TABLES FINDING THE STRAINS RAILWAY BRIDGE TRUSSES UNDER THE ACTION OF A CONCENTRATED LOAD SYSTEM. - REPRINTED FROM STRAINS IN FRAMED STRUCTURES. SECOND EDITION. BY A. J. DUBOIS, PROFESSOR OF CIVIL ENGINEERING IN SHEFFIELD SCIENTIFIC SCHOOL OF YALE COLLEGE. NEW YORK : JOHN WILEY & SONS, 15 ASTOR PLACE. 1885. COPYRIGHT, 1883, BY JOHN WILEY & SONS. s u? -v & PREFACE. THESE Tables are intended to aid those engaged in the calculation of trusses. The system of concentrated loads annexed, is very closely that generally laid down in the specifications of our principal railroads. The use of the tables will be found sufficiently illustrated for all those for whom they are designed. The principles upon which the calculations are based are given at length in the author's work, "Strains in Framed Structures'' from which these Tables are reprinted. December 10, 1884. TABLE I. CONCENTRATED LOAD SYSTEM. SHEAR. UNIVERSITY TABLE I. CONCENTRATED LOAD SYSTEM. SHEAR. EXPLANATION OF TABLE. THE load-system adopted is given in Table I. It consists of two locomotives with tenders, followed by train ; the wheel-weights and distances being given in the first column. The locomotive agrees closely with the " standard consolidated engine," usually specified by the best railroad and bridge companies. It is believed that the load-system assumed is such as will give, in every case, results slightly in excess of the heaviest possi- ble loading which can actually occur in practice. The use of Table I. is quite simple. The length of span is /. The load always comes on from right, The maximum shear at any point, distant x from the left end, is given by one of four formulas. These formulae, and the limits between which they hold good, are given at the head of the table. For \\\ to limit, \ . pi.. >Shear = M/ , \ ., > int, \ /* 8)+ -( I ., 7 ,,., second wheel at point, \ I Limit to be found from table on right, pi 15000. . -- r 15000. I (II.) (III.) From x = limit to x I 8, first wheel at point, Shear = ^-' (/*) + -=(/ x 8) r I I I "row x I 8 to x first wheel at point, From x I 8 to x /, ) , /i , . \ Shear = fj (I x). (IV.) WEIGHTS, LBS. Distances. I-* or l-x-8. p A WEIGHTS, LBS, Distances. | /-.r or i-x-S. P A Span. Limit Span. Limit. feet x. feet. x. , /, =15000 ft. I / I8 = 1 5000 ft. 9' 8 4 335000 14370000 27 1 8.6 6l 38.5 a /2 = 25000 j O /= 12000 95 28 '9 62 39i 5 25000 O 1 5 347000 15510000 29 19.4 63 39f 2 J /3 = 2 5 5 , /20= 12000 IOO 3 19.9 64 39i SI 5 50000 125000 rt 10 359000 16710000 3 1 2O.6 65 39i O / 4 = 25000 10 ^ / 2I = 12000 no 32 21-3 66 39i J 5 75000 375000 5 371000 18030000 33 22 67 39| fs = 25000 15 p a = 12000 "5 34 227 68 ^ 7 100000 750000 5 383000 19410000 35 234 69 40?, pf, 15000 22 / 23 = I 2000 r 20 3 6 24.1 70 4'i 5 115000 1080000 5 395000 20850000 24.8 7' 415 0) /, = 15000 27 / 24 = 1 2OOO 125 38 25.5 72 42j *3 c 5 130000 1-485000 rt IO 407000 22350000 39 26.2 73 4*1 OJ p, 1 5000 32 w p 25 = 12000 "35 40 26.8 74 4 2 i ' 5 145000 1965000 5 419000 23970000 4' 27.2 75 4 2 5 /, = 15000 37 p 2 6 ! 2 O 140 42 276 76 43i * * * 9 160000 2520000 5 431000 25650000 43 28 77 433 /io= 15000 46 / 27 = T2000 '45 44 S8 7 78 44i ; 8 175000 3210000 5 443000 27390000 45 29.4 79 445 Q / = 25000 5 54 20OOOO ^560000 rt / 28 = I 2000 IO 150 455000 29190008 46 47 30.1 30.8 80 Si 45i 45i E /12 = 25000 11 59 O / 2 , = I 2000 1 60 48 3'-5 82 8 5 225000 6035000 5 467000 3IIIOOOO 49 32.2 83 4 li J3 />,3 = 25OOO 64 /jo = I 2OOO " 165 50 329 84 i 5 250000 7635000 5 479000 33090000 51 33-6 85 463 /1 4 = 25000 69 / 3I = 12000 170 52 34-3 86 47 i 7 275000 9360000 5 491000 35130000 53 35 87 4 Zl /= 15000 76 /32 = I 2000 175 54 35-4 88 4**H u 5 / I6 = 15000 j 81 290000 10500000 rt O / 33 = 12000 IO 185 503000 37230000 55 56 1 89 90 4^ c s 305000 11715000 5 515000 39450000 57 36.6 9 1 48 i r* / = 15000 86 /= 12000 190 58 37 92 48! 5 320000 13005000 5 527000 41730000 59 37-4 93 48 1 / = 15000 9 1 ^35 liUUU '95 60 375 94 47i TABLE I. CONCENTRATED LOAD SYSTEM. SHEAR. / = length of span. x = distance from left end, in feet, of any point at which the maximum shear is required. Values of P and A to be taken from table for corresponding / x, or / x 8. From x o to x 8, I (I.) , . . . , . ' > second wheel at point,} , Shear = -j(lx) -- r From x =8 to limit, \ . pi,, a . P., A , , , J , . > Shear = ~(l x+ 8) + -=(/ x) -- r 15000. (II.) second -wheel at point, \ / v . / / Limit to be found from table on right, pi = 15000. from x = limit to x = / 8. | _, pi., P , . A ( HI -) first -wheel at point, } Shear = T (/ ~ x) + 7 (/ ~ * ~ 8) ~ T From x=i-Stox = I, ) _ /. first wheel at point, \ bhear ~J (l x >~ WEIGHTS, LBS. Distances /- X or /-- r-8. P A Span, feet. Limit. Span. Limit. Span. Limit. Span. feet. Limit. Span. Limit, Span. Limit. x. feet. x. feet. x. x* feet. x. feet. x. # 12000 f, '95 /36 = I 2OOO s 2OO 539000 44070000 1 47* 473 128 129 62.5 63.2 161 162 79. 79 : 194 9'B 2n 227 228 89ft 89i 260 261 9'i 9'ft u 10 551000 46470000 47i '3 639 "63 80) 196 9 2 3 229 89ft 262 9' ft O Py, 12000 2IO 98 471 64.6 164 80: "97 9 2 I*z 230 89ft 263 9'i! 5 563000 48990000 99 47 i 132 65-3 I6 5 81: 198 9'l 23' 89!! 264 / 3 a 1 2000 215 100 474 '33 66 1 66 81: - 199 9' ft 232 9J 265 9 2 !} 5 575000 51570000 IOI 474 '34 66.4 167 Si 200 89i 233 9zi 266 9 2 I pyi = I2OOO 22O 1 02 47.6 '35 66.8 168 81; 20 1 234 9f 267 9 2 ft S 587000 54210000 103 48 136 67.2 169 82 2O2 88| 235 9ft 268 9 2 I \ /40 1 2OOO 225 104 48.4 '37 67.8 170 82; 2O3 88ft 236 9l 269 93?? d 10 599000 56910000 105 48.8 138 68.5 17' 83: 2O4 88| 237 9'uV 270 93fz (J / 4 l = I 20OO 235 106 49.2 '39 69.2' 172 8^ 205 89?^ 238 91 ?? 271 93z I S 6lIOOO 59730000 107 49.6 140 69.9 '73 84] 206 89ft 239 272 94 \ / = 1 20OO 240 108 5 141 70.6 '74 84 : 207 9T2 240 9"i 273 94ft / 43 = 12000 ' 5 245 623000 62610000 109 IIO 50.4 50.9 142 '43 7i-3 72 '75 176 84 : 84! 208 209 9^1*2 241 242 9 2 ft 9' H 274 275 93l, 93ft ' 5 635000 65550000 in 516 144 72-7 '77 85: - 210 9H 243 9 2 A 276 93s /4 = 12000 250 112 52-3 MS 73-4 178 85; 211 9OzV 244 9 2 i 277 9jft IO 647000 68550000 "3 53 146 74.1 179 86 212 9i 245 93?* 280 rt . CJ /4 S = 12000 260. 114 53-7 M7 74.6 1 80 86; 2I 3 9^2f 246 93?5 281 9il c 659000 71670000 "5 54-4 148 75 181 87: 214 9'ft 247 93ft 285 9 2 jV /46 = 12000 265 n6 55- ' 149 75-4 182 87; 215 9'ft 248 93J 286 9'l S 67IOOO 74850000 117 55-8 150 75-8 "83 5 216 9'i 249 93ft 287 9'Jf / 47 = 12000 270 n8 '5' 76.2 184 88^ V 217 250 92| 291 93 A s 683000 78090000 119 57.2 152 76.6 185 88J \ 218 9'8 251 9ft 292 934 /,8 = t2OOO 275 1 20 57.8 '53 77 1 86 89, V 219 92^1 '252 93 2 93 93ft U 10 695000 81390000 121 58.2 "54 77-4 187 8 9 3 f 2 2O 253 9ft 294 93 f? u ' /4, = 12000 > S 285 707000 84810000 122 I2 3 58.6 59 '55 "56 781 188 189 90, goJ I 221 222 92^ 254 255 m 296 94J /so = 12000 s 290 719000 88290000 124 125 60.4 '57 158 7ft 78| 190 191 90, 90 1 223 224 W 256 257 & 297 298 94 s /SI = I 2000 295 I2O 61.1 "59 192 9' 225 9 2 ft 258 9ii 299 94A 5 731000 91830000 127 61.8 160 78| "93 9'i 1 226 89! 259 9'? 300 /S2 = 1 2OOO 300 TABLE II. CONCENTRATED LOAD SYSTEM. * In applying II. to a. framed girder, if the panel length is more than 8 feet, we must put instead of 15000 (= pi), that portion of pi only, which, by the law of the lever, takes effect at the 1st apex on left of pi. TABLE I. (i.) CONCENTRATED LOAD SYSTEM. SHEAR. / = length of span. x = distance from left end, in feet, of any point at which the maximum shear is required. Values of P and A to be taken from table for corresponding / x, or / x 8. From x = o to x = 8, second wheel at point, From x = 8 to limit, \ fa = - rom x = o m, . ., ... ., j , , * + + > Shear = -(/ x+ 8) 4- -r(/ x) -- r 15000. second wheel at point, \ / . / / Limit to be found from table on right, /i = 15000. (II.) From x limit to x = I 8, | , fa . first wheel at point, | Shear =-(/_. From x = I 8 to x = /, , ..... first wheel at point, x = /, | _, fa . .. > Shear = T-(/ x). int, \ I* (IV.) WEIGHTS, LBS. Distances /- x or t-x-1. P A Span. Limit. Span. Limit. Span Limit. Span, feet. Limit Span. Limit. Span. Limit. feel. x. feet. x. feet. x. X. feet. x. feet x. TABLE II. CONCENTRATED LOAD SYSTEM. MOMENTS. TABLE II. CONCENTRATED LOAD SYSTEM. MOMENTS. EXPLANATION OF TABLE. FOR the maximum moment at any point of any span given in the table, simply multiply the value of the reaction Jf by the value of x, the distance of point from the left end, and subtract the value of /. The index of p, in the last column, shows the number of the wheel which must rest on the point, and hence the position of the load-system on the span. The load-system itself is given in Table I. Thus, for span of 200 feet : At 5 feet from left end, the reaction at left end is R 305175 Ibs. The moment is Kx= 305 1 75 x 5= 1525875- The second wheel of the system must rest on the point. At 10 feet from left, the reaction is j? = 306850 Ibs. The moment is fix m = 306850 x 10 120000 = 2948500. The second wheel of the system must rest on the point. At 20 feet from left, the reaction is J? = 293600 