Pencoyd Iron Works ^.ScP Roberts Company V ) X J J Ji — ^ ^ — ^ IN Construction 3 Back of Foldout Not Imaged steel in Construction. CONVENIENT RULES, FORMULA AND TABLES FOR THE STRENGTH OF STEEL SHAPES USED AS BEAMS, STRUTS, SHAFTS, ETC., MADE BY THE PENCOYD IRON WORKS, A. & P. ROBERTS COMPANY, PHILADELPHIA, PA. STEEt DEPARTMENT, l\i.iirjFACTURERD CF OPEN HEAPTH STF.EI^.^HAP.tiS, BARS, FORG- BRIDGE ANi) CONSTRoCTICN DEPARTMCNT, DESIGNERS AND MANUFACrURERS OF BUILDINGS, BRIDGES, VIADUCTS, TURNTABLES, ETC. TENTH EDITION. 1898. PENCOYD IRON WORKS A. & P. ROBERTS CO. PHILADELPHIA, PA. MAIN OFFICE, 261 S. Fourth Street, Philadelphia, Pa. Branch Offices; 100 Broadway, New York City 27 State Street, Boston, Mass. Agencies: , , . , ^ ^ J ■ ' • ' ' Equitable Building, Baltimore, E. W. CRAMER, \ ? I I'l Tao Rooker*', Cuirago, Ills. ' ' ■■> WM. V. iCELLEY, 150G I'isher Building, Chicago, Ills. GOOD & WATERMAN, Security Building, St. Louis, Mo. JAMES W. PYKE & CO., 35 St. Francois Xavier St., Montreal, Canada. Copyrighted, 1808 J. F. CORLETT, Perry-Payne Building, Cleveland, O. PREFACE. Two years have elapsed since the Ninth Edition of this book was issued. During this time the contents have been thoroughly revised and much new matter added. A number of new sections will be found in the lists, especially large beams and angles. The text and tables have, as in former editions, been very carefully prepared under the supervision of Mr. James Christie, and we trust may be of value to all who have occasion to use the products of the Pencoyd Iron Works. A. & P. Roberts Company. Pencoyd, Pa., February 16, 1898. -9 37 7 2. PENCOYD BEAMS. Bevel of flange 2 inches per foot. jr" 4 ^ Dimensions in inches. Section JVum- ber. Size of Beam. Weight Pounds per Foot. Area of Section. W. F. a K 0. R. M. ■ T. 240 B 24 80.0 23.53 .50 7.00 1.14 .60 4.50 .81 20.70 241 B 24 85.0 25.00 .56 7.06 1.14 .60 4.50 .81 20.70 13 on n Ofi An .00 1.21 .64 4.50 .88 20.48 243 B 2A 95.0 27.92 .62 7.48 1.21 .64 4.50 .89 20 48 244B 2A 100.0 29.42 .68 7.54 1.21 .64 4.50 .89 20 48 200 B 20 65.0 19.12 .50 6.25 1.03 .55 4.00 .74 16.92 201 B 20 70.0 20.59 .56 6.31 1.03 .55 4.00 .74 16.92 202 B 20 75.0 22.06 .64 6.39 1.03 .55 4.00 .75 16.92 203B 20 80.0 23.53 .63 6.75 1.12 .61 4.25 !82 16!52 204B 20 85.0 25.00 .70 6.82 1.12 .61 4.25 .82 16.52 205 B 20 90.0 26.47 .78 6.90 1.12 .61 4.25 .83 16.52 206B 20 95.0 27.94 .74 7.24 1.25 .68 4.50 .92 15.86 207B 20 100.0 29.41 .81 7.31 1.25 .68 4.50 .93 15.86 180 B 18 55.0 16.18 .46 6.00 .92 .46 3.75 .65 15.19 181 B 18 60.0 17.65 .54 6.08 .92 .46 3.75 \ .65 15.19 182B 18 65.0 19.12 .63 6.17 .92 .46 3.75 to .66 15.19 183 B 18 70.0 20.59 .62 6.50 1.01 .52 4.00 .73 14.76 184B 18 75.0 22.06 .71 6.58 1.01 .52 4.00 \ .74 14.76 185 B 18 80.0 23.53 .79 6.66 1.01 .52 4.00 .74 14.76 186 B 18 85.0 25.00 .74 7.00 1.16 .61 4.50 .83 14.04 187B 18 90.0 26.47 .82 7.08 1.16 .61 4.50 .84 14.04 150B 15 42.0 12.35 .41 5.50 .83 .41 3.25 .60 12.47 151B 15 45.0 13.23 .45 5.54 .83 .41 3.25 .60 12.47 152 B 15 50.0 14.70 .48 5.82 .90 .46 3.50 .65 12.21 153 B 15 55.0 16.18 .58 5.92 .90 .46 3.50 .66 12.21 154B 15 60.0 17.65 .55 6.17 1.04 .57 3.75 .77 11.82 155 B 15 65.0 19.12 .65 6.27 1.04 .57 3.75 .78 11.82 156 B 15 70.0 20.58 .63 6.43 1.17 .69 4.00 .89 11.41 157B 15 75.0 22.06 .73 6.53 1.17 .69 4.00 .90 11.41 158B 15 80.0 23.53 .83 6.63 1.17 .69 4.00 .91 11.41 2 PENCOYD BEAMS. Dimensions in inches. Section dum- ber. Size of Beam. Weight Pounds per Foot. Area of "J Section. W. F. C. E. 0. It T 120B 12 31.5 9.26 .35 5.00 .74 .35 3.00 % to .52 9.76 121B 12 35.0 10.29 .42 5.07 .74 .35 3.00 .■52 9.76 122R 12 40.0 11.76 .42 5.25 .88 .48 3.25 \io% .65 9.35 123B 12 45.0 13.23 .54 5.37 .88 .48 3.25 \to\ .66 9.35 124B 12 50.0 14.70 .55 5.68 .98 .56 3.50 \ to % .74 9.04 125B 12 55.0 16.18 .56 5.75 1.10 .67 3.50 .86 8.68 126 B 12 60.0 17.65 .68 5.87 1.10 .67 3.50 3/4 to .87 8.68 127B 12 65.0 19.12 .80 5.99 1.10 .67 3.50 % to \ .88 8.68 lOOB 10 25.0 7.35 .31 4.66 .67 .31 2.75 \ .47 7.96 lOlB 10 30.0 8.82 .44 4.79 .67 .31 2.75 .48 7.96 102R 10 35.0 10.29 .44 5.00 .81 .43 3.00 .60 7.47 103B 10 40.0 11.76 .59 5.15 .81 .43 3.00 .61 7.47 90R 9 21.0 6.18 .29 4.33 .63 .29 2.50 % .44 7.09 91B 9 25.0 7.35 .39 4.43 .63 .29 2.50 :4 .45 7.09 92Ii 9 30.0 8.82 .56 4.60 .63 .29 2.75 % .45 7.09 93B 9 35.0 10.29 .72 4.76 .63 .29 2.75 .46 7.09 SOB 8 18.0 5.29 .27 4.00 .58 .27 2.25 .42 6.21 81 B 8 20.5 6.03 .34 4.07 .58 .27 2.25 % .42 6.21 82B 8 23.0 6.76 .44 4.17 .58 .27 2.50 .41 6.21 83B 8 25.5 7.50 .53 4.26 .58 .27 2.50 «4 .42 6.21 3 PENCOYD BEAMS. Dimensions in inches. SecHon Num- ber. Size Beam. ^Veifflit Pounds per Pool. Area of Section. W. F. a E. 0. R. M. T. 70 B 7 15 0 4.41 .25 3.66 .53 .25 2 00 '4 .39 5.34 71B 7 17.5 5.15 .34 3.75 .53 .25 2.00 \ .39 5.34 72 B 7 20.0 5.88 .45 3.86 .53 .25 2.25 % .38 5.34 60 B 6 12.25 3.60 .23 3.33 .49 .23 1.75 .36 4.46 Dili 0 14. /O Q AA A Q 1. 10 % .37 4.46 62 B 6 17.25 5.07 .46 3.56 .49 .23 2.00 % .36 4.46 50B 5 9.75 2.87 .21 3.00 .44 .21 1.75 > .31 3.59 51 B 5 12.25 3.60 .34 3.13 .44 .21 1.75 % .32 3.59 52B 5 14.75 4.34 .49 3.28 .44 .21 2,00 % .32 3.59 408 4 7.50 2.20 .19 2.66 .40 .19 1.50 \ .29 2.72 41 B 4 8.50 2.50 .24 2.71 .40 .19 1.50 \ .29 2.72 42 B 4 9.50 2.79 .32 2.79 .40 .19 1.75 .28 2.72 433 4 10.50 3.09 .39 2.86 .40 .19 1.75 .28 2.72 SOB 3 5.50 1.62 .17 2.33 .35 .17 1.25 .26 1.85 31 B 3 6.50 1.91 .24 2.40 .35 .17 1.25 .27 1.85 32B 3 7.50 2.20 .34 2.50 .35 .17 1.50 .25 1.85 63B 6 32.3 9.49 .50 4.88 .87 .50 3.00 % to % .66 3.00 to to 37.4 10.99 67B 6 41.0 12.06 .63 5.25 l.OS .62 3.25 \ to % .81 2.60 to to 46.1 13.56 4 PENCOYD CHANNELS. f F Bevel of flange 2 inches per foot. —Tr -> Dimensions iu inches. Section Num- ber. Size of Chan- Weight Pounds per Foot. Atscl of Section. W. F. C. E. 0. R. M. T. 150C 15 33.0 9.70 .40 3.40 .90 .40 2.00 3/> tn 7/o 4 to /g .63 12.35 151C 15 35.0 10.29 .42 3.42 [go !40 2.00 \ to % .64 12!35 152C 15 40.0 11.76 .52 3.52 .90 .40 2.13 \ to % .63 12.35 153C xo R9 .yu .40 2.25 \ to % .63 12.35 10 50.0 14.70 .63 4.00 1.05 .49 2.50 \ to % .74 11.89 155C 15 55.0 16.18 .72 4.09 1.05 .49 2.63 %to7/Q .73 11.89 120C 12 20.5 6.03 .28 2.94 .72 .28 1.75 .48 9.91 121C 12 25.0 7.35 .39 3.05 .72 .28 1.88 .47 9.91 122C 12 30.0 8.82 .51 3.17 .72 .28 2.00 .47 9.91 123C 12 35,0 10.29 .50 3.50 .95 .45 2.00 \ to % .70 9.17 124C 12 40.0 11.76 .62 3.62 .95 .45 2.13 '\ to % .70 9.17 lOOC 10 15.0 4.41 .24 2.60 .63 .24 1.50 % .42 8.16 lOlC 10 20.0 5.88 .38 2.74 .63 .24 1.63 \ .42 8.16 102C 10 25.0 7.35 .45 2.91 .76 .36 1.75 \ to % .55 7.68 103C 10 30.0 8.82 .60 3.06 .76 .36 1.88 '•\ to % .55 7.68 104G 10 35.0 10.29 .75 3.21 .76 .36 2.00 \ to % .56 7.68 90C 9 13.25 3.90 .23 2.43 .60 .23 1.38 .41 7.25 91C 9 15.00 4.41 .28 2.48 .60 .23 1.38 % .42 7.25 92C 9 20.00 5.88 .38 2.72 .71 .32 1.50 % .52 6.87 93C 9 25.00 7.35 .54 2.88 .71 .32 1.63 \ .53 6.87 128C 12 20.5 6.03 .28 2.61 .73 .34 1.50 % .53 9.49 to to to to 12 32.0 9.41 .56 2.89 .73 .34 1.75 \ .53 9.49 PENCOYD CHANNELS. T F Bevel of flange 2 inches i i/i per foot. j* — ^ —Tr ->. IW. Dimensions in inches. Section Num- ber. Size of Chan- nel. Weight Pounds per Foot. Area of Section. W. F. C. F. 0. 80C 8 11.25 3.31 .22 2.26 .56 .22 1.25 81C 8 13.75 4.04 .30 2.34 .56 .22 1.38 82C 8 16.25 4.78 .33 2.55 .65 .28 1.50 BSC 8 18.75 5.51 .42 2.64 .65 .28 1.50 84C 8 21.25 6.25 .52 2.74 .65 .28 1.56 70C 7 9.75 2.87 .21 2.09 .52 .21 1.13 71 C / O.DU 31 2 19 52 .21 1 25 72C 7 14.75 4.34 !36 2^46 !60 !25 l!50 73C 7 17.25 5.07 .46 2.56 .60 .25 1.50 74C 7 19.75 5.81 .57 2.67 .60 .25 1.63 60C 6 8.00 2.35 .20 1.92 .49 .20 1.06 61C 6 10.50 3.09 .27 2.14 .53 .22 1.25 62C 6 13.00 3.82 .40 2.27 .53 .22 1.38 63C 6 15.50 4.56 .52 2.39 .53 .22 1.50 50C 5 6.50 1.91 .19 1.75 .45 .19 1.06 51C 5 9.00 2.65 .32 1.88 .45 .19 1.19 52C 5 11.50 3.38 .47 2.03 .45 .19 1.31 40C 4 5.25 1.54 .18 1.58 .41 .18 0.94 41C 4 6.25 1.84 .24 1.64 .41 .18 1.00 42C 4 7.25 2.13 .32 1.72 .41 .18 1.06 30C 3 4.00 1.18 .17 1.41 .38 .17 0.81 31C 3 5.00 1.47 .25 1.49 .38 .17 0.88 32C 3 6.00 1.76 .35 1.59 .38 .17 1.00 R. % % % % % % to \ % to % % to % ^2 I/2 to % \ to % ^2 to % }^ H2 For 2]/^', 2" and \%" channels, see plate 18. 6 PENCOYD ANGLES. EVEN LEGS. Dimensions in inches. Weight in pounds. Section Number. Size. Thickness. Weight per Foot. Area of Section. Section Number. Size. Thickness. Weight per Foot. A rea of Section. 880A 8x8 \ 26.4 7.76 553A 5 X 5 18.2 5.35 881A 8x8 -A 29.8 8.76 554A 0 X 0 % 20.1 5.91 882A 8x8 % 33.2 9.76 555A 5 X 5 22.0 6.47 883A 8x8 36.6 10.76 556A 5 X 5 % 23.8 7.00 884A 8x8 % 39.0 11.47 557A 5 X 5 13. l(i 25.6 7.53 885A 8x8 i§ 42.4 12.47 558A 5 X 5 % 27.4 8.06 886A 8x8 % 45.8 13.47 559A 5 X 5 29.4 8.65 887A 888A 8x8 8x8 if 1 49.3 52.8 14.50 15.53 440A 4 X 4 R It) 8.2 2.41 660A 661A 662A 663A 664A 665A 666A 6x6 6x6 6x6 6x6 6x6 6x6 6x6 % ^ % \i % 14.8 17.3 19.7 22.0 24.4 26.5 28.8 4.35 5.09 5.79 6.47 7.18 7.79 8.47 441 A 442 A 443A 444A 445A 446A 447A 4 x4 4 x4 4 x4 4 x4 4 x4 4 x4 4 x4 /s -1, 16 \ -9, lb' % ai 10 % 9.8 11.3 12.8 14.5 15.8 17.2 18.6 2.88 3.32 3.76 4.21 4.65 5.06 5.47 667A 6x6 it 31.0 9.12 668A 669A 6x6 6x6 % 33.4 35.9 9.82 10.56 350A 351A 352A 31,12 X 31/2 31/2 X 31/2 31/2 X 31/2 liS % ll' 7.1 8.5 9.8 209 2.50 2.88 550A 5x5 % 12.3 3.62 353A X 31/2 -',!> 11.1 3.26 551A 5x5 14.3 4.21 354A 31/2 X "S^k n iif 12.4 3.65 552A 5x5 \ 16.3 4.79 355A 31/2 X 31/2 % 13.7 4.03 The length of leg is nominal, and correct only for least tliickness. 8 PENCOYD ANGLES. EVEN LEGS. Dimensions in inches. Weight in pounds. Section Number. 1 Size Thickness. Weight per Foot. Area of Section. Section Number. Size. Thickness. Weight per Foot. Area of Section. 330A 3 X 3 ■V4 1 /I /I 220A 2 X 2 IB 2.5 0.74 331 A 3 X 3 5 fe ft 1 D.i 1 70 991 A 2 X 2 '4 3.2 0.94 332A 3 X 3 % 7.2 2.12 222A 2 X 2 R re 4 0 1.18 333A 3 X 3 Iff 8.3 2.44 223A 2 X 2 % 4.8 1.41 334A 3 X 3 ^2 9.4 2.76 335A 3 X 3 1% 10.4 3.06 2.1 336A 3 X 3 % 11.5 3.38 175A 13/, X 1% 0.62 176A 1% X 1% 2.8 0.82 177A 13/4 X 134 3.5 1.03 275A 2% X 2% ^4 4.5 1.32 178A 134 X 134 % 4.1 1.21 276A 23/4 X 2% 5 Iff 5.5 1.62 277A 2-74 X Z% % 6.6 1.94 278A 2% X 2^/4 ITS 7.7 2.26 150A i^2 ^ l ^2 % 1.2 0.35 279A 2% X 2% 8.6 2.53 151A 1^2 X 1^/2 1^ 1.8 0.53 152A Vi2 X 1^2 2.4 0.71 250A 2\ X 2\ 1 iT 3.1 0.91 153A II/2 X 11,42 2.9 0.85 251A 2\ X 2H2 \ 4.1 1.21 154A 11,^ X llj^ % 3.5 1.03 252A 2H2 X 2\ 5.0 1.47 253A 21/2 X 2\ % 5.9 1.74 125A 114 X 114 % 1.0 0.29 254A TH^ X 2H^ *j /Ji 6.9 2.03 126A II4 X 11,4 1.5 0.44 255A 2H2 X 2\ 7.8 2.29 127A 114 X 114 \ 2.0 0.59 225A 2\ X 2\ A- 2.7 0.79 226A 2\ X 2\ \ 3.6 1.06 llOA 1 X 1 ^8 0.8 0.24 227A 2\ X 2\ 4.5 1.32 lllA 1 X 1 _3 15 1.2 0.35 228A 2\ X 2\ % 5.4 1.59 112A 1 X 1 \ 1.5 0.44 The length of leg is nominal, and correct only for least thickness. 9 PEI^COYD ANGIiES. UNEVEN LEGS. Dimensions in inclies. Weight in pounds. 860A 861A 862A 863A 864A 865A 866A 867A 868A 730A 731A 732A 733A 734A 735A 736A 737A 738A 650A 651A 652A 653A 654A 655A 656A 657A 658A 659A 640A 641A 642A 643A 644A 645A 646A Size. 8 x6 8 X 6 8 X 6 8 X 6 8 X 6 8 X 6 8 X 6 8 X 6 8 X 6 x3\ X 3\ X 3^2 x3i/2 X31/2 x3i^ X31/2 X31/2 x3\ 61/2x4 61^x4 61/2 X 4 6V2x4 6%x4 6\ X 4 61^x4 61/2 X 4 61/2 X 4 x4 x4 x4 X 4 x4 x4 x4 23.0 258 28.7 31.7 33.8 36,6 39.5 42.5 45.6 17.0 19.0 21.0 23.0 24.8 26.7 28.6 30.5 32.5 12.9 15.0 17.0 19.0 21.2 23.4 25.6 27.8 29.8 31.9 12.2 14.3 16.3 18.1 20.1 22.0 23.8 6.76 7.59 8.44 9.32 9.94 10.76 11.62 12.50 13.41 5.00 5.59 6.18 6.76 7.29 7.85 8.41 8.97 9.56 3.79 4.41 5.00 5.59 6.24 6.88 7.53 8.18 8.77 9.38 3.59 4.21 4.79 5.32 5.91 6.47 7.00 1 § Size. 647A 6 x4 648A 6 X 4 649A 6 x4 630A 631A 632A 633A 634A 635A 636A 637A 638A 639A 500A 501A 502A 503A 504A X31/2 x3i^ x3i^2 X31/2 x3i^ x3i/2 x3i/2 X31/2 x3i/2 x3i/2 51/2 X 31/2 51/2 X 31/2 51/2 X 31/2 517^ X 31/2 51^ X 31/2 540A 5 X 4 541A 5 x4 542A 5 x4 543A 5 x4 544A 5 x4 545A 5 x4 546A 5 x4 510A 511A 512A 513A 514A 515A 516A 517A X31/2 X31/2 X 31/2 X31/2 X31/2 X31/2 X31/2 X31/2 hi 25.6 27.4 29.4 11.6 13.6 15.5 17.1 19.0 20.8 22.6 24.5 26.5 28.6 11.0 12.8 14.6 16.2 17.9 11.0 12.8 14.6 16.2 17.9 19.6 21.3 8.7 10.3 12.0 13.6 15.2 16.8 18.4 20.0 The length of leg is nominal, and correct only for least thickness. 10 PENCOYD A^faiiES. UNEVEN r,EGS. Dimensions in inches. Weight in pounds. Size. 530A 5 X 3 531A 5 X 3 532A 5 X 3 533A 5 X 3 534A 5 X 3 535A 5 X 3 536A 5 X 3 537A 5 X 3 450A 4^/2x3 451A 41/2 X 3 452A 41/2X 3 453A 41/2 X 3 454A 4172 X 3 455A 41(^x3 456 A 41/2 X 3 457A 41^2 X 3 410A 4 x3\ 411A 4 x3\ 412A 4 X 31^2 413A 4 ii3\ 414A 4 X 3^;^ 415A 4 x3H2 416A 4 X 3\ 417A 4 x3y.2 430A 4 X 3 431A 4 X 3 432A 4 X 3 433A 4 X 3 434A 4 X 3 435A 4 X 3 300A 31/2x3 301A 31^x3 302A 3\x3 303A 31/2x3 304A 31/2 X 3 305A 3I7I2X3 8.2 2.41 9.7 2.85 11.2 3.29 12.8 3.76 14.2 4.18 15.7 4.62 17.2 5.06 18.7 5.50 7.7 2.26 9.1 2.68 10.5 3.09 11.9 3.50 13.3 3.91 14.7 4.32 16.0 4.71 17.4 5.12 7.7 2.26 9.1 2.68 10.5 3.09 11.9 3.50 13.3 3.91 14.7 4.32 16.0 4.71 17.4 5.12 7.1 2.09 8.5 2.50 9.8 2.88 11.1 3.26 12.4 3.65 13.8 4.06 6.6 1.94 7.8 2.29 9.1 2.68 10.3 3.03 11.6 3.41 12.9 3.79 =5^ Size. 310A 311A 312A 313A 314A 316A 317A 318A 325A 326A 327A 328A 329A 320A 321A 322A 323A 324A 200A 201 A 202A 203A 204A 205A 206A 207A 208A 209A 215A 216A 217A 218A 210A 211A 212A 213A 31/2 X 21^ 31/2 X 21/2 3^2 X 2H2 3\ X 2\ 3\ X 2^2 31/2 X 2 31/2 X 2 31/2x2 3 3 3 3 3 t2\ x2\ X 2\ x2^2 3 X 2 3 X 2 3 x2 3 X 2 3 X 2 21/2 X 2 21/2 X 2 21/2 X 2 21/2 X 2 2^2x2 2^2x2 2\ Xl^2 21/4 xll/2 2\ X 11^ 2\ X13/2 2 xl\ 2 xlJ/2 2 xll/2 2 xli^ 2 xll/4 2 xl\ 2 xl\ 2 xl\ 4 The length of leg is nominal, and correct only for least thickness. 11 PENCOYD ANGLES. SQUARE BOOT ANGL,ES. Size 171 Inches. 40A4 x4 35A'3| X 31 30A.3 x3 28A 2| X 2' 25A:2ix2j 24A|2|x2i 20 A 2 x2 18A!l| X 1| ISA'IJ X li 12A li X 1| lOA 1 X 1 Approximate Weight in Pounds per Foot for Various Thicknesses in Inches. 1 t _3 1 4 5 rs 1 ^6 4 1 \l 1 1 .125 .1875 .25 .3125 .375 .4375 .50 .5625 .625 .6875 .75 .875 9.8 11.4 13.0 14.6 16.2 7.1 8.5 9.911.4 4.9 6.1 7.2 8.3 9.4 4.5 5.6 6.7 7.8 8.9 4.1 5.1 6.1 7.1 8.2 3.6 4.5 5.4 3.3 4.1 4.9 2.9 3.6 4.4 1.80 2.4 3.0 1.53 2.04 2.55 0.82 1.16 1.53 ANGLE COVERS. Size in Inches. 33A3 x3 27A 2| X 2| 26A|2|x2i 23Ai2ix2i 22A2 x2 Approximate Weight in Pounds per Foot for Various Thicknesses in Inches. f i 1 3 4 5. .125 .1875 .25 .3125 .375 .4375 .50 .5625 .625 .6875 .75 .875 4.8 5.9 7.1 8.2 9.3 10.4 11.5 4.4 5.5 6.6 7.7 8.8 3.0 4.0 5.0 6.0 7.0 8.1 2.6 3.5 4.4 5.3 2.4 3.2 4.0 4.8 SPECIAIi ANGLES. Size in Inches. 278A2|x2J 415A4i X 14 Approximate Weight in Pounds per Foot for Various Thicknesses in Inches. .125 .1875 3.6 \ .25 4.2 4.9 ^ 1 I -h .3125 .375 .4375 5.3 6.4 .50 .5625 .625 ,6875 .75 .875 12 PENCOYD DECK BEAMS. Depth in Inches. \ j i07i Numbers. imum Fiange Uh in Inches. Inimum Web ■ness in Inches. Minimum Weight per Foot in Pounds. Approximnte Weight in Pound s per Foot for each I'hickness of Web, in Inches. :ased Thickness nches for each litioniil Pound per Foot. Sect %^ Ml Thick iff % 7, Iff t'ff % U % hicn in 1 Ada 111/2 115D 5.25 .406 32.2 33.4 35.8 38.2 40.7 43.1 45.6 .026 10 lOOD 5.25 .375 28.0 28.0 30.2 32.3 34.4 36.5 38.6 .029 9 90D 5.00 .375 25.0 25.0 26.9 28.8 30.7 32.6 .033 8 SOD 4.62 .343 21.0 21.8 23.5 25.2 26.9 28.6 .037 7 TOD 4.25 .343 18.0 18.5 20.0 21.5 23.0 24.5 .042 6 60D 3.75 .312 14.5 14.5 15.8 17.1 18.3 19.6 .049 5 SOD 3.25 .312 11.511.512.5 1 1 13.6 14.7 15.8 .059 PENCOYD BULB ANGLES. 10 lOOA 3.62 .500 25.6 25.6 28.6 31.5 .022 9 90A I i 3.50 .484 22.5 23.2 26.0 .023 8 80A 3.37' .453, 19.5 21.3 23.7 .026 7 7'OA 3.19| .406' 16.0 17.1 19.2 .030 6 60A 3.00 .359 12.7 13.2 15.1 17.1 19.0 .033 5 50A 2.75j .312! 9.7 9.7 11.4 13.0 .038 13 PENCOYD TEES. For details see lithographs— Plates Nos. 23, 24, 25 and 26. EVEN TEES. UNEVEN TEES. Section Number. Szze m Inches. Weight per Foot. Section Number. 440T 4 X 4 in Q Kn 1 441T 4 X 4 lo. / DO 1 335T 7 n 00 I 336T 'J '2 ^ /2 9 0 54 T 337T 11.0 42 r 330' r 3 X 3 6.5 43 r 331T 3 X 3 1.1 44 T 225'r 91/0 X ^ '2 ^ /2 5 0 ^.i^ T ^0 1 226r /2 ^ 5.8 38 T 227T 21?i:> X 2I/2 6.6 39 T 222'r 91/7 X 2Va 4.0 OU 1 223T 91/, T 91/, 4.0 ox 1 220T 2 X 2 3.5 117T 1^/j X 13/, 2.4 33' r 115T 11/-. T 11/^ X /2 A ± /2 2 0 0^ 1 1121' Vi4 X II/4 1 5 00 i HOT 1 X 1 lio 36T ^0 i 29r 25T 26T 27r 24T 20T 22T 21T 23T 17T 18T 15T 12T Size in Inches. x4 X 5V4 X31/2 x4 X 2 X 3 x3 X41/2 31/2 X 3 3^7^ X 3 3 X 11/2 X 21/2 X 2 V2 X21/2 X 2% X 31/2 x3i'2 2''/4 X 1\ 2% X 2 2% X II/4 21/2 X 2% 21/2 X 3 21,^ X ^ 2 X 2 xlJ, 2 X 1 2 X \\ r\ X IjV l'^/4 X II/4 1^4 X l i MISCELLANEOUS SHAPES. Section Number. Section. Size in Inches. Weight per Foot in Pounds. 217M Heavy Rail. 6 50.0 210M 260M Floor Bars. 3ji^ X 4 X 3X X 1/4 to 1/2 2V2 X 6 X 2^/2 X 1/4 to % 7.1 to 14.3 9.8 to 14.7 SIZES OF PENCOYD BARS. FLATS. '^9 X % inches to % inches. 1 X 1/4 " % " X \ " 1 " 1 IVq X 1/4 " 1 " X 5/q " ■*-16 '0 1 " 1^ X " 1 1\ X 1/4 " 1 1^ X 5/8 " 1 1% X V4 " 114 " m X % " 1 11/8 " 1^ X 1/4 " 114 " IM X 34 " 114 " 1% X 1/4 " 1\ " 134 X 14 " 1\ " m X % " 1% " 2 X 14 " 11/2 " 2^ X 1% inches to 2 inches. 214 X 14 " 17/8 2,^ X II/2 " 2 2% X % " 1% 2\ X 14 " 1% 2% X 14 " % 3 X 14 " 2 3V4 X 14 " 7/g X 14 " 4 X 14 " 21/2 41/^ X 14 " % 5 X 14 " 21^42 6 X 14 " 21/2 7 X 14 " ' 2\ 8 X 14 " 21/3 9 X 14 " 2% 10 X 14 " 2H2 12 X 34 2\, ROUNDS. \. ^, %. H. %. ii %. \i 1. 1^, 11/8, 1^, 114, 1^, 1%, lA. 11^, lA, 1%, 1=^4. 2, 21/8, 214, 2%, 21^, 2%, 234, 27/8, 3, 31/8, 314, 3%, 31^, 3%, 334, 37/8, 4, 41/8, 414, 43/8, 41^, 4%, 434, 47/8, 5, 514, 51^42, 534, 6, 61^, 7 inches. HALF ROUNDS. ^, %. H. ^^4. H. ft. 1. 11/8, IV4, 1%, 11^, 1%, 1%, 2, 214, 21^, 3, 31,42, 4, 41/2 inches. SQUARES. \. A. %, ti ^4 l^. A. 1t^. 1^4. 1%. 1 - - 1^4, 17/8. 2, 21/8, 2\, 2%, 21/2, 2%, ■8. fl. 1. 11^, 1%. 234, 27/8, 3, 31/8, 314, 33/8, 31^, 3%, 334, 37/8, 4, 41/8, 414, 43/8, 41^, 4%, 434, 47/8, 5 inches. RIVET SIZES. so 31 38 87 38 39 41 46 ■^^i 'S^t 6?> 6 4> ^T) «?J 47 49 5 8 54 5 5 57 61 62 63 "5?! •B'4) 6?) ^4) "S"?! 1??, 1A> lit. inches. BOLT SIZES ^?TH FULL. 1 9 5 113 137 151 2) T^) 16> ?> Tff> T6> ^> lr?> li> 1A> 1? inches. 15 OPEN-HEARTH STEEL AXLES. Axles for locomotive and car service are made at Pencoyd of open-hearth steel, to conform to either the drop or me- chanical test, as may be required. The results below, taken as an average of a number of tests, represent the quality of material used for this purpose. TRANSVERSE TEST. iVutnber of Axles. Diameter of Hub Seal. Diameter of Centre. Weight of Ram. Height of Fall. Number of Bloics. 14 4| 1640 29 86 26 5t\ 4| 1640 25 37 TENSILE TEST. Average of 12 testsj. I'Jlastie Limit. Ultimate Strength. Elongation. Reduction of Area. 45320 79230 In 2". 22.7 /• 38"/ The blooms are worked at a single uniform heat, undei heavy hammers, to the finished forging. Locomotive and passenger car-axles are furnished rough-turned throughout ; those for freight service, with journals forged and rough - turned. The process of manufacture thus indicated produces axley of the highest standard of excellence. 16 STRUCTURAL STEEL. The strength of structural steel depends largely on the amount of the constituent elements that are associated with the iron, and each of which affect more or less the hardness and strength of the metal. The principal of these are carbon, manganese, silicon, phosphorus and sulphur, the first-named being purposely retained as useful or necessary, the others being rejected, as far as practicable, as objectionable when in excess of certain minute proportions. The grade and character of the steel is usually known by the percentage of contained carbon. Steel used in struc- tures usually varies in tensile strength from 55,000 to 70,000 lbs. per square inch of section, or from .10 to .25 per cent, of carbon. The following table exhibits the physical characteristics of Open-Hearth Basic Steel of the various grades, the results derived from an extensive series of tests indicating the ten- dency of a total average of the composition hereafter de- scribed to approximate to the figures given in table. The predominant elements other than carbon averaged throughout the series as follows : manganese, .40 ; phos- phorus, .04 ; sulphur, .05 per cent. Any increase of these elements is attended with an increase of tensile strength and reduced ductility, and vice versa. The tensile strength of the steel is also affected to some extent by the tempera- ture at which it is finished, and the rate of cooling, these influences being more apparent in the grades containing highest carbon. Therefore the values given have only a general significance, and individual tests may vary widely above or below the figures in the table. For Bessemer or open-hearth acid process steel, the ten- sile strength will ordinarily be greater for the same per- centage- of carbon given in this table, for the reason that the proportions of phosphorus and sulphur, and sometimes manganese, are usually higher than in open-hearth basic steel, each of these elements contributing to strength and hardness in the steel. 17 OPEN-HEARTH BASIC STEEL. nUige of rbon. Tensile Strength in Pounds per Square Inch. Ductility. Ultimate Strength. lilastic Limit. Stretch in S Id dies. Reduction of Fractured Area. .Uo .09 .10 .11 .12 .13 04UUU 54800 55700 56500 57400 58200 32500 33000 33500 34000 34500 35000 32 per cent. 31 31 30 30 29 60 per cent. 58 57 56 55 54 .14 .15 .16 .17 .18 .19 59100 60000 60800 61600 62500 63300 35500 36000 36500 37000 37500 38000 29 28 28 27 27 26 53 52 51 50 49 48 .20 .21 .22 .23 .24 .25 64200 65000 65800 66600 67400 68200 38500 39000 39500 40000 40500 41000 26 25 25 24 24 23 47 46 45 44 43 42 For convenient distinguishing terms, it is customary to classify steel in three grades : " mild or soft," " mtdium" and "hard," and although the different grades blend into each other, so that no line of distinction exists, in a general sense the grades below .15 carbon may be considered as " soft" steel, from .15 to .30 carbon as "medium," and above that "hard " steel. Each grade has its own advantages for the particular purpose to which it is adapted. The soft steel is well adapted for boiler plate and similar uses, where its high ductility is advantageous. The medium grades are used for general structural purposes, while harder steel is especially adapted for axles and shafts, and any service where good wearing surflices are desired. Mild steel has superior welding jiroperty as compared to hard steel, and will endure higher heat without injury. Steel below .10 car- bon should be capable of doubling flat without fractui-e, after being chilled from a red heat in cold water. Steel of J8 .15 carbon will occasionally submit to the same treatment, but will usually bend around a curve whose radius is equal to the thickness of the specimen ; about 90 per cent, of specimens stand tlie latter bending test without fracture. As the steel becomes harder, its ability to endure this bend- ing test becomes more exceptional, and when the carbon ratio becomes .20, little over twenty-five per cent, of speci- mens will stand the last-described bending test. Steel hav- ing about .40 per cent, carbon will usually harden sufficiently to cut soft iron and maintain an edge. ELASTICITY. As the material elongates or shortens under stress, the change of length is directly proportionate to the stress, and tlie material recovers its original length after removal of the stress, until the elastic limit is reached, when changes of length are no longer regular and permanent set takes place, or the destruction of the material has begun. In good material the stress at elastic limit, for either ten- sion or compression, is usually about six-tenths of the ulti- mate tenacity. The ductility, under tensile stress, is usually measured by the total elongation in a given length, or by the percentage of reduction of the fractured area, or by both. The elasticity is measured by the change of length under stress below the elastic limit of the material. The elasticity of the various grades of steel are practically uniform, that is, each material will exhibit a uniform change of length under uniform stress below the elastic limit; but, as the elastic limit of the higher grades is greater than that of the lower or softer grades, the former will elongate or shorten to a greater extent than the latter before its elasticity is injured. This property is expressed by a modulus, which for either material will average about 29,000,000 lbs. That is, if the change of length could be extended sufficiently, it would re- quire 29,000,000 lbs. per square inch of section to double the original le«igtli under tensile strain, or to shorten the length one-half under compression. Therefore, steel will extend or shorten oTjonVooo part of its normal length, for every pound per sectional inch in change of load. 19 RESILIENCE OF STEEL. Eesilience is the amount of work done to produce a cer- tain deformation in material. It is usually measured in inch-pounds. The total resilience is the work done in caus- ing rupture or maximum deformation. The elastic resil- ience is the work done when the material is strained to the elastic hmit. The work done by a load applied gradually, up to the elastic limit, is equal to one-half the product of the final stress, by the extension, or other deformation. Above the elastic limit the extensions increasing in a greater ratio than the loads, the work is approximately equal to two thirds of the product of the maximum stress by the extension. When a load is applied instantaneously the momentary elastic deformation is twice that resulting from the same load applied gradually. If the load is applied with percussion, the work is denoted by the product of the weight into the total fall. The modulus of elastic resilience, is the work done on one cubic inch of material by a load gradually applied to the elastic limit. Modulus of elastic resilience = i squareof elastic lijnit, Modulus of Elasticity, or elastic resilience = resilience X vol-i ume of material in cubic inches. Taking 3 grades of steel— mild, medium and hard— and ascertaining their respective elastic limits to be 35,000, 45,000 and 55,000 lbs. per square inch of section, and each grade having equal moduli of elasticity, say 29,000,000 lbs. The modulus of elastic resilience For Mild Steel = 21.1 inch-pounds. For Medium Steel = 34.9 " " For Hard Steel =52.2 " Similarly the elastic resilience per cubic inch, or modulus of resilience of a rectangular beam supported at both ends and loaded at the middle, is s quare of stress on extreme fibres at elastic limit . Modulus of Elasticity. 20 EXPANSION BY HEAT. Soft steel or iron will extend about jj-soss V^^^ of its length for each degree F. of elevation of temperature. For a vai'iation in temperature of 100 degrees F., the change in length will be about one inch in 125 feet. SPECIFIC GRAVITY. The specific gravity of steel varies according to the purity of the metal, and also according to the degree of condensa- tion imparted by the process of rolling or forging. As a rule, mild steel has a higher specific gravity than hard steel, and both are lower than perfectly pure iron, but about two per cent, higher than ordinary commercial iron. Structural steel in comparatively small sections having the composition denoted in the previous table of tensile strength, has the following specific gravity, corresponding to given carbon ratio : Carbon, Per cent Specific Gravily. Weight per Cubic Fool in Pounds. .10 7.860 489.92 .20 7.858 489.80 .30 7.856 489.67 In the form of rolled beams and largest commercial sec- tions the weight will be slightly less than this. The tables in this book are all calculated on a basis of 489.6 lbs. per cubic foot, or the sectional area in square inches multiplied by 3.4 equals the weight in pounds per foot. 21 Tables for Pencoyd Beams. The following tables for beams give the greatest safe loads in net tons, evenly distributed, including the v^^eight of the beam. The results are obtained by the methods described on pages 182 to 187, and correspond to an extreme fibre stress of 16,000 lbs. per square inch of section, or approxi- mately about one-half the elastic limit of the material, pre- suming that steel of the milder grades is used. LIMITS FOR THE SAFE LOAD. These loads are given as the greatest safe loads, and the beams are entirely reliable for them under ordinary condi- tions. For the loads given in italics in the beam tables, the weh of the beam should be stiffened at the end to prevent crip- pling, or the load should not exceed that calculated by the formula for Maximum Load in Tons given on page 187, and in the Tables of Elements of the several sections, pages 18S to 203. If, however, the conditions of the service involve the introduction of forces not considered in the tables, the character of the load must be considered, and the mode of application of the same. If the load is suddenly applied, especially if accompanied by impact, the resulting dynamic stresses will not be expresed by formuke which are derived from static consideration alone. Freedom from vibration, or excessive deflection has usually to be provided for, or the beam may be of considerable length without lateral sup- port. In many such cases it may be necessary to take smaller loads for beams than those given in tables. In general, the following limitations of the tabulated safe loads will be proper for the specified conditions : 22 Character of Service. Greatest Safe Loads. Quiescent load, subject to little vibration, as in ordinary floors, etc., especially where beams are short. As in tables. Fluctuating loads, causing vibration, espe- cially if the beams are long as com- pared to their depth. One-fifth (l) less than the tables. When loads are suddenly applied with slight impact, or exposed to vibration from machinery or rapidly moving loads. One third (^"t less than the tables. The beams, if of considerable length, are supposed to be braced horizontally, and it is safest to limit the application of the tabular loads to beams whose lengths between lateral supports do not exceed twenty times the flange width. Our experience has been that a beam without lateral sup- port is more stable than is commonly supposed. In an open-webbed beam, the top flange acts as a simple strut, and is liable to lateral flexure when the unsupported length is considerable. But in a solid beam the parts in tension sustain the parts in compression, and prevent the buckling which would otherwise occur. Experiments have shown a reduction of about one-third of the normal modulus of rupture when the length of the beam becomes 80 times its flange width. But as the long beam may suff'er if exposed to accidental cross strains, we recommend the greatest safe load to be reduced in such a ratio for long beams that when the length is seventy times the flange width the greatest safe loads will be reduced one-half. This will give safe loads, corresponding to given lengths, as follows : BEAMS WITHOUT LATERAL SUPPORT. Length of Beam. Proportion of Tabular Load Forming Greatest Safe Load. 20 times flange width. 30 " 40 " 50 " (50 " 70 " Whole tabular load. 9 '< " 1 0 8 << " 1 0 7 < < << 1 0 fi ' < < ' 23 DEFLECTION. The tabular deflections are derived from the coefficients on pages 188 to 191, as described on page 187. If the load on the beam is reduced below that of the tables, the deflec- tion will be less than that given in the tables, in the direct ratio of the loads. The greatest safe load in the middle of the beam is exactly one-half (J) of the distributed load, and the deflection for the former will be eight-tenths of the deflection corre- sponding to the distributed load as given in the tables. If the load is placed out of centre on the beam, it will bear the same ratio to the load at the centre that the square of half the span bears to the product of the segments of the beam formed by the position of the load. Example.— A 15- inch No. 150B I beam, 16 feet between supports, will safely carry an evenly distributed load (by the tables) of 19.7 tons, and deflect under same .29 inches. The greatest safe load in the middle will be one-half the above, viz., 9.8 tons, and the resulting deflection j\ of the former, or .23 inches. If the weight is concentrated 3 feet out of centre, or 5 feet and 11 feet from the ends, then the square of half the span being 64, and the product of the segments being 55, the greatest safe load will be ^'^^ = 11.4 tons. 55 If a beam of above size and length is used without any lateral support, reduce the safe load in the ratio aforesaid. Thus the flange is 6.4 inches wide, and the length 30 times this ; therefore the greatest safe load will be of the results in the example. If beams are supported as described hereafter, the greatest safe loads and corresponding deflections will bear the given ratios to the tabulated loads and deflections, for the same length and section of beams. 24 Character of Beam. Greatest Safe Load. Deflection. Fixed at one end, with the load concentrated at the other end. One-eighth (I) part of the tabular load. Three and one- fifth {31) times the tabular de- flection. Fixed at one end, with the load uniformly dis- tributed. One-fourth Q) part of the tabular load. Two and two- fifths (2f ) times the tabular de- flection. Rigidly fixed at both ends, with a load in the middle of beam. Same as the tabu- lar load. Four-tenths of the tabular deflection. Rigidly fixed at both ends, with the load uni- formly distributed. One and one-half times the tabular load. Three- tenths (A) of the tabular deflec- tion. Continuous beam loaded in middle. Same as the tabu- lar load. Four-tenths of the tabular deflection. Continuous beam load uniformly distributed. One and one-half (IJ) times the tabular load. Three- tenths (A) of the tabular deflec- tion. BEAMS WITH FIXED ENDS. By beams "rigidly fixed," as denoted in the previous table, we mean that the beam must be so securely fastened at both ends, by being built into solid masonry, or so firmly attached to an adjacent structure, that the connection would not be severed if the beam was exposed to its ultimate load. In this case the beam is of the same character as if con- tinuous over several supports, or as if consisting of two cantilevers, the space between whose ends was spanned by a separate beam. CONTINUOUS BEAMS. If a beam is continuous over several supports, and is equally loaded on each span, the greatest safe loads and the resulting deflections on any intermediate span will be as given in the preceding table. But the end spans of such a beam, being only semi-continuous, must be either of a shorter span than the intermediates, or, if of the same length, the load must be diminished. 25 HORIZONTAL SHEARING OP BEAMS. In beams of very short spans or beams with heavy loads concentrated near supports, when the bending moments will be small in comparison with the reactions at the supports, the beams may fail by longitudinal shearing. The intensity of the longitudinal shear at any section is the product of the vertical shear for that section and the statical moment of the section included between the plane of shear and the extreme fibres, divided by the product of the moment of inertia of the beam section and the thick- ness of the beam at the section where the shear is considered. The liability to horizontal shearing will not occur in beams for the lengths and loads given in the tables. The following table gives the lengths under which beams should be designed to resist longitudinal shear when uni- formly loaded to produce a fibre strain of 10,000 pounds per square inch, and are based on a working shearing stress of 12,000 pounds per square inch. Size o f Beam in Indies. Length of Span in Feet. I Size of Beam in Inches. Length of Span in Feet. 24 9.0 8 4.3 20 7.3 7 3.9 18 6.9 6 3.7 15 6.0 5 3.0 12 5.6 4 2.6 10 5.0 3 2.1 9 4.8 SPACING AND DEFLECTION OP BEAMS. The proper spacing of beams depends on the amount and character of load and the length of span. Permissible de- flection as well as positive strength must be considered. If tlie load is motionless, and especially if the span is small in comparison with the depth of beam, it M'ill be safe to proportion the beams for the "greatest safe loads," as in preceding tables. If, on the contrary, the floors are subject to vibration, or the action of moving loads, and especially if the span is great in proportion to depth of beam, it becomes necessary to consider the deflection, which may become so great as to be a source of injury to the structure. It is considered good practice to limit the deflection to ^\ of an inch per foot of span, or the total deflection not to exceed part of the span. For I beams subjected to the loads given in the tables, this deflection occurs when the depth of the beam is about 2V of the span, or, approximately, twice the depth of the beam in inches gives the span in feet, having a deflection ofsio- , . . The following tables indicate for each beam this hmita- tion for deflection. Those in heavy type above the dark line deflect less, and those in fine type below the same line deflect more than of the span. If the spans are un- usually long, it is best to reduce the deflection below this limit, and maintain the depth of the beam not less than of the span. It has been demonstrated that the greatest mass of people that can be packed on any floor will not exceed in weight 80 lbs. per square foot. The weight of the beams will depend on the span, for which see a general rule farther on. Within the limits of practical spans for rolled I beams, it will be found that a floor is safe for a packed mass of people when the beams are not strained above the " great- est safe load " of the tables, under the following rating : I beam joists with wooden floor = 100 lbs. per sq. foot. Wooden floor and plastered ceilings = 110 " " " 4^^ brick arches and concrete fining = 150 " " " 27 These figures represent the total weight of floor itself and the imposed load. Floors proportioned as follows for given purposes will be satisfactory. The weight of the material may be included in the figures. Character of Floor. TjOadper Square Fool. Lightest floors, plank covering, Lightest floors, brick arches, I^ight warehouse floors, 100 lbs. 150 " 200 " 200 " 250 " 250 " 300 to 500 lbs. Halls of audience, Warehouses in vchich heavy pieces are moved, . . . . Shop floors for light machinery, .... Shop floors for heavy machinery, . . RULE FOR THE WEIGHT OF FLOOR BEAMS. The following rule gives a close approximation to the actual weight of floor beams, when the beams are propor- tioned according to the tables. Load per sq. ft. in lbs. X square of spa n injt. ^ lbs. of beams per sq. ft. of 1000 X depth of beams in ins. ~ floor. Example.— K floor of 16 feet span bears 200 lbs. per sq. ft., required the weight of floor beams if 12^^ beams are used. 200 X 25G , ,^ 1000 X 12 ■ P®"" ^1- °^ beams. To the foregoing must be added the weight of the ends of the beams built into the supports, or a length at each end about the same as at the depth of the beam. The following table gives the weights of beams per square foot of floor, for a load of 100 lbs. per square foot, the beams, as in the pre- ceding tables, subject to a stress of 16,000 lbs. per square inch. For greater floor loads the weight of beams increases iu direct proportion. Thus, for a floor to carry 200 lbs. per square foot, the weight of floor beams will be twice that of the table. Also, if the floor beams are proportioned for a lower fibre stress, the weight of beams will increase in inverse ratio. Thus, if the fibre strain allowed is 12,000 lbs. per square inch, the weight of beams will be increased as 12 to 16, or one-third heavier than the table. 28 PENCOYD I BEAMS. L,EAST WEIGHT OF FLOOR BEAMS IN POUNDS. For each square foot of floor, including ends at supports, based on a load of 100 pounds per square foot of floor. For heavier loads, the weights of beams are proportionately increased. Size of I Beam Clear Span of Beams in Feet. 8 1 10 1 16 1 18 1 20 22 j 24 26 28 Inches. Least Weight of Floor Beams in Pounds. 24 0.6 0.8 1.1 1.4 1.7 2.0 2.4 2.9 3.3 3.8 20 0.7 0.9 1.3 1.6 2.0 2.4 2.9 3.4 3.9 4.5 18 0.7 1.0 1.4 1.7 2.2 2.7 3.2 3.7 4.3 5.0 15 0.8 1.2 1.5 2.0, 2.5 3.0 3.6 4.2 4.9 5.7 12 0.6 1.0 1.4 1.8 2.3 2.9 3.6 4.3 5.1 5.9 6.8 10 0.7 1.1 1.6 2.1 2.7 3.4 4.1 5.0 5.8 6.8 9 0.8 1.2 1.7 2.3 2.9 3.7 4.5 5.3 6.4 8 0.9 1.3 1.9 2.5 3.2 4.1 5.1 6.0 7.0 7 1.0 1.5 2.1 2.9 3.7 4.7 5.7 6.9 6 1.1 1.7 2.4 3.3 4.2 5.4 6.4 5 1.3 2.0 2.9 4.0 5.1 6.4 29 24" I BEAM— No. 240 B. 80 POUNDS PER FOOT. Flange width 7.00 i Area in square iuches. . . . 23.5.3 Web thicliness 50 | Eesistance 175.95 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow cue-half of the tabular load. Deflection for centre load will be of the tabular deflection. For figures in small type deflection is excessive. Span Feet. Greatest Safe Load in Net Tons. Deflection in Inches. Greatest Distance in Feet Between Centres of Beams for Distributed Load ax Below. 100 Pounds ^ Foot. 125 Pounds per Square Foot. 150 Pounds per Seiiiare Fool. 175 Pounds per Sq^iarc Fool. 10 .07 187.7 150.1 . 125.1 107.2 11 85:31 .09 155.1 124.1 103.4 88.6 12 y8.20 .10 130.3 104.3 00. y 13 72.18 .12 111.0 88.8 74.0 63.5 14 67.0J !l4 95.8 76.6 63.8 54.7 15 62.56 .16 83.4 66 7 00. D 11.1 16 .18 73.3 58.7 48.9 41.9 17 55-20 !21 64.9 52.0 43.3 37.1 18 52-13 .23 57.9 46.3 38.6 33.1 19 49-39 .26 52.0 41.6 34.7 29.7 on 46.g2 46.9 37.5 31.3 26.8 21 44.69 .31 42.6 34.0 28.4 24.3 22 42.65 .35 38.8 31.0 25.8 22.2 23 40.S0 .38 35.5 28.4 23.7 20.3 24 39.10 .41 32.6 26.1 21.7 18.6 25 37.54 .45 30.0 24.0 20.0 17.2 26 36 09 .48 27.8 22.2 18.5 15.9 27 34.76 .52 25.7 20.6 17.2 14.7 28 33.51 .56 23.9 19.1 16.0 13.7 29 32.36 .60 22.3 17.9 14.9 12.8 30 31.28 .64 20.9 16.7 13.9 11.9 31 30.27 .69 19.5 15.6 13.0 11.2 32 29.33 .73 18.3 14.7 12.2 10.5 33 28.44 -78 17.2 13.8 11.5 9.8 N. B.— For loads given in Italics webs must be stiffened, or loads must not exceed maximum loads given in column XV, pages 188 to 191. 30 24" I BEAM— No. 241 B. 85 POUNDS PEK FOOT. Flange width 7.06 I Area in square inches . . . . 25.00 Web ihickuess 56 | Resistance 181.81 Greatest safe load in net tons luiiformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be yo of the tabular deflection. For figures in small type deflection is excessive. Span in Feet. Greatest Safe Loud in Net Tons. Ijejieciion in Inches. Greatest Distance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pounds per SQitare Fool. 125 Pounds per S<^nare Foul. 150 Pounds per Sfjuare Foot. 175 Pounds per Square Fool. 10 g6.()6 .07 193.9 155.1 129.3 110.8 80.80 .09 160.3 128.2 106.8 91.6 12 .10 134.7 107.7 89.8 77.0 13 74-58 .12 114.7 91.8 76.5 65.6 14 .14 98.9 79.2 66.0 56.5 15 04.04 .16 86.2 68.9 57.5 49.2 16 60.60 .18 75.8 60.6 50.5 43.3 17 57-03 .21 67.1 53.7 44.7 38.3 18 53-^7 .23 59.9 47.9 39.9 34.2 19 51-03 .26 53.7 43.0 35.8 30.7 20 48.48 .29 48.5 38.8 32.3 27.7 21 46.17 .31 44.0 35.2 29.3 25.1 22 44.07 .35 40.1 32.1 26.7 22.9 23 42.16 .38 36.7 29.3 24.4 21.0 24 40.40 .41 33.7 26.9 22.4 19.2 25 38.79 .45 31.0 24.8 20.7 17.7 26 37.29 .48 28.7 22.9 19.1 16.4 27 35.91 .52 26.6 21.3 17.7 15.2 28 34.63 .56 24.7 19.8 16.5 14.1 29 33.44 .60 23.1 18.5 15.4 13.2 30 32.32 .64 21.5 17.2 14.4 12.3 31 31.28 .69 20.2 16.1 13.5 11.5 32 30.30 .73 18.9 15.2 12.6 10.8 33 29.38 .78 17.8 14.3 11.9 10.2 K. B.— For loads given in Italics webs must be stiffened, or loads must not exceed maximum loads given in column XV, pages 188 to 191. 31 24" I BEAM— No. 242 B. 90 POUNDS PER FOOT. Flange width 7.42 I Area in square inches .... 26.47 Web thickness 0.56 | Resistance 196.4 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be of tbe tabular deflection. For figures in small type deflection is excessive. Span in Feet. Greatest Safe Load in Net Tons. jjejieciion in Inches. Greatest Distance in Feet Between Centres q Beams for Distributed Load as Below. 100 Pounds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. 10 104.74 .07 209.5 167.6 139.7 119.7 11 .09 173.1 138.5 115.4 98.9 12 .10 1^0.0 97.0 83.1 13 80.^7 .12 124.0 99.2 82.6 70.8 74.82 .14 106.9 85.5 71.3 61.1 10 .16 yo.i 53.2 16 65-47 .18 81.8 65.5 54.6 46.8 17 61.61 .21 72.5 58.0 48.3 41.4 1ft .23 64.7 51.7 43.1 36.9 19 55. /J .26 58.0 46.4 38.7 33.2 20 52-37 .29 52.4 41.9 34.9 29.9 21 49.88 .31 47.5 38.0 31.7 27.1 22 47.61 .35 43.3 34.6 28.8 24.7 23 45.54 .38 39.6 31.7 26.4 22.6 24 43.64 .41 36.4 29.1 24.2 20.8 25 41.90 .45 33.5 26.8 22.3 19.1 26 40.29 .48 31.0 24.8 20.7 17.7 27 38.79 .52 28.7 23.0 19.2 16.4 28 37.41 .56 26.7 21.4 17.8 15.3 29 36.12 .60 24.9 19.9 16.6 14.2 30 34.92 .64 23.3 18.6 15.5 13.3 31 33.79 .69 21.8 17.4 14.5 12.5 32 32.73 .73 20.5 16.4 13.6 11.7 33 31.74 .78 19.2 15.4 12.8 11.0 N. B. — For loads given in Italics webs must be stifienedj or loads must not exceed maximum loads given in columns XV, pages 188 to 191. 32 24" I BEAM— No. 243 B. 95 POUNDS PER FOOT. Hange width 7.48 I Area. in square inches . . . 27.!)2 Wtih thickness 0.62 | Resistance 202.3 Breatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be jV of the tabular deflection. For figures in small type deflection is excessive. Span in Feet. Greatest Safe Load in Net Tons. Dejiectxon in Inches. Greatest Distance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pounds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. 10 107.87 .07 215.7 172.6 143.8 123.3 11 gS.o6 .09 178.3 142.6 118.9 101.9 12 8g.8() .10 149.8 119.9 99.9 85.6 13 82.9S .12 127.7 102.1 85.1 73.0 14 / / -'O .14 110.1 88.1 73.4 62!9 15 .16 95.9 76.7 63.9 54.8 16 67.42 .18 84.3 67.4 56.2 48.2 17 .21 HA. f\ oy. / AO Q 42.7 18 59-93 .23 66.6 53.3 44.4 38.1 19 56.77 .26 59.8 47.8 39.8 34.3 20 53.93 .29 53.9 43.1 36.0 30.8 21 51.37 .31 48.9 39.2 32.6 28.0 22 49.03 .35 44.6 35.7 29.7 25.5 23 46.90 .38 40.8 32.6 27.2 23.3 24 44.94 .41 37.5 30.0 25.0 21.4 25 43.15 .45 34.5 27.6 23.0 19.7 26 41.49 .48 31.9 25.5 21.3 18.2 27 39.95 .52 29.6 23.7 19.7 16.9 28 38.52 .56 27.5 22.0 18.3 15.7 29 37.20 .60 25.7 20.5 17.1 14.7 30 35.96 .64 24.0 19.2 16.0 13.7 31 34.80 .69 22.5 18.0 15.0 12.8 32 33.71 .73 21.1 16.9 14.0 12.0 33 32.69 .78 19.8 15.9 13.2 11.3 N. B.— For loads given in Italics webs must be stiflfened, or loads must not sxceed maximum Ipads giv^n in column XV, pages 188 to 191. 33 24" I BEAM— No. 244 B. 100 POUNDS PER FOOT. Flange width 7.54 | Area in square inches .... 29.45 Web thickness 0.68 | Resistance 208.1 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs, For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be jq of the tabular deflection. For figures in small type deflection is excessive. Span in Met. Greatest tSafe Load in Net Tons. Deflection in Inches, Greatest Distance in Feet Between Centres oj Beams for Distributed Load as Below. 100 Pounds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. 10 iw.gg .07 222.0 177.6 148.0 126.8 11 loo.go .09 183.5 146.8 122.3 104.8 12 92.49 .10 154.2 123.3 102.8 88.1 13 .12 131.4 105.1 87.6 75.1 14 79.28 .14 113.3 90.6 75.5 64.7 15 73-99 .16 98.7 78.9 65.8 56,4 16 69.37 .18 86.7 69.4 57.8 49.6 17 65.29 .21 /D.o DJ..0 Q 18 61.66 .23 68.5 54.8 45.7 39.1 1Q OR 61.5 49.2 41.0 35.1 20 55.50 .29 55.5 44.4 37.0 31.7 21 52.85 .31 50.3 40.3 33.6 28.8 22 50.45 .35 45.9 36.7 30.6 26.2 23 48.26 .38 42.0 33.6 28.0 24.0 24 46.25 .41 38.5 30.8 25.7 22.0 25 44.40 .45 35.5 28.4 23.7 20.3 26 42.69 .48 32.8 26.3 21.9 18.8 27 41.11 .52 30.5 24.4 20.3 17.4 28 39.64 .56 28.3 22.7 18.9 16.2 29 38.27 .60 26.4 21.1 17.6 15.1 30 37.00 .64 24.7 19.7 16.5 14.1 31 35.80 .69 23.1 18.5 15.4 13.2 32 34.68 .73 21.7 17.3 14.5 12.4 33 33.63 .78 20.4 16.3 13.6 11.6 N. B. — For loads given in Italics webs must be stiflfened, or loads must no exceed maximum loads given in column XV, pages 188 to 191. 34 20" I BEAM— No. 200 B. 65 POUNDS PEB FOOT. Hange width 6.25 | Area in square inches 19.12 Veb thickness 50 | Resistance 117.97 Jrcatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be xo of tl'e tabular deflection. For figures in small type deflection is excessive Span hi Feet. Greatest Safe Load in Net Tons. Dejtectxon in Inches. Greatest Distance in Feet Between Centres 0/ Beams for Distributed Load as Below. 100 Pounds per Sguave Foot. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. 10 62.g2 .09 125.8 100.7 83.9 71.9 11 .10 104.0 83.2 69.3 59.4 12 J'' •'to .12 01.^ Dy.y Oo.o 49.9 13 48.40 .14 74.5 59.6 49.6 42.6 14 OA .17 64.2 51.3 42.8 36.7 15 AT 0^ .19 00. y AA n 37.3 32.0 16 3Q'33 .22 49.2 39.3 32.8 28.1 17 37.01 .25 43.5 34.8 29.0 24.9 18 34.95 !28 38.8 31.1 25.9 22.2 19 33.11 .31 34.9 27.9 23.2 19.9 20 31.46 .34 31.5 25.2 21.0 18.0 21 29.9S .38 28.5 22.8 19.0 16.3 22 28.60 .41 26.0 20.8 17.3 14.9 23 27.36 .45 23.8 19.0 15.9 13.6 24 26.22 .49 21.9 17.5 14.6 12.5 25 25.17 .54 20.1 16.1 13.4 11.5 26 24.20 .58 18.6 14.9 12.4 10.6 27 23.30 .62 17.3 13.8 11.5 9.9 28 22.47 .67 16.1 12.8 10.7 9.2 29 21.70 .72 15.0 12.0 10.0 8.6 30 20.97 .77 14.0 11.2 9.3 8.0 31 20.30 .82 13.1 10.5 8.7 7.5 32 19.66 .88 12.3 9.8 8.2 7.0 33 19.07 .93 11.6 9.2 7.7 6.6 N. B. — For loads given in Italics webs must be s tiffened, or loads must not xceed maximum loads given in column XV, pages 188 to 191. 35 20" I BEAM— No. 201 B. 70 POUNDS PER FOOT. Fliinge witUh 6.31 I Area in square inches . . . . 20 5!) Web tliickaess 0.56 | Resistance . . 122. 'JC Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 llis For a load in middle of beam, allow one-ljalf of the tabular load. Deflection for centre load will be x*o of the tabular deflection. For figures in small type deflection is excessive. Span in Greatest iSafe Load in Net Tons. Deflection in Inches. Greatest Distance in Feet Between Centres oj Beams fur Jyislributed Load as Below. 100 Pounds per Square Fool. 125 Pounds per Square Fool. 150 Pounds per Square Fool. 175 Pounds per Square Foot. 10 .09 131.1 104.9 87.4 74.9 JLi 39-39 in .±u 108.3 86.7 72.2 61.9 12 34A? 12 91.1 72.8 60.7 52.0 13 .14 77.6 62.1 51.7 44.3 1^ 46 82 17 66.9 53.5 44.6 38!2 ID A.'>. nc\ ^0. /u 1 Q 58.3 46.6 38.8 33.3 16 40.97 .22 51.2 41.0 34.1 29.3 1 7 '3.9. RR 00. 00 .^0 45.4 36.3 30.2 25.9 io 9ft 40.5 32.4 27.0 23.1 19 34.50 .31 36.3 29.1 24.2 20.8 20 32.78 .34 32.8 26.2 21.9 18.7 21 31.21 .38 29.7 23.8 19.8 17.0 22 29.80 .41 27.1 21.7 18.1 15.5 23 28.50 .45 2A.8 19.8 16.5 14.2 21 27.31 .49 22.8 18.2 15.2 13.0 25 26.22 .54 21.0 16.8 14.0 12.0 26 25.21 .58 19.4 15.5 12.9 11.1 27 24.28 .62 18.0 14.4 12.0 10.3 28 23.41 .67 16.7 13.4 11.1 9.6 29 22.60 .72 15.6 12.5 10.4 8.9 30 21.85 .77 14.6 11.7 9.7 8.3 31 21.14 .82 13.6 10.9 9.1 7.8 32 20.48 .88 12.8 10.2 8.5 7.3 33 19.86 .93 12.0 9.6 8.0 6.9 N. B. — For loads given in Italics webs must be stiffened, or loads must not exceed maximum loads given in columns XV, pages 188 to 191, 36 20" X BEAM— No. 202 B. 75 POUNDS PER FOOT. flange width 6.39 | Area in square inches . . . 22.0G Web thickness 0.64 | Resistance 127.77 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be of the tabular deflection. For figures in small type deflection is excessive. Span in Feel. Greatest Greatest Distance in Feet Between Centres of Beams for Distr ibuted Load as Below. Safe Loud Net Tons. Deflection 100 Pounds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. 10 11 12 68.15 61.95 56.79 .09 .10 .12 136.3 112!6 94.7 109.0 90!l 75.7 on Q 75.1 63.1 77 Q 64.4 54.1 13 14 15 52.42 48.68 45.43 .14 .17 .19 80.7 69!5 60.6 64.5 55!6 48.5 53 8 46!4 40.4 rtO.L 39.7 34.6 16 17 18 42.59 40.08 37.86 .22 .25 .28 53.2 47.2 42.1 42.6 37.7 33.7 35.5 31.4 28.0 30.4 26.9 24.0 1Q ±y 20 21 00.0/ 34.07 32.45 .31 .34 .38 37.7 34.1 30.9 30.2 27.3 24.7 25.2 22.7 20.6 21.6 19.5 17.7 22 23 24 30.98 29.63 28.39 .41 .45 .49 28.2 25.8 23.7 22.5 20.6 18.9 18.8 17.2 15.8 16.1 14.7 13.5 25 26 27 27.26 26.21 25.24 .54 .58 .62 21.8 20.2 18.7 17.4 16.1 15.0 14.5 13.4 12.5 12.5 11.5 10.7 28 29 30 24.33 23.50 22.72 .67 .72 .77 17.4 16.2 15.1 13.9 13.0 12.1 11.6 10.8 10.1 9.9 9.3 8.7 31 32 33 21.98 21.30 20.65 .82 .88 .93 14.2 13.3 12.5 11.3 10.7 10.0 9.5 8.9 8.3 8.1 7.6 7.2 N. B.— For loads given in Italics webs must be stiffened, or loads must not sceed maximum loads given in column XV, pages 188 to 191. 37 20" I BEAM— 5fo. 203 B. 80 POUNDS PER FOOT. Flange width 6.75 I Area in square inches .... 23.53 Web thickness 0.63 | Resistance 140.44 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be of the tabular deflection. For figures in small type deflection is excessive. Span in Feel. Greatest Safe Load Net Tons. Deflection in Inches. Greatest Distance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pounds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Fool, 175 Pounds per Square Foot. 10 74-90 .09 11Q R QQ Q 85 6 11 68.09 .10 123.8 99.0 82.5 70!7 12 62.42 .12 104.0 83.2 69.4 59.4 13 57.62 .14 00. D 59 1 50.7 14 53.50 .17 76.4 61.1 5i!o 43!? 15 49.93 .19 66.6 53.3 44.4 38.0 16 46.81 .22 58.5 46.8 39.0 33.4 17 44.06 .25 51.8 41.5 34.6 29.6 18 41.61 .28 46.2 37.0 30.8 26.4 19 39.42 .31 41.5 33.2 27.7 23.7 20 37.45 .34 37.5 30.0 25.0 21.4 21 35.67 .38 34.0 27.2 22.6 19.4 22 34.05 .41 31.0 24.8 20.6 17.7 23 32.57 .45 28.3 22.7 18.9 16.2 24 31.21 .49 26.0 20.8 17.3 14.9 25 29.96 .54 24.0 19.2 16.0 13.7 26 28.81 .58 22.2 17.7 14.8 12.7 27 27.74 .62 20.5 16.4 13.7 11.7 28 26.75 .67 19.1 15.3 12.7 10.9 29 25.83 .72 17.8 14.3 11.9 10.2 30 24.97 .77 16.6 13.3 11.1 9.5 31 24.16 .82 15.6 12.5 10.4 8.9 32 23.41 .88 14.6 11.7 9.8 8.4 33 22.70 .93 13.8 11.0 9.2 7.9 N. B.— For loads given in Italics webs must be stiffened, or loads must not exceed maximum loads given in column XV, pages 188 to 191. 3S 20" I BEAM— No. 204 D. 86 POUNDS PER FOOT. Flange width 6.82 I Area in square inches 25.00 Web thickness 0.70 | Resistance 145.31 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be r o of t^e tabular deflection. For figures in small type deflection is excessive Span in Feel. Greatest Safe Load in Net Tons. Deflection in Inches, Greatest Distance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pounds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. ~ 10 77-50 .09 155.0 124.0 103.3 88.6 11 70.45 .10 128.1 102.5 85.4 73.2 12 64.58 .12 107.6 oD.i 71 ft 61 5 13 59.61 .14 91.7 73.4 61.1 52.4 14 55.36 .17 79.1 63.3 52.7 45.2 15 51.67 .19 68.9 55.1 Q 16 48.44 .22 60.6 48.4 40.4 34.6 17 45.59 .25 53.6 42.9 35.8 30.6 18 43.06 .28 47.8 38.3 31.9 27.3 19 40.79 .31 42.9 34.4 28.6 24.5 20 38.75 .34 38.8 31.0 25.8 22.1 21 36.90 .38 35.1 28.1 23.4 20.1 22 35.23 .41 32.0 25.6 21.4 18.3 23 33.69 .45 29.3 23.4 19.5 16.7 24 32.29 .49 26.9 21.5 17.9 15.4 25 31.00 .54 24.8 19.8 16.5 14.2 26 29.81 .58 22.9 18.3 15.3 13.1 27 28.70 .62 21.3 17.0 14.2 12.2 28 27.68 .67 19.8 15.8 13.2 11.3 29 26.72 .72 18.4 14.7 12.3 10.5 30 25.83 .77 17.2 13.8 11.5 9.8 31 25.00 .82 16.1 12.9 10.8 9.2 32 24.22 .88 15.1 12.1 10.1 8.7 33 23.48 .93 14.2 11.4 9.5 8.1 N. B. — For load given in Italics web must be stiffened, or load must not exceed maximum load given in column XV, pages 188 to 191. 39 20" I BEAM— No. 205 B. 90 POUNDS PEB FOOT. Flange width 6.90 I Area in square inches 2G.47 Web thickness 0.78 | Resistance 150.17 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be l o of the tabular deflection. For figures in small type deflection is excessive. Span in Feei. Greatest Safe Load in Net Tons. Deflection in Inches. Greatest Distance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pmmds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. 10 80.09 .09 160.2 128.1 106.8 91.5 11 72.81 .10 132.4 105.9 88.3 75.7 12 66.74 .12 111 2 89 0 74.2 63 6 13 61.61 .14 94.8 75.8 63.2 54.2 14 57.21 .17 81.7 65.4 54.5 46.7 15 53.39 .19 71.2 57.0 47.5 40 7 16 50.06 .22 62.6 50.1 41.7 35.8 17 47.11 .25 55.4 44.3 37.0 31.7 18 44.50 .28 49.4 39.6 33.0 28.3 19 42.15 .31 44.4 35.5 29.6 25.4 20 40.05 .34 40.1 32,0 26.7 22.9 21 38.14 .38 36.3 29.1 24.2 20.8 22 36.41 .41 33.1 26,5 22.1 18.9 23 34.82 .45 30.3 24.2 20.2 17.3 24 33.37 .49 27.8 22.2 18.5 15.9 25 32.04 .54 25.6 20.5 17.1 14.6 26 30.80 .58 23.7 19.0 15.8 13.5 27 29.66 .62 22.0 17.6 14.6 12.6 28 28.60 .67 20.4 16.3 13.6 11.7 29 27.62 .72 19.0 15.2 12.7 10.9 30 26.70 .77 17.8 14.2 11.9 10.2 31 25.84 .82 16.7 13.3 11.1 9.5 32 25.03 .88 15.6 12.5 10.4 8.9 33 24.27 .93 -14.7 11.8 9.8 8.4 40 20" I BEAM— No. 206 B. 95 POUNDS PER FOOT. Flange width 7.24 I Area in square inches .... 27.94 Web thickness ; 0.74 | Resistance 160.19 (rreatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be jo of the tabular deflection. For figures in small type deflection is excessive. Span in Feet. Greatest Safe Load in Net Tom. Defleclion in Inches. Greatest instance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pounds per Square Foot. 125 Pounds per Siitiare Foot. 150 Pounds per SQUiire Foot. 175 Pounds per SQuare Foot. 10 86.4T .09 172.8 138.3 115.2 98.8 1 1 li lO.OO in 142.8 114.3 95.2 81.6 1 9 .12 1 90 n Qfi n 80.0 68.6 13 66.47 .14 102.3 81.8 68.2 58.4 1 A Di. 1 7 88.2 70.5 58.8 50.4 1 iO ^1 fin /O.o 61 4 51.2 43.9 16 54.00 .22 67.5 54.0 45.0 38.6 L 1 Pin QQ .ZD 59.8 47.8 39.9 34.2 1 Q 9ft 53.3 42.7 35.6 30.5 19 45.48 .31 47.9 38.3 31.9 27.4 20 43.20 .34 43.2 34.6 28.8 24.7 21 41.15 .38 39.2 31.4 26.1 22.4 22 39.28 .41 35.7 28.6 23.8 20.4 23 37.57 .45 32.7 26.1 21.8 18.7 24 36.00 .49 30.0 24.0 20.0 17.1 25 34.56 .54 27.6 22.1 18.4 15.8 26 33.23 .58 25.6 20.5 17.0 14.6 27 32.00 .62 23.7 19.0 15.8 13.5 28 30.86 .67 22.0 17.6 14.7 12.6 29 29.79 .72 20.5 16.4 13.7 11.7 30 28.80 .11 19.2 15.4 12.8 11.0 31 27.87 .82 18.0 14.4 12.0 10.3 32 27.00 .88 16.9 13.5 11.3 9.6 33 26.18 .93 15.9 12.7 10.6 9.1 N. B. — For load given in Italics web must be stiffened, or load must not exceed maximum load given in column XV, page 189. 41 20" X BEAM— No. 207 B. lOO POUNDS PER FOOT. Flange width 7.31 I Area in square inches .... 29.41 Web thickness 0.81 | Resistance . . 164.96 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load -will be of the tabular deflection. For figures in small type deflection is excessive. Span ■in Feet. Greatest Safe Load Net Tons. Deflection in TiicJies. Greatest Distance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pounds per Sqimre Fool. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. 10 88.98 .09 178.0 142.4 118.6 101.7 11 ou.oy 147.1 117.7 98.0 84.1 12 74.15 .12 123.6 98.9 82.4 70.6 13 68.44 .14 105.3 84.2 70.2 60.2 14 Oo.iDD 1 1 .1/ 90.8 72.6 60.5 51.9 15 59.32 .19 79.1 63.3 52.7 45.2 16 55.61 .22 69.5 55.6 46.3 39.7 17 52.34 .25 61.6 49.3 41.1 35.2 18 49.43 .28 54.9 43.9 36.6 31.4 19 46.83 .31 49.3 39.4 32.9 28.2 20 44.49 .34 44.5 35.6 29.7 25.4 21 42.37 .38 40.4 32.3 26.9 23.1 22 40.44 .41 36.8 29.4 24.5 21.0 23 38.69 .45 33.6 26.9 22.4 19.2 24 37.07 .49 30.9 24.7 20.6 17.7 25 35.59 .54 28.5 22.8 19.0 16.3 26 34.22 .58 26.3 21.1 17.6 15.0 27 32.95 .62 24.4 19.5 16.3 13.9 28 31.78 .67 22.7 18.2 15.1 13.0 29 30.68 .72 21.2 16.9 14.1 12.1 30 29.66 .77 19.8 15.8 13.2 11.3 31 28.70 .82 18.5 14.8 12.3 10.6 32 27.81 .88 17.4 13.9 11.6 9.9 33 26.96 .93 16.3 13.1 10.9 9.3 42 18 " I BEAM— No. 180 B. 65 POUNDS PER FOOT. Flange width 6.00 I Area in square inches. . . . 16.18 Web thickness 0.46 | Resistance 89.89 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be xV of the tabular deflection. For figures in small type deflection is excessive. Span in Feet. Greatest Safe Load Net Tons. Deflection in XncJies. Greatest Distance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pounds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Fool. 1/0 Pounds per Square Foot. 10 47-94 .10 95.9 16.7 63.9 54.8 11 4.3-58 .12 79.2 63.4 52.8 45.3 12 .39-95 .14 66.6 53.3 44.4 38.0 13 36.88 .16 56.7 45.4 37.8 32.4 14 34-24 .19 48.9 39.1 32.6 28.0 15 31.96 .21 42.6 34.1 28.4 24.4 16 29.97 .24 37.5 30.0 25.0 21.4 17 28.20 .28 26 5 22.1 19.0 18 26.64 .31 29.6 23!7 19.7 16!9 19 26.6 21.2 17.7 15.2 20 23.97 .38 24.0 19.2 16.0 13.7 21 22.83 .42 21.7 17.4 14.5 12.4 22 21.79 .46 19.8 15.8 13.2 11.3 23 20.85 .50 18.1 14.5 12.1 10.4 24 19.98 .55 16.7 13.3 11.1 9.5 25 19.18 .60 15.3 12.3 10.2 8.8 26 18.44 .64 14.2 11.3 9.5 8.1 27 17.76 .69 13.2 10.5 8.8 7.5 28 17.12 .75 12.2 9.8 8.2 7.0 29 16.53 .80 11.4 9.1 7.6 6.5 30 15.98 .86 10.7 8.5 7.1 6.1 31 15.47 .92 10.0 8.0 6.7 5.7 32 14.98 .98 9.4 7.5 6.2 5.4 33 14.53 1-04 8.8 7.0 5.9 5.0 N. B.— For loads given in Italics webs must be stiffened, or loads must not exceed maximum loads given in column XV, pages 188 to 191. 43 18' I BEAM— No. 181 B. 60 POUNDS PER FOOT. Flange width 6.08 I Area in square inches . . . . 17.65 Web thickness 0.54 | Resistance 94.43 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of tlie tabular load. Deflection for centre load will be j'o of the tabular deflection. For figures in small type deflection is excessive. Span ■in Feel. Greatest Safe Load Net Tons. Deflection in Indies. Greatest Distance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pounds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. 10 50-36 .10 100.7 80.6 D / . J. 0 / .0 11 45-78 .12 83!2 66!6 55.5 47.6 12 41.97 .14 70.0 56.0 46.6 40.0 13 38.74 .16 59.6 47.7 39 7 14 35.98 .19 5l!4 4l!l 34!3 29.4 15 33.58 .21 44.8 35.8 29.8 25.6 16 31.48 .24 39.4 31.5 26.2 22.5 17 29.63 .28 on 0 23.2 19.9 18 27.98 .31 31.1 24.9 20.7 17.8 19 26.51 27.9 22.3 18.6 15.9 20 25!l8 .38 25.2 20.1 16.8 14.4 21 23.98 .42- 22.8 18.3 15.2 13.1 22 22.89 .46 20.8 16.6 13.9 11.9 23 21.90 .50 19.0 15.2 12.7 10.9 24 20.99 .55 17.5 14.0 11.7 10.0 25 20.15 .60 16.1 12.9 10.7 9.2 26 19.37 .64 14.9 11.9 9.9 8.5 27 18.65 .69 13.8 11.1 9.2 7.9 28 17.99 .75 12.8 10.3 8.6 7.3 29 17.37 .80 12.0 9.6 8.0 6.8 30 16.79 .86 11.2 9.0 7.5 6.4 31 16.25 .92 10.5 8.4 7.0 6.0 32 15.74 .98 9.8 7.9 6.6 5.6 33 15.26 1.04 9.2 7.4 6.2 5.3 N. B. — For loads given in Italics webs mu.st be stiffened, or loads must not exceed maximum loads given in column XV, pages 188 to 191. 44 18" I BEAM— No. 182 B. 65 POUNDS PER FOOT. Flange width G.17 I Area in square inches .... 19.12 Web thickness 0.63 | Resistance 98.86 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be xV of the tabular deflection. For figures in small type deflection is excessive. Span Feet. Greatest /Safe Load in Net Tons. Deflection in Indies. Greatest Distance in Feet Between Centres of Beams for Distributed Load as Below. 100 Pounds per Square Foot. 125 Pounds per Square Foot. 150 Pounds per Square Foot. 175 Pounds per Square Foot. 10 52.73 .10 105.5 84.4 70.3 60.3 11 47.93 .12 87.-1 69.7 58.1 49.8 12 43.94 .14 73.2 58.6 48.8 41.9 13 40.56 .16 62.4 49.9 41.6 35.7 14 37.66 .19 53.8 43.0 35.9 30.8 15 35.15 .21 46.9 37.5 31.2 26.8 16 32.95 .24 41.2 33.0 27.5 23.5 17 31.01 .28 36.5 29.2 24.3 20.8 18 29.29 .31 32.5 26.0 21.7 18.6 19 27.75 .34 29.2 23.4 19.5 16.7 20 26.36 .38 26.4 21.1 17.6 15.1 21 25.11 .42 23.9 19.1 15.9 13.7 22 23.97 .46 21.8 17.4 14.5 12.5 23 22.92 .50 19.9 15.9 13.3 11.4 24 21.97 .55 18.3 14.6 12.2 10.5 25 21.09 .60 16.9 13.5 11.2 9.6 26 20.28 .64 15.6 12.5 10.4 8.9 27 19.53 .69 14.5 11.6 9.6 8.3 28 18.83 .75 13.5 10.8 9.0 7.7 29 18.18 .80 12.5 10.0 8.4 7.2 30 17.58 .86 11.7 9.4 7.8 6.7 31 17.01 .92 11.0 8.8 7.3 6.3 32 16.48 .98 10.3 8.2 6.9 5.9 33 15.98 1.04 9.7 7.7 6.5 5.5 45 18" I beam-No. 183 b. 70 POUNDS PER FOOT. Flange width 6.50 I Area in square inches .... 20.59 Web thickness 0.63 | llesistance 109.08 Greatest safe load in net tons uniformly distributed. Fibre stress 16,000 lbs. For a load in middle of beam, allow one-half of the tabular load. Deflection for centre load will be yo of the tabular deflection. For figures in small type deflection is excessive. Span in Greatest iSafe Load in Net Tons. Deflection in Inches. Greatest Distance in Feet Between Centres of Beams for Distributed Load as Beloiv. 100 Pounds per SQuaTC Foot. 125 Pounds pev S(iuare Foot. 150 Pounds pev Square Foot. 175 Pounds pev Sguave Foot. 10 ■^8.18 .10 116.4 93.1 77.6 66.5 \1 52.89 .12 96.2 76.9 64.1 55.0 12 48.48 .14 80 8 64 6 13 44.75 .16 68.8 55.1 45.9 39.3 14 41.55 .19 59.4 47.5 39.6 33.9 15 38.78 .21 SI 7 41.4 CO Tji rH CO ^ 03 rH 03 rH I-H rH rH CQ O N 00 int- CJ> rH Km °o2 CO 5 cv] q 00 ^, tfj rH CO rH COrH Cd rH l-H rH 0) cvj q ^1 CO c 7.0 1.19 0.95 0.79 0.68 0.59 0.53 0.47 0.43 0.39 0.36 336T SH2 X 31/0 9.0 1.54 1.24 1.03 0.88 0.77 0.69 0.62 0.56 0.51 0.47 337T 31/2 11.0 1.99 1.59 1.32 1.13 0.99 0.88 0.79 0.72 0.66 0.61 30T 3 xl\ 4.0 0.21 0.17 0.14 0.12 0.11 0.09 0.08 0.08 0.07 o.oe 31T 3 x2V.2 5.0 0.56 0.45 0.37 0.32 0.28 0.25 0.22 0.20 0.19 0.17 32T 3 x2H2 6.0 0.68 0.54 0.45 0.39 0.34 0.30 0.27 0.25 0.23 0.21 33T 3 x2H2 7.0 0.80 0.64 0.53 0.46 0.40 0.35 0.32 0.29 0.27 0.25 34T 3 x2\ 8.0 1.04 0.83 0.69 0.59 0.52 0.46 0.42 0.38 0.35 0.32 330T 3 x3 6.5 0.99 0.79 0.66 0.56 0.49 0.44 0.39 0.36 0.33 0.30 331T 3 x3 7.7 1.15 0.92 0.76 0.65 0.57 0.51 0.46 0.42 0.38 0.35 35T 3 x3i(2 8.3 1.56 1.25 1.04 0.89 0.78 0.69 0.62 0.57:0.52 0.48 36T 3 x3i42 9.5 1.77 1.42 1.18 1.01 0.89 0.79 0.71 0.64 0.59 0.54 108 PENCOYD TEES. SAFE LOAD IN NET TONS UNIFORMLY DISTRIBUTED. Fibre Stress 16,000 lbs. per Sq. In. Section No. Size Flange by Stem. Inches. m. per Foot in Lbs. Length of Span in Feet. 1 2 3 4 5 6 7 8 Safe Load in Net Tons. 28T 2% X 1% 6.6 2.67 1.33 0 89 0.67 0.53 0.44 0.38 0.33 29T 2% X 2 7.2 3.52 1.76 l!l7 o!88 o!70 0.59 0.50 0.44 25T 2\ X 114 3.3 0.59 0.29 0.20 0.15 0.12 0.10 0.08 0.07 225T 2^ X 21/2 5.0 2.35 1.17 0.78 0.59 0.47 0.39 0.33 0.29 226T 2\ X 21/2 5.8 2.93 1.46 0 73 0.59 0.49 0.42 0.37 227T 2^2 X 21/2 6.6 3.36 1.68 1.12 o!84 o!67 0.56 0.48 0.42 26T 21/2 X 2% 5.7 3.20 1.60 1.07 0.80 0.64 0.53 0.46 0.40 27T 6.0 3.79 1.89 1.26 0.94 0.76 0.63 0.54 0.47 24T 2\x fs 2.2 0.16 0.08 U.UO 0.04 0.03 0.03 0.02 0.02 222T 2\ X 21/4 4.0 1.65 0.82 0.55 o!41 o!33 0.27 0.23 0.21 223T 2^4 X 2\ 4.0 1.76 0.88 0.59 0.44 0.35 0.29 0.25 0.22 20T 2 X ^ 2.0 0.16 0.08 0.05 0.04 0.03 0.03 0.02 0.02 21T 2 X 1 2.5 0.37 0.18 0.12 0.09 0.07 0.06 0.05 0.05 22T 2 xl^ij 2.0 0.27 0.13 0.09 0.07 0.05 0.04 0.04 0.03 23T 2 X 3.0 0.80 0.40 n 07 U.Z/ U.ID 0.13 0.11 0.10 220T 2 x2 3.5 1.39 0.69 0.46 0.35 0.28 0.23 0.20 0.17 17T 1% X 1^ 1.9 0.32 0.16 0.11 0.08 0.06 0.05 0.05 0.04 18T J- /4 J- '4 3 5 0.75 0.37 0.25 0.19 0.15 0.12 0.11 0.09 117T 2^4 0.80 0.40 0.27 0.20 0.16 0.13 0.11 0.10 15T 1^2 X ^ 1.4 0.16 0.08 0.05 0.04 0.03 0.03 0.02 0.02 115T i\ X ly^ 2.0 0.64 0.32 0.21 0.16 0.13 0.11 0.09 0.08 '12T 114 X if 1.2 0.16 0.08 0.05 0.04 0.03 0.03 0.02 0.02 n2T 114 X 1% 1.5 0.48 0.24 0.16 0.12 0.10 0.08 0.07 0.06 HOT 1 X 1 1.0 0.27 0.13 0.09 0.07 0.05 0.04 0.04 0.03 109 SUPPORTS AND CONNECTIONS FOR BEAMS AND GIRDERS. When the span becomes too great, or the loads excessive for rolled beams, refer to the tables on pages 127 to 137 for the strength of riveted girders of the several sections described. When the support of the beam or girder is formed on masonry, a bearing plate should be provided for the ends of the beams to distribute the pressure over a sufficient area. The permissible pressure per unit of area varies widely according to the building laws of the locality. The figures given are the mean of the various extremes. Ordinarv br}ck, lime mortar, 5 tons per square foot ; hard brick, cement mortar, 10 tons per square foot ; rubble masonry in cement, or cement concrete not less than one month old, 10 tons per square foot; first-class masonry, parallel layers, natural bed, sandstone, 18 tons per square foot ; limestone, 20 tons per square foot ; granite, 30 tons per square foot. The following table has been calculated with these permissi- ble loads. Depth of Beam or Channel. Inches. Bearing on Wall. Inches. Plates. Safe Bearing Values in Net Tons. Plates on Size in IncJies. Thick- ness in Inches. Common Brick Work, Lime Mortar. First- class Brick Work or Cement Concrete. First- class Masonry. *24, 20, 18 16 16 X 16 1 8.9 17.8 35.6 15 12 12 X 16 6.7 13.3 26.7 12 12 12x 12 5.0 10.0 20.0 10 and 9 10 10 X 10 % 3.5 6.9 13.9 8 and 7 8 8 X 10 H 2.8 5.6 11.1 6 and 5 6 6x6 % 1.3 2.5 6.0 4 and 3 6 6x6 1.3 2.5 5.0 *For short spans of 24" and 20" I beams special plates must be calculated. When two or more beams are used together, they should be tied at intervals with fitted separators between 'them as described on page 257. These separators should be spaced near the supports, and at intervals of 5 or 6 feet. The standard angle connections for framing "I" beams are described on pages 254 to 260. These connections have been designed to provide for beams of the sizes and length of spans given in the table on page 260. If the beams are much shorter, and the total load supported greater than described, it may become necessary to design special con- nections, to provide for the increased end shear. 110 APPROXIMATE FORMULiE FOR ROLLED BEAMS. The following rules for the strength and stiffness of rolled beams of various sections are intended for convenient appli- cation in cases where strict accuracy is not required. The rules for rectangular and circular sections are correct, while those for the flanged sections are approximate and limited in their application to the standard shapes as given in our tables. They will be found to give results which have been proved by experiment to be sufficiently accurate for practical purposes. When the section of any beam is increased above the standard minimum dimensions, the flanges remaining unaltered, and the web alone being thickened, the tendency will be for the load as found by the rules to be in excess of the actual, but within the limits that it is possible to vary any section in the rolling, the rules will apply without any serious inaccuracy. The loads are the same as in the beam tables, producing a fibre stress of 16,000 lbs. per square inch, on the assumption that the steel referred to has a tenacity about 20 per cent, in excess of iron. These loads will be approximately one-half of loads that would injure the elasticity of the material. The rules for deflection apply to any load below the elastic limit, or less than double the greatest safe load by the rules. If the beams are long without lateral support, reduce the loads for the ratios of width to span, as described on page 23. Example. — A 12-inch No. 120 B I beam, area 9.27 square inches, 15 feet span, by the tables, will support a dis- tributed load of 13 tons, and by the approximate rule 3390_X 9^_7X_12 _ 25,140 pounds, lo The deflection by the rule will also be found nearly as in the tables. Ill The preceding rules apply to beams supported at each end. For beams supported otherwise alter the coefficients of the table as described below, referring to the respective columns indicated by number. CHANGES OF COEFFICIENTS FOR SPECIAL FORMS OF BEAMS. Kind of Beam. Coefficient for Safe Load. Coefficient for Deflection. Fixed at one end, loaded at the other. One-fourth (1) of the coeffi- cient of col. II or III. One- sixteenth (yV) of the co- efficient of col. VI. Fixed at one end, load evenly distributed. One-fourth {\) of the coeffi- cient of col. IV or V. Five-forty- eighths (^V) of the coefficient of coL VII. Both ends rigidly fixed, or a continuous beam, with a load in middle. Twice the coeffi- cient of col. II or III. Four times the coefficient of col. VI. Both ends rigidly fixed, or a continuous beam with load evenly dis- tributed. One and one- half ) times the coefficient of col. IV orV. Five times the coefficient of coi. VII. It will be observed that these rules apply only to the in- termediate spans of continuous beams; when continuity does not occur at the ends, the conditions are altered. If, however, the outer ends of a continuous beam overhang the end-supports from one-fifth to one-fourth of a span, and bear the same proportion of load as the parts between supports, then the outer spans may be of same length as the intermediate spans, subject to the same load, and the strength and stiffness are determined by the same rules; otherwise the outer spans ought to be only four-fifths of the 114 length of the intermediate spans when the load is dis- tributed, or three-fourths of the same when the load is con- centrated in the middle ; or, if the lengths of spans are all alike, the loads on outer spans ought to be reduced in the same proportion. The following table exhibits the relative proportion of strength and stiffness existing between various classes of beams when they have the same lengths and uniform cross- section; the deflections being comparative figures for the same loads on any beam. Kind of Beam. Fixed at one end — loaded at the other . . Fixed at one end — load evenly distributed Supported at both ends — load in middle . Supported at both ends — load evenly dis- tributed Continuous beam — load in middle . . Continuous beam— load evenly distributed [ The load and deflection of a beam supported at both ends I and loaded in the middle have been taken as the units for i comparison. Beams of uniform length and section will be equally strained when loaded in the ratio described in the tirst column, or if the beams are loaded equally, within their elastic limits, the respective deflections will be in the ratio described in second column. Maximum Load as Deflection 16 6 1 U5 BEAMS FOR SUPPORTING IRREGULAR LOADS. When a beam has its load unequally distributed, the proper size of the beam can be determined by finding the maximum bending moment and proportioning the beam accordingly. Equilibrium is obtained when the bending moment is equal to the moment of resistance. That is, when the external force multiplied by the leverage witli which it acts is equal to the strength of the material in the cross-section of the beam multiplied by the leverage with which it acts. The resistance of a beam is found by dividing the moment of inertia of the section by the distance from neutral axis to extreme fibres, and this value for any rolled section will be found in the tables, pages 188 to 211. This tabulated resist- ance, multiplied by the limiting fibre stress on the beam, is the measure of strength of the section. RULE FOR BEAMS BEARING IRREGULAR LOADS. Finding by the methods described on pages 220 to 226 the maximum bending moment on the beam,, divide the bend- ing moment by the limiting fibre stress, and select from the tables, pages 188 to 211 a beam whose resistance is not less than this quotient. The greatest safe fibre stress in our tables is 16,000 lbs. The stress should be modified for various considerations, as described on pages 22 and 23. Example.— An I beam 8 feet long is to be fixed at one end and loaded at the other with 5,000 lbs. and carrying also an evenly distributed load of 8,000 lbs. What size of beam should be used so as not to be strained over 16,000 lbs.? Moment for end load = 5,000 X 96 = 480,000 inch-lbs. " " distributed load =-M?y<^= 384,000 " " Total = 864,000 " " Divide this bending moment by the fibre stress afore- -116 said, and select from column XI, page 189, beams whose resistances are nearest the quotients, as follows : 15 inch. No. 153 B. 55.0 pounds per foot. In some instances the maximum bending moment can be most readily found by the use of diagrams, as described on pages 220 to 226. When this is done use any convenient scale, making all loads and all distances respectively of the same denominations. The maximum bending moment can then be measured to scale. Example.— k beam 20 feet long between supports will carry three loads, which we will call A, B and C. A = 4,000 lbs. and is 4 feet from one end of the beam. C = 6,000 lbs. and is 3 feet from the other end of the beam. B = 5,000 lbs. and is 5 feet from Cand 8 feet from A. Required a suitable beam, not strained over 12^000 lbs. Describe a diagram as in Fig. 2, page 226, when the follow- ing bending moments will be obtained : At point A: For load A, 12,800 B, 8,000 C, 3,600 Total, 24,400 At point B. For load 5, 24,000 A, 10,800 C, 6,400 Total, 41,200 At point C. For load C, 15,300 B, 9,000 A, 2,400 Total, 26,700 The maximum moment at 5 = 41 ,200 foot-pounds or 494,400 inch-pounds. Dividing by 10,000 and 12,000, select from column XI, page 189, the following beams, whose resistances are nearest these quotients, and use the lighter beam. 15-inch beam. No. 150 B, 42.0 lbs. per foot. 12-inch " No. 122 B, 40.0 " " " Note.— The tables of elements, except where otherwise specified, are calculated for dimensions in inches and weights in pounds, consequently in examples of above character it is necessary to obtain bending moments in inch-pounds. 117 BEAMS SUBJECTED TO COMPOUND STRESSES. When the bending stresses on a beam are compounded by- extraneous forces, producing additional stresses of tension, compression or torsion, then the longitudinal stresses result- ing from bending stresses are modified in extent or direction. No general rules can be given for such conditions, as every particular case requires its own proper determination. The following methods, though not strictly correct, will give safe practical results for ordinary cases. WHEN THE BEAM IS SUBJECT TO EXTERNAL FORCES PRODUCING EITHER TENSION OR COMPRESSION, BUT IS SUPPORTED TO RESIST LATERAL FLEXURE. Rule.— Find by methods previously described, the section of beam required to resist bending, then allowing from 10,- 000 to 16,000 pounds per square inch for the compression or tension according to the material or factor of safety used, add the two sectional areas together, which will give the section of beam required. Example.— A beam having a clear span of 15 feet, bearing a uniform load of 500 pounds per lineal foot, is subjected to compression if it forms half a 30-foot truss as in Fig. 6, page 229, or to tension if forming a member in a roof chord in either case, say 18,000 pounds. Required a suitable beam strained about 12,000 pounds per square inch. The total uniform load is 15 X 500 = 7500 pounds. The bending moment due to same is 7500 X 15 X 12 8 : 168,- 750 inch-pounds. This divided by 12,000 gives a resistance of 14.1. From the tables, column XI, page 191, we find that the I beam having a resistance nearest to this 14.1 is an 8-inch I beam No. 80 B, area 5.29 square inches. Now the increase in area to be made for the tension or compression is 18000 ^ -j^ 5 square inches, making the total area 6.79 square 12000 ^ inches. 118 WHEN THE BEAM IS SUBJECT TO COMPRESSION AND IS LIABLE TO FAIL LIKE A HORIZONTAL STRUT BY LATERAL FLEXURE. Rule. — Consider first the resistance as a strut and then make the necessary increment of section to resist the bend- ing stress, remembering that if the addition is made to the flanges then only flange stresses have to be considered, but if the increased area is obtained by thickening the web of I beam or channel section, then the additional area so ob- tained should be treated as a rectangular section whose thickness is the amount added to the web, and whose depth is the depth of the beam. Example. — A trussed girder of the form exhibited in Fig. 6, page 229, is a box section made up of two channels sep- arated with flanges outward, and plated top and bottom. The whole girder is 30 feet long and is loaded 1,000 pounds per lineal foot. The compression resulting from the truss- ing is 25,000 pounds. The structure has no lateral bracing. What will be safe proportions for it, the stresses not to exceeed one-fifth of the ultimate, or 10,000 pounds per square inch ? It is evident that we have to consider it as a flat- ended strut 30 feet long, liable to fail horizontally, and also as a series of three beams each 10 feet long and loaded with 10,000 pounds evenly distributed. Trying two hght 6-inch channels, each 3.09 square inches section, separated 4| inches so as to be covered by 9-inch plates, we have (omitting the plates in this calculation) the radius of gyration around vertical axis (see page 194) = 2.29 inches, ^ = 157, one-fifth of ultimate (by Table 3, page 162) = 4,500 pounds per square inch, or 4,500 X 6.18 = 27,810 pounds safe resistance, n S/" K >\ maximum bending moments (see page 222), X 10,000 8 = 150,000 inch-pounds. The plates act with a leverage equal to the depth of the 119 channel, viz., 6 inches; = 25,000 pounds tension on top or compression on bottom plate, which, allowing for 10,000 pounds per square inch, and allowing for loss by rivets, will require a plate f inch thick. Taking the last example, if it was desired to form the sec- tion from a pair of channels, latticed top and bottom, with no cover plates, we would have to consider the section added to the channels (being on the web alone) as a simple rectan- gular section. Trying two 10-inch channels, separated 6^ inches, flanges outward, and having least radius of gyration, for the pair = 3.90 i = 92.3. Safe load = 9,060 pounds per square inch. r As the compression is 25,000 pounds, there are required 2.7 square inches for this purpose. -r, ,1 ^ 1 no 1 ,100 X area X 10 mnnn By the formula, page 112, = 10,000, from which the area to resist bending is found to be 9.1 square inches. Giving a total area for two channels of 11.8 square inches, or two 10-inch channels No. 101 C, weight 20 pounds per hneal foot will be required. In cases where the load is concentrated at the truss points, there being no bending stress, the resistance as a strut has only to be considered, and when braced laterally the strut length is reduced to the distances between bracing. Flexure and Tension. When the tension forces are larger in comparison with the flexural forces, and where greater refinement is required, the resulting stresses on the beam can be closely approxi- mated by the following formulae. Mc S = aFP ^+ bE Here 5= the extreme fibre stress as affected by the tension forces, M= bending moment, due to load, c = distance from neutral axis to extreme fibres, 1= moment of inertia of sec- 120 tion of beam, F~ tension force, I = length of beam, E = modulus of elasticity of material of beam, a and b are constants depending on the method of supporting beam and nature of load. For a beam supported at the ends, and loaded at the middle, - == 12, while for the same a beam uniformly loaded, - = 9.6. Having found S, add a F it to -T where = tension force and ^ = area of beam A F section. Then -S" + gives the maximum fibre stress on the extreme fibres. Example. — An eye-bar, 20 feet long, 8 inches deep, and 2 inches thick, is strained 10,000 pounds per square inch of section, and carries besides its weight a concentrated cen- tral load of 1,000 pounds. What is the extreme fibre stress ? Bar weighs 1,100 pounds. Bending moment, due to concentrated load = 5,000 ft.-lbs. " uniform " = 2,750 " 7,750 -=10.8 160,000 lbs. 7,750 ft.-lbs. =93,000 in.-lbs. 9 93,000 X_4 _o J, oF^ 85.3 X 1 X 160,000 X 57,600 ' ~b E 10.8 X 29,000,000 S-{- = 3,243 + 10,000 = 13,243 lbs. extreme fibre stress. Compression and Flexure. When the compressive forces are large as compared with the flexural forces, and the beam is confined laterally, so that it cannot fail in that direction as a strut, a close approxi- mation to the extreme fibre stress is given by the following formulae. Mc S = a Ft' b E F and the maximum unit stress is as before, + — A For combined flexure and torsion, see page 234. 121 STRESSES ON BEAMS RESULTING FROM LOADS SUDDENLY APPLIED AND FROM PERCUSSION OR IMPACT. When the force acting on a beam is rapidly applied the momentary resulting stresses are greater than the perma- nent static eflect due to the same load without motion. This live load effect will depend on the rapidity of its application, until extreme rapidity or instantaneous applica- tion occurs, when the momentary stresses become double in amount as compared with the static effect of the same load. If this instantaneously applied load is accompanied with percussion or impact the resulting stresses depend on the energy of the body in motion. The following formula have been proposed to ascertain the fibre stress and deflection resulting from impactive forces: D = d-{-s/27nhd-\-d' _ _35 P ™"3 5 P -f 17 W D = dynamic deflection due to fall of load P. d = static " " static load P. T= extreme fibre stress due to fall of load P. S= " " " " static load P. W= weight of beam. P= " load. h =z height of fall. These formulse apply to beams supported at both ends and the load falling on the middle of the beam. The percussion due to the action of a swiftly moving body, will cause local concentrated stresses or distortion at the area of contact, the effects of which are not emlraced in this consideration. 122 BEAMS OF ANGLE AND TEE SECTION. It is frequently convenient to use angle or tee sections for roof ])urlines and similar purposes. The length of span may be so great as compared to depth in these cases, that deflection instead of excessive fibre stress is the measure of utility. An even-flanged angle or tee will deflect slightly less than an equally loaded rectangular section of the same depth and sectional area ; but the extreme fibre stress of the former will be greater than in the rectangular section. Therefore, for long beams, where deflection reaches the permissible limit before fibre stress becomes excessive, the rule for beams of angle and tee section given on page 113 will safely apply. If, however, the fibre stress must be kept lower than this rule indicates, refer to the columns " resistance," pages 204 to 211, and apply as described on page 116. Example. — A 4-inch X 4-inch tee, 3.98 square inches area, has a resistance of 2.02 (see column VII, page 204). Re- quired its greatest safe load distributed over a beam of 10 feet span. 120 W By the method on page 222 bending moment = — g — = 2.02 X 16,000 pounds, or W= 2,155 pounds nearly. By the rule on page 113, column V, the safe load would be 1^770^3^89j-lrHrH (NCgCM tNlCNlc!l tMCOOJ COOOCO COCOCO OOOOCO 'S9uou[ Ul IpacMoaoacocMCMCoiMOJcooacoojoqcgojcMcocMCM RSfVlj; MaOQ fO ytPