Digitized by the Internet Archive in 2015 https://archive.org/details/handbookforenginOOpott HANDBOOK Engineers, Architects, and otherWorkers IRON AND STEEL, CONTAINING TABLES OF CAPACITY OF I BEAMS AND CHANNELS OF IRON AND STEEL, ' AS MANUFACTURED BY THE POTTSVILLE IRON AND STEEL CO. OF POTTSVILLE, PENNA. ALSO, DESIGN AND CALCULATION IRON AND STEEL FLOORS, PLATE GIRDERS, ETC., AND OTHER INFORMATION OF SERVICE TO WORKERS IN IRON. ’ . A . ^ BY . ^ ^ o j j j . 3 D.;C.;BpANDC';-.» ^ ^ MEMBER OF AMERICAN SOCIETY OF CIVIL ENGINEERS. ' ,'-'j ^ - 7887.- ^ p, 7 BY PRINTED BY J. B. LIPPINCOTT COMPANY, PHILADELPHIA. Copyright, 1887, by pottsville Iron and Steel Co. — G- . R . TT-F»r d e rsori,, — TTeoT. Eit 2* r. N t. rolung^Al Pottsville Iron and Steel Company, POTTSVILLE ROLLING MILLS MANUFACTURERS OF SOLID ROLLED I BEAMS, ANGLES, CHANNELS, T IRON, ROLLED OF EITHER IRON OR STEEL. ••• BEST REFINED MERCHANT BARS, Shafting, Bridge Iron, Etc. RIVETED GIRDERS AND COLUMNS OF EVERY DESCRIPTION. ••• General Office, Pottsville, Penna. OFFICERS. C. M. Atkins President. William Atkins Treasurer, John M. Callen Secretary. I William Atkins General Manager, William Brazier . . . Superintendent of Rolling Mills. Wm. H. Knowlton Chief Engineer. Joseph Summons Master Mechanic, CORRESPONDENTS WILL PLEASE ADDRESS POTTSVILLE IRON AND STEEL CO., pottsville, penna. AGENTS. Wm. H. Wallace & Co. . 131 Washington St., New York. J. F. Bailey 257 S. Fourth St., Philadelphia. A. G. Tompkins & Co 8 Oliver St., Boston, Mass. Ni CONTENTS. PAGE Remarks on the tables of capacity 41 Tables of capacity of wrought-iron I beams .... 45 Tables of capacity of wrought-iron channels .... 73 Tables of capacity of steel I beams 97 Tables of capacity of steel channels 125 On determining the capacity of beams and channels . 148 On the properties of I beams and channels 155 Table of properties of I beams 159 Table of properties of channels 160 On concentrated loading 161 On absolute maxima bending moments on stringers . 165 On the use of the tables of capacity 173 On plate girders 179 Single- webbed plate girders 188 Box girders 205 Buckled plates 212 Buckled plate floors 214 Trussed girders 220 Flitch beams 228 Bending moments and shearing forces 234 7 PAGE POTTSVILLE IRON AND STEEL CO., Moments of inertia for simple shapes 235 Moments of inertia for compound shapes 236 Bearing of girders on brick walls 240 Girders formed of beams 240 Weight of fire-proof floors 244 Standard separators for beams 245 Position of centre of inertia of a compound section . 246 Columns and posts 247 Strength of wrought- and cast-iron columns 248 Strength of wrought-iron columns 249 CrushiVig loads on timber and stone 250 Strength of timber posts 251 Wooden beams and girders 252 Shearing and bearing value of rivets 255 Bearing values and moments of resistance of pins . . 256 Wind pressure on roofs 257 Weight of roof coverings 258 Angles of roofs 259 Weight of bar iron 262 Upset ends and weights of clevises and sleeve nuts . . 264 Weight of wrought-iron bars 265 Weight of wrought-iron flats 266 Weights for plates over twelve inches 267 Weight of bars over one inch in thickness 269 Weight of square-headed bolts 270 Weight of square and hexagon nuts 270 Weight of rivets and rivet heads 271 8 POTTSVILLE, PENNA., U. S. A. PAGE Weight of square-headed machine bolts 272 Sizes and weights of square and hexagon nuts .... 273 Standard sizes of wrought-iron washers . 274 Cast heads and washers for combination bolts .... 274 Weight of larger sizes of hexagon nuts 275 Weight of nut and bolt heads 275 Weight per square foot of iron and steel . American and Birmingham wire gauges . Weight of cast-iron pipe Weight of wrought-iron welded tubes . . Weight of ship spikes I Number of nails and tacks to the pound . j Weight of railroad spikes Weight of railroad bars Weight of railroad splices Note on brick arches for floors Weight of materials Weight of timber Plastering American slating Shingling Painting and glazing Skylight and floor glass I Weight of flagging Brick work and masonry Weight of galvanized and black iron . . Table of inches in decimal parts of a foot 9 276 278 279 280 I 281 ! 282 282 283 283 284 284 285 285 286 286 287 288 288 288 289 292 POTTSVILLE IRON AND STEEL CO. PAGE Table of fractions of an inch expressed decimally . . 294 Measurements of length 295 Measurements of weights 295 Measurements of capacity 295 Measurements of surface 295 Table of squares and cubes 296 Length of a circular arc 300 Trigonometrical functions 301 Natural sines, etc 302 Properties of circular arcs 303 Proportions of the circle and its equal 304 Areas of circles 306 Circumferences of circles 307 Constants relating to the circle 308 Constants relating to logarithmic systems 308 Constants relating to gravity 309 Reduction multipliers 309 Thermometers 310 10 ! SHAPES OF STEEL Manufactured by the IRONU^'STEEI CompaN^ 1 1 POTTSVILLE, PENNA., U. S. A. 13 .1 POTTSVILLE IRON AND STEEL CO., i6 POTTSVILLE, PENNA., U. S. A . 7 , 00 tH w a o m H • 7 ' '8 I <3 a “ t2! 16 ’ r 17 i8 POTTSVILLE, PENNA., U.S. A. '9 POTTSVILLE IRON AND STEEL CO. No. 27 3" BEAM 24 LBS P. Y. ' 2 - No. 28 3" BEAM 20 LBS P. Y. No. 29 3'' BEAM 16 LBS P. Y. 1 9I” - — 20 POTTSVILLE, PENNA., U. S. A. i^-lNCH CHANNEL 21 POTTSVILLE IRON AND STEEL CO., No 32 Depth of channel, in inches. Width of flange, in inches. Thickness of web, in inches. Weight per yard, in lbs. 12 3 T5 90.0 12 3 ts y 97.5 12 sys T5 105.0 12 % 112.5 12 sy H 120.0 12 3 tb % 127.5 12 3% 135.0 12 3 /b % 142.5 12 3K 150.0 No. 33 Depth of channel, in inches. Width of flange, in inches. Thickness of web, in inches. Weight per yard, in lbs. 12 2% A 64.0 12 21^ % 71.5 12 2% A 79.0 12 m 86.5 r No. 34 Depth of channel, in inches. Width of flange, in inches. Thickness of web, - in inches. Weight per yard, in lbs. 12 2^ TB 62.0 12 m % 69.5 12 2% A 77.0 12 2M y 84.5 i M 22 POTTSVILLE, PENNA., U. S. A. lO" No. 35 Depth of channel, in inches. Width of flange, in inches. Thickness of web, in inches. Weight per yard, in lbs. 10 2§f % 60.0 10 2% A 66.25 10 211 72.5 10 3 A 78.75 10 % 85.0 10 H 91.25 10 3A % 97.5 10 3^ li 103.7 10 3tb Vs 110.0 10 3% If 116.25 10 3^ 1 122.5 10 31/^ lA 128.75 No. 36 Depth of channel, in inches. Width of flange, in inches. Thickness of web, in inches. Weight per yard, in lbs. 10 2M A 48.0 10 2A % 54.0 10 2% A 62.0’ ^32 1.3 I No. 37 Depth of channel, in inches. Width of flange, in inches. Thickness of web, in inches. Weight per yard, in lbs. 9 23^ 52.00 9 2A 57.75 9 2^ M 63.50 9 2lf a 69.25 9 2% 75.00 9 2if u 80.75 9 3 M 86.50 .IS. U 3 POTTSVILLE IRON AND STEEL CO., m No. 38 Depth of channel, in inches. Width of flange, in inches. Thickness of weh, in inches. Weight per rard, in lbs. 9 2^ 37.00 9 2K TB 42.75 9 2* % 48.50 9 2% ■fe 54.25 No. 39 Depth of channel. Width of flange. Thickness of web. Weight per yard. 8 2t"b 40 8 2% % 45 8 2A 50 8 55 8 2A A 60 8 2% % 65 8 m H 70 ■N32^ No. 40 Depth Width Thickness Weight of of of per channel. flange. web. yard. 8 2A 30 8 2>^ A 35 24 POTTSVILLE, PENNA., U. S. A. No. 41 Depth of channel. Width of flange. Thickness of ■web. Weight per yard. 1 7 2^4 A 35.0 7 Sx-V 4 39.5 7 24 A 44.0 7 2^ 4 48.5 7 24 53.0 7 2^s 4 57.5 No. 42 Depth of channel. Width of flange. Thickness of web. Weight per yard. 7 2 * 25.0 7 2^ 29.5 7 24 34.0 6 " No. 43 Depth of channel Width of flange. Th’k’ss of web. Weight per yard. 6 2 4 30.00 6 2^ TS 33.75 6 24 4 37.50 6 2^ A 41.25 6 24 4 45.00 6 2A A 48.75 6 24 4 52.50 y POTTSVILLE IRON AND STEEL CO., 6 " No. 44 Depth of channel Width of flange. Th’k’ss of web. Weight per yard. 6 A 22.50 6 m H 26.25 6 m ipB 30.00 l ' 4 ' 5 " No. 46 Width of flange. Th’k’ss of web. Weight per yard. m TB 17.00 IH 20.25 m TB 23.50 % 26.75 I y a' No. 48 Width of flange. Th’k’ss of web. Weight per yard. m A 15.0 m 17.5 m A 20.0 IB % 22.5 26 POTTSVILLE, PENNA., U.S. A. ANGLES WITH EQUAL LEGS. In ordering give either -weight or thickness, never both. Length of leg inoreases with the weight. 27 1 POTTSVILLE IRON AND STEEL CO., ANGLES WITH UNEQUAL LEGS. In ordering give either weight or thickness, never both. Length of leg increases with the weight. 28 1 POTTSVILLE, PENNA., U. S. A. T IRON. 29 30 POTTSVILLE, PENNA., U. S. A. POTTSVILLE IRON AND STEEL CO.’S Standard Brackets. For fastening Beams to headers. 1 4;^-^ FOR 15" BEAMS if. — 4 ^: — •>) FOR 12 " AND lOM" BEAMS — ulf-l / ic- .r- POR 9" AND 8 " BEAMS 1 1 i: 1 I 1; ' III. • ' 1 U- 3 ”-^ FOR 7" AND e" BEAMS ALL HOLES ARE {%" DIAMETER FOR %" BOLTS. ALL BRACKETS ARE CUT PROM STANDARD ANGLE IRON, EXCEPT WHEN OTHERWISE ORDERED. 31 POTTSVILLE IRON AND STEEL CO., GIRDERS. 32 POTTSVILLE, PENNA., U.S. A. 33 POTTSVILLE IRON AND STEEL CO., 34 POTTSVILLE, PENNA., U.S.A. BUILT COLUMNS. -Ol c c ) TZ7- ) iTl 4 35 POTTSVILLE IRON AND STEEL CO., 36 ROOFS FOR POTTSVILLE IRON AND STEEL OO.’S ROLLING MILL, POTTSVILLE ROOFS FOE POTTSVILLE IRON AND STEEL OO.'S ROLLING MILL, P< POTTSVILLE IRON AND STEEL CO., 38 50 ft.- POTTSVILLE, PENNA., U. S. A. V J PRICE CURRENT. SUBJECT TO CHANGES OF MARKET WITHOUT NOTICE. 39 5 POTTSVILLE IRON AND STEEL CO., LIST OF REFINED BAR IRON MADE BY POTTSVILLE IRON AND STEEL CO. ORDINARY SIZES. No Extra. Round and Square Flat Iron Flat Iron £ to 2 in. I to 4 in. X i to in. 4 | to 6 in. X i to I in. EXTRA SIZES. Round and Square. I and in ^ and j 3 g in Ts in f in 2 ^ to 2 | in 3 to 3 ^ in 3 |t 0 4 in 4 s to 4 J in 4 s to 5 in 5s to in 5 | to 6 in EXTRA SIZES. Flats. I to 6 in. X i and in I X Ts in 4 to 6 in. X Is to 2 in 4 to 6 in. X 2^ to 3 in 7 X I to I in 7 X Is to 2 in 7 X 2| to 3 in 8 X s to I in 8 X Is to 2£ in 9 X I to I in 9 X Is to 2 in lo X I to I in 10 X Is to 2i in 11 X s i^o 1 in 11 X Is to in 12 X i to I in .' 12 X Is to 2| in PER LB. PER TON. i&o. $2 24 ^oC- 4 48 tIjC. 8 96 TffC. II 20 TSO. 2 24 6 72 5 r T(J^* II 20 _6_p 10^* 13 44 iIjC* 17 92 I c. 22 40 ItoC. 33 60 PER LB. PER TON. ^4 48 tV- 8 96 TqO. 4 48 tV- 8 96 tV- 6 72 T%C. 8 96 TqC- 13 44 -10^- 8 96 tV- 13 44 T%C. 13 44 foC- 17 92 ToC. 17 92 I c. 22 40 TSO. 20 16 lylgC. 24 64 T®oO. 20 16 ItsC. 24 64 6 to 12 in. wide, £ and xs in- thick = extra. For cutting to specified lengths, from to ^^c. per lb. 40 POTTSVILLE, PENNA., U. S. A. REMARKS ON THE TABLES OF CAPACITY OF POTTSVILLE ROLLING MILLS’ SHAPES OF IRON AND STEEL. TABLES OF BEAMS AND CHANNELS, Showing the safe load for varying spans, deflexions under the safe load, and proper spacing of shapes for loads varying from loo to 200 lbs. per square foot. The first column gives the span in feet. The second column gives the safe load in nett tons (2000 pounds), uniformly distributed, which the shape will carry for the spans given in the first column, the extreme fibre stress being 6.0 tons per square inch for iron shapes, and 7.8 tons per square inch for steel shaj'ies. The third column gives the deflexion at centre of span for the safe loads given in second column. The fourth column gives the weight of the shape for a length equal to the span given in the first column. The fifth to tenth columns give the maximum distance apart that the shapes can be placed to safely carry loads of 41 POTTSVILLE IRON AND STEEL CO., lOO to 250 pounds per square foot, the spans being as in the first column. At the head of each page of the Tables of Capacity are given : 1. The material of which the shape is made. 2. The kind of shape, number, and weight per yard. 3. The depth of shape, width of flange, and thickness of web. 4. The expression for the safe load in nett tons. 5. The maximum shear which the shape can bear without crippling of the web. 6. The span limit, — i.e., the span corresponding to the above maximum shear. EXTREME FIBRE STRESSES And reduction of safe loads due to lateral deflexion. The safe loads given in the following series of tables include the weight of the shapes themselves, and assume that lateral dejlexion does not occur. Should the length of span exceed almut thhdy times the width of flange, the extreme fibre stress should be reduced, or else the shapes should be stayed together. A table is given on page 43, which shows the reduction of fibre stresses in shapes of iron and steel, and likewise gives the proportion of the tabular loads which the shapes will stand, corresponding to the reduced unit stress. 42 POTTSVILLE, PENNA., U. S. A. REDUCTION OF THE EXTREME FIBRE STRESSES And proportion of the tabular safe loads which must be used when the ratio of span to the flange width of shape exceeds 30. Ratio of spaa to flange width of shape. Corresponding extreme flbre stress for iron shapes. Corresponding extreme fibre stress for steel shapes. Proportion of the tabular safe loads which must be used. 30 5-93 771 0.99 35 5-71 7-43 0-95 40 5-31 6.90 0.88 45 4.98 6.48 0.83 50 4.67 6.07 0.78 55 4-36 5-67 073 60 4.07 5-29 0.68 65 3-79 ! 4-93 0.63 70 j ’54 i 4.60 0-59 75 3-29 1 4.28 0-55 80 3-07 i 3-99 0.51 85 2.86 372 0.48 90 2.67 348 045 95 2.50 i 3-25 0.42 100 2-33 3-03 0-39 The above table is computed from the expression f Pc where ' 5000 \w/ p^, = reduced fibre stress. fj, = one-third the modulus of rupture. 1 = length of span I . . n • 1*-!, r Both in same units of dimension, w = flange width j Note. — T he exact ratio of span to flange width, for which the fibre stress is that used in the tables, is 28.86. 43 POTTSVILLE IRON AND STEEL CO., MAXIMUM SHEAR AND CORRESPONDING SPAN LIMIT. Besides the capacity of the beam to resist transverse load- ing, there is also a limit to the load which may be put on a beam, as regards its web resistance. A beam may be amply strong, as concerns its flange area, and yet unable to sustain the load, due to a very thin web. Ihe maximum shear which a beam can safely bear is determined by the following expressions : For iron shapes. 3.0 tons For steel shapes, „ 4.0 tons 1 + rh/2-|= ^ 0 L t J ^L"-J 3000 3000 where h denotes the height of shape in inches, and t denotes the thickness of web in inches. As for beams under uniformly distributed loads, the end shear F^ is one-half the total load on the beam, we see that we can load no beam greater than this amount without ex- ceeding the safe shearing stress. By dividing the coefficient for one foot span by this maxi- mum load, we get the “ span limit,” and for less spans we cannot use the tabular loads, since they are greater than twice the maximum shear. The maximum shear and the span limit are given at the head of each Table of Capacity of shapes, and we can see, by inspection of column two in these tables, whether in any case the safe load there given is greater than twice the maximum allowable shear. If so, the safe load will be determined by twice the shear value. If the deflexion of the shape exceeds one-thirtieth (-J^) of an inch per foot of span, there is danger of the plaster of the ceiling cracking. This limit has been indicated in the tables by a heavy black line. For spans below this line, shapes should not be used where there is a plaster ceiling, or, if used, the load should be decreased until the corre- sponding deflexion is less than one-thirtieth (-J^) of an inch per foot. 44 POTTSVILLE, PENNA., U. S. A. TABLES OF THE CAPACITY OF WROUGHT-IRON X BEAMS THE EXTREME FIBRE STRESS BEING 6.0 TONS PER SQUARE INCH, WHICH IS TWO-SEVENTHS OF AND THE UNSTAYED LENGTH OF FLANGE NOT EXCEEDING THIRTY TIMES ITS WIDTH. The span, which is thirty times the flange width, is denoted by a dotted line on the tables, and for lengths greater than this, the tabular safe load must be reduced by multiplying it by the factors given in table on page 43, or else some method of staying the flanges be employed. UNDER UNIFORMLY DISTRIBUTED TRANSVERSE LOADS, THE MODULUS OF RUPTURE; X A 45 POTTSVILLE IRON AND STEEL CO., IRON I BEAMS. 15" X BEAM. SHAPE No. 1. 250 LBS. PER YARD. Depth, 15". Width of flange, 5%". Thickness of web, bale load in nett tons — ^ — . Span m feet Maximum shear = 33.06 tons. Span limit for uniformly distributed load of twice the maximum shear = 6.53'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. § g 1 GO Deflexion, in incbe Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. 1 per square foot. 10 43.20 0.09 833 34-55 II 39-27 O.II 917 28.56 12 36.00 0.14 1000 34-28 30.00 24.00 13 33-23 0.16 1083 34-08 29.21 25-56 20.44 14 30-85 0.19 1167 35-25 29.38 25.18 22.03 17.62 15 28.80 0.21 1250 38.40 30.72 25.60 21.94 19.20 15-36 16 27.00 0.24 1333 33-75 27.00 22.50 19.28 16.87 13-50 17 25.41 0.27 1416 29.89 23.91 19.92 17.08 14.94 11-95 18 24.00 0.30 1500 26.66 21-33 17.77 15-23 13-33 10.66 19 22.73 0-33 1583 23-92 19.14 15-95 13.67 11.96 9-57 20 21.60 0-37 1667 21.60 17.28 14.40 12.34 10.75 8.64 21 20.57 0.41 1750 19-59 15-67 13,06 II. 19 9-79 7-83 22 19.63 0.45 1833 17.84 14.27 11.89 10.19 8.94 7-13 23 18.78 0.49 1917 16.33 13.06 10.88 9-33 8.16 6.53 24 18.00 0.53 2000 15.00 12.00 10.00 8.57 7-50 6.00 25 17.28 0.58 2083 13.82 11.09 9.21 7-89 6.91 5-54 26 16.61 0.63 2167 12.77 10.23 8.51 7-30 6.38 5-11 27 16.00 0.68 2250 11.85 9-48 7-90 6.77 5-92 4-74 28 15.42 0.73 2333 II.OI 8.81 7-34 6.29 5-50 4-40 29 14.89 0.78 2417 10.27 8.21 6.84 5-87 5-13 4.10 30 14.40 0.84 2500 9.60 7-67 6.40 5-48 4.80 3-83 31 13-93 0.90 2583 8.98 7.19 5-98 5-13 4-49 3-59 32 13-50 0.96 2667 8.43 6.75 5.62 4.82 4.21 3-37 33 13.09 1.02 2750 7-93 6.34 5.28 4-53 3-96 317 46 POTTSVILLE, PENNA., U. S. A. IRON I BEAMS. 15" I BEAM. SHAPE No. 2. 200 LBS. PER YARD. Depth, 15". Width of flange, SyV'- Thickness of web, Safe load in nett tons = -7; r^-7 — Span in leet Maximum shear = 20.35 tons. Span limit for uniformly distributed load of twice the maximum shear = 9.09'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. § .s 0 Deflexion, in inches 1 Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 11 12 13 14 37-00 33-64 30.83 28.46 26.43 00000 M M W M b 667 733 800 867 934 30.21 a^ t'- C^ ro 29.36 25.02 21.58 30-58 25.69 21.89 18.88 29.60 24.46 20.55 17-51 15.10 15 : 24.67 0.21 1001 32.8926.31 21.93 18.79 16.44 13.16 16 : 23.13 0.24 1067128.91 23.13 19.27 16.52 14-45 11.56 17 : 21.76 0.27 ii34!25-6o i20.481i7.07 14.63 12.80 10.24 18 1 20.56 0.30 1201 22.84 18.27 15-23 13-05 11.42 9.14 19 i 19-47 0.33 1267 20.49 16.3913.66 II. 71 10.24 8.20 20 18.50 0.37 i334|I8.5o 14.80 !i2.33 10.57 9-25 7-40 21 17.62 0.41 1401 16.78 13-42 II. 19 I 9-59 8-39 6.71 22 16.82 0.45 1467 15-29 12.23 10.19 8.74 7.64 6.12 23 16.09 0.49 1534 13-99 II. 19 9-33 7-99 6-99 5.60 24 15.42 0-53 1601 12.85 10.28 8-57 7.89 7-34 6.42 5-14 25 14.80 0.58 1668 11.84 9-47 6.77 5-92 4-74 26 14.23 0.63 1734 10.95 8.76 7-30 6.26 •5-47 4-38 27 13.70 0.68 1801 10.15 8.12 6.77 5-80 5-07 4.06 28 13.21 0.73 1868 9-44 7-55 6.29 5-39 4-72 3-78 29 12.76 0.78 1934 8.80 7-04 5-87 5-03 4-40 3-52 30 12.33 0.84 2001 8.22 6.58 5-48 4-70 4.11 3-29 31 11.94 0.90 2068 7-70 6.16 5-^3 4-40 3-85 3-08 32 11.56 0.96 2134 7-23 5.78 4.82 4-13 3.61 2.89 33 II. 21 1.02 2201 6.79 5-43 4-53 3-88 3-39 2.72 47 POTTSVILLE IRON AND STEEL CO., IRON I BEAMS. 15" I BEAM. SHAPE No. 3. 150 LBS. PER YARD. Depth, 15". Width of flange, 5". Thickness of web, §|". Safe load in nett tons — -7; . Span m leet Maximum shear = 12.60 tons. Span limit for uniformly distributed load of twice the maximum shear = 11.19'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. 1 0 CO Deflexion, in inchei Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 11 12 13 28.20 25.64 23-50 21.69 p p p p M M W 0 hh mD 500 550 600 650 26.70 26.11 22.25 26.64 22.38 19.07 28.20 23-31 19.58 16.68 2^.56 18.65 15-67 13-35 14 20.14 0.19 700 28.77 23.02 19.18 16.44 14.38 II.51 15 18.80 0.21 750 25.07 20.06 16.71 14-33 12.53 10.03 16 17.63 0.24 800 22.04 17-63 14.69 12.59 11.02 8.82 17 16.59 0.27 850 19.52 15.62 13.01 II. 15 9.76 7.81 18 15-67 0.30 900 17.41 13-93 II. 61 9-95 8.71 6.96 19 14.84 0.33 950 15.62 12.50 10.41 8.92 7.81 6.25 20 14.10 0-37 1000 14.10 11.28 9.40 8.06 7-05 5-64 21 13-43 0.41 1050 12.79 10.23 8.53 7-31 6.39 5-12 22 12.82 0.45 1 100 11.65 9-32 7-77 6.66 5-82 4.66 23 12.26 0.49 1150 10.66 8.53 7.11 6.09 5-33 4.26 24 11-75 0-53 1200 9-79 7-83 6.53 5-59 4-89 3-92 25 11.28 0.58 1250 9.02 7.22 6.01 5-15 4-51 3.61 26 10.85 0.63 1300 8.35 6.68 5-57 4-77 4.18 3-34 27 10.44 0.68 1350 7-73 6.18 5-15 4.42 3-86 3-09 28 10.07 0.73 1400 7.19 5-75 4-79 4.11 3-59 2.88 29 9-72 0.78 1450 6.70 5-36 4-47 3-83 3-35 2.68 30 9.40 0.84 1500 6.27 5.02 4.18 3-58 3-13 2.51 31 9.10 0.90 1550 5-87 4.70 3-91 3-35 2-93 2.35 32 8.81 0.96 1600 5-51 4.41 3-67 3-15 2.75 2.20 33 8.55 1.02 1650 5.18 4.14 i 3-45 2.96 2.59 2.07 48 POTTSVILLE, PENNA., U. S. A. IRON I BEAMS. 15" I BEAM. SHAPE No. 4. 125 LBS. PER YARD. Depth, 15". Width of flange, 4%". Thickness of web, tV'. c r , J • 228.0 Safe load in nett tons = . Span m leet Maximum shear = 10.73 tons. Span limit for uniformly distributed load of twice the maximum shear = 10.62'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. "o a CO Deflexion, in inchei Weight of beam. 100 lbs._ per si^uare foot. 125 lbs. per square foot. 150 lbs. per square fcot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 11 , 12 ' 22.80 20.73 19.00 0.09 O.II 0.14 417 458 500 25-36I 25-13 21 . II 26.06 21.54 18.10 22.80 18.24 18.84 15.08 15.83 12.67 13 17-54 0.16 542 26.981 21.58 17.99 15.42 13-49 10.79 14 16.29 0.19 583 23.27 18.62 15.51 13.30 11.63 9-31 15 15.20 , 0.21 625 20.27,16.22 13-51 11.58 10.13 8.II 16 14.25 0.24 667 17.81 14.25 11.87 10.18 8.91 7.12 17 13-41 0.27 709 1578 12.62 10.52 9.02 7-89 6.31 18 12.67 0.30 750 14.08 11.26 9-39 8.05 7-04 5-63 19 12.00 0-33 792 12.63 lO.IO 8.42 7.22 6.31 5-05 20 11.40 0.37 834 11.40 9.12 7.60 6.51 5-70 4-56 21 10.86 0.41 87510.34 8.27 6.89 5-91 5-17 4.14 22 10.36 0.45 917 9-42 7-54 6.28 5-38 4.71 3-77 23 9.91 0.49 959 8.62 6.90 5-75 4-93 4-31 3-45 24 9-50 0-53 1000 7-92 6.34 5.28 4-53 3-96 3-17 25 9.12 0.58 1043 7-30 5-84 4.87 4.17 3-65 2.92 26 : 8.77 0.63 1084 6.75 5-40 4-50 3-86 3-38 2.70 27 8.44 0.68 1125 6.25 5-00 4.17 3-57 3-13 2.50 28 8.14 0-73 1168 5.81 4-65 3-87 3-32 2.91 2.32 29 7-86 0.78 1 1209 5-42 4-34 3.61 3.10 2.71 2.17 30 7.60 0.84 1250 1 5-07 4.06 3-38 2.90 2-53 2.03 31 7-35 0.90 j 1292 , 4-74 3-79 3.16 2.71 2.37 1 1-90 32 7-13 0.96 1 1334 4.46 3-57 2-97 2-55 2.23 1 1.78 33 6.91 1.02 1375 4.19 3-35 2-79 2-39 j 2.09 i 1.68 1 49 POTTSVILLE IRON AND STEEL CO., IRON I BEAMS. 12" X BEAM. SHAPE No. 5. 170 LBS. PER YARD. Depth, 12". Width of flange, 5 %". Thickness of web, Safe load in nett tons = -7:; . Span in feet Maximum shear = 20.80 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.86'. Distance apart, in feet, centre to centre of I beams, for safe loads of Span, in feet. § 1 C/D Deflexion, in inclie Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 11 12 13 14 24.40 22.18 20.33 i8-77 1743 0.12 0.14 0.16 0.20 0.23 567 624 680 737 794 19.92 19.25 16.60 19.36 16.50 14-23 20.16 16.94 14-43 12.45 19.52 16.13 13-55 11-55 9.96 15 16.27 0.26 850 17-35 14.46 12.39 10.84 8.68 16 15-25 0.30 907 19.06 15-25 12.71 10.89 9-53 7.62 17 H -35 0.34 964 16.88 13-50 11.25 9-65 8.44 6.75 18 13-56 0.38 1021 15-07 12.06 10.05 8.61 7-53 6.03 19 12.84 0.42 1077 13-51 10.81 9.01 7.72 6.75 5-40 20 12.20 0.46 1134 12.20 9.76 8.13 6.97 6.10 4.88 21 11.62 0.51 1190 11.07 8.86 7-38 6.33 5-53 4-43 22 11.09 0.56 1247 10.08 8.06 6.72 5-76 5-04 4-03 23 10.61 0.62 1304 9-23 7-38 6.15 5-27 4.61 3-69 24 10.17 0.67 1361 8.48 6.78 5-65 4.84 4-24 3-39 25 9.76 0-73 1418 7.81 6.25 5-21 4.46 3-91 3.12 26 9-38 0-79 1474 7.22 5-78 4.81 4-13 3.61 2.89 27 9.04 0.84 1530 6.70 5-36 4-47 3-83 3-35 2.68 28 8.71 0.91 1588 6.22 4-98 4.15 3-55 3-11 2.49 29 8.41 0.98 1644 5-80 4.64 3-87 3-31 2.90 2.32 30 8.13 1.05 1700 5-42 4-34 3.61 3.10 2.71 2.17 31 7.87 1. 12 1758 5.08 4.06 3-39 2.90 2.54 2.03 32 7-63 1.20 1814 4-77 3.82 3.18 2.73 2.38 1.91 33 7-39 1.27 1871 4-48 3-58 2-99 2.56 2.24 1-79 50 POTTSVILLE, PENNA., U. S. A, IRON I BEAMS. 12" I BEAM. SHAPE No. 6. 125 LBS. PER YARD. Depth, 12". Width of flange, 4^^". Thickness of web, r , ^ ■ 185.00 Safe load m nett tons = -7;; . — . — span in feet Maximum shear = 13.02 tons. Span limit for uniformly distributed load of twice the maximum shear = 7.10'. • Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. <0 a 'TS i CO Deflexion, in inche! Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 18.50 0.12 416 14.40 II 16.82 0.14 458 15-35 12.25 12 15.42 0.17 500 17-13 14.69 12.90 10.32 13 14.23 0.20 542 14.65 12.55 10.96 8.77 14 13.21 0.23 583 15.09 12.59 10.79 9.46 7-54 15 12.33 0.26 625 1315 10.96 9.40 8.25 6-57 16 11.56 0.30 667 1445 II. 61 9-65 8.25 7.22 5.80 17 10.88 0.34 708 12.81 10.27 8.55 7-31 6.40 5-13 18 10.28 0.38 750 1143 9-15 7.61 6.53 5-71 4-57 19 9-74 0.42 792 10.25 8.21 6.83 5.84 5.12 4.10 20 9-25 0.46 833 9.28 7.40 6.19 5.28 4.64 3-70 21 8.81 0.51 875 8.39 6.70 5-59 4.81 4.19 3-35 22 8.41 0.56 915 7-65 6.10 5-07 4.68 3.82 3-05 23 8.04 0.61 956 7.01 5-59 4.64 3-99 3-50 2-79 24 7.71 0.66 1000 6.45 5.16 4-30 3-67 3.22 2.58 25 7.40 0.72 1042 5-95 4.76 3-95 3-35 2-97 2.38 26 7.12 0.78 1083 548 4-38 3.66 3-15 2-74 2.19 27 6.85 1 0.84 1125 5-07 4.04 3-38 2.88 2.58 2.02 28 6.61 0.91 1167 4-73 3-77 3-14 2.69 2.36 29 6.38 0.98 1208 4.40 3-52 2.92 2.66 2.20 30 6.17 1.05 1250 4.12 3.28 2.74 2-35 2.06 31 5-97 1. 12 1292 3-85 3.08 2-53 2.19 32 5.78 1. 19 1333 3.61 2.90 2.41 33 5.61 1.26 1375 2.69 2.70 51 POTTSVILLE IRON AND STEEL CO., IRON I BEAMS. 12" I BEAM. SHAPE No. 7. 100 LBS. PER YARD. Depth, 12". Width of flange, 4 jV'- Thickness of web, /g". 1 1 • J.44.UU bate load in nett tons = -7^ ^ ^ — . bpan in leet Maximum shear = 10.63 tons. Span limit for uniformly distributed load of twice the maximum shear = 6.77'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per spare foot. 125 lbs. per spare foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 14.40 0.12 333 14.40 11.52 II 13.09 0.14 367 13.60 11.90 9-52 12 12.00 0.17 400 13-33 11.43 10.00 8.00 13 11.08 0.20 433 13-63 11.36 9-74 8.52 6.81 14 10.28 0.23 467 14.68 11.74 9-79 8.39 7.34 5.87 15 9.60 0.26 500 12.80 10.24 8-53 7-31 6.40 5-12 16 9.00 0.30 533 11.25 9.00 7-50 6.43 5.62 4-50 17 8.47 0-34 567 9.96 7-97 6.64 5-55 4-98 3-98 18 8.00 0.38 600 8.89 7. II 5-93 5.08 4-45 3-55 19 7.58 0.42 633 7.98 6.38 5-32 4-56 3-99 3-19 20 7.20 0.46 667 7.20 5-76 4.80 4.11 3.60 2.88 21 6.86 0.51 700 6-53 5.22 4-35 3-73 3-27 2.61 22 6.55 0.56 733 5-95 4.76 3-97 3-40 2.97 2.38 23 6.26 0.61 767 5-44 4-35 3-63 3 -II 2.72 2.17 24 6.00 0.66 800 5.00 4.00 3-33 2.86 2.50 25 576 0.72 833 4.61 3-69 3-07 2.63 26 5-54 0.78 867 4.26 3-41 2.84 27 5-33 0.84 900 3-95 3.16 2.63 28 5-14 0.91 933 3-67 2.94 29 4.96 0.98 967 3-42 2.74 30 4.80 1.05 1000 3.20 2.56 31 4.64 1. 12 1033 2.99 32 4.50 1. 19 1067 2.81 33 4-36 1.26 1100 2.64 1 52 POTTSVILLE, PENNA., U. S. A. IRON I BEAMS. 10W' I BEAM. SHAPE No. 8. 135 LBS. PER YARD. Depth, Width of flange, 5". Thickness of web, Safe load in nett tons = -7; . Span in leet Maximum shear = 13.27 tons. Span limit for uniformly distributed load of twice the maximum shear = 6.86'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. j 1 ,

9-25 0.21 360 12. 33 10.28 8.81 7.71 6.16 13 8.54 0.24 390 1314 10.51 1 8.76 7-51 6.57 5.26 14 7.93 0.28 420 11-33 9.06 7-55 6.47 5-67 4-53 15 : 7.40 i 0-33 450 9.87 7.89 6.58 5-64 4-93 3-95 16 ! 6.94 0.37 480 8.68 6.94 5-79 4.96 4-34 3-47 17 6.53 0.41 510 ; 7.68 6.14 5.12 4-39 3-84 3-07 18 6.17 0.46 540 6.86 5-48 4-57 3-92 3-43 2.74 19 5-84 0.52 570 : 6.15 4.92 4.10 3-51 3.08 2.46 20 5-55 0.58 ' 600 i 5-55 4.44 3-70 3-17 2.78 2.22 21 5-29 0.64 j 630 5.04 4.03 3-36 2.88 2.52 2.02 22 1 5-05 0.70 660 4-59 3-67 3.06 2.62 2.29 23 1 4-83 0.76 690 4.20 3-36 2.80 2.40 2.10 24 4.63 0.83 720 3-83 3.06 2-55 2.19 25 4.44 0.91 750 3-55 2.84 2.37 2.03 26 4.27 0.98 780 3-28 2.62 2.19 27 4.11 1.05 810 3-04 2.43 2.03 28 3-96 i-i 3 840 2.83 2.26 29 3-83 1. 21 870 2.64 2 . II 30 370 1.29 900 2.471 31 3-58 1.38 930 2.311 32 3-47 1.48 960 2.17 33 3-36 X.58 990 2.04 57 POTTSVILLE IRON AND STEEL CO. IRON I BEAMS. 9" I BEAM. SHAPE No. 13. 90 LBS. PER YARD. Depth, 9". Width of flange, 4%". Thickness of web, 3 ^". r- 1 • q8.oo baie load in nett tons = -j:; — ^ — ; — r . span in teet Maximum shear = 11.18 tons. Span limit for uniformly distributed load of twice the maximum shear — 4.39'. 58 POTTSVILLE, PENNA., U. S. A. IRON I BEAMS. 9" I BEAM. SHAPE No. 14. 85 LBS. PER YARD. Depth, 9". Width of flange, 4^". Thickness of web, xV'- Safe load in nett tons = -7=: — . Span m leet IMaximum shear = 9.22 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.20^ Span, in feet. 1 Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of § 0 s2 CO , Deflexion, in inchei 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 9.60 0.16 283 19.20 15-36 12.80 10.97 9.60 7.68 II 8.73 0.19 312 15.87 12.70 10.58 1 9.07 7-93 6-35 12 8.00 0.23 340 13-33 10.66 8.89 7.62 6.66 5-33 13 7-38 0.27 368 12.12 9.70 8.08 6.93 6.06 4-85 14 6.86 0.31 397 9.80 7-84 6.53 5.60 4.90 3-92 15 6.40 0-35 425 8.53 6.82 5.68 4-87 4.26 3-41 16 6.00 0.40 453 7-50 6.00 5.00 4.28 3-75 3.00 17 5.65 0.46 482 6.65 5-32 4-43 3-80 3-32 2.66 18 5-33 0.51 510 5-92 4-73 3-94 3-38 2.96 2.36 19 5-05 0-57 538 5-32 4-25 3-55 3-04 2.66 2.13 20 4.80 0.63 567 4.80 3-84 3.20 2.74 2.40 i 21 4-57 0.70 595 4-35 3-48 2.90 2.49 2.17 1 i 22 4-36 0.77 623 3-96 3-17 2.64 2.26 23 4.17 0.84 652 3-63 2.90 2.42 2.07 24 4.00 0.91 680 3-33 2.66 2.22 25 3-84 0.99 708 3-07 2.42 26 3-69 1.07 737 2.84 2.27 27 3-56 1. 16 765 2.64 2. II 28 343 1.24 793 245 29 3-31 1-33 822 2.28 30 3.20 143 850 2.13 31 3.10 1-53 878 2.00 32 3.00 1.63 907 33 2.91 i- 74 j 935 , 59 POTTSVILLE IRON AND STEEL CO., IRON I BEAMS. 9" I BEAM. SHAPE No. 15. 70 LBS. PER YARD. Depth, g". Width of flange, 4". Thickness of web, Safe load in nett tons = -7^ — . Span in feet Maximum shear = 7.33 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.05'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 7.40 0.16 233 14.80 11.84 9.87 8.46 7.40 5-92 II 6.73 0.19 256 12.24 979 8.16 6.99 6.12 4.90 12 6.17 0.23 280 10,28 8.22 6.85 5.87 5-14 4.II 13 5-69 0.27 303 8.75 7.00 5-83 5.00 4.37 3*50 14 5-29 0.31 326 7-56 6.05 5-04 4-32 378 3.02 15 4-93 0-35 350 6.57 5.26 4-38 375 3.28 2.63 16 4-63 0.40 373 579 4-63 3.86 3-31 2,89 2.32 17 4-35 0.46 396 5.12 4.10 341 2.93 2.56 2.05 18 4.11 0.51 419 4-57 3.66 3-05 2.61 2.28 19 3-89 0.57 443 4.09 3-27 2.73 2.34 2.04 20 370 0.63 466 370 2.96 2.47 2. 1 1 21 3-52 0.70 489 3-35 2.68 2.23 22 3-36 0.77 513 3-05 2.44 2.03 23 3.22 0.84 536 2.80 2.24 24 3.08 0.91 559 2.57 2.06 25 2.96 0.99 583 2-37 i 26 2.85 1.07 606 2.19 27 2.74 1. 16 629 2.03 28 2.64 1.24 652 29 2.55 1-33 676 30 2.47 1-43 699 31 2.39 1-53 722 32 2.31 1.63 746 33 2.24 1.74 769 60 POTTSVILLE, PENNA., U. S. A IRON I BEAMS. 8" Z BEAM. SHAPE No. 16. 80 LBS. PER YARD. Depth, 8". Width of flange, 45V'. Thickness of web, Safe load in nett tons = -r:; ^ — - — . Span in leet I ^Maximum shear = 10.20 tons. Span limit for uniformly distributed load of tsvice the maximum shear = 3.77'. Span, in foot. Safo load, in notl tons. Defloxion, in inchos. Woight of boam. ' Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 7.70 0.18 266 15.40 12.32 10.26 00 bo 0 7.70 6.16 II 7.00 0.22 293 12.73 10.18 8.48 7.28 6.36 5-09 12 6.42 0.26 320 10.70 ' 8.56 7-13 6 . II 5-35 4.28 13 5-92 0.30 346 9.II 7.29 6.07 5.20 4-55 3-64 14 550 0-35 373 ' 7-85 6.28 5-23 ' 449 3-92 3-14 15 5-13 0.40 400 6.84 5-47 4-56 ' 3-91 342 2.73 16 4.81 0.46 426 6.01 4.80 4.01 343 3.00 2.40 17 4-53 0.52 453 5-66 4-53 3-77 3-23 2.83 18 4.28 0.58 480 4-75 3.80 3.16 2.71 2.37 j 19 4-05 0.64 506 4-25 340 2.83 2.43 20 3-85 0.71 532 3-85 3.10 2.56 21 3-67 0.79 560 3-50 2.80 22 3-50 0.86 586 3.18 2.54 23 3-35 0.94 613 2.91 24 3.21 1.03 640 2.67 25 3.08 1. 12 666 2.46 26 2.96 1.20 692 27 2.85 1-30, 720 28 2-75 1.40 746 29 2.66 1.50 773 30 2.57 1.60 800 31 2.48 1.71 826 32 2.41 1.82 853 1 33 1 2-33 1-93 880 1 . 1 61 POTTSVILLE IRON AND STEEL CO. IRON I BEAMS. 8" I BEAM. SHAPE No. 17. 65 LBS. PER YARD. Depth, 8". Width of flange, 4". Thickness of web, o r 1 1 • UO.UU bale load in nett tons = -7^ ^ — - — . bpan in feet Maximum shear = 5.23 tons. Span limit for uniformly distributed load of twice the maximum shear = 6.50'. Span, in feet. Safe load, in nett tons. ! Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 6.80 0.18 216 13.60 10.88 9.06 7-77 6^8o 544 II 6.18 0.22 238 11.23 8.98 7.48 6.41 5.62 449 12 5-67 0.26 260 945 7-56 6.30 540 4.72 378 13 5-23 0.30 282 8.04 6.43 5-36 4-59 4.02 3.21 14 4.86 0-35 304 6.94 5-55 4.62 3-96 347 2.77 15 4-53 0.40 325 6.04 4-83 4-03 345 3.02 2.41 16 4-25 0.46 347 5-31 4-25 3-54 3-03 2.66 2.12 17 4.00 0.52 369 4.70 3-76 3-13 2.68 2-35 18 3-78 0.58 390 4.20 3-36 2.80 2.40 19 3-58 0.64 412 3-76 3.00 2-51 20 340 0.71 432 340 2.72 21 3-24 0.79 454 3.08 2.46 22 3-09 0.86 476 2.81 23 2.96 0.94 498 2.57 i 24 2.83 1.03 520 25 2.72 1. 12 542 26 2.62 1.20 564 27 2.52 1.30 586 28 243 1.40 608 29 2.34 1.50 629 30 2.21 1.60 648 31 2.19 1.71 672 32 2.12 1.82 694 33 2.06 1-93 714 62 POTTSVILLE, PENNA., U.S. A. IRON I BEAMS. 7 " Z BEAM. SHAPE No. 18. 65 LBS. PER YARD. Depth, 7". Width of flange, 3 jV'- Thickness of web, §|". ■ 55-00 Safe load in nett tons = ; — = — . Span in feet Maximum shear — 8.18 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.36'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs, per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 5-50 0.20 217 1 1. 00 8.80 7-33 6.29 5-50 4.40 II 5.00 0.25 239 9.09 7.27 6.06 5-19 4-54 3-64 12 4-58 0.29 260 7-63 6.10 5-09 4-36 3.81 3-05 13 4-23 0-35 282 6.51 5.21 4-34 372 3-25 2.60 14 3-93 0.40 304 5.61 449 3-74 3.21 2.81 2.24 15 3-67 0.46 326 4.89 3-91 3.26 2.79 2.44 16 3-44 0.52 347 4-30 344 2.87 2.46 2-15 17 3-24 0.59 369 3.81 3-05 2.54 2.18 18 3.06 . ; 0.66 390 340 2.72 2.27 19 2.89 0.74 412 3-04 2.43 2.03 20 2.75 : 0.82 434 2.75 2.20 21 2.62 0.90 456 2.50 2.00 22 2.50 0.99 477 ! 2.27 1 23 2-39 1.08 499 2.08 24 2.29 1. 17 520 25 2.20 1.27 543 26 2.12 1.38 564 j 27 2.04 1.49 586 28 1.96 1.60 608 1 1 29 1.90 1.72 629 30 1.83 1.84 650 31 1.77 1.96 673 Span limit for tabular safe 32 1.72 2.08 694 loads ^ = g.oob 33 1.67 2.20 716 POTTSVILLE IRON AND STEEL CO., IRON I BEAMS. 7" I BEAM. SHAPE No. 19. 55 LBS. PER YARD. Depth, 7". Width of flange, Thickness of web, Safe load in nett tons = Span in leet Maximum shear = 5.31 tons. Span limit for uniformly distributed load of twice the maximum shear = 4.70'. 64 POTTSVILLE, PENNA., U.S. A. IRON I BEAMS. 6" I BEAM. SHAPE No. 20. 5^0 LBS. PER YARD. Depth, 6". Width of flange, 2 ^". Thickness of web, §§". Safe load in nett tons 36.00 Span in feet ’ Maximum shear = 6.39 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.82'. 65 POTTSVILLE IRON AND STEEL CO, IRON I BEAMS. 6" I BEAM. SHAPE No. 21. 40 LBS. PER YARD. Depth, 6". Width of flange, zYs'- Thickness of web, Safe load in nett tons = 32.00 Span in feet ‘ Maximum shear = 3.30 tons. Span limit for uniformly distributed load of twice the maximum shear = 4.85'. POTTSVILLE, PENNA., U. S. A. IRON I BEAMS. 5" I BEAM. SHAPE No. 22. 40 LBS. PER YARD. Depth, 5 ". Width of flange, Thickness of web, 25.00 Safe load in nett tons = Maximum shear = Span in feet ’ 5.03 tons. Span limit for uniformlj^ distributed load of twice the maximum shear = 2.48'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. § 0 1 Deflexion, in inches Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. • per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 3 4 5 6 7 8 8.34 6.25 5.00 4.17 3-57 3.12 0.02 0.04 0.07 O.IO 0.14 0.18 40 53 67 80 93 107 55-6o 31-25 1 20.00 13-90 10.20 7.80 44.48 25.00 16.00 II . 12 8.16 6.24 1 37.06 20.83 13-33 9-27 6.80 5-20 31-77 17-83 11-43 7-94 5-83 4.46 27.80 15.62 10.00 6-95 5-10 3-90 22.24 12.50 8.00 5-56 4.08 3-12 9 10 11 12 j 2.87 2.50 2.27 1 2.08 0.23 0.28 0-34 0.41 ' 120 I 133 146 160 6.38 5-00 4-13 3-47 5-10 4.00 3-31 2.78 4-25 3-33 2.75 2.31 3-65 2.85 2.36 3-19 2.50 2.06 2-55 2.00 13 1.92 0.48 : 173 2.95 2.36 1 1 14 1.79 0.56 187 2.05 15 1.67 0.64 200 1 I j 1.56 0-73 213 17 1.47 0.82 227 18 1-39 0.92 240 19 1.32 1.03 253 20 1.25 1. 14 267 21 1. 19 1.26 280 22 1. 14 1.38 293 1 23 1.09 307 2| 1.04 1.65 320 I 25 1. 00 1.79 333 26 0.96 1-93 347 67 POTTSVILLE IRON AND STEEL CO., IRON I BEAMS. 5" I BEAM. SHAPE No. 23. 30 LBS. PER YARD. Depth, 5". Width of flange, 2^". Thickness of web, Safe load in nett tons = ^ — •. Span m feet Maximum shear = 1.90 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.05'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 3 6.40 0.02 30 42.66 34.12 28.44 24-37 21-33 17.06 4 4.80 0.04 40 24.00 19.20 16.00 13-71 12.00 9.60 5 3-84 0.07 50 15-36 12.28 10.24 8.77 7.68 6.14 6 3.20 O.IO 60 10.66 8.52 7.10 6.09 5-33 4.26 7 2.74 0.14 70 7.82 6.25 5.21 4-47 3-91 3-12 8 2.40 0.18 80 6.00 4.80 4.00 3-42 3.00 2.40 9 2.13 0.23 90 4-74 3-79 3.16 2.71 2.37 10 1.92 0.28 100 3-84 3.08 2.56 2.19 II 1-75 Q -34 no 3-19 2.55 2.12 12 1.60 0.41 120 2.66 2.12 13 1.48 0.48 130 2.27 14 1-37 0.56 140 15 1.28 0.64 150 16 1.20 0-73 160 17 1.13 0.82 170 18 1.07 0.92 180 19 1. 01 1.03 190 20 0.96 1. 14 200 21 0.91 1.26 210 22 0.87 1.38 220 23 0.83 151 230 24 0.80 1.65 240 25 0.77 1.79 250 26 0.74 1-93 260 68 POTTSVILLE, PENNA., U. S. A. IRON I BEAMS. 4" I BEAM. SHAPE No. 24. 30 LBS. PER YARD. Depth, 4". Width of flange, 2xV'. Thickness of web, §|". Safe load in nett tons = ^ ^ . Span in feet Maximum shear = 4.74 tons. Span limit for uniformly distributed load of twice the maximum shear — 1.45'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 3 4.66 0.03 30 31.16 24.92 20.77 17.80 15.58 12.46 4 3-50 0.06 40 17-50 14.00 11.66 10.00 8.75 7.00 5 2.80 0.09 50 11.20 8.96 7.46 6.40 5.60 4.48 6 2-33 0.13 60 7-77 6.22 5.18 4.44 3.88 3-II 7 2.00 0.17 70 5-71 4-56 3.81 3.26 2.85 2.28 8 1-75 0.23 80 4-37 3-49 2.91 2.49 2.18 9 1.55 0.29 90 3.22 2-57 2.14 10 1.40 0.36 100 2.80 2.24 II 1.27 0.43 no 2.31 12 1. 17 0.51 120 13 1.08 0.60 130 14 1. 00 0.70 140 15 0-93 0.81 150 16 0.87 0.91 160 17 0.82 1.03 170 18 0.78 1. 16 180 19 0.74 1.29 190 20 0.70 1-43 200 21 0.67 1.58 210 22 0.64 1-73 220 23 0.61 1.89 230 24 0.58 2.06 240 25 0.56 2.23 250 1 26 1 0.54 2.41 260 1 j 69 POTTSVILLE IRON AND STEEL CO., IRON I BEAMS. 4" I BEAM. SHAPE No. 25. 24 LBS. PER YARD. Depth, 4". Width of flange, Thickness of web, . Safe load in nett tons = -7^ — . Span in feet Maximum shear = 3.39 tons. Span limit for uniformly distributed load of twice the maximum shear == 1.68'. 70 POTTSVILLE, PENNA., U.S. A. IRON I BEAMS. 4" I BEAM. SHAPE No. 26. 18 LBS. PER YARD. Depth, 4". Width of flange, 2%". Thickness of web, or, j • 8.8 o safe load m nett tons = -7^ ^ — 7 . bpan in leet Maximum shear = 1.73 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.54'. 71 6 POTTSVILLE IRON AND STEEL CO., POTTSVILLE, PENNA., U. S. A. TABLES OF THE CAPACITY OF Wrought -Iron Channels THE EXTREME FIBRE STRESS BEING 6.0 TONS PER SQUARE INCH, WHICH IS TWO-SEVENTHS OF AND THE UNSTAYED LENGTH OF FLANGE NOT EXCEEDING THIRTY TIMES ITS WIDTH. The span, which is thirty times the flange width, is denoted by a dotted line on the tables, and for lengths greater than this, the tabular safe load must be reduced by multiplying it by the factors given in table on page 43, or else some method of staying the flanges be employed. UNDER UNIFORMLY DISTRIBUTED TRANSVERSE LOADS, THE MODULUS OF RUPTURE; POTTSVILLE IRON AND STEEL CO., IRON CHANNELS. 15" CHANNEL. SHAPE No. 30. 225 LBS. PER YARD. Depth, 15". Width of flange, 5gV'. Thickness of web, igV'. r. . 332.00 Safe load m nett tons = -p:; ; — ^ . Span m feet Maximum shear = 42.85 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.88'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 55-33 0.03 450 8 41.50 0.07 600 10 33-20 O.II 750 37-94 33-20 26.56 12 27.67 0.15 900 36.90 30.75 26.35 23.06 18.45 14 23.71 0.21 1 1050 33-87 27.10 22.58 19-35 16.93 13-55 16 20.75 0.27 1200 25-94 20.75 17.29 14.82 12.97 10.38 18 18.44 0.34 1350 20.49 16.39 13.66 II. 71 10.24 8.20 20 16.60 0.43 1500 16.60 13.28 11.07 9-49 8.30 6.64 22 15.09 0.52 1650 13.72 10.98 9-15 7-84 6.86 5-49 24 13-83 0.62 1800 H.52 9.22 7.68 00 5-76 4.61 26 12.75 0.73 1950 9.81 00 6.54 5.61 4-90 3-92 28 11.86 0.84 2100 8.49 6.79 5.66 4-85 4-24 3-40 30 11.07 0.96 2250 7-38 5-90 4-92 4.22 3-69 2-95 32 10.37 1. 10 2400 6.48 5.18 4-32 3-70 3-24 2.59 34 9-79 1-25 2550 5-76 4.61 3-84 3-29 2.88 2.30 74 POTTSVILLE, PENNA., U. S. A. IRON CHANNELS. 15" CHANNEL. SHAPE No. 30. 175 LBS. PER YARD. Depth, 15". Width of flange, 4%". Thickness of web, „ . , , . 281.00 Safe load in nett tons = -7^ ; — ;; . Span in feet Maximum shear = 26.98 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.20'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 46.83 ' 0.03 350 8 35-13 0.07 467 j 35-13 10 28.10 O.II 583 32.12 28.10 22.48 12 23.42 0.15 700 31.22 26.02 22.30 19-51 15.61 14 20.07 0.21 : 817 28.67 22.94 19. II 16.38 14-33 11.47 16 17-56 0.27 933 21.95 ,17-56 14.63 12.54 10.97 8.78 18 15.61 0.34 ; 1050 17-34 Oo bo 11.56 9.91 8.67 6.94 20 14.05 0.43 1 1167 14.05 11.24 9-37 8.03 7.02 5.62 22 12.77 0.52 1283 II. 61 9-29 7-74 6.63 5.81 4-64 24 II. 71 0.62 1400 9.76 7.81 6.51 5-58 4.88 3-90 26 10.81 0.73 1517 8.32 6.66 5-55 4-75 4.16 3-33 28 10.04 1 0.84 1633 7.17 5-74 4-78 4.10 3-58 2.87 30 9-37 0.96 1750 6.25 5.00 4.17 3-57 3-12 2.50 32 8.78 1. 10 1867 5-49 ! 4-39 3-66 I 3-14 2.74 2.20 34 8.26 1-25 1983 1“ i s i 3-89 3-24 ' 2.78 2-43 1-94 75 POTTSVILLE IRON AND STEEL CO., IRON CHANNELS. 15" CHANNEL. SHAPE No. 31. 1 74i LBS. PER YARD. Depth, 15". Width of flange, Thickness of web, if". Safe load in nett tons = . Span in feet Maximum shear = 29.87 tons. Span limit for uniformly distributed load of twice the maximum shear = 4.44'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. I Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square fcot. 250 lbs. per square foot. 6 44.17 0.03 349 1 8 33-13 0.07 465 41.41 33-13 10 26.50 O.II 582 42.40 35-33 30.29 26.50 21.20 12 22.08 0.15 698 36.80 29-44 24-53 21.03 18.40 14.72 14 18.93 0.21 814 27.04 21.63 18.03 15-45 13-52 10.81 16 16.56 0.27 931 20.70 16.56 13.80 11.83 10.35 8.28 18 14.72 0.34 1047 16.36 13.09 10.91 9-35 8.18 6.54 20 13-25 0.43 1163 13-25 10.60 8.83 7-57 6.62 5-30 22 12.05 0.52 1280 10.95 8.76 7-30 6.26 5-47 4-38 24 11.04 0.62 1396 9.20 7-36 6.13 5.26 4.60 3.68 26 10.19 0.73 1513 -d- 00 6.27 5-23 4.48 3-92 3-14 28 9.46 0.84 1629 6.76 5-41 4-51 3-86 3-38 2.70 30 8.83 0.96 1745 5-89 4.71 3-93 3-37 2.94 2.36 32 8.28 1. 10 1861 5.18 4.14 3-45 2.96 2.59 2.07 34 7-79 1.25 00 00 4 - 3.66 3-05 2.62 2.29 1.83 76 POTTSVILLE, PENNA., U. S. A. IRON CHANNELS. 15" CHANNEL. SHAPE No. 31. 1 25 LBS. PER YARD. Depth, 15". Width of flange, 3II". Thickness of web, M". 211.00 Safe load in nett tons — . Span m leet Maximum shear = 13.23 tons. Span limit for uniformly distributed load of twice the maximum shear = 8.00'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. § 0 cS CO Deflexion, in inches Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square feot. 200 lbs per square foot. 250 lbs. per square foot. 6 j 8 10 35-17 26.38 21.10 0.03 0.07 O.II 250 333 417 33-76 28.13 24.11 32.97 21.10 26.38 16.88 12 17-58 0.15 500 29.30 23-44 19-53 16.74 14.65 1 1.72 14 15-07 0.21 583 21-53 17.22 14.35 12.30 10.76 8.61 16 13-19 0.27 667 16.49 13.19 10.99 9-42 8.24 6.60 18 11.72 0.34 750 13.02 10.42 8.68 7-44 6.51 5-21 20 : 10.55 0.43 833 10.55 8.44 ; 7-03 6.03 5-27' 4.22 22 9-59 0.52 1 917 8.72 6.98 ! 5-81 4-98 4-36 3-49 24 j 8.79 i 0.62 1000 7-33 5.86 4-89 4.19 3-66 2-93 26 ' 8.12 0-73 1083 6.25 5.00 4.17 3-57 3.12 2.50 28 7-54 0.84 1167 5-39 4-31 3-59 3-08 2.69 2.16 30 7-03 0.96 1250 4.69 3-75 3-13 2.68 2.34 32 6-59 1. 10 1333 4.12 3-30 2-75 2.35 2.06 34 6.21 1.25 1417 3-65 2.92 2.43 2.09 1 77 POTTSVILLE IRON AND STEEL CO., IRON CHANNELS. 12"CHANNEL. SHAPE No. 32. 1 50 LBS. PER YARD. Depth, 12". Width of flange, 33^". Thickness of web, ^|". o r- 1 J • 170.00 Safe load m nett tons = ^ . Span m feet Maximum shear = 30.49 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.80'. Span, in feet. j Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 28.33 0.05 300 8 21.25 0.08 400 35-42 30-36 26.56 21.25 10 17.00 0.13 500 34.00 0 Cl M 22.67 19-43 17.00 1 13.60 12 14.17 0.19 600 23.62 18.90 15-75 13-50 II.81 9-45 14 12.14 0.26 0 0 17-34 13-87 11.56 9.91 8.67 6.94 16 10.63 0.34 800 13.29 10.63 8.86 7-59 6.64 5-32 18 9.44 0.43 900 10.49 8.39 6.99 5-99 5-24 4.20 20 8.50 0.54 1000 8.50 6.80 5-67 4.86 4-25 3-40 22 7-73 0.65 1 100 7-03 5.62 4.69 4.02 3-51 2.81 24 7.08 0.77 1200 5-90 4.72 3-93 3-37 2-95 2.36 26 6.54 0.90 1300 5-03 4.02 3-35 2.87 2.51 2.01 28 6.07 1.05 1400 4-34 3-47 2.89 2.48 2.17 30 5-67 1.20 1500 3-78 3.02 2.52 2.16 78 POTTSVILLE, PENNA., U. S. A. IRON CHANNELS. 12" CHANNEL. SHAPE No. 32. 90 LBS. PER YARD. Depth, 12". Width of flange, 3". Thickness of web, ^y'. Safe load in nett tons = -7^ — — . Span m leet Maximum shear = 10.45 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.79'. Span, in feet. 0 0 Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 20.17 0.05 180 33-6 i 26.89 8 15-13 0.08 240 30.26 25.22 21.62 18.91 15-13 10 12.10 0.13 300 1 24.20 19-36 16.13 bo 12.10 9.68 12 10.08 0.19 360 o^ bo 0 13-44 11.20 9.60 8.40 6.72 14 8.64 0.26 420 12.34 9-87 8.23 7-05 6.17 4.94 16 7-56 0.34 480 9-45 7-56 6.30 5-40 4.72 3-78 18 ! 6.72 0.43 540 7-47 00 4.98 4-27 3-73 2.99 20 1 6.05 0.54 600 6.05 00 4- 4-03 3-46 3.02 2.42 22 5-50 0.65 660 5.00 1 ; 4.00 1 3-33 2.86 2.50 2.00 24 5-04 0.77 720 4.20 3-36 2.80 2.40 2.10 26 4.65 0.90 780 3-58 2.86 2-39 2.05 1 28 4-32 1.05 00 0 3-09 2.47 2.06 30 4-03 I.20j 900 2.69 2.15 79 POTTSVILLE IRON AND STEEL CO., IRON CHANNELS. 12" CHANNEL. SHAPE No. 34. 84^ LBS. PER YARD. Depth, 12". Width of flange, 2 \%". Thickness of web, „ ^ . 102.00 Safe load in nett tons . Span m feet Maximum shear = 13.00 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.96'. Distance apart, in feet, centre to centre of CO § beams, for safe loads of 1 .s g" § 1 0 *9 1 rO 0 § 100 lbs. square foot. 125 lbs. square foot. 150 lbs. square foot. 175 lbs. square foot. 200 lbs. square foot. 250 lbs. square foot. Oh CO CO V (=> 0 1. 1, 6 17.00 0.05 179 32.38 28.33 22.66 8 12.75 0.08 225 25-50 21.25 i8.22 15.92 12.75 10 10.20 0.13 282 20.40 16.32 13.60 11.65 10.20 8.16 12 8.50 0.19 338 14.16 11-33 9.44 8.09 7.08 5.66 14 7.28 0.26 394 10.40 8.32 6.93 5-94 5.20 4.16 16 6.37 0.34 450 7.96 6.37 5-31 4-50 3-98 3.18 18 5.66 0.43 507 6.29 5-03 4.19 3-59 3-14 2.51 20 5.10 0.54 564 5.10 4.08 3-40 2.91 2-55 2.04 22 4-63 0.65 619 4.21 3-36 2.81 2.40 2. II 24 4-25 0.77 676 3-54 2.83 2.36 2.02 26 3-92 0.90 732 3.01 2.41 2.01 28 3-64 1.05 788 2.60 2.09 30 340 1.20 846 2.26 ■A 80 POTTSVILLE, PENNA., U. S. A. IRON CHANNELS. 12" CHANNEL. SHAPE No. 34. 62 LBS. PER YARD. Depth, 12". Width of flange, 2%". Thickness of web, ^V'- r , , • 84.00 Safe load in nett tons = -7; ^ — 7 . bpan m feet Maximum shear = 5.70 tons. Span limit for uniformly distributed load of twice the maximum shear = 7-3j'- 1 1 Span, in feet. Safe load, in nett tons. '' 1 1 Deflexion, in inches. 1 Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 14.00 0.05 124 46.66 37-33 31. II 26.66 23-33 18.66 8 10.50 0.08 164 26.25 21.00 17-50 15.00 13.12 10.50 10 8.40 0.13 206 0 bo 0 13-44 11.20 9.60 8.40 6.72 12 7.00 0.19 248 11.66 9-33 7-77 6.66 5-83 4.66 14 6.00 0.26 0 00 8.56 6.85 5-71 4.89 4.28 3-42 16 5-25 0.34 331 6.56 5-25 4-37 3-75 3-28 2.62 18 4.66 0.43 : 375 5-17 4.14 3-45 2-95 2-59 20 4.20 0.54 417 4.20 3-36 2.80 2.40 22 3.82 0.65 ^ 454 3-47 2.77 2.31 24 3-50 0.77 , 496 2.91 2-33 i 26 3-23 0.90 537 2.48 28 3.00 1.05 00 U-) 1 j 30 2.80 1.20 620 81 POTTSVILLE IRON AND STEEL CO IRON CHANNELS. 10" CHANNEL. SHAPE No. 35. 1 28 LBS. PER YARD. Depth, lo". Width of flange, Thickness of web, i^g". Safe load in nett tons = . - — . Span m leet Maximum shear = 30.16 tons. Span limit for uniformly distributed load of twice the maximum shear = 1.86'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs per square foot. 250 lbs. per square foot. 6 18.66 0.04 256 31.10 24.80 8 14.00 0.09 341 28.00 23-33 20.00 17-50 14.00 10 11.20 0.15 426 22.40 17.92 14-93 12.80 11.20 8.96 12 9-33 0.22 512 15-55 12.44 10.36 8.88 7-77 6.22 14 8.00 0.30 597 11.42 9.14 7.62 6.53 5-71 4-57 16 7.00 0.40 682 8.75 7.00 5-83 5.00 4-37 3-50 18 6.22 0.50 768 6.91 5-52 4.61 3-94 3-45 2.76 20 5.60 0.62 852 5.60 4.48 3-73 3.20 2.80 2.24 22 5-09 0.76 938 4-63 3-70 3.08 2.64 2.31 24 4.66 0.92 1024 3.88 3 -II 2-59 2.22 26 4.31 1.08 1109 3-31 2.59 2.21 28 4.00 1.24 1194 2.85 2.28 30 3-73 1.42 1278 2.42 82 POTTSVILLE, PENNA., U. S. A. IRON CHANNELS. 10" CHANNEL. SHAPE No. 35. 60 LBS. PER YARD. Depth, lo". Width of flange, 2§^". Thickness of web, 66.00 Safe load in nett tons = -p; : — Span in teet Maximum shear = 7.61 tons. Span limit for uniformly distributed load of twice the maximum shear = 4.34'. Distance apart, in feet, centre to centre of 1 beams, for safe loads of 1 a a 0 "o 0 Span, in feet. 0 CO .3 0 'g q=l St 0 100 lbs. per square fo 125 lbs. per square fo 150 lbs. per square fo 175 lbs. per square fo 200 lbs. per square foi 250 lbs. per square fO' 6 I 1. 00 1 0.04 120 36.66 29-33 24.44 20.95 18.33 14.66 8 i 8.25 0.09 160 20.62 16.50 13-75 11.78 10.31 8.25 10 6.60 ! 0.15 ' 200 1 13.20 10.56 8.80 7-54 6.60 5.28 12 5.50 0.20 ! 240 9.16 7-33 6.11 5-23 00 3-66 14 4.71 0.30 280 6.73 5-38 4-48 3-84 3-36 2.69 16 4.12 0.40 320 5-15 4.12 3-43 2.94 2.57 2.06 18 3.66 0.50 360 4.06 3-25 2.72 2.32 20 3-30 0.62 400 3-30 2.64 2.20 22 3.00 0.76 440 2.72 2.18 24 2.75 0.92 480 2.29 1.83 26 2-53 1.08 520 1-95 28 2-35 1.24 560 30 2.20 1.42 600 i 83 POTTSVILLE IRON AND STEEL CO., IRON CHANNELS. 10" CHANNEL. SHAPE No. 36. 62 LBS. PER YARD. Depth, lo". Width of flange, 2%". Thickness of web, xV'- o , 1 • 64.00 Safe load in nett tons = ^ Span m feet Maximum shear = 9.81 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.26'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of "o ,0 £ i 1 s. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 10.67 0,04 124 35-57 28.46 23-71 20.33 17.78 14.23 8 8,00 0.09 165 20.00 16.00 13-33 11-43 10,00 8.00 10 6.40 0.15 207 12.80 10.24 8.53 7-31 6.40 5-12 12 5-33 0.22 248 8.88 7.10 5-93 5-07 4-44 3-55 14 4-57 0.30 289 6.53 5.22 4-35 3-74 3-27 2.61 16 4.00 0,40 331 5.00 4.00 3-33 2.86 2.50 2.00 18 3-55 0.50 372 3-94 3-15 2.62 2.25 1-97 00 up 20 3.20 0.62 413 3.20 2.56 2.13 1.83 1.60 1.28 22 2.91 0,76 454 2.65 2.12 1.76 I-51 1.32 1.06 24 2,67 0.92 496 2.23 1.78 1-49 1.28 1. 12 26 2.46 1.08 537 1.88 1.50 1.25 1.08 28 2.29 1.24 579 1.64 I- 3 I 1.09 30 2.13 1.42 620 1.42 1. 14 84 POTTSVILLE, PENNA., U.S. A. IRON CHANNELS. 10" CHANNEL SHAPE No. 36. 48 LBS. PER YARD. Depth, lo". Width of flange, 234". Thickness of web, iV'- Safe loan m nett tons = . Span in feet Maximum shear = 5.58 tons. Span limit for uniformly distributed load of twice the maximum shear = 4.66'. Span, in foot. | 1 Safe load, in nett tons. Deflexion, m inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square fcot. 250 lbs. per square foot. 6 8.66 0.04 96 28.87 23.09 19.24 16.42 14-43 11-54 8 6.50 0.09 128 16.25 13.00 10.83 9-30 8.12 6.50 10 5.20 0.15 160 10.40 8.32 6-93 5-94 5.20 4.16 12 4-33 0.22 192 7.22 5.77 4.81 4.12 3.61 2.89 14 371 ! 0.30 224 5-30 4.24 3-53 3-03 2.65 2.12 16 3-25 0.40 256 4.06 3-25 1 2.71 1 ' 2.32 18 2.88 0.50 288 3.20 2.56 20 2.60 0.62 320 2.60 22 ; 2.36 0.76 352 24 2.17 0.92 384 26 2.00 1.08 416 28 1.86 1.24 448 1 30 1-73 1 1.42 1 480 1 85 POTTSVILLE IRON AND STEEL CO., IRON CHANNELS . 9". CHANNEL. SHAPE No. 37 . 52 LBS. PER YARD. Depth, 9". Width of flange, 2^". Thickness of web, ^ f 1 - -1 • 53.00 Span in feet Maximum shear = 6.37 tons. Span limit for uniformly distributed load of twice the maximum shear = ■ 4.16'. Distance apart, in feet, centre to centre of § beams, for safe loads of 1 § •S § 1 I 0 0 £ "o c2 M 2 0 ^ £ ^ a I "o ^ £ 1 1 £ 1 CO CO ■g '§ Et 1 ^ § & 00 *0 cr* CVJ CO E^ 6 8.83 0.03 104 2943 23-54 19.62 16.82 i 14.71 11.77 8 6.63 O.IO 139 16.58 13.26 11.05 9.48 8.29 6.63 10 5-30 0.18 173 10.60 8.48 7.07 6.06 5-30 4.24 12 4.41 0.26 208 7*33 5.86 4.89 4.18 3-67 2-93 14 3.78 0-35 243 540 4-32 3.60 3-09 2.70 2.16 16 3-31 0.46 277 4.14 3 - 3 ^ 2.76 2.36 2.07 1.65 i8 2-95 0.58 312 3.28 2.62 2.19 1.88 1.64 I- 3 I 20 2.65 0.71 347 2.65 2.12 1.77 1.52 1-32 1.06 22 2.41 0.86 381 2.19 1-75 1.46 1.25 I.IO 24 2.20 1.03 416 1.83 1.46 1.22 1,04 26 2.04 1.20 451 1-57 1.26 1.05 28 1.90 1.40 485 1.36 1.09 30 1.77 1.60 520 1. 18 86 j POTTSVILLE, PENNA., U. S. A. IRON CHANNELS. 9" CHANNEL. SHAPE No. 38. 37 LBS. PER YARD. Depth, g". Width of flange, Thickness of web, 37.00 Safe load in nett tons = ^ — t . Span in feet Maximum shear = 3.69 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.01'. Distance apart, in feet, centre to centre of 0 beams, for safe loads of Span, in feet. § 1 eg Deflexion, in inche: Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 6.17 0.03 74 20.56 16.45 13-71 11-75 10.28 8.23 8 4-63 O.IO 87 11-57 9.26 7.71 6.61 00 4-63 lO 370 0.18 123 7.40 5-92 4-93 4-23 3-70 2.96 12 3-17 0.26 148 5-29 4-23 3-53 3.02 2.64 2.13 14 2.64 0-35 173 3-77 3.02 2.51 2.15 1.89 I-5I 16 2.31 0.46 197 2.89 2.31 1-93 1.65 1-45 1. 16 18 2.06 0.58 222 2.29 bo 1-53 1. 16 1-15 20 1.85 0.71 247 1.85 1.48 1 1.23 1.06 22 1.68 0.86 271 1-53 1.22 1.02 24 1-54 j 1-03 296 1.28 1.02 26 28 1.42 i 1 1.20 321 1.09 1.32 1.40 345 1 30 1.23 1.60 ! 370 Span limit for tabular safe load = 5.40'. 87 POTTSVILLE IRON AND STEEL CO. 1 IRON CHANNELS. 8" CHANNEL. SHAPE No. 39. 40 LBS. PER YARD. Depth, 8". Width of flange, Thickness of web, yV'« Safe load in nett tons = -7^ — 3^00 ^ Span m feet Maximum shear = 5.25 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.43'. Distance apart, in feet, centre to centre of beams, for safe loads of 1 Span, in feet. 1 .2 i *2 Deflexion, in inche Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 6.00 0.05 80 20.00 16.00 13-30 11.42 10.00 8.00 8 4-50 O.II 107 11.25 9.00 7-50 6.42 5.62 4-50 10 3.60 0.20 133 7.20 576 4.80 4.1 1 3.60 2.88 12 3.00 0.30 160 5.00 4.00 3-33 2.85 2.50 2.00 14 2.57 0.40 187 370 2.96 2.46 2. II 1.85 1.48 16 2.25 0.50 213 2.80 2.24 1.86 1.60 1.40 1. 12 18 1 2.00 0.66 240 2.22 1.77 1.48 1.26 I.II 20 1.80 0.80 267 1.80 1.44 1.20 1.02 88 POTTSVILLE, PENNA., U. . S. A. IRON CHANNELS 8" CHANNEL. SHAPE No. 40. 30 LBS. PER YARD. Depth, 8". Width of flange, 2 !jV'. Thickness of web, Safe load in nett tons = 26.00 span m teet Maximum shear = 3.58 tons. Span limit for uniforml}' distributed load of twice the maximum shear = ^ 3 - 63 '- Distance apart, in feet, centre to centre of o beams, for safe loads of 1 S s=: ,o ,0 ,0 S 3 3 ^ 1 M £ rO £ ^ ce ^ £ ^ ce ^ £ a- o •g s ^ 1 i i to cr* cva w CO CO i=L, ! ^ Si. s I. ! 6 4-33 0.05 60 1443 11-54 9.62 8.27 7.21 1 1 5-77 8 3-25 O.II 80 8.13 6.50 5-42 4-65 4.07 3-25 10 2.6o 0.20 100 5.20 4.16 3-47 2.97 2.60 2.08 12 2.17 0-30 120 3.62 2.90 2.41 2.06 1.81 1-45 14 1.86 0.40 140 2.64 2. II 1.76 I- 5 I 1.32 1.06 i6 1.63 0.50 160 2 04 1.63 00 rn 1. 17 1.02 i8 1.44 ! 0.66 180 1.60 1.28 1.07 1 Span limit for tabular safe 20 1.30 i 0.80 1 1 200 1.30 1.04 load = 5.10'. 89 POTTSVILLE IRON AND STEEL CO, IRON CHANNELS. 7 " CHANNEL. SHAPE No. 41 . 35 LBS. PER YARD. Depth, 7". Width of flange, Thickness of web, o r 1 , • 27.00 hale load in nett tons = ^ — . hpan in leet Maximum shear = 4.91 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.75'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 4-50 0.05 70 15.00 12.00 10.00 8.57 7-50 6.00 8 3-37 0.13 93 8.43 6.74 5.62 4.82 4.21 3-37 lO 2.70 0.23 117 540 4.32 3.60 3-09 2.70 2.16 12 2.25 0.34 140 3-75 3.00 2.50 2.14 1.88 1.50 14 1-93 0.49 163 2.76 2.21 1.84 1.72 1.38 I. II 16 1.68 0.60 187 2.10 1.68 1.40 1.20 i.05 18 1.50 0.76 210 1.67 1-34 I. II Span limit for tabular safe 20 1-35 0.94 233 1-35 1.08 load = 5 . 70 '. 90 POTTSVILLE, PENNA., U.S. A, IRON CHANNELS. 7" CHANNEL. SHAPE No. 42. 25 LBS. PER YARD. Depth, 7". Width of flange, 2". Thickness of web, gV'. 20.00 Safe load in nett tons = . ^ — • Span in feet Maximum shear = 2.74 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.65'. Distance apart, in feet, centre to centre of . beams, for safe loads of g CO § ■ s . 1 1 a =§ 1 .2 CJ -Tlf 0 4 £ ^ £ cS J £ 2 ^ s:5 uo or* CN2 W * 0 P LO cr* CV3 V3 CO CO Ps S. 6 3-33 0.05 50 II. 10 8.88 7.40 6.34 5-55 444 8 2.75 0.13 67 6.87 5-50 4-58 3-92 344 2-75 10 2.00 0.23 83 4.00 3.20 2.67 2.57 2.00 1.60 12 1.67 0.34 100 : 2.78 2.22 00 1-59 1-39 I. II 14 143 0.49 II7 2.04' 1.63 1.36 1. 17 1.02 16 1.25 0,60 133 1.25 1.04 18 I. II 0.76 150 1.23 Span limit for tabular 20 1. 00 0.94 167 1. 00 safe : load = 5.10'. 91 POTTSVILLE IRON AND STEEL CO., IRON CHANNELS. 6" CHANNEL. SHAPE No. 43. 30 LBS. PER YARD. . Depth, 6". Width of flange, 2 ". Thickness of web, Safe load in nett tons = Span in feet ' Maximum shear = 3.30 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.30'. Distance apart, in feet, centre to centre of § beams, for safe loads of 0 &d § 0 .2 i "o ^0 .0 1 "o .2 .=2 1 cS i 0 ^ cti M 2 ^ cS 3 ^ «• CD S g £ a 0 S M § S I' i 1 i I- a CO CO $ 0 a 0 A a a 6 3-33 0.05 60 II. II 8.88 7.40 1 6.34 5-55 444 8 2.75 0.15 80 6.87 5-49 4-58 3-92 3-43 2.74 10 2.20 0.26 100 4.40 3-52 2.93 2.51 2.20 1.76 12 1.83 0.38 120 3-05 2.44 2.03 1.74 1.52 1.22 14 1-57 0.58 140 2.25 1.80 1.50 1.28 1. 12 0.90 16 1.38 0.70 160 1-73 1.38 I-I 5 18 1.22 0.87 180 1-37 1.09 Span limit 20 1. 10 1.08 200 1. 10 for tabular safe load = 5- 10'- 92 POTTSVILLE, PENNA., U. S. A. IRON CHANNELS. 6" CHANNEL SHAPE No. 44. 223^ LBS. PER YARD. Depth, 6". Width of flange, Thickness of web, ^V'- 1 6.00 Safe load in nett tons = ^ — r . Span in leet Maximum shear = 2.00 tons. Span limit for uniformly distributed load of twice the maximum shear = 4.00'. Span, in feet. j ! Safe load, in nett tons. Deflexion, in inches. . Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 2.67 0.05 45 8.90 1 7.12 5-93 00 0 LO 445 3-56 8 2.00 0.15 60 5.00 4.00 3-33 2.85 2.50 2.00 10 1.60 0.26 75 3.20 2.56 2.13 1.83 1.60 1.28 12 1-33 0.38 90 2.22 1.78 1.48 1.26 I. II 14 1. 14 0.58 105 1.63 1.30 1.08 16 1. 00 0.70 120 1-25 1. 00 18 0.89 0.87 135 Span limit for tabular safe 20 0.80 1.08 150 load = = 4.20'. 93 POTTSVILLE IRON AND STEEL CO. IRON CHANNELS. 5" CHANNEL. SHAPE No. 45. 26 LBS. PER YARD. Depth, 5". Width of flange, i%". Thickness of web, Safe load in nett tons = . Span in feet Maximum shear = 2.97 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.53'. 1 Span, in feet. 1 Safe load, in nett tons. i Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foct. 6 2.50 O.II 52 8.33 6.64 5-55 4.76 4.17 3-32 8 1.88 0.21 69 4.70 3-76 3-13 2.69 2.35 1.88 10 1.50 0-33 87 3.00 2.40 2.00 I.71 1.50 1.20 12 1-25 0.48 104 2.08 1.66 1.38 I.19 1.04 14 1.07 0.60 I 2 I 1-53 1.22 1.02 16 0.94 0.80 139 1. 17 0.94 18 0.84 1. 00 156 Span limit for tabular safe 20 0-75 1.30 173 load = = 4.80'. 94 POTTSVILLE, PENNA., U. S. A. IRON CHANNELS. 5" CHANNEL. SHAPE No. 46. 17 LBS. PER YARD. Depth, 5". Width of flange, i%". Thickness of web, jV'* ^ ^ . 10.00 Safe load in nett tons = ^ — ;; . Span in leet Maximum shear = 1.90 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.60'. Span, in feet. 1 Safe load, in nett tons. Distance apart, in feet, centre to centre of beams, for safe loads of Deflexion, in inche: Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 1.67 O.II 34 5-55 4.44 370 3-17 |2.78 2.22 8 1.25 0.21 46 3-^3 2.50 2.09 1.79 1-57 1.25 10 1. 00 0-33 58 2.00 1.60 1-33 1. 14 1. 00 0.80 12 0.83 0.48 70 1.38 1. 10 0.92 0.79 0.69 14 0.71 0.60 82 1.02 0.82 0.68 16 0.63 0.80 94 0.79 0.63 18 0.55 1. 00 106 o.6i Span limit 20 0.50 1.30 118 0.50 for tabular safe load - 4.40', 95 POTTSVILLE IRON AND STEEL CO 96 POTTSVILLE, PENNA., U.S. A, T A B Iv K S OF THE CAPACITY OF STEEL I BEAMS THE EXTREME FIBRE STRESS BEING 7.8 TONS PER SQUARE INCH, WHICH IS TWO-SEVENTHS OF AND THE UNSTAYED LENGTH OF FLANGE NOT EXCEEDING THIRTY TIMES ITS WIDTH. The span, which is thirty times the flange width, is denoted by a dotted line on the tables, and for lengths greater than this, the tabular safe load must be reduced by multiplying it by the factors given in table on page 43, or else some method of staying the flanges be employed. UNDEfl UNIFORMLY DISTRIBUTED TRANSVERSE LOADS, THE MODULUS OF RUPTURE; 97 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. I 15" I BEAM. SHAPE No. 1. 252^ LBS. PER YARD. I Depth, 15". Width of flange, Thickness of web, Safe load in nett tons = i — -z — . Span in feet Maximum shear = 44.08 tons. Span limit for uniformly distributed load of twice the maximum shear = 6.39'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. 0 0 M 0 CO Deflexion, in inche; Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 56.36 0.12 842 II 51-24 0.14 926 12 46.97 0.18 lOIO 31-31 13 43-36 0.21 1094 33-35 26.68 14 40.26 0.25 1178 32.86 28.75 23.01 15 37-57 0.27 1263 33-39 28.62 25.04 20.04 16 35-23 0.31 1346 35-23 29-35 25.16 22.02 17.61 17 33-15 0-35 1431 39.00 31.20 26.00 22.28 19.50 15.60 18 31-31 0.39 1515 34.80 27.82 23,20 19.88 17.40 13-91 19 29.66 0.43 1599 31-23 24-97 20.82 17.84 15.61 12.48 20 28.18 0.48 1684 28.18 22.54 18.78 16.10 14.09 11,27 21 26.84 0.53 1767 25-56 20.45 17.04 14.60 12.78 10.23 22 25.62 0.58 1851 23-30 18.62 15-53 13-31 11.65 9-31 23 24.51 0.64 1936 21.31 17-05 14.21 12.18 10.66 8.52 24 23.48 0.69 2020 19.56 15-65 13.04 II. 18 9-78 7.82 25 22.54 0.75 2103 18.03 14.42 12.02 10.30 9.02 7.21 26 21.68 0,82 2189 16.68 13-35 II. 12 9-53 8.34 6.67 27 20.87 0.88 2261 15.46 12.33 10.31 8.83 7-73 6.17 28 20.13 0.95 2356 14.38 11.50 9-59 8.22 7.19 5-75 29 19-45 1.02 2441 13-41 10.73 8.94 7.66 6.70 5-36 3 “^ 18.78 1.08 2525 12.52 10.02 8-35 7-15 6.26 5-01 31 18.18 1. 17 2609 11-73 9-38 7.82 6.70 5-86 4-69 32 17.61 1.25 2693 II.OI 8.80 7-34 6.29 5-50 4-40 33 17.08 1-33 2777 10.35 8.28 6.90 5-91 5-17 4.14 POTTSVILLE, PENNA., U. S. A. STEEL I BEAMS. 15" I BEAM. SHAPE No. 2. 202 LBS. PER YARD. Depth, 15". Width of flange, 5rV'. Thickness of web, Safe load in nett tons = ^ — •. Span in leet ^Maximum shear = 27.11 tons. Span limit for uniformly distributed load of twice the maximum shear = 8.87'. 0 Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. 0 e$ Ci OQ Deflexion, in inchei Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 11 12 13 14 48.10 43-73 40.08 37.00 34-36 0.12 0.14 o.i8| 0.21 0.25 673 741 808 875 943 1 i i i 133-36 '32.53 28.46 32.73 28.05 24.54 31.80 26.69 22.77 19.64 15 32.07 0.27 1010 i *34-21 28.51 24.43l2i.38 17.10 16 30.06 0.31 1077 30.06! 25. 05 '21. 47 48. 79 15-03 17 28.29 0-35 1145 33.28I26.62 22.19 19.02 16.64 13-31 18 26.72 0.39 1212 29.69 ;23-75 19-79 16.97 14.84 11.88 19 25-32 0.43 1279 26.64 !2I.3i 17.76 15.22 13.32 10.66 20 24.05 0.48 134724.05 19.24 16.03 13-74 12.02 9.62 21 22.90 0.53 I4I4'2I.8i 17-45 14-54 12.46 10.90 8.72 22 21.86' 0.58 1481 19.87 15.90 13.25 11.35 9-93 7-95 23 20.91 0.64 1549 18.18 14.54 12.12 10.39' 9-09 7.27 24 20.04 0.69 1616 16.70 13.36 II. 13 9.54: 8.35 6.68 25 19.24 0.75 1683 15-39 12.31 10.26 8.79! 7.69 6.16 26 18.50 0.82 1751 14.23 11.38 9-49 8.13' 7. II 5-69 27 17.81 0.88 1818 13-19 10.55 8.79 7.54: 6.55 5.28 28 1 17-18 0.95 1885 12.27 9.82 8.18 7.01 6.13 4.91 29 1 16.59 I 1.02 1953 11.44 ' 9-15 7-63 6.54 5.72 4-58 30 16.03 1 1.08 ; 2020 10.69 8.55 7.13I 6.11 5.34 4.28 31 15-52 i 1-17 2087 lO.OI 8.01 1 6.67 5.72' 5.00 4.00 32 15-03 1 1-25 2155 9-39 . 7-51 6.26 5.37 4.69 3-76 33 14.58 ^-33 2222 8.84 7.07 ’ 5-89 5-05 4-42 3-54 99 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 15" I BEAM. SHAPE No. 3. 15 VA LBS. PER YARD. Depth, 15". Width of flange, 5". Thickness of web, r- r 1 1 • 366.60 bate load m nett tons = -7^ ; — . bpan in teet Maximum shear = 16.80 tons. Span limit for uniformly distributed load of twice the maximum shear = 10.91'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. § 1 1 Deflexion, in inchei Weight of beam. 100 lbs. per spare foot. 125 lbs. per spare foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 11 12 13 36.66 33-33 30-55 28.20 0.12 0.14 o.i8i 0.21 505 556 606 657 34.70 33-95 28.92 34-63 29.09 24.79 36.66 30.30 25.46 21.69 29-33 24.24 20.37 17-35 14 26.19 0.25 707 37-41 29.93 24-94 21.38 18.70 14.97 15 24-44 0.27 757 32.59 26.07 21.73 18.62 16.30 13.04 16 22.91 0.31 808 28.64 22.91 19.09 16.37 14.32 11.46 17 21.56 0-35 859 25-36 20.29 16.91 14.49 12.68 10.15 18 20.37 0-39 909 22.64 18.II 15.09 12.94 11.32 9.06 19 19.29 0.43 959 20.30 16.24 13-53 11.60 10.15 8.12 20 18.33 0.48 1010 18.33 14.66 12.22 10.47 9.17 7-33 21 17.46 0.53 1060 16.62 13-30 11.08 9-50 8.30 6.65 22 16.66 0.58 iiii 15.15 12.12 lO.IO 8.66 7.58 6.06 23 15-94 0.64 1161 13.86 11.09 9-24 7-92 6.93 5-55 24 15.28 0.69 1212 12.74 10.19 8.49 7.28 6.37 5-09 25 14.66 0.75 1263 11-73 9-38 7.82 6.99 5.87 4-69 26 14.10 0.82 1313 10.84 8.67 7-23 6.19 5.42 4-33 27 13-58 0.88 1363 10.06 8.05 6.71 5-75 5-03 4.02 28 13,09 0.95 1414 9-35 7-48 6.23 5-34 4.68 3-74 29 12.64 1.02 1465 8.72 6.98 5-81 4-98 4.36 3-49 30 12.22 1.08 1515 8.15 6.52 5-43 4.66 4.08 3-26 31 11.82 1. 17 1565 7.62 6.10 5-08 4-35 3.81 3-05 32 11.46 1.25 1616 7.16 5-73 4-77 4-09 3-58 2.87 33 II. II 1-33 i 1666 1 6.74 5-39 4-49 3-85 3.37 2.70 100 POTTSVILLE, PENNA., U.S. A. STEEL I BEAMS. 15" I BEAM. SHAPE No. 4. 126!4 LBS. PER YARD. Depth, 15". Width of flange, 4^". Thickness of web, /b". Safe load in nett tons = — . Span in teet Maximum shear = 14.30 tons. Span limit for uniformly distributed load of twice the maximum shear = 10.36'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. 0 Deflexion, in inches Weight -of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 j 11 1 12 ! 29.64 26.94 24.70 0.12 0.14 0.18 421 463 505 32.93 32.65 27.44 33.87 27.99 23.52 29.64 24.49 20.58 23.71 19.59 16.46 13 22.80 0.21 547 35.07 28.06 23.38 20.04 17.54 14.03 14 21.17 0.25 589 30.24 24.19 20.16 17.28 15.12 12.10 15 19.76 0.27 631 26.35; 21.08 17.57 15.06 13.18 10.54 16 18.53 0.31 673 23.l6il8.53 15.41 13.23 11.58 9.27 17 17.44 0.35 715 20.521 16.42 13.68 11.73 10.26 8.21 18 16.47 0-39 757 18.301 14.64 12.20 10.46 9.15 7.32 19 15.60 0.43 800 I6.42li3.i4 10.95 9.38 8.21 6.57 20 14.82 0.48 842 14.82' 11.86 9.88 8.47 7.41 5-93 21 14. II 0.53 884 13.44 ,10.75 8.96 7.68 6.72 5.38 22 1347 0.58 926 12.25 9.80 8.17 7.00 6.12 4.90 23 12.89 0.64 968 II. 21 8.97 7.47 6.41 5.60 4.48 24 12.35 0.69 1010 10.29 8.23 6.86 5.89 5.15 4.12 25 ' 11.86 0.75 1052 9.49 7.59 6.33 5.42 4.75 3-79 26 ; 11.40 0.82 1094 8.77 7.02 5.85 5.01 4.39 3.51 27 i 10.98 0.88 1136 8.14 6.51 5.43 4.65 4.07 3.26 28 ' 10.59 0-95 1178 1 7.56 : 6.05 5.04 4.32 3.78 3.02 29 ' 10.22 1.02 1220 7.04 5.63 4.69 4.02 3.52 2.81 30 9.88 1.08 1262 6-59 5.27 4.39 3-77 3.30 2.63 31 9-56 1. 17 1305 6.17 4.94 4.12 3.52 3.08 2.47 32 9.26 1.25 1347 ! 5-79 4.63 3.86 3.31 2.80 2.31 33 8.98 1-33 1389 ' 5-44 ! 4.35 3.63 3-11 2.72 2.18 101 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 12" X BEAM. SHAPE No. 5. 171% LBS. PER YARD. Depth, 12". Width of flange, 5%". Thickness of web, Safe load in nett tons = . Span m leet Maximum shear = 27.72 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.72'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 31-72 0.15 573 36.25 31-72 25-38 II 28.84 0.18 630 34-96 29-97 26.22 20.98 12 26.43 0.22 687 35-24 29-37 25-17 22.02 17.62 13 24.40 0.26 744 35-23 28.18 23-49 20.13 17.62 14.09 14 22.66 0.30 802 32.37 25.90 J 21.58 L 18.50 16.18 12.95 15 21.15 0.34 859 28.20 22.56 18.80 16.II 14.10 11.28 16 19.82 0-39 916 24.78 19.82 16.52 14.16 12.39 9.91 17 18.66 0.44 973 21.95 17-56 14.63 12.54 10.97 8.78 18 17.62 0.49 1030 19.58 15.66 13-05 II. 19 9-79 7.83 19 16.71 0.55 1088 17-59 14.07 11-73 10.05 8.80 7.04 20 15.86 0-59 1145 15.86 12.69 10.57 9.06 7.93 6.34 21 15.10 0.66 1202 14.38 11.50 9-59 8.22 7.19 5-75 22 14.42 0.73 1260 13. II 10.49 8.74 7-49 6.55 5-24 23 13-79 0.79 1317 11.99 9-59 7-99 6.85 6.00 4.80 24 13.22 0.86 1374 11.02 8.82 7-35 6.30 5-51 4.41 25 12.69 0.94 1431 10.15 8.12 6.77 5.80 5-07 4.06 26 12.20 I.OI 1489 9-38 7-50 6.25 5-36 4.69 3-75 27 11-75 1.09 1546 8.70 6.g6 5.80 4-97 4-35 3-48 28 11-33 1. 18 1603 8.09 6.47 5-39 4.62 4-05 3-24 29 10.94 1.27 1660 7-54 6.03 5-03 4.31 3-77 3.02 30 10.57 1.36 1718 7-05 5-64 4-70 4-03 3-52 2.82 31 10.23 1.46 1775 6.60 5.28 4-40 3-77 3-30 2.64 32 9-92 1-55 1832 6.20 4.96 4-13 3-54 3.10 2.48 33 9.61 1.64 1889 5-82 4.66 3-88 3-33 2.91 2.33 102 POTTSVILLE, PENNA., U.S.A, STEEL I BEAMS. 12" Z BEAM. SHAPE No. 6. 1 26^ LBS. PER YARD. Depth, 12". Width of flange, 4%". Thickness of web, 3 ^". Safe load in nett tons = — . Span in feet Maximum shear = 17.34 tons. Span limit for uniformly distributed load of twice the maximum shear = 6.94'. - Distance apart, in feet, centre to centre of CO beams, for safe loads of C ~ 0 I 1 i - » g 0 0 © g .g- 1 J •2 -2 zr ^ ^ ^ ^ ^ M s 2 cS 2 S § C/D g § srsrsr "S ^ ^ © © 0 CO p* PL- PL, 0 i 1* pH © pH 10 24.10 0.15 421 32.13 27.5424.10 19.28 II 21.90 0.18 463 31.8626.54 22.75 19.91 15-93 12 20.08 0.22 505 33.47 26.77 22.31 19.12 16.73 13-38 13 18.53 0-26 548 28.51 22. 8l 19.01 16.29 14-25 11.40 14 17.21 0.30 59024.5819.6616.39 14.05 12.29 9-83 15 16.06 0.34 632 21.41 17.13 14.27 12.24 10.71 8.57 16 15.06 0.39 674 18.83 12.55 10.76 9.41 7-53 17 14.17 0.44 716 16.67 13.34 II. 12 9-53 8.34 6.67 18 13-39 0-49 75814-8811.90 9.92 8.50 7-44 5-95 19 12.66 0.55 800 13.33 10-66, 8.88 7.62 6.66 5-33 20 12.05 0.59 842 12.05 9-64 8.03 6.88 6.03 4.82 21 11.47 0.66 885 10.92 8.74 7.28 6.24 5-46 4-37 22 10.95 0.73 927 9.95 7.96 6.64 569 4-98 3-98 23 10.48 0.791 969 9-1 1 7-29 6.07 5.21 4-56 3-65 24 10.04 0.86, loii 8.37 6 . 6 g 5.58 4-78 4.18 3-35 25 9.64 0.94 1053 7-71 6.17 5.14 4.41 3-86 3-09 26 9.27 i.oi 1095 7.12 5.70 4.75 4-07 3-56 2.85 27 8.92 1.09; 1137 6.61 5.28 4.40 3-78 3-31 2.64 28 8.61 1. 18, 1179 6.15 4.92 4.10 3-52 3.08 2.46 29 8.31 1.27 1222 5.73 4.58 3.82 3-27 2.87 2.29 30 8.03 1.36' 1264 5-35 4-28 3.57 3.06 2.68 2.14 31 7-77 1-46' 1306 5.01 4.01 3.34 2.86 2.50 2.00 32 7-53 1-55 1348 4-70 3-76 3-14 2.69 2.35 1.83 33 7.30 1.64 1390 4.42 3.54 2.95 2-53 2.21 1-77 103 7 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 12" I BEAM. SHAPE No. 7. 101 LBS. PER YARD. Depth, 12". Width of flange, 4xV'- Thickness of web, /g"* r- r 1 1 • 187.20 Safe load in nett tons = — ^ — . Span m feet Maximum shear = 14.18 tons. Span limit for uniformly distributed load of twice the maximum shear = 6.60'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. J CO Deflexion, in inchei Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 18.72 0.15 337 37-44 29-95 24.96 21.39 18.72 14.98 II 17.02 0.18 370 30.95 24.76 20.63 17.69 15-47 12.38 12 15.60 0.22 404 26.00 20.80 17-33 14.86 13.00 10.40 13 14.40 0.26 438 22.15 17.72 14-77 12.66 11.07 8.86 14 13-37 0.30 471 19.10 15.28 12.73 10.91 9-55 7.64 15 12.48 0.34 505 16.64 13-31 11.09 9-51 8.32 6.66 16 11.70 0.39 539 14.63 11.70 9-75 8.36 7-31 5-85 17 1 1. 01 0.44 572 12.95 10.36 8.63 7-40 6.47 5.18 18 10.40 0.49 606 11.56 9-25 7.71 6.61 5-78 4.62 19 9.85 0-55 640 10.37 8.30 6.91 5-93 5.18 4-15 20 9-36 0-59 673 9-36 7-49 6.24 5-35 4.68 3-74 21 8.91 0.66 707 8.48 6.78 5-65 4.85 4-24 3-39 22 8.51 0.73 741 7-74 6.19 5.16 4-42 3-87 3.10 23 8.14 0.79 774 7.08 5.66 4-72 4-05 3-54 2.83 24 7.80 0.86 808 6.50 5.20 4-33 3-71 3-25 2.60 25 7-49 0.94 842 5-99 4-79 3-99 3-42 2.99 2.40 26 7.20 I.OI 875 5-54 4-43 3-69 3-17 2.77 2.22 27 6.93 1.09 909 5-13 4.10 3-42 2.93 2.56 2.05 28 6.69 1. 18 944 4.78 3.82 3-19 2.73 2.39 29 6.46 1.27 977 4.46 3-57 2.97 2.55 2.23 30 6.24 1.36 1010 4.16 3-33 2.77 2.38 2.08 31 6.04 1.46 1044 3-90 3.12 2.60 2.23 32 5.85 1-55 1077 3.66 2-93 2.44 2.09 33 5-67 1.64 iiii 3-44 2.75 2.29 1-97 104 POTTSVILLE, PENNA., U. S. A. STEEL I BEAMS. ' 10H"X BEAM. SHAPE No. 8. 136^ LBS. PER YARD. I Depth, Width of flange, 5". Thickness of web, i Safe load in nett tons = -7; — 7 . Span in feet Maximum shear = 17.69 tons. Span limit for uniformly distributed load of twice the maximum shear = 6.69'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of bsam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 23.67 0.18 455 47-34 37-87 31-56 27-05 23.67 18.93 II 21.52 0.21 500 39.12 31-30 26.08 22.39 19.56 15-65 12 19.72 0.25 546 32.87 26.29 21.91 18.78 16.43 13-15 13 18.21 0.30, 591 28.02 22.41 18.68 16.01 14.01 II . 21 14 1 16.91 0-35 637 24.16 19-33 16.10 13.80 12.08 9.66 15 ' 15-78 0.40 682 21.04 16.84 14.03 12.02 10.52 8.42 16 14.80 0.46 728 18.50 14.80 12.33 10.57 9-25 7-40 17 13.92 0.51 773 |I 6.36 13.10 10.92 9-36 8.19 6.55 18 13-15 0.57 819 14.61 11.69 9-74 8.35 7-30 5-84 19 12.46 ' 0.64 864 13.12 10.49 8.74 7-49 6.56 5-24 20 11.84 0.70 910 '11.84 9-47 7-89 6.74 5-92 4-74 21 11.27 0.78 955 10.73 8.59 7.16 6.13 5-37 4-29 22 10.76 0.86 1001 1 9-78 7-83 6.52 5-59 4.88 3-91 23 10.30 0.94 1046 ^ 8.95 7.17 5-97 5-11 4-48 3-59 24 , 9.86 1. 01 1092 8.22 6.57 5-48 4-70 4.11 3-29 25 9-47 I. II 1137 i 7-58 6.06 5-05 4-33 3-79 3-03 26 9.10 1.20 1183 7.00 ; 5.60 4.67 4.00 3-50 2.80 27 8.77 1.29 00 M 6.50 5.20 4-33 3-71 3-25 2.60 28 8.46 1-39 1274 6.04 1 4-83 4-03 3-45 3.02 2.42 29 8.16 1.48 1319 5-63 4-50 3-75 3-22 2.81 2.25 30 7.89 1-59 1365 5.26 4.21 3-51 3.01 2.63 2.10 31 7.64 1.69 1410 4-93 3-94 3-29 2.82 2.47 1.92 32 7.40 1.81 1456 4-63 3-70 1 3-09 2.64 2.31 1.85 33 7.18 1.92 1501 4-35 3-48 2.90 2.49 2.18 1.74 105 I POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 10K" I BEAM. SHAPE No. 9. 106 LBS. PER YARD. Depth, Width of flange, 4xV^- Thickness of web, 34^'. Safe load in nett tons = 7 :; — . . Span in feet Maximum shear = 16.17 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.39'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. a -S a 0 cS Deflexion, in inchei Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square fdot. 250 lbs. per square foot. 10 1743 0.18 354 34.86 27.89 23-24 19-92 17-43 13-94 II 15.85 0.21 389 28.81 23-05 I9.2I|I6.47 14.41 11.52 12 14-53 0.25 425 24.22 19.38 16.15 13.84 12 . II 9.69 13 1341 0.30 460 20.63 16.50 13-75 11.80 10.32 8.25 14 12.45 0-35 495 17.80 14.24 11.86 10.16 8.90 7.12 15 11.62 0.40 531 15-49 12.39 10.33 i 8.85 7-75 6.20 16 10.90 0.46 566 13-63 10.90 9-09 1 7-79 6.81 5-45 17 10.25 1 0.51 602 12.06 9-65 8.04 1 6.89 6.03 4.88 18 9.68 1 0.57 637 10.76 8.60 7.17 1 6.15 5-38 4-30 19 9.18 0.64 672 9.66 7-73 6.44 j 5-52 4-83 3-86 20 8.72 0.70 708 8.72 6.98 5.81 4-98 4-36 3-49 21 8.30 0.78 743 7.90 6.32 5-27 4-52 3-95 3.16 22 7.92 0.86 778 7.20 5-76 4.80 4.10 3.60 2.88 23 7.58 0.94 814 6-59 5-27 4-40 3-77 3-30 2.64 24 7.27 I.OI 849 6.06 4-84 4-04 3-46 3-03 2.42 25 6.97 I. II 885 5-58 4.46 3-72 3-19 2-79 2.23 26 6.71 1.20 920 5.16 4-13 3-44 2-95 2.58 2.07 27 6.46 1.29 955 4-78 3-83 3-19 2-73 2-39 1.92 28 6.23 1-39 991 4-45 3-56 2.97 2.54 2.23 1.78 29 6.01 1.48 1026 4-15 3-32 2.76 2-37 2.07 1.66 30 5.81 1-59 1061 3-87 3.10 2.58 2.21 1-94 1-55 31 5.62 1.69 1097 3-63 2.90 2.42 2.07 1.81 1-45 32 5-45 1.81 1132 3-41 2-73 2.27 1-95 1-74 1.36 33 5.28 1.92 1168 3-20 2.56 2.14 1.83 1.60 1.28 106 POTTSVILLE, PENNA., U. S. A. STEEL I BEAMS. ^ 0 y 2 "X BEAM. SHAPE No. 10 . 91 LBS. PER YARD. Depth, loy". Width of flange, 4>^". Thickness of web, M"* 140.60 Safe load in nett tons = -5 ^ — 7 — . Span in leet ^Maximum shear = 12.10 tons. Span limit for uniformly distributed load- of twice the maximum shear = 6.14'. 1 Span, in feet. 1 Safe load, in nett tons. Deflexion, in inches. Weight of- beam. Distance apart, in feet, centre to centre of beams, for safe loads of j! ^ 03 1 ^ ( 0 i 2 ^ \ : "o 1 1 \ tn ^ 1 ^ 1 "o 1 £ i ^ 1 <0 1 ^ 1 ^ 1 .0 M £ i 1 0 .0 <=> C <1 OQ W a-> S 2 10 14.96 0.18 29-92, 23-94 19-95 17-iOj 14.96 11.97 11 12 13 14 15 16 17 18 19 13-59 12.46 11.50 10.68 9-97 9-35 8.80 8.31 7.87 0.21 0.25 0.30 0-351 0.40 0.46I 0.51 0-571 0.64 334 364 394 425 455 485 516 546 576 24.71 20.77 17.70 15.26 13-30 11.70 10.35 9-23 8.28 19.77 16.62 14.16 12.21 10.64 9-35 8.28 7-38 6.63 16.47 13-85 11.80 10.17 8.87 7.80 6 .go 6.15 5-52 14.12' 11.87 10. II 8.72 7.60 6.68 5-92 5-27 4-73 12.35 10.38 8.85 7-63 6.65 5.85 5.18 4.62 4.14 9.88 8.31 7.08 Lio 5-32 4.68 4.14 3-70 3-32 20 7.48 0.70 607 7.48 5-98 i 4-99 4-27 3-74 2.94 21 7.12 0.78 637 6.78 5-42 4-52 3-88 3-39 2.71 22 6.80 0.86 667 6.18 4-94 4-12 1 3-54 3-09 2.47 23 6.51 0.94 698 5.66 4-53 ! 3-78 1 3-23 2.83 2.26 24 6.23 I.OI 1 728 , 5-19 4-15 : 3-40 2.97 2.60 2.08 25 5-98 I. II 758 , 4.78 3-83 3-19 1 2.73 2-39 26 5-75 1.20 1 789 j 4-42 3-54 2-95 2-53 2.21 27 5-54 1.29 819 4.10 3-28 2.74 2-35 2.05 28 5-34 1-39 849 3.81 3-05 2-54 2.17 29 5.16 1.48 880 3-56 2.85 2.37 2.03 30 4-99 1-59 910 3-33 2.661 2.22 31 4.82 1.69 940 3-11 2.49 2.07 32 4.67 1.81 971 2.92 2.34 33 4-54 1.92 1001 ^ 2.75 2.20 107 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 10"XBEAM. SHAPE No. 11. 1 06 LBS. PER YARD. Depth, lo". Width of flange, 4%". Thickness of web, Safe load in nett tons = -7:^ ! — 7 — . Span m feet Maximum shear = 15.85 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.29'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. 0 ns a 0 Deflexion, in inchei Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square fcot. 200 lbs. per square foot. 250 lbs. per square foot. 10 16.77 0.20 353 33-54 26.83 22.36 19.17 16.77 13-42 II 15.24 0.23 389 27.71 22.17 18.47 15-83 13.86 11.08 12 13.98 0.27 424 23-30 18.64 15-53 13-31 11.65 9-32 13 12.90 0.31 459 19.85 15.88 13-23 11-34 9-93 7-94 14 11.98 0.36 495 I7.II 13.69 1 1. 41 9.80 8.56 6.84 15 II. 18 0.43 530 14.91 11-93 9-94 8.52 7.46 5-96 16 10.48 0.48 566 13.10 10.48 8.73 7-49 6.55 5-24 17 9.87 0-53 601 II. 61 9.29 7-74 6.64 5.81 4.64 18 9-32 0,60 636 10.31 8.25 6.87 5-89 5.16 4.12 19 8.83 0.68 671 9.26 7.41 6.17 5-29 4-63 3-70 20 8-39 0.75 707 8-39 6.71 5-59 4-79 4.20 3-36 21 7-99 0.83 742 7.61 6.09 5-07 4-35 3-81 3-04 22 7.62 0.91 777 6-93 5-54 4.62 3-96 3-47 2.77 23 7.29 0.99 813 6.34 5-07 4-23 3-63 3-17 2.54 24 6.99 1.08 848 5-83 4.66 3-89 3-33 2.92 2-33 25 6.71 1. 18 883 5-37 4-30 3-58 3-07 2.68 2.15 26 6.45 1.27 919 4.96 3-97 3-31 2.83 2.48 1.99 27 6.21 1.36 954 4.60 3-68 3-07 2.63 2.30 28 5-99 1.47 989 4.28 3-42 2.85 2.44 2.14 29 30 31 32 33 5.78 5-59 5-41 5-24 5.08 1-57 1.68 1.79 1.92 2.04 1025 1060 1095 1131 1166 4.00 3-73 3-49 3.28 I08 3.20 2.98 2.79 2.62 2.46 2.67 2.49 2-33 2.19 2.05 2.29 2.13 2.00 2.00 108 POTTSVILLE, PENNA., U. S. A. STEEL I BEAMS. 10"! BEAM. SHAPE No. 12. 91 LBS. PER YARD. Depth, lo". Width of flange, 4%". Thickness of web, Safe load in nett tons = ^ — . Span in feet Maximum shear = 13.05 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.58'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feat, centre to centre of beams, for safe loads of 0 ^ s i 1 0 pH j .1 J £ Ph 1 ! -• s . M £ — o3 c=> a 0 M 1 0 ,0 M 1 0 p ,p M £ 1 . 10 11 1456 13-24 0.20 0.23 303 334 29.12 24.07 123-30 19-41 19. 26^16.05 16.64 13-75 14.56 12.03 11.65 9-63 12 13 14 15 16 17 18 12.13 11.20 10.40 9.71 9.10 8.56 8.09 0.27 0.31 0.36 0.43 0.48 0-53 j 0.60 364 20.20 394,17-23 425 14.86 455 12.95 485 11.38 516 10.07 546 8.99 16.16 T3.78 11.89 10.36 9.10 8.06 1 7-19 13-47 11-49 9.91 8.63 7-59 6.71 5-99 11-54 9-85 8.49 7.40 6.50 5-75' 5-14 lO.IO 8.61 7-43 6.47 5-69 5-03 4-49 8.08 6.89 5-94 5.18 4-55 4-03 3.60 19 7.66 0.68 576 8.06 6.45 5-37 4.61 4-03 3.22 20 7.28 0.75 607 7.28 5.82 4-85 4.16 3-64 2.91 21 6.93 0.83 637 6.60 5.28 4.40 3-77 3-30 2.64 22 6.62 0.91 667 6.02 4.82 4.01 3-44 3.00 2.41 23 6.33 0.99 698 5-50 4.40 3-67 3-14 2-75 2.20 24 6.07 1.08 728 5.06 4-05 3-37 2.89 2-53 2.02 25 5.82 1. 18 758 4.66 3-73 3 -II 2.66 2-33 26 5.60 1.27 789 4-31 3-45 2.87 2.46 2.15 27 5-39 1.36 ' 819 3-99 3-19 2.66 2.28 28 5.20 1.47 : 849 3-71 2-97 2-47 2.12 29 5.02 1-57 880 3-46 2-77 2.31 30 4-85 1.68 910 3-23 2.58 2.15 31 4.69 1.79 940 3-03 2.42 2.02 32 4-55 1.92 971 2.84 2.27 33 4.41 2.04 1001 1 2.14 i 109 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 9" I BEAM. SHAPE No. 13. 91 LBS. PER YARD. Depth, g". Width of flange, 4%". Thickness of web, 3^". r , • 127.40 bale load in nett tons = ^ — . bpan in leet Maximum shear = 14.90 tons. Span limit for uniformly distributed load of twice the maximurii shear = 4.28'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. § c3 0 1 Deflexion, in inche: ■Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. lO 12.74 0.20 303 25.48 20.38 16.99 14.56 12.74 10.19 II 11.58 0.25 334 21.05 16.84 14.03 12.03 10.52 8.42 12 10.62 0.30 364 17.70 14.16 11.80 lO.II 8.85 7.08 13 9.80 0.35 394 15.08 12.06 10.05 8.62 7-54 6.03 14 9.10 0.40 425 13.00 10.40 8.67 7-43 6.50 5.20 15 : 8.49 0.46 455 11.32 9.06 7-55 6.47 5.66 4.53 16 1 7-96 0.52 485 9-95 7.96 6.63 5-69 4-97 3-98 17 7-49 0.60 516 8.81 7-05 5.87 5-03 4.40 3-52 18 7.08 0.66 546 7.88 6.30 5-25 4-50 3-94 3-15 19 6.70 0.74 576 7-05 5-64 4.70 4-03 3-52 2.82 20 6-37 0.82 607 6.37 5.10 4-25 3-64 3.18 2-55 21 6.07 0.91 637 5.78 4.62 3-85 3-30 2.89 2.31 22 5-79 1. 00 667 5.26 4.21 3-51 3.01 2.63 2.10 23 5-54 1.09 698 4.82 3.86 3.21 2.75 2.41 24 5-31 1. 18 728 4-43 3-54 2.95 2-53 2.21 25 5.10 1.29 758 4.08 3.26 2.72 2-33 2.04 26 4.90 1-39 789 3-77 3.02 2.51 2.15 27 4.72 151 819 3-50 2.80 2-33 2.00 28 4.55 1.61 849 3-25 2.60 2.17 29 4-39 1-73 880 3-03 2.42 30 4-25 1.86 910 2.83 2.26 31 4.11 1.99 940 2.65 2,12 32 3-98 2.12 971 2.49 33 3.86 2.26 1001 2-34 i 10 POTTSVILLE, PENNA., U. S. A. STEEL I BEAMS. 9" Z BEAM. SHAPE No. 14. 86 LBS. PER YARD. Depth, g". Width of flange, 4^". Thickness of web, bate load in nett tons = -7:; : — 7 . bpan in feet Maximum shear = 12.29 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.05'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per spare foot, 125 lbs. per spare foot. 150 lbs. per spare foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 12.42 0.20 286 24.84 19.87 16.56 14.20 12.42 9-93 II 11.29 0.25 315 20.53 16.42 13-70 11-73 10.27 8.21 12 j 10-35 0.30 344 :i 7.25 'i 3.8 o 11.50 9.86 8.62 6.90 13 ' 9-55 0.35 372ii4-7o 11.76 9.80 8.40 7-35 5.88 14 8.87 0.40 401 12.67 10.14 8.45 7-24 6-34 5-07 15 8.28 0.46 430 1 1 .04 8.83 7-36 6.31 5-52 4.41 16 7.76 0.52 458 9.70 7.76 1 6.47 1 5-54 4-85 3-88 17 7-31 0.60 487 8.60 6.88 5-73 4.92 4-30 3-44 18 6.85 0.66 516 7.61 6.09 5-07 4-35 3.81 3-05 19 6.54 0.74 544 6.88 5-50 4-59 3-93 3-44 2.75 20 6.21 0.82 573 6.21 4.98 4.14 3-55 3-II 2.49 21 5-92 0.91 601 5-64 4-51 3-76 3.22 2.82 2.25 22 5-65 1. 00 630 5-14 4.11 3-43 2.94 2-57 2.06 23 5-40 1.09 659 4.70 3-76 3-13 2.68 2-35 24 5-i8 1. 18 687 4-32 3-45 2.88 2.47 2.16 25 4-97 1.29 716 3-98 3.18 2.65 2.27 26 4.78 i-39| 745 3.68 2.94 2.45 2.10 27 1 4.60 I-5L 773 3-41 2-73 2.27 28 4.44 1.61 802 3-17 2.54 2. II 29 4.28 1-73 831 2-95 2.36 30 4.14 i.86| 859 2.76 2.21 31 4.00 1.99 888 2.58 2.06 32 3.88 2.12 917 2-43 33 1 3-77 2.26 1 945 2.28 i Ill POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 9" I BEAM. SHAPE No. 16. 70Ji LBS. PER YARD. Depth, 9". Width of flange, 4". Thickness of web, Safe load in nett tons — . Span in feet Maximum shear = 9.77 tons. Span limit for uniformly distributed load of twice the maximum shear = 4.93'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. § 1 Deflexion, in inchei Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. ! 10 9.62 0.20 236 19.24 15-39 12.83 10.99 9.62 7.70 II 8.74 0.25 259 15.89 12.71 10.59 9.08 7-94 6.36 12 8.02 0.30 283 13-37 10.70 8.91 7.64 6.68 5-35 13 7.40 0-35 307 11.38 9.10 7-59 6.50 5-69 4.55 14 6.88 0.40 339 9-83 7.86 6.55 5.62 4.91 3-93 15 . 6.41 0.46 354 8.55 6.84 5-70 4-89 4-27 3-42 ; 16 6.01 0.52 378 7-51 6.01 5.01 4-29 3-75 3.00 1 17 5.66 0.60 401 6.66 5-33 4-44 3.81 3-33 2.66 ; 18 5-34 0.66 424 5-93 4-74 3-95 3-39 2.96 2.37 ■ ^9 5.06 0.74 448 5-33 4.26 3-55 3-05 2.66 2.13 20 4.81 0.82 471 4.81 3-85 3.21 275 2.41 21 4-58 0.91 495 4-36 3-49 2.91 2.49 2.18 ■ 22 4-37 1. 00 519 3-97 3.18 2.65 2.27 } 23 4.18 1.09 542 3-63 2.90 2.42 2.07 1 24 4.01 1. 18 566 3-34 2.67 2.23 25 3-85 1.29 590 3.08 2.46 2.05 26 370 1-39 613 2.85 2.28 1 27 3-56 I-5I 637 2.64 2. II 28 3-44 1.61 661 2.46 29 3-32 173 684 2.29 1 * 30 3.21 1.86 708 2.14 31 3.10 1.99 732 2.00 32 3.00 2.12 755 33 2.92 2.26 778 II 2 A POTTSVILLE, PENNA., U. S. A. STEEL I BEAMS. 8" I BEAM. SHAPE No. 16. 81 LBS. PER YARD. Depth, 8". Width of flange, 43V'. Thickness of web, 3 ^". „ ^ . 100.10 Safe load in nett tons = ^ ^ — . bpan m feet Maximum shear = 13.60 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.68'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. ■ Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 0 .0 ^ £ C 5 ^ 2 ^ 0 ^ 2 ‘ ^ 5 1 E« I 0 £ 0 i=Lt 0 ,0 J £ i 1 E. 0 M £ 0 E § ^ E .0 M £ <0 m cy* ea c/a {=U 10 lO.OI 0.23 270 20.02 16.02 13-35 11.44 lO.OI 8.01 11 12 13 14 9.10 8.34 7.70 7-15 0.29 0.34 0-39 0.46 297 324 350 377 16.54 13.90 11.85 10.21 13-23 II. 12 9.48 ■8.17 1 1. 00 9-27 7.90 6.81 9-45 7-95 6.77 5-83 8.27 6-95 5-93 5 -II 6.62 5-56 4-74 4.08 15 6.67 0.52 404 8.89 7. II 5-93 5.08 4-45 3-55 16 6.26 0.60 431 7.82 6.26 5.21 4-47 3-91 3-13 17 5-89 0.68 458 6-93 5-54 4.62 3-96 3-47 2.77 18 5-56 075 485 6.18 4.94 4.12 3-53 3-09 2.47 19 5-27 0.83 512 5-55 4.44 3-70 3-17 2.78 2.22 20 5.00 0.92 539 5.00 4.00 3-33 2.86 2.50 2.00 21 4.77 1.02 566 4-54 3-63 3-03 2-59 2.27 22 4-55 1. 12 593 4.14 3-31 2.76 2-37 2.07 23 4-35 1.22 620 378 ’ 3-02 2.52 2.16 24 4.17 1-34 647 3-47 : 2.78 2.31 25 4.00 1.46 i 674 3.20 1 2.56 2.13 26 3-85 1.56 701 2.96 1 2.37 27 370 1.69 728 2.74 2.19 28 3-57 1.82 755 2-55 2.04 29 3-45 1-95 782 2.38 1 30 3-34 2.08 809 2.23 1 31 3-23 2.22 836 2.08 32 3-13 2.36 863 33 3-03 2.51 890 II3 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 8" I BEAM. SHAPE No. 17. 65% LBS. PER YARD. Depth, 8". Width of flange, 4". Thickness of web, r. r 1 1 • 00. 4 U bate load in nett tons = — ^ — . bpan m feet Maximum shear = 6.97 tons. Span limit for uniformly distributed load of twice the maximum shear = 6.34'. 0 c /5 Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. CtJ 0 Deflexion, in inche B 'o 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot, 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 8.84 0.23 219 17.68 14.14 11-79 lO.IO 8.84 7.07 II 8.04 0.29 241 ^14.62 11.69 9-75 8.35 7-31 5.85 12 7-37 0.34 263 12.28 9.82 8.19 7.02 6.14 4.91 13 6.80 0-39 285 10.46 8.37 6.97 5-98 5-23 4.19 14 6.31 0.46 307 9.01 7.21 6.01 5-15 4-51 3.61 15 5.89 0.52 329 7.85 6.28 5-23 4.49 3-93 3-14 16 5-53 0.60 350 6.91 5-53 4.61 3-95 3-46 2.77 17 5.20 0.68 372 6.12 4.89 4.08 3-49 3.06 245 18 4.91 0.75 394 546 4-37 3-64 3.12 2.73 2.19 19 4-65 0.83 416 4.89 3-91 3.26 2.79 245 20 4.42 0.92 438 4.42 3-54 2.95 2-53 2.21 21 22 23 24 25 26 27 28 29 30 31 32 33 4.21 4.02 3-84 3.68 3-54 340 3-27 3.16 3-05 2-95 2.85 2.76 2.68 1.02 1. 12 1.22 1-34 1.46 1.56 1.69 1.82 1-95 2.08 2.22 2.36 2.51 460 482 504 526 548 569 591 613 635 657 679 701 723 4.01 3-65 3-34 3-07 2.83 2.62 2.42 2.26 2.10 3.21 2.92 2.67 2.46 2.26 2.09 2.67 2.40 2.23 2.05 2.29 2,09 2.01 II4 POTTSVILLE, PENNA., U. S. A. STEEL I BEAMS. 7" Z BEAM. SHAPE No. 18. 65% LBS. PER YARD. Depth, 7". Width of flange, 3yV'* Thickness of web, §|". Safe load in nett tons = ^ — - — . Span in leet Maximum shear = 10.90 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.28'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs, per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 11 12 7-15 6.50 5-96 0.26 0-33 0.38 219 241 263 14.30 11.82 9-93 11.44 9.46 7-94 9-53 7.88 6.62 8.17 675 5-67 7-15 5-91 4-97 572 473 3-97 13 5-50 0.46 285 8.46 6.77 SM 4-83 4-23 3-38 14 511 0.52 307 7-30 5-84 4.87 4.17 3-65 2.92 15 4-77 0.60 •329 6.36 5-09 4.24 3-63 3.18 2.54 16 4-47 0.68 351 5-59 4-47 373 3.20 2.29 2.23 17 4.21 0.77 373 4.96 3-97 3-31 2.83 2.48 18 3-97 0.86 394 4.41 3-53 2.94 2.52 2.20 19 376 0.96 416 3-96 317 2.64 2.26 20 3-58 1.07 438 3-58 2.86 2-39 2.05 21 3-41 1. 17 460 3-25 2.60 2.17 22 3-25 1.29 482 2.95 2.36 23 3 -II 1.40 504 2.70 2.16 24 2.98 1.52 526 2.48 25 2.86 1.65 548 2.29 26 275 1.79 570 2.12 27 2.65 1.94 592 28 2-55 2.08 614 29 2.46 2.24 636 30 2.38 2-39 657 31 2.31 2-55 679 Span limit for tabular safe 32 2.23 2.70 701 loads = = 9.00', 33 2.16 2.86 723 II5 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 7" I BEAM. SHAPE No. 19. 553^ LBS. PER YARD. Depth, 7". Width of flange, 3iV'» Thickness of web, Safe load in nett tons = -p; — — . Span in feet Maximum shear = 7.08 tons. Span limit for uniformly distributed load of twice the maximum shear = 4,62'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 11 12 6.53 5-94 5-45 0.26 0-33 0.38 185 204 222 13.06 10.80 9.08 10.45 8.64 7.26 8.71 7.20 6.05 7.46 6.17 5-19 6.53 540 4-54 5-23 4-32 3-63 13 5-03 0.46 241 7-74 6.19 5.16 4.42 3.87 3.10 14 4.67 0.52 259 6.67 5-34 4-45 3.81 3-34 2.67 15 4-36 0.60 278 5.81 4-65 3-87 3-32 2.91 2.32 16 4.09 0.68 297 511 4.09 341 2.92 2.56 2.04 17 3-85 0.77 315 4-53 3.62 3.02 2.59 2.27 18 3-63 0.86 334 4-03 3.22 2.69 2.30 2.02 19 3-44 0.96 352 3.62 2.89 2.41 2.07 20 3-27 1.07 371 3-27 2.62 2.18 21 311 1. 17 389 2.96 2.37 22 2.97 1.29 408 2.70 2.16 23 2.84 1.40 426 2.47 24 2.72 1.52 445 2.27 25 2.61 1.65 463 2.09 26 2.51 1.79 482 27 2.42 1.94 500 28 2.33 2.08 519 29 2.25 2.24 537 30 2.18 2.39 556 31 2. II 2-55 574 Span limit for tabular safe 32 2.04 2.70 593 load = -8K'. 33 1.98 2.86 612 1 16 POTTSVILLE, PENNA., U.S. A. STEEL I BEAMS. 6" I BEAM. SHAPE No. 20. 50K LBS. PER YARD. Depth, 6". Width of flange, 35V'. Thickness of web, c r 1 j • 46.80 bale load in nett tons = -7; ^ — 7 . bpan m feet Maximum shear = 8.52 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.75'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 10 4.68 0-33 168 9-36 7-49 6.24 5-35 4.68 3-74 II 4-25 0.38 185 7.61 6.09 5-07 4-35 3.80 3-04 12 3-90 0.44 202 6.50 5.20 4-33 3-71 3-25 2.60 13 : 3.60 0.52 219 5-54 4-43 3-69 3.16 2.77 2.21 14 3-34 0.61 236 4-77 3.82 3.18 2.72 2-38 ; 1.91 15 3.12 0.70 253 4.16 3-33 2.77 2.38 2.08 16 2.92 0.78 269 3-65 2.92 2.43 2.09 17 : 2.75 0.89 286 3-23 2.58 2.15 18 2.60 1. 00 ! 303 2.88 2.30 19 2.46 ' 1. 12 320 2-59 2.07 20 1 2.34 1-23 337 2-34 21 2.23 1-36 353 2.12 22 2.13 ; 1.49 370 23 2.04 ! 1.64 387 24 1.95 1.78 404 25 1.87 1.94 421 26 1.80 2.09 438 27 1.74 2.26 454 28 2-43 471 1.07 29 I.61 2.60 488 30 1.56 2.78 505 Scan limit for tabular safe 31 I5I 2-95 522 load = = 8.10'. 32 1.46 3.12 539 33 1.42 3-29 555 II7 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 6" X BEAM. SHAPE No. 21. 40^ LBS. PER YARD. Depth, 6". Width of flange, Thickness of web, Y4' • Safe load in nett tons = ^ — ;; . Span m feet IMaximum shear = 4.41 tons. Span limit for uniformly distributed load of twice the maximum shear = 4.72'. I18 POTTSVILLE, PENNA., U. S. A. STEEL I BEAMS. 5" I BEAM. SHAPE No. 22. 40'A LBS. PER YARD. Depth, 5". Width of flange, Thickness of web, Safe load in nett tons = : . Span in leet Maximum shear = 6.71 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.48'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. § Deflexion, in inchei Weight of beam. too lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 3 11.09 0.03 40 29-57 4 8.32 0.05 54 27-73 23-77 20.80 16.64 5 6.65 0.09, 68 26.60 21.28 17-73 15.20 13-30 10.64 6 5-55 0.13 80 18.50 14.80 12.33 10.57 9-25 7-40 7 4-75 0,18 94 13-57 10.86 9-05 7-75 6.79 5-43 8 4.16 0.23 108 10.40 8.32 6-93 5-94 5-20 4.16 9 3-69 0.30 120 8.20 6.56 5-47 4.69 4-10 3.28 10 3-33 0.36 135 6.66 5-33 4-44 3.81 3-33 2.67 II 3-03 0.44 148 5-51 4.41 3-67 3-15 2.76 2.21 12 2.77 0-53 162 4.62 3-70 3.08 2.64 2.31 13 2.56 0.62 175 3-94 3-15 2.63 2.25 14 2.38 0.73 189 3-40 2.72 2.27 15 2.21 0.83 202 2-95 2.36 16 2.08 0.95 216 2.60 2.08 17 1-95 1.07 229 2.29 18 1.85 1. 19 242 2.06 19 I 75 1-34 256 20 1.67 1.48 269 21 1.58 1.64 283 i 22 151 1.79 296 1 23 1-45 1.96 310 24 1.38 2.14 322 25 1-33 2-33 337 26 1.28 2.53 350 1 1 19 / POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 5" I BEAM. SHAPE No. 23. 30^A LBS. PER YARD. Depth, 5". Width of flange, 2^". Thickness of web, Safe load in nett tons = — - — . Span m teet Maximum shear = 2.54 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.00'. 120 POTTSVILLE, PENNA., U. S. A. STEEL I BEAMS. 4"Z BEAM. SHAPE No. 24. 30K LBS. PER YARD. Depth, 4". Width of flange, 2/g". Thickness of web, Safe load in nett tons = — ^ Span in leet Maximum shear = 6.32 tons. Span limit for uniformlj'^ distributed lo'ad of twice the maximum shear = 1.44'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. 0 c5a Deflexion, in incbei Weight of beam. 100 lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. | 3 4 5 6 6.07 4-55 3-64 3-03 0.04 0.08 0.12 0.17 30 40 51 61 40.47 22.75 14.56 10. 10 32.38 18.20 11.65 8.08 26.98 15.17 9.71 6.73 23.13 13.00 8.32 5.77 20.24 11.38 7.28 5.05 16.19 1 9.10 i 5.83 : 4.04 1 7 2.60 0.22 i 71 7-43 5-94 4.95 4.25 3.72 2.97 8 2.28 0.30 81 570 4.56 3.80 3.26 2.85 2,28 j 9 2.02 0.38 91 4.49 3-59 2.99 2.57 2.25 1 10 1.82 0.47 lOI 3-64 2.91 2.43 2.08 ! II 1.65 0.56 III 3.00 2.40 2.00 : 12 1.52 0.66 I 2 I 2-53 2.02 i 13 1.40 0.78 I3I 2.15 1 14 1.30 0.91 I4I 1 15 1. 21 1.05 152 1 16 1. 14 1. 18 162 1 17 1.07 1-34 172 18 1. 01 1-51 182 1 19 0.96 1.68 192 i 20 0.91 1.86 202 21 0.87 2.05 212 22 0.83 2.25 222 23 0.79 2.46 233 24 0.76 2.68 243 25 0-73 2.90 253 26 0.70 3-13 263 121 POTTSVILLE IRON AND STEEL CO., STEEL I BEAMS. 4" I BEAM. SHAPE No. 25. 24K LBS. PER YARD. Depth, 4". Width of flange, 2]^". Thickness of web, xV'- Safe load in nett tons = Span m feet Maximum shear = 4.51 tons. Span limit for uniformly distributed load of twice the maximum shear = '1.61. 122 POTTSVILLE, PENNA., U.S.A. STEEL I BEAMS. 4" I BEAM. SHAPE No. 26. 18!4 LBS. PER YARD. Depth, 4". Width of flange, 2)4". Thickness of web, xV'* Safe load in nett tons = ^ — . Span m feet Maximum shear = 2.31 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.47'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square, foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 3 4 5 6 i 3.80 1 2.85 2.28 1.90 0.04 0.08 0.12 0.17 18 24 30 36 |25-33 14.25 1 9-12 6.33 j 20.26 1 1 .40 7-30 5.06 T6.89 9-50 6.08 4.22 14.47 8.14 5-21 3.62 12.67 7-13 4-56 3-17 10.13 570 3-65 2.53 7 1.63 0.22 42 4.66 i 3-73 1 3-07 ^ 2.66 2.33 8 1-43 0.30 ' 48 3-58 2.86 2-39 2.05 9 1.27 0.38 55 2.82 2.26 10 1. 14 0.47 61 2.28 II 1.04 0.56 67 12 0-95 0.66 73 I i 13 0.88 0.78 79 1 1 1 14 0.81 0.91 85 1 ! 15 0.76 1.05 91 16 0.71 1. 18 97 17 0.67 1-34 103 18 0.63 151 109 19 0.60 1.68 115 20 0.57 1.86 121 21 0-54 2.05 128 22 0.52 2.25 134 23 0.49 2.46 140 24 0.48 2.68 146 25 0.46 2.90 152 26 0.44 3-13 158 1 123 POTTSVILLE IRON AND STEEL CO., 124 POTTSVILLE, PENNA., U. S. A. \. t T TABLES OF THE CAPACITY OF STEEL CHANNELS THE EXTREME FIBRE STRESS BEING 7.8 TONS PER SQUARE INCH, WHICH IS TWO-SEVENTHS OF AND THE UNSTAYED LENGTH OF FLANGE NOT EXCEEDING THIRTY TIMES ITS WIDTH. The Span, which is thirty times the flange width, is denoted by a dotted line on the tables, and for lengths greater than this, the tabular safe load must be reduced by multiplying it by the factors given in table on page 43, of else some method of staying the flanges be employed. UNDER UNIFORMLY DISTRIBUTED TRANSVERSE LOADS, THE MODULUS OF RUPTURE; POTTSVILLE IRON AND STEEL CO., STEEL CHANNELS. 15"CHANNEL. SHAPE No. 30. 227% LBS. PER YARD. Depth, 15". Width of flange, Thickness of web, igV'. 431.60 Span in feet ’ f Maximum shear = 57.08 tons. Span limit for uniformly distributed load of twice the maximum shear = 3.78'. Distance apart, in feet, centre to centre of beams, for safe loads of Span, in feet. .2 1 .0 Deflexion, in inche Weight of beam. 100 lbs. per square fcot. 125 lbs. per square foot. 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 71.93 0.04 455 8 53.95 0.09 606 10 43.16 0.14 758 43.16 34.53 12 35-97 0.19 909 39-97 34.26 29.97 23.98 14 30-83 0.27 1061 44.04 35-23 29.36 25-17 22.02 17.62 16 26.98 0.35 1212 33-73 26.98 22.49 19.27 16.86 13.49 18 23.97 0.44 1364 26.63 21.30 17.75 15.22 13.31 10.65 20 21.58 0.56 1515 21.58 17.26 14.39 12.33 10.79 8.63 22 19.62 0.68 1667 17.84 14.27 11.89 10.19 8.92 7.14 24 17.98 0.81 1818 14.98 00 9-99 8.56 7-49 5-99 26 16.60 0.95 1970 12.77 10.22 8.51 7-30 6.38 5-II 28 15.42 1.09 2121 1 1. 01 8.81 7-34 6.29 5.50 4.40 30 14.39 1.25 2273 9-59 7.67 6.39 5-48 4-79 3-84 32 13.49 1-43 2424 8.43 6.74 5.62 4.82 4.21 3-37 34 12.69 1.62 2576 7.46 5-97 4.97 4.26 3-73 2.98 126 POTTSVILLE, PENNA., U. S. A, STEEL CHANNELS. 15"CHANNEL. SHAPE No. 30. 1 76M LBS. PER YARD. Depth, 15". Width of flange, 4%". Thickness of web, 365.30 Safe load in nett tons = -5 : — y — Span in feet Maximum shear = 35.66 tons. Span limit for uniformly distributed load of twice the maximum shear = 5.01'. Span, in feet. Safe load, in nett tons. Deflexion, in inches. 1 Weight of beam. Distance apart, in feet, centre to centre of beams, for safe loads of 100 lbs. per square foot. 125 lbs. per square foot. j 150 lbs. per square foot. 175 lbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 60.88 0.04 354 8 45.66 0.09 471 45.66 10 36.53 0.14 589 41.75 36.53 29.22 12 30.44 0.19 707 40.58 33-82 28.99 25-36 20.29 14 26.09 1 0.27 825 37.27 29.82 24.85 21.30 18.63 14.91 16 22.83 0.35 943 28.54 22.83 19.03 16.31 14.27 11.42 18 20.29 0.44 1 060 22.54 18.03 15-03 12.88 11.27 9.02 20 18.27 0.56 1178 18.27 14.62 12.18 10.44 9-13 7-31 22 16.60 0.68 1296 15.09 1 1 2.07 10.06 8.62 7-54 6.04 24 15.22 0.81 1414 12.68 10.14 8.45 7-25 6.34 5-07 26 1 14.05 0.95 1532 10.81 00 b^ Cn 7.21 6.18 5-40 4-32 28 13.05 1.09 1650 9-32 7.46 6 ; 2 I 5-33 4.66 3-73 30 12.17 1.25 1767 8.11 6.49 5-41 4-63 4.05 3-24 32 , 11.42 1.43 1885 7.14 5.71 4.76 4.08 3-57 2.86 34 ■ 10.74 1.62 2003 6.32 5.06 4.21 3-61 3.16 2-53 27 POTTSVILLE IRON AND STEEL CO., STEEL CHANNELS. 15"CHANNEL. SHAPE No.31. 1 76^ LBS. PER YARD. Depth, 15". Width of flange, Thickness of web, ig". Safe load in nett tons = Span m feet Maximum shear — 39.74 tons. Span limit for uniformly distributed load of twice the maximum shear = 4.33'. 0 Distance apart, in feet, centre to centre of beams, for safe loads of .s 0 • S -S 0 ‘g a rS 0 0 ^ £ 2 ^ 0 M £ 0 ^ i g 1 - 0 2 £ p -^' £ <=> cs 0^ CQ w .1 ^ £ ^ cd • 0 S3 CQ 6 5742 0.04 353 1 i 8 43.06 0.09 470 13.06 10 3445 0.14 588 39-37 34-45 27.56 12 28.71 0.19 705 38.28 31.90 27-34 23-92 19.14 14 24.61 0.27 823 35 -i 6 28.13 23-44 20.09 17.58 14.06 16 21-53 0-35 940 26.91 21-53 17.94 15-38 13.46 10.76 18 19.14 0.44 1058 21.27 17.02 14.18 12.15 10.63 8.51 20 17.23 0.56 1175 17-23 13.78 11.49 9-85 8.61 6.89 22 15.66 0.68 1293 14.24 11-39 9-49 8.14 7.12 5-70 24 14.35 0.81 1410 11.96 9-57 7-97 6.83 5-98 4-78 26 13-25 0-95 1528 10.19 8.15 6.79 5.82 5-09 4.08 28 12.30 1.09 1645 8.79 7-03 5.86 5-02 4-39 3-52 30 11.48 1.25 1763 7-65 6.12 5.10 4.37 3.82 3.06 32 10.77 1-43 1880 6.73 5.38 4-49 3-85 3-36 2.69 34 10.13 1.62 1998 5-96 4-77 3-97 3-41 2.98 2-38 POTTSVILLE, PENNA., U. S. A, STEEL CHANNELS. 15" CHANNEL. SHAPE No.31. 1 26^ LBS. PER YARD. Depth, 15". Width of flange, 3|f'. Thickness of web, gi". 274.30 Safe load in nett tons = ^ — 7 . Span in leet Maximum shear = 17.67 tons. Span limit for uniformly distributed load of twice the maximum shear == 7.76'. : Distance apart, in feet, centre to centre of I beams, for safe loads of j g : ; ^ ^ 1 - B g ,0 "o ^ s .=2 S £ f ^ ^ 1 *o 1 0 1 ^ a A ~ s 0 ,0 0 i 1 i S' 0 ^ 1 § ^ CM CO — • bpan m leet Maximum shear = 2.54 tons. Span limit for uniformly distributed load of twice the maximum shear = 2.56'. Span, in feet. J 1 Distance apart, in feet, centre to centre of beams, for safe loads of Deflexion, in inche Weight of beam. ICO lbs. per square foot. 125 lbs. per square foot. 150 lbs. per square foot. 175 tbs. per square foot. 200 lbs. per square foot. 250 lbs. per square foot. 6 2.17 0.14 34 7-23 5.78 4.82 i 4-13 3.61 2.89 8 1.62 1 1 0.27 46 i i 4-05 3-24 2.70 2.31 2.02 1.62 1 10 1.30 0-43 59 1 2.60 2.08 j ^ 1-73 1 1 ' 149 i 1.30 1.04 12 1.08 0.62 1 71 . 1.80 1.44 1 1.20 1 1.03 0.90 0.72 14 0.93 0.78 00 1-33 1.06 0.89 0.76 0.67 16 0.81 1.04 95 ‘ I.OI 0.81 0 C^ ''I p 00 18 0.72 1.30 107 0.80 0.64 0-53 Span limit 20 0.65 1.69 120 0.65 0.52 for tabular safe load = 4.4c/. 147 POTTSVILLE IRON AND STEEL CO., ON DETERMINING THE CAPACITY, ETC., OE BEAMS AND CHANNELS. Let S = area of section. 1 = length of span. w = load per linear unit of beam. W = total load uniformly distributed. Mo = maximum bending moment of external forces. h = height of shape. y = distance from neutral axis to that edge of shape which first ruptures, and which in symmet- rical sections is one-half the height. f = extreme fibre stress (generally taken in tons per square inch) on that side of the neutral axis which first ruptures. I = maximum moment of inertia of section. J = minimum moment of inertia of section. = maximum radius of gyration, = minimum radius of gyration, c — coefficient for one foot span. 8 1 For iron shapes = = 4 R. For steel shapes = ^ = 5.2 R. R = modulus of section = = for a symmetrical shape = -j— . A = maximum deflexion (generally given in inches). 148 V POTTSVILLE, PENfgA., U.S. A. Let Fq = the maximum shear permissible. For iron shapes, F^ 3,00 tons rV For steel shapes, F^ = ' 3000 4.00 tons 1 + r-fT 3000 q = a factor dependent upon form of section, and is the ratio I m' h''^ S h y s h y since — = square of radius of gyration. If the shape is symmetrical, y = — , or m' = - ; 2 2 then 2 I Ti^ li^ In the above, I denotes simply a moment of inertia. If the least moment of inertia be in question, the above relations are also ap- plicable, replacing I by J, and r by rj, and h and y being taken in the direction of the least moment of inertia. E = coefficient of elasticity, which for iron shapes = 13,000 tons per square inch, steel shapes == 14,500 tons per square inch. 5 WF A = ~ET supported at both ends, and uniformly loaded over its entire length. 149 1 POTTSVILLE IRON AND STEEL CO., WP Let = 8~E^ beam fixed at one end, and uniformly loaded over its entire length. P P A A A A 48 E I beam supported at both ends, and having a concentrated load, P, at the centre. P P 3EI the other. for beam fixed at one end, and loaded at P 13 for beam fixed at both ends, and 192 E I having a concentrated load, P, at the centre. W 13 for beam fixed at both ends, and 307 E I uniformly loaded over its entire length. The relation between the external and molecular forces of a beam subjected to transverse loading is expressed by ° y the second member of which is called the moment of resist- (I) When the beam is supported at its ends, and uniformly loaded over its entire length, the maximum moment due to external forces is at the centre of the beam, and is given by W1 the expression, The moment of resistance of the beam should at least equal this, and for beams of sym- metrical sections, in which y is equal to one-half the height, the general expression (i) becomes W1 2f I from which we get W h 16 f I 1 h (2) ( 3 ) 150 POTTSVILLE, PENNA., U.S.A If, as is usually the case, we take the length of beam in feet and the height in inches, then equation (3) becomes W = ^n: 3 1' h' (4) in which 1' denotes the span of beam in feet, and h" the height in inches. In beams of iron we take as the safe working extreme fibre stress f, 6.0 tons per square inch, this being two-sevenths (I) of the modulus of rupture. In beams of steel we take as the safe working extreme fibre stress f, 7.8 tons per square inch, which is likewise two-sevenths (|-) of the modulus of rupture of steel beams. Then, for iron beams, we get from (4), by making f = 6.0 tons. (5) and for steel beams we get, by making f = 7.8 tons, W 10.4 I 1' h" ( 6 ) in both of which expressions W is the safe load, in nett tons, uniformly distributed. If we consider the span 1 ' to l^e one foot, then we have what has been called the coefficient for one foot of span, — i.e.. For iron beams. ( 7 ) For steel beams. P 10.4 I h" (8) Now, on page 148, we have called — the 77 ioduliis of the y section, and denoted it by the letter R, As in symmetrical sections y = ^ h", the 77 todnlus for 2 such sections is R 2 I ( 9 ) 5 POTTSVILLE IRON AND STEEL CO., Whence the safe load could be written, For iron beams, W = t 5 ( 10 ) For steel beams. (II) and the coefficients for one foot span could be written. For iron beams. II u ( 12 ) For steel beams. C = 5.2R (13) From the foregoing expressions many useful relations can be obtained. I. Given the load in nett tons, W, on a beam; 1, the span in feet ; h, the height in inches ; I, the moment of inertia of the beam. Required the extreme fibre stress f ? f = Awi'*^ ( 14 ) 4 ^ II. Given the load in nett tons, W, on a beam ; 1', the span in feet ; f, the extreme fibre stress. Required the modulus of the section ? f Wb 2 f ( 15 ) III. Given the load in rjett tons, W, on a beam ; f, the extreme fibre stress; h", the height of the beam, and I its moment of inertia; or R, the modulus of the section. Re- quired the span for which the beam will safely carry the assumed load, W ? \ = ^ L _L W P' f w 2 I IV, Given the span V in feet ; the extreme fibre stress, f ; the height, h" of the beam, and I, its moment of inertia; or R, the modulus of the section. Required the load which | the beam will carry ? 52 POTTSVILLE, PENNA., U.S. A. 4 f I _ 2 f 2 I 3 I'h" ~ 3 1'!^ 2 f ^ — -i7 R 3 1 ' (I?) Examples on the use of the foregoing expressions : Example I. Given a 12" I beam of iron, 125 pounds per yard, whose span centre to centre of end bearings is 10 feet, carrying a load of 15 tons, uniformly distributed over its length. Required the extreme fibre stress, f ? Here W= 15.0 tons; r = 10.0 feet; h = 12" and referring to the table “On the Properties of I Beams,” page 159, we find for a 12" I beam, 125 pounds per yard, the moment of inertia I to be 279. Making these substitutions in expression (14), we get f= vX ^5-oX loX 4 = 4.84 tons per square inch. Example II. Given a load of 9.75 tons, uniformly dis- tributed on a span whose length centre to centre of end bearings is 12.0 feet, and having a height limiting us to the use of a lOj" I beam. Required the moment of inertia of the necessary loj" I beam, assuming the extreme fibre stress to be 6.0 tons ? Here we have W = 9.75 tons ; V = 12.0 feet; h = loj" ; f = 6.0 Making these substitutions in expression (15), we get P 2 I _ 3 ^, 9 - 7 S X 12.0 ~ loi" ~ 2 ^ 6.0 I 5 ^ = 29.25 i.e., R = 29.25 I =29.25 X 5-25 = 153-56 Referring to the table “ On the Properties of I Beams,” we find that a loj" I beam of iro 7 t, 90 pounds per yard, 153 POTTSVILLE IRON AND STEEL CO., ] shape No. lo, has a value of R = 29.0, and a moment of inertia = 151. Hence this shape meets the requirements. Example III. Given a 12" I beam of iron, 125 pounds , per yard, whose moment of inertia is, as per table “ On the | Properties of I Beams,” 279.0; or whose modulus R is i 46.25; also, given the load to be carried is 9.25 tons, and j the extreme fibre stress to be limited to 6.0 tons. Required | the span centre to centre of end bearings, for which this i beam could be used ? j We have, then, h"=i2"; 1 = 279.0; R = 46.25; W = 9.25 tons; ' f = 6.0 tons per square inch. . Substituting these values in expression (16), we get ' ,, 4 6.0 279.0 l' = — X X - = 20.00 feet ; 1 3 ^ 9.25 ^ 12 or, using the modulus R instead of the moment of inertia I, ; we get from (16) l' = — X ----- X 46.25 = 20.00 feet. 3 ^ 9.25 Thus, 20.0 feet is the limiting span of this beam, for the assumed load and fibre stress. Example IV. Suppose we have a span of 15 feet, and ! that we wish to use a 15" I beam of wrought iron, 150 pounds per yard. Required the safe load which we can put on this beam, when the fibre stress is limited to 5.0 tons per square inch ? We have given, in the table “On the Properties of I Beams,” R = 70.50, We also have given l'=i5.o, and f = 5.0 tons. Inserting these values in expression (17), w'e get W = ^ X 1^5 0 ^ that is, our safe load is 15.66 tons, uniformly distributed over length of beam. 154 POTTSVILLE, PENNA., U.S.A. ON THE PROPERTIES OF I BEAMS CHANNELS OF IRON AND STEEL, MANUFACTURED BY THE POTTSVILLE IRON AND STEEL CO. The tables “On the Properties of I Beams and Channels” are calculated for the minimum and maximum weight to which these shapes are rolled. The plates illustrate how the increase of weight is effected, which is simply by increasing the distance apart of the rolls ; consequently, the increase in width in flanges is the same as increase in thickness of web. I beams, channels, and angle irons may be rolled to any weight intermediate between the minimum and maximum weights as given. T iron can be rolled to but one weight. Columns Nos. lo and 1 1 in the tables for I beams and chan- nels, pages 159, 160, give coefficients, by means of which the safe uniformly distributed load for any I beam or channel on the list can at once be obtained, when we know the span. We have only to divide the coefficient by the span in feet, when the result is the safe load in nett tons, uniformly distributed, that the I beam or channel will carry. The fibre stresses upon which these coefficients are based are for iron shapes, 6.0 tons per square inch ; for steel shapes, 7.8 tons per square inch. Should any case arise in which a lower fibre stress is desirable, the coefficient is simply reduced in the same pro- portion. For example : the coefficient for a fibre stress of 6.0 tons per square inch on a 12" I beam of iron, 125 pounds per yard, is given by the table as 185. Should we wish the fibre stress to be but 4.0 tons, this being two-thirds of 6.0 tons, the coefficient is reduced in same proportion, — viz., to 185 = 123.33. 55 POTTSVILLE IRON AND STEEL CO., The resistance to bending of a beam of any kind is proportional to the modulus of the section of the beam. If two beams of different forms be subjected to the same loading, that one will be the more economical which, with a given value of the 7 ?iodulus of section, has the smaller sectional area, S. In other words, the greater the ratio R the more economical the beam. For example : looking in the tables on pages 159, 160, we find that a 6" I beam of 5.0 square inches sectional area has a modulus of 9,00, and also that an 8" channel of 4.00 square inches sectional area has a modulus of 9.00. Thus it is seen that, for the same modulus in each case, the 8" channel has 20 per cent, less sectional area than the 6" I beam, and hence weighs 20 per cent, less for a given length ; whence the 8" channel is the more economical shaj^e. Moreover, it is a stiffer shape than the 6" I beam, for, with the same loads and span, that shape has the less deflexion, because its moment of inertia is greater. Thus, for the 6" I beam of 5.0 square inches area, the value of I is 27.0; whilst that for the 8" channel of 4,00 square inches sectional area is 35.25. Hence, if these shapes be protected against lateral deflexion, it would be more economical to use the 8" channel than the 6" I beam, for the weakness of the channel is in its small width of flange, it having only a flange width of whilst the I beam has dgV'- In columns 8 of the tables on pages 159, 160, we have given, for each shape, the values of what Rankine has called q, which is the ratio 2 I T^'s that is, 2 I R h^""hS This shows that for two beams of the same depth, that one is the more economical which has the greater value of the . R ratio or, in other words, that whose value of q is the greater. 156 POTTSVILLE, PENNA., U.S. A. For example : consider shape No. 34 in the list of chan- nels, — viz., the 12" channel of 6.20 square inches sectional area, and the 12" channel of 8.45 square inches sec- tional area. The former has q = 0.281 and R = 21.0 ; the latter has q = 0.25 1 and R = 25.50. Again, the former has 25-50 R 21 _ 1,1 1 R — z= - — = 3. 387 ; and the latter has -7- S 6.2 ' S 8.45 3.002. It is evident, then, that the 12" channel, 6.2 square inches area, has a greater capacity for its weight than the 12" chan- nel, 8.45 square inches area. Thus it appears that the strength of beams does not increase in proportion to their increase of weight. We should then, always use the mini- mum or standard se.ction of a shape, rather than one ob- tained by widening the rolls. Of course, this applies only to shapes subjected to transverse loading. From the values of q given in the tables on pages 159, 160, we can then at once see the relative economy of the shapes. Another very desirable use to which these values of q can be put is as follows ; From the fundamental expression y see (i), page 150 which, for symmetrical shapes, becomes 2 I we get, by substituting for — its equivalent, qh S, M.^fqhS Whence, transposing, M, f qh f ■ qh (19) (20) area of shape for given values of is inversely pro- portional to qh ; that is to say, the greater the value of qh, the less the area of beam required to resist the bending moment with an extreme fibre stress, f. For example : 157 POTTSVILLE IRON AND STEEL CO., I suppose we have given a load of 13 tons uniformly distrib- 13 I A.' 12" uted over a span of 14.0'; then Mp=: ^ ^ = 273 inch-tons bending moment at centre. The extreme - M 273 fibre stress is to be limited to 6.0 tons : then = t o 45.5; whence S = area of beam required f " qh 45-5 qh Now, looking at the table “ On Properties of I Beams,” we find fora 12" I beam, 12,5 square inches, q = 0.310, whence qh = o.3i X 12" = 3,72; and for a lo^" I beam, 13.5 square inches, q = 0.316, whence qh = loj X = 3.32 ; whence for the former, 45*5 S = = 12.20 square inches, 3.72 and for the latter. S = ~ * 3 * 7 ° square inches; that is, using a 12" I beam, we need only 12.2 square inches of area; whilst, if we use a loj" I beam, we require 13.70 square inches of area. It is evident, then, that for ike j sat/ie maxmium mo?nent, and same extretne fibre stresses, that ! beam is the more economical which has the larger value of . By inspection of the tables on pages 159, 160, we see ' that for the standard or minimum roll of I beams, the value of q departs but little from 0.31. For channels, the value j of q for the standard rolls is about 0.28, and for the heavier rolls q is about 0.25. Thus, | I beams, standard rolls, q = o.3I. Channels, minimum rolls, q = 0.28. Channels, maximum rolls, q = o.25. Now, substituting these constants in equation (19), we get Mg = 0.31 fh S, for I beams of standard rolls. Mq=o. 28 fh S, for channels of minimum rolls. M^ = o. 25 fh S, for channels of maximum rolls. 158 POTTSVILLE, PENNA., U. S. A, PROPERTIES OF I BEAMS OF IRON AND STEEL. 1 2 3 1 4 5 6 : ^ i * 1 9 1 10 11 13 13 Neutral axis at centre of shape and perpendicular to web. Neutral axis coincident with web. -S Area of shape, in square in .s 1 a 0 Coefficient for one foot span. 0 Shape No. •2 0 (S Width of flange, ir "0 'o Maximum moment inertia I. Radius of gyration ",F cy "!r Pi 00 0 s \ H cJi ^ a II H Minimum moment inertia J. Radius of gyration I 15 25.0 SI 1 813.0 6.38 0.289 108.0 432.0 563-7 40.84 1.28 2 15 20.0 5 j% Fi 8 694.0 5-89 0.309 92-5 370.0 q 00 33-79 1.30 3 15 15.0 5 M 528.0 5-93 0.313 70.5 282.0 366.6 18.34 1. 10 4 15 1 12.5 4 A TS 430.0 5 . 87 | 0.306 57-0 228.0 296.4 13-13 1.03 5 ' 12 17.0 5 f 367.0 4-65 0.300 61.0 244-0 317-2 24.47 1.20 6 12 12.5 4 l \i 279.0 4.72 0.310 46.25 185.0 240.9 14-50 1.08 7 12 10. 0 4 t 6 Tg: 218.0 4.66 0.303 36.0 144.0 187.2 8.74 0.94 8 10^ 13-5 5 239.0 4 -i 7 | 0.316 45-5 182.0 236.7 17.90 1-15 9 lOj 10.5 4 f i: 176.0 4.08 0.301 33-5 134-0 174-3 9-52 0.95 10 lOj 9.0 4 ^ i m: 151.0 4.12 0.309 29.0 116.0 149.6 7-36 0.90 II 10 10.5 4 t I 5 161.0 ! 3-92 0.307 32.25 129.0 167.7 11.08 1.03 12 10 9.0 48 1 TB, 139-0 3-93 0.310 28.0 III.O 145-6 8.30 0.96 13 9 ' 9.0 48 ! i IIO.O ! 3.50 0.302 24-5 98.0 127.4 8.18 0.95 14 9 1 8.5 4 s /b 107.0 ' 3-54 0.309 24.0 96.0 1.24.2 7.60 0-94 15 9 7.0 4 ! i 83.0 3 - 45 ^ 0.294 18.5 1 74-0 96.2 5-37 0.88 16 8 ' 8.0 4 35 5 77.0 3.10 0.300 1 19.25 77-0 100. 1 6.60 0.91 17 8 6.5 4 fg 69.0 3.26 0.332 17.0 68.0 88.4 ! 5-83 0.95 18 7 6.5 3 t 5 is 48.0 2.72 0.300 1 13-75 55-0 71-5 4.11 1 0.79 19 7 5-5' 31 ^: 43-0 2.80 1 0.320 ! T 2.5 50.0 65-4 3-51 0.80 20 6 5-0 35'5 27.0 2.33 0.301 9-0 36.0 46.8 2.65 0-73 21 6 4.0 3 s S ‘ 24.0 2.44 0.332 8.0 32.0 41.6 2.22 0-74 22 5 4 - 0 , 2l8 L 16.0 1.94 0.301 6.25 25.0 33-3 1-75 0.66 23 5 30 2s tIt: 12.0 2.00 0.320 4-8 19.2 25.0 1-39 0.68 24 ^ 1 3-0 2/6i 7.0 1.50 0.281 ■ j 3-5 14,0 18.2 0.82 0.52 25 4 1 2.4 2s 1 TB 5-6 ^•53 0.293 1 2.8 II. 4 14-56 0.58 0.51 26 _4 i 1.8 4-4 1.56; 0.306 2.2 8.8 II. 4 0.40 0.47 j :i 159 POTTSVILLE IRON AND STEEL CO, PROPERTIES OF CHANNEL BEAMS OF IRON AND STEEL. 1 2 3 4 5 6 7 8 9 10 11 12 j .3 14 Neutral axis at centre of shape and Neutral axis 1 perpendicular to web. parallel to web. % Coefficient for CO § 0 one foot span. 0 s-T’ ct ^ % S 3 'S 0 0 ■ -^3 be 0 1^ U >•> b£) ICO 00 1-^ ih li i-| 1 0 0 ! Shape No. 2 0 1 S M 0 3 a 53 . 1 '" s 0 II CVJ 1'^ ! Iron n channel ^ 1 1 c /3 a 1 a''" ;a 0 c /2 3 a ll 3 °'i 5 22.5 5 ?f+ 623.0 5.26 0.246 83.0 332.0 431.6 39-32 1.32 1.25 30 15 17-5 3 527.0 5-48 0.268 70.25 281.0 365.3 31-41 |i -34 1.23 31 15 17-45 411 ^ J .3 497.0 5-34 0.254 66.25 265.0 344-5 23-13 ;i-i 5 1-03 31 15 12.5 3 lf 3 _i 64 396.0 5-63 0.282 52.75 211.0 274-3 17-54 1. 18 1.08 32 12 15-0 ! 3 i xi: 255 -o 4-13 o. 237 | 42-5 170.0 221.0 11-43 0.87 1. 01 32; 12 9.0 3 1 X^6i 181.5 4-49 0.280 30.25 0.255 26.5 121.0 157-3 7.11 0.89 0.84 33 12 8-65 1 013I ^ 1 a 1 159.0 4.28 106.0 137-8 1 4.98 0.76 0.68 33 12 6-4 1%: 133-0 4-56 0.288 22.0 88.0 114-4 1 3-92 0.78 0.70 34 12 8.45 5 ■ 153-0 4-25 0.251 25-5 102.0 132.6 5-04 0.77 0.68 34 12 6.2 2f- 16 125-5 4-50 0.281 ,21.0 84.0 109.2 4.00 0.80 0.71 35 10 12.875 3 i 1X^6 140.0 3-29, I0.217, 28.0 16.5 112.0 145-6 7-79 0.78 0.84 35 10 6.0 2§i 3 > H ' 82.0 3-69 0.272 66.0 85.3 3-73 0.79 0.69 36 10 6.2 2f X^6 80.0 3 - 59 ; 0.258 16.0 64.0 83.2 3-02 0.70 0.61 36 10 4.8 2^ -/b 65.0 13 - 69 ; 0.272 13-0 52.0 67.6 2.40 0.71 0.59 37 9 8.65 3 • 2 3 32 83-0 3-10, 0.237 18.5 74-0 96.2 4-90 0.75 0.74 37 9 5-2 2i 60.0 3-39; 0.284 13-25 53-0 68.9 2.81 0.74! 0.68 38 9 5-42 2t T6 53-5 3-14 0.244; 12.0 48.0 62.4 2.04 0.61 0.54 38 i 9 3-7 2 IB i 42.0 3-38; 0.282; 9-25 37-0 48.1 1-52 0.64 0.55 39 8 7.0 2H X6 51-0 2.70 0.2281 12.75 51.0 66.3 2.85 0.64 0.67 0.63 39 ' 8 4.0 2X6 X6 35-25 2 - 97 , 0 a^ o_ 9-0 36.0 45.8 1.78 0.59 40 8 3-5 2g # 28.25 2-84 0.2531 7-0 28.0 36.7 1. 10 0.56 0.46 40 8 3-0 2X6 -i 25-5 2-92 0.267 6-5 26.0 33-2 1. 00 0.58 0.47 41 7 5-75 2x"6 5 33-5 2-41 0.237 9-5 38.0 49-4 2.29 0.631 0.62 41 7 3-5 2i T6 24.0 2.60 0.276 6.75 27.0 35.1 1-47 0.65; 0.58 7 3-4 2g M 21.0 2.48 O.251I 6.0 24.0 31.2 1.08 0.56 0.48 42' 7 2.5 2 35 17.0 2.62' 0.281; 5-0 20.0 26.0 0.86 0.59 0.50 43 6 5-25 -?3 2s .5 8 23.0 2.09^ 0*243! 7-75 31-0 39-9 2.02 0.62 0.65 43 6 3-0 2 16.25 2-33 0.300 5-5 22.0 28.2 1-14 0.62 0.63 44 6 3-0 T 1 3 ^16 X6 14-5 2.21 0.271 4-75 19.0 24-7 0.80; 0.51 0.52 44 6 2.25 1x6 3 X6 12.25 2.33 0.302 4-0 16.0 20.8 0.61 0.52 0.52 45 5 3-9 2^ 5 12.5 1-79 0.256 5-0 20.0 26.0 ^• 37 i 0.59 0.63 45 5 2.6 t 7 Ig i 9-5 1 - 93 , 1-77 0.300 3-75 15.0 19-5 0.87; 0.58 0.61 46 5 2-675 1 I 13. ^16 8.5 0.252 3-4 13-6 17-7 0.62, 0.48 0.46 46 5 1.70 i if X6 6.25 1-92 1 0.295 2-5 10. 0 13-0 0.41 0.49 0.46 47 4 3-15 2t’6 16 7-0 1-47 0.272 3-5 14.0 18.2 1-14 o.6oj 0.68 47 4 2-4 1| i 5-75 1-55 0.300 2-9 II. 6 15.08 0.83^ 0-59 0.67 48 4 2.25 Ifg -g 4-7 1-44: 0.261 2 - 35 ' 9-4 12.22 0.56; 0.50 0-49 48 4 1-5 Ig xb 3-65 i.56j0.304 .,s.| 7-3 9-5 0.38', 1 o- 5 oj 0.50 i6o POTTSVILLE, PENNA., U. S. A. CONCENTRATED LOADING. If there be a concentrated load P on a span 1 , and divid- ing the span into two segments, x and 1 — x ; then x being the distance from the left support say, 1 — x is the distance of P from the right support. The reaction at left support is, then, -r •P'-t and the bending moment is a maximum under the load, and is P t(i-x)x = -j-(1x_x^) (■) For a uniformly distributed load of W on the same span 1 , the maximum bending moment is at the centre, and is given \V 1 . P / \ by — . Equating this with ^ ( lx — x^j , we get whence W = 8p{t-4} 0) If the concentrated load be at the centre of the span, x = ^, and, substituting this value of x in (2), we get W=2P ^ (3) Equation (2) gives the equivalent uniformly distributed load W, whose centre bending moment is equal to the maximum moment caused by the load P distant x from left support. Equation (3) shows that the uniformly distributed load W will cause the same bending moment at centre as the load W P concentrated at the centre ot span. In other 61 I POTTSVILLE IRON AND STEEL CO., words, if a beam of span 1 sustain, with a given fibre stress, a load, P, concentrated at the centre, it will also sustain, with the same fibre stress, a uniformly distributed load, W, equal to 2 P, — i.e., double the load if uniformly distributed. Example. Suppose a load of 8 tons to be concentrated at a point 12 feet from the left support of an i8 feet span. The reaction at the left support = -|- A — x\ = jg — 12^ = — — = 2§ tons. The maximum bending moment is under the load of 8 tons, and is — x^^ “ Yg ^ 12 2 X = 32 foot-tons. From equation (2) we find = 64 X ~ 14-22 Ions. If the fibre stress is to be 4.15 tons per square inch, and the metal to be of iron, then, as iron beams in Tables of Capacity are figured for 6.0 tons extreme fibre stress, we should look in them for a beam of 18' span, which has a capacity of — ^ — X 14-22 = 20.56 tons. Looking opposite 4-15 18' spans, we find that a 15" I beam of iron, shape No. 2, 200 pounds per yard, will carry 20.55 tons. This, then, k the beam which will carry a load of 8 tons situated 12' from the left support of an 18' span, the fibre stress being 4. 1 5 tons per square inch. These results could also be obtained in the following way : The maximum bending moment for the concentrated load of 8 tons, 12 feet distant from the left support of an 18' span, is 32 foot-tons = 384 inch-tons. Now, M^=f.-^ = fR M whence R == 162 POTTSVILLE, PENNA., U. S. A. Now. if f be taken 4.15 Ions per square inch, then 3^4 R 4-15 92.53 Looking in table of “ Properties of I Beams,” we find that for R = 92.50, the beam is 15" I, 200 pounds per yard. This beam, then, will do. If the concentrated load of 8 tons be at the centre of an 18 feet span, the maximum bending moment is under the PI 8 X 18 load, and is = = 3 ^ foot-tons. The ‘‘ equiva- 4 4 lent” uniformly distributed load is2P = 2X8 = i6 tons, , IT .16X18 . - , whose bending moment is = 36 foot-tons, the same O as above. Thus, a beam which will carry 16 tons uniformly distributed, will also carry, at the same fibre stress, a load of 8 tons concentrated at the centre of the span. If the fibre stress is to be 4^ tons, then, in the Tables of Capacity, we must look for an iron beam which has a tabular capacity of —r X 16= 22.61 tons at 18' span. For 18' span in the 4 i tables, we find that a 15" I beam of iron, 250 pounds per yard, will carry 24.00 tons, which is rather more than we need. To find the exact weight of a 15" I beam which will answer our purpose, use the equation = f qh S ; whence S f qh Now = 36 foot-tons = 432 inch-tons. f = 4]- tons, the required extreme fibre stress, h = 15". q =0.309 for 15" i beam, 200 pounds per yard, from table of “ Properties of I Beams.” Then S = required area : 432 , ^ ^ ^ - = 22. oosquare inches ; 41X0.309X15 ^ whence we need a 15" iron I beam, 220 pounds per yard. 63 POTTSVILLE IRON AND STEEL CO., If the required fibre stress had been the same as in the tables, — viz., 6.0 tons for iron, — we would have found that, 1 for the given span of 1 8 feet, the capacity of a 15" I beam ^ of iron, 150 pounds per yard, was 15.66 tons, which is rather ■ less than the l6 tons uniformly distributed load for which \ we were seeking, and using the same method as before, — i viz., the equation Mq= f qh S, — we would have j M 422 i S = V — ^ = 7 — — = 15-33 square inches ; ! f qh 6.0X0.313X15 ^ z.e., we require a 15" I beam of iron, 153!^ pounds per yard. The centre deflexion for a beam under a uniformly dis- . tributed load, W, is f of that for the same load concentrated at the centre of the span. Inversely, the deflexion for a beam under a concentrated load, P, at centre of span is 1.6 times that for the same load uniformly distributed over the span. As in using the tabular loads to find the beam which will carry a centre concentrated load, we double the concen- trated load, and seek for a beam to carry such load ; then, to find the deflexion for the concentrated load, we must take = 0.8 of the tabular deflexion. 2 Another example. Having given a beam of certain kind, weight, and span, to find what load concentrated at a point X from the left support it can safely carry. Suppose we have a 12" iron I beam, 125 pounds per yard, on a span of 15 feet. From Tables of Capacity, we find it will carry 12,33 tons, uniformly distributed, the fibre stress being 6,0 tons. Now, what load concentrated at a point distant 4.0' from the left support will it carry, the fibre stress being the same ? From W 1 “ 8 “ we get P W F 8 (lx — x2) 12.33 X 15 X 15 8 (15 X 4 -16) 7.88 tons ; that is, a concentrated load of 7.88 tons, 4 feet from one end, will be carried by the 12" iron I beam, 125 pounds per yard, with the same extreme fibre stress as is produced by 12.33 tons uniformly distributed over the span. 164 r POTTSVILLE, PENNA., U. S. A. [Written for “ Engineering News,” in 1884, by J. C. Bland, C.E.] A Method of Computing the Absolute Maximum Bending Moment on Stringers, due to the Passage across them of a Series of Concentrated Moving Loads. From an analytical consideration of the effects produced on the stringers of railway bridges by the passage across them of a series of concentrated weights, such as the wheels of a locomotive, the following principles are found to flow : 1. That the maximum bending moment always occurs U7ider a load, 2. That the maximum bending moment occurs under one or the other of the two loads, between which the resultant of the total number of loads considered passes. 3. That if the resultant of the total number of loads considered passes through a load, the maximum bending moment occurs under that load. 4. Calling the load under which the maximum bending moment occurs the cintical load, and x its distance from the left support, then, when the critical load is in the position causing the maximum bending moment, its distance from the left support is less than the half span, if the resultant of the total number of loads considered lies to the right of the critical load; and greater than the half span, if the re- sultant lies to the left. 5 . Calling Z the distance from the resultant of the total number of loads considered to the load on the right, and A the distance apart of the two loads between which the re- sultant passes, the distance of the load on the left from such resultant is A — Z. mu 1 , Z 1 A — Z 1 hen X = h , or X = 2 ' 2 ’ 2 2 according as the critical load is on the right or the left of such resultant. 165 POTTSVILLE IRON AND STEEL CO., 6 . Then when the critical load is in the position causing ! the maximum bending moment, the centre of the span divides equally the distance between the resultant and the critical load, or, in other words, the critical load and the resultant of the total number of loads considered are sym- metrically placed with reference to the centre of the span. 7 . That the expression for the maximum bending moment can always be put in one or the other of the two forms. («) If the critical load lies to the right of the resultant of the total number of loads considered. M. 2 . P 4 t' T 2 . Pd ^Tp" )] (0 {l)) If the critical load lies to the left of the resultant of the total number of loads considered. M O 2 . P 4 1 (2) where 2 . P =: number of loads on span, expressed in terms of the load on each pair of drivers. For example, if there are loads on the span of less amount than those on the drivers, express them in terms of the driver load. Thus the four pairs of drivers and the first pair of tender wheels, being on the span, express the tender wheel load as a P, whence the total number of loads, 2.P = 4 P-f-aP = ( 4 -f-a) P. Let 1 = span. Z = as already defined in 5 . A — Z = as already defined in 5 . 2 . Pd = sum of the moments of loads on span around the critical load as origin, no regard being had as to sign ; that is, no regard being had to the sense of the moments. 8 . That the expression for Z and for A — Z can always be put in the form 2b Pd 2 . P where 2b Pd = summation of the moments of loads on the 166 POTTSVILLE, PENNA., U. S. A. span around the critical load as origin, regard being had to sign ; that is, regard being had to the sense of the moments. 9, Whence the maximum bending moment is always given by the following general expression : which can be used instead of equations (i) and (2). 10. That is, the cases where the resultant of the total number of loads considered passes between two of the loads, the maximum bending occurring under one or the other of these two loads, then in whichever of the expressions for Mq, considering first one and then the other as the critical load, the term is the greater, that one gives the absolute maximum bending moment due to the passage of number of loads considered across the span. For example: consider the “Erie"’ consolidation engine, in the case where five loads are on the span, — viz., the four drivers and the first pair of tender wheels. Where Pj= P2 =: P^, hence call P . = ii.o tons. Pj= 7.26 tons = a P; whence “ = tt¥o = 0-66 d = 4.5 feet, d| = 5.75 feet, dj = 7.083 feet. 167 9 POTTSVILLE IRON AND STEEL CO., From these values it is found that the line of action of the resultant of these loads passes between Pg and Pg; whence by 2, the maximum bending moment will occur under the loads Pg or Pg. Let us first consider Pg as the critical \o2idi, and apply our equation (4). Then 2.P = 4P + aP = (4 + a)P. = 4.66 P . Taking moments of loads around Pg as an origin, we have on the right of Pg, now counting moments whose tendency is opposite to the hands of a watch as positive, and those whose tendency is same as the hands of a watch as negative, then the moments on the left of Pg are positive, and those on the right of Pg are negative ; whence also, as 2 . Pd is sum of moments without regard to the sign, M^e have P4 d -j- P5 (d -f dg) — P I d -|- a (d -j- dg) | on the left of Pg, p, d + Pj(d + cy = p|2d + ci,} 2h Pd P Then 2 . Pd = p|2d + d 4 +d + a (d + dg)| = P I 3 d -f ^1 + ® (d + ^3) I 2i.Pd_d + di — a (d +dg) 2 . P 4 + a and 168 POTTSVILLE, PENNA., U. S. A. Substituting these values in equation (4), we get M. 4 -f- « -[ d + dj — a (d dg; 4 -[- a 3 - j- dj -I- g (d -f- clg 4 + ® ']} Inserting in the above the values given for the distances | between loads, etc., we get -2 M. 4.66 Xii.o|l + ^^— 11.543I = 12.815 |l + :^—ii,543| . o 1 , 4-005 = 12.8151 + — 147.923 Now, suppose our span is 30 feet; then lV+= 12.815 X 30 + — 147.923 = 236.66 foot-tons. Let us now take another case at random, say the three pairs of drivers, Pj, P2, Pg. The distance dj being gener- ally greater than d, and the driver loads alike, it is evident the line of action of the resultant will pass between the loads Pj and P2. It is the case in the “ Erie” engine we are considering for illustrations. Let us take Pg as the critical load ; then 2 .P =3P. 2i.Pd = P (dj — d). 2 . Pd =P (dj+ d). Whence and 21 . Pd _ dj — d 169 POTTSVILLE IRON AND STEEL CO. whence M = 3 P Inserting the values given for the load, P, and the dis- tances, d and dj, we get 3X + 6.833} = 8.251 + ^:^ — 56,375 Now, suppose the span is 15 feet ; then Mo =8.25 X 15 + ~ 56-375 =67.47 foot-tons. If we had chosen the three driver loads, P2, P3, P^, we see that the resultant passes through the load Pg, since the other two loads are equally distant, d, from it ; whence the critical load is Pg. Here, then, 2 . P == 3 P. 21 . Pd = P (d — d) =: O. 2 . Pd = P (d + d) = 2 Pd. ,,,, 21 . Pd . / 2 . Pd\ 4 , Whence - ^ ^ = o and 2 ^ - p -j ~ ^ ^ whence Inserting the values for P and d, we get M„ = X^{l-6 Now, suppose the span to be 15 feet; then Mo = 8.25 X 15 — 49-5 = 74.25 In passing, we might notice that this choice of loads gives a greater result than the loads P^, Pg, Pg. 8.25 1—49-5 70 POTTSVILLE, PENNA., U. S. A. Let us now take the four drivers, Pj, P2, P3, P^. It is readily seen that in usual cases the resultant of the four loads pass between the loads P2 and Pg. Let us take the load Pg as the critical load; then we have 2 . P = 4 P. 2 L Pd = P (d + d + d^) — Pd = P (d + dj). 2 . Pd =P (d + d + d,) + Pd = P (3 d + d,). Whence 21 . Pd _ d + d 2 . P ~ 4 whence M = 3 cl + cl, Inserting the values of P, d and d, for the “ Erie” engine, we get >.566 ^ ] “j 9-625 y = II 1 + 7^^ — 105.875 Mo=ii + Suppose the span to be 21 feet; then II X 21 + — 105.875 = 128.56 foot-tons. Let us now take Pg as the critical load. We then get 21 . Pd = Pd, — P (d + 2 d) = — P (3 d — d,) and 2 . Pd = Pd, + P (d + 2 d) = P (3 d + d,) whence 21 . Pd 2 . P 3 d — d, , / 2 . Pd 1 and 2 3 d + d. 171 POTTSVILLE IRON AND STEEL CO. Now ■ Pd y ^ 3d — ^ ^ 3d-d, y whence Inserting the values of P, d and dj for the “ Erie” engine, we get It is noticed that this result is less than that given by choosing P3 as the critical load. Sufficient illustrations have been given to show how easy of application is the general expression (4), When any number of loads are considered, the two loads between which the resultant passes can generally be deter- mined by inspection, — if not easily seen, the determination is readily found. Then apply the expression (4), first con- sidering the load on one side, then the load on the other side of the resultant as the critical load. Whichever gives the greater value of M^, is the expression to use in com- puting the bending moments for that number of loads within the limits of span, both superior and inferior. Considering any particular engine, a table can be calculated showing the bending moments and limits of span for one, two, three, four, five, etc., loads in succession. Computing for a 21 feet span, we get II X 21 + 105.875 = 127.09 foot-tons. 172 POTTSVILLE, PENNA., U. S. A. ON THE USE OF THE TABLES OF CAPACITY. In the table showing the reduction of extreme fibre stresses due to ratio of flange length to flange width, we notice that for fifty ratios the extreme fibre stress for steel shapes is reduced to 6.07 tons per square inch, which is very nearly that for which the capacity of the iron shapes has been calculated. If, then, when we find that the tabular safe load of an iron shape would fulfil the requirements, but, by reason of the beam being zmstayed, we have to reduce its load to 77 per cent, of its tabular capacity, we can substitute the steel shape of the same sectional area, and all our requirements are satisfied. For example: Take a 15” iron I beam, 150 pounds per yard, at 21' span. Its tabular capacity is 13.43 tons; but 21 ^ 'yl 1 2 ’^ its ratio of length to flange width = = 50.4; whence its fibre stress should be 4.64 tons, instead of 6.0 tons, and hence it will carry but 0.773 of its tabular capacity, — viz., only 0.773 X 13-43 = tO-38 tons. Now, looking at the same shape in steel, we see its tabular capacity is 17.46 tons, and the ratio of its unstayed length to flange width being as before, the reduced safe load will be 0.773 X i 7 - 4 ^ = 13.50 tons. Thus it is seen that the steel I beam, which has 15.0 square inches sectional area, will carry, when imstayed its full length of 21.0 feet, the same load which the iron I beam of same sectional area would carry if stayed, so that POTTSVILLE IRON AND STEEL CO., its unsupported length of flange was no greater than 30 times its flange width. The limit to the 15" iron I beam, in order to use the tabular loads, would be 30 X 5 " = — i.e., in order to use a fibre stress of 6.0 tons per square inch ; and the steel I beam, unstayed for its full length, could be used at the same extreme fibre stress of 6.0 tons. These facts are of use in designing the floor joist of a building, for frequently, by simply substituting steel shapes I of same sectional areas as the iron ones, and which weigh only a little more per foot, we can do away with the neces- sity of some method of staying the flanges, or of having to use much heavier beams of iron. It is also to be remembered that steel beams and channels cost no more per pound than iron ones; whence any saving in weight by the use of steel shapes is a like saving in cost. Suppose the area of a floor surface to be 20' X 28', and we desire to find the beam requisite to carry a total loading I of 200 pounds per square foot. We would, of course, place the beams with their length in smaller dimension of the floor area ; then the span centre to centre of the beams will be about 21 feet. Suppose, also, that by reason of using brick arches between the beams to carry the external floor load the distance apart of the beams is limited to 5'.o". Examining our Tables of Capacity of Iron I Beams, we find that a 12" I beam, 125 pounds per yard, shape No. 6, might answer; as for 2I feet span, and 200 pounds per square foot, the distance apart should not be greater than 4.19 feet. But the flange width is , and the ratio of 21 feet to flange width is 52 ; whence this exceeding the ratio 30, the extreme fibre stress must be reduced from the tab- ular amount — viz., 6.0 tons — to about 4.5 tons; in other words, the safe load from 8.81 tons — the tabular safe load — to 0.75 X 8.81 =6.61 tons, and likewise the distance apart will be now 0.75 \ yig = 3.14 feet. Now, this distance will be too close for the beams, so we should have to select another shape. Looking at span 21 feet under 12" iron I beam, 170 pounds, shape No. 4, we find that for 200 pounds per square foot, the spacing may be 5.53 feet. The ratio of length to 174 POTTSVILLE, PENNA., U. S. A. 21 ^ 12 flange width is — = 47; whence the distance 5.53 5t should be reduced to about 0.8 X 5-53 = 4-42 feet. We might make six spaces of 4'. 8" in the 28 feet length of floor, and hence would require five 12" I beams of iron, 170 pounds per yard, 21 ',6" long each, weighing 4 n all 6090 pounds. Now, looking at a steel 12" I beam of 126^- pounds per yard (12.50 square inches area), we find that for 21 feet span, under the tabular loads, it may be spaced 5.46 feet. But the ratio of length of beam to flange width being 21 X 12 /ill" 4t6 54, the distance can only be 0.74 X 5.46 = 4.04 feet. Making seven spaces in the 28,0 feet, of 4'.02" each, we require 6 steel I beams, 126J pounds per yard, 21 '.6" long each, weighing in all 5430 pounds. Thus, even with one more beam, by using the steel, we save a weight of 660 pounds, or about ii per cent.; and this is also a saving in cost of II per cent., because steel beams and channels cost no more per pound than do iron ones. Suppose we have a floor area 18' X 32', and a total floor load of 200 pounds per square foot, and that we wish to make 4.0 feet spaces between centres of beams. Placing the beams in short way of floor area, they will be 19 feet span centre to centre of bearings; and in 32 feet of length we will have eight spaces of 4 feet each, or require 7 beams, say 19.J feet long each. Assuming the flange width about 4^" = f of a foot, if beams are unstayed laterally, the ratio of unstayed flange to flange width will be l8 -f- f =48; whence, by looking at Table of Reduction of Fibre .Stresses and Tabular Loads, we see that tabular capacity will have to be multiplied by about 0.8, and tabular spacing also by 0.8; whence, in order to use the Tables of Capacity, if we divide the required spacing by 0.8, it will give us a spacing which, if we find the cor- responding beams in the tables, they will fulfil our condi- tions. Thus, = 5.00 feet. 0.8 Now, looking in Tables of i ! 75 POTTSVILLE IRON AND STEEL CO., Iron I Beams, at 19 feet spans, we find, under column of 200 pounds per square foot, that a 10^ I beam of iron, 135 pounds per yard, will carry 9.58 tons, and be spaced 5.02 feet apart. Now, flange width of loj I, 135 pounds, is 5"; whence ratio of unstayed length to flange width is IQ 12 = 46 ; then tabular safe load and tabular spacing will have to be multiplied by about .81. Thus, tabular load X 0.81 = 9.58 X 0.81 = 7.75 tons; and tabular spacing X 0.81 = 5.02' X = 4-o6 feet; that is, we can use lOj" I beams of iron, and spacing them 4.0 feet apart will compensate for the reduction of capacity due to beams being unstayed. We found the reduced safe load to be for this beam 7.75 tons, and this will be seen to be right, for the load to be carried is 19' X 4^ apart X 200 pounds per square foot — 15,200 pounds = 7,60 tons ; whence weight is 7 — io|" I beams (iron), 135 pounds per yard, 19^' long = 6142 pounds. To see what steel beam will satisfy the conditions. The spacing which we wish to use is 4.0 feet, and in Tables of Steel I Beams we And for a 19 feet span and 200 pounds per square foot of load, that the spacing is 4.14 feet, and load carried 7.87 tons, but, bearing in mind the reduction of strength by reason of beams not being stayed, we should look in the steel tables for a beam which will have a spacing under the 200 pounds column of = 5.0', and a load of 7.60 ^ g = 9.50 tons. The nearest to this is a io|" I beam of steel, 106 pounds per yard, shape No. 9, 9.18 tons safe load, and 4.83 feet spacing. It is evident that a little increase of section in this beam would add enough to strength so as to make it answer our purpose. To find what weight of this shape we would need, we have from Table of Properties of I Beams, 9 = 0.301, say 0.30, and using equation (20), page 157, we have S Mq f qh 76 POTTSVILLE, PENNA., U. S. A. I Now Mq W1 “F” 7.60 X 19X12 8 216.6 inch-tons. f = 0.80 X 7-8 = 6.04 tons per square inch, q =0.30. h = io|". Then area required = S 216.6 6.04 X 0.3 X 10^ 216.6 19-03 11.38 square inches. Or a 10 I beam [steel) of shape No. 9, and weighing 115 pounds per yard (11.38 square inches area). Now from (18), page 156, R=rqh S==o .3 X lo^X 11.38 = 35-85 whence safe load for steel beams (see equation (ll), page 152) is W 5.2 R r 5-2 X 35-85 19 9.81 tons, ; and reducing this by multiplying by 0.8, we get 9.81 X 0.8 = 7.85 tons as the safe load, when beam is wtstayed in its j length of 19 feet. I Then for the weight of the steel beams, 7 beams, io|" I I steel, 1 15 pounds per yard, igl feet long = 5232 pounds. Now loj" I iron beams, 135 pounds per yard, weighed for the 7 of 19.} feet each, 6142 pounds; whence a saving of 910 pounds in the floor joist, or almost 15 per cent., like- wise a saving of 15 per cent, in cost. I i 1 78 POTTSVILLE, PENNA., U. S. A. ON PLATE GIRDERS 179 POTTSVILLE IRON AND STEEL CO., 'i ;!! '^i i8o POTTSVILLE, PENNA., U. S. A. PLATE GIRDERS. Let 1 = h = w a F. Fo f = Pc = □c" = □t II span, centre to centre of end bearings. height of girder, centre ■ to centre of gravity of flanges. Both in same linear units. load per linear unit of span, reaction at left abutment, a. reaction at right abutment, a^. shear at section distant x from left abutment, shear at end of girder = maximum shear, bending moment at section distant x from left abutment. flange stress at section distant x from left abutment. allowable stress per square inch in compres- sion. 1 + 5000 reduced compression unit, due to length of unstayed portion of upper flange as regards its width, allowable stress per square inch in tension, allowable shearing stress per square inch on the web plates. allowable shearing stress per square inch on rivets. allowable bearing stress per square inch on rivets. — ^ = gross sectional area required in upper flange at centre of span. = nett sectional area required in lower tjh flange at centre of span. 81 1 POTTSVILLE IRON AND STEEL CO., The bending moment, at a section distant x from the left abutment, is the algebraic swn of the moments around X, of all the external forces acting between the left abut- ment and the section x. The shear, at a section distant x from the left abut- ment, is the algebraic sum of all the external forces acting between the left abutment and the section x. Plate girder under a uniformly distributed load, w, per linear unit. (1) (2) (3) F(x-hp) = w(x + p) =w|^ — (x + I (4) The shear at any point x is the differential coefficient of the bending moment at the point x, and equations (2) and (4) could be derived directly from (i) and (3). Thus, and = 4-w(x + p) (6) TVT Wl M — X WX2 wx / 2 2 2 \ F, = — - wx = w (1- 2 \ 2 (>-x) also M wl (x-Hp) ^ (.+p)_w^ 182 POTTSVILLE, PENNA., U. S. A. Now, flange stress at point x is and flange stress at point x -j- p is + _w(x + p)/ \ h “ V V (7) ( 8 ) The difference of these flange stresses is the stress on the rivets in the distance p, — i.e., M (x + p) pi 2 px Wp I , But shear at the section distant ment is F — P"| {^-(- + 4)} I (- + I) (9) from left abut- whence equation (9) could be written M(x + p) M TT D JB. (10) that is, the stress on the rivets in the distance p, is the shear at the middle of the distance p, multiplied by the ratio of the distance p to the height h. Or, if the distance p be the pitch of the rivets, the stress on the rivet is the shear at that rivet multiplied by the pitch and divided by height of girder. Thus, generally, calling a the stress on a rivet distant x from the abutment, Fx-P (”) i.e., stress on rivet at section x is the shear at x multiplied by the pitch and divided by height of girder. '83 POTTSVILLE IRON AND STEEL CO., From (ii) we get h a ( 12 ) that is, the pitch of the rivet at any section x is the allow- able stress on the rivet multiplied by the height of girder and divided by the shear at the rivet. If we take the stress on the rivets in a distance, h, equal to the height of the girder, and say n the number of rivets in such distance ; then that is, the number of rivets in the distance h, multiplied by the mean stress on each rivet, is the shear at a point distant from the abutment. If, in (13), we make x — o, then the stress on the rivets in the distance from the abutment to the section h — that is, in a distance from end of girder equal to height — is In other words, ^ wl 2 (14) wl wh Now, — ^ is the flange stress at the point h ; whence M, (15) i.e., the entire flange stress at a point whose distance from the abutment is equal to the depth of girder, must be con- veyed to the flange angles by means of the rivets which connect the flange angles to the web. But we must bear in mind that from o to h the flange stress increases from o to and if we proportioned the number of rivets by (14) and (15), a would be the meatt stress on the rivets in the distance h; we should, however. 184 POTTSVILLE, PENNA., U.S. A, determine the number from the maximum stress in the dis- tance h, — that is to say, in (14) make h = o, and then wl n a = — In other words, the number of rivets required in a distance from end supports equal to depth of the girder is (16) where is the end shear, which is equal to the reaction, and a the allowable stress on the rivet. If we divide both members of the above equation by h, the height in feet, then number of rivets per foot h a shear per foot. divided by allowable stress on the rivet. Now, considering the connexion of the two flange angles to the web sheet, the rivet may be sheared out between the angles, or it may crush the bearing on the web sheet. The stress on the rivet must then not exceed its shearing value nor its bearing value. The rivet being in double shear, — i.e., there being two shearing areas, one on each side of the web, — its shearing value is 2 fj.ga, where f^.^ is the allowable shearing stress per square inch on rivets, and a the area of the rivet. The rivet having a bearing on the web sheet of dt, where d is the diameter of the rivet, and t the thickness of the web, its bearing value is being the allow- able bearing stress per square inch; whence a must not exceed 2 nor f,.bdt, — i.e., Fx.P — 2 f„a, and frb-dt whence for shearing, F . p area of rivet, a = 2 f„h and for bearing, F . D thickness of plate, t — , ^ , (18) f,b • hd 185 POTTSVILLE IRON AND STEEL CO., TABLE OF SHEARING VALUE OF RIVETS For allowable units of from 3.0 to 4.0 tons per square inch. Diam. Area Value of rivets in single shear at the following allowable shearing units = fj-g of of rivet, rivet, d. 3.0 tons 3.25 tons 3.50 tons 3.75 tons 4.0 tons 4.5 tons per per per per per per spare in. square in. square in. square in. square in. square in. 0.1963 0.59 0.64 0.69 0.74 0.79 0.88 9 // lU 0.2485 0.74 0.81 0.87 0-93 0.99 1. 12 5// 0.3068 0.92 1. 00 1.07 I-I 5 1.23 1.38 \r 0.3712 I. II 1. 21 1.30 1.39 1.48 1.67 r 0.4417 1-33 1.44 1-54 1.66 1.77 1.99 13// 1 (i 0.5185 1.56 1.69 1.81 1.94 2.07 2-33 7 // S 0.6013 1.80 1-95 2.10 2.25 2.40 2.70 l" 0.6903 2.07 2.24 2.42 2.59 2.76 3.16 0.7854 2.36 2-55 2.75 2.94 3 -H 3-53 ^tV' 0.8866 2.66 2.88 3.10 3-32 3-55 3-99 Ig 0.9940 2.98 3-23. 3-48 3-73 3-98 4-47 TABLE OF BEARING VALUE OF RIVETS For allowable units of 6.0, 7.5, and 9.0 tons per square inch. Bearing value for different thicknesses of plates = ^5 X d X t. Thickness of plate, t. Bearing unit frb= 6.0 tons. Bearing unit frb= 7.5 tons. Bearing unit frb= 9.0 tons. Diameter of rivet, d. Diameter of rivet, d. Diameter of rivet, d. Iff 4 0.75 0.94 1-13 1-31 0.94 1. 17 1. 41 1.65 I-I 3 1. 41 1.69 1.96 T%" 0.94 1. 17 1. 41 1.64 1. 17 1.46 1.76 2.05 1.41 1.76 2. II 2.46 1" 1-13 1. 41 1.69 1.97 1. 41 1.76 2. II 2.46 1.69 2. II 2.53 2.95 7 ff 1-31 1.64 1.97 2.30 1.64 2.05 2.46 2.87 1.97 2.46 2.95 3-44 1.50 1.88 2.25 2.63 1.88 2-34 2.81 3.28 2.25 2.81 3-38 3-94 1.69 2. II 2.53 2-95 2. II 2.64 3.16 3-69 2.53 3.16 3.80 4-43 5 // 8 1.88 2.34 2.81 3.28 2.34 2-93 3-52 4.10 2.81 3-52 4.22 4.92 W' 2.06 2.58 3-09 3.61 2.58 3.22 3-87 4-51 3-°9 3-87 4.64 5-41 r 2.25 2.81 3-38 3-94 2.81 3-52 4.22 4.92 3-38 4.22 5.06 5-90 186 POTTSVILLE, PENNA., U. S. A. The thickness of web of a girder is generally limited to f of an inch for practical reasons ; and, besides filling the . maximum shear . , . , , condition , it- must also resist the tendency to buckling ; that is, the unit stress on the web should be determined by Pps 5.00 tons (19) The girder should be divided into panels by the use of stiffening angle iron on the web sheet, and the length of such panels should generally be about the depth of the girder, unless the girder be quite shallow, in which case the .panels may be about one and one-half times the depth. In equation (19) it is allowable to consider h as the ver- tical distance m the clear between the angle iron flanges. The permissible unit stresses on plate girders are deter- mined from the following relations, where 0 denotes the ratio of the minimum stress to the maximum stress. . X t Compressive unit stress, f^ = if tons (2 -[- 0). (a) Tensile unit stress, f^= 2 tons (2 -j- (j)). (< 5 ) Shearing stress on web plate, fp^ == if tons (2 -|- ^). [c) Shearing stress on rivets, frg= i^} tons (2 -j- (f). [d) Bearing stress on rivets, frb= 3 tons (2 4 - ^). (e) In plate girders under uniformly distributed loads the stresses are in same ratios as the loads, and ^ may then denote the ratio of the dead load to the total load. : In plate girders used in buildings and warehouses the j loads are all dead, and then (p becomes unity, and the above 1 permissible unit stresses become | f^, = 5-00 tons per square inch on gross area. I fj. = 6.00 tons per square inch on nett area. < fpg= 5.00 tons per square inch on nett area. j = 4.50 tons per square inch on rivet area, fjjj = 9.00 tons per square inch on bearing area of rivet. 187 POTTSVILLE IRON AND STEEL CO., Taking as a unit of comparison, the expressions (^a), (c), (d), (^e) are in the following ratios: fc = I ff fps=fc=fff frs = I ff frb = 2f,3=I^-f^. And, taking f^ as a unit of comparison, we get ft =|fc- fps=fc- frs == 0-9 fc- L 2 C=I.8f EXAMPLE I. SINGLE-WEBBED PLATE GIRDER. Suppose we have a girder 32' o" long, centre to centre of end bearings, and it is required to carry 128 tons uni- formly distributed over its length. Dividing the span into eight panels of 4' o" each ; at each panel point we will use a pair of angle iron stiffeners, one on each side of the web. We will make the girder 40" deep out to out of flange angles, which will be the effective depth in this case, as when the flange plates are considered, the 40" will be about the dis- tance centres of gravity of the flange areas. Our unit stresses are f^ = 5.00 tons; f^. =: 6.00 tons; fp^ = 5.0 tons ; f^g = 4.50 tons ; f^t, = 9-0 tons ; and using 14" flange plates, the ratio of length to width of flange (sup- posing the flange tmstayed in its length) will be 32 -j- = 27.43, whence compressive unit stress f^ is reduced to 5.00 5.00 Pc 7^—; T-, = = 4-35 tons. 1 + 5000 (2743) [.150 This will be the maximum permissible unit stress on the upper flange. 188 POTTSVILLE, PENNA., U. S. A. We then have given 1 = span centre to centre of end bearings = 32 feet, h = effective height =: 40" = 3^ feet, w = load per linear foot = — 4.0 tons. Then bending moment at any point x from left abutment is given by — = Yx (32 — x) = 2.0^32 x — x2^ For bending moment at centre of span we have X = — in the equation ^1 — x^ i.e., wF 4.0 X X M = — ^ ^ =512 ft. -tons = 6144 in, -tons. 0 0 Whence flange stress at centre of span is M. 6144 . = = 153.60 tons. h 40 The flange section required at centre of span to resist compression is 6144 . , Y = jr = 35-31 square inches gross. Pch 4.35 X 40" i ^ The flange section required at centre of span to resist tension is M. 6144 ^ ^ rt = -? — 77 = 25.60 square inches nett. fjh 6.0 X 40 For compression flange — i.e., for upper flange — use Sq. in. 2 angle irons, 6" X X 4^ pounds per yard = 9.60 5 flange plates, 14" X 1” = 26.25 Total gross section used in upper flange = 35-^5 189 POTTSVILLE IRON AND STEEL CO., For tension flange — i.e., the lower flange — use 2 angles, 6" X X 4^ pounds per ’ yard = 9,60 Deduct 4 holes, i" diameter X ¥' = 2.00 = 7.60 4 plates, 14 X f = 21.00 Deduct 4 (2 holes, i" X I") = 3-00 = 18.00 Total nett section used in lower flange = 25.61 In deducting for rivet holes in the tension flange to get the neU area, the rivet holes are taken larger than diam- eter of the rivet. In above we have assumed rivets; whence holes are taken i" diameter. Having now determined the sections to be used at the centre of span, the next step is to find where the several flange plates begin and end, — i.e., the lengths of the various flange plates. The pair of flange angles and the first flange plate (the first flange plate is the one next the flange angles) extend from end to end of girder, and the other flange plates should extend about two rivet pitches beyond the points where they should stop theoretically. In order to determine these points, we take the general equation for the section required at any point distant x from left abutment, — viz.. Pch 2 p^h 32 X — x^ 7-25 _ 4.0X (32 — x) “ 2 X 4.35 X 3 ^ I 32 X — x2 I i.e., square inches required at any point x of the girder I 32 X — x2 1 where x is taken in feet. Now, to find the 29 point where the second flange should begin, equate the areas of the two flange angles and first flange plate, — viz., 9.60 -f- 5.25 = 14.85 square inches to (32 x — x‘^) ; i.e.. Whence 14.85 (32 X — X2) 32 X 107.66 — o 190 POTTSVILLE, PENNA., U. S. A. i.e., X = i6 ± ■/ 256 — 107,66 = 16 ztV 148.34 = 16 ± 12.18 = 3.82' or 28.18' These are distances which, measured from one end of the effective span, give the two points at which the second flange plate begins and ends; it is, therefore, 24.36 feet long nett. From the above an expression can be deduced which is general, — viz.. where x is the distance in feet from centre of end supports to the point where it is necessary to add another flange plate, and Qj." is the sectional area just at the point x ; w is the load per linear foot of girder; p^ is the unit stress in com- pression ; h is the height in feet. The foregoing is for the compression flange, and p^ is the compressive unit; and hence is the gross sectional area at the point x. To adapt the expression to the tension flange, change p^, to fj, and consider as the nett sectional area at the point X, — i.e., for tension flange, To continue with upper flange. For the point where it is necessary to begin the third flange plate. The area of the two flange angles and the first and second flange plates is 9.60 -|- 5.25 -f 5.25 = 20.10 □" ; i.e., □/= 20.10, and _ 2 X 4-35 X 3.^ _ 29 w 4.0 4 191 POTTSVILLE IRON AND STEEL CO., X = I6 ± V - 1 9X20.10 = i6 dz 1/ 256 — 145.72 = 16 ±2 V 110,28 = 16 ± 10.50 = 5.5' or 26.50' whence third plate is 26.5. — 5.5 = 21.0' long nett. To find the length of the fourth flange plate. The area of the two flange angles and the first, second, third flange plates is 9.60 -h 3 X 5-25 = 25-35 □/ = 25.35; whence x = I6±^j ^ ^ (25.35^ = 16 ± X 256 — 183.78 = 16 zt V 72,22 = 16 dr 8.50 - 7.50' or 24.50' whence fourth flange plate is 24.50 — 7.50 = 17.0' long nett. To find the length of the fifth or last flange plate. The area of the two flange angles and the first four flange plates = 9.60 -j- 4 X 5-25 = 30.60 i.e., = 30.60; whence x=i6dr^/^i6^ —^^30.60^ = 16 dr X 256 — 221.84 = 16 dr X 34.16 = 16 dr 5.84 = 10.16' or 21.84' whence fifth flange plate is 21.84 — 10.16 = 1 1.68' long nett. Conclusion : • First flange plate, 14 X 1 5 length of girder. Second flange plate, 14 X f ? 24.36' long nett, make 25^' long. Third flange plate, 14 X 21.00' long nett, make 22^' long. Fourth flange plate, 14 X s’ i 7 -Oo' long nett, make i8|' long. Fifth flange plate, 14 X I- n.68' long nett, make 13J' long. The above lengths are just abotit the proper lengths; the i 192 POTTSVILLE, PENNA., U. S. A. actual “ bill” length can be determined when we fix on the pitch of the rivets in each panel. Another way to determine the lengths of flange plates is as follows : The centre section required in upper flange is I—, // □c" Transposing, 8p,h PcMDcl 8 w ii)' 2 p,h This is the equation of a parabola, in which we may con- sider 1 and as variables, and calling — = y. 2 p^h where y represents the distance from the centre of span to point corresponding to Q". See diagram, page 194. Similarly, if we are considering the lower or tension flange. To illustrate, as this is an inverse method. The = 35.31 Q". Now, 2 angles and 4 flange plates = 9.60 4 X 5-25 = 30.60 whence difference = 35-31 — 30-60 = 4 - 8 i . Then -i/ 2 Pcl^ ,/— 2X4-35 X3i ,/— y= V ^w— \ 7A y X 4.0 = X =2.69l/ir but X for flange plate, or Jii'st plate on top, = 4.81 29 193 POTTSVILLE IRON AND STEEL CO., I Lengths of flange plates should exceed the above nett , lengths by about two rivet pitches at each end. Flange angles and first flange plates should extend full length of the girder. POTTSVILLE, PENNA., U. S. A. Whence y = 2.69 |/ 4 gi — 2.69 X 2.19 = 5.89' half length of top plate = 5.89'; whence length of top flange plate = 11.98 feet nett. Now, for the fourth flange plate, or the second plate from top, = 4.81 5.25 = 10.06 Q", or, as we saw before, 35.31 — 30.06 =: 10.06 Q”; then y — 2.69 f 10.06 = 2.69 X 3-17 = 8.53' i.e., full length of fow'th flange plate = 2 X 8.53 = 17.06 feet nett. For the third flange plate, or third plate from top, □" = 10.06 + 5.25 =: 15.31. or full length of third flange plate = 2 X iO-52 = 21.04 feet nett. For the second flange plate, or fourth plate from top, Q" = 15.31 X 5.25 = 20.35 then y = 2.69 |/ 20.35 = 2.69 X 4-51 = 12.13' or full length of second flange plate = 2 X 12.13 =r 24.26 feet ; and the first flange could stop at y = 2.69 X 1/ 25.60 = 2.69 X 5-o6 = 13.61 or full length of first flange plate = 2 X i3-6i = 27.22'; but we will continue this plate from end to end of girder. Now, for lower flange plates, use the expression The nett sectional area required at centre of span is 25.60 1 square inches, and from plates used we have the following values of square inches, — viz., ' y — 2.69 1/ 13.31 = 2.69 X 3-91 = 10-52' 195 POTTSVILLE IRON AND STEEL CO., For fourth flange plate, 14 X f? = 4*5 lowest plate. For third flange plate, 2 — 14 X f » D'' = 9-0 For second flange plate, 3 — 14 X |> i 3-5 For first flange plate, 4 — 14 X f> □" = 18.0 Q"; i.e., plate next flange angles. And ' w ’ 4.0 ^ Then general expression becomes y = 3.16 X Q". Y or fourth flange plate, Q" = 4.5 nett; then y = 3.16 = 3.16 X 2.12 = 6.70' i.e., half length = 6.70', whence full length — 2 X 6.70 = 13.40' long nett. For third flange plate, Q" = 9.0 Q" nett; then y = 3.16 = 3.16 X 3-0 = 948' i.e., half length = 9.48', or full length = 2 X 94^ = 18.96' long nett. For second flange plate, Q" = 13.5 Q" nett; then y = 3.i6 /“i3:5 = 3.16 X 3-67 = ii-6o' i.e., half length = 11.60', whence full length = 2 X H-6o = 23.20' long nett. For first flange plate, Q" = 18.00 Q" nett; then y = 3.i6 3.16 X 4 - 24 = 1340' i.e., half length = 13.40', or full length = 2 X 134° = 26.80' long nett. But the first flange plate, being next to the flange angles, it should extend the full length of girder. Conclusion : First flange plate, 14 X I > required length = 26.80' nett ; make full length. Second flange plate, 14 X f 5 required length = 23.20' nett; make 25.0'. 196 POTTSVILLE, PENNA., U. S. A. Third flange plate, 14 X f 5 required length = 18.96' nett; make 20.5'. Fourth flange plate, 14 X f > required length = 13.40' nett; make i5-0'. The above lengths are about the proper lengths to be used ; the actual “ bill” lengths can be determined when the pitch of rivets in each panel is known, and a drawing is made. To determine the thickness of the web sheet in each panel, we will need the shear at centre of each panel. To determine the diameter and pitch of the rivets in each panel, we will find the shears at each panel point, and, deter- mining the diameter and pitch of rivets at these points, will continue such pitch to next panel point towards the centre of span. In other words, the pitch of the rivets in any panel will be determined by the shear at the end of such panel towards abutment. The general expression for the shear at any point is Then shear at Supports, X = o ; whence = 4 X 16 = 64.00 tons. Centre of first panel, x = 2.0'; whence F2 = 4 X ^4 = 56.00 tons. First panel point, x = 4.0'; whence F^ = 4 X 12 = 48.00 tons. Centre of second panel, x = 6.0' ; whence F^ = 4 X = 40.00 tons. Second panel point, x = 8.0' ; whence Fg = 4 X 8 = 32.00 tons. Centre of third panel, x = lo.o'; whence Fj^ = 4 X ^ = 24.00 tons. Third panel point, x =z 12.0'; whence F^2 = 4 X 4 = 16.00 tons. Centre of fourth panel, x = 14.0'; whence F^^ = 4 X 2 = 8.00 tons. Fourth panel point, or centre of span, x = 16.0'; whence F^. = 4 X o = o tons. 197 POTTSVILLE IRON AND STEEL CO., To resist the crippling of the web sheet, the unit stress should be determined from 5.0 tons 1 + I /h\2 3000 \ r)’ where h may be taken as the distance in the clear between the flange angles, and which here = 40" — 2X4^^ = 32"; and t is the thickness of the web in inches. We will use no web sheet less than f" thick; whence for h ps t= I"; y = then p^ t = xV'; t= i"; 4=^4; then Pj t = iV'; t= f"; -r = 5i; then p 5-0 341 5-0 2.78 5-0 2.37 5-0 2.08 5-0 :.87 1.47 tons per sq. in. 1.80 tons per sq. in. 2.1 1 tons per sq. in. 2.40 tons per sq. in. 2.69 tons per sq. in. Now, at any panel centre, we should have ppsht = F^; whence F where t and h are in inches. If we take t in inches and h in feet, the above becomes 12 . Pps . t i.e., 12 . Pp3 . t = shear at centre of panel divided by the height in feet = shear per foot at centre of panel. Now 12 . pp3 . t for f" web = 12 X 147 X I = 6.62 tons per foot ; and 12 . pp3 . t for web = 12 X i-8o X tV = 945 tons per foot ; and 198 POTTSVILLE, PENNA., U. S. A. I2.Pps t for y web 12 X 2.1 IXI = : 12.66 tons per foot ; i and I 2 .Pps . t for yY' Aveb — = I 2 X 2 - 40 Xt¥^ = 16.2 tons per foot ; j and j I 2 .Pps . t for 1" web : 12X2.69X1 = : 20.18 tons per foot. j And at centre of j First panel, F^ h = 56.00 ^s¥ = : 16.80 tons per foot. j Second panel, F^^h- h = 40.00 s¥ = : 12.00 tons per foot. j Third panel, F^ h- h -- 24.00 -^s¥ = : 7.20 tons per foot. Fourth panel, F^^ ^ h = 8.00 : 2.40 tons per foot. Now, remembering that in any case 12 . Pp^ . t = we can use, by inspection of above, In first panel, a web. In second panel, a web. In third panel, a web. In fourth panel, a f" web. For in first panel we require a resistance of 1 6.80 tons per foot, and by using a web, we have 16.20 tons per foot. In second panel we require a resistance of 12.00 tons per foot, and by using a web, we have 12.66 tons per foot. In third panel Ave require a resistance of 7.20 tons per foot, and by using a f" web, we have 6.62 tons per foot, which is close enough. In fourth panel we require a resist- ance of 2.40 tons per foot, and using no web less than |" thick, we have 6.62 tons per foot. It is desirable to make as few joints in the web as possible, even at the expense of weight of iron ; so we will use a Aveb, extending from end of girder to the second panel point, and a web between the second panel points, from each end. 'Ihere will then be but two joints in web, and at points where the shear = 32.00 tons ; for at the distance x = 8, ^8 = 4 X 8 = 32-00 tons. The splice will be proportioned after we have determined the diameter and pitch of the rivets. To determine the diameter and pitch of the rivets. The 1 number of rivets per foot required at any point distant x 199 10 POTTSVILLE IRON AND STEEL CO., from the abutment = shear per foot at the point divided by the allowable stress on the rivet, — i.e.^ n per foot = Now shear per foot at the point X =o, or end of girder = 64 tons 3^'= 19.20 tons per foot. X = 4.0', or first panel point = 48 tons 3^' = 14.40 tons per foot. X = 8.0', or second panel point = 32 tons ^ 3^' = 9.60 tons per foot. X = 12.0', or third panel point = i6 tons -i- 3^' = 4.80 tons per foot. X = 16.0', or fourth panel point = o 3^' = o. And using rivets ; a y rivet in double shear between the flange angles at 4,5 tons per square inch = 2 X 2.70 = 5.40 tons. (See Table of Shearing Value of Rivets.) And a rivet in a web, with a bearing unit of 9.0 tons per square inch, has a value of 4.43 tons. (See Table of Bearing Value of Rivets.) Also, a in a f" web has a bearing value of 2.95 tons. Whence the bearing values in both cases of and f" web is less than the shearing values, and we see the allowable stress a in the panels which have a yY' web is 4.43 tons, and in the panels which have a f" web is 2,95 tons ; then In first panel. n per foot 19.20 443 4.33; i.e., we require 4J rivets diameter per foot; whence 12'' pitch = — j- ■= 2.77", which we can call 2f". 4i In second panel, having a web, n per foot = — — — 3.25 = 3.69" pitch say, 3^" pitch. 443 200 POTTSVILLE, PENNA., U. S. A. In third panel, having a f" web, 9.60 n per foot 2-95 3-25 = 3-69" pitch, say 3J" pitch. In fourth panel, having a f" web. n per foot z= z= 1.625 = 7.38" pitch, say 6" pitch, because the flange plates being f" thick, the pitch in them to angles (the rivets “ breaking joint” with those in flange angles to web) is limited to 16 X f = 6". Whence we have i I In first panel, web -j-y' ; pitch = 2|" in flange angles to web. In second panel, web pitch = in flange angles to web. In third panel, web f" ; pitch = 3I" in flange angles to web. In fourth panel, web f" ; pitch = 6 " in flange angles to web. And the pitch in flange plates to flange angles will be the same in each panel as above, and “ break joint” with them. But the flange plates being 14" wide, and the horizontal leg of the flange angles being 6" wide each, there should be two lines of rivets in each horizontal leg,— z>., four lines of rivets in the flange plates ; whence the pitch of rivets on each line should be double the pitch of rivets in the vertical leg of angle to web in the panel under consideration, and so arranged that no more than two holes are deductive in each angle iron, for, in proportioning the tension flange, a deduction for two holes is made in each angle iron. Now for the joint between the and f" webs, at the point 8.0 feet from abutment. The shear at this point is 32 Fg = 4 (16 — 8) =: 32.0 tons. The shear per foot = — = 33 9.60 tons per foot. The shearing unit on plate fpg = 5.oo tons ; whence we need = 6.4 -square inches nett area in a vertical section of the splices. These splices are 40 — 2 X 4 = 32" long in height, and one on each side of web. I 201 POTTSVILLE IRON AND STEEL CO., The nett sectional area of these splices is 2 1 32 — number of rivet holes in the height of 32" |t", where t is the thickness of each vertical splice plate. Now, the number of rivets required on each side of the vertical joint in the vertical dimension of splice is = 32.00 tons allowable stress on the rivet = 32.00 2.95 == 1 1,8, say 12 ; the allowable stress being for bearing in f" web, that being less than the shearing value of a rivet in double shear. Then pitch required vertically 30^^ 12 rivets 2 1", say 2f"; or, as plate is 32" long, and extreme rivet holes should be 1^" from ends, we have a height of 32 — 2 X = 29"; and having 12 rivets, there are ii spaces; whence spacing or pitch = 'll =: 2.63", if evenly pitched = say 2|". The stiffeners may be made of 3^-" X ?>h'' X angle irons, two at each panel point, and on opposite sides of web. At the intermediate panel points, where no splice occurs, the “ fillers” between vertical stiffening angles and web sheet are 3I" X 3^" long in height, being same as thickness of flange angles. At splice in web, the splices are ] 7" X 3 '^" long in height, and on them, one on each side ! of girder, is a 3J" X 3 j ^ X angle iron stiffener, as at i other points. There are two vertical lines of rivets, 4" apart ‘ horizontally, the vertical pitch being 2^", as determined ! above. At ends of girder over supports there should be , two pairs of stiffeners, as per sketch, the distance apart of which is governed by thickness of wall on which the girders rest. For girders bearing such heavy loads as this, the “filler” plate should extend from back to back of the pair ‘ of stiffeners. Thus, if bearing were i8" wide, the stiffeners back to back would be 18"; and the “fillers” could then be 18" X 32" high, one on each side of web. The distance ! apart, centre to centre of stiffeners, would then be 15"== | say five spaces, at 3" each; and the vertical pitch in the stiffeners could be 3" likewise. If there were but one pair of stiffeners over end support, | and but one line of rivets vertically, the pitch should be the 202 POTTSVILLE, PENNA., U. S. A. same as determined for first panel, — viz., 2|". Taking the girder 33'. 6" long from end to end, the approximate bill and weight of this girder is as follows, bearing in mind that the web sheets should be less in height than the distance out to out of angles, to allow for inequality of sheared edges of web, and the lengths of the web plates less in length, for a like reason : Upper flange. Two 6" X A” X i" angles, 48 pounds per yard, 33'. 6" long Lbs. 1070 One plate, 14 X 33'-6" long ' One plate, 14 X f? 25'. 6" long One plate, 14 X f > 22'. 6" long - One plate, 14 X 18'. 6" long One plate, 14 X long ^ 1 1 3I linear feet. 2000 Lower flange. Two 6" X 4 -" X angles, 48 pounds per yard, 33'. 6" long 1070 One plate, 14 X |, 33'-6" long One plate, 14 X f ? 25'.o" long One plate, 14 X f> 2o'.6" long One plate, 14 X fj long 94 linear feet . 1660 Rivet heads, 1st, in flange plates to angles. 16 lines I" rivet heads, 5^" pitch, g^' long 'i 16 lines I" rivet heads, 7" pitch, 16' long j- . . 200 16 lines I" rivet heads, 12" pitch, 8' long J 2d, in flange angles to web. 4 lines rivet heads, 2|" pitch, gl' long '1 4 lines I” rivet heads, 3J" pitch, 16' long j- . , 100 4 lines !■" rivet heads, 6" pitch, 8' long J Two ends over supports. Eight 3^" X SV X I" angles, 24.9 pounds per yard, 3'.3" Four plates, 18" X Y ■> long Twenty lines rivet heads, 3" pitch, 3J' . . . 203 215 325 55 POTTSVILLE IRON AND STEEL CO., Four stiffeners. L^s. Eight 3^" X S¥' X I" angles, 24.9 pounds per yard, ^'- 3 " 215 j Eight bars, 3^" X ¥'> 2'.8" long 125 Eight lines rivet heads, 3" pitch, 3^' . . . . 25 Two splices. Four 3^" X S¥' X f angles, 24.9 pounds per yard, 3'.3" 105 Four flats, 7" X ¥' ^ 2'.8" long 125 Eight lines rivet heads, 2|" pitch, 3^' .... 25 j Three web sheets. i Two plates, 39|" X tV'» 8'.8^" = 1285 pounds | ! One plate, 39 |" X '= 790poundsi i i I Flanges . I Ends . . . I Stiffeners . S Splices . . • Web sheets ! i 9390 I The bearing pressure on brick walls should not exceed I 8.0 tons per square foot, and if the above girders rest on ! brickwork, the bearing area needed is -= 8,0 square feet ! =1152 square inches. This would require a stone 5.0 feet ; long if the wall be 18” wide, for 60 X 18 = 1080 square inches. I For such heavy girders there should be a pilaster built under the ends, and, covering it and the wall, should be set I a stone block not less than 5" thick. I On stone, the bearing should not exceed 300 pounds per ) square inch ; whence area of plate required under ends of the girder, between it and the stone, is 64 tons ^0.15 tons = 427 square inches, say 18" wide, 24" long, which equals 432 square inches. Its thickness should be, for such a heavy girder, i".^ 9390 Lbs. 6100 595 365 255 2075 204 POTTSVILLE, PENNA., U. S. A. EXAMPLE II. DOUBLE-WEBBED PLATE GIRDER; i.e., a Box Girder. j Taking the same effective span, height, and load as in I Example I., we have I 1 = 32'.o". 1 h = 3'.4" = 40". w = 4.0 tons. j = 512 foot-tons = 6144 inch-tons. I As the width of a single top flange plate may not exceed ! thirty times the distance centre to centre of rivets across the I plate, allowing 2" from centre of each rivet hole to edge of I plate, for a i f" plate, maximum width = 30 X I + ^ X 2" = 15.25". plate, maximum width = 30 X i ^ X 2" = 19.00". I plate, maximum width = 30 X f + 2 X 2" = 22.75". f " plate, maximum width = 30 X f + 2 X 2" = 26.50". If, then, we use a 20" plate, its distance across centres of rivet holes will be about 16", and its thickness must be = 0.53"; or, we might say, the minimum thickness of first flange plate = Y • The ratio of length of girder to width of flange = 32 -4- if = 19, , I / = 1.120 -44; I H ( I 5000 V Pc which is the maximum permissible stress on upper flange. Then required at centre of upper flange M 6144 6144 Pch" 4-47 X 40 178.8 and LH/' required at centre of lower flange 6144 6144 ^ = 34.36 □" gross. 6 X 40 240 = 25.60 □" nett. 205 li| li f 11 I I! li i i POTTSVILLE IRON AND STEEL CO., For compression flange — z.e., the top flange — use Sq. in. 2— 3l X X i angles, 33.6 lbs. per yard = 6.72 I first top plate, 20 X i = 10.00 I second top plate, 20 X i = 10.00 I third top plate, 20 X f = 7-50 Total gross section used in upper flange = 34-22 For tension flange — t.e., the lower flange — use Sq. in., nett. 2— 3^ X 3i X J angles, 33.6 lbs. per yard = 6.72 Deduct holes, i" X = 1.00= 5.72 3 flange plates, 20 X f = 22.50 Deduct 3 (two holes, i" X f) = 2.25 = 20.25 Total nett section used in lower flange = 25.97 To determine lengths of upper flange plates, we have ^ 7-45 y" □"= 2.73 1/ □" For third top flange plate, O" = 34.36 — 26.72 = 7.64 then y = 2.73 4/ 7-64 = 2.73 X 2.76 = 7-53'; whence full nett length = 2 X 7-53 = i5-o6 feet. 1 For second top flange plate, Q" = 34-36 — 16.72 = 17.64 Q", then y = 2.73 17.64 = 2.73 X 4-20 = 1 1.47'; whence full nett length = 2 X H-47 = 22.94 feet. For first top flange plate, Q" = 34.36 — 6.72 = 27.64 then y = 2.73 4/ 27.64 = 2.73 X 5-26 = 14.36' ; whence full nett length = 2 X ^4-36 = 28.72 feet. This plate, how- ever, must extend the full length of girder from end to end. For lengths of lower flange plates, we have ^ 1 2 f h' / / 2 X 6 X 3 s / y-v ; '/□"-V ^ = l/ 10 1/ □"=3.16 1/ □" 206 POTTSVILLE, PENNA., U. S. A. For third flange plate, Q" = 25.60 — 19.22 = 6.38 Q", then y = 3.16 -j/ 6.38 = 3. 16 X 2.53 = 7-99' ; whence full nett length = 2 X 7-99 = 15-98 f^^t. For second flange plate, Q" = 25.60 — ■ 12.47 = then y = 3.16 X"iXi3 = 3-l6 X 3*62= 11.44'; whence full nett length =; 2 X H-44 = 22.88 feet. For first flange plate, Q" = 25.60 — 5.72 = 19.88 Q", then y == 3.16 = 3.16 X 4-46 = 14.09' ; whence full nett length = 2 X 14.09 = 28.18 feet. This plate, how- ever, should extend full length of girder from end to end. Conclusion : Upper flange. First flange plate, 20 XJ; required length == 28.72'; make full length. Second flange plate, 20 X J 5 required length = 22.94'; make 24'. 6". Third flange plate, 20 X f 5 required length = 15.06'; make 16'. 6". Lower flange. First flange plate, 20 X 1 5 required length, 28.18'; make full length. Second flange plate, 20 X f j required length, 22.88'; make 24'. 6". Third flange plate, 20 X required length, 15.98'; make I7'.6". The shears per foot on each web sheet at centre of panels are In first panel, 16.80 ~ 2 =z 8.40 tons per foot. In second panel, 12.00 -f- 2 = 6.00 tons per foot. In third panel, 7.20 2 = 3.60 tons per foot. In fourth panel, 2.40 2 = 1.20 tons per foot. 207 POTTSVILLE IRON AND STEEL CO., where h = 40 — 2X3 j = 33” and, considering f" as the minimum thickness to be used, we get for t = I" ; = 88 ; then Pp^ = = 1.40 tons per sq. in. t=xV'; t = ; Y = 66 ; then Pp 5.00 2.92 5.00 2.45 1. 7 1 tons per sq, in. 2.04 tons per sq. in. and 12 Ppgt for f" M^eb = 12 X 1-40 X f = 6.30 tons per foot, and 12 Ppgt for web = 12 X XtV = 9-®*^ and 12 Ppgt for web — 12 X 2.04 X J = 12.24 tons per foot. Now, remembering that 12 Pp^t should equal or exceed F we can, by inspection of above, proportion the web sheets. In first panel, need 8.40 tons per foot resistance. A ^y' web has 9.00 tons ; whence use ^y' web in first panel. In second panel, need 6.00 tons per foot resistance, A f" web has 6,30 tons ; whence can use f" web in second panel. And as no web sheet may be less than f", all other web sheets are f". We shall splice the web at the second panel point, so use a plate for each web, from o to 8' from centre of end supports, and a f" web between the second panel points from each end. There will then be but two splices in each web, and at a point where the shear is 16.00 tons on each web, or a total of 32.0 tons per girder. To determine the rivet diameter and pitch, Zx r h n per foot = 208 POTTSVILLE, PENNA., U. S. A. Now shear per foot on eac/i web at the point X = o, or end of girder = 19.20 2 = 9.60 tons per foot. X = 4', or first panel point = 14.40 2 = 7. 20 tons per foot. X = 8 ', or second panel point = 9.60 2 = 4.80 tons per foot. X = 12', or third panel point = 4.80 -^2 = 2.40 tons per foot. X = 16', or fourth panel point = 0 = 0 tons per foot. Using rivets ; a rivet in single shear in connexion of flange angle to web at 4.5 tons per square inch = 2.70 tons. And a rivet in a web at 9.0 tons per square inch, has a bearing value of 3.44 tons ; also, a rivet in a -| plate has, at 9.0 tons per square inch, a bearing value of 2.95 tons. Whence, the shearing value being the less in each case, the allowable stress a on the rivets in all the panels is 2.70 tons. In the first panel we have 9.60 per foot 3-56 = 3-37”, say 3' 2.70 which equals a pitch of 12 In the second panel we have 7 20 n per foot = ~ = 2§ = 4U' pitch. In the third panel we have 4.80 per foot 2.70 Result in each web. .78 = 6|", say use 6" pitch. First panel, web pitch = 3" in flange angle to web. Second panel, web ^y', pitch = in flange angle to web. Third panel, web pitch = 6" in flange angle to web. Fourth panel, web pitch = 6" in flange angle to web. Maximum pitch in flanges = 16 X f = whence no pitch greater than 6" throughout girder. Whence in flange plates. Over first panel, pitch 3", and “ breaking joint” with those in web, 209 POTTSVILLE IRON AND STEEL CO., ‘ breaking joint” with breaking joint” with Over second panel, pitch 4J", and those in web. Over third panel, pitch 6", and ‘ those in web. Over fourth panel, pitch 6", and “ breaking joint” with those in web. For the joint between the and f" web, the shear on each web= 16.00 tons; the allowable stress a on the rivet being due to single shear = 2.70, then number of rivets required on each side of the vertical joint = = 5.9, say 6 required. The height of the splice plate being 40 — 7" = 33" ; then pitch required vertically = -y z=: 5.5". This we will make 4^", to agree with pitch in the adjoining panels. The splice plate we will make 7 X 33^^ two rows of rivets. All stiffeners will be 3" X 7)' X have fillers of 3" X Y ^ 33" the splice we will use two stiffeners, 3” X 3” X f oil web, and set back to back. At the end supports will use three stiffeners of 3" X 3” X I" angle iron on each web, and one filler plate, 18 X 33" long in height, and the vertical pitch in each will make 4^". If we used but one stiffener here, the pitch would have to be 3", the same as in first panel of flange rivets. The bear- ing plate will be as in Example I., — viz., i8" X ^4-'' X Taking the girder 33'.6" long, out to out, the approximate bill and estimated weight will be Lbs. Upper flange. Two 3J" X 3¥' X ¥' angles, 33.6 pounds per yard, 33'.6" long 75 ° One plate, 20 X h 33'-^" long I One plate, 20 X ¥ 24'-6" long |- 74J linear feet. 2,365 One plate, 20 X i6'.6" long J Lower flange. Two 3J" X 3¥' X ¥' angles, 33.6 pounds per yard, 33'.6" long 75 ° One plate, 20 X h 33 ' long One plate, 20 X f, 24'-6" long \ 75J linear feet. 1,910 One plate, 20 X h long I POTTSVILLE, PENNA., U. S. A. Rivet heads, ist, in flange plates to angles. 8 lines f" rivet heads, 3" pitch, 9^-' long 8 lines rivet heads, 4^^" pitch, 8' long j- . . 165 8 lines rivet heads, 6" pitch, 16' long J 2d, in flange angles to web. 8 lines rivet heads, 3" pitch, 9^' long 'j 8 lines rivet heads, pitch, 8' long . . 165 8 lines rivet heads, 6" pitch, 16' long J Two ends over supports. Twelve angles, 3 X 3 X s"> 21.6 pounds per yard, 3'.3" 280 Four plates 18" X ¥'> -‘ 9 " 33 ° Forty lines y rivet heads, 4J" pitch, 3J' long . 75 Four stiffeners per web. Eight angles, 3 X 3 X 21.6 pounds per yard, 3 '- 3 " 185 Eight bars, 3 X ^'.9" no Sixteen lines y rivet heads, 4-^-" pitch, 3^' long . 30 Two splices in each web. Eight angles, 3 X 3 X 21.6 pounds per yard, 3 '- 3 " 185 Four flats, 7 X 2'. 9" 130 Sixteen lines y rivet heads, 4J" pitch, 3^' long . 30 Six web sheets. Four plates, 39I X 8'. 8^" = 2040 \ Two plates, 39^ X i = 1580 i — ’ 11,080 Lbs. Flanges Ends 685 Stiffeners 325 Splices 345 Web sheets 1 1 ,080 Whence box girder of same depth as single-webbed girder weighs 18 per cent. more. This is due principally to limiting the web sheets to a minimum thickness of ■§". 21 1 POTTSVILLE IRON AND STEEL CO., BUCKLED PLATES. Buckled plates are rectangular or square wrought iron or steel plates, shaped under the hammer, so as to have a slight convexity in the middle and a flat rim around the four sides, called the “ fillet.” They are so placed that ihe convex part is compressed and the flat fillet stretched; and when they are crippled, it is usually by the convex part crushing. The plates in general use are made most frequently 3 feet square, the curvature about 2", and the fillets about 2". The thickness varies from to f", the plates being amply sufficient for floors of buildings. The plates are those used for roadway bridge floors, under a heavy road covering. The stiffness of buckled plates is as the square of the thickness, and inversely as the curvature. According to the table of safe loads published by the inventor, Mr. Mallet, a 36" square buckled plate has the following values for varying thicknesses : thickness, safe load per plate = 5,600 pounds, thickness, safe load per plate = 10,000 pounds. tV' thickness, safe load per plate = 14,000 pounds, f" thickness, safe load per plate = 20,000 pounds. In using these plates, they generally rest on the upper flanges of beam, to which they are riveted, and the trans- verse joints between the buckled plates are covered by X irons, with a minimum horizontal flange of 4". These ± irons are also riveted to the fillets. An iron platform is then formed, thoroughly connected together; and on this surface is laid a concrete covering, if for building purposes. If for bridge roadway, asphalt covering is used, 'on which is laid the Belgian block roadway. It is easily seen that the widths of the flanges of the beams on which the buckled plates rest should not be less than about 4". 212 POTTSVILLE, PENNA., U.S. A. The actual dimensions of a buckled plate for 3'.o" spacing of beams, showing the rivet pitch, etc., are given by the fol- lowing sketch. The rise or convexity of this plate is rather larger than usual. A rivet spacing of lo" is quite close enough. In laying the plates, the transverse joints “break joint” with one another. The sketch, however, shows them in the same transverse line. The weights of 36" square buckled plates are as follows : thick, 45 pounds per plate; yV' 7^ pounds per plate; thick, 90 pounds per plate ; thick, 115 pounds per plate ; f" thick, 135 pounds per plate. POTTSVILLE IRON AND STEEL CO., ! BUCKLED PLATE FLOORS. A very excellent floor is made by using buckled plates on the floor joist, instead of brick arches between them. The buckled plates are generally 3 feet square and thick, and are riveted to the top flanges of the I beam joist, which are likewise spaced 3 feet apart. Over the transverse joints of the buckled plates are riveted ± irons. The transverse joints should generally “ break joint” with the adjacent ones. Above the buckled plates is concrete, the top surface of which should be about i" above the crown of the buckled plate, — that is, about 4" above the top flanges of beams. (See sketch, page 213.) If the transverse joints of plates be in one line, the JL iron may be made in one continuous length. The weight of a floor of this kind, with a ceiling hung to the bottoms of the beams, will be about 60 pounds per square foot, which is 10 pounds /ess than the weight of floor formed of brick arches between the beams, and covered with concrete up to a little above level of tops of beams. One great advantage of using a buckled plate floor is that the beams are stayed laterally, and their tabular capacity can always be used. Another advantage is that, by the thorough binding to- gether of the entire floor system, it is likely to be much more rigid than other floors designed for same loads. In cases where ceilings are necessary, they may be hung to bottom of beams, by means of wire netting, with the usual fastenings; or small joist may be laid transversely between the beams and the ceiling attached thereto. In ordinary warehouses there is generally no need for ceilings. In such cases, the floor load due to beams, buckled plates, and concrete covering may be taken 50 pounds per square foot, instead of 60 pounds, as given above. 214 POTTSVILLE, PENNA., U. S. A. Suppose we have a floor area of 63' X ^8' inside of walls. If we divide it into four spaces lengthwise by three girders, making the two central spaces 16'. o", then the two end spaces from centre of girder to centre of wall will be i6'.o". Into these girders frame floor joist spaced 3' apart, and running lengthwise, then there will be 6 spaces in the width, of 3'.o" each. The buckled plates next the wall will be carried on channels of same depth as the floor joist, and around the inner edge of all walls will be a 4" X 3" X angle iron (the 4" leg set vertically), to confine the concrete. These angles set over the fillets of the buckled plates. In each panel, then, there will be five lines of I beams lengthwise of area, and two lines of channels next the long way of the wall. There are also three transverse girders \ into which are framed the five lines of I beams and two lines of channels. Suppose we wish the floor to carry an extraneous load of 100 pounds per square foot, the weight , of the buckled plate floor being 60 pounds per square foot, ‘ the total load per square foot will be 160 pounds. Each floor joist will then carry 3' wide X pounds X 16' long, or 48 square feet at 160 pounds == 3.84 tons. As these joists are stayed laterally by the buckled plates, we can use the full tabular capacity, and looking in the tables at the 16' span line, we find that an S" I beam of iron, 65 . pounds per yard, will carry 4.25 tons, and the deflexion is 215 POTTSVILLE IRON AND STEEL CO., 0.46". The channel iron against wall will carry but one- half the load on the beams ; whence from tables we find that an 8" channel of iron, 40 pounds per yard, will answer, as its safe load is 2.25 tons, and deflexion 0.50". Each transverse girder carries an area of 16' X ^8' = 288 square feet. This, at 160 pounds per square foot, has a load of 23.04 tons. The effective span of the girder is about 19', and looking at 19' span line in the tables, we find there, if the upper flange is stayed laterally, that a 15" I beam of iron, 250 pounds per yard, will do, as it carries 22.73 tons (which is close enough to the load required), and has a deflexion of 0.33". Or, looking in the Tables of Steel Beams, we find that at 19' span, a 15" I beam of 20.00 square inches area, — i.e., 202 pounds per yard, — will do, as it carries, when flange is stayed, 25.32 tons. In framing the 8" floor joist into the 15" I beam girder, if the top flanges are placed on the same level, the flanges of girder can be considered stayed. The joist, however, may be framed into girder 4" below the bottom of its top flange, in which case the top of concrete is level with top of girder. In this case the flange of girder beam cannot be considered as stayed. Assuming the girder flange 5J", the 19 X 12. ratio of unstayed length to flange width is 5 ? about 40 ; whence tabular loads must be multiplied by 0.88, — that is to say, we can only place an extreme fibre stress of 6.90 tons on the steel beam, instead of 7.8 tons, the tabular fibre stress. Since f qh S = M^, and 23.04 X 20 X 12 . . , Mq— — — = 691.2 inch-tons, we get 691.2 fqh 6.9X0.3X15 22.26 square inches ; i.e., we need a 15" steel I beam, 22.26 square inches area, or 225 pounds per yard. The ends of all beams which rest on walls should have 216 POTTSVILLE, PENNA., U.S. A. loose bearing plates of iron, say 8" square, and say f" thick. Also there should be riveted on the webs two angle irons, to form “ check angles.” An approximate estimate for this floor will read as follows : 1st. Girders with flanges not stayed. Lbs. 90 7,050 880 Three steel I beams, 15" deep, 225 pounds per yard, 1 9'. 6" long 4,390 Six bearing plates, 12 X f, l^-O" long ....... 90 Twelve “check” angles, 3 X 3 X f angles, 21.6 pounds per yard, 12" long Ten floor joist, 8"' iron I beams, 65 pounds per yard, 16'. 6" long Ten floor joist, 8" iron I beams, 65 pounds per yard, i6'.o" long Four floor joist, 8" iron channels, 40 pounds per yard, 1 6'. 6" long Four floor joist, 8" iron channels, 40 pounds per yard, 16'. o" long Fourteen bearing plates, 8 X f , o'-8" long .... Twenty check angles on 8" I beams, 3 X 3 X f angles, o'. 6" long 75 Four check angles on 8" channels, 3 X 3 X f an- gles, o'. 6" long 15 One hundred and twenty buckled plates, 36" square, thick, at 90 pounds each 10,800 Ninety-six transverse joint covers, 4 X 2 X ¥ J-’s, 24 pounds per yard, 3'.o" long . 2,305 162 linear feet of Two lines, 63' each, curb angles Two lines, 18' each, curb angles 850 95 4 X 3 X 1 an- gle iron, 24.9 lbs. per yard . 1350 Connexions of joist to girders contain 72 pieces 3 X 3 X f angles, 21.6 pounds per yard, o'.6" long . 260 Allowance for rivet heads 28,250 350 28,600 217 POTTSVILLE IRON AND STEEL CO., Lbs. per Lbs. sq. ft. Girders, bearings, and check angles. 4,570 = 4.03 Floor joist, bearings, check angles, and connexions 9,225 = 8.14 Buckled plates, ± covers, and rivet heads 13,455 = 11.87 Curb angles i,350 = 1.19 28,600 = 25.23 Area of floor surface = 63' X '^9' — ^34 square feet. 2d. Girders with top flanges stayed, by the joist being so framed into them that all top flanges are on same level. On page 216 we found that a 15" steel I beam, 202 pounds per yard, would answer, and previous estimate is changed only in the weight of the three steel girders ; whence it would now read Lbs. per Lbs. sq. ft. Girders, bearings, and check angles. 4,120 = 3.63 Floor joist, bearings, and check an- gles 9,225 8.14 Buckled plates, X covers, and rivet heads 13,455 = 11.87 Curb angles i,35o = 1.19 28,150 = 24.83 Suppose the floor joist are laid in direction of short length of floor area; then there will be 21 spaces of 3' each, — i.e., 20 floor joist, 19' span, 2 joist of channels, 19' span. Each joist will carry 1 8 X 3 X pounds = 4.32 tons. Looking at 19' span line in the tables, we find that we can use a 9" iron I beam, 85 pounds per yard, as this will carry a safe load of 5.05 tons, and has a deflexion of 0.57”. Looking in steel tables, we find that an 8" I beam of steel, 65.75 pounds per yard, will sustain a safe load of 4. 91 tons, and has a deflexion of 0.75". Now, this .75" deflexion is greater than -jL" per foot of span. If, then, we dare not exceed the limit of per foot = 0.6^", we shall have to reduce the safe load to 0-63 0-75 X 4.91 = 0-^3 X 4-91 = 4.08 218 POTTSVILLE, PENNA., U.S. A. tons. This is less than 4,32 tons, the load required to be carried, whence we shall have to use a heavier beam. A 9" I beam of steel 7o| pounds will answer, since its deflexion being 0.74, we shall have to take 0-63 0.74 = 0.85, its tabular load = 0.85 X 5 -^^^ =4*30 tons. Thus we can use, having a plaster ceiling, a 9" iron beam, 85 pounds per yard, or a 9" steel beam, 7o| pounds per yard. We will use for the intermediate joist 9” I beams of steel, 70^1 pounds per yard, and for the joist next walls, 9" iron channels, 42.75 pounds per yard, as they will carry 2.72 4.32 tons, a little more than the required load of =2.16 tons. The approximate weight is as follows : Lbs. Twenty 9" steel I beams, 7o| pounds per yard, 19'. 6" long 9,200 Two 9" iron channels, 42I pounds per yard, ig'.6" long , 550 Forty-four bearing plates, 8 X I > o'. 8” long .... 300 Forty-four check angles, 3 X 3 X f angles, 21.6 pounds per yard, o'. 6" 160 Buckled plates, 126, at 90 pounds apiece Hj340 Transverse joint cover's, 120', 4 X 2 i f , 3.0' long . 2,880 Curb angles, as in Estimate 1st Ij350 Allowance for rivet heads 350 26,130 Lbs. per Lbs. sq. ft. Floor joist, bearings, and check angles . * 10,210 = 9.00 Buckled plates, ± covers, and rivet heads i4;57o = 12.85 Curb angles 1,350= 1.19 26,130 = 23.04 A saving of over 8 per cent, in weight, which is likewise an 8 per cent, saving in dollars and cents, as steel beams cost no more per pound than iron ones. 219 ] POTTSVILLE IRON AND STEEL CO., TRUSSED GIRDERS. Given a trussed girder whose span centre to centre of end pins is 32 feet, whose depth is 3J feet centre to centre of chord pins, and carrying a load of 4.0 tons per linear foot. From these dimensions we have tangent (j) = io| -h 1+ = 3,20, and secant (j) = ~ lof = 3.35. The load on eacli post, Bb, B'b', is 42§ tons, since each carries the load due to one-half a panel length on each side of it. This stress of 42§ tons, coming down the post Bb, is resolved at pin b on the chord bars bb', and on the diagonal bars Ab. On the chord bars bb' the stress is 42§ X tan. (j) = 42f X 3-2 = 136.53 tons. On the diagonals Ab the stress is 42I X (j) = 42f X 3-35 = 143.06 tons. This last, coming through the pin A, is resolved on the upper chord, and is 42I X tan. cp = 136.53 tons, which is the thrust from A to A'. Whence we have the following stresses ; In upper chord, AB, BB', B'A', 42§ X tan. ^ = 136.53 tons. In lower chord, bb', 42f X tan. (p = 136.53 tons. In diagonal bars, Ab and A'b', 42§ X sect, (p = 143.06 tons. In vertical posts, Bb and B'b', 42! tons = 42I tons. The unit stress f^ for compression is as given before, — viz., if tons (2 -f (^) = if X 3 = 5-00 tons. The unit stress for rolled bars is 10 per cent, greater than that given for shape iron in tension, — viz., it is 2.2 tons (2 -(- 6) = 6.60 tons,

3 Wli w Eccentric Loading. 1 BEAMS WITH SUPPORTED ENDS. 234 POTTSVILLE, PENNA., U. S. A. MOMENTS OF INERTIA For Simple Shapes. _ (bh" — bi — 4 . bh . bi hi (h — hi)2 “■ 12 (bh — bi hi) ^Vhere A = area of circle. Ah2 12 12 Where A = area — bh. bt3 _ At2 12 12 Where A = area = bt. i 235 POTTSVILLE IRON AND STEEL CO., MOMENTS OF INERTIA For Compound Shapes. Two channels, with lacing, arranged thus : X Y r 1 •X. 0 .X.0 etc. i J X Line ab = neutral axes of channels, S = area of each channel. Xq = distance from neutral axis of channel to axis of compound shape YY. J = least moment of inertia of the channel. I = greatest moment of inertia of the channel. Moment of inertia, axis YY, = 2[J + X„^S] Radius of gyration, axis YY, = V-- ts° = V + -g- = 1/ ' Moment of inertia, axis XX, = 2 I Radius of gyration, axis YY, =vi-v|.=.. 236 POTTSVILLE, PENNA., U. S. A. Required the least radius of gyration of a column formed of two lo" channels, 6o pounds per yard, placed 6" apart, back to back of webs, as shown in figure. The distance from back of a lo" channel, 6o pounds to the neutral axis of such channel, is given by the Table of Properties of Channels as 0.69"; therefore the distance from neutral axis of channel to neutral axis of compound shape is [- 0.69" = 3.69". We also find the radius of gyration of the channel ij to be 0.79 (see column 13 of Table of Properties above referred to). Our formula is • which for the lo" channel post is ; r = ^3.69^ + 0.792 = 3.77 I I The radius of gyration when the axis is perpendicular to 1 web is, for the 10" channel, 60 pounds per yard, as per j table, 3.69”. ! Thus, we find that the column is slightly weaker in the direction of plane of channels than in a direction perpen- dicular to such plane. Suppose we wish to form a post of two 12 ” channels, 90 pounds per yard, and that we desire to know how far apart in the clear to place these channels in order that both radii of gyration be the same. We simply equate the expressions VK' + and rj; whence I Xq 2 = rj 2 i-j ^ = (i-j -j- i-j ) (rj — i-j ) Now for the 12 " channel, 90 pounds, the table gives us ri = 4-49 ; i-j = o.89. 4.49 + 0.89 = 5.38 I 4.49 — 0.89 = 3.60 V = 5-38 X 3-6o = 19.37 = 1/19-37 = 4-40” 1 237 Therefore and and therefore POTTSVILL^ IRON AND STEEL CO., Now the distance from back of 12" channel, 90 pounds to its neutral axis, is, as per table, 0,84. Therefore distance of back of channel from centre of compound shape = — 0.84 = 4.40 — 0.84 = 3.56". Thus channels should l)e placed apart 2 X 3-56 = 7- 12", say 7 inches in the clear. TWO CHANNELS AND I BEAM. ab 3= neutral axis of channel. Sj = area of channel. S2 = area of beam. = least moment of inertia of channel. J2 = least moment of inertia of beam. = greatest moment of inertia of channel. I2 —’greatest moment of inertia of beam. Moment of inertia, axis YY, ^CL Y. ^l2+2[J + X,2.SJ Radius of gyration, axis YY, Moment of inertia, axis XX, = J2 + 2 Ii Radius of gyration, axis XX, 238 POTTSVILLE, PENNA., U. S. A. Required the moments of inertia of a column, formed as above, of two lo" channels, 48 pounds per yard, and one 12" I beam, 125 pounds per yard. First, axis being YY. Maximum moment of inertia of 12" I, 125 pounds = 279.0. Least moment of inertia of 10" channel, 48 pounds = 2.40; distance from back of channel to neutral axis = 0.59; whence = one-half depth of beam -|- 0.59 = 6 . 59 - Therefore total moment of inertia of column, the axis being YY, is The area of compound section = 12.5 Q" 2 y( 4.8 = 22.1 Q". Therefore radius of gyration, axis being as above, is Second, the axis being XX. Least moment of inertia of 12" I beam, 125 pounds = 14-50 Twice maximum moment of inertia of 10" channel. Moment of inertia of compound section, axis XX = 144.50 The radius of gyration is Thus, around the axis YY the compound section, formed of one 12" beam, 125 pounds, and two lo" channels, 48 pounds, is more than twice as strong as around the axis XX, provided, of course, the condition of ends of columns is the same; as, for example, both fixed ends. = 279.0 + 2 X 208.45 = 695.90 48 pounds = 130.00 239 POTTSVILLE IRON AND STEEL CO BEARING OF GIRDERS ON BRICK WALLS. The pressure on a brick wall should not exceed 8 tons per square foot; hence when beams are used for floor joist, their bearings on wall should be so proportioned as not to exceed the above limit. This is conveniently done by means of a loose f" plate of wrought iron. The ends of girders and floor joist should have “ check angles” at their wall ends, thus checking the walls from falling outwards in case of fire. The depth which the beam extends in the wall must not be less than 8 inches. The thrust of the brick arches is taken up by tie rods f to I inch in diameter, spaced from 5 to 8 apart, the holes for which are punched in middle of web. GIRDERS FORMED OF BEAMS Placed side by side, and beams placed one over the other, and riveted along the flanges. In supporting heavy walls, the beams can be placed side by side, or be coupled, as in the following sketches. The width of wall to be supported sometimes prevents the use of more than two beams under them ; and in such cases, if two beams cannot be found sufficient to carry the load, two coupled beams can be used, as shown by Fig. 2 ; or, if they be found insufficient, two sets of three beams each, placed one over the other, can be used. (See Fig. 3.) The coupled and trebled beams are used in lieu of plate girders. If plate girders be used, they would be with a single web, and the wide top flange necessary to carry wall would make the use of heavy vertical stiffeners a necessity. In using coupled and trebled beams, cast-iron separators 240 POTTSVILLE, PENNA., JTFl JVP2 U.S. A. jypj are needed, and are generally made of depth of the com- pound shape. Between brick work and top of beams should be placed a slate or granite plate 2\" to 5" thick, to get an even bearing for wall. This plan of carrying heavy walls is much used by the United States Government in the Public Buildings. X X z ^ 4 7i Ik . Two I beams coupled, as in the above sketch. Required the moment of inertia? Both beams being of same depth and weight. Let h = height of beam, then — = distance from centre of inertia of single beam to centre of inertia of compound 241 POTTSVILLE IRON AND STEEL CO., shape. Let S = area of one beam, then 2 S = area of compound section. I = moment of inertia of each single beam, axis XX. 1 ^ = moment of inertia of compound shape, axis XX. Then 2 q Ic = 2 I + — C ^ q Now, for the standard or minimum rolls of each I beam, q has the average value, 0,33 ; whence 2q + i ^ 2X0-33 + 1 ^ q 0-33 ^ Ic=5l If be the modulus of this compound shape, then 2.T 2 . h h = 2.5R where R is the modulus for the single beam. Whence the moment of resistance of the coupled beams is 2^ times that for a single beam. For maximum rolls of a beam, q has the average value of 0.3 ; whence 2 q + I = 5 - 33 » and = 5.33 I The modulus R^ then becomes 2,67 . R. Thus, for the heavier rolls of beams, the moment of resistance of the coupled beams is 2.67 times that for a single beam. Comparing the coupled beams with two beams of same depth and weight, placed side by side, the coupled beams 242 POTTSVILLE, PENNA., U. S. A. are 1.25 stronger than if the two beams be placed side by side, if the sections be the minimum rolls; and 1.33 times stronger if the sections be the heavier rolls. The rivets connecting the flanges together should be or f" diameter, dependent upon the thickness of the flanges, and the pitch should be about 6" or 8" staggered. At ends of beams the pitch of rivets should be from 3" to 4" for a length of twice the depth of the compound shape. Three beams riveted to- gether as in adjoining sketch. Each beam being of same depth and weight. Let h = height of each beam ; then h is the distance from centre of inertia of out- side beams to centre of inertia of compound shapes. Let S = area of each beam ; then 38= area of compound section. I = moment of inertia of each beam, when referred to its own neutral axis. = moment of inertia of compound shape. Then ^ I -f 2 I^I + h 2 S j = 3 I + 2 h^S but 2 h 2 S = q Lor minimum rolls, = 15 I. Lor maximum rolls, = 16 I. Lor minimum rolls, = 5 R. Lor maximum rolls, R^ = 5.33 R. 243 POTTSVILLE IRON AND STEEL CO Comparing the trebled beams with 3 beams of the same depth and weight, placed side by side, the trebled beams are 1.66 times stronger than if the 3 beams be placed side by side, if the beams be the minimum rolls; and 1.78 times stronger if the sections be the maximum rolls. FIRE-PROOF FLOORS. The dead weight of a fire-proof floor, comprising 4" brick arches, levelled up to top of beam with concrete, the ceiling and the flooring will run about 70 pounds per square foot of floor surface. The live weight, equal to a dense crowd of people, is taken at 80 pounds per square foot. The total weight is then assumed 150 pounds per square foot, exclusive of weight of beams themselves. The following loads are exclusive of weight of arches and beams : Lbs. per square foot. Dense crowd of people 80 Floors of houses 50 Theatres, churches 80 Ball rooms 90 Warehouses . 250 Factories 200 to 450 Snow, 30 inches deep 15 Lbs. per cubic foot. Brick walls 112 Stone walls 116 to 144 244 POTTSVILLE, PENNA., U. S. A. STANDARD SEPARATORS OF POTTSVILLE IRON AND STEEL CO. Width, m inches. Height, in inches. Number of bolts. Length of bolt, in inches. Distance apart, in inches. Weight of beam per yard, in pounds. Weight of separators ana bolts, in pounds. 5 15 2 7 ^ 8 200 22.29 42 - 15 2 8 150 20.06 4 f 12 2 7i 6 170 17.2 4 i i 2 6 125 16.06 4 j ! loi I 6^ L In centre 135 1345 4 I 6 U 105 11-97 3 l 10^ I 5^ 90 10.82 4 _ ! 9 1 6^ 1 r 90 10.88 3 f 9 I 5 ^ t t 85 8.5 3f 9 I 5 l i 70 8.4 3i 8 I 5 ^ r (C 80 7.88 3 l 8 I 5 ^ r u 65 7-5 3 i 7 j 5 ? u 65 6.8 3l 7 I 4j r u 55 6.76 3 . 6 I 4 | 50 5-73 H 6 I 4 | 1 ! u 40 5-2 All standard separators are i" thick. All separator holes are diameter for f" bolts. All standard separators made for close girders, except when ordered otherwise. 245 POTTSVILLE IRON AND STEEL CO., POSITION OF CENTRE OF INERTIA OF A COMPOUND SECTION. When a compound section is formed of vertical plates, to 'which are attached angle irons at their extremities, if the angles are similar and similarly placed, the centre of inertia is at the centre of the vertical plates. If a flange plate be added to one side of the section, the position of the centre of inertia will be shifted from the centre, upwards if the plate be on top, downwards if the plate be on the bottom. For the amount of such moving of the centre of inertia from centre of vertical plates Let S = total area of section. h =: vertical height out to out of angle iron flanges, b = breadth of top flange plate, t = thickness of top flange plate. E = distance of centre of inertia of compound sec- tion from the centre of vertical plates ; in other words, the eccentricity of the centre of inertia. Then F^i + H i.e., the eccentricity E = the ratio of area of top plate to total area of section multiplied by one-half the total height of the section. In well-designed chords of above “ make up,” the value of r is about f the height, and the value of q about 90 per 246 i I POTTSVILLE, PENNA., U.S. A. cent, of r, — viz., about (For fe;y heavy sections q is about 0.30.) For purposes of calculation, r may be taken I h, and q = ^ ; whence qh = — . In some very favorable sections q may run as high as 0.38, and r from 0.40 to 0.42 times the height. COLUMNS AND POSTS. The table of the ultimate and safe strength of hollow, cylindrical wrought- and cast-iron columns is given on page 248. It is computed by Gordon’s formula for varying values of the ratio of length to diameter. The factor of safety for cast-iron columns has been taken at 6, and that for wrought- iron columns at 4. It is assumed that the ends are fixed in direction, such as having planed bearings on capitals and bases. The table on the ultimate and safe strength of wrought- iron columns is computed according to Rankine’s formula for varying values of the ratio of the length to the least radius of gyration, and for the three conditions of square end bear- ings, one square end bearing and the other pin end, and for both ends with pin bearings. The factor of safety used in the tables for safe strength is 5. If the column be subjected to loads without vibration, the factor could be 4. To illustrate the use of this table, suppose we wish the ultimate strength of 15" I beam, 125 pounds per yard, when used as a post, its ends being fixed, and having an unsup- ported length of S' 6 ". Referring to the Tables of the Properties of I Beams, we find that the least radius of gyration, r^, is given as 1.03"; the length being S' 6 " = 102" ; the ratio — = = sav r 1.03 100; for which, on looking at the table, we find the ultimate strength to be 32,000 pounds per square inch. The section of the 15" l)eam being 12.5 Q", the ultimate strength is then I2| X 32,000 pounds = 400,000 pounds. 247 POTTSVILLE IRON AND STEEL CO. Strength of Hollow, Cylindrical WROUGHT- AND CAST-IRON COLUMNS When fixed at the ends. Computed by Gordon’s formula, P = fS I + c m same units. Let P = ultimate strength, in pounds, per square inch. S = sectional area, in square inches. 1 = length of column, I , , h = diameter of column, J Y- = ratio of length to diameter, h r f 40,000 pounds for wrought iron. — 1 8o,c ■ ■ ,000 pounds for cast iron. C = for wrought iron, and for cast iron. For cast iron. For wrought iron. P = 80,000 S I + . ny 800 \ h / 40,000 S I / 1 \2 3000(h) Ratio of length to diameter, 1 h Maximum load, per square inch. Safe load, per square inch. Cast iron. Wrought iron. Cast iron, factor of 6 . Wrought iron, factor of 4 . 8 74,075 39,164 12,346 9791 10 71,110 38,710 11,851 9677 12 67,796 38,168 11,299 9542 14 64,256 37,546 10,709 9386 16 60,606 36,854 10,101 9213 18 56,938 36,100 9,489 9025 20 53,332 35,294 8,889 8823 22 49,845 34,442 8,307 8610 24 46,510 33,556 7,751 8389 26 43,360 32,642 7,226 8161 28 40^404 31,712 6,734 7928 30 37,646 30,768 6,274 7692 32 35,088 29,820 5,848 7455 34 32,718 28,874 5,453 7218 36 30,584 27,932 5,097 6983 38 28,520 27,002 4,753 6750 40 26,666 26,086 4,444 6522 42 24,962 25,188 4,160 6297 44 23,396 24,310 3,899 6077 46 21,946 23,454 3,658 5863 48 20,618 22,620 3,436 •5655 50 19,392 21,818 3,262 5454 52 18,282 21,036 3,047 5259 54 17,222 20,284 2,870 5071 56 16,260 19,556 2,710 4889 58 15,368 18,856 2,561 4714 60 14,544 18,180 2,424 4545 248 POTTSVILLE, PENNA., U. S. A, Ultimate and Safe Strength of WROUGHT-IRON COLUMNS. p = ultimate strength per square inch. 1 = length of column, in inches, r = least radius of gyration, in inches. For square end bearings. I + ),ooo \ r / For one pin and one square bearing, 40,000 I +■ For two pin bearings. ,000 \ r / P = 30 40,000 I +■ ),ooo \ r / For safe working load on these columns,' use a factor of 4 when used in buildings, or when subjected to dead load only ; but when used in bridges the factor should be 5. Ultimate strength, in pounds, Safe strength, in pounds, per per square inch. 1 square 1 inch, factor of 5 . r Square ends. Pin and square end. Pin ends. r Square ends. Pin and square ends. Pin ends. 10. 0 39,944 39,866 39,800 10. 0 7989 7973 7960 15.0 39,776 39,702 39,554 15.0 7955 7940 7911 20.0 39,604 39,472 39,214 20.0 7921 7894 7843 25.0 39,384 39,182 38,788 25.0 7877 7836 7758 30.0 39,118 38,834 38,278 30.0 7821 7767 7656 35-0 38,810 38,430 37,690 35-0 7762 7686 7538 40.0 38,460 37,974 37,036 40.0 7692 7595 7407 45-0 38,072 37,470 36,322 45-0 7614 7494 7264 50.0 37,646 36,928 35,525 50.0 7529 7386 7105 55-0 37,186 36,336 34,744 55-0 7437 7267 6949 60.0 36,697 35,714 33,898 60.0 7339 7143 6780 65.0 1 36,182 34,478 33,024 65.0 7236 6896 6605 70.0 ! 35,634 34,384 32,128 70.0 7127 6877 6426 75-0 ! 35,076 33,682 31,218 75-0 7015 6736 6244 80.0 : 34.482 32,966 30,288 80.0 6896 6593 6058 85.0 ; 33,883 32,236 29,384 85.0 6777 6447 5877 90.0 : 33,264 31,496 28,470 90.0 6653 6299 5694 95-0 32,636 30,750 27,562 95-0 6527 6150 5512 100.0 32,000 30,000 26,666 100.0 6400 6000 5333 105.0 . 31,357 29,250 25,786 105.0 6271 5850 5157 ! POTTSVILLE IRON AND STEEL CO., AVERAGE ULTIMATE CRUSHING LOADS. TIMBER. Weight Lbs. per cubic foot, persq. in. Ash 48 8600 Beech, unseasoned 53 7700 Beech, seasoned 43 9300 (!!!edar, unseasoned ... ... 56 5700 Cedar, seasoned 50 6500 1 Oak, unseasoned 54 4200 1 Oak, seasoned 67 6000 1 Pine, pitch 6800 j Pine, yellow, unseasoned 5300 Pine, yellow, seasoned 5400 Pine, white, unseasoned 35 5000 Poplar, unseasoned 3100 Poplar, seasoned 5100 Sycamore 7000 Spruce, unseasoned 6500 Spruce, seasoned 6800 STONE AND CEMENTS. ( j Mean-tons per sq. foot. Limestone Sandstone . • . 425 Brick • . 175 Ordinary crack . . 25 In cement First-class cement Concrete . . 40 Portland cement 250 LEAST WIDTH OF SQUARE PINE POSTS, IN INCHES. Breaking Load in Tons. POTTSViLLE, PENNA., U.S. A. ! - q q q q q q q q q q q q q q ri vO d '-d CO i-i i-I ^ d^^ ^ on 10 rj 00 CO Onno CO 0 (N 0 00 ir^u-)U-)'c}-'^cococococN CM C^ >-> ID q q q q q q q q q q q q q q rivd On o’ lAcoco'^oo ■cj-co'^r^ci 00 Loc^ OnO coo OOOnO ^ 'cj-'ct-^'d-cococooi M C'l i-i M HH 10 ' qqqqqqqqqqqqqq 00 l>. 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(O cq ^00 q On CM <000 CO CM cd I-I CO 0’ d- 0 uo cd 0’ On rdNo’ uo uo nOuococoCM i-h i-h m i-h VO i 10 I cq uouoCOCOhh i-hnO u-)NO CO ^ CO i-h o’ d cnI NO cm’ o’ 06 no’ uo ct cd cd cm’ cm’ ^ CO I-I I-I I-H I-I 10 tp-NO 00 00 cq Tf upoq cq M U-) d id u^ rf cd CM CM CM I-H hH 1 ' CO 9.9 6.1 3-9 2.7 2.0 1.4 0.92 0.76 CO Height. M -cJ-nO CO 0 cm tJ-nO 00 0 cm tJ-nO 00 0 w H mmmhhi-hCMCMCMCMCMCoS Ph Ph Height. I 251 POTTSVILLE IRON AND STEEL CO., STRENGTH OF TIMBER POSTS. Formula for the ultimate strength of square or rectangular posts of moderately seasoned white and yellow pine, with ends flat and fixed : P == f Where P = crushing load per square inch, f = 5000 pounds per square inch. 1 = length of post, in inches, h = least width of post, in inches. = ratio of length to least width. WOODEN BEAMS AND GIRDERS. From the general equation = q f h S we can deter- mine the carrying capacity of wooden beams. Now for rectangular sections, q being equal to 2 » becomes h2 q = 1, since r^, for rectangular section, is — ; whence the general expression becomes (I) For beams uniformly loaded over their length, and supported at the ends, M O W1 (2) 252 POTTSVILLE, PENNA., U. S. A. where W is the total load on beam and 1 is the span; and this must be equated to second member of (i). Thus \V 1 _ fhS " 8 ' ~ ( 3 ) For beams of seasoned white pine for building purposes we may take f, the extreme fibre stress, as 1200 pounds per square inch ; then W 1 “ 8 ~ 1200 h S whence W 1 = 1600 h S (4) ( 5 ) If 1 be taken in feet, and h in inches, and S, the area, in square inches, then (5) becomes W.l' = 122 hS that is. W = 400 h S ( 6 ) ( 7 ) that is, the uniformly distributed total load in pounds which a beam can safely carry is (the height in inches multiplied by the area of beam in square inches, and divided by the span in feet) X factor Now the area S = bh; whence (7) becomes W = 400 b h^ d V j If in this, (8), the breadth be taken as l", W = 400 ( 8 ) ( 9 ) We give a table of carrying capacities of i" broad white pine beams of varying depths for varying spans. For any beam whose width is b inches, merely multiplying the tab- ular number by such breadth b, and we get the capacity for the beam in question. 253 SHEARING AND BEARING VALUE OF RIVETS. POTTSVILLE, PENNA., L>. S. A. Bearing value for different thicknesses of plate, at 6.0 tons per square inch. Diameter of rivet X thickness of plate X 6.0 tons. 0 0 0 Ln ^ q 1 -; vC vd 'O I::!; ro LO 0 cs 00 q vo 0 rqo M HH 0 0 LO On CS W) 0 fO vn ON C 4 10 ON 0 T;f tJ- id mio' «'r.j 0 0 m 0 m On VO VO t^OO 00 00 On q moo H-( tT !>. m d" d" d" m m m m mvo On 0 0 0 r^mrOM Ooovo ^ rqvo ON q m 0 m ro m (“d d" d" 'd m m — lO vo 0 000 r^mmooo mONmOvo 000 "^on 00 q mvq 00 hh mvq 00 ci fdrdrdrdd-'dd-'d :.i=o ^00 t^Ovo 0 mONCO M Ttoo M moo i-H m rq moq q q m rq on n tE d d d rdmrdrdrdd-d- 0 0 0 0 m cs m mvo x^ 0 i-< ox m mvo x^oo on 0 ONw romxqq\i-i romx^O Moiddddrdrdmrd'd 0 x^ m 01 ONoo tE m 0 00 m 01 0 cxo x^vo m 01 HH 0 00 x^vo mvq oqqq^voooOMrom M M HH d ci oi d oi 00 m rd m 00 m m 0 moo ^vo oi m ov m x^ HH ^ 0 vo m ONvo 01 00 m HH M m '^vo 00 ON M Ttvo x^ ON H-i MMi-iMi-ii-ioioioxoioioird cc;x mvo x^ x^ 1^00 00 0 0 >-i )-i M ■^00 oio 1-1 rEoo oivo M mONxox^ 00 ON i-i (V) tE mvo 00 ON >-i 01 00 mvo ddi-HMi-ii-ii-ii-iMoicvioioioi ■■"H ooo x^moi Ovo x^moi onx^ 0 ox romx^ONO m ^mx^OvO oi xq«oq ON 0 >-i 01 tE mvo x^oo ON i-( d d d d d hH h-I l-i M h-H id l-J M 01 01 olvD 0 TEx-~>-(mONOivo 0 'd-oo 01 vO mm-^rorooi >-* O O Onoo 00 mvO x^oo ON 0 <-i 01 ro m mvO x^ d d d d d >-<■ id id id id id id id id ■qouT ’hs jod suo; O '0 ‘Jtoqs oiSuTS i-H i-H ovmO -^mm^Ei-ivo O 01 01 00 moo --E 01 I-H d m 0 x^ mvo d rq q- m x^ On i-H rq moo q fOvO ON oq d d d d d id hd id id d" d' d' d' rd T 8 AU JO ■BOjy 1 tE m ro moo doo mmm^vD O m ' OOvOCOvOwi-hCO'-hO mvo tE x^ I-H mON-i^O i>-^i-i 0 ONOO 00 ON 0 I-H I-H I-H d ro m d" mo 0 x^oo on i-h d d d d d d d d d d d d d >d •J 9 AU JO JOJOUTBIQ 1 255 POTTSVILLE IRON AND STEEL CO., BEARING VALUES AND MOMENTS OF RESISTANCE OF PINS. Diameter of pin, d, in inches. 1 Area of pin, S, in spare 1 inches. j Diameter X area, d S. Bearing value for 1" thickness of bearing. Moments of resistance for fibre stresses of 1 Mo = f = inch-tons, j 6.0 tons per sq. in. 7.5 tons per sq. in. 7.5 tons per sq. in. 8.0 tons per sq. in. 9.0 tons per sq. in. 10.0 tons per sq. in. 12.5 tons per sq. in. Values, in tons. Values, in inch-tons. 2 3-142 6.28 12.00 15.00 5-89 6.28 7-07 7-85 9.81 3-546 7-54 12.75 15.94 7-07 7-54 8.48 9.42 11.78 3-976 8.95 13-50 16.88 8.39 8.95 10.07 II. 19 13-99 2:^ 4-430 10.52 14-25 17.81 9.86 10.52 11.84 13-15 16.44 2^ 4-909 12.27 15.00 18.75 11.50 12.27 13.81 15-34 19.18 2% 5-412 14.21 15-75 19.69 13-32 14.21 15.98 17.76 22.20 2^ 5-940 16.34 16.50 20.63 15-32 16.34 18.38 20.42 25-53 ^Vs 6.492 18.66 17-25 21.56 17-49 18.66 20.99 23.32 29-15 3 7.069 21.21 18.00 22.50 19.88 21.21 23.86 26.51 33-14 33 ^ 7.670 23-97 18.75 23-44 22.47 23-97 26.96 29.96 37-45 3 K 8.296 26.96 19.50 24-38 25.28 26.96 30.33 33-70 42.12 3 % 8.946 30.19 20.25 25-31 28.30 30.19 33-97 37-74 47.18 3 >^ 9.621 33-67 21.00 26.25 31-57 33-67 37.88 42.09 52.61 3 % 10.321 37-41 21-75 27.19 35-09 37-41 42.11 46.79 58.49 3 % 11.045 41.42 22.50 28.13 38.83 41.42 46-59 51.77 64.71 3 % 11-793 45-70 23-25 29.06 42.84 45-70 51.41 57-12 71.40 4 12.566 50.26 24.00 30.00 47.11 50.26 56.54 62.82 78.52 4I4 13-364 55-13 24-75 30.94 51.68 55-13 62.02 68.91 86.14 4'4 14.186 60.29 25-50 31.88 56.52 60.29 67.82 75.36 94.20 4 % 15-033 65-77 26.25 32.81 61.66 65-77 73-99 82.21 102.76 43 ^ 15-904 71-57 27.00 33-75 67.09 71-57 80.51 89.46 111.83 A % 16.800 77-70 27-75 34-69 72.84 77-70 87.41 97.12 121.40 45 ^ 17.721 84.18 28.50 35-63 78.92 84.18 94.70 105.22 131-52 4 % 18.665 90.99 29.25 36-56 85-30 90.99 102.37 113-74 142.18 5 19-635 98.18 30.00 37-50 92.04 98.18 110.45 122.72 153-40 5 % 20.629 105.72 30.75 38-44 99.11 105.72 118.94 132.15 165.19 534 21.648 113-65 31-50 39-38 106.55 113-65 127.85 142.06 177-58 5^/4 22.691 121.96 32.25 40.31 114.34 121.96 137.21 152.45 190.56 534 23-758 130.67 33-00 41-25 122.51 130.67 147.00 163.34 204.18 5/4 24.850 139-78 33-75 42.19 131.04 139-78 157-25 174.72 218.40 5 % 25.967 149-31 34-50 43-13 139.98 149-31 167.98 186.64 233-30 5 . 3 | 27.109 159-26 35-25 44.06 149-31 159.26 179.17 199.08 248.85 6 28.274 169.64 36.00 45.00 159.04 169.64 190.85 212.05 265.06 6% 29.465 180.47 36-76 45-94 169.19 180.47 203.03 225.59 281.99 634 30.680 191-75 37-50 46.88 179.77 191-75 215.72 239.69 299.61 63/4 31.919 203.48 38.25 47.81 190.76 203.48 228.92 254-35 317-94 634 33.183 215.69 39-00 48.75 202.21 215.69 242.65 269.61 337.02 6^ 34.472 228.38 39-75 49.68 214.10 228.38 256.92 285.47 356.84 6^ 35.785 241.55 40-50 50.63 226.45 241-55 271.75 301-94 377-42 634 37.122 255.21 41-25 51-56 239.26 255-21 287.11 319.01 398.76 7 38.485 269.40 42.00 52.50 252.56 269.40 303.08 336.75 420.94 734 41.282 299.29 43-50 54-38 280.58 299.29 336.70 374-11 467-64 734 44.179 331.34 45-00 56.25 310.63 331-34 372.76 414.18 517-73 734 47.173 365.60 46.50 58.13 342.75 365-60 411-30 457-00 571-25 8 50.265 1 402.12 1 48.00 60.00 1 376.99 402.12 ‘ 452.39 ' 502.65 628.31 256 POTTSVILLE, PENNA., U.S. A, WIND PRESSURE Upon the inclined surfaces of roofs. If P = intensity of wind pressure in pounds per square foot upon any surface normal to its direction, and (j) = angle made by roof surface with the direction of wind, then the normal pressure on the roof surface is given by = P. sin 1.84 cos (p — I. Let Pj^, P^, be the components of this normal force P^^, parallel and perpendicular respectively, to the direction of wind ; then Ph = P„. sin (j), and P^ = P^^. cos 0. If P be assumed to blow horizontally, then 0 is angle made by roof surface with the horizontal, and Pj^ is perpen- dicular to roof surface, and Pj^ and P^ are respectively parallel and perpendicular to direction of wind, — that is, respectively horizontal and vertical wind forces. TABLE OF NORMAL PRESSURES And vertical and horizontal components for varying inclina- tions of roof surface to direction of wind, when P = 40 pounds. Angle of roof. Pounds per square foot of surface. Pn Pv Ph 5 ° 5-0 4.9 0.4 10° 9-7 9.6 1-7 20° 18.1 17.0 6.2 30° 26.4 22.8 13.2 40° 33-3 25-5 21.4 50° 38.1 24-5 29.2 60° 40.0 20.0 34-0 70° 41.0 14.0 38.5 257 POTTSVILLE IRON AND STEEL CO, TABLE OF MULTIPLIERS For any wind intensity p pounds per square foot. Angle of roof, <^, 5 ° 10°. 20°. 30 °. 40 °. 50 °. 60 °. Pj^ = p (the wind unit) X 0.125 0.24 0.45 0.66 0.83 0.95 1. 00 Pv = p (the wind unit) X 0.122 0.24 0.42 0.57 0.64 0.61 0.50 pj^ =r p (the wind unit) X 0.010 0.04 0.15 0-33 0-53 0-73 0.85 Thus, for instance, if the angle of roof to the horizontal be 20°, and the wind be assumed as blowing horizontally, we find, from preceding table, that the force of wind normal to roof surface is i8.i pounds per square foot, the horizontal and vertical components of which are respectively 17.0 pounds per square foot and 6.2 pounds per square foot. The horizontal component tends to turn the roof framing about the leeward side considered as a fulcrum, and also to slide it off the walls; the vertical component acts as a one- sided load on the windward side of roof trusses. The trusses and framing should be proportioned to resist these eccentric loadings, and not for a uniform load distributed over whole surface of roof. Usually, the computation of the stresses is most quickly done by means of the Graphical method. WEIGHT OF ROOF COVERINGS In pounds per square foot. Lbs. Slate, yY' thick, on i" boards lo.o Slate, thick, on i" boards 7-5 Corrugated iron. No. 20, on 1” boards 6.0 Felt on boards, 3 ply, on i" boards = 3-5 Tin on i" boards 4-0 258 POTTSVILLE, PENNA., U. S. A. Lbs. Slate on T purlins 12.0 Corrugated iron and laths 6.0 i Slate or iron laths lo.o j When slate is used on purlins of T irons, the purlins should be 2 X 2 X 4 » pounds per yard, and spaced from 10" to 12" apart, the spacing between rafters (jacks and principals, or between jacks and jacks) should be about 5 feet. ANGLES OF ROOFS. Proportion of rise to span. Angle. Slope. Proportion of rise to span. Angle. Slope. 18° 25' 3 to I % 53° 00' ^tO I X 26° 35' 2 to I •% 56° 20' %tO I 33 ° 42' 45 ° 00' to I I to I I 63° 30' M to I 259 POTTSVILLE IRON AND STEEL CO., POTTSVILLE, PENNA., U. S. A. I T T TABLES OF WEIGHTS COMPILED FROM VARIOUS SOURCES. POTTSVILLE IRON AND STEEL CO., WEIGHT OF BAR IRON. Size, Square bar, Round bar, Area, Area, in inches. 1 foot long. 1 foot long. in □ inches. in 0 inches. 0.0132 0.0104 0.0039 0.0031 0.0526 0.0414 0.0156 0.0123 3 1 6 0.1184 0,0930 0.0351 0.0276 i 0.2105 0.1653 0.0625 0.0491 5 1 6 0.3290 0.2583 0.0976 0.0767 i 0.4736 0.3720 0.1406 0.II04 tV 0.6446 0.5063 O.I914 0.1503 1 2 0.8420 0.6612 0.2500 0.1963 1.0660 0.8370 0.3166 0.2485 1 1.3160 1.0330 0.3906 0.3068 1 1 1 6 4 1.5920 1.2500 0.4727 0.3712 1.8950 1.4880 0.5625 0.4418 1 3 1 6 2.2230 1.7460 0.6603 0.5185 7 8 2.5790 2.0250 0.7656 0.6013 1 5 2.9600 2.3250 0.8790 0.6903 I 3.3680 2.6450 1 .0000 0.7854 1 T6 3.8030 2,9860 1. 1290 0.8868 1 F 4.2630 3-3480 1.2660 0.9940 TF 4.7500 3.7270 1 .4090 1. 1070 1 4 5.2630 4-1330 1.5620 1.2270 TF 5.8020 4-5570 1.7230 1-3530 3 8 6.3680 5.0010 1.8910 1.4850 7 1 6 6.9600 5.4660 2.0670 1.6230 1 2' 7-5780 5-9520 2.2500 1.7670 TF 8.2230 6.4530 2.4390 1.9160 1 8.8970 6.9850 2.6410 2.0740 1 1 1 6 9.6460 7-5780 2.8640 2.2500 3 4 10.3100 8.I010 3-0630 2.4050 1 3 1 6 11.0700 8.6930 3.2870 2.5810 7 8 11.8400 9.3000 3-5160 2.7610 1 5 TF 12.6400 9-9300 3-7520 2.9480 2 13.4700 10.5800 4.0000 3.1420 i 15.2100 11.9500 4.5160 3-5460 1 4 17.0500 13.2900 5.0620 3-9760 3 . 8 19.0000 14.9200 5.6400 4-4300 F 21.0500 16.5300 6.2500 4.9080 f 23.2100 18.2300 6.8890 5.4120 3 4 25.4700 20.0100 7.5600 5-9390 7 8 27.8400 21.8700 8.2640 6.4920 3 30.3100 23.8100 9.0000 7.0690 F 32.8900 25.8300 9.7640 7.6700 1 4 35-5700 27.9400 10.5610 ^2960 3 8 38.3600 30.1300 11.3880 8.9460 1 9 41.2600 32.4100 12.2500 9.6210 262 POTTSVILLE, PENNA., U. S. A. WEIGHT OF BAR IRON. Size, in inches. Square har, 1 foot long. Round bar, 1 foot long. Area, in □ inches. Area, in 0 inches. 1 44.250 34.760 13-138 10.321 4 47-370 37.200 14.065 11.045 i 50.550 39.720 15.010 11-793 4 53-^90 42.330 16.000 12.566 i 57.290 45-010 17.012 13-364 i 60.820 47.780 18.058 14.186 A 8 64.470 50.630 I9.14I 15-033 68.210 53-570 20.254 15.904 a 8 72.030 56.590 21.385 16.800 3 4 75-990 59.690 22.556 17.721 i 80.000 62.830 23.748 18.655 5 84.200 66.130 25.000 19-635 i 88.440 69.480 26.260 20.629 4 92.810 72.910 27-557 21.648 s 8 97.280 76.430 28.884 22.690 1 101.900 80.020 30.250 23-758 5 8 106.600 83.700 31.641 24.851 f III .400 87.460 33-060 25-967 8 116.300 91.310 34-516 27.109 6 1 2 1. 300 95-230 36.000 28.274 1 4 131.600 103.300 39-063 30.679 j 142.300 III .800 42.250 33-183 3 4 153-500 120.500 45-562 35-785 7 165.000 129.600 49.000 38.485 177.000 139.000 52.562 41.282 189.500 148.800 56.250 44.179 1 202.300 158.900 60.062 47-173 8 215.600 169.300 64.000 50.266 i 229.300 1 80. 1 00 68.062 53-456 243.400 191.100 72.250 56.745 3 4 247.900 202.500 76.562 60.132 9 272.800 214.300 81.000 63-617 i 288.200 226.300 85-563 67.201 304.000 238.700 90.250 70.882 I 320.200 251.500 95.062 74.662 10 336.800 264.500 99.800 78.540 1 4 353-900 277.900 105.400 82.516 i 371.300 291.600 1 10.230 86.590 3. 4 389.200 305-700 115-550 90.763 II 1 407.500 320.100 ! 1 21. 000 95-033 i 426.300 : 334.800 126.540 99.402 445.400 1 349-800 132.220 103.870 3. 4 465.000 1 365-200 138.060 108.430 12 1 485.000 ! 380.900 i 144.000 113.100 263 POTTSVILLE IRON AND STEEL CO., TABLE GIVING DIMENSIONS OF UPSET ENDS 1 And weights of clevises and sleeve nuts for round and square bars. ROUND BARS. Weight of clevises Bar. Upset ends. and sleeve nuts for upset ends. Weight Diameter Length Iron required One One a per foot, Area. of upset. of upset. to make upset. devise. sleeve. in lbs. in inches. in inches. in inches. in lbs. in lbs. 0 1 1.50 0.441 I 4 3 f 5 f 5 7 2.00 0.601 if 4 3 6f 5 I 2.65 0.785 If 4 2f 6f 8 4 3-35 0.994 4 2f 7 i 8 4-13 1.227 If 4 and 6 2 and 3 l\ 9 7 3 5.00 1.484 If 4 and 6 ig and 2f 9 12 6.00 1.767 if 4 and 6 2f and 3f i 3 f 13 If 7.00 2-073 2 4 and 6 2I and 3^ 135 13 If 8.10 2.405 2f 4 and 6 2i and 3i 20i 16 if 9-30 2.761 2f 6 3 20J 16 2 10.60 3-141 2| 6 2f 25 f 18 2f 12.00 3-546 2f 6 2f 25 f 18 2i 13-30 3-976 2f 6 2f 25 2f 15.00 4-430 2f 6 2f 25 16.50 4.908 2f 6 2f 30 2f 18.20 5-411 3 6 2 30 SQUARE BARS. Weight of clevises Bar. Upset ends. and sleeve nuts for upset ends. .s Weight Diameter Length Iron required One One per foot, Area. of upset. of upset. to make upset. devise, sleeve. CO ^ § 0 in lbs. in inches. in inches. in inches. in -lbs. in lbs. 1 1.80 0.5625 if 4 4 6f 5 7 s 2.57 0.7656 If 4 5 7 i 8 1 3-36 1. 000 If 4 4 7 i 9 if 4.26 1.266 If 4 4 9 12 5.26 1.562 if 4 4 i 3 i 13 JF 5.80 1-725 2 4 4 i 3 f 13 , 6.36 1.891 2 4 4 13I- 13 Its 6.96 2.067 2f 4 f 4 20J 16 If 7-57 2.250 24 4 f 4 20| 16 It's S.22 2.439 2f 4 f 4 25 f 18 If 8.89 2.641 2f 4 f 4 25 i 18 Iff 9.64 2.864 2f 4 i 3 f 25 i 18 i| 10.31 3-063 2f 4 l 4 25 Iff 11.07 3.287 •2f ,1 3 4t 3 f 25 if 11.84 3-516 2f 5 3 l 25 III 12.64 3-752 2f 5 3 t 25 2 13-47 4.000 2f 5 3 f 1 30 264 WEIGHT OF WROUGHT-IRON BARS. > POTTSVILLE, PENNA., U. S. A. Width. mmmmmmmm WCJWN fOCOfOCO iDiniDin THICKNESS, IN INCHES. -< t^ONi-i romr^ONP) -^f-oo N^O O \n o\ cn f^Mvoo -^oo N ro (N >o 0 -^oo ro t-^ 10 Tj- f) M o\ r^\0 -^rOHO oo'Oioro rn ro Tt- -.i- in uS inid \0 t^cd d\ d o" w N cn - 4 - mid id t^od di vOvO'^'^'^rorom mQOoo t^O O ro ro h 0 OsCO i^vo i MinoN^'OC^MXooN cn ^ onO '^cnoco vO’^mo c^mrOM 1 fncofO’^'^intom \d t^oo on 6 m i-i oi ro tj- 10 lAvo t^oo m 01 00 ir> r) owo ro 0\ ro 0 -^oo w on rovo 0 tj- h 10 On rovo O-^t^HiTioocoroM oomroO c^^t-MON roroTj-Tj-'^ioto mvo c^oo cdoNO'-' mojcO'^ lAvo* vd i ■^00 nvOmioon'*^ t^mmro m 000 no rh-^roO Thi-icom wo^CN ONNO ro 0 no ro 0 OJ rororO'^-^'>i-ir> idno* no 00 * On On 0 * 6 m oi ro ro in in m .i-vo Cl w P) moo p) m, 00 N o ■l^oo O mio oi m m.oo oiopooi mpioo-^ Mt^rno lowoom Npjmropo-ii-d-d- m mid lO t^od od di d d >-< pi pi rd rn -"i- 1 - 1 , iH cj M ONOO coNOmm roMONt^ wnmoo NOmtNO oonO'^h roNO co>H'^i*c^oroNOnt^ro ONinMvo ncO'^O inMt^ro; oi d ci ro ro ro ^ rj- in inNO no t^od 00* on O'. 6 m w ci ci rd 1 M p.. ro Clio P) 00 m M tmo oi piTpp^oi pimp^o po moo O i M roio 00 M Tj-10 Cl p) P) P' rooo rooo 'j-oi '*'0 momw pipipjpirordrocd Tj-d-mmididodd-ododdid d«i-ipi , ! 01 p' w moo P) 10 Clio comrOM ooioroo t^..*-P)Oi| 00 w roo ooorom p^pjp~p) iowiom mqmq TT ’ w pi Pi pi pi ro ro ro rd 'i- 'i- m mio id P' P~oo oo oi Oi Oi O O j X' ' 1 00 0 >- Pi ro ^ mio P'OiMro mp.-OiPi ^iMO oo O Pi '^lO oo lOCi^romP-Oii-i rop.-Piio 0 ^oo ro w m O '*-cq q iq H d pi ci pi pi pi rd rd rd mm mio id P^ P~oo oo oo oi Oi ! P~iO ^ ro w oioo lO m Pi OO m pi omO ro o-.'O ro 0 P^ ..p 0 ^lO 00 0 Pi PO m p^ O'. POio O Tp p.. M m 00 q iq q ^ ” T M M q pi pi pi pi Pi pi PO PO 'p d" m m mio lo p^ p^ p^oo oo lOPioO’POmMp.^ ro -pio p'' oi M PI Ip m p~oo O Pi ro mio Pi 'pmp^oiO Pi PO moo H ” T 9 '9 *9 9 ' 9 M d w M w pi pi pi pi pi rd ro ro d- mm miO lO lO lO P' j J moo Pi moo mtpp.- Mp.-rociiOPiCOm mp^'PQ lOrooim 0 PO -P m p^oo O' i-i roio 00 « 'pio Oi pi P^ q 9 q' 9 " 9 d d d d d d d d pi pi pi pi rd rd rd rd d- d- ..p m mm miO .ip m mio lO p' p>oo oo 0 Pt ro 'p mio P'CO oi 0 w Pi ro ^ oooiOHpiro.pmiOOi'-'ro mr^ci'-' romp^q q q"iq oq d d d d d d d d d d pi pi pi pi pi rd rd rd rd d- d- d- d- d- Width. mmmmmmmm mrnmm minmio 265 WEIGHT OF WROUGHT-IRON FLATS. POTTSVILLE IRON AND STEEL CO., vovo^vo t^r'.t^t^000000c» OnOnOnOnOOOO hhhh m THICKNESS, IN INCHES. rH w iTioo rooooicON ^o^^ot>‘M^OQ csOoot^io^c^H ON ^ CO H q 0 ’ H H c^‘ ro invd vd c^oo* On d H ci C^(NC^O) WNCaiN COfOCT 00 M VO M 0\ '^SO 0 00 vq m m q o oo m w fo mvo’ t^OO* On 0* ") m comroro mmroro lOlCO ph|H ■^rOMM MOONt^'O'OlOrOOwQO.OO t^vo -.4- N (N 0 00 0\ t-' fO H 0\\0 ■^CNOOO'O 'd-MOC^lOrOMONt^u^C^HOO 00 On d H d N rd iri\o vdtdooo \00 HM'rdrd-.j- vnvo' td hm(nn nn(NN ncjinoi OMromrororomrororomro COC4VOO ^I^H-^COC^VOonC^'OO 'O'^HON'OrOHOo mroOt^^MO t^od On (d» d w d d ro ^ id uS vd d.oc HMHH MCJMN -i H N d rn rn rn -vi- Ti- in mvo vd vd t^oo c» t» ov ov 0 ►-12 ThHOOm NOOVDN OOVOMOVVD^O^ ;v|-H 00 ^ tl T PS 00 M in ov mvD 0 -"i- w vnoo n vd 0 rn vd 00 dv dv dv d d H H d (N d N ^ ^ ^ ^ OO o H m ■^vo ooosOCJ'^mvoooOw mvo oo o h cj vc “ os N m 00 H ^ S H ^ d. o mvo 0 ro vo q^ q m qs q mcq h d. d-od 00 00 dv dv dv d d d H d « d d d d n ^HOOirjC^ OsThHOOir^cs ^ ^ ^ H VO On ro q ^CO H VO 0 m m •^oo H '^00 H '«^-o6 H ^i-od H cd H mod h mod n mod oi cj(Nro ro^O’«^^T^ mm mvo vo vo t^oo oo oo on os On 0 HMH HHHHH hHHHH HMMHH HHHHMod h rj- o' cono’ On m' lOoO i-i fONO Ohh hng)(ncs rororo-.^--,*- ■^irNioNOinvONONOf^t^t^ MfCO Hh ^ 0 ^ T^oo nmo Tht^HVOO roi^O'^r^* nO’^t^w^ ro q ^ H onno ^ HoovoroM oomroQt^ irjq Onvo h H d-vd On d ^ d. d rd idod h ^ vd on d to d. d rd tdod h tJ* 000 Ohhm(n c^NMroro roro^*^^ mmm mvo vo roQro TJ•^xaN 0 ^^J mr^OoOH rovo oo m ro vo tJ-i^oncn tj- mOm OtoONOH vonr^cioo rooo roo**^ on’^On-^Oi^ rdvo od H fovd od H rdvd od w rd vd od h rdvd od h rdvd On h OnOnOn 0000*h MMMC4C') CNJCsrororo rOTf*^-«i-Thm oiON OCiromw '^mc^(NM m t^oo 0 w ro '^vo On 0 t^0rovoONC4moN M moo h tj- o ro q rovq O". q ^ On mod 0 d d- ON H od h ro mod d n m on h '^vo oo cooOOn OnOnOnOnO 000 mm hmc^(nci OJiNrorororo hOm 0HHN-.fio tONO -Ni- NO U1ND NO 03 M m ^ ^ ON 0 H (N ro lONO t^oo On O H n ro t)- lONO On O H M ro o' IN -^No od 0 CN -Nt-Nd od w rd ud rd on h rd id td 6 (d -d-No' r^OO 00 OOOOOOOnON OnOnOnOO OOOwh mhCNNCNO) ro 0 On vo m m '«^vo itn m -^co t>*vo vo m m ”^00 t^vo no H 0 00 t^vo m*^ro dHOoot^vom-^roq moo t^vo t1- 0 d H* m d. On m’ rd mod On d d -^Nd od d d Tf-vd od d d '*i* r^CO 00 OOOOOOOnON OnOnOnOO OOOmmm nOoo NO^roHoo NDioroOoo t^io-^MH oncnOon r^NO roONO root^-^o t^-jt-HOO-N^ HOOioisqN loroONOroq (N)'..*-id tdoNOW'Ni- intdcdotN -^'ot^ONO n '^no r^ on m NONONO NONor^r^r^ t^oo oo ooooooooon onononOnonO HOr^NOrOHOO->J- H ONNO NOrO HOONOrOH OONOrOHOONO m 0 ON 'll- On rooo ro (N w no h no q 10 q 10 On -,i-NO rd od 0 H r^ NO td On o' M ro iono oo On h m tJ- iono oo 10 10 10 iono NONONO NONONof^r^ t^t^t^r^f^cooooocococo \x CiK OONO NOCOONIOO voroON-Nt-O t^roONOro OnCNOOiohM 0 IN 1000 0 roNO 00 H rONO On H-^j-r^ONq no' od ON o' H rd ■4- id no' od On o' H rd ^no CO On 0 h ro ^ mmmmm mm mvo no vovononovo no r^OioooroON-'J-r) rooo no h r^ rooo ro on -nI-co ro On ^ O OnOO OHwCNiro rON^--^ iono no r^ r^oq oo_ Onco_ on On q h od o' H 0 ) rd Ti- IONO rdod cd 0 h in' rd tJ- iono' idod on O n rd ro'^'d" Tj-'^-.d-ioio lomioioio loio iono no no vO 0 '^ 00 (NVO 0 ^ 000 JVO 0 '^ 00 C^ '^oo N vo NO 0 Thoo mOoo NOtr^roMO oot^m^j-CQ OOvq'tq'^ *T H d d r^ Tt* mvd t^od dv d h d d ro tJ* m no c^oo on 0 rorom roromroro rororo-^'^ Width. t^OO Ov 0 H ro Ti- mNO t*^00 On 0 m ro iono t^OO Ov 0 rorom mmmmm mmmm mNO POTTSVILLE, PENNA., U. S. A. WEIGHT OF BARS OVER ONE INCH IN THICKNESS, Per lineal foot of length. .s WIDTH, IN INCHES. g g i I 2 3 4 5 6 7 8 •J hV 3-6 7.2 10.7 14-3 17.9 21.5 25.0 28.6 ItV 3-8 7.6 II.4 15.2 19.0 22.7 26.5 304 If ^T6 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 IjT 1 4-2 8.4 12.6 16.8 21. 1 25-3 29-5 33-6 If Ife ‘ 4-5 8.9 13-3 17.7 22.1 26.5 31.0 354 It\ If i 4-7 9-3 13-9 18.5 23.2 27.8 324 37-0 T 3 Is T 7 ^16 ! 4-9 ] - 14-5 19.4 24.2 29.1 33-9 38.8 ItV : 51 lO.I 15.2 20.2 25-3 30-3 354 40.4 If T ^ ■^16 ! 5-3 10.6 15.8 21. 1 26.3 31.6 36.9 42.2 It% If ' 5-5 10.9 16.4 21.9 27.4 32.8 38.3 43-8 If ill ^16 1 5 -/ 11.4 17.0 22.7 28.4 34-1 39-8 454 Hi If 1 5-9 11.8 17.6 23.6 29-5 35-6 41.3 47.2 If HI 6.1 12.2 18.3 24.4 30-5 36.6 42.7 1 48.8 HI If 6.3 12.6 18.9 25-3 31-5 37-9 I 44.2 50.6 If T 1 5 ije 6.5 13.0 19.6 26.1 32.6 39-2 i 45-7 52.2 HI 2 6.7 134 20.2 26.9 33-7 40.4 47.2 53-8 2 269 POTTSVILLE IRON AND STEEL CO., BOLTS, WITH SQUARE HEADS AND NUTS. Weight of one hundred of the enumerated sizes. HOOPES & TOWNSEND, PHILADELPHIA. Length, in inches. 13^" 4.16 10.62 23.87 39-31 4.22 11.72 25.06 41.38 2 4-75 12.38 26.44 45-69 73.62 % 5-34 12.90 28.62 49-50 76.00 23^ 5-97 14.69 29.50 51-25 79-75 2^ 6.50 16.47 31.16 53-00 83.00 3 17.87 32.44 56.00 85-38 127.25 3 /^ 18.94 39-75 63.12 93-44 140.56 4 , ^ 20.59 42.50 74.87 108.12 148.37 228.0 296.0 43^ 21.69 44.87 79.62 113.12 158.76 239-0 310.0 5 23.62 48.81 83.00 122.00 167.25 250.0 324.0 25.81 S'! .38 87.88 128.62 174.88 261.0 338.0 6 26.87 53-31 92.38 131-75 204.25 272.0 352.0 56.87 96.88 139-56 214.69 283.0 366.0 7 , ^ 59-12 99.87 145-50 228.44 294.0 370.0 73 ^ 61.87 105.75 150.88 235-31 305-0 384-0 8 64.44 109.50 157.12 239.88 316.0 398-0 9 70-50 118.12 169.62 258.12 338-0 426.0 10 77.00 128.13 184.00 276.18 360.0 454-0 II 82.88 136.19 195-13 295-69 382.0 482.0 12 86.37 144.87 209.75 311-94 404.0 510.0 13 92.00 155-50 219.37 335-81 426.0 538.0 14 97-75 163.58 237-50 351.88 448.0 566.0 15 103.25 170.75 249.06 391-75 470.0 594-0 Franklin Institute Standard Sizes SQUARE AND HEXAGON NUTS. Number of each size in loo lbs. These nuts are chamfered and trimmed. HOOPES & TOWNSEND, PHILADELPHIA. "Width. Thickness. Me. Size of holt. No. of square. No. of hexagon. h 1 \l i 8140 9300 TB t’s 3000 6200 f IB I 2320 3120 25 32 TB 7 16 1940 2200 7 i 1180 1350 li IB m TB 920 1000 Its 5 m 5 8 738 830 ij I- 5 f 420 488 T 7 7 8 7 8 280 309 I- I u I 180 216 Is H 130 148 2 It i-rg li 96 III 2t% i| I-S5 i§ 70 85 2| li I 32 12 60 70 270 POTTSVILLE, PENNA., U. S. A. f. WEIGHT OF RIVETS. Per hundred. Length from under head. Length, DIAMETER , IN INCHES. in inches. H % % • I 13^ xK I] 5-4 12.6 21-5 28.7 43-1 65-3 91-5 123.0 I.i, 6.2 13-9 237 31.8 47-3 70.7 98.4 133-0 If 6.9 15-3 25.8 34-9 51-4 76.2 105.0 142.0 2 7.7 16.6 27.9 37-9 55-6 81.6 II 2.0 150.0 8-5 18.0 30.0 41.0 59-8 87.1 II9.O 159-0 2^ 9.2 19.4 32.2 44-1 63.0 92-5 126.0 167.0 2f lO.O 20.7 34-3 47.1 68.1 98.0 133-0 176.0 3 10.8 22.1 36.4 50.2 72.3 103.0 140.0 184.0 3 f II -5 23-5 38.6 53-3 76.5 109.0 147-0 193-0 3 k 12.3 24.8 40.7 564 80.7 II4.O 154-0 201.0 3 l 13-1 26.2 42.8 594 i 84.8 120.0 161.O 210.0 4 13-8 27.5 45-0 62.5 1 89.0 125.0 167.0 218.0 4 f 14.6 1 28.9 47.1 65.6 93-2 I3I-O 174-0 227.0 4 j 15-4 1 30.3 49.2 68.6 97-4 136.0 181.O 236.0 4 f 16.2 ! 31.6 51-4 71.7 102.0 142.0 188.0 244.0 5 i 16.9 33-0 53-5 74.8 1 106.0 147-0 195-0 253-0 1 5 f 177 ' 34-4 55-6 77.8 IIO.O 153-0 202.0 1 261.0 i 5 ? 18.4 i 357 577 80.9 II4.0 158.0 209.0 i 270.0 i 5 f 1 19.2 ' 37-1 59-9 84.0 II8.0 163.0 216.0 ; 278.0 j 6 20.0 ; 38-5 62.0 87.0 122.0 169.0 223.0 287.0 j 6^ 21.5 41.2 66.3 93-.2 ^ I3I-O 180.0 236.0 304-0 ' 7 23.0 43-9 70.5 99-3 ' 139-0 I9I.O 250.0 321.0 7 k 24.6 46.6 74.8 106.0 147-0 202.0 264.0 338.0 8 26.1 49.4 79.0 112.0 156.0 213.0 278.0 355-0 8| : 27.6 52.1 83-3 118.0 164.0 223.0 292.0 372.0 9 29.2 54-8 87.6 124.0 173-0 234-0 306.0 1 389-0 406.0 9 ? 307 57-6 91.8 130.0 181.O 245.0 319-0 10 32.2 60.3 96.1 136.0 189.0 256.0 333-0 423-0 10^ , 33-8 63.0 lOI.O 142.0 198.0 267.0 347-0 440.0 ii" 1 35-3 '36.8 657 105.0 148.0 206.0 278.0 361.0 i 457-0 II? 1 68.5 109.0 155-0 214.0 289.0 375-0 474.0 12 38.4 71.2 113-0 161.0 223.0 300.0 388.0 491.0 Heads. 1.8 57 10.9 13-4 22.2 38.0 57-0 82.0 1 i 271 POTTSVILLE IRON AND STEEL CO., Table showing the average weight, in pounds, of one hundred MACHINE BOLTS Of various sizes and lengths, having square heads and square nuts. Lengths % A 34 1% % % % 1 4 6 9 % 15 21 30 35 2 4^ 7 II 17 24 33 % 39 68 234 534 8 1234 19 26% 37 43 74 116 3 6 % 9 14 21 29% 40% 48 81 124 185 3 % 7 10 1534 23 3234 44 52 87 132 196 4 7 % II 1734 25 35 47 % 56% 93 140 207 4 ^ 8^ 12 1834 27 37% 51 61 100 149 218 5 9 M 1334 20 29 40 54 % 65 106 158 229 sK 10 14^ 2134 31 42% 58 69 112 166 240 6 10% 1534 2334 33 4534 61% 74 118 174 251 63 ^ “34 1634 25 35 4834 65 r^\ 00 125 182 262 7 12^ 17M 26% 37 51% 68% 82% 131 190 273 7 K 13 18^ 2834 39 53 % 72 87 137 198 284 8 ^3% 20 3034 41 56 75 % 91 143 207 295 9 34 45 6134 82% 100 155 223 317 10 37 % 49 67 89% 109 168 240 339 II 41 53 7234 96% II8 180 256 360 12 4434 57 78 103% 127 192 272 382 13 8334 110% 135 205 289 404 14 89 117% 144 217 306 426 15 94 % 124% 153 230 323 448 16 100 131% 162 242 340 470 17 105% 138% I7I 255 357 492 18 III 145% •179 267 374 514 19 116% 152% 188 280 391 536 20 122 159% 197 292 408 558 272 POTTSVILLE, PENNA., U. S. A, Sizes and weights of SQUARE AND HEXAGON NUTS. 1 ?ranklin Institute Hoopes & Townsend's Standard Sizes. Regular Sizes. Square. Hexa- gon. Square. Hexagon. 'o o ' 1 :ght, each, in lbs. ;ght, each, in lbs. 1 ^ [ght, each, in lbs. i i ght, each, in lbs. E-> ^ ■ ’p 3 E-i s $ i * i 0.012 O.OII i 1 ■t 0.015 i i 0.012 T®S TS 0.033 0.016 i TS 0.028 5 8 TB 0.023 3 1 ' 16 1 0.043 0.032 f 1 0.049 3 4 3 8 0.040 TB M [ 0.052 1 0.045 : g 1 0.072 1 TS 0.046 i 1 1 0.085 0.074 I i 0.119 I TS O.III 1 % U : 9 ! 0.109 0.100 j ig i 0.154 I 1 0.II4 6 8 ^TB f : 0-135 1 0.120 li 6 « 1 0.244 Ig i 0.187 1 3 4 0.238 0.205 if * 0.370 Ig z 0-339 7 Its 1 0-357 , 0.32 li 1 1 0.465 Ig I 0.446 I If I 0-556 j 0.46 ' If I 0.714 1 If Ig 0.667 H III ig ■0.769 0.68 1 Ig 1 1.05 2 Ig 1. 00 li 2 li : 1.04 0.90 2i ij 1-39 ! 2 If 1.04 If -7 3 2ts If 1*43 1. 18 2g Ig 2.22 1 1 2f lA 1-39 I* i 2| j i^ ! 1.67 1-43 i 3 Ig 3.12 2f Ig 2.33 1 3 i Ig 3.50 2 3 ^ 2 525 2? 3 f 2f 5-75 2^ 1 ! 4 i 2f 7.25 2f 4 i 3 10. 0 3 1 1 4 f 3 f ! 12.0 POTTSVILLE IRON AND STEEL CO., « Standard sizes of WROUGHT-IRON WASHERS. Number in loo pounds. Thickness Size of bolt. Diameter, Size of hole, Number in in inches. in inches. of wire gauge. Number. in inches. 100 lbs. 1 f\ i6 1 4 29,300 f a 8 16 _5_ 1 6 18,000 I tV 14 3 8 7,600 T6 II f 3^300 I II T6 2,180 1 1 1 6 II 1 2,350 If 1 3 1 6 II 2 . 4 1,680 2 3 1 ■32 10 i 1,140 2^ 8 I 580 2| li 8 If 470 3 If 7 If 360 3 If 6 If 360 CAST HEADS AND WASHERS, For combination bolts. Diameter of bolt, I in inches. Diameter of head or washer, j in inches. Weight of head, in lbs. Weight of washer, in lbs. Diameter of bolt, in inches. Diameter of head or washer, in inches. Weight of head, in lbs. I ^ 1 Weight of washer, in lbs. 2f 0.32 0.32 If 6| 7.0 7.0 f 3 0.67 0.61 If 7 f 8.3 8.3 3 4 3 f 0.91 0.78 T 7 •■•8 7 l 10.4 10.4 7 8 3 l 0.95 0.89 2 8f 12.4 12.4 I 4 f 1-7 1-75 2f 8 | 134 134 If 4 | 2.3 2-3 2f 9 f 15.8 15.8 If 5 f 3-0 3-0 2f 9 f 17-5 17-5 If 5 | 4.2 4.2 2f 9 f 20.0 20.0 I^ 6f 5-2 5-2 274 POTTSVILLE, PENNA., U.S. A. WEIGHT OF LARGER SIZES OF FORGED HEXAGON NUTS Diameter of bolt, in inches. Weight, in lbs. Diameter of bolt, in inches. 1 Weight, in lbs. 2i 8 1 20 2f 9 3i 22 2j 3l 23 2f 11 3i 24 2| 3t 25 2i 14 3l 27 3 i 17 4 29 Note. — The above is the weight of iron required to forge one nut of the sizes given. 1 Weight, in lbs., of NUT AND BOLT HEADS. For common-sized nuts and heads, the following table is close enough for ! estimating the weights. HEAD AND NUT. HEAD AND NUT, 1 i Diameter of bolt. Square. 1 Hexagon. Diameter of bolt. 1 j Square. Hexagon. 1 i i 0.021 0.017 T 1 2.56 2.14 .3 8 0.70 0-57 li 4.42 3-77 i 0.164 0.128 If 7.00 5.62 t 0.321 ’ 0.267 2 10.5 00 Ln 3 . 4 0-55 0.43 2j 21.0 17.2 7 8 0.88 0.73 3 36.4 28.8 I 131 1. 1 ■I- 275 i POTTSVILLE IRON AND STEEL CO., Weight of ONE SQ. FOOT OF SHEET IRON OR STEEL. Birmingham Gauge. Thickness, in inches. No. of gauffo. Iron. Steel. In decimals. In fractions. 0000 0.454 29 64 18.35 18.54 000 0.425 _55_ 12 8 17.18 17-35 00 0.380 49 12 8 15-36 15-51 0 0.340 1 1 ¥2 13-74 13-87 I 0.300 1 9 12.13 12.25 2 0.284 9 32 11.48 11-59 3 0.259 33 12 8 10.47 10.57 4 0.238 3 1 12 8 9.62 9-72 5 0.220 3V 8.89 8.98 6 0.203 8.21 8.29 7 0.180 _2^3_ 12 8 7.27 7-35 8 0.165 6.70 6.74 9 0.148 1 9 12 8 5-98 6.04 10 0.134 5-42 5-47 II 0.120 tW 4-85 4-90 12 0.109 61- 4.41 4-45 ' 13 0.095 -S2 3-84 3.88 14 0.083 3-35 3-39 15 0.072 2.91 2.94 16 0.065 tV 2.63 2.65 17 0.058 2.34 2.37 18 0.049 1.98 2.00 19 0.042 1.70 1.71 20 0.035 1. 41 1-43 21 0.032 sV 1.29 1.30 22 0.028 1-13 1. 14 23 0.025 1. 01 1.02 24 0.022 0.889 0.898 25 0.020 0.808 0.816 26 0.018 0.722 0.735 27 0.016 6¥ 0.647 0.653 28 0.014 0.568 0.572 29 0.013 0.525 0.531 30 0.012 0.485 0.490 31 0.010 0.404 0.408 32 0.009 0.364 0.367 33 0.008 1 12 8 0.323 0.326 34 0.007 0.283 0.286 35 0.005 0.202 0.204 276 F POTTSVILLE, PENNA., U. S. A. r r r 1 I t- Weight of ONE SQ. FOOT OF SHEET IRON OR STEEL. American Gauge. Thickness, in inches. No. of grauKe. Iron. steel. In decimals. In fractions. 0000 0.46 1 5 3 2 18.63 18.87 000 0.41 1 3 3 2 16.58 16.80 00 0.365 tl 14.77 15.00 0 0.325 fi 1315 13-32 I 0.289 19 6¥ 11.70 11.86 2 0.257 1 7 6¥ 10.43 10.57 3 0.229 1 5 64 9.29 9.42 4 0.204 1 3 ■64 8.27 8.38 5 0.182 3 T6 7.37 7.46 6 0.162 1 1 ■64 6.56 6.64 7 0.144 9 64 5.84 5-92 8 0.128 ■§■ 5.20 5-27 9 0.H4 4.63 4.69 10 0.102 ■61 4.12 4.18 II 0.091 3 3 2 3-67 3-72 12 0.080 3-27 3-31 13 0.072 2.92 2.95 14 0.064 1 1 6 2.59 2.63 15 0.057 2.31 2.34 16 0.050 2.05 2.08 17 0.045 1.83 1.86 18 0.040 1.63 1.65 19 0.036 1.45 1.47 20 0.032 1 3 2 1.29 I- 3 I 21 0.028 I.I 5 i.i6 22 0.025 1.03 1.04 23 0.023 0.91 0.92 24 0.020 0.81 0.82 25 0.018 0.72 0.73 26 0.016 ■64 0.64 0.65 27 0.014 0:57 0.58 28 0.013 0.51 0.52 29 O.OII 0.46 0.47 30 0.010 0.41 0.41 31 0.009 0.36 0.37 32 0.008 0.32 0.33 33 0.007 0.29 0.29 34 0.006 0.25 0.26 35 0.005 0.23 0.23 277 POTTSVILLE IRON AND STEEL CO. AMERICAN AND BIRMINGHAM WIRE GAUGES Thickness, in inches. HASWELL No. of gauge. Thickness of American gauge. Thickness 1 of Birmingham' gauge. No. of gauge. Thickness of American gauge. Thickness of Birmingham gauge. 0000 0.46 0.454 17 0.0452 0.058 000 0.4096 0.425 18 0.0403 0.049 00 0.3648 0.38 19 0-0359 0,042 0 0.3248 0.34 20 0.0319 0-035 I 0.2893 0.30 21 0.0284 0.032 2 0.2576 0.284 22 0.0253 0,028 3 0.2294 0.259 23 0.0225 0.025 4 0.2043 0.238 24 0.0201 . 0.022 5 0.1819 0.22 25 0.0179 0.02 6 0.1620 0.203 26 0.0160 0,018 7 0.1443 0.18 27 0.0142 0.016 8 0.1285 0.165 28 0.0126 0.014 9 O.II44 0.148 29 0.0112 0.013 10 O.IOI9 0.134 30 O.OI 0.012 II 0.0907 0.12 31 0.0089 0.01 12 0.0808 0.109 32 0.0079 0.009 13 0.0719 0.095 33 0.007 0,008 14 0.0641 0.083 34 0.0063 0.007 15 0.057 0.072 35 0.0056 0.005 16 0.0508 0.065 36 0.005 0.004 278 POTTSVILLE, PENNA., U.S. A. CAST-IRON PIPE. Weight of a lineal foot. I j Thickness of metal, in inches. Bore, , in inches. % % % I LBS. LBS. LBS. LBS. LBS. LBS. LBS. LBS. LBS. 2 5-5 8.7 12.3 I6.I 20.3 24.7 29-5 34-5 39-9 2} 6.8 10.6 14.7 19.2 24.0 29.0 34-4 40.0 46.0 3 7.9 12.4 17.2 22.2 27.6 32.3 39-3 45-6 52.2 9.2 14-3 19.6 25-3 31-3 37-6 44.2 51.0 58.3 4 10.4 16.1 22.1 28.4 35-0 41.9 49.1 56.6 64.4 4 ? II. 7 18.0 24-5 315 38.7 46.2 54-0 62.1 70.6 5 12.9 19.8 27.0 34-5 42.3 50.5 59-9 67.7 76.7 14.1 21.6 29-5 37-6 46.0 54-8 63.8 73-2 82.9 6 153 23-5 31-9 40.7 49-7 59-1 68.7 78.7 89.0 7 17.8 27.2 36.9 46.8 57-1 67.7 78.5 89.8 lOI.O 8 20.3 30.8 41.7 52.9 64.4 76.2 88.4 lOI.O 1 14.0 9 22.7 34-5 46.6 59-1 71.8 84.8 98.2 II 2.0 126.0 10 1 25.2 38.2 51-5 65.2 79.2 93-4 108.0 123.0 138.0 1 II 27.6 41.9 56.5 71-3 86.5 102.0 118.0 134.0 150.0 12 30.1 45-6 61.4 77-5 93-9 III.O 128.0 145.0 163.0 13 I 32.5 49.2 66.3 83.6 lOI.O 119.0 138.0 156.0 175.0 14 35-0 52.9 71.2 89.7 109.0 128.0 147.0 167.0 187.0 15 37-4 56.6 76.1 95.9 116.0 136.0 157-0 178.0 199-0 16 39-1 60.3 81.0 1 102.0 123.0 145.0 167.0 189.0 212.0 18 1 44.8 67.7 90.9 114.0 138.0 162.0 187.0 21 1. 0 236.0 20 49-7 75-2 lOI.O 127.0 153.0 179.0 206.0 233-0 261.0 22 54-6 82.6 III.O 139-0 168.0 197.0 226.0 255-0 285.0 24 59-6 89.9 120.0 151.0 182.0 214.0 245.0 278.0 310.0 26 64-5 97-3 I3I.O 164.0 198.0 231.0 266.0 300.0 335-0 28 69.4 105.0 140.0 176.0 212.0 249.0 286.0 323-0 360.0 30 74.2 112.0 150.0 188.0: 227.0 266.0 305-0 345-0 384-0 Note. — F or each joint, add a foot to length of pipe. 279 POTTSVILLE IRON AND STEEL CO., WROUGHT-IRON WELDED TUBES. For steam, gas, or water. inch and below, butt welded ; proved to 300 pounds per square inch, hydraulic pressure. i3^ inch and above, lap welded ; proved to 500 pounds per square inch, hydraulic pressure. TABLE OF STANDARD DIMENSIONS. MORRIS, TASKER & CO., LIMITED. Inside diameter, in inches. Actual outside diameter, in inches. Thickness, in inches. Actual inside diameter, in - inches. Internal area, in inches. External area, in inches. Weight per foot of length, in pounds. Number of threads per inch of screw. 0.405 0.068 0.270 0.0572 0.129 0.243 27 i 0.54 0.088 0.361 0.1041 0.229 0.422 i8 3 8 0.675 0.091 0.494 0.1916 0.358 0.561 18 i 0.84 0.109 0.623 0.3048 0.554 0.845 14 3 4 1.05 0.II3 0.824 0.5333 0.866 1.126 14 I 1-315 0.134 1.048 0.8627 1-357 1.670 1.66 0.140 1.380 1.496 2.164 2.258 1.9 0.145 I.611 2.038 2.835 2.694 2 2.375 0.154 2.067 3-355 4-430 3-667 III 2.875 0.204 2.468 4-783 6.491 5-773 8 3 3-5 0.217 3-067 7.388 9.621 7-547 8 4.0 0.226 3-548 9.887 12.566 9-055 8 4 4-5 0.237 4.026 12.730 15.904 10.728 8 5-0 0.247 4.508 15-939 19-635 12.492 8 5 5-563 0.259 5-045 19.990 24.299 14.564 8 6 6.625 0.280 6.065 28.889 34-471 18.767 8 7 7.625 0.301 7-023 38.737 45-663 23.410 8 8 8.625 0.322 7.982 50-039 58.426 28.348 8 9 9.688 0.344 9.001 63.633 73-715 34-077 8 10 10.75 0.366 10.019 78.838 90.762 40.641 8 280 POTTSVILLE, PENNA., U.S. A, WROUGHT-IRON WELDED TUBES. Extra strong. 1 Thickness, j Actual inside Actual inside Nominal Actual outade Thickness, double extra I diameter. diameter. Diameter. diameter. extra strong. double extra strong. extra strong. strong. f ! 0.405 O.IOO j 0.205 4 ! 0.54 0.123 0.294 S 8 0.675 0.127 0.421 0.84 0.149 0.298 0.542 0.244 4 1.05 0.157 0.314 0.736 0.422 I 1-315 0.182 0.364 0.951 0.587 1.66 . 0.194 0.388 1.272 0.884 I? 1.9 0.203 0.406 1.494 1.088 2 2-375 0.221 0.442 1-933 I -49 1 Q.— 2.875 0.280 0.560 2-315 1-755 3 3-5 0.304 0.608 2.892 2.284 ol ; 4-0 0.321 0.642 3-358 2.716 4 1 4-5 0.341 0.682 3 - 8 i 8 3-136 SHIP SPIKES. Number in one hundred pounds. J 1 I 1 1 J 1 Number ^ 1 .1 Number ' ® t 1 1 Number g ! •S 1 in • s g in ' •2 .s in cT f I 100 lbs. 1 -s i N 100 lbs. "S) 100 lbs. w 1 1 -J 1 3 i 1-^ T ; 3 1910 1 A 5 461 9 T6 7 190 ^ 1 3^ 1 1585 1 T V 5i- 423 9 T6 7 l- 180 4 1 1326 Tj6 6 402 9 T6 8 170 4 42" 1 1223 ! 6J 321 9 T6 160 i I 5 1025 2 5“ 340 T6 9 150 A 1 3 1010 1 5i 312 TF 10 140 a 1 6 3-2- 963 ^ 6 298 1 8 140 5 1 6 4 810 i ^ 61 280 ' 1 9 120 _5_ 1 6 4f 605 1 ; * 7 261 , 5 8 10 no _5_ 1 6 ' 5 583 ' i 1 240 5, 8 II 100 5 lj6 6 521 : 1 i 8 223 i I 10 80 T% i 4 542 ; ! _9_ 1 1 6 6 221 ; 3 - 4 15 60 tV 1 4i 503 1 1 1 6 200 1 POTTSVILLE IRON AND STEEL CO NUMBER OF NAILS AND TACKS PER POUND. NAILS. TACKS. Title. Length, No. nails Title. Length, No. tacks in inches. per lb. in inches. per lb. penny fine. 760 I oz. 1 S' 16,000 3 I4- 480 I J A 10,666 4 T 1 At 300 2'' “ i 8,000 5 i| 200 2^ “ 6,400 6 2 160 3 “ s 8 5.333 7 a 128 4 “ _v_ 1 6 4,000 8 2i 92 6 “ T^6 2,666 9 2I 72 8 “ t 2,000 1,600 10 <( 3 60 10 “ 1 1 1 6 12 3t 44 12 “ 3 4 1.333 16 3 l 32 14 “ 1 3 16 1.143 20 u 4 24 16 “ ¥ 1,000 888 30 a 4‘i 18 18 “ 1 5 1 6 40 “ 5 14 20 “ I 800 50 “ S? 12 22 “ ItV 727 60 6 10 24 “ If 666 6 “ fence. 2 80 8 “ 22 - 50 10 “ 3 34 12 3t 29 j 5 pounds of 4 penny, or 3% pounds of 3 penny, will lay 1000 shingles ; j 5% pounds of 3 penny fine will put on 1000 laths, 4 nails to the lath. ! RAILROAD SPIKES. Length, Thickness, No. in Length, Thickness, No. in in inches. in inches. 100 lbs. in inches. in inches. 100 lbs. 4 f t'f 351 1 237 4j 267 52 “ 5k T¥ 193 5 1 473 1 146 5 T¥ 326 6 1 207 5 1 2 260 6 175 5 T6 197 6 1 I3I 5 1 172 J. 282 POTTSVILLE, PENNA., U.S. A. RAILROAD BARS. Table showing the number of tons per mile correspond- « ing to the following weight of rails per lineal yard. Ton of 2240 pounds. Weight per yard, in lbs. Tons per mile. Weight per yard, in lbs. 1 Tons per mile. 8 TO 1 280 •*■^•2240 I 52 8 i.MS§ 12 i 84 ne 56 88 16 25 - 2 ¥ 4 % 57 89 -MI§ 25 39 AYO 60 94.#2 ¥o 30 62 97 - 2 ¥ 4°0 35 55 64 100. 40 62.^110 65 102.2%% 45 68 50 70 no Calculated for “ single track” (2 rails). Multiply the pounds per yard by if, and the result will be the number of tons (of 2240 pounds) per mile of single track. RAILROAD SPLICE OR “FISH” JOINTS. The ordinary length of splice plates is 23" or 24", with 4 bolts of f" diameter to each pair of plates. The average weight of the plates is 16 pounds, and of the 4 bolts (with single nuts), 4 pounds, making 20 pounds total weight per “joint.” If double or “jam” nuts are used, the weight of the 4 bolts will be 5J pounds, or 2\\ pounds per joint. “SINGLE TRACK.” Lengths of rail, in feet. Nnmber of joints per mile. Pounds of plates per mile. Pounds of bolts per mile. Total weight per mile. 18 588 9408 2352 11,760 21 528 8448 2112 10,560 24 440 7040 1760 8,800 25 423 6768 1692 8,460 27 391 6256 1564 7,820 30 352 5632 1408 7,040 Note. — I f double nuts are used, add 37^ per cent, to the weight of the bolts. 283 POTTSVILLE IRON AND STEEL CO., NOTE ON BRICK ARCHES FOR FLOORS. The apjDroxiraate number of bricks, and the cost of brick work in arches for floors, will depend somewhat upon the size and cost per thousand of bricks. With bricks 8^- X 4 X 2, and joints of mortar from to between them, edgewise arches will require about 8 bricks per square foot of floor, and endwise arches will require ibg. Estimating the average cost of hard brick at ^10 per thou- sand, and the cost of laying, including mortar, centres, scaflblding, etc., at ^10 per thousand more, or $20 per thou- sand in place, the edgewise arches will cost 16 cents per square foot, and the endwise arches 33 cents per square foot, put up complete. WEIGHTS OF MATERIALS. Per cubic foot. Water • 62.3 Fire brick i37-0 Brick work 112.0 Coal, anthracite, solid . . 100.0 Coal, anthracite, broken ^7.0 Coal, bituminous 77-0- 90.0 Coke 62.0-104.0 Granite 164.0-172.0 Plaster of Paris 73.^ Limestone 169.0-175.0 Masonry 1 16.0-144.0 Sandstone 144.0 Slate 178.0 Common gravel 109.0 Mud 102.0 Mortar 98.0 Concrete 125.0 Common soil i37-0 Glass . 165.0 I bushel of bituminous coal weighs 80 pounds. 28 bushels = I ton of 2240 pounds. 284 POTTSVILLE, PENNA., U. S. A. WEIGHT OF TIMBER. Lbs. per cubic foot. Lbs. per foot, B. M. Relative strength for cross breaking. Crushing weight per so. inch in tons of 2000 lbs. Ash 47 3-9 149 4-3 Beech, white II5 Beech, red 43 3-6 144 4.6 Chestnut . . . • 33 2.8 II 2 Cedar, American white . . 50 4.2 63 2.8 Elm 34 2.8 51 Hemlock 95 Locust 44 3-7 Maple 49 4.1 White oak 45 3-8 145 2.8 Live oak 70 5.8 155 White pine 30 2-5 102 2-5 Yellow pine 33 2.8 98 2.7 vSpruce 86 Black walnut 42 3-5 I 2 I 3-0 PLASTERING. The plastering of inside walls of buildings generally consists of three separate coats of mortar. A plasterer, aided by one or two laborers, can average from lOO to 150 square yards a day of first coat; 90 to 100 yards of second coat ; and about 50 yards for the third coat. One thousand laths, X 4 ^ cover 660 square feet, and a carpenter can nail up laths at the rate of 50 square yards per day, in common square rooms. 285 POTTSVILLE IRON AND STEEL CO., AMERICAN SLATING. Slating is estimated by the “ square,” which is the quantity required to cover loo square feet. The slates are usually laid so that the third laps the first three inches. Therefore to compute the number of slates of a given size required per square : Subtract 3" from the length of the slate, multiply the remainder by the width, and divide by 2. This will give the number of square inches covered per slate ; divide 14,400 (the number of square inches in a square) by the number so found, and the result will be the number of slates required. The following table gives the number of slates per square for the usual sizes : NUMBER OF SLATES PER SQUARE. Size, in inches. Pieces per square. Size, in inches. Pieces per square. Size, in inches. Pieces per square. 6 X 12 533 8X 16 277 12 X 20 141 7 X 12 457 9 X 16 246 14 X 20 121 8X 12 400 10 X 16 221 II X 22 137 9 X 12 355 9 X 18 213 12 X 22 126 7 X 14 374 10 X 18 192 14 X 22 108 8 X 14 327 12 X 18 160 12 X 24 114 9 X 14 291 10 X 20 169 14 X 24 98 10 X 14 261 II X 20 154 16 X 24 86 The weight of slate per cubic foot is about 174 pounds, or per square foot of various thicknesses as follows : Thickness, Weight, Thickness, Weight, Thickness, Weight, in inches. in Ids. in inches. in Ids. in inches. in lbs. 1 . 81 i 3.62 4 7*25 2.71 3 8 5-43 The weight of slating laid per square foot of surface cov- ered will, of course, depend on the si^e used. The weight of 10 X slate, thick, for example, per square foot of roof, would be 5.86 pounds. SHINGLING. An average shingle 7J" wide in 8 ^" courses shows 64 making 3 shingles to a square foot of roof, including waste. They are usually laid in 3 thicknesses. 286 I POTTSVILLE, PENNA., U. S. A. PAINTING AND GLAZING. Painting is measured by the superficial yard, girting every part of the work that is covered by paint, and allowing an addition to the actual surface for covering deep quirks of moulding. Generally estimates are made for each coat of paint at a certain price per superficial yard. WINDOW GLASS. NUMBER OF LIGHTS PER BOX OF FIFTY FEET. j j Inches. No. Inches. No. 1 Inches. No. Inches. No. ! 6 X 8 150 12 X 18 33 ' 16 X 44 10 1 26 X 32 9 7X9 II5 12 X 20 30 1 18 X 20 20 1 26 X 34 8 8 X 10 90 12 X 22 27 1 18 X 22 18 26 X 36 8 8 X II 82 12 X 24 25 , 1 18 X 24 17 26 X 40 7 8 X 12 75 12 X 26 23 ' 1 18 X 26 15 26 X 42 7 8 X 13 70 12 X 28 21 j 18 X 28 14 26 X 44 6 8 X 14 64 12 X 30 20 18 X 30 13 26 X 48 6 8 X 15 60 12 X 32 18 1 18 X 32 13 26 X 50 6 8 X 16 55 12 X 34 17 1 18 X 34 12 26 X 54 5 9 X II 72 13 X 14 40 18 X 36 11 26 X 58 5 9 X 12 67 13 X 16 35 1 18 X 38 II 28 X 30 9 9 X 13 62 13 X 18 31 ! 18 X 40 10 28 X 32 8 9 X 14 57 13 X 20 28 18 X 44 9 28 X 34 8 9 X 15 53 13 X 22 25 20 X 22 16 28 X 36 7 9 X 16 50 13 X 24 23 20 X 24 15 28 X 38 7 1 9 X 17 47 , 13 X 26 21 20 X 26 14 28 X 40 6 9 X 18 44 13 X 28 19 20 X 28 13 28 X 44 6 1 9 X 20 40 13 X 30 18 20 X 30 12 28 X 46 6 1 10 X 12 60 j 14 X 16 32 20 X 32 11 28 X 50 5 10 X 13 55 14 X 18 29 20 X 34 II 28 X 52 5 10 X 14 52 14 X 20 26 20 X 36 10 28 X 56 4 10 X 15 48 14 X 22 23 20 X 38 9 30 X 36 7 10 X 16 45 14 X 24 22 20 X 40 9 30 X 40 6 10 X 17 42 14 X 26 20 20 X 44 8 30 X 42 6 10 X 18 40 14 X 28 18 20 X 46 8 30 X 44 5 10 X 20 36 14 X 30 17 20 X 48 8 30 X 46 5 10 X 22 33 14 X 32 1 16 20 X 50 7 30 X 48 5 10 X 24 30 14 X 34 15 20 X 60 6 30 X 50 5 10 X 26 28 14 X 36 14 22 X 24 14 30 X 54 4 10 X 28 26 14 X 40 13 22 X 26 13 30 X 56 4 10 X 30 24 14 X 44 II 22 X 28 12 30 X 60 4 10 X 32 22 15 X 18 27 22 X 30 II 32 X 42 5 10 X 34 21 15 X 20 24 22 X 32 10 32 X 44 5 II X 13 50 15 X 22 22 22 X 34 10 I 32 X 46 5 1 II X 14 47 15 X 24 20 22 X 36 1 9 32 X 48 5 ; II X 15 44 ( 15 X 26 18 22 X 38 9 ' 32 X 50 4 1 II X 16 ' 41 15 X 28 17 22 X 40 8 32 X 54 4 i II X 17 , 39 , 15 X 30 16 22 X 44 8 32 X 56 4 II X 18 ! 36 15 X 32 15 22 X 46 , 7 32 X 60 4 I II X 20 33 1 16 X 18 25 22 X 50 i 7 34 X 40 5 II X 22 30 16 X 20 23 24 X 28 1 II 34 X 44 5 II X 24 27 16 X 22 20 24 X 30 j 10 34 X 46 1 II X 26 25 16 X 24 19 24 X 32 1 9 34 X 50 4 II X 28 23 16 X 26 17 24 X 36 i 8 34 X 52 4 II X 30 21 16 X 28 16 24 X 40 1 8 34 X 56 4 II X 32 20 16 X 30 15 24 X 44 1 7 36 X 44 5 II X 34 19 16 X 32 14 24 X 46 7 36 X 50 4 12 X 14 43 16 X 34 13 ' 24 X 48 6 36 X 56 4 12 X 15 40 16 X 36 12 24 X 50 ' 6 36 X 60 3 12 X 16 38 16 X 38 12 24 X 54 j 5 36 X 64 3 12 X 17 1 35 16 X 40 II 24 X 56 ■ 5 40 X 60 3 287 POTTSVILLE IRON AND STEEL CO., SKYLIGHT AND FLOOR GLASS. LENNOX PLATE GLASS CO. WARD & CO., AGENTS, PHILADELPHIA. Weight per cubic foot, 156 pounds. WEIGHT PER SQUARE FOOT. TMckness, in inches. Weight, in lbs. Thickness, in inches. Weight, in lbs. Thickness, in inches. Weight, in lbs. h 1.62 -i 4.88 .3 4 9-75 _ 3 _ 16 2.43 6.50 I 13.00 3-25 1 8.13 FLAGGING. Weight per cubic foot, 168 pounds. WEIGHT PER SQUARE FOOT. Thickness, in inches. Weight, in Ids. Thickness, in inches. Weight, in Ids. Thickness, in inches. Weight, in lbs. I 14 4 56 7 98 2 28 5 70 8 II 2 3 42 6 84 BRICK WORK AND MASONRY. Stone work is estimated by the perch of 25 cubic feet. Brick work is estimated by the thousand, and for various thicknesses of wall runs as follows : 9" wall, or I brick in thickness, 14 bricks per superficial foot. 13" wall, or bricks in thickness, 21 bricks per superficial foot. 18" wall, or 2 bricks in thickness, 28 bricks per superficial foot. 22" wall, or 2^ bricks in thickness, 35 bricks per superficial foot. For each additional half brick in thickness count seven (7) bricks per superficial foot. One square yard of paving requires 36 bricks when laid flat, or 82 when laid on edge. A g” wall will weigh 84 pounds per square foot of side surface; a 13" wall, 1 21 pounds; an 18" wall, 168 pounds; assuming weight per cubic foot of brick work at 112 pounds. 288 POTTSVILLE, PENNA., U. S. A. GALVANIZED AND BLACK IRON. Weight, in pounds, per square foot of galvanized sheet iron, both flat and corrugated. The numbers and thicknesses are those of the iron before it is galvanized. When a flat sheet (the ordinary size of which is from 2 to 2J feet in width by 6 to 8 feet in length) is converted into a corrugated one, with corrugations 5 inches wide from centre to centre, and about an inch deep (the common sizes), its width is thereby reduced about jL part, or from 30 to 27 inches ; and consequently the weight per square foot of area covered is increased about i part. When the corrugated sheets are laid upon a roof, the over- lapping of about 2j inches along their sides, and of 4 inches along their ends, diminishes the covered area about ^ part more ; making their weight per square foot of roof about part greater than before. Or the weight of corrugated iron per square foot in place on a roof is about greater than that of the flat sheets of above sizes of which it is made. No. by Birmingliam ■wire gauge. BLACK. GALVANIZED. Thickness, in inches. Flat, in lbs. Flat, in lbs. Corrugated, in lbs. Corrugated, on roof, in lbs. 30 i 0.012 0.485 0.806 0.896 1.08 29 0.013 0.526 1 0.952 1. 14 28 : 0.014 0-565 i 0.897 0.997 1.20 27 0.016 0.646 0.978 1.09 1.30 26 0.018 0.722 1.06 1. 18 1. 41 25 0.020 0.808 1. 14 1.27 1.52 24 0.022 0.889 1.22 1.36 1.62 23 0.025 1. 01 1-34 1.49 1.79 22 0.028 : 1-13 1.46 1.62 1-95 21 0.032 ! 1.29 1.63 1 . 81 2.17 20 0.035 I.4I 1-75 1.94 2-33 19 0.042 1.69 2.03 2.26 2.71 18 0.049 1.98 2.32 2.58 3-09 17 0.058 2.34 2.68 2.98 3-57 16 0.065 1 2.63 2.96 329 3-95 15 0.072 1 2.91 3-25 3.61 4-33 14 0.083 3-36 3-69 4.10 4.92 13 0.095 1 3-84 4.18 4.64 5-57 Note. — The galvanizing of sheet iron adds about one-third of a pound to its weight per square foot. Nos. 20 to 22 are the usual sizes for roof coverings. 289 POTTSVILLE IRON AND STEEL CO. 290 POTTSVILLE, PENNA., U. S. A. ! i I ) i : TABLES OF MEASURES i j I i COMPILED FROM VARIOUS SOURCES. TABLE OF DECIMAL PARTS OF A FOOT FOR EACH ONE-THIRTY-SECOND OF AN INCH. POTTSVILLE IRON AND STEEL CO., M MD Onm •^t^O vni >.0 M M CM CM CM 1-0 10 10 C 5 ^o^c^o^o^o^o^o^o^o^o^o^cj^o^c 3 ^o^ 0 roC^iOMCX) -^OmO CMOO -^OmO CMOO ro 1 O 0 C 3 M COMO 0 ^ M On CM Ti- On CM rococO'^'^'iJ-'^i-OioiO ionO mO no no OOCOOOOOOOOOOOCOCXDOOOOOOOOOOOOOO 0 a> OnD CMOO -^OnO CMOO '^OnO coOniom 0 CM 10 0 CO 1000 0 conO 00 t-i rONO (On 10 10 10 VOVO NO NO NO r^oo 00 00 00 i>. (31 00 r^coC^LOH-i r^roCNiOM r^roONiOM nO Oni-h ^t^CTNCM -Nj-t^O lOf^O CO 10 NO nO> r^OO COOO (OnOnCUnOnO 0 0 nOnOnOnOnDnOnOnOnOnOnOnOnO 00 1 cocOnlowOO ^OnD CMOO 'chOO CMOO ^ CO LOOO i-i CO NO (Oni-h "chNO OnCM ■r^t^ONCM OOOOOOOGnOnCjnOOOOmmmwcm U-) LO LO un NO NO lO'Oi nOnOnOnOnOnOnOnO ONOCMOO'ChONOCMOO^ONOCOONlOM 0 CM 10 0 CO 1000 0 conO 00 c-i conO (On 0 0 0 0 I-H M >-( 1-4 CN) CM CM CM CO CO CO CO lOlOlOiOlOlOiOiOlOlONOl-OiOiOlOiO 1 VO IT) r^COGNLOl-l t^CO-i wo O N woco O (“O woco 1-1 cc M or t^CO cooooo OOOOO O O O I-I ’-1 cococccocococccccccc oooooo o o^ r ^"0 0 . wol-i t^coOwo^ r^roOwo>-( 11 ON -^t^ON wor^O N woco O OOOOOOOOn-iiiNNNNroi t^co CO CO CO CO oc cc 00 CO CO 00 CO cn CO rOOwonCO -i-OO NCO ^OO NCC CO O roo OC 1 On ^t^ON O n n n n N N N N ''■O'^C'OOO'^-'^"^ CO CO NCO -+-00 NCO ^oo roowon wor^o N WOOC O rowox n rOO 00 n N N • r <0 ro O OO ^ tJ- lid" wo wo wo wo O O OOOOOvCOOO'COOOOO'O t^roOwon r^'‘‘OOwon t^ooOwon n T^O ON ^r^ON wot^O N WOCO O of -rf icf lyo WO wo woiC o; o r^co wowowowowowowowowowowowowowowowo lO 1 ^OOwonOO ofOO NCO ofOO NCO of ‘ CO O ^OO CO n On oft^ON WOO O O O i>«co CO CO 00 O O O 1 lO OONCOofOONCOofOOOOOwon 1^0 O N woco O CO woco n rOO 00 n , I--CO cococo OOOOO O O O n n ro CO CO CO CO CO CO CO CO CO Tf of ^ ^ ^ rr 1 CO fi.COOwont^coOwonr^rOOwont^ ! n of O ON ofr^ONiyor^O N woco O OOOOOOOOnnncUMCSMro N N N N CO CO '“O CO CO 1 ^ CO CO CO CO CO CO 1 n ! N ' '“OOwonCO ofOO NCO ofOO N:X) of I CO O '“OOCC n ofo On -^t^ON ■'^ 1 ^ O n n n NH C) CJ M M ro oo CO CO of of of 1 NNNNCJNNNNNNNNNNN 1 « 1 i - ! I OOC’COofOONCO-fOOooOwon wo O N woco O oo woco n 1-00 CO n of , I N N oio <-o oo oo of of -f of wo 1-0 wo woO O '‘O o 1-n •-I “'O o u-i — c^ vn 1-1 I ON Ti-t^ON Lor^O N u~)X) O ^ -i- Ln Lo loO O O 1^ 1^00 ° OOOOOOOOOOOOOOOO I POTTSVILLE IRON AND STEEL CO., TABLES OF DECIMAL PARTS OF AN INCH FOR EACH ONE-SIXTY-FOURTH. 1 64 0.015625 1 9 64 0.2969 5 8 0.6250 sV 0.03125 5 1 6 0.3125 21 3 2 0.6562 6¥ 0.04687 ii 0.3438 43 64 0.6719 1 1 6 0.0625 If 0.3594 1 1 T6 0.6875 6T 0.07812 I 0.3750 23 3 2 0.7188 0.09375 M 0.4063 4 0.7500 eV 0.10937 0.4219 25 32 0.7812 0.1250 A 0.4375 13 1 6 0.8125 9 64 0.1406 15 32 0.4688 2 7 32 P bo 4 ^ 5 32 0.1563 3 1 61 0.4844 1 0.8750 0.1718 1 0.5000 If 0.8906 T®6 0.1875 11 32 0.5312 29 3 2 0.9062 V 3 2 0.2187 3 5 64 0.5469 1 5 1 6 0.9375 if 0.2344 9 1 6 0.5625 If 0.9531 0.2500 1 9 3 2 0.5938 31 3 2 0.9688 -32 0.2813 3 9 61 0.6094 6l 0.9844 POTTSVILLE, PENNA., U. S. A. MEASUREMENTS OF LENGTH. Miles. Rods. Yards. Feet. Inches. I. 320. 1760. 5280. 63360. 0.003125 I. 5-5 16.5 198. 0.000568 0.1818 I. 3 - 36. 0.00019 0.0606 0.0333 I. 12. 0.0000157 0.00505 0.0277 0.08333 I. Prussian foot = 12.356 inches. Prussian mile = 4.6804 English miles. German mile = 4.6105 English miles. Russian verst = 3500 feet = 0.6629 English mile. MEASUREMENT OF WEIGHTS. Tons. Cwts. Pounds. Ounces. I. 20. 2240. 35840. 0.050 I. 112. 1792. 0.0089 I. 16. 0.0625 I. I pound = 27.7 cubic inches of distilled water at 40° Fahrenheit. MEASUREMENT OF CAPACITY. Cubic yards. Barrels. Bushels. Cubic feet. Gallons. Cubic inches. I. 5.6103 25.2467 27. 201.97 46656. 0.1782 I. 4-5 4.8125 36. 8316. 0.0396 0.222 I. 1.2438 8. 2150. 0.2078 0.804 I. 7.476 1728. j 1 0.0277 0.125 0.13369 I. 231- 1 0.000578 0.00433 Bushels are here calculated without cones. \ I bushel = 2150.42 cubic inches of distilled water at 40° Fahrenheit. I Its dimensions are 18^^ inches diameter inside, 8 inches deep, and when ^ heaped the cone must be 6 inches high, or = 2748 cubic inches. I The imperial gallon = 277.274 cubic inches. I MEASUREMENT OF SURFACE. Sq. miles. Sq. acres. Sq. rods. Sq. yards. Sq. feet. Sq. inches. .001562 640. I. 0.00625 102400. 160. I. 0.033 3097600. 4840. 30-25 I. O.III 27878400. 43560. 272.25 9 - I. 0.00694 4014489600. 696960. 39204. 1296. 144. I. 295 G POTTSVILLE IRON AND STEEL CO., TABLE OF SQUARES AND CUBES Of all numbers from i to 500. No. Squares. Cubes. No. Squares. Cubes. I I I 50 25 00 125 000 2 4 8 51 26 01 132 651 3 9 27 52 2704 140 608 4 16 64 53 28 09 148 877 5 25 125 54 29 16 157 464 6 36 216 55 30 25 166 375 7 49 343 56 31 36 175 616 8 64 512 57 32 49 185 193 9 81 729 58 33 64 195 112 10 I 00 I 000 59 34 81 205 379 II I 21 I 331 60 36 00 216 000 12 I 44 I 728 61 37 21 226 981 13 I 69 2 197 62 38 44 238 328 14 I 96 2 744 63 39 69 250 047 15 2 25 3 375 64 40 96 262 144 16 2 56 4 096 65 42 25 274 625 17 2 89 4913 66 43 56 287 496 18 3 24 5 832 67 44 89 300 763 19 3 61 6 859 68 46 24 314 432 20 4 00 8 000 69 47 61 328 509 21 4 41 9 261 70 49 00 343 000 22 4 84 10 648 71 50 41 357 911 23 5 29 12 167 72 51 84 373 248 24 5 76 13 824 73 53 29 389 017 25 6 25 15 625 74 54 76 405 224 26 6 76 17 576 75 56 25 421 875 27 7 29 19 683 76 57 76 438 976 28 7 84 21 952 77 59 29 456 533 29 8 41 24 389 78 60 84 474 552 30 9 00 27 000 79 62 41 493 039 31 9 61 29 791 80 64 00 512 000 32 10 24 32 768 81 65 61 531 441 33 10 89 35 937 82 67 24 551 368 34 II 56 39 304 83 68 89 571 787 35 12 25 42 875 84 70 56 592 704 36 12 96 46 656 85 72 25 614 125 37 13 69 50 653 86 73 96 636 056 38 14 44 54 872 87 75 69 658 503 39 15 21 59 319 88 77 44 681 472 40 16 00 64 000 89 79 21 704 969 41 16 81 68 921 90 81 00 729 000 42 17 64 74 088 91 82 81 753 571 43 18 49 79 507 92 84 64 778 688 44 19 36 85 184 93 86 49 804 357 45 20 25 91 125 94 88 36 830 584 46 21 16 97 336 95 90 25 857 375 47 22 09 103 823 96 92 16 884 736 48 23 04 no 592 97 9409 912 673 49 24 01 117 6/9 98 1 96 04 941 192 POTTSVILLE, PENNA., U. S. A, TABLE OF SQUARES AND CUBES, ETC. No. Squares. Cubes. No. Squares. Cubes. 99 98 01 970 299 156 2 43 36 3 796 416 100 I 00 00 I 000 000 157 2 46 49 3 869 893 lOI I 02 01 I 030 301 158 2 49 64 3 944 312 102 I 04 04 I 061 208 159 2 52 81 4 019 679 103 I 06 09 I 092 727 160 2 56 00 4 096 000 104 I 08 16 I 124 864 161 2 59 21 4 173 281 105 I 10 25 I 157 625 162 2 62 44 4 251 528 106 I 12 36 I 191 016 163 2 65 69 4 330 747 107 I 14 49 I 225 043 164 2 68 96 4 410 944 108 I 16 64 I 2 SQ 712 165 2 72 25 4 492 125 109 I 18 81 I 2 Q^ 02 Q 166 2 75 56 4 574 296 no I 21 00 I 331 000 167 2 78 89 4 657 463 III I 23 21 I 367 631 168 2 82 24 4 741 632 II 2 I 25 44 I 404 928 169 2 85 61 4 826 809 113 I 27 69 I 442 897 170 2 89 00 4 913 000 114 I 29 96 ■ I 481 544 171 2 92 41 5 000 21 1 115 I 32 25 I 520 875 172 2 95 84 5 088 448 116 I 34 56 I 560 896 173 2 99 29 5 177 717 117 I 36 89 I 601 613 174 3 02 76 5 268 024 118 I 39 24 I 643 032 175 3 06 25 5 359 375 1 19 I 41 61 I 685 159 176 3 09 76 5 451 776 120 I 44 00 I 728 000 177 3 13 29 5 545 233 121 I 46 41 I 771 561 178 3 16 84 5 639 752 122 I 48 84 I 815 848 179 3 20 41 5 735 339 123 I 51 29 I 860 867 180 3 24 00 5 832 000 124 I 53 76 I 906 624 181 3 27 61 5 929 741 125 1 56 25 I 953 125 182 3 31 24 6 028 568 126 I 58 76 2 000 376 183 3 34 89 6 128 487 127 I 61 29 2 048 383 184 3 38 56 6 229 504 128 I 63 84 2 097 152 185 3 42 25 6 331 625 129 I 66 41 2 146 689 186 3 45 96 6 434 856 130 I 69 00 2 197 000 187 3 49 69 6 539 203 131 ! I 71 61 2 248 091 188 3 53 44 6 644 672 132 I 74 24 2 299 968 189 3 57 21 6 751 269 133 I 76 89 2 352 637 190 3 61 00 6 859 000 134 I 79 56 2 406 104 191 3 64 81 6 967 871 135 I 82 25 2 460 375 192 3 68 64 7 077 888 136 I 84 96 2 515 456 193 3 72 49 7 189 057 137 I 87 69 2 571 353 194 3 76 36 7 301 384 138 I 90 44 2 628 072 195 3 80 25 7 414 875 139 I 93 21 2 685 619 196 3 84 16 7 529 536 140 1 I 96 00 2 744 000 197 3 88 09 7 645 373 141 I 98 81 2 803 221 198 3 92 04 7 762 392 142 2 01 64 2 863 288 199 3 96 01 7 880 599 143 2 04 49 2 924 207 200 4 00 00 8 000 cxx) 144 2 07 36 2 985 984 201 4 04 01 8 120 601 145 2 10 25 3 048 625 202 4 08 04 8 242 408 146 2 13 16 3 112 136 203 4 12 09 8 365 427 147 2 16 09 3 176 523 204 4 16 16 8 489 664 148 2 19 04 3 241 792 205 4 20 25 8 615 125 149 2 22 01 3 307 949 206 4 24 36 8 741 816 150 2 25 00 3 375 000 207 4 28 49 8 869 743 151 2 28 01 3 442 951 208 4 32 64 8 998 912 152 2 31 04 3 51 I 808 209 4 36 81 9 129 329 153 2 34 09 3 581 577 210 4 41 00 9 261 000 154 2 37 16 3 652 264 211 4 45 21 9 393 931 155 2 40 25 3 723 875 212 4 49 44 9 528 128 297 POTTSVILLE IRON AND STEEL CO., TABLE OF SQUARES AND CUBES, ETC. No. Squares. Cubes. No. Squares. Cubes. 213 4 53 69 9 663 597 270 7 29 00 19 683 000 214 4 57 96 9 800 344 271 7 34 41 19 902 51 I 215 4 62 25 9 938 375 272 7 39 84 20 123 648 216 4 66 56 10 077 696 273 7 45 29 20 346 417 217 4 70 89 10 218 313 274 7 50 76 20 570 824 218 4 75 24 10 360 232 275 7 56 25 20 796 875 219 4 79 61 10 503 459 276 7 61 76 21 024 576 220 4 84 00 10 648 000 277 7 67 29 21 253 933 221 4 88 41 10 793 861 278 7 72 84 21 484 952 222 4 92 84 10 941 048 279 7 78 41 21 717 639 223 497 29 II o8q 567 280 7 84 00 21 952 000 224 5 01 76 II 239 424 281 7 89 61 22 188 041 225 5 06 25 II 390 625 282 7 95 24 22 425 768 226 5 10 76 II 543 176 283 8 00 89 22 665 187 227 5 15 29 II 6 q 7 08^ 284 8 06 56 22 906 304 228 5 19 84 II 852 352 285 8 12 25 23 149 125 229 5 24 41 12 008 989 286 8 17 96 23 395 656 230 5 29 00 12 167 000 287 8 23 69 23 639 903 231 5 33 61 12 326 391 288 8 29 44 23 887 872 232 5 38 24 12 487 168 289 8 35 21 24 137 569 233 5 42 89 12 649 337 290 8 41 00 24 389 000 234 5 47 56 12 812 904 291 8 46 81 24 642 171 235 5 52 25 12 977 875 292 8 52 64 24 897 088 236 5 56 96 13 144 256 293 8 58 49 25 153 757 237 5 61 69 13 312 053 294 8 64 36 25 412 184 238 5 66 44 13 481 272 295 8 70 25 25 672 375 239 5 71 21 13 651 919 296 8 76 16 25 934 336 240 5 76 00 13 824 000 297 8 82 09 26 198 073 241 5 80 81 13 997 521 298 8 88 04 26 463 592 242 5 85 64 14 172 488 299 8 94 01 26 730 899 243 5 90 49 14 348 907 300 9 00 00 27 000 000 244 5 95 36 14 526 784 301 9 06 01 27 270 901 245 6 00 25 14 706 125 302 9 12 04 27 543 608 246 6 05 16 14 886 936 303 9 18 09 27 818 127 247 6 10 09 15 069 223 304 9 24 16 28 094 464 248 6 15 04 15 252 992 305 9 30 25 28 372 625 249 6 20 01 15 438 249 306 9 36 36 28 652 616 250 6 25 00 15 625 000 307 9 42 49 28 934 443 251 6 30 01 15 813 251 308 9 48 64 29 218 112 252 6 35 04 16 003 008 309 9 54 81 29 503 629 253 6 40 09 16 194 277 310 9 61 00 29 791 000 254 6 45 16 16 387 064 311 9 67 21 30 080 231 255 6 50 25 16 581 375 312 9 73 44 30 371 328 256 6 55 36 16 777 216 313 9 79 69 30 664 297 257 6 60 49 16 974 593 314 9 85 96 30 959 144 258 6 65 64 17 173 512 315 9 92 25 31 255 875 259 6 70 81 17 373 979 316 9 98 56 31 554 496 260 6 76 00 17 576 000 317 10 04 89 31 855 013 261 6 81 21 17 779 581 318 10 II 24 32 157 432 262 6 86 44 17 984 728 319 10 17 61 32 461 759 263 6 91 69 18 191 447 320 10 24 00 32 768 000 264 6 96 96 18 399 744 321 10 30 41 33 076 161 265 7 02 25 18 609 625 322 10 36 84 33 386 248 266 7 07 56 18 821 096 323 10 43 29 33 698 267 267 7 12 89 19 034 163 324 10 49 76 34 012 224 268 7 18 24 19 248 832 325 10 56 25 34 328 125 269 7 23 61 19 465 109 326 10 62 76 34 645 976 298 POTTSVILLE, PENNA., U. S. A. TABLE OF SQUARES AND CUBES, ETC. No. Squares. Cubes. 1 "«• Squares. Cubes. 327 10 69 29 34 965 783 384 14 74 56 56 623 104 328 10 75 84 35 287 552 ! 385 14 82 25 56 066 625 329 10 82 41 35 611 289 386 14 89 96 57 512 456 330 10 89 00 35 937 000 387 14 97 69 57 960 603 331 10 95 61 36 264 691 388 15 05 44 58 411 072 332 II 02 24 36 594 368 389 15 13 21 58 863 869 333 II 08 89 36 926 037 390 15 21 00 59 319 000 334 II 15 56 37 259 704 391 15 28 81 59 776 471 335 II 22 25 37 595 375 392 15 36 64 60 236 288 336 II 28 96 37 933 056 393 15 44 49 60 698 457 337 II 35 69 38 272 753 394 15 52 36 61 162 984 338 II 42 44 38 614 472 395 15 60 25 61 629 875 339 II 49 21 38 958 219 396 15 68 16 62 099 136 340 II 56 00 39 304 000 397 15 76 09 62 570 773 341 II 62 81 ■ 39 651 821 398 15 84 04 63 044 792 342 II 69 64 40 001 688 399 15 92 01 63 521 199 343 II 76 49 40 353 607 400 16 00 00 64 000 000 344 II 83 36 40 707 584 401 16 08 01 64 481 201 345 II 90 25 41 063 625 402 16 16 04 64 964 808 346 II 97 16 41 421 736 403 16 24 09 65 450 827 347 12 04 09 41 781 923 404 16 32 16 65 939 264 348 12 II 04 42 144 192 405 16 40 25 66 430 125 349 12 18 01 42 508 549 406 16 48 36 66 923 416 350 12 25 00 42 875 000 407 16 56 49 67 419 143 351 12 32 01 43 243 551 408 16 64 64 67 917 312 352 12 39 04 43 614 208 409 16 72 81 68 417 929 353 12 46 09 43 986 977 1 410 16 81 00 68 921 000 354 12 53 16 44 361 864 411 16 89 21 69 426 531 355 12 60 25 44 738 875 ; 412 16 97 44 69 934 528 356 12 67 36 45 118 016 1 i 413 17 05 69 70 444 997 357 12 74 49 45 499 293 j 414 17 13 96 70 957 944 358 12 81 64 45 882 712 17 22 25 71 473 375 359 12 88 81 46 268 279 1 416 i 17 30 56 71 991 296 360 12 96 00 46 656 000 i 17 38 89 72 511 713 361 13 03 21 47 045 881 i 418 17 47 24 73 034 632 362 13 10 44 47 437 928 ' 419 17 55 61 73 560 059 363 13 17 69 47 832 147 420 17 64 00 74 088 000 364 13 24 96 48 228 544 421 17 72 41 74 618 461 365 13 32 25 48 627 125 I 422 1 7 80 84 75 151 448 366 13 39 56 49 027 896 1 423 17 89 29 75 686 967 367 13 46 89 49 430 863 424 1797 76 76 225 024 368 13 54 24 49 836 032 1 425 18 06 25 76 765 625 369 13 61 61 50 243 409 426 18 14 76 77 308 776 370 13 69 00 50 653 000 i 427 18 23 29 77 854 483 371 13 76 41 51 064 811 428 18 31 84 78 402 752 372 13 83 84 51 478 848 1 429 18 40 41 78 953 589 373 13 91 29 51 895 117 ! 430 18 49 00 79 507 000 374 13 98 76 52 313 624 ’ 431 18 57 61 80 062 991 14 06 25 52 734 375 , 432 18 66 24 80 621 568 376 14 13 76 53 157 376 433 18 74 89 81 182 737 377 14 21 29 53 582 633 434 18 83 56 81 746 504 378 14 28 84 54 010 152 435 18 92 25 82 312 875 379 14 36 41 54 439 939 436 ; 19 00 96 82 881 856 380 14 44 00 54 872 000 1 437 19 09 69 j 83 453 453 381 14 51 61 55 306 341 438 19 18 44 1 84 027 672 382 14 59 24 55 742 968 , 439 19 27 21 84 604 519 383 14 66 89 56 181 887 440 19 36 00 I 85 184 000 299 POTTSVILLE IRON AND STEEL CO., TABLE OF SQUARES AND CUBES, ETC. No. Squares. Cubes. No. Squares. Cubes. 441 19 44 81 85 766 121 471 22 18 41 104 487 III 442 19 53 64 86 350 888 472 22 27 84 105 154 048 443 19 62 49 86 938 307 473 22 37 29 105 823 817 444 19 71 36 87 528 384 474 22 46 76 106 496 424 445 19 80 25 88 121 125 475 22 56 25 107 171 875 446 19 89 16 88 716 536 476 22 65 76 107 850 176 447 iq q8 oq 89 314 623 477 22 75 29 108 531 333 448 20 07 04 89 915 392 478 22 84 84 109 215 352 449 20 16 01 90 518 849 479 22 94 41 109 902 239 450 20 25 00 91 125 000 480 23 04 00 no 592 000 451 20 34 01 91 733 751 481 23 13 61 III 284 641 452 20 43 04 92 345 408 482 23 23 24 III 980 168 453 20 52 09 92 959 677 483 23 32 89 II2 678 587 454 20 61 16 93 576 664 484 23 42 56 1 13 379 904 455 20 70 25 94 196 375 485 23 52 25 II4 084 125 456 20 79 36 94 818 816 486 23 61 96 II4 791 256 457 20 88 49 95 443 993 487 23 71 69 II5 501 303 458 20 97 64 96 071 912 488 23 81 44 I16 214 272 459 21 06 81 96 702 579 489 23 91 21 I16 930 169 460 21 16 00 97 336 000 490 24 01 00 II7 649 000 461 21 25 21 97 972 181 491 24 10 81 I18 370 771 462 21 34 44 98 611 128 492 24 20 64 1 19 095 488 463 21 43 69 99 252 847 493 24 30 49 II9 823 157 464 21 52 96 99 897 344 494 24 40 36 120 553 784 465 21 62 25 100 554 625 495 24 50 25 I2I 287 375 466 21 71 56 loi 194 696 496 24 60 16 122 023 936 467 21 80 89 101 847 563 497 24 70 09 122 763 473 468 21 90 24 102 503 232 498 24 80 04 123 505 992 469 21 99 61 103 161 709 499 24 90 01 124 251 499 470 22 09 00 103 823 000 500 25 00 00 125 000 000 LENGTH OF CIRCULAR ARC. Huygen’s approximation. Huygen’s approximation to length of a circular arc : A = chord of any circular arc. B =r chord of half that arc. R == radius of the circular arc. L = length of the circular arc. or, as it is usually written, L = 2 B + J (2 B — A). 300 POTTSVILLE, PENNA., U. S. A. TRIGONOMETRICAL FUNCTIONS. — = cosine b = tangent Therefore, angle A. “ A. » A. I b sine A a I b cosine A c I c tangent A a cosecant angle A. secant “ A. cotangent “ A. I 1 a = b X sine A, 1 b = a X cosecant A. ^ c = b X cosine A. 1 j I I b =: c X secant A. a = c X tangent A. c = a X cotangent A. 301 POTTSVILLE IRON AND STEEL CO NATURAL SINES, ETC. Deg. Sine. Cover. Cosecant Tangent. Cotang. Secant. Versin. Cosin. Deg. O 0.0 1. 00000 Infinite. 0.0 Infinite. 1.00000 0.0 1 .00000 90 I 0.01745 0.98254 57.2986 0.01745 57.2899 1.00015 0.0001 0.99984 89 2 o.o-:?48q 0.96510 28.6537 0.03492 28.6362 1 .00060 0.0006 0-99939 88 3 0.05233 0.94766 19.1073 0.05240 19.0811 1.00137 0.0013 0.99862 87 4 0.06975 0.93024 14-3355 0.06992 14.3006 1.00244 0.0024 0.99756 86 5 0.08715 0.91284 11-4737 0.08748 11.4300 1.00381 0.0038 0.99619 85 b 0.10452 0.89547 9.5667 0.10510 9-5143 1.00550 0.0054 0-99452 84 7 0.12186 0.87813 8.2055 0.12278 8.1443 1.00750 0.0074 0.99254 83 8 0.13917 0.86082 7.1852 0.14054 7-1153 1.00982 0.0097 0.99026 82 9 0.15643 0.84356 6.3924 0.15838 6.3137 1.01246 0.0123 0.98768 81 lO 0.17364 0.82635 5.7587 0.17632 5.6712 1.01542 0.0151 0.98480 80 11 0.19080 0.80919 5.2408 0.19438 5-1445 1.01871 0.0183 0.98162 79 12 0.20791 0.79208 4-8097 0.21255 4.7046 1.02234 0.0218 0.97814 78 13 O.224QS 0.77504 4-4454 0.23086 4 - 33 H 1.02630 0.0256 0.97437 77 14 0.24192 0.75807 4-1335 0.24932 4.0107 1.03061 0.0297 0.97029 76 15 0.25881 0.74118 3-8637 0.26794 3-7320 1.03527 0.0340 0.96592 75 16 0.27563 0.72436 3.6279 0.28674 3-4874 1.04029 0.0387 0.96126 74 17 0.29237 0.70762 3-4203 0.30573 3.2708 1.04569 0 0436 0.95630 73 18 0.30901 0.69098 3.2360 0.32491 3-0776 1.05146 0.0489 0.95105 72 19 0.32556 0.67443 3-0715 0.34432 2.9042 1.05762 0.0544 0.94551 71 20 0.34202 0.65797 2.9238 0.36397 2.7474 1.06417 0.0603 0.93969 70 21 0.35836 0.64163 2.7904 0.38386 2.6050 1.07114 0.0664 0.93358 69 22 0.37460 0.62539 2.6694 0.40402 2.4750 1.07853 0.0728 0.92718 68 23 0.39073 0.60926 2.5593 0.42447 2.3558 1 .08636 0.0794 0.92050 67 24 0.40673 0.59326 2.4585 0.44522 2.2460 1.09463 0.0864 0.91354 66 25 0.42261 0-57738 2.3662 0.46630 2.1445 1.10337 0.0936 0.90630 65 26 0.43837 0.56162 2.2811 0.48773 2.0503 1.11260 0.1012 0.89879 64 27 0.45399 0.54600 2.2026 0.50952 1.9626 1.12232 0.1089 0.89100 63 28 0.46947 0.53052 2.1300 0.53170 1.8807 1-13257 0.1170 0.88294 62 29 0.48480 0.51519 2.0626 0.55430 1.8040 1-14335 0.1253 0.87461 61 30 0.50000 0.50000 2.0000 0.57735 1.7320 1.15470 0-1339 0.86602 60 31 0.51503 0.48496 1.9416 j 0.60086 1.6642 1.16663 0.1428 0.85716 59 32 0.52991 0.47008 1.8870 0.62486 1.6003 1.17917 0.1519 0.84804 58 33 0.54463 0.45536 1.8360 0.64940 1-5398 1.19236 0.1613 0.83867 57 34 0.55919 0.44080 1.7882 0.67450 1.4825 1.20621 0.1709 0.82903 56 35 0.57357 0.42642 1-7434 0.70020 1.4281 1.22077 0.1808 0.81915 55 36 0.58778 0.41221 1.7013 0.72654 1-3763 1.23606 0.1909 0.80901 54 37 0.60181 0.39818 1.6616 0.75355 1.3270 1.25213 0.2013 0.79863 53 38 0.61566 0.38433 1.6242 0.78128 1.2799 1.26901 0.2119 0.78801 52 39 0.62932 0.37067 1.5890 0.80978 1.2348 1.28675 0.2228 0.77714 51 40 0.64278 0.35721 T -5557 0.83909 1.1917 1.30540 0.2339 0.76604 50 41 0.65605 0-34394 1.5242 0.86928 I. 1503 1.32501 0.2452 0.75470 49 42 0.66913 0.33086 1.4944 0.90040 1.1106 1-34563 0.2568 0.74314 48 43 0.68199 0.31800 1.4662 0.93251 1.0723 1.36732 0.2686 0.73135 47 44 0.69465 0.30534 1-4395 0.96568 1-0355 1.39016 0.2806 0.71933 46 45 0.70710 0.29289 1.4142 1.00000 I. 0000 I.4I42I 0.2928 0.70710 45 Cosin. Versin. Secant. Cotang. Tangent. Cosecant Cover. Sine. POTTSVILLE, PENNA., U. S. A. PROPERTIES OF CIRCULAR ARCS. c C D V. A B = c. CD=v = r(i — cos. (p). Given, chord A B == c, and ver. sine C D = v, required Given, chord A B and radius C E, to find rise C D. radius r. 2 then A + DC^ 2 D C C E .e. 303 POTTSVILLE IRON AND STEEL CO., Given, the radius and rise or vers, sine, to find the chord A B. A D = ^ C E"— (C E — C D)2 = 2 ^ 2 vr — ' TABLE OF PROPORTIONS OF THE CIRCLE AND ITS EQUAL. The diameter of any circle X — the circumfer- ence. The circumference of any circle X ( — z = 0-31831) : the diameter. 3 -I 4 I The square of the diameter X ( ^ = 0.7854^ = the ea. ^ The square of the circumference X = 0.07958^ - the area. \ 3 -i 4 i / The diameter of a circle X (V^ 0-7854 = 0.8862) = side of equal square. The circumference of a circle X (y 0.07958 = 0.2821) =r side of equal square. The side of any square X ( — 0^0 = 1.1284 ) = diam- eter of equal circle "" G.8862 ) The side of any square X f q 2821 ~ ~ circum- ference of equal circle. POTTSVILLE, PENNA., U. S. A. Square of side X ( ^ — = *-27324366) 1= square of \o.7»54 / diameter of equal circle = so-called round inches. Round inches X ~ 0-0546^ Square of diameter of equal circle X 0.7854 = square of side. Area of segment of circle = area of sector of equal radius, less area of triangle. Area of parabola = base X f height. Area of ellipse = longest diameter X shortest diameter X -7854- Area of any regular polygon = sum of its sides X perpendicular from its centre to one of its sides, divided by 2. Surface of cylinder = area of both ends -f- length X circumference. Surface of segment = height of segment X whole cir- cumference of sphere of which it is a part. Cubic contents of a cylinder = area of one end X length. 305 1 POTTSVILLE IRON AND STEEL CO., AREAS OF CIRCLES. Advancing by eighths. AREAS. Diam. I .0 •K % 0 0.0 0.0122 0.0490 0.1104 0.1963 0.3068 0.4417 0.6013 I 0.7854 0.9940 1.227 1.484 1.767 2.073 2-405 2.761 2 3.1416 3.546 3-976 4-430 4.908 5-411 5.939 6.491 3 7.068 7.669 8.295 8.946 9.621 10.32 11.04 11.79 4 12.56 13.36 14.18 15-03 15.90 16.80 17.72 18.66 5 19.63 20.62 21.64 22.69 23.75 24-85 25-96 27.10 6 28.27 29.46 30.67 31-91 33.18 34-47 35-78 37-12 7 38.48 39.87 41.28 42.71 44-17 45.66 47-17 48.70 8 50.26 51.84 53-45 55-08 56.74 58.42 60.13 61.86 9 63.61 65.39 67.20 69.02 70.88 72.75 74-69 76.58 10 78.54 80.51 82.51 84-54 86.59 88.66 90.76 92.88 II 95.03 97.20 99.40 101.6 103.8 106. 1 108.4 no. 7 12 II^.O II5.4 117.8 120.2 122.7 125.1 127.6 130.1 13 132.7 135.2 137-8 140.5 143-1 145.8 148.4 151.2 14 153.9 156.6 159-4 162.2 165.1 167.9 170.8 173.7 15 176.7 179.6 182.6 185.6 188.6 191.7 194.8 197.9 16 201.0 204.2 207.3 210.5 213.8 217.0 220.3 223.6 17 226.9 230.3 233.7 237.1 240.5 243-9 247.4 250.9 18 254.4 258.0 261.5 265.1 268.8 272.4 276.1 279.8 19 283.5 287.2 291.0 294.8 298.6 302.4 306.3 310.2 20 314.I 318.1 322.0 326.0 330.0 334-1 338.1 342.2 21 346.3 350.4 354-6 358.8 363-0 367-2 371.5 375.8 22 380.1 384.4 388.8 393-2 397-6 402.0 406.4 410.9 23 415.4 420.0 424-5 429.1 433-7 438.3 443.0 447-6 24 452.3 457.1 461.8 466.6 471-4 476.2 481.1 485-9 25 490.8 495.7 500.7 505-7 510.7 515-7 520.7 525-8 26 530.9 536.0 541 -I 546.3 551.5 556.7 562.0 567-2 27 572.5 577-8 583-2 588.5 593-9 599-3 604.8 610.2 28 615.7 621.2 626.7 632.3 637.9 643-5 649.1 654-8 29 660.5 666.2 671.9 677.7 683.4 689.2 695.1 700.9 30 706.8 712.7 718.6 724.6 7.30.6 736.6 742.6 748.6 31 754.8 760.9 767.0 773-1 779-3 785.5 791.7 798.0 32 804.3 810.6 816.9 823.2 829.6 836.0 842.4 848.8 33 855.3 861.8 868.3 874-9 881.4 888.0 8q4.6 901-3 34 907.9 914-7 921.3 928.1 941.6 948.4 955.3 35 962.1 969.0 975.9 982.8 989.8 996.8 1003.8 1010.8 36 1017. 9 1025.0 1032. I 1039.2 1046.3 1053.5 1060.7 1068.0 37 1075.2 1082.5 1089.8 1097. 1 1104. 5 1111.8 1119.2 1126.7 38 1134. 1 1141.6 1149. I 1156.6 1164.2 1171.7 1179.3 1186.9 39 1194.6 1202.3 1210. 0 1217. 7 1225.4 1233.2 1241. 0 1248.8 40 1256.6 1264.5 1272.4 1280.3 1288.2 1296.2 1304.2 1312. 2 41 1320.3 1328.3 1336.4 1344-5 1352.7 1360.8 1369.0 1377.2 42 1385.4 1393.7 1402.0 1410.3 1418.6 1427.0 1435-4 1443-8 43 1452.2 1460.7 1469.1 1477.6 1486.2 1494-7 1503-3 1511-9 44 1520.5 1529.2 1537-9 1546.6 1555-3 1564.0 1572.8 1581.6 45 1590.4 1599.3 1608.2 1617.0 1626.0 1634-9 1643-9 1652.9 306 POTTSVILLE, PENNA., U. S. A, CIRCUMFERENCES OF CIRCLES. Advancing by eighths. CIRCUMFERENCES. 1 'UIBIQ .0 Vs -14 0 0.0 0.3927 0.7854 1.178 1-570 1-963 2-356 2.748 I 3141 3-534 3-927 4-319 4.712 5-105 5-497 5.890 2 6.283 6.675 7.068 7.461 7-854 8.246 8.639' 9.032 3 9-424 9.817 10.21 10.60 10.99 11.38 11.78 12.17 4 12.56 12.95 13.35 13-74 14.13 14-52 14-92 15-31 5 15-70 16.10 16.49 16.88 17-27 17-67 18.06 18-45 6 18.84 19.24 19-63 20.02 20.42 20.81 21.20 21.59 7 21.99 22.38 22.77 23.16 23-56 23-95 24-34 24-74 8 25-13 25-52 25-91 26.31 26.70 27-09 27-48 27.88 9 38. 27 28.^ 29.05 29-45 29.84 30.23 30.63 31.02 10 31-41 31.80 32.20 32-59 32.98 33-37 : 33-77 34-16 II 34-55 34-95 35-34 35-73 36.12 36-52 36.91 37-30 12 37-69 38.09 38.48 38.87 39-27 39-66 40.05 40.44 13 40.84 41-23 41.62 42.01 42-41 42.80 43-19 43 58 14 43-98 44-37 44-76 45.16 45-55 45-94 46.33 46.73 15 47.12 47-51 47-90 48.30 48.69 49.08 49-48 49-87 16 50.26 50.65 51-05 51-44 51-83 52.22 52.62 53-01 17 53-40 53-79 54-19 54-58 54-97 55-37 55-76 56.15 18 56.54 56.94 57-33 57-72 58.11 58.51 58.90 59-29 19 59-69 60.08 60.47 60.86 61.26 61.65 62.04 62.43 20 62.83 63.22 63.61 64.01 64-40 64-79 65.18 65-58 21 65-97 66.36 66.75 67-15 67-54 67-93 68.32 68.72 22 69.11 69-50 69.90 70.29 70.68 71-07 71-47 71.86 23 72.25 72-64 73-04 73-43 73-82 74-22 74-61 75-00 24 75-39 75-79 76.18 76-57 76.96 77-36 77-75 78.14 25 78-54 78.93 79-32 79-71 80.10 80.50 80.89 81.28 26 81.68 82.07 82.46 82.85 83-25 83-64 84-03 84-43 27 84.82 85.21 85.60 86.00 86.39 86.78 87-17 87-57 28 87.96 88.35 88.75 89-14 89-53 89.92 90.32 90-71 29 91.10 91.49 91-89 92.28 92.67 93-06 ' 93-46 93-85 30 94-24 94-64 95-03 95-42 95.81 96.21 96.60 96-99 31 97-39 97-78 98-17 98-57 98.96 99-35 99-75 100.14 32 100.53 100.92 101.32 101.71 102.10 102.49 102.89 103.29 33 103.67 104.07 104.46 104.85 105.24 105.64 106.03 106.42 34 106.81 107.21 107.60 107-99 108.39 108.78 109.17 109.56 35 109.96 110.35 110.74 11113 111-53 1 1 1. 92 112.31 II2.7I 36 113.10 113-49 113.S8 114.28 114-67 115.06 115-45 115-85 37 116.24 116.63 117.02 117-42 117.81 118.20 118.60 118.99 38 119.38 119.77 120.17 120.56 120.95 121.34 121.74 122.13 39 122.52 122.92 123.31 123.70 124.09 124.49 124.88 125-27 40 125.66 126.06 126.45 126.84 127-24 127.63 128.02 128.41 41 128.81 129.20 129-59 129.98 130.38 130.77 131.16 131-55 42 131-95 132.34 132-73 133-13 133-52 133-91 134-30 134-70 43 135-09 135-48 135-87 136-27 136.66 137-05 137-45 137-84 44 138-23 138.62 139.02 139-41 139.80 140.19 140.59 140.98 45 141-37 141.76 142.16 142.55 142.94 143-34 143-73 144.12 307 I POTTSVILLE IRON AND STEEL CO., CONSTANTS RELATING TO THE CIRCLE. Constant. Log. Circumference of circle = n X diam. 'I Surface of sphere = tt (diam.)2 1 3-14159 0.49715 Area of circle — n X (radius)2 j Circumference of circle = 2 77 X radius . 2 77 6.28318 0,79818 Area of circle = 77 X (diam.)2 . . . ^77 0.785398 1.89509 Surface of sphere = 4 77 X (radius)2 . , 477 12.56637 I. 09921 Volume of sphere = 1 77 X (diam.)3 . 0.52359 1. 71900 Volume of sphere = 577 (radius)^ . . . 4.18879 0.62209 Square of tt 772 9.86960 0.99430 Square root of 77 yw 1.772454 0.24857 Cube root of tt 1.46459 0.16572 360° expressed in seconds 1296000 6.11261 360° expressed in minutes 21600 4-33445 Arc equal radius expressed in seconds . 206264.8 5-31442 Arc equal radius expressed in minutes . 3437-747 3-53627 Arc equal radius expressed in degrees . 180 77 57-29578 1.75812 Length of arc, i" — sin i" sin i" 0.000004848 6.68557 Length of arc, 1' — sin i' sin 1" 0.0002909 4-46373 CONSTANTS RELATING TO LOGARITHMIC SYSTEMS. Constant. Log. Base of Napierian system 1 2.7182818 0.43429 Modulus of Brigg’s system M 0.434294 1.63778 Reciprocal of modulus K 2.302585 0.36222 1 308 POTTSVILLE, PENNA., U-S. A. CONSTANTS RELATING TO GRAVITY. Constant. Cubic inch of distilled water at 62° F., in grains .... 252.458 Cubic inch of distilled water at 60° F., in grains .... 252.500 Cubic inch of distilled water at 4° C., in grains . . . . 252.890 Cubic foot of distilled water at 60° F., in ounces av. . . 997.310 Cubic foot of distilled water at 60° F., in pounds av. . . 62.33184 Cubic inch of mercurj" at 32° F., in grains 3438.8 Cubic inch of mercurj' at 32° F., in pounds av 0.49125 Seconds pendulum, in inches, at London 39-139 Seconds pendulum, in inches, at Pole 39.218 Seconds pendulum, in inches, at Latitude 45° 39.118 Seconds pendulum, in inches, at Equator 39.018 Gravity, in feet, at London 32.1908 Gravity, in feet, at Pole 32.2552 Gra\-ity, in feet, at Latitude 45° 32.1736 Gravity, in feet, at Equator 32.0907 REDUCTION MULTIPLIERS. ;,Bo,R CON VER r:-NG Cotistadt. Barometric inches ^2? F.V iht<> pou’i Js per«t,uare inch^ " \ . Barometric millimerres f ) j’jto kHo^pamnitS per Square centimetre Kilogrammes per square centimetre into pounds per square inch Foot-pounds into kilogrammetres C/.4Q125 0.00136 14.22263 0.13825 309 POTTSVILLE IRON AND STEEL CO. HEAT. THERMOMETERS. To convert the degrees of different thermometers, from one into the other, use the following formula : F stands for degrees of Fahrenheit, or 212° C stands for degrees of Celsius, or 100° R stands for degrees of Reaumur, or 80° boiling point. F = 32 and F = -|- 3^ for degrees above freezing point. F = — 32 and F — 32 for degrees below freezing point. 5 (F — 32) and R 4 (F — 32) for degrees above freezing point. ^ 5 (F + 32) _ ^ for degrees below freezing point. Zero of Celsius or Reaumur is = -j- 32° Fahrenheit. Zero of Fahrenheit = — 17 - 77 ° C. or — 14.22° R. I. How much is 8° Celsius above zero in Fahrenheit? 9X8 72 = 14.4 -|- 32 = 46,4° above. 2. ^How much i^<.8° Celsius below zero in Fahrenheit? F = ^ ^ = 14.4 — 32 = 17.6° above. - ^ . 5 .5 , _ C ^ ^ cc, X. ■ 4 I , ^ t c ' ' In cases zvher.ejhe product is sntalt^ than ^2, it indicates that the degree is above zero of Fahrenheit. See Example 2. 3. How much is 19° Celsius below zero in Fahrenheit? T 7 9 X 19 5 32 = 34.2 — 32 = 2.2° below Fahrenheit. 310