Ibs. The moment is Rx m = 293600 x 20 320000 = 5552000. The third wheel of the system must rest on the point. To find the moment at a point not given by the table, find the reaction R for this point by interpolation, and then proceed as before. Thus, At 30.7 feet from left, the reaction is 280650 (280650 278060)3*5 = 278837. The moment is Rx m 278837 x 30.7 645000 = 791520. The fourth wheel of the system must rest on the point. If, however, this point falls between two "fields" find the moment by interpolation. Thus, At 45.4 feet from left, we have the moment at 45, 255050 x 45 1095000 10382250. The moment at 46 -is 270290 x 46 1900000 = 10533340. At 45.4, then, we have 10382250 + (10533340 10382250)^, = 10442686. The fifth or sixth wheel at point, indifferently. In general, it will not be necessary to interpolate, but will be sufficient to take the nearest foot given in the table. To find the moment at any point of a span not given in the table, find the moment at the same point for the two nearest spans given, and interpolate. Thus, span 204 feet, moment at 10 feet from left: The moment at 10 feet from left, for a span of 200 feet, is 2948500. The moment at 10 feet from left, for span of 210 feet, is 3063330. The moment at 10 feet from left, for 204 feet span, is, then, 2948500 + (3063330 - 2948500) 1% = 2994432. The second wheel of system at point, vi TABLE II. CONCENTRATED LOAD SYSTEM. MOMENTS. = J?x SPAN, SPAN, SPAN, SPAN, 10 ii 12 13 feet. feet. feet. feet. JC y? m X ^ m .r j? m X i? m I 32500 I 34090 I 375oo I 40384 2 3 2/500 22500 o A 2 3 29545 25000 {>, 2 3 31250 27083 P* 2 3 34615 28846 A 4 17500 4 20454 4 22916 4 25000 5 12500 5 25909 S 18750 S 2 53 6 21363 6 37500 ri Pi 6 7 40384 346i5 IO N A 1 " SPAN, SPAN, SPAN, SPAN, M '5 16 >7 feet. feet. feet. feet. JC K m X R in AT R m jr K m I 42857 , 45000 I 46875 T 50000 2 375 T 40000 2 42187 2 44117 3 32142 A 3 35000 o A 3 37500 o f, 3 39705 o A 4 26785 4 30000 4 32812 4 35 Z 94 5 23214 5 25000 5 28125 5 30882 6 7 42857 37500 1^1 N A 6 8 45000 40000 35000 PI A 6 8 46875 42187 37500 N ft 6 8 50000 44117 39705 w> fl /. 9 35294 Vlll APPENDIX. MOMENTS. = Rx m. SPAN, SPAN, SPAN, SPAN, 18 19 20 21 feet. feet. feet. feet. X y? m ^ y? m X R m X * in i 52777 i 55263 \ 57500 i 59523 2 3 47222 41666 o A 2 3 5OOOO 44736 o P* 2 3 52500 47500 o * 2 3 54761 50000 o / 4 37500 4 39473 4 42500 4 45238 5 33333 5 35526 5 37500 5 40476 6 52777 6 55263 6 57500 6 59523 I 47222 41666 1 Pi 8 50000 44736 8, P, 21 52500 47500 8 h 8 54761 50000 8 9 37500 9 10 39473 35526 9 10 42500 37500 ~ 9 10 45238 40476 N ti ii 357H SPAN, SPAN, SPAN, SPAN, 22 2 3 24 2 5 feet. feet. feet. feet. .r /? . * R m X R m X R m I 61363 i 63043 i 65208 i 67200 2 56818 2 58695 2 60416 2 62600 3 52272 o A 3 54847 O P> 3 56250 o P* 3 58000 o P* 4 5 47727 43181 4 5 50000 45652 4 5 52083 47915 4 5 54000 50000 1 6 61363 6 63043 6 65208 6 67200 7 56818 7 58695 7 60416 7 62600 8 52272 8 8 8 56250 8 8 58000 Q 9 10 ii 47727 43181 38636 N 9 10 ii 50000 45652 41304 ft n Pi 9 10 it 52083 479 '5 43749 M Pi 9 10 ii 54000 50000 46000 N M ti 12 36956 12 39582 12 42000 13 38000 CONCENTRATED LOAD SYSTEM. IX MOMENTS. M., Rx m. SPAN, SPAN, SPAN, SPAN, 26 27 28 29 feet. feet. feet. feet. X R m * R m x R m .* A' m i 69038 i 70740 i 72321 i 74306 2 64615 2 66481 2 68213 2 69820 3 4 60192 55769 o A 3 4 62222 57962 o A 3 4 64106 60000 o A 3 4 65855 61889 O A 5 5 '923 5 53703 5 55891 5 57924 6 50000 6 5 '783 6 53958 6 69038 7 64615 7 66481 7 68213 7 69820 8 9 60192 55769 8 8 9 62222 57962 g 8 9 64106 60000 R 8 65855 61889 g 10 1 1 51923 48076 2 Pi IO II 53703 50000 10 M A 10 ii 5589' 51783 8, CI M /3 IO ii 57924 5395 s 10 N /3 12 44230 12 46296 12 48212 12 49993 13 40384 13 42592 >3 44640 3 46544 "4 53333 1 A M 55533 CO /3 14 15 57578 53612 cr />3 SPAN, SPAN, SPAN, SPAN, 3 31 3 2 33 feet. feet. feet. feet. X R m JC R m ' R m X R , , 76166 i 77903 I 79531 i 81060 2 71833 2 73709 2 75468 2 77121 3 4 67500 63666 o A 3 4 69516 65322 o A 3 4 71406 67343 o A 3 4 69242 o A. 1 56000 * 61612 57903 * 63281 59687 I 65303 61363 . 71833 7 73709 7 75468 7 77121 8 67500 8 69516 8 71406 8 9 IO ii 63666 59833 56000 N A 9 IO ii 65322 61612 57903 N M A 9 IO ii 67343 63281 59687 N /3 9 10 ii 69242 65303 61363 1 /3 12 52166 12 54193 12 56093 12 57878 '3 48333 '3 50483 3 52500 '3 54393 14 IS 59500 55666 CO A 14 61290 53870 1 A '4 15 16 63436 59373 5578o H /3 M 15 16 65454 61514 57574 N />3 i? 54090 APPENDIX. MOMENTS. /r = Rx m. SPAN, SPAN, SPAN, SPAN, 34 35 36 37 feet. feet. feet. feet. X R m jr R m X R m JC R m I 82941 I 84714 I 86388 1 87972 2 3 4 78676 74852 71029 o p* 2 3 4 80571 76428 72714 o A 2 3 4 82361 78333 74305 /* 3 4 84054 80135 76216 o A \ 67205 63382 69000 65285 ^ 70694 67083 72297 68702 8 78676 74852 I 80571 76428 7 82361 78333 84054 80135 9 71029 9 72714 8 9 74305 S 9 76216 X to 67205 1 fit IO 69000 Si P* IO 70694 LO />< IO 72297 & /3 ii 63382 N II 65285 ii 67083 N ii 68702 N 12 '3 59558 56176 12 '3 61571 57857 12 '3 63472 5986i 12 '3 65108 6I5I3 14 67353 14 69143 M 70833 14 725'3 16 i? 63528 59705 55822 n n /3 >5 16 !I 65428 61714 58000 54286 w to /3 15 ID 17 18 67221 63611 60000 563^8 N n /3 :i "7 18 68512 65000 61486 57937 fj m /3 '9 54460 SPAN, SPAN, SPAN, SPAN, 38 38 39 39 feet. feet. feet. feet. jr R m X R I/I jr R m X R m I 89473 14 74737 I 91282 14 76538 2 85657 15 70921 2 87179 15 72819 3 4 81842 78027 o P* 16 '7 67105 63685 PI ro /3 3 4 83461 79743 o A 17 69102 65384 w fO /3 5 74211 18 60263 76025 18 62050 6 70395 6 72307 19 74737 ^4 19 76538 -n A 7 85657 7 87179 8 81842 v?T 8 83461 ^ 9 78027 9 79743 10 74211 Wl ft IO 76025 v~> A, ii 70395 II 723 7 12 66974 12 68589 '3 63553 '3 65256 CONCENTRATED LOAD SYSTEM. XI MOMENTS. M,, = Rx m. SPAN, SPAN, SPAN, SPAN, 40 41 42 43 feet. feet. feet. feet. X R m X J? m X R m X J? m I 93000 I 94634 i 96190 I 97674 2 89000 2 90731 2 92380 2 93953 3 4 85000 8i375 o A 3 4 86829 82926 A 3 4 88571 84761 A 3 4 90232 86511 o A 7775 S 79390 80952 82790 6 74125 6 75853 6 77500 6 79069 7 89000 7 90731 7 92380 7 93953 8 85000 8 86829 8 88571 8 90232 9 81375 g 9 82926 8 9 84761 g 9 86511 9 10 7775 ") ft 10 79390 o ft 10 80952 to ft 10 82790 *n A ii 74125 ii 75853 ii 77500 ii 79069 12 70500 12 72317 12 74047 12 75697 3 66875 13 68780 3 7059S '3 72325 14 78250 14 79877 14 81784 H 83604 9 74625 71000 A 15 1 6 76341 72804 ft 15 16 77975 745 2 3 jj ft J| 79883 76162 A 17 67375 ro 17 69267 n fO 17 71071 ro 17 72790 H CO 18 65730 18 67618 18 69417 18 81875 g '9 78250 "-> A 19 79S77 g 19 81784 g 19 83604 g 20 74625 * 20 21 76341 720 4 "i <3" A 20 21 77975 74523 ft v? A 20 21 79883 76162 *T1 J? A 22 72790 SPAN, SPAN, SPAN, SPAN, 44 44 45 45 feet. feet. feet. feet. X R in X R m X R X R OT , 99090 M 85340 I 100444 14 87000 2 95454 15 81704 S 2 96888 83444 3 4 5 91818 88181 84545 O A 10 17 18 78067 7443 ' 7H35 N m A 3 4 93333 89777 86222 A ii 80000 76333 72777 Cl rt A 6 80909 6 82666 7 79111 19 85340 iq 87000 7 95454 20 81704 g 20 83444 g 8 91818 21 78067 *!- A 8 93333 21 80000 >o A 9 88181 g ^J 7443' vo 9 89777 _ 22 76333 v?r 10 84545 "i ft 10 86222 23 72777 ii 80909 ! ii 82666 to M 3 12 77272 12 79111 *" '3 73977 13 75555 Xll APPENDIX. MOMENTS. M,. = Rx m. SPAN, SPAN, SPAN, SPAN, 46 47 48 49 feet. feet. feet. feet. X R m X R 1 m X /? m X R m i 101739 I 102978 i 104479 i 105918 2 98260 2 99574 2 100834 2 102346 3 94782 T 96170 3 975o 3 98775 4 91304 P* 4 92765 o P* 4 94166 o A 4 9559 o ft 3 7 87826 84347 80869 7 89361 85957 82553 7 90833 87500 84166 7 92244 88978 85712 8 94782 8 96170 8 97500 8 98775 9 91304 Q 9 92765 o 9 94166 o 9 95509 Q 10 n 87826 84347 w ft 10 ii 89361 85957 10 ft 10 ii 90833 87500 N f 10 ii 92244 88978 to M ft 12 80869 " 12 82553 12 84166 " 12 85712 1-1 13 77391 '3 79148 13 80833 13 82446 14 88586 14 90424 '4 92187 '4 93874 15 85107 Q 15 86701 Q 15 88541 g IS 90302 g ID 17 18 81629 78151 74673 rt f> ft 16 17 18 83297 8> Ps 16 i? 18 84895 81563 78229 Cl n pi 16 17 18 86729 8 3 T 59 79893 N fO Pi '9 88586 19 90424 19 92187 19 93874 20 21 22 23 85107 81629 78151 74673 tO ^ p4 20 21 22 2 3 24 86701 83297 79893 76489 73085 < ^- vo A 20 21 22 23 24 88541 84895 81563 78229 74896 A 20 21 22 23 24 90302 86729 83159 79893 76628 o ^ P4 25 73363 SPAN, SPAN, SPAN, SPAN, 5 5 5 1 Si feet. feet. feet. feet. jr J? m X R m X R m X R m I 107300 14 95500 I 108627 14 97057 2 103800 92000 g 2 105196 15 93626 g 3 100300 16 88500 g ii 3 101764 16 90195 g Pi 4 96800 o t i? 85000 H n 4 98333 o ft 17 86764 ro 93600 18 81500 5 94901 IB 83332 6 90400 6 91764 7 87200 7 88627 if) 9=1500 19 97057 20 92000 20 93626 8 100300 21 88500 g 8 101764 21 90195 9 96800 22 85000 to ?4 9 98333 Q 22 86764 t. 10 ii 12 13 93600 90400 87200 84000 to M P* 2 3 24 25' 81500 78300 75100 3 10 ii 1 2 "3 94901 91764 88627 8549 N ft 23 24 2 C 26 83332 79901 76764 73 62 7 TJ- VO CONCENTRATED LOAD SYSTEM. XIII MOMENTS. = Rx m. SPAN, SPAN, SPAN, SPAN, 5 2 53 54 55 feet. feet. feet. feet. .* ^ m AT R m X R m ;r K m I 109903 , 111132 I 112314 i *134Sl 2 106538 2 107830 2 109074 2 110272 3 i3!73 3 104528 3 105833 3 107090 4 99807 A 4 101226 o A 4 102592 A 4 103909 o A | 96442 93076 1 979 2 4 94622 | 99351 96111 1 10x5727 97545 7 90000 7 91320 7 92870 7 943 6 3 8 I03I73 8 104528 8 I0 5 8 33 / 8 107090 9 99807 o 9 101226 9 102592 o 9 103909 Q 10 ii 96442 93076 u"i M A 10 it 97924 94622 n PI A 10 ii 9935 1 96111 in w A 10 ii 100727 97545 "1 A 12 90000 M 12 91320 M 12 92870 1-1 12 94363 '3 86923 '3 88301 13 89629 13 91181 14 98557 14 IOOOOO 14 101388 14 102727 15 95192 o 15 96697 g 15 98147 15 99544 16 17 91826 88461 M A 17 93395 90093 N A 16 17 94906 91665 ft 16 17 96362 93181 \ A 18 85095 <*j 18 86791 fO 18 88425 M 18 90000 N '9 81730 19 83489 19 85184 iq 86817 20 81943 20 83635 20 95'92 20 96697 21 91826 21 93395 21 94906 21 96362 22 88461 K 22 90093 o 22 91665 22 93181 23 24 3 85095 81730 78364 75288 8, A 23 24 3 86791 83489 80187 76885 "1 vj A 23 24 25 26 88425 85184 8i943 78702 fl 3 A Z 3 24 25 2O 90000 86817 83635 80454 10 A 27 73867 27 75462 2 l 77272 28 74090 SPAN, SPAN, SPAN, SPAN, 56 56 56 56 feet. feet. feet. feet. X R m X R * m X R m X R m , 115000 8 108303 14 104285 21 97767 2 111428 9 105178 Q 15 100892 22 94642 3 108303 10 102053 X 16 97767 33 gI5'7 Q 4 5 105178 102053 o A ii 12 98928 95803, N ^3 17 18 94642 9 1 S 1 7 ro A 24 1 c 88392 85267 VI f A 6 98928 3 92678 19 88392 26 82142 *o 7 95803 20 85267 27 79017 28 75892 XIV MOMENTS. M x = Jfx m. SPAN, SPAN, SPAN, SPAN, 57 58 59 60 feet. feet. feet. feet. X R m * R m X * m X R m i 116491 i "793 1 i 119322 i 120666 2 112983 2 114483 2 115932 2 "7333 3 4 109475 106405 '03335 A 3 4 i i 1034 107586 104569 A 3 4 S 112542 109152 105762 o /2 3 4 114000 110666 o fr 6 100265 6 101552 6 102796 6 104000 7 97195 7 98534 7 99830 7 101083 8 9 109475 106405 8 9 111034 107586 8 9 112542 109152 8 9 114000 . 110666 10 ii 12 '3 103335 100265 97195 94124 N A IO ii 12 104569 101552 98534 955'? 1 A IO ii 12 13 105762 102796 99830 96864 1 /3 IO ii 12 1 07333 104000 101083 98166 ' /3 14 15 105790 102457 15 107241 103965 14 15 108643 105423 H 15 IIOOOO 106833 IO 99124 g IO 100689 o IO 102203 Q 16 103666 o \l 96054 92984 A 17 18 97413 94396 o 1 A 17 98983 95761 /3 17 18 100500 97333 /3 '9 89914 ro 19 9'379 n 19 92796 n 19 94166 " 20 86843 20 88361 20 89830 20 91250 21 83773 21 85345 21 86864 21 88333 22 96054 22 97413 22 98983 22 100500 23 24 84 14 23 24 94396 9 '379 23 24 95761 92796 2 3 24 97333 94166 2 5 26 43 83773 80703 77633 | A 2 5 26 27 28 8836: 85345 82327 79309 ! A 20 28" 89830 86864 83897 80931 ! A 25 26 27 28 91250 8S333 85416 82500 I A 29 74563 2 9 76293 29 77965 29 79583 3 74500 30 76666 CONCENTRATED LOAD SYSTEM. XV MOMENTS. M x = Rx - m. SPAN, SPAN, SPAN, SPAN, 61 62 63 64 feet. feet. feet. feet. X A> m X R in X A' m X X m I 122377 , 124032 I 125634 I 127187 2 118688 2 120403 2 122063 2 123671 3 115409 3 116774 3 118492 3 120156 4 112131 P* 4 H3548 o A 4 114920 o A 4 116640 o A 108852 '5573 | 110322 107096 | 111746 108571 | 113125 IIOOOO 7 102295 7 103870 7 105396 7 106875 8 115409 8 116774 8 118492 8 120156 9 112131 9 H3548 g 9 114920 g 9 116640 Q 10 ii 108852 1 5573 n A 10 ii 110322 107096 M ft 10 ii 111746 108571 m A 10 ii 113125 IIOOOO *o A 12 102295 12 103870 12 105396 12 106875 '3 99426 '3 100644 '3 IO2222 '3 103750 '4 111311 14 112580 H II3808 14 "539 15 108196 '1 109516 15 IIO792 15 112031 16 17 18 105081 101966 98851 N Ps 16 17 18 106451 103386 100322 N Pi 16 17 18 107777 104761 IOI745 N A ID 17 18 109061 106093 103124 g A ] 9 95737 '9 97257 ft '9 98729 19 100156 CO 20 92622 20 94193 20 957U 20 97188 21 B9753 21 91128 21 92698 21 94219 22 101966 23 103386 22 IO476I 22 106093 2 3 98851 23 100322 23 IOI745 23 103124 24 95737 24 97257 24 98729 24 100156 25 92622 25 94193 o 2 5 95713 25 97188 20 27 28 9753 86885 84016 "1 3 f* 26 27 28 91128 88365 85483 u-l vS" P* 27 28 86904 $ A 26 al 94219 91250 88281 to -ft A 29 81148 29 82660 2Q 84126 29 85546 3 78279 30 79837 3 81348 30 , 82812 3 1 75410 31 770IS 3' 78570 31 80078 32 75792 32 77343 * XVI APPENDIX. MOMENTS. M x = Rx m. SPAN, SPAN, SPAN, SPAN, 65 66 67 68 feet. feet. feet. feet. X R m .r K m * m jr A' m i 128692 i 130530 i ' 3 2 3' 3 i 134044 2 3 125231 121769 2 3 126742 123333 3 128582 124850 2 3 130367 126691 4 118308 PZ 4 119924 o ft 4 121492 ft 4 123014 o A 7 114846 11138; 108308 7 116515 113106 109696 7 118134 114776 111417 7 119706 116398 1*3089 8 121769 8 I2 3333 8 124850 8 126691 9 118308 Q 9 119924 g 9 121492 o 9 123014 o 10 u 12 114846 11138? 108308 1 Pi 10 ii 12 116515 113106 109696 N A 10 ii 12 118134 114776 111417 1 A 10 ii 12 i 19706 "6398 113089 in PI A 13 105230 13 106666 3 108059 '3 109780 14 116923 14 118408 14 119850 '4 121250 IS 113615 115151 116641 15 118088 16 i 10307 16 111893 1 6 "3432 ID 114927 Ii 107384 104461 ft 11 108635 105756 ft 11 110223 107014 A 18 111765 108603 A 19 101538 ro 19 102878 ft 19 104178 M '9 105441 ft 20 98614 20 IOOOOO 20 101342 20 102647 21 95691 21 97119 21 98506 21 99853 22 92769 22 94241 22 95671 22 97055 23 104461 23 105756 23 107014 2,3 108603 24 101538 24 102878 24 104178 24 105441 2 5 26 98614 95691 25 26 IOOOOO 97119 20 101342 98506 26 102647 99853 28 89847 & A 27 28 94241 91363 & A 27 28 95671 92835 & A 27 28 97055 94220 in A 29 86924 >O 2Q 88484 O 29 90000 VO 29 91471 * 3 3' 84232 81538 3 31 85705 82954 30 3' 87163 84327 30 V 88656 85863 32 78845 32 80302 32 8'7'5 32 83068 33 89847 1 A 33 p* 1095000 A 33 34 92835 90000 f A 33 34 94220 91471 IO9500O A CONCENTRATED LOAD SYSTEM. MOMENTS. = J?x m. UNIVERSITY XVII Sl'AN, SPAN, SPAN, SPAN, 69 70 7' 72 feet. feet. feet. feet. X * m X * m x R m X * m i 35724 I '37357 i 139295 , 141180 2 132101 2 '3375 2 '35422 2 137361 3 128478 3 130214 3 131901 3 '35541 4 124855 o p* 4 126642 Pi 4 128380 o f* 4 130070 ff 5 121231 5 123071 5 124859 5 126600 6 117971 6 119500 6 121338 6 123129 7 114710 7 i 16285 7 117816 7 119658 8 i 28478 8 130214 8 131901 8 '3354' 9 124855 g 9 126642 g 9 128380 g 9 130070 g 10 ii 121231 117971 & ft 10 ii 123071 119500 N A 10 ii 124859 121338 & Pi 10 ii 126600 123129 8, Pi 12 114710 '"' 12 116285 "" 12 117816 W 12 i 19658 M 3 111449 3 113071 '3 114646 '3 116187 '4 122970 M 1 2464 1 14 126264 '4 127853 15 i 19492 15 I2I2I2 15 122882 15 124520 16 17 116375 113260 . 16 17 117784 II47I2 g 16 17 119501 116118 \ p. 16 '7 121187 "7853 n Pi .8 i 10144 pi 18 111641 PI Pi 18 113090 ro 18 114520 fl t*S '9 107028 r*1 '9 108570 ro '9 110062 '9 "1534 20 103912 20 105500 20 107035 20 108547 21 101158 21 102427 21 119501 21 121187 22 113260 22 1I47I2 22 116118 22 "7853 23 110144 23 111641 23 113090 23 114520 24 107028 24 108570 24 110062 24 '"534 25 103912 25 105500 2 5 107035 25 108547 26 101158 26 102427 o 26 104006 g 26 105562 27 28 98405 95652 $ P4 28 99713 97000 & A 11 100978 98302 * A 27 28 102576 99589 & ft 29 92897 29 94284 VO 29 95626 O 29 96951 O 30 90144 30 91570 30 92949 30 943 12 3 1 8739 88857 3' 90274 3' 91672 3 2 84637 32 33 86143 83428 32 33 87598 84921 32 33 89039 86395 33 95652 34 35 92897 90144 f Pi 34 35 94284 91570 f ft 34 9 95626 92949 90274 I ft 34 35 3 6 96951 943 '2 91672 f Pi - XV111 APPENDIX. MOMENTS. = Rx m. 1 SPAN, , 73 feet. SPAN, 74 feet. SPAN, fe 7 el SPAN, 76 feet. X R m X j? m X R ; X- R m i 2 3 4 7 143013 139246 '35479 131712 128287 124863 121438 N A I 2 3 4 '44797 141081 137365 133649 129933 126555 o A I 2 3 4 146533 142866 139200 "35533 131866 128200 o A I 2 3 4 1 148223 144605 140986 137368 133750 130131 o A 8 9 10 u 12 13 141081 137365 133649 129933 126555 123176 119798 10 Cl A 8 9 10 ii 12 '3 142866 139200 '35533 131866 . 128200 124866 I2I533 "i w A 8 9 10 ii 12 13 144605 140986 137368 133750 I3 OI 3' 126513 123223 o N A 8 9 10 ii 12 13 '35479 131712 128287 124863 121438 118013 A '4 15 16 17 18 '9 20 29383 126095 122807 119520 116232 "2945 IIOOOO N (O A 14 !i il 19 20 131216 127635 '2439' 121148 117904 114661 111418 c* n A '4 15 16 11 '9 133000 129460 125933 122733 "9533 "6333 M CO A '4 '5 16 '7 18 '9 134776 131249 127762 124266 121118 "7959 O N f) A 20 21 22 23 24 2 5 26 2 7 28 29 30 3' 32 129466 "5933 122733 "9533 "6333 i'3'33 109933 107066 104200 101333 98466 95600 93066 "1 $ \ A 20 21 22 23 24 25 26 27 28 29 3 3' 131249 127762 124266 121118 117959 i i 4802 111644 108486 105657 102828 IOOOOO 97170 *si 3 A 21 22 23 24 25 2O 2! 29 30 3 1 S 2 33 122807 119520 116232 112945 IIOOOO 107054 104108 101164 98218 95616 93012 90410 87807 U"l ^S" A 21 22 23 24 26 S 29 3 3 1 32 33 I2439I 121148 117904 114661 111418 108513 105607 102701 99797 96891 94323 9'75 6 89188 -i? A 3 2 33 34 36 P 108486 105657 102828 IOOOOO 97170 94341 91841 f Ps 33 34 35 36 37 38 104200 101333 98466 95600 93066 9533 tO A 34 35 3 37 98218 95616 93012 90410 I A 34 P 37 99797 96891 943 2 3 91756 I A . CONCENTRATED LOAD SYSTEM. XIX MOMENTS. = Rx m. SPAN, SPAN, SPAN, SPAN, 77 78 79 80 feet. feet. feet. feet. X * m X * m X * in X * m I 149870 I 151666 I I534I7 I 55'*S 2 146298 2 147948 2 149746 2 151500 3 142727 3 M4423 3 146075 3 "47875 4 '39155 o p2 4 140897 o / 2 4 142594 Pi 4 144250 o /2 I 132013 I "3737" '33845 \ 139"3 | 140812 '37375 7 128442 7 130319 7 132151 7 '33937 8 142727 8 '44423 8 146075 8 M7875 9 I39I55 n 9 140897 g 9 142594 o 9 144250 Q 10 ii "35584 132013 I ft 1. n I3737I "33845 | fl 10 ii "391 13 135632 . 1 fl 10 ii 140812 '37375 & A 12 128442 M 12 130319 M I ** 132151 | - 1 12 '33937 "* '3 124871 '3 126793 '3 128670 '3 130500 '4 136429 14 138074 '4 140000 "4 141874 17 132987 "29545 126104 g Pi 3 '7 134677 131280 127882 M f, 3 "7 136328 132974 129620 N fl 15 16 '7 138250 134624 "3'3'2 M ^3 18 122662 " 18 124484 ro 18 126265 18 128000 19 119546 '9 121088 '9 140000 IQ 141874 20 132987 20 "34677 20 136328 20 138250 21 129545 21 131280 21 132974 21 134624 22 126104 22 127882 22 129620 22 '3'3 12 Q 2 3 122662 23 124484 Q 23 126265 g 23 128000 g 24 y 119546 116429 "33'2 1 VO p. 24 > r 26 121088 118010 "4933 ! ft 24 26 122910 119556 116518 3 A 24 2 5 26 124687 '21374 118062 3 27 110195 27 111857 27 113480 2 7 115062 28 107077 28 108780 28 110442 28 112062 29 104286 29 105702 29 107404 3 101494 29 124687 30 uSoio 30 "9556 30 "21374 3' i'33'2 3" "4933 3' 116518 31 118062 32 110195 32 111857 32 113480 32 115062 33 107077 108780 110442 33 112062 34 35 36 104286 101494 98701 S? fl 34 35 3 6 105702 102946 100190 10 IT ft 34 9 107404 104366 101644 S? A 34 109062 106062 103062 f A 38 95909 93116 38 97433 94677 P 98923 96201 38 "00375 97687 39 90650 39 91923 39 93480 39 95000 40 90759 40 92312 XX APPENDIX. MOMENTS. M x = Rx m. SPAN, SPAN, SPAN, SPAR, 81 82 83 84 feet. feet. feet. feet. JC K m X * m X m * * m I 156790 153209 I 2 158414 154878 I 2 160180 156506 i 2 161904 158273 3 149629 3 '5I34I 3 153012 3 154642 4 146049 o ft 4 147804 o ft 4 149518 o p* 4 151190 o A 7 142469 139074 "35679 7 144268 140731 137378 3 7 146024 142530 139036 1 7 M7738 144285 140833 8 149629 8 I$341 8 153012 S 154642 9 146049 g Q 147804 Q 9 149518 O 9 151190 g 10 ii 12 '3 142469 139074 135679 132283 M /3 10 ii I ** '3 144268 140731 137378 134024 1 A 10 ii 12 '3 146024 142530 139036 135722 VO Pi IO ii '3 147738 . 144285 140833 137300 P? ft '4 143702 '4 145487 '4 147228 14 148938 15 140122 g 15 I4I95 1 g 15 '43734 9 15 '45475 9, 16 136542 g ft 16 138414 g Pi 16 140239 g ft 16 142023 g ^ '7 132962 N '7 jj, 17 136746 ro i? '38570 fo 18 129691 18 I3 ' 3 ' 4 18 133251 18 135118 '9 143702 '9 145487 '9 147228 '9 148938 20 140122 20 141951 20 143734 20 '45475 21 136542 21 138414 21 140239 g 21 142023 o 22 23 24 132962 129691 126418 ft 22 23 24 134877 I3I341 128109 I P* 22 23 24 136746 '33251 1=9757 1 A 22 23 24 138570 135118 131666 1 A 25 123147 *O 2 1 124877 2 5 126564 2 5 128214 20 119876 26 121645 26 123372 2D 125059 27 116604 27 118413 28 113641 27 136746 27 138570 28 '3'34' 28 13325' 28 135118 29 126418 29 128109 29 129757 30 128214 30 123147 30 124877 30 126564 o 32 121903 g 3' 119876 3' 121645 32 120179 u-l A 34 "5594 oJ ft 3 2 116604 32 118413 34 "3794 o 35 112440 g 33 34 113041 110678 33 34 115182 112255 36 38 108010 102227 37 109582 106726 9 107715 104752 $ A 9 109328 106401 $ 37 3 39 101789 99135 96481 I 39 103475 100548 97926 39 120179 1 ft 38 39 125059 121903 i ft, 40 93826 40 95304 M 4' 91172 4> 92682 40 1 332 5 ' $ 40 135118 $ 4' '29757 8 p 7 4' 131666 h 42 126564 N 42 128214 CONCENTRATED LOAD SYSTEM. XXI MOMENTS. = Rx m. SPAN, SPAN, SPAN, SPAN, S 86 8? 88 feet. feet. feet. feet. X R m j; R m X j? m .c R m i 163588 I 165232 i 166839 i 168579 i 160000 2 161685 2 163333 2 164943 3 156412 3 I58I39 3 159827 3 161477 4 152824 o A 4 '54593 o A 4 156321 o A 4 158011 o A 149412 5 151046 5 152816 5 '54545 6 146000 6 147674 6 149310 6 '5'079 7 142588 7 144302 7 '45977 7 '47613 8 156412 8 158139 8 159827 8 161477 9 152824 o 9 '54593 Q 9 156321 o 9 158011 o 10 ii 149412 146000 i*~i H A 10 ii 151046 147674 LO M A 10 ii 152816 149310 ""i n A 10 ii '54545 151079 LO C) A 12 142588 ** 12 144302 I 2 '45977 M 1 2 '47613 l ~ l 13 '39 1 ?? '3 140930 '3 142643 '3 M43I7 '4 150587 '4 152383 '4 '54'37 '4 '5595' 15 M7I7S g '5 148837 g 15 150632 o 15 152386 Q 16 17 M3763 I4035 1 PI A 16 '7 145464 142092 8 A 16 17 147125 143792 8 A 16 '7 148919 '45454 8 A 18 '36939 rt 1 8 138720 fO 18 140458 ro 18 142158 !> 19 133528 '9 '35348 '9 137125 '9 138863 20 I47I75 20 148837 20 1 50632 20 152386 21 143763 21 145464 21 147125 21 148919 22 I4035 1 Q 22 142092 Q 22 143792 O 22 '45454 Q 2 3 24 136939 133528 u-i 3 A 23 24 138720 135348 V) 3 A 23 24 140458 137125 1 A 23 24 142158 138863 1O 3- A 3 130115 126704 25 26 131976 128604 2 5 '33793 '3459 >o -y p 26 '35567 132272 vO 27 127126 27 i 28976 27 14035' 27 142092 28 136939 28 138720 28 140458 28 142158 29 '33528 29 135348 29 '37'25 29 138863 3 130115 8 30 '3'976 30 '33793 o 30 135567 Q 3 1 32 126704 123586 LO A 3' 32 128604 125232 & g 1 A 3' 32 130459 127126 i? A 3' 32 132272 i 28976 in 8" A 33 120469 3.3 122150 33 123792 33 125680 34 "735' 34 119068 34 120746 34 122385 35 114233 35 115986 35 117701 35 ' '9373 36 1 335 28 a 36 135348 ' 9 36 I37'25 36 138863 37 38 130115 1 26704 1 A 3 131976 128604 1 A 3 '33793 i3 459 1 A % 135567 132272 1 A 39 127126 M 39 128976 - 39 14035' 39 142092 40 136939 8 40 138720 8 40 140458 40 142158 41 133528 8^ A 4i 135348 1 A 4i 137125 8 4' 138863 42 !30"5 Wl 42 131976 "i N 42 '33793 Si A 42 '35567 o A 43 126704 43 128604 43 '30459 o 43 132272 IT) 44 127126 44 128976 xxu APPENDIX. MOMENTS. M, = Rx m. SPAN, . SPAN, SPAN, SPAN, 89 89 90 90 feet. feet. feet. feet. X * m * Jf m X R m X - m i 2 3 4 170280 166685 163089 159662 156235 A 40 42 43 44 143819 140561 137303 134044 130786 2550000 A i 2 3 4 171943 168388 164832 161277 157888 o A 40 4' 42 43 44 145610 142222 139000 '35777 132555 I A 6 152808 o 154500 7 149382 7 151110 8 9 163089 159662 45 143819 N f! A 8 164832 161277 45 145610 r^ CO * 10 ii 156235 152808 A 10 ii 157888 154500 N A 12 149382 I ~ I 12 151110 *"* '3 '45955 '3 147721 '4 157527 '4 159166 17 154100 150673 147246 1 A :i '7 155776 152388 149000 1 A 18 143819 fO 18 145610 n '9 140561 '9 142222 20 154100 20 155776 21 150673 21 152388 22 147246 Q 22 149000 Q 23 24 143819 140561 1 A 23 24 145610 142222 * A 2 5 137303 \o 25 139000 26 134044 2O '35777 27 130786 27 28 143819 28 145610 2 9 140561 29 142222 3 137303 o 30 139000 Q 3' 32 134044 130786 1 A 3' 32 '35777 132555 A 33 127527 M 33 129333 - 34 124269 34 126110 35 I2IOIO 35 122888 36 140561 e 36 142222 g 38 '37303 134044 1 A 37 38 139000 '35777 | A 39 130786 39 132555 M CONCENTRATED LOAD SYSTEM. XX111 MOMENTS, X = J?x m. SPAN, SPAN, SPAN, SPAN, 9 1 9' 92 92 feet. feet. feet. feet. X * m * R X ff m * J? m i '7357' 28 14736' i '75l6 3 28 149075 2 3 170054 166538 29 30 144011 140660 . 2 3 171684 168206 29 30 145760 142444 4 163021 159505 ft 3' 32 '37473 134286 1 ft 4 164728 161250 o ft 3' 32 139129 '35977 1 ft 7 I56I53 1 52802 33 34 131100 127912 M 7 '5777' 154456 33 34 132825 129673 M 35 124725 35 126521 8 166538 8 168206 9 10 ii 12 163021 159505 I56I53 I 52802 M ft 36 39 144011 140660 '37473 134286 1 f 9 10 ii 12 164728 161250 '5777' 154456 M 36 37 38 39 145760 142444 139129 '35977 I ft '3 149450 '3 151141 40 4' 14736' 144011 , 40 4' 149075 145760 . '4 160933 '4 162662 '5 157417 n 42 140660 8 Pi 15 159183 g 42 142444 8 Pi 16 '7 18 154065 IS07I3 I4736I M CO ft 43 44 137473 134286 . " 16 '7 18 '55705 152390 149075 1 S3 43 44 139129 '35977 '9 I44OII g '9 145760 20 I574I7 45 46 144011 N ft 20 I59I83 45 46 149075 145760 ft 21 154065 21 155705 22 I507I3 o 22 152390 g 23 24 25 I4736I I44OII 140660 3 A 23 24 149075 145760 142444 1 A 26 '37473 2O 139129 27 134286 27 '35977 XXIV APPENDIX. MOMENTS. M x = Rx m. SPAN, SPAN, SPAN, SPAN, 93 93 94 94 feet. feet. feet. feet. X - m X A 1 m X A' m X A' m , I7688I 28 150752 I 178563 28 152392 2 173279 29 147472 2 175000 29 149147 3 4 I 7 169838 166397 1 62956 I595I6 156075 o A 3' 32 33 34 144192 140913 137634 I3I397 $ A 3 4 7 168031 164627 161223 157819 A 3' 32 33 34 145902 142658 '39413 136168 '33083 I A 35 128279 35 130000 3 125161 3" 126913 8 169838 8 171436 9 166397 s 9 168031 o 10 ii 12 13 162957 I595I6 156075 I5 2 795 N A t 39 40 144192 140913 137634 I345'6 I A 10 ii 12 '3 164627 161223 157819 I544I4 1 A 37 38 39 40 145902 142658 136168 1 A 14 164354 41 147472 '4 166010 4' 149147 . II 17 160913 157472 I5403I N A 42 43 44 144192 140913 137634 to A 15 16 17 162605 159201 155796 | A 42 43 44 145902 142658 I394I3 1 A 18 150752 ro 18 152392 '9 M7472 19 149147 45 150752 8 45 152392 8 46 147472 Jo A 46 149147 to A 20 160913 47 144192 w 20 162605 47 145902 fO 21 157472 21 159201 22 I5403I o 22 155796 23 24 150752 147472 1 A 23 24 152392 149147 :? A 2 5 I44I92 \o 25 145902 26 140913 26 142658 27 137634 27 I394I3 - CONCENTRATED LOAD SYSTEM. MOMENTS. M, = Rx m. UNIVERSITY SPAN, SPAN, SPAN, SPAN, 95 95 96 96 feet. feet. feet. feet. X R ; X R m X K m X R m I 180211 4' 150788 I 181822 4' 152552 2 3 4 176684 '73157 169631 166263 f* 42 43 44 147578 144367 141157 1 ft 2 3 4 178333 174843 I7I354 167864 A 42 43 44 149219 146042 142865 I ft 6 162894 6 '6453' 7 159526 45 46 150788 7 161197 45 46 155885 152552 8 '73'57 47 48 147578 144367 VO t^ o CO pa 8 '74843 47 48 149219 146042 S ft 9 169631 g 9 I7I354 o 10 ii 166263 162894 1 ft 10 ii 167864 '6453' r ft 12 159526 '- t I ** 161197 *" '3 156157 '3 157864 '4 '67631 '4 169374 \l 17 164262 160894 '575 2 5 1 ft '7 165884 162551 159218 n ft 18 I54I57 R 18 155885 to '9 150788 '9 152552 20 164262 20 165884 21 160894 21 162551 22 157525 n 22 159218 o 23 24 I54I57 150788 | A 23 24 155885 152552 * A 147578 VO 2 5 149219 VO 26 '44367 26 T46o42 27 141157 27 142865 28 I54I57 28 155885 29 150788 29 152552 30 147578 3 149219 3' 144367 8 3' 146042 8 32 33 141157 137948 I h 32 33 142865 139689 f ft 34 134738 34 136512 35 131686 35 '33335 36 i 28634 36 '33'4 37 147578 37 149219 38 39 144367 141157 1 ft 38 39 146042 142865 1 ft 40 137948 40 139689 XXVI APPENDIX. MOMENTS. = Rx m. SPAN, SPAN, SPAN, SPAN, 97 97 98 98 feet. feet. feet. feet. X * m X - X R m X K i 2 3 4 183525 179948 176494 A 4! 42 43 44 150978 147679 '44535 141391 2550000 A i 2 3 4 185193 181653 178112 174693 o 41 42 43 44 155968 152703 149438 146173 H A i 169587 166134 | 171275 167857 7 162835 a 157576 154278 8 7 164438 45 46 159234 155968 47 150978 Si A 47 & A 8 176494 48 147679 T 8 178112 48 149438 M 9 173041 g 49 I4453S 9 174693 Q 49 146173 10 ii 169587 166134 N A 10 ii 171275 167857 1 A- 12 162835 1-1 12 164438 W 13 159536 '3 161173 14 171082 '4 172754 II 167628 164175 8 15 169335 165917 8 17 160875 N pi 17 162500 w /3 18 157576 ro 18 159234 to 19 154278 19 155968 20 167628 20 169335 21 164175 21 165917 22 160875 Q 22 162500 g 23 24 157576 i 54278 1 A 24 159234 155968 I A 25 150978 VO 25 152703 >o 26 147679 26 149438 27 144535 27 146173 28 157576 28 159234 29 154278 29 155968 30 150978 3 152703 3! 147679 8 3i 149438 g 32 144535 o\ A 3 2 146173 M A 2 3 4 184960 181490 178020 o A 42 43 44 156050 152850 149650 U"> w A 5 172924 5 '7455 6 169545 b 171200 7 166161 41 160858 7 167850 45 162600 40 157625 Q 46 159250 5 8 9 179818 176313 47 48 49 '54393 151160 147928 "1 fN. W ro A 8 9 181490 178020 47 48 49 156050 152850 149650 r-N, N to / 10 ii 172929 169545 ^> N A 5 144696 10 ii '7455 171200 >> N A 12 166161 M 12 167850 13 162777 '3 164500 5 178020 i /,0 H 174393 '4 176000 15 171000 o 15 172650 g l6 '7 167625 164241 A 16 17 169300 165950 A 18 160858 to 18 162600 n 19 157625 '9 159250 20 171009 20 172650 21 167625 21 169300 22 164241 o 22 165950 2 3 24 160858 157625 0 A 34 141615 34 '43 2 5 35 '38534 35 140200 36 '35454 36 13715 37 '54393 37 156050 38 39 151160 147928 I A 3 39 152850 149650 1 A 40 144696 40 146450 XXV111 APPENDIX. MOMENTS. M, = Rx m. SPAN, SPAN, SPAN, SPAN, "3 103 105 105 feet. feet. feet. feet. X * m jr R m X - m X A' m I 7 3 193281 189796 186310 42 43 164368 161115 157963 I Pi i 2 1 196438 193019 189600 4' 42 43 167619 164429 161234 1 4 182941 o /2 44 154611 10 4 186180 o fl 44 158048 io 5 179572 45 151504 182761 45 154858 6 176203 6 "79457 7 172834 7 176152 46 164368 Q 46 167619 Q 8 9 186310 182941 47 48 49 161115 157963 154611 PI P> 8 9 189600 186180 47 48 49 164429 161234 158048 N ft 10 ii "79572 176203 & A 10 ii 182761 "79457 | h 12 '3 172834 169466 50 5' 182941 179572 Pa 12 13 176152 172848 So 170952 A S2 176203 Q "4 181067 H 184400 * 17 18 177669 174271 170873 167620 M CO * 15 16 '7 18 180953 177619 173286 170952 I fl 5" 5 2 53 182761 179457 176152 00 /.o 19 164368 '9 167619 20 177669 20 180953 21 174271 21 177619 22 170873 Q 22 173286 24 167620 164368 & PA 23 24 170952 167619 & ft 3 161115 157963 V 2 5 26 164429 161234 <0 27 154611 27 158048 28 167620 28 170952 29 164368 29 167619 30 161115 164429 3' "57963 V 161234 8 32 154611 Pi 32 158048 10 Ps 33 i5 I 54 6 33 154858 g 1 34 148398 34 151668 35 145290 148621 36 142183 36 "45574 3 39 161115 157963 154611 1 Po 39 164429 161234 158048 | ft 40 151504 40 154858 CONCENTRATED LOAD SYSTEM. XXIX MOMENTS. x = Rx m. SPAN, SPAN, SPAN, SPAN, 108 1 08 IIO IIO feet. feet. feet. feet. X * m X R m X * m X R m I 200953 4' 172684 I 203827 4' 176017 2 197629 42 169443 8 2 200563 42 172726 8 3 4 194305 190981 o f* 43 44 166202 162962 1 A 3 4 197300 194036 o * 43 44 169545 166362 to A 187657 45 159861 5 190772 45 163181 6 184333 6 187509 7 181009 7 184245 46 172684 o 46 176017 p, 8 9 194305 190981 47 48 49 169443 166202 162962 N A 8 9 197300 194036 47 48 49 172726 169545 166362 N CO A 10 II 187657 184333 1 A 10 ii 190772 187509 I Pi 12 181009 w g 12 184245 *" o '3 177685 5 51 175925 172684 8, A '3 180981 50 S' 179308 176017 & A '4 '5 189333 185981 * '4 'S 192581 189181 * 16 \l '9 182629 179277 175925 172684 ! A 52 53 54 184333 181009 177685 I Ao 16 '7 18 '9 185890 182599 179308 176017 1 f, 53 54 187509 184245 180981 00 /.o 20 185981 20 189181 21 22 182629 179277 21 22 185890 182599 55 203827 8 A. 23 24 175925 172684 1 A 23 24 179308 176017 I A 25 '69443 vO 25 172726 VQ 26 166202 26 169545 27 162962 27 166362 28 175925 28 179308 29 172684 29 176017 3 169443 172726 3 1 166202 O 31 169545 g 33 162962 159861 i? A 32 33 166362 163181 s 2 3 187460 55 200468 8 /I0 24 180957 ? /< 24 184207 >n p t 25 '77753 VO 2 5 180956 v? 27 28 171346 168144 27 28 174660 171512 56 i 207765 204539 | AI 5 201313 N 29 180957 29 184207 * 30 '77753 3 180956 3 r 174550 O 3! 177809 32 171346 8 A 32 174660 33 168144 g\ T< 171512 ?? 5 34 165046 -I 168364 M 35 161949 35 165216 36 158852 36 162172 37 '77753 38 174550 8 39 171346 8 ft 4 168144 CONCENTRATED LOAD SYSTEM. XXXI MOMENTS. M x = Rx m. SPAN, SPAN, SPAN, SPAN, 1 20 1 20 125 125 feet. feet. feet. feet. X A' m X * m X A> m JT R m \ 2 3 218058 214866 211675 38 39 40 185883 182766 179650 1 A I 2 225040 221880 218720 40 4' 42 187424 184432 181440 \ A 4 208483 A 4' 176533 - 4 215560 o 43 I7 8 44 8 S.' 5 205291 5 212400 p* 6 202200 6 209336 7 I99IO8 42 43 44 189000 185883 182766 1 2>7 * 206272 203208 44 45 46 190416 187424 184432 1 A 8 211675 45 179650 !/! 47 181440 io 9 208483 46 176533 8 48 178448 10 205291 . 9 215024 g A ii 202200 M 12 '3 I99IO8 196016 47 48 189000 185883 3 49 5 190416 187424 g 49 182766 10 ft 10 212400 51 184432 & A 14 207800 5 179650 176533 ii 12 209336 206272 a M A S 2 53 181440 178448 N 15 16 204583 201466 1 3 203208 17 198350 b 1 P^ 52 189000 S4 190416 Q '9 195233 I92II6 CO 53 S4 185883 182766 > A 14 15 215024 211840 55 S 6 187424 184432 IO A 20 iSgOOO SS 179650 o" ID 208752 S7 181440 % 56 '76533 17 205664 18 202576 N /"a 21 22 23 24 201466 198350 195233 I92Il6 , P 201466 198350 I Ao '9 20 21 199488 196400 193408 58 205664 202576 199488 VO Ao 25 iSgOOO * T CrXS-> MT" J 4 10 5 OO J 22 205664 2 7 28 179650 g 205291 2O22OO 1 23 24 202576 199488 196400 193408 | 61 62 206272 203208 N A. 29 192116 >s 27 190416 V? 3 189000 28 187424 3 1 185883 2Q 184432 32 33 182766 179650 A 3 181440 63 215024 A- 34 '76533 6 r 37 I734i6 170389 167372 3 1 32 193408 190416 - 187424 " 34 184432 8 181440 S A ^6 178448 8' 37 175456 ^O 172464 39 '69472 xxxn APPENDIX. MOMENTS. M x = Rx m. SPAN, 130 feet. SPAN, 130 feet. SPAN, / 3S feet. SPAN, /35 feet. X ^ m jr y? m X R m .r R m i 2 3 4 1 8 231946 228815 225684 2 22 553 219422 216383 2I 3345 210306 N M A 40 41 42 43 44 194783 191813 188844 185968 183090 I A I 2 3 4 1 238429 235414 232400 229385 226370 223354 220339 217324 o A A 40 41 42 43 44 45 202042 199094 196146 193287 190428 187568 8 A 45 46 47 48 49 194783 191813 188844 185968 183090 *o in N A 46 47 48 49 5 199094 196146 193287 190428 187568 10 10 N A 9 10 ii 222152 218998 215936 A 9 10 ii 12 3 228498 226072 223035 219998 216961 pi SO 5 1 52 53 54 194783 191813 188844 185968 183090 10 r-. N ro /a 12 13 213345 210306 tn N M A Si 5 2 53 54 55 199094 196146 193287 190428 187568 r-, N C*) A 14 15 16 11 '9 20 21 228498 226072 223035 219998 216961 213924 210887 207939 N CO A 14 15 16 17 18 19 20 21 222152 218998 215936 212875 209814 206752 203690 200721 n A P $ J94783 191813 188844 185968 tv. 1 A 56 i 59 60 61 62 63 199094 196146 193287 190428 -n & ST A 61 209814 206752 203690 f *o Ao A. 22 23 24 25 26 27 28 29 3 219998 216961 213924 210887 207939 204991 202042 199094 196146 u-i A 213924 210887 207939 204991 iO . A. 3' 32 33 34 35 36 37 38 39 207939 204991 202042 199094 196146 193287 190428 187568 184708 m $ A 63 64 65 222152 218998 215936 r^ r^. Ai 3 1 3 2 33 34 35 36 i 39 200721 197752 194783 191813 188844 185968 183090 180214 177326 U-l - 00 Q 26818! 10 258942 48 214486 10 265333 g ii 256079 A ii 262484 g 12 253'97 2 12 259636 M 13 250354 49 5 225254 2221:41 13 14 256787 253938 219829 8 14 261880 52 217116 u-l A 15 258942 214486 N 15 265333 16 256079 54 211849 16 262484 17 253197 g '7 259636 18 250354 2 18 256787 8 '9 20 21 247491 244628 241840 & P 222541 219829 217116 | '9 20 21 25393 s 251089 248313 fO /3 22 239053 58 214486 r^ A 22 245537 2 3 236255 59 211849 f) 23 242761 60 209212 24 247491 24 253938 25 26 244628 241840 61 62 219829 217116 25 26 251089 248313 27 28 29 239053 236255 2 "?34^7 ! A 64 214486 211849 A 11 2 9 245537 242761 239986 Tj- A 3 .V 237211 3' 32 227967 225254 $ 233467 230680 31 32 234507 231804 67 1 10 33 236255 68 225254 8, 33 242761 34 233467 o (4 239986 Q 35 36 230680 227967 225254 f A 69 70 244628 241840 p 35 36 37 237211 234W 231804 f A 38 222541 72 236255 II 38 229101 73 233467 74 230680 XXXVI APPENDIX. MOMENTS. M x = J?x m. SPAN, SPAN, SPAN, SPAN, -65 165 170 170 feet. feet. feet. feet. X R m X * m X R m X R m 39 40 41 42 226397 223696 221072 218447 in $ ft 76 H 231804 229101 226397 223696 t-* Pn I 2 3 4 281535 278717 275900 273082 40 42 43 230235 227611 224987 222364 1095000 ft 43 215823 80 221072 5 270264 A 6 267517 44 45 46 47 231804 229101 226397 223696 | ft Si 82 83 231804 229101 226397 i- M CO PK 8 264770 262023 44 45 46 47 48 238317 235624 232929 230235 227611 1 A 9 274188 48 221072 10 271353 ii 268687 a ^ 49 5 231804 229101 12 "3 14 265823 263059 260294 - 49 50 Si 238317 235624 232929 5' 5 2 226397 223696 ! P7 S3 230235 227611 M 53 221072 Cl 15 271353 S4 224987 54 218447 16 268687 17 265823 18 263059 55 235624 55 229101 '9 260294 8 ft S6 232929 56 8 226397 223696 221072 1 A 20 21 22 257529 254764 252000 8 S9 230235 227611 224987 m A 218447 215823 t-5 23 249235 60 222364 24 260294 61 232929 61 62 226397 223696 g 25 26 257529 254764 62- 230235 227611 A 63 64 65 221072 218447 215823 1 P-, 27 28 29 252000 249235 246470 ! ft 64 65 224987 222364 1 3 243705 66 67 237211 234507 j 3 1 32 33 238317 235624 66 67 68 243705 241010 238317 Sn /.o 68 fro 235624 69 229101 34 246470 70 72 73 248313 245537 242761 239986 r^ 35 36 39 243705 241010 238317 235624 232929 m ft 70 7' 72 73 74 254764 252000 249235 246470 243705 | ,., 74 237211 r~ 75 241010 75 234507 78 238317 CONCENTRATED LOAD SYSTEM. XXXV11 MOMENTS. M, = Rx m. SPAN, SPAN, SPAN, SPAN, 170 ^75 '75 '75 feet. feet. feet. feet. X R m X * m X R m X R m 77 78 79 235624 232930 230235 I A- i 2 3 287451 284645 281840 42 43 231508 228890 in 8 ft 77 78 79 242114 239428 236742 \ A. So 227611 " 4 5 279034 276228 o A 80 234125 ** b 27349 ' 81 82 238317 235624 g 8 270754 268017 44 4S 244800 242114 g 81 82 244800 242114 83 84 232929 230235 227611 M 00 * 46 47 48 239428 236742 234125 1 A 83 84 85 239428 236742 234125 u-t Jj A* 9 280194 10 277370 Q 86 231508 ii 274616 g 87 228890 12 13 14 271862 269108 266353 fl f 49 So Si 244800 242114 239428 88 226273 5 2 236742 "-) 53 234125 IS 277370 16 274616 19 2O 21 22 23 271862 269108 266353 263600 260914 258228 255542 ri pi 54 55 56 I 244800 242114 239428 236742 234125 231508 228890 "I ft - 24 252857 61 62 63 64 239428 236742 234125 231508 A 2 5 26 27 263600 260914 258228 28 255542 6S 228890 29 252857 & P4 31 32 33 247485 244800 242114 66 67 68 250171 247485 244800 1 60 34 252857 70 239428 250171 39 40 247485 244800 242114 239428 236742 234125 f Ps 72 73 74 9 258228 255542 252857 250171 247485 244800 A. XXXV111 APPENDIX. MOMENTS. = Rx m. SPAN, SPAN, SPAN, SPAN, 1 80 180 180 185 feet. feet. feet. feet. X R m X R m X * m X R m i 2 3 4 I 293372 290577 287783 284988 282194 279466 A 42 43 44 240610 238000 235391 232777 f * 80 Si 82 240610 238000 235391 | A. i 3 4 i 299037 296318 293600 290881 288162 285443 o A I 276738 274010 45 46 248444 245833 8 83 84 245833 243221 8 282724 280005 47 243221 5 A 8c 240610 X 48 240610 & 86 238000 Si A. 9 10 ii 286200 283388 280644 8 49 '238000 87 88 89 235391 232777 230166 00 9 10 ii 292204 289404 286669 8 A 12 13 14 277900 275!55 272410 ' ft 50 S 2 53 54 55 248444 245833 243221 240610 238000 235391 1 A A 90 227621 For all values of x below x 67, a uniformly dis- tributed load of 3000 Ibs. per ft. will give greater moments than this table. 12 '3 H 283934 281120 278464 " 15 16 17 18 "9 20 21 22 2 3 283388 280644 277900 2 75'55 272410 269665 266988 264310 261633 | * 15 ID ? 2O 21 22 3 289404 286669 283934 281120 278464 275729 270388 267717 1 A 56 P S 2 45833 243221 240610 238000 235391 I 24 258955 24 265047 61 245833 25 26 27 28 29 3 269665 266988 264310 261633 258955 256277 1 A 62 f 3 64 67 243221 240610 238000 235391 232777 230166 1 A 25 26 27 28 29 30 275729 273058 270388 267717 265047 262377 T A 3 1 2 53655 *O 31 259770 33 34 251055 248444 245833 68 69 70 251055 248444 245833 1 Ao 32 33 34 257165 254560 2 5'955 35 256277 7 1 72 243221 240610 35 262377 3 39 40 251055 248444 245833 243221 f Pi 73 74 75 258955 256277 253655 . 37 38 39 40 257165 254560 251955 249350 if A ?6 251055 77 248444 78 245833 """ 79 243221 CONCENTRATED LOAD SYSTEM. XXXIX MOMENTS. M, = Rx m. SPAN, SPAN, SPAN, SPAN, 185 185 190 190 feet. feet. feet. feet. X * m * R m X S m X R m 4' 246810 80 246810 I 304657 41 252932 42 43 44 244269 241729 239188 \r\ A 8l 82 83 84 244269 241729 239188 236647 1 fa 2 3 4 301947 299236 296526 293815 A 42 43 44 '45 250396 247859 245322 242785 I h 6 291167 46 254560 25'955 85 246810 8 288520 285872 46 258069 47 249350 86 244269 47 255469 g 48 246810 8 Pf> 87 241729 a 48 252932 8 ft 49 244269 8\ oo oo 239188 8 9 298145 49 250396 & 5 241729 89 236647 ^j- fa 10 295418 o 5 247859 5 r 239188 90 234106 oo II 292692 . 9' 231566 12 289965 M ?' S 2 249350 92 93 229024 230284 '3 14 287238 284511 51 5 2 258069 255469 53 246810 o 53 252932 o 54 9 57 244269 241729 239188 236647 o Cl A For all values of x below x= 57, a uniformly dis- tributed load of 3000 Ibs. per ft. will give greater moments than this table. \l 17 18 '9 20 21 22 295418 292692 289965 287238 284511 281785 279122 276459 /.* 93 94 95 232894 230420 227946 '5 287845 53 54 55 56 259056 256522 253989 25M55 2550000 A 93 94 9 239035 236564 234153 00 16 298471 For all values of 17 18 295815 293158 57 248922 97 yS 229333 226923 x below x 50, 19 290502 Q a uniformly dis- tributed load of 3000 Ibs. per ft. will give greater moments than this table. 20 21 22 23 24 287805 285189 282532 279876 277219 N ro A 58 59 60 61 62 259056 256522 253989 251455 248922 3275000 A For all values of x below x = 45, a uniformly dis- tributed load of 3000 Ibs. per ft. 2 5 26 287845 285189 a 259056 256522 this table. 27 28 282532 279876 i 253989 25I45S 1 A 29 30 277219 274563 S A 6? 68 248922 246450 * 3' 271969 MJ 269374 33 34 266779 264184 69 70 266779 264184 g 71 26l <$Q /I0 72 259056 vo' 35 36 274563 271969 g 73 256522 57 269374 O 38 39 40 266779 264184 261589 ff 5 74 75 76 274563 271964 269374 1 fu 77 266779 ~ 7 264184 CONCENTRATED LOAD SYSTEM. Xli MOMENTS. M, = Rx m. SPAN, SPAN, SPAN, SPAN, 200 200 200 210 feet. feet. feet. feet. X * m X * m jr K m X * m I 3 '5955 41 265170 7Q 267700 I 327090 2 313260 42 262640 8 80 265170 2 324466 3 4 310565 307870 o A 43 44 260110 257580 255050 f A 00 00 OO U) 10 262640 260110 257580 1 A, 3 4 321842 319219 3 ' 6 595 o A 6 302540 8 4 25505 6 3'39?i 7 299905 85 252580 7 3' '347 8 297270 46 270290 8 308723 47 267700 48 265170 86 262640 9 309560 4P 262640 8 6 87 260110 Q 321028 10 306850 260110 M 88 257580 10 3 l8 333 ii 304200 o 5 257580 89 255050 II 315694 g 12 3 '55 8 * 90 252580 12 3 '3056 X t. 13 298900 n J^Z Qi 250110 13 310418 11 296250 293600 291010 S 2 53 S4 267700 265170 262640 8 92 93 94 247640 245170 242700 N OO A* '4 '5 16 307780 305142 302561 55 S6 260110 257580 f, A 9 240290 237880 17 19 2O 3 OI 55 298900 296250 293600 8 57 255050 99 IOO 235470 233060 230650 228300 '7 18 '9 20 3 '3056 310418 307780 305142 5 8 265170 21 22 23 24 25 291010 288420 285750 283240 280650 Cl A 61 62 63 262640 260110 257580 25505 252580 1 ; For all values of x below jr=4i, a uniformly dis- tributed toad of 21 22 23 24 25 302561 299980 297400 294818 292237 M A 3000 Ibs. per ft. will give greater 26 291010 288420 64 262640 260110 moments than this table. 26 27 302561 299980 29 30 3' 32 285750 283240 280650 278060 275470 3 A 67 68 69 257580 255050 252580 250110 1 A 28 29 3 3 1 32 297400 294818 292237 289713 287190 ! A 33 272880 284666 34 270290 70 270290 34 35 282142 279618 9 280650 278060 72 73 74 265170 262640 260110 in Ao 36 289713 37 275470 O 37 287190 8 272880 284666 & A 39 40 270290 267700 1 A 75 76 278060 275470 8 A. 39 40 282142 279618 8' 77 272880 r^ 78 270290 xlii APPENDIX. MOMENTS. = Rx m. SPAN, 210 feet. SPAN, 2IO feet. SPAN, 220 feet. SPAI> 220 feet r, X * m * R m * - m * g m 41 42 43 44 45 46 277152 274684 272218 269751 267284 264818 u A i 8 82 8l 284666 282142 279618 277152 274684 272218 269751 !->. Pn ; i 337977 335363 33 2 75o 33 I 36 327522 324963 322404 o A 4 4 4 44 4 46 288808 286344 283881 281418 278954 276544 h A K 47 279618 85 3 '0845 47 2QI27I 48 49 50 277152 274684 272218 1 A 8? 259884 c 10 332217 72Qt;oo 48 49 288808 286344 g 5' 52 269751 267284 88 8q 269751 267284 ii 12 13 327017 324445 T2I572 ct A 5 5' 52 281418 278954 1 A 90 264818 !<: 3'930o j 276544 54 274684 92 259884 3 310720 -86 4 55 56 272218 269751 267284 264818 Lf N A 94 95 96 97 257417 254951 252542 250132 2 47723 N CO A. 16 '7 18 TO 327017 324445 321872 1 283881 281418 278954 276544 M A CQ 27/168/1 ya 00 2 453'3 242904 20 316726 jj A & 61 272218 269751 IOO 240551 22 23 3'4'54 311581 309008 M ro 60 283881 62 63 64 267284 264818 262351 PI A 101 102 250132 247723 g 24 25 306436 303862 61 62 63 64 281418 278954 276544 274 1 "1C A '03 245313 ^? PI$ ro 65 66 272218 104 I0 5 242904 24055' I 26 27 311581 66 269317 67 68 69 70 267284 264818 262351 259884 1 A r or all values of x below x = 33, uniformly dis- ributed load of 29 3 3 1 32 309008 306436 303862 3'344 298826 296308 ! A 69 70 278954 276544 274135 271726 1 A will give greater 34 1C 293790 72 277152 g his table. ^COO.-.Q 73 74 75 274684 272218 267284 to 36 g 39 40 298826 296308 293790 291271 j-> $ A 73 74 75 76 286344 283881 281418 278954 ft 'IO CONCENTRATED LOAD SYSTEM. xliii MOMENTS. M, = Rx m. SPAN, SPAN, SPAN, SPAN, 220 230 230 230 feet. feet. feet. feet. t K m X R m X R m X A' m 77 296308 I 348960 4' 300495 78 305416 78 293790 2 346356 42 298033 I 9 302956 79 291271 3 3437S 2 43 295573 o 80 300495 So 81 288808 286344 4 34H47 338543 P* 44 4S 293112 290651 f A 81 82 298033 295573 g 82 83 283881 281418 \ ft, 7 33599' 333440 46 47 288243 285834 84 293112 290651 | fa 84 278954 8 330886 85 288243 1^ 85 276544 86 285834 86 87 88 89 274135 271726 269317 266909 9 10 n 343268 340651 338086 48 49 50 51 300495 298033 295573 293112 1 ft 67 88 89 283425 281017 278608 12 335521 g A S 2 290651 2* 3 332955 S3 288243 90 288243 90 276544 H 330390 9' 285834 9' 274135 'S 327825 92 283425 92 93 94 P 97 98 99 100 IOI 271726 269317 266909 264553 262200 259844 257490 255136 252781 248072 10 00 p 54 55 56 57 58 59 298033 295573 293112 290651 288243 285834 I A 93 94 95 96 97 98 99 100 IOI 102 103 104 281017 278608 276251 273 8 94 271538 269182 266826 264520 262216 259912 257608 N OO * 16 17 18 '9 20 21 22 23 24 2S 338086 3355 21 332955 330390 327825 325312 322800 320286 317773 315260 1 A 60 61 62 295573 293112 290651 288243 , A 102 259844 61 28^814 N" IO4 105 257490 255'36 252781 1 A3 26 27 325312 322800 a 283425 281017 n 3 264520 262216 fa 28 29 320286 3'7773 67 2 06 I 107 108 259912 257608 $ 106 107 108 262200 259844 257490 1 /> 30 3 r 32 315260 312800 310338 S A 68 69 70 288243 285834 1 A 109 266826 109 I 10 252781 o 33 34 30777 305416 7i 28IOI7 no III 264520 262216 For all values of x below .r = 23, a uniformly dis- tributed load of 3000 Ibs. per ft. will give greater moments than P 302956 300495 A 112 "3 "4 "5 259912 257608 2553 3 25305 1 Below x = 6, a uniform load of 3000 Ibs. per ft. | 72 73 74 75 76 77 300495 298033 295573 293II2 290651 288243 ! . P 39 40 3 '0338 307877 305416 302956 f this table. gives greater moments than this table. xliv APPENDIX. MOMENTS. M x = Rx - m. SPAN, 240 feet. SPAN, 240 feet. SPAN, 240 feet. 1 - SPAN 250 feet. X A' m X A' m X A> m X A' lit I 2 3 4 8 359579 357033 354487 35!94i 349395 346900 344404 341908 / 41 42 43 44 45 46 47 48 3"758 309350 306941 3 4532 302125 299766 297408 295050 f t 80 81 82 83 84 85 86 87 88 3H758 309350 306941 304532 302125 2 99766 297408 295050 292691 r*, t^ Pi e 8 370260 367720 365180 362640 360100 3576o8 355'66 352624 o P* 9 10 ii 354350 35!79i 349232 49 50 Si 309350 306941 3 4532 1 89 90 9i 290332 287975 285616 c 10 ii 365072 362520 '3 14 '5 340675 344116 34I55 8 339000 " f 52 53 54 302125 299766 297408 1 ?6 92 93 94 295050 292691 290332 12 13 14 I"! 3575" 355008 352504 1 ^oooo N P* QC .(. 16 55 306941 96 285616 347544 17 18 '9 20 21 22 346675 344116 341558 339000 336491 333982 M f> ft S 6 I 61 304532 302125 299766 297408 295050 292691 10 IO N Pi 97 98 99 100 IOI 1 02 10; 203258 280900 278541 276232 273925 271616 269308 LO Tt N 00 ft, 17 18 '9 20 21 22 357512 355008 35 2 504 350000 347544 345088 8 8 tt J 33'475 23 -3426^2 ro 2 4 2 5 26 320900 326458 324000 62 63 .64 6r 302125 299766 297408 10 P 104 I0( 106 278541 276232 24 25 26 340176 337720 335264 rr N ;l 333982 33'475 67 292691 290332 fO 107 108 109 269308 267000 27 28 345088 3426T2 30 3 r 3 2 33 34 35 36 326458 324000 32I54I 319082 316625 314166 3"758 IO <3 A 68 69 70 7i 72 73 299766 297408 295050 292691 290332 287975 1 f-*. O ^t- A IIO in 112 3 14 15 16 17 IS 264741 262482 260225 257966 255/08 253500 251291 249082 246875 to -^- /I3 29 30 31 3 2 33 34 35 36 340176 337720 335264 332808 330352 327896 325440 3 2 3032 10 X P* 244666 H 39 40 321541 319082 316625 314166 10 Pi 74 75 ?6 % 79 306941 304532 302125 299766 297408 295050 10 , Plo 20 242509 \. uniform load of 3000 Ibs. per ft. gives greater moments than this table. 38 39 40 332808 330352 327896 325440 uo Ps CONCENTRATED LOAD SYSTEM. xlv MOMENTS. T* = Rx - m. SPAN, SPAN, SPAN, SPAN, 250 250 250 260 feet. feet. feet. feet. X R m X A' m X R m X R m 41 42 43 44 323032 320624 318216 315808 So Si 82 83 323032 320624 318216 315808 121 122 123 I2 4 262968 260752 258536 256320 0770000 #4 I 2 3 4 380857 378369 3758o 37339 2 o 45 3 '3400 84 3 '3400 "25 254152 5 370903 FI 46 47 48 311040 308680 306320 85 86 87 31 1040 308680 306320- | A. Tor all values of I 368415 365926 88 303960 * x below _r = 120, 49 5 5 1 320624 318216 315808 . 89 90 92 301600 299288 296976 294664 tributed load of 2700 Ibs. per ft. will give greater moments than 9 10 ii 375892 373345 370845 5 2 3 I 34 6 12 368345 53 311040 13 365845 w f* 54 308680 93 303960 H 363345 w 94 301600 15 360845 95 299288 16 358391 55 318216 315808 96 97 296976 294664 57 313400 8 90 292352 g 17 368345 S& i 61 311040 308680 306320 303960 1 ft 99 IOO 101 IO2 103 290040 287776 285512 283248 280984 N oo fa 18 '9 20 21 22 365845 363345 360845 358391 355937 1 Pi 104 278720 277456 274192 23 24 20 353484 351030 348576 346169 62 o"5 313400 311040 308680 a 306320 303960 301600 N r'l P* 107 108 283248 280984 77 355937 68 299288 tog no 278720 277456 29 353484 351030 69 70 7i 72 73 74 308680 306320 303960 301600 299288 296976 4075000 A 112 "3 114 116 117 n8 274192 271928 269664 267400 265184 262968 260752 258536 9445000 fti 30 3 1 32 33 34 35 36 37 348576 346169 34376i 341353 338945 334176 L/1 3 A I IQ 75 315808 120 . 254'52 76 3 '3400 O 77 311040 O Ao 78 308680 o 79 306320 1 xlvi APPENDIX. MOMENTS. M x = Jfx m. SPAN, SPAN, SPAN, \ SPAN, 260 260 260 270 feet. feet. feet. feet. X * m X R m X R m X R * 38 39 40 341353 338945 336538 334176 75 JQ 327091 324730 322369 320007 I Ao 116 7 118 119 274530 272353 270176 268000 1 A3 I 2 3 4 391292 388807 386322 42 331814 g 7Q 3'7645 VO 1 20 265822 c\ 38135' O P, 43 44 329453 327091 ? A oO 315284 121 263646 7 3789H 376470 45 324730 374029 46 47 48 322369 320007 3 '7645 Si 82 33 lg i4 329453 327091 122 I2 3 124 272353 270176 268000 9 386532 84 85 86 87 88 89 00 324730 322369 320007 3^645 315284 312922 310607 I * 125 126 127 128 129 130 265822 263646 261468 259291 257"5 254984 | Pu 10 II 12 '3 14 15 16 384036 381584 379'3 2 376681 374228 371777 PI A 49 50 5i 52 53 33"8i4 329453 327091 32473 322369 | A 54 320007 308291 J3 i 55 3 '7645 92 305976 For all values ol x below x ~ 105 56 I 61 327091 324730 322369 320007 3^645 315284 10 A 93 94 9 315284 312922 310607 308291 305976 303661 a uniformly dis- tributed load of 2700 Ibs. per ft will give greater moments than this table. 18 9 20 21 22 23 24 376681 374228 371777 369325 366874 364421 361969 H A 99 301345 O 25 359518 62 32473 IOO 101 299076 296807 * OO A. 2O 357tio 6 3 322369 294537 64 67 68 320007 317645 3 '5284 312922 310607 N A 103 104 I0 5 106 107 292269 290000 287776 285553 283330 27 28 29 3 3' 366874 364421 361969 3595i8 357110 A 32 354703 O 69 320007 108 292269 33 34 352295 349888 9 70 317645 O 109 290000 3S 347480 7' 31 ^284 no 287776 o 36 72 73 312922 310607 o^ Pi III 112 285553 283330 "T As 37 342755 74 308291 "3 281107 114 278883 "5 276707 CONCENTRATED LOAD SYSTEM. xlvii MOMENTS. = Rx m. SPAN, SPAN, SPAN, SPAN, 270 270 270 280 feet. feet. feet. feet. X * m * R m - X R m X * m 38 352295 77 333347 118 281444 i 401839 39 349888 78 331028 o 119 279258 o 2 399357 40 347480 79 328711 8 P\o j 120 277118 8 3 396875 41 345 118 Q 80 326392 "-> 121 274977 j 13 4 394392 Q 42 342755 O A 81 324074 10 122 272836 5 5 391910 f 43 34039 1 S Pi 123 270695 6 389471 44 338029 7 387032 45 335665 82 340391 8 38459 2 46 47 333347 33 IQ 28 83 84 338029 335665 124 '25 279258 277118 8 5 333347 126 274977 9 397100 86 331028 I2 7 272836 10 3946o6 48 49 345" 8 342755 87 88 328711 326392 I A. 128 129 270695 268555 | n 12 392156 389706 8 A 50 34039' O 89 324074 E" '3 266458 r^ fu '3 387257 N P2 5 1 338029 8 j, 90 321800 131 264362 o 14 384806 *" S 2 335665 8 P6 319525 132 262266 '5 382357 53 333347 w 92 317251 260169 16 37995 54 331028 93 3'4977 '34 258073 55 328711 94 312703 '35 255977 17 389706 56 % 61 338029 335665 333347 331028 328711 326392 1 9 97 98 99 IOO 321800 319525 3I725 3 '4977 312703 310428 For all values of x below x = 74, a uniformly dis- tributed load of 2700 Ibs. per ft. will give greater moments than 18 '9 20 21 22 23 24 387257 384806 382357 379950 377542 375'35 372727 r-i A 62 324074 IOI 308155 * / 12 this table. 2 5 370321 IO2 305880 CO 20 367956 103 303607 27 365593 63 333347 104 301332 64 331028 IO 5 299102 a 328711 326392 1 r 106 296873 28 29 375'35 372727 67 fr 3 370321 68 321800 107 305880 367956 g 69 3'9525 108 303607 3 2 365593 1 A 109 301332 33 363228 Tj- IIO 299102 34 360863 70 7i 328711 326392 in 112 296873 294643 * Pn 35 36 358500 72 73 74 8 324074 321800 319525 3^7251 3'4977 r^ * P9 "3 "4 "5 116 "7 292414 290184 288000 285814 283629 35377' 351406 xlviii APPENDIX. MOMENTS, = Rx m. SPAN, 280 SPAN, 280 SPAN, 280 SPAN, feet. feet. feet. fr* feet. X K m X Jt X * m X * m 39 40 42 43 44 45 46 47 48 49 360863 358500 356135 353771 351406 348043 346678 . 344356 342035 339713 337393 j? PI 77 78 79 So 81 344356 342035 339713 337392 335071 I * 118 119 1 20 121 122 292764 290571 288420 286271 284121 Tf A l A 5 6 8 412113 409675 407237 404800 402362 399965 397568 395'72 o A 82 83 84 85 351406 348043 346678 344356 12' 121 126 292764 290571 288420 286271 9 407722 86 87 88 89 90 92 93 342035 339713 337392 335071 332793 335 r 4 328235 325957 1 fa 13 129 130 '32 33 284121 281970 279821 275606 273500 271392 269286 O* *. IO ii 12 13 14 15 ID 405274 402825 400377 397928 395480 393031 390624 1 A 50 52 53 54 55 351406 348043 346678 344356 342035 339713 1 P* J 94 323070 '33 137 138 139 140 265156 263092 261028 258963 256943 r or all values o 17 18 '9 20 21 22 2 3 2 4 400377 397928 39548o 393031 390624 385810 PI ro A % 61 62 346678 344356 342035 339713 337392 335071 in in ft 9 97 98 99 IOO 332793 330514 328235 325957 323678 321442 IOI 1 02 03 04 319206 316971 3 r 4735 312500 00 , x below jr=6i, a uniformly dis- tributed load ol 2700 Ibs. per ft. will give greater 2 ^ 26 2 7 380995 378630 376264 64 344356 342035 67 68 69 3397 '3 337392 335071 332793 3305M in CO /a 07 08 09 308113 305921 303730 301535 moments than this table. 28 29 30 3' 385810 383402 380995 378630 32 376264 O 373897 m A 70 339713 IO 310307 34 \B" 7 1 337392 II 308113 369165 72 335071 o 12 305921 36 366843 73 332793 in ft '3 303730 , 37 364516 74 75 3305M 328235 ^ 15 301535 299343 i 38 362192 76 325957 16 297150 17 294957 CONCENTRATED LOAD SYSTEM. xlix MOMENTS. = Rx m. SPAN, SPAN, SPAN, SPA.V, 290 290 290 300 feet. feet. feet. feet. X R m X A' m X A 5 m X A' m 39 40 37I53I 369'65 77 78 355260 352977 R 118 "9 301655 I 2 422463 420026 41 366843 79 350694 g . 120 299537 o ^ 417590 42 43 364516 362192 g 80 81 348411 346128 "i VO 121 122 297420 295302 10 T * 4 S 4'5'53 412716 o A 44 359868 1 t 82 343793 12 5 293185 6S 6 410320 45 357543 gN Pt '24 2 9 ro6 7 7 407923 46 355260 " 125 288950 8 405526 47 352977 83 359868 * 48 350694 84 357543 49 50 348411 346128 85 86 355260 352977 126 '27 297420 295302 9 10 418080 415633 87 350694 o 128 293185 ii 413226 88 34841 i 8 rU 129 291067 12 410820 g 5' 359868 89 346128 '30 288950 _ 13 408413 g f* 357543 O 90 343793 '3' 286832 g '4 406006 M 53 54 355260 352977 A 9' 92 341509 339226 I3 2 133 284715 282597 o" Pu 403600 55 350694 - 93 336943 "34 280480 56 348411 I3S 278402 130 276326 17 410820 94 346128 '37 274250 18 408413 P 357543 355260 9 343793 341509 130 272174 '9 20 406006 403600 59 60 61 62 63 352977 350694 348411 346128 343793 1 Pi 97 98 99 IOO IOI 339226 336943 33466o 332418 330177 b,. '39 140 141 142 284715 282597 280480 278402 o fill 21 22 23 24 25 401233 398866 396500 394'33 , 391766 to Pi 102 327935 '43 276326 26 389400 '03 3 2 5693 oo 144 274250 " 27 387033 64 352977 104 323452 '45 272174 % 67 68 69 350694 348411 346128 343793 341509 3275000 ft !o6 107 108 109 321251 319051 316851 314651 3'245 r For all values of x below x = 51 , a uniformly dis- tributed load of 28 29 3 3 1 396500 394'33 391766 389400 2700 Ibs. per ft. will give greater moments than 33 34 387033 384666 382300 1 P* 70 350694 no 321251 7' 72 348411 346128 g III 112 319051 316851 0, this table. 9 379933 377606 73 343793 Jo Po "3 3'465' fa 375280 74 341509 cT "4 3I245 1 ON 38 372953 75 339226 * 115 310290 76 336943 116 308131 "7 305972 . APPENDIX. MOMENTS. M x = JRx m. T , SPAN, SPAN, SPAN, 300 300 300 feet. feet. feet. X R m jr R m X R m 39 40 382300 379933 78 79 363/26 361440 9 120 310606 42 3776o6 375280 So 81 359'53 356866 to Ao 121 122 308480 306353 1 A3 43 44 372953 370626 f> 82 83 354620 352373 10 I2 3 124 304226 . 302100 1 45 368300 i? Ps 125 300013 46 366013 M * 47 48 49 5 363726 361440 359153 356866 84 8 5 86 87 368300 366013 363726 361440 126 127 128 308480 306353 304226 88 89 359 '53 356866 129 302100 300013 5' 370626 90 354620 8 A. 131 297926 52 368300 o 9i 352373 (^ 132 295840 53 54 366013 363726 1 A 92 93 350126 347880 '33 >34 293753 291666 r^ A4 55 361440 94 345633 '35 289620 O 56 359153 95 343426 136 287573 96 341220 ' 3 l 285526 138 283480 57 368300 '39 281433 58 366013 97 350126 140 279386 i 361440 fj 98 99 347880 345633 141 277340 61 359153 io IOO 343426 62 356866 IOI 341220 o 142 289620 63 354620 1 02 103 339013 336806 w fa '43 144 287573 285526 104 334600 oo '45 283480 9 64 363726 105 332393 146 281433 oo As a 361440 359' 53 1 06 330186 327980 147 148 279386 277340 - 67 356866 Si ft 108 325773 '49 275293 68 354620 r*% w 69 352373 ro 70 350126 109 3346oo no III 332393 330186 '50 283480 N f~) A6 7 1 359 : 53 112 327980 M 72 73 74 75 76 356866 354620 352373 350126 347880 ! ft 114 "1 116 117 325773 323566 321400 319233 317066 o\ A3 For all values of x below JT = 45, a uniformly dis- tributed load of 77 345633 118 314900 2700 Ibs. per ft. will give greater moments than this table. CONCENTRATED LOAD SYSTEM. UK VSITY ILLUSTRATION OF THE USE OF THE TABLES. A FEW illustrations will make clear the use of the tables. ist, SINGLE SYSTEM OF BRACING. Take, for instance, the Pratt truss, worked out on p. 107, Fig. 99. Here we have / = 90 feet required to find the maximum strains due to live load. For any upper flange, as A, Table II. for span 90 feet, p. xxii., gives at once the greatest moment. Thus, since the centre of moments for A is at the foot of the post ab, we must find the maximum moment at ten feet from the left end. For this point, the table gives at once, Maximum moment = Rx m = 157888 X 10 125000 = 1453880; dividing this by lever arm of A, which is 10 feet, we have at once, A = 145388 pounds = 72.69 tons. In like manner, for E, we have ^ = 40 ; and hence E X 10 = Rx m = 145610 X 40 2550000 = 3274400; hence E = 327440 pounds = 163.72 tons. So for any flange, upper or lower, the greatest strain due to such a rolling load as our tables assume can be at once and easily found. This rolling load is believed to be such as to give greater strains than can ever occur in practice. To the strains thus found, we must, of course, add the strains due to dead load. If we assume this at 0.5 ton per foot, or 5 tons at each upper apex, as on p. 107, we have at once for A, since the re-action at left is 20 tons, A X 10 = 20 X 10, or A '= 20 tons ; E x 10 = 20 x 40 5 (30 + 20 + 10), or E = 50 tons. The total strains are, therefore, A = 72.69 + 20 = 92.69 tons ; E = 163.72 + 50 = 213.72 tons. Comparing these with the strains found on p. 107, viz., A = 100.33, ar >d E 22 3> tons, ; we see that the method given there gives us greater strains than our table. This would indicate that our "locomotive excess " of 33 tons, there adopted, is somewhat large, and that * 28 tons would nearer meet the requirements of practice, and cause the values of p. 107 and i those found by use of the table to agree quite closely. For any diagonal, zsfg; we can easily find the requisite shear from Table I. Thus, we have, in present case, / = 90, x 40, / x 50, / x + 8 = 58. We see at once, from Ill APPENDIX. Table I., p. iii., that the limit for span 90 feet is 48^ ; hence, for x = 40, we must use formula II. We have, then, 115000 1715000 3210000 Shear = 58 -} 50 ^ 15000 = 56222 = 28.1 tons. 90 90 90 To this add the dead-load shear, which is 5 tons, and we have shear for fg 33. i tons. The shear found on p. 108, for 33 tons locomotive excess, is 40 tons. As before remarked, the results there given are somewhat large, and a locomotive excess of 28 tons would give a closer agreement. The preceding, if followed carefully, will fully explain the use of our tables in all cases where we have but a single system of bracing. 2d, DOUBLE, OR MULTIPLE, SYSTEM. For any flange, find from Table II. the greatest moment for its nearest centre of moments, and then find what uniform load will give this same moment at the same point ; calculate the flange for this uniform load divided into apex loads, and acting upon each system. If x is the distance from left end to centre of moments, and p is the uniform load per unit of length, then (/ x) is the moment. Put this equal to the moment found from Table II., and the value of / can be found, in pounds per foot, which would give the same moment as the table, at the given point. The flange can then be calculated for this uniform load. Each flange should thus be calculated for its own equivalent uniform load. For any brace, find the greatest shear at the foot of it from Table II. ; then find the equivalent uniform moving load ; divide this into apex weights, and calculate the brace for this loading. If m is the uniform moving load per unit of length, coming on from right and extending m y x \z up to a distance of x from the left end, then the shear is - -. 2/ Put this equal to the shear found from Table II., and the value of m can be found in pounds per foot, which would give the same shear as the table. The brace can then be calculated for this uniform moving load. Each brace should thus be calculated for its own equivalent uniform load. Iligiw :.( i 4/ / -^.-. ;' , m i m -. - .-;. I ,. 1 , - : ma - 1 i 1 '-:- & : .'"":' ''"' m " : ' ";\v- :: "" 1 m m I S I .,..,.,.-: ' . : w : - . ' ' : , . - _ ;^. 1 ^^^1^ i i i i " i i Hi -