure, 22. root, 8. Steel, 234. Stairs, Cost of, 345. Stairways, 342. Notes on, 247. Stable dimensions, 232. Steam heating, 300. Steel (see structural steel), square, 234. Stiffeners, 122. Stone, 162. beams, 119. Cost of, 331. Data on cut, 331. finishes, 184. masonry, 182. INDEX. 379 Stone, Strength of, 73. Stonework, Estimating, 328. Notes on, 180. Strain, 69. Street service, 290. Strength of masonry mate¬ rials, 73. materials, 68. metals, 70. rivets and pins, 128. timber, 71. Stress, 68. and frame diagrams, 141. Stresses, Compressive and ten¬ sile, 146. in roof trusses, 142. Principles of, 140. Stringer cut, Miter bevel for, 247. Structural design, 62. steel columns, 103. steel column, Design of, 106. Structures, Loads on, 62. Stucco work, Estimating, 355. Studs, Number of, 336. Surface, Radiating, 308, 310. Surfaces, Lines and plane, 35. Curved, 39. Surveyor’s square measure, 23. Tables, 250. (See the topic in question.) Tacks, spacing of lead pipe, 299. Temperature, Effect of, on masonry, 188. Tensile strength of cement, 166. Terra cotta, 164. Testing and installation, 326. of drainage, 275. Tile roofs, 354. Timber, Qualities of, 213. Selecting, 214. Strength of, 71. Tin roofing, 253. roofs, 353. Tower, Siding a, 230. Trapezium, 36. Trapezoid, 36. Treads and risers, Propor¬ tioning of, 247. Triangle, 35. of forces, 140. Troy weight, 24. Truss, Fink roof, 147. Howe roof, 143. plank, 229. Trusses, Design of roof, 149. Roof, 140. Stresses in roof, 142. T shapes, Properties of, 87, 88. Tubes, Vertical, 303. Tubs, Laundry, 289. Ultimate Strength, 69. Urinals, 286. Ventilation, 314. Forced, 316. Heating and, 300. Natural, 315. Vents, Seat, 283. Verandas, Cost of, 346 Volute, Roman Ionic, 59. Wainscoting, 342. Walks and floors, Cement, 195. Walls, Retaining, 206. Thickness of, 178. Waterproofing, 191. Wash basins, 280. Washout closets, 281. Water closets, 280. pipes, Size of, 293. supply and distribution,'290. Water proofing walls, 191. Web, Proportioning, 120. Wedge, 41. Weight (see article in ques¬ tion). Weights and measures, 22. Specific gravities and, 29. Wind and snow loads, 67. Window frames, Cost of, 344. Windows, 242. Area of, 242. Cost of, 345. Construction of, 244. Design of. 242. 380 INDEX. Wind pressure, 67. pressure on roofs, 68. Wooden beams, 115. beams, Loads for, 116. columns, 95. columns, Design of, 96. Wood, Imperfections in, 215. Woods, Hardness of, 213. Specific gravity of, 31. used in building, 208. Wrought-iron and steel pipes, 269. Z bars, Properties of, 89. The International System OF EDUCATION BY MAIL •- • The method of correspondence instruction in the indus¬ trial sciences of the International Correspondence Schools was originated in 1891, by Thomas J. Foster, President of the Schools, and was first used in the Correspondence School of Mines. Distinctive Features of the International System 1. Courses of Instruction for particular occu¬ pations, in which only such facts, processes, and principles are taught as are necessary to qualify the student therein. 2. Textbooks, Question Papers, and Drawing Plates, prepared for each Course; Principles applied in examples of practical value to the stu¬ dent; Frequent Revision, to keep pace with latest methods in trades and manufactures. 3. Thorough examination and correction of the written work of the student, and full, clear, and exact written explanations of all difficulties met with in studying- ADMINISTRATION BUILDINGS OF International Correspondence Schools Scranton, Pa. Erected in 1898 650,000 Students and Graduates. Faculty of 358 Professors and Assistants ESTABLISHED 1891 THE ORIGINAL Our Standing and Responsibility The International Textbook Company, Proprietors of the International Correspondence Schools, is incorporated under the laws of Pennsylvania, and has a paid-up capital ot $3,000,000. Its administration buildings and its mammoth printery and instruction building were erected expressly for the purposes of correspondence instruction, at a cost of nearly a million dollars. The administration buildings, two in number, are situated at 434-436 Wyoming Avenue, are five and four stories high, respectively, and contain the business departments of the Schools. The printery and instruction building is situated at the corner of Wyoming Avenue and Ash Street. It is two and three stories high, and contains the instruction, illustrating, and printing departments of the Schools. References We refer to the commercial agencies, or to any bank officer, teacher, clergyman, or public official in Scranton, as to our responsibility and reputation. We will repay the traveling expenses of any person or committee who may come to Scranton and find that we have made misrepresentations as to the practicability and efficiency of our method of instruc¬ tion and Courses of study, or as to our financial standing. We will, further, refer a person, intending to enroll, to a student in his locality, with whom he may correspond. From J. A. Linen, Esq. President First National Bank, Scranton, Pa. This Bank ranks third in the roll of honor of National Banks in the United States We regard the Schools as an educational institution of a very superior character. The officers and managers are men of integrity and business capacity, and stand high in this community. J* L INEN * 3 System of Instruction Each Course is made up of a series of Instruction Papers, clearly written and fully illustrated. When the student enrolls, the first two Instruction Papers are sent to him. After carefully studying the first Instruction Paper, he writes his answers to the Examination Questions at the end of the Paper, sends his work to the Schools for examination and correction, and continues with his second Paper. When the sets of answers are received at the Schools, they are care¬ fully examined. If an error is discovered, it is not only indicated in red ink, hut, if considered advisable, a careful explanation of that particular problem is written on the back of the sheet. ’ Papers are passed if a mark of 90 per cent, has been attained. The answers are then returned, accompanied by a Percentage Slip and the third set of Papers. The student always has at least one Paper to study while the answers to the previous Paper are being examined and corrected. How We Teach Drawing The first Instruction Paper on Drawing and a mailing tube for returning the finished Plate are sent to the student. Detailed directions are given for the use of instruments and making the first Plate. Beginning with simple lines, the student is advanced to actual working drawings, to pen-and- ink rendering, to drawing from nature, from cast, and from the figure, and to water-color rendering. Special Instruction When a student desires assistance from his Instructors, he uses an “Information Blank” provided for the purpose. When considered necessary, or on request, a “Special Instructor” is assigned to give personal attention to his case, until the subject is completed. A Certificate of Progress is granted on the completion of each Division of a Course, and a Certificate of Proficiency, or Diploma, is awarded when the student passes his final examination. 4 Advantages of the System 1. You Study at Home.— You do not have to leave home to secure the education; the education comes to you. 2. No Time Lost From Work. —You can keep right on With your work, and study during spare hours. This is the only system of education that enables the student to com¬ bine education and experience by immediately using in his daily work the knowledge gained through his studies. 3. You Study When It Is Convenient. —Our Schools never close. You can study when and where you please. Failure is impossible to those that try. 4. We Teach Everywhere. —You can move from place to place while studying. \Ye teach wherever the mails reach. We have students in every country. 5. No Books to Buy.— You have no textbooks to buy. We furnish all Instruction Papers, return envelopes, and information Blanks. We prepay all postage on mail sent by us to the student. All that it need cost you, outside of the price of your Course, is the postage on matter sent to us. 6. Instruction Private.— Instruction is conducted pri¬ vately. None need know you are a student except ourselves. 7. Only Spare Time Required.— Your studies need not interfere with business or social engagements. 8. Written Explanations _Written explanations are always with you, and can be studied repeatedly. 9. Each Student a Class by Himself.— Our student’s written examinations enable his Instructor to detect Aveak points and assist him. Each student is a class by himself, because the Instructor attends to him alone. 10. Study Assures Success. —The successful comple¬ tion of any Course, and our Diploma, is assured to all that can read and write and will study as we direct. 11. Backward Students Assisted.— We take great pains with backward students; they become our best friends. 12. Prepared for Examinations.— Our Courses prepare the student for examinations; he learns to express himself clearly in writing, and remembers what he writes. 13. Open to All.— Our Schools are open to all—both sexes—“seven to seventy.” 5 Bound Volumes Furnished to Students Realizing the great value of the Instruction Papers and Drawing Plates to those that have studied them, and the desirability of preserving them for reference, the Schools have had them reprinted and bound into handsome half¬ leather volumes. The number furnished varies from one to Bound Volumes of the Complete Architectural Course ten volumes, according to the Course for which the student enrolls. He has the use of them as long as he lives up to his contract. Their contents correspond to the set of the Instruc¬ tion Papers and Examination Questions sent to the student throughout his Course, and are supplied in addition to them. Each set gives the student thorough and complete instruc¬ tion concerning the theory and practical application of the principles underlying the trade or profession on which they treat. Containing as they do the complete Course in perma¬ nent form, the volumes constitute ail unequaled reference library, available at all times. 6 What the International Correspondence Schools Are Doing First—Teaching Mechanics the Theory of Their Trades In nearly every machine shop, drafting room, industrial plant, etc., we have students that have secured promotion and advances in salary through study in our Schools. The increased value of an employe that masters the theory of his trade or profession brings prompt and substantial recognition. Experience in teaching 650,000 students has proved that any one that can read and write English is able to keep right on with his work, and at the same time acquire a technical education. You do not have to leave home or quit work. Our prices are low, our payments easy, and you have no textbooks to buy. If you are dissatisfied with your salary, you can increase your earning capacity by study at home, and fit yourself for the highest positions in your trade or profession. THROUGH THIS PLAN Machinists and Apprentices Firemen and Oilers Linemen and Electricians Carpenters, Etc. Miners and Mine Bosses Chainmen and Surveyors Tinsmiths Plumbers, Etc. Assistant Chemists Have Become Have Become Have Become Have Become Have Become Have Become Have Become Have Become Have Become Mechanical Draftsmen. Steam Engineers. Electrical Engineers. Architects and Builders. Foremen and Managers. Civil Engineers. Pattern Draftsmen. Sanitary Engineers. Chief Chemists. 7 What the International Correspondence Schools Are Doing Second—Helping Misplaced People to Change Their Work The man that would succeed as an electrical, mechanical, or civil engineer, or architect is filling a iflO-a-week position as salesman or assistant bookkeeper. The woman that would be valuable in an office, drafting room, or laboratory position is earning a poor living as clerk, housekeeper, or seamstress. These conditions exist because people do not know of any practical plan to change to the occupation of their choice. We have solved the problem. We have qualified hundreds for salaried positions in new lines of work, at their homes, in spare hours, and at small expense. They held their old positions until they changed to the new, with a salary better than before. They are now earning while learning, and earn more as they learn more. THROUGH THIS PLAN Clerks, Salesmen, Bookkeepers, Women, Mechanics, Farmers, Laborers, Teachers, Telegraphers, Drivers, HAVE BECOME Draftsmen, Surveyors, Architects, Engineers, Chemists, Stenographers, Accountants, Ad Writers, Window Dressers. 8 What the International Correspondence Schools Are Doing Third—Enabling Young People to Sup¬ port Themselves While Learning Professions Young men or women obliged to earn their own living are not debarred from a successful career because they have not the time or means to attend college. By our method of education by mail they can qualify at home, in spare time, and at small cost, for minor positions and rapidly advance. A few months’ study of Mechanical or Architectural Drawing with us will qualify young men for positions as assistant draftsmen in machine works or electrical manu¬ factories, or with architects. Here they can combine study with work, and advance. Through the Surveying and Mapping Course they can qualify as surveyors on engineer¬ ing corps, and through further study with us advance to the highest positions. Those that desire to enter on business life can qualify, through our instruction, for good positions as bookkeepers or stenographers, ad writers, window dressers, etc. THROUGH THIS PLAN Men J } Have Become Draftsmen, Electricians, Surveyors. Young Women 9 The School of Mechanical Engineering Mechanical Course. —This is intended For all those that desire a thorough knowledge of engineering calculations, mechanical drawing, and the design of steam engines, boil¬ ers, and modern machinery. It is a complete treatise on the drafting-room practice of mechanical engineering. Mechanical Engineering Course.— This is intended for machinists, draftsmen, machine designers, mechanical engi¬ neers, apprentices, foremen, superintendents, etc. This Course comprises a thorough and exhaustive treatment of the subject of mechanics, supplemented by a complete treatise on modern shop practice, and is the most thorough Course in practical mechanical engineering ever published. Shop Practice Course. —This is divided into five parts, as follows: Machine-Shop Practice is intended for all those that wish to get a thorough knowledge of modern machine- shop practice. Toolmaking is intended for those that desire information in regard to the latest and most approved tool¬ making methods. Patternmaking covers thoroughly every branch of patternmaking. Foundrywork gives thorough instruction in all phases of foundrywork. Blacksmithing and Forging is intended to give blacksmiths, helpers, etc. a thorough knowledge of the best methods employed in their trade. Increased Salary Over 100 Per Cent. Having been obliged to make my own way before I had a chance to get a practical education, I soon found that the man with the working educa¬ tion got the pay, while the others got the hard work. After studying from textbooks and at night schools with but little success, I enrolled in the 1.0. S. Since I enrolled I have secured better employment, and my pay has been increased over 100 per cent. I am now first-class machinist for the U. S. Government. Hugh J. White, Washington, D. C. 10 The School of Mechanical Engineering Refrigeration Course.— Graduates of this Course will understand the principles of refrigeration, the design and construction of refrigerating apparatus, and its installation, testing, and operation. Gas Engines Course.— This is intended for all that desire to manufacture and install gas or oil engines, and for all that operate or repair them, or wish to qualify as gas engineers. Farm Machinery Course. —This is intended for traction engineers, threshers, and farmers. Graduates will thoroughly understand the principles of operation of farm machinery and be able to run traction engines. The School of Steam Engineering Steam=Electric Course.— This is a complete Course on steam engineering and electric-lighting and railway work, and is intended for engineers, superintendents, etc. of large electric-lighting or railway plants. Complete Steam Engineering Course. —This Course, as its name implies, is a complete treatise on stationary engi¬ neering, and is intended for engineers, superintendents, etc. in large steam plants using little or no»electric apparatus. A Chief Engineer’s Opinion I wish I could make my remarks about the I. C. S. Steam Engineering Courses strong enough to induce every engineer to enroll. The knowledge gained has been very valuable to me. I have the satisfaction of knowing not only the how but the why of my work. I now have charge of the Spring Garden Station of the Phila¬ delphia Water Department, the largest plant owned by the city. The cost of an I. C. S. Course is insignificant. Clarence D. Wiluason, 1723 Norris SL, Philadelphia, Pa. 11 The School of Steam Engineering Advanced Engine Running Course.— This Course will qualify engineers, firemen, etc. to take charge of medium- sized steam plants. Engine Running Course.— This Course is intended for engineers, firemen, helpers, etc. in small plants, and to qualify any one to get a start in steam engineering. Engine and Dynamo Running. —This is intended for those who wish to qualify to operate and care for the appa¬ ratus in small steam-electric plants. The School of Marine Engineering Marine Engineers’ Course.— This Course is intended for coal passers, firemen, water tenders, oilers, and other em¬ ployes of steam vessels. The graduate will be qualified to pass marine license examination for any grade to which he is eligible by law. The School of Locomotive Running Trainmen and Carmen’s Scholarships. —These three Scholarships provide trainmen with special instruction on air brakes, train rules, train heating, car lighting, etc. What We Do for Marine Firemen I had studied a good many versions of the so-called “Complete Treatise on the Steam Engine,’’ but I had never found what I wanted to know until I enrolled in the Schools. Ten times what I have paid for my Scholarship would not buy my Course from me. I have risen from the position of fire¬ man to that of chief engineer of an ocean-going steamer. Every promise you made has been faithfully kept, and you have even done more for me than I expected. Sherman Mallery, Norfolk, Va. 12 The School of Locomotive Running Locomotive Running Scholarships.—These six Scholar¬ ships are very popular with locomotive firemen and engi¬ neers. They furnish instruction in the construction and management of the locomotive and its various appliances and fittings. Air Brake Scholarships.—These five Scholarships are intended for enginemen and air-brake inspectors. They pro¬ vide complete instruction on Westinghouse and New York air brakes. The Roundhouse Scholarships.—These three Scholar¬ ships include either New York or Westinghouse air-brake instruction, together with instruction on locomotive boilers. The School of Electrical Engineering Electrical Engineering Course.—This is intended for superintendents of electrical establishments, factory artisans, draftsmen, designers, inventors, and all others that wish a thorough knowledge of the design of electrical apparatus. Electrical Course.—This is intended for those that desire to qualify for any electrical position that does not require a knowledge of mechanical engineering. Electric Railways Course.—This will qualify the student to construct and maintain electric railways under any system. An Electrical Engineer’s Experience I have always thought the cost of my I. C. S. Electrical Course trifling compared with the benefits received. The last Papers of the Course on Elec¬ tric Machine Design are especially valuable. Through the Schools, I was appointed electrician for Moncton, N. B. For some time I have been in¬ stalling complete plants of all kinds, making the specifications myself. During the past year, I have had more work than I could handle. Geo. M. Macdonald, Box 185 , Moncton , N. B. 13 The School of Electrical Engineering Advanced Electric Railways Course.—This Course is a complete treatise on steam engineering as applied to electric- railway plants, and is intended for superintendents, engi¬ neers, etc. in large electric-railway plants. Advanced Electric Lighting Course.—This Course is a complete treatise on steam engineering as applied to electric- lighting plants. It is intended for superintendents, engi¬ neers, etc. in large electric-lighting plants. Electric Lighting and Railways Course. — This is intended for dynamo tenders, stationary engineers, installa¬ tion engineers, and all who work around electric-railway or lighting plants. Electric Lighting Course.—This will qualify the student to successfully install and operate electric arc- and incandes¬ cent-lighting systems. Dynamo Running Course.—This is a short but complete Course on the operation and care of dynamos. It is intended for dynamo tenders and for those who wish to get a start in electrical work. Electric Car Running Course.—This Course will qualify the student to direct the equipment of a modern electric car, operate it safely under all conditions, and pass any motorman’s or car inspector’s examinations. Interior Wiring.—This will qualify the student to do electric-light wiring and bellwork. From Conductor to Head Barnman I am a student in the Electric Car Running Course, and am pleased to say that the knowledge gained from my Course has enabled me to accept a much better position. When I en¬ rolled, I was a motorman for the Ogdensburg Street Railway Company, but after applying myself to my Course for some time, I was promoted to head barnman for the above company, with a better salary, and have also been promised another increase. John Henry O’Neill, 129 New York Avc., Ogdensburg , N.Y. 14 The School of Electrotherapeutics Complete Electrotherapeutic Course. —Graduates of this Course will be qualified to make all modern and approved applications of the electric current in the diagno¬ sis and treatment of disease. Neurological Electrotherapeutic Course. —This is in¬ tended for physicians and medical students that desire a knowledge of the treatment by electricity of the diseases of the brain, spinal cord, peripheral nerves, and muscles. Gynecological Electrotherapeutic Course. —This is in¬ tended for physicians that wish to make a special study of the diseases peculiar to women. Surgical Electrotherapeutic Course. —This is intended for surgeons and general practitioners. Eye, Ear, Nose, and Throat Electrotherapeutic Course. This is intended for physicians and specialists. Dental Electrotherapeutic Course. —This is a complete up-to-date treatise on electricity as used in dental operations. Roentgen Rays Course. —This includes instruction in the manipulation and care of all up-to-date apparatus used by recognized Roentgen ray workers. Nurses’ Electrical Course. —The information contained in this Course will increase the efficiency and earning capac¬ ity of any nurse, and will make her more valuable to the attending physician. Genito=Urinary Electrotherapeutic Course. —This Course is especially intended for the genito-urinary specialist. Prominent Physicians Commend Our Course International Correspondence Schools, , Scranton, Pa. Gentlemen :—After having completed the Electrothera¬ peutic Course I can tell you that this Course is, in mv opinion, a wonderful piece of work. The physician folds everything for intelligently applying electricity, aim at the same time is not bothered with superfluous things—hypothe¬ sis, opinions, names, etc. I call them superfluous in a.prac¬ tical Course which aims at nothing but giving t ie student a thorough knowledge of electricity so far as it is used as a therapeutic and diagnostic agent. Dr. A. Decker, 1*25 Orchard St ., Chicago , III. 15 The School of Telephone and Tele¬ graph Engineering Telephone Engineering Course.— This Course will qual¬ ify students to maintain and manage telephone switchboards and exchanges, make repairs anywhere in the system, and take general supervision of a plant. Telegraph Engineering Course.— This is intended for telegraph operators in commercial or railroad business, the military or the signal service. It gives thorough instruction in all branches of telegraphy. Graduates will be qualified to fill the most responsible positions. The School of Civil Engineering Civil Engineering Course.— This Course is intended for practicing bridge, railroad, municipal, or hydraulic engi¬ neers, surveyors, and engineers’ assistants that wish to review former studies, to acquire a thorough knowledge of other branches of the profession by studying those special branches of engineering in which they lack knowledge, or to become qualified as consulting engineers. The instruction is suffi¬ ciently advanced and comprehensive to insure to the graduate the technical training necessary to the successful prosecution of his professional work. Responsible Position Before He Finished Study I wish here to say that before I had finished the instruction in “Bat¬ teries,” in the I. C. S. Telephone Engi¬ neering Course, the Schools helped me to obtain the position I now occupy, that of assistant electrician for the American Bell Telephone Company, at Goshen, Ind. The only recommendations I carried were the Schools’ records of my progress in the Course, as far as I had gone. My technical training has been con¬ ducted by mail entirely. W. H. Fox, Goshen, Ind. 16 The School of Civil Engineering Bridge Engineering Course.— This is intended for sur¬ veyors, draftsmen, bridge engineers, and their assistants, and employes in bridge works. Graduates will, with some experience, be able to design and superintend the construc¬ tion of modern highway and railroad bridges. Surveying and Mapping Course.— This is intended for rodmen, chainmen, engineers’ assistants, and all that wish to become surveyors. Graduates will he qualified to survey railroads, farm properties, etc. Railroad Engineering Course. —Graduates of this Course will have the necessary education to survey and map out proposed locations for railroads, or to fill responsible posi¬ tions in the work of construction or the maintenance-of-way department. Hydraulic Engineering Course.— This is intended for those interested in irrigation, water supply, etc. Graduates will have the necessary education to design and install water-power plants, hydraulic machinery, and water-supply and irrigation systems. Municipal Engineering Course. —This is intended for municipal engineers and contractors, city surveyors, and their assistants. It will qualify the student to survey and make maps and estimates of proposed sewerage systems, street improvements, pavements, etc., and to superintend their construction. Earned $30 as Teacher: Earns $100 as Surveyor When I enrolled in the I. C. S., I was teaching school at $30 a month. After studying three months, I secured a, position as draftsman and assistant surveyor at $70 a month, but soon after beginning work was offered $100 a month. In his spare time a man 2 an gain as good an education in the international Correspondence Schools, Scranton, Pa., as at the best colleges. [ heartily recommend the Schools. Lloyd G. Smith, Deputy County Surveyor, Chinook, Choteau Co., Mont. 17 ihe School of Mathematics and Mechanics This is our largest School. In it are made all the prelim¬ inary examinations and corrections in mathematics and mechanics for the other Schools. The Principal is assisted by 13 Special Instructors and 130 Examiners. While most of the mathematical subjects are taught in connection with other Courses, the following can be taken separately: Arithmetic Course, Part 1 .— This Course includes in¬ struction from the simplest definitions of Arithmetic up to and including ratio and proportion. Arithmetic, Parts 1 and 2.—This Course includes all the subjects in Part 1, together with instruction in the sub¬ jects: Percentage, Interest, Notes, Bank Discount, Stocks and Bonds, Average or Equation of Payments, Partnership, and Alligation. Algebra Course.—This is a thorough Course in Algebra, including instruction in Quadratic Equations, the Remain¬ der Theorem, the Binomial Formula, Progressions, Loga¬ rithms, etc. Advanced Algebra Course.—This Course is intended for teachers of Algebra, for engineers, and for all others that desire thorough instruction in higher algebra. Kellar, the Greatest Living Magician, Testifies Montour House, Opposite Court House, J. L. Riehl, Proprietor. Danville, Pa., May 2. Dear Sir: —In reply to your request for my opinion regard¬ ing the International' Correspondence Schools, I beg to say that I consider the system of Instruction the very best that can be desired, and judging from their Course in Arithmetic, in which 1 am enrolled, I think any one of ordinary intelli¬ gence can acquire a thorough knowledge of mathematics by carefully reading and observing the rules of the Instruc¬ tion Papers. The system is so very simple that any one who can read may learn. Yours truly, Harry Kellar (Magician). 18 The School of Chemistry General Chemistry Course.—This is a Course in gen¬ eral and analytical chemistry, and is intended for those who desire to obtain a general knowledge of chemistry and ana¬ lytical methods and thus prepare, in as short a time as possible, for general laboratory work. Since the Course includes an exhaustive treatment of organic chemistry, it enables the student to prepare -for responsible positions in the manufacture of coal-tar products and various other organic materials. This Course also prepares the student for such positions as pharmaceutical chemist, toxicologist, etc. Chemistry and Chemical Technology. The student in this Course receives, in addition to a thorough training in general and analytical chemistry, full detailed instruction in the most important branches of applied chemistry. Separate Courses in the following branches of applied chemistry are given: Chemistry and Manufacture oi Sul¬ phuric Acid; Chemistry and Manufacture of Alkalies and Hydrochloric Acid; Chemistry and Manufacture of Iron and Steel; Chemistry and Packing-House Industries; Chemistry and Manufacture of Cottonseed Oil and Products; Chemistry and Manufacture of Leather; Chemistry and Manufacture of Soap; Chemistry and Manufacture of Cement; Chemistry and Manufacture of Paper; Chemistry and Manufacture of Sugar; Chemistry, Petroleum, and Manufacture of I roducts, Chemistry and Manufacture of Gas. Drug Clerk Becomes a Chemist I started early in life to earn my living by clerking, and my lot was cast in a drug store. Before I enrolled in the Chemistry Course, I made sev¬ eral attempts to educate myself, but with little success. Thanks to the Schools, I have mastered chemistry to a degree that my ambition had nei ei pictured. Soon after taking up mj Course, I took charge of the laboratoi > at E. E. Bruce & Co., wholesiile drug¬ gists, at a good salary, which has since been increased 45 per cent. H. B. Molyneaux, Omaha , JSeo. 19 The School of Drawing Mechanical Drawing Course.—The student that com¬ pletes this Course will be able to execute neat mechanical drawings. We have met with remarkable success in teaching this subject to thousands entirely ignorant of drawing, hun¬ dreds of whom are now earning good salaries as draftsmen and designers. We guarantee to qualify ANY ONE to make neat mechanical drawings that follows our directions. Architectural Drawing Course.—The student that com¬ pletes this Course will be able to make general and detail drawings of architectural structures, and will be thoroughly qualified to take a position in an architect’s office. We guarantee to qualify ANY ONE to make neat architectural drawings that follows our directions. If you wish to learn Mechanical or Architectural Drawing, or desire to become a mechanical or electrical engineer, or architect, and support yourself while learning either of these professions, send for special circular entitled “ Support Yourself.” Drawing Outfit Free Every student in either of these two Courses is furnished with the Complete Drawing Outfit No. 1, valued at $13.55. He is permitted to retain this Outfit for use indefinitely, pro¬ vided he observes the terms of his Contract for Scholarship. Dentist to Draftsman When I enrolled in the I. C. S. Me¬ chanical Drawing Course, I was prac¬ ticing dentistry. After partially finish¬ ing my Course, I commenced making drawings for the Smith Metallic Pack¬ ing Co., occasionally receiving as high as $15 fora single drawing, and having some of my work taken in preference to that done by the Master Mechanic of a Mexican railway. I have now become Chief Draftsman for the Smith Metallic Packing Company, Chicago. M. E. Hoag, 861 Monadnock Bldg., Chicago, III. 20 The School of Architecture Complete Architectural Course.—This is intended for architects, draftsmen, contractors and builders, carpenters, masons, bricklayers, building tradesmen, and all others desirous of qualifying themselves to design and construct buildings. Graduates will he able to design, prepare working drawings and specifications for building operations, calculate quantities, estimate costs, and will have a thorough knowl¬ edge of iron and steel construction. Architectural Drawing and Designing Course.—This is intended for carpenters, contractors, architectural draftsmen, and all that wish to learn architectural drawing, history, and design. Building Contractors’ Course.—This will qualify car¬ penters, masons, bricklayers, and other building tradesmen to make and read plans, estimate accurately, and undertake general contracting and building. This is a practical Course in building construction, containing practical instruction for practical men. Architectural Drawing Course.—This Course is de¬ scribed under “ The School of Drawing.” See previous page. Students in this Course have been so successful that we will forfeit $100 to any student of our Architectural Drawing Course that will study as we direct, whom we cannot qualify to make neat architectural drawings. From Telegraph Operator When I began studying in the Com¬ plete Architectural Course of the In¬ ternational Correspondence Schools, of Scranton, Pa., I was a telegraph operator and knew nothing whn fever of drawing, or of the profession that I am now following. I have given up my partnership at Fainnount and am now well established here, with good prospects for a very successful busi¬ ness. My income at present is three times what I was receiving when I enrolled. _ ,, ... .. John C. Tibbetts, Grafton, W. Va, 21 to Architect t . The School of Design Ornamental Design Course.—This provides instruction in freehand drawing, sketching from nature, and conven¬ tionalizing of natural forms as a basis for decorative design, history of ornament, details of color, and construction of all typical elements, composition, pencil, pen, wash-drawing and water-color work, and the application of design to china, wall paper, lace, book covers, embroidery, furniture, stained glass, interior decoration, rugs, carpets, oilcloths, etc. The instruction is carefully graded from the simplest instru¬ mental work to the more complicated water-color rendering of practical designs. Drawing, Sketching, and Perspective Course.—This is intended for teachers that wish to qualify for the position of drawing inspector; also, for all that desire a thorough knowledge of freehand and perspective drawing. Even if the Course is taken only for developing artistic tastes and perceptions, it is invaluable. The School of Sheet-Metal Work Sheet=MetaI Pattern Drafting Course.—This Course is intended for tinsmiths, cornice makers, architectural sheet- iron workers, coppersmiths, plumbers, etc. Graduates will be able to develop all kinds of sheet-metal patterns. Doubled His Salary Since Enrolling Before I enrolled in the I. C. S., my education consisted of but four terms in a country district school. I took up the Sanitary Plumbing, Heating, and Ventilation Course and the Sheet-Metal Pattern Draft¬ ing 1 Course, and have received great benefits from my instruction. When I enrolled, my salary was $9 a week. I am now foreman of a large shop doing plumbing, heating, venti¬ lating, and cornice work. B. M. Richards, Box W5, Everett , Wash. 22 The School of Plumbing, Heating, and Ventilation Sanitary Plumbing, Heating, and Ventilation Course. This affords an education in plumbing, heating, and ven¬ tilation that will qualify any plumber, steam titter, or gas- fitter to fill the highest positions in his line of work. It is of particular value to such men as aspire to become master plumbers, general contractors, or heating engineers. Sanitary Plumbing and Gas=Fitting Course.—This Course enables plumbers, gas-fitters, and apprentices to do their work easier, better, and more economically, and to pass examinations for license. Heating and Ventilation Course.—This is intended for steam fitters, plumbers, and heating and ventilating engi¬ neers. It will qualify the student to install any system of heating or ventilation. Sanitary Plumbing Course.—This is intended for plumbers and plumbing apprentices that do not care to study gas-fitting or heating and ventilation. It will qualify the student to pass any examination required of plumbers. Gas-Fitting Course.—This will qualify the student to calculate illumination required, test systems, put up combi¬ nation fixtures, or make drawings of proposed installations. From Journeyman to Master Plumber and Gas-Fitter I am under many obligations to the I. C. S. I have recently passed an examination and obtained a first-class Master Plumber’s license. It has been of inestimable benefit to me. I most heartilv recommend the Schools, espe¬ cially to plumbers who are desirous of gaining an insight to the technical theories of the trade, which equips them to earn larger wages and the best positions as workmen. Michael L. Sylvia, Plumber and Gas-Fitter , Hew Bedford , Mass. 23 The School of Mines Full Mining Course.—This is intended for mine super¬ intendents, foremen, mining engineers, and others that wish a thorough education in all branches of coal and metal mining. It fits the student to superintend either coal or metal mines, or to pass mine foreman’s or State Mine Inspect¬ or’s examinations. Complete Coal Mining Course.—This is intended for mining engineers, mine officials, and miners that wish a com¬ plete education in the methods and machinery used in coal mining. It embraces a study of every detail necessary to fit a student for any position in or around either anthracite or bituminous mines, or pass the examinations for mine fore¬ man or State Mine Inspector. Short Coal Mining Course.—This contains only the information absolutely necessary to qualify persons to pass the mine foreman’s examinations, and those that finish it will have a good knowledge of the art of mining. Metal Mining Course.—This is intended for mine offi¬ cials, metal miners, or men engaged in ore dressing and mill¬ ing. It qualifies the student to take charge of modern metal mines or mining and milling machinery. Metal Prospectors’ Course.—This will qualify the stu¬ dent to make assays of ores and prospect for gold, silver, and other valuable minerals. Salary Increased $500 Per Year Before I had finished the Complete Coal Mining Course, I obtained a first- grade Certificate of Competency as mine foreman, and also a position where my salary was increased $500 per year. * I am successfully handling the mine in which I am employed as inside manager and foreman. From the information gained in my Course. 1 can master the most complicated problems in mine management, and do all my own surveying and platting. James Parton, Monongahela City , Pa. 24 The School of Metallurgy Complete Metallurgy Course.—This Course is intended for metallurgists, investors, and others who desire a knowl¬ edge of the metallurgy of gold, silver, copper, lead, and zinc. It will give the student a broad field of usefulness and will enable him to direct metallurgical operations of any kind whatever. Milling Course.—This provides instruction for millmen, bosses, and superintendents of milling operations, and will thoroughly qualify the student for the highest positions in this particular branch of metallurgy. The Course deals with the dry methods of gold and silver extraction. Hydrometallurgical Course.—This Course fully explains the wet methods of treating ores for gold and silver extrac¬ tion, and also includes thorough instruction in electro¬ metallurgy. It is intended for helpers, foremen, and super¬ intendents in hydrometallurgical work, electrochemists, electricians, etc. Smelting Course.—This Course deals with the prelim¬ inary treatment and the reduction of ores of the common metals and the refining of the crude products. Graduates of this Course will be qualified to take charge of all kinds of smelting operations. The School of Commerce Failed Before; Succeeded With Us I had attended night school and had spent nearly §100 on textbooks without success before I heard of the I. C. S. The only thing I am sorry for is that I did not hear of them sooner. I had no trouble in understanding the Complete Commercial Course that I took; my instructors taught me every¬ thing by mail easily, simply, and accu¬ rately. The value of what I learned is shown by the fact that during the year my salary has been increased 25 per cent. Ernest Brunelli, Gardiner , N. Mex. 25 The School of Commerce Complete Commercial Course.—This Course is intended for young men or women, in the city or country, that wish to equip themselves with a business education. Graduates will be able to keep books by single or double entry, or perform the work of stenographer or correspondent. They will also have a thorough knowledge of modern office methods, card systems, etc., as used by the most successful and up-to-date commercial houses. Bookkeeping and Business Forms Course.—This Course is intended for bookkeepers, stenographers, etc. that wish a business education. Many professional bookkeepers have taken this Course to get the up-to-date labor-saving methods that it contains. Complete Stenographic Course.—This Course will qual¬ ify the student for the position of stenographer. Faithful study and practice will enable him in a few months to acquire the necessary speed, and, as competent stenographers are always in demand, he can readily secure a good position. The School of English Branches English Branches Courses.—These Courses, two in num¬ ber, are intended for those that lack a common-school educa¬ tion, or wish to try Civil-Service Examinations. Success Won From Defeat I made three attempts to improve myself at night school, but gave up each time, as I was so backward. So lip to 1895 I could only write my name and read a little. I then took the English Branches Course and can now write and spell well. While studying, I worked 84 hours per week, as in the steel business it is necessary to work Sundays. I am now a foreman, and my salary has been increased 60 per cent. My ability to hold the position is due to the Schools. Michael Sullivan, Latrobe , Pa. 26 The School of Textiles Complete Cotton Course.—This Course is intended to qualify those that complete it for the position of superin¬ tendent, or purchasing or selling agent, of a cotton mill. It will also greatly increase the efficiency of agents, superin¬ tendents, overseers, second and third hands, mechanics, spinners, loom fixers, weavers, and all other workers in a cotton mill. Cotton Carding and Spinning Course.—This is intended for yarn-mill superintendents, carders, spinners, section hands, card grinders, and all employed in cotton-yarn mills. It is also recommended for cotton-machinery erectors, yarn agents, hosiery-mill superintendents. Cotton Designing Course.—This Course is intended for designers and assistant designers, agents, superintendents, overseers, and second hands in weave rooms; section hands, loom fixers, weavers, in cotton mills; dry-goods merchants, salesmen in commission houses, jobbers, and all men or women working in cotton mills, interested in cotton design¬ ing, or desirous of qualifying for any of the foregoing posi¬ tions. Cotton Spinning and Warp Preparation Course.—This is intended for superintendents of thread mills, boss spin¬ ners, second and third hands in spinning rooms, overseers of beaming, slasher tenders, and all men employed in cotton- yarn mills. A Shipping Clerk’s Advancement As a result of your training by mail I am at present bookkeeper for the Randolph Manufacturing Co., at Franklinville, N. C. When I enrolled in your Complete Cotton Course I was working as shipping clerk for the same concern, at a salary only half what I am now receiving. 1 heartily indorse instruction by mail in Textile Design, as conducted by the I. C. S. The lessons are plain and to the point, and contain only information that is valuable. Hugh Parks, Franklinville, N. C. 27 The School of Textiles Cotton Warp Preparation and Plain Weaving Course. This is intended for superintendents of weave mills, boss weavers, fixers, second and third hands in weave rooms, weavers, slasher tenders, etc. It is also recommended for those having a good knowledge of yarn-mill machinery that wish to qualify as general mill superintendents. Fancy Cotton Weaving Course.—This Course is in¬ tended for designers and assistant designers, agents, super¬ intendents, overseers, and second hands in weave rooms, section hands, loom fixers, weavers, and all others that desire a knowledge of warp preparation and weaving ma¬ chinery for fancy goods. Cotton Carding, Spinning, and Plain Weaving Course. This Course is intended for those that desire to qualify for the position of superintendent or overseer in mills making plain cotton goods. Theory of Textile Designing Course.—This is intended for those that have a good knowledge of warp preparation and weaving machinery, but whose knowledge of the theory of designing is not complete. It is recommended to boss weavers, overseers, second hands, and others that desire instruction on the analysis and reproduction of fabrics, and the drafting of designs. Almost every textile designer in the country is hampered in his business by the lack of com¬ petent designers. Worker’s Advancement When I enrolled in your Cotton Carding and Spinning Course I was section hand in the card room of Mill No. 3 of the Eagle & Phoenix Mill Co., of Columbus, Ga. I am now second hand in their Mill No. 1. Your train¬ ing has increased my salary and bet¬ tered my prospects. Correspondence instruction is the only means by which millmen may qualify themselves for promotion. Mv advice to ambitious young men is that they enroll in the I. C. S. and study in their spare time. A. W. Pitts, Phoenix City, Ala. 28 The School of Textiles Complete Textile Designing Course.—This is intended for designers, assistant designers, agents, superintendents, overseers, and second hands in weave rooms; and for section hands, loom fixers, and weavers in cotton, woolen, worsted, or silk mills. Woolen and Worsted Designing Course.—This Course is intended for designers and assistant designers, agents, superintendents, overseers, and second hands in weave rooms; section hands, loom fixers, and weavers in woolen and worsted mills; dry-goods merchants, salesmen in com¬ mission houses, jobbers. Complete Woolen Course.—This Course is intended for agents, superintendents, overseers, and section hands in woolen mills, master mechanics, weavers, loom fixers; in fact, for any that hold a position in a woolen mill. Woolen Carding and Spinning Course.—This is espe¬ cially recommended to superintendents, boss carders, boss spinners, section hands, card and mule erectors, woolen- machinery salesmen, woolen-yarn agents and merchants, and also for the superintendents and overseers of knitting mills using woolen yarns. Woolen Warp Preparation and Weaving Course.—This is intended for all that desire a knowledge of the preparing of woolen warps, and the weaving and elementary designing of woolen goods. Promoted to Pattern Weaver When I enrolled for your Textile Designing Course I was a weaver. Since then, the instruction I have gained from it, together with my prac¬ tical experience, has enabled me to advance to the position ot pattern weaver, with the Springville Manu¬ facturing Company. As a result of my experience, I am free to state that 1 consider your correspondence instruc¬ tion in the manufacture of textiles to be all that is claimed for it. C. W. Seifert, 128 West Main St., Rockville, Conn. 29 The School of Pedagogy Teachers’ Course.—This Course is intended especially for men'and women that wish to qualify for remunerative and responsible positions in the teaching profession. Methods of Teaching Course.—This Course provides teachers with thorough instruction in the best modern methods of teaching, and enables them to qualify for the highest salaried positions. Drawing, Sketching, and Perspective Course.—This is described under the School of Design, page 22. The School of Lettering and Sign Painting Lettering and Sign Painting Course.—This is intended for sign painters, window dressers, designers of lithographs, book and magazine covers, advertising matter, etc., wood and metal engravers, jewelers, stone cutters, wood carvers, draftsmen, stencil makers, retail merchants, clerks, and all others that wish a knowledge of correct styles of lettering. Show=Card Writing Course.—This is intended for busi¬ ness men, clerks, window trimmers, letterers, and all others that desire a knowledge of effective and artistic show-card writing. It includes the only complete and up-to-date instruction on the subject that has ever been prepared. Plates Are Unexcelled I think your Course is the most satisfactory that can be given. The Bound Volumes constitute a refer¬ ence library that is the best to be had, and even if I did not go through the Course, I have it printed so plain¬ ly that I could teach myself without assistance, and your lettering Plates are unexcelled: (hey are the correct thing. My positionnow is Sign and Ticket Writer for the Robert Simpson Co., Limited, Department Store, of Toronto. Sidney Smith, 414 Ossington Ave., Toronto , Ont. , Can. 30 Lettering The School of French French Course.—This is intended for people of culture, civil engineers, business men, and all that desire a conversa¬ tional knowledge of the French Language. The Course is taught by a system of instruction with the phonograph, designed and used only by the Schools. The School of German German Course.—This is taught with the aid of the pho¬ nograph, and is intended for professional and business men and all that come in contact with German-speaking people. The School of Spanish Spanish Course.—This Course is intended for lawyers, physicians, professional and business men, and all those whose duties bring them in contact with the Spanish-speak¬ ing people of South America, Cuba, Philippines, or Spain, This Course is taught with the aid of the phonograph. The School of Navigation Ocean Navigation Course.—This Course will qualify seamen, etc. to pass examinations for master or mate of ocean-going vessels. It is the most complete Course on this subject that has ever been published, and graduates ot this Course will be qualified to pass any nautical examination in the United States or foreign countries. Lake Navigation Course.—This Course is intended par¬ ticularly for those that wish to pass examinations for masters or pilots of lake and coast vessels, and also tor those that wish to increase their grade of license. It is the first and only Course on this subject that has yet appeared. Graduates of this Course will be qualified to pass examinations for master’s or pilot’s license for vessels engaged in lake and coast navigation. 31 The School of Advertising Advertising Course.—This Course is designed to teach the student how to analyze any article of merchandise, find its selling points, and write and lay out a first-class ad that will so present these selling points as to impel the reader to become a purchaser of the article advertised. The Course also includes instructioh in the preparation of miscellaneous retail advertising matter; retail advertising management; department-store advertising; and the estab¬ lishment of an ad-writing business to be conducted at home or in an office. The Course is designed to qualify the stu¬ dent to write good advertising for any or all retail lines of business, including department stores, and to train him for later advancement to the position of advertising manager. The School of Window Dressing The Window Dressing Course.—This Course is an elaborate treatise on window dressing, store decoration, etc. in all its branches. It embraces practically every form of commercial decorative treatment, for nearly all classes of business. The Course is an epitome of the ideas and writings of the most prominent decorators in this country. This Course will not only advance the window dresser to the front ranks of his profession, but will also qualify any one to become a competent window dresser. The School of Law Commercial Law Course.—This Course is designed to aid persons to become better equipped to conduct their busi¬ ness; through it an opportunity is offered them to attain a knowledge of the well-established legal rules and principles that apply to and govern business transactions. The Course will be found especially useful by the fol¬ lowing: Law students, mercantile persons, manufacturers, superintendents, bankers, insurance officials, bookkeepers, administrators, justices, conveyancers, etc. 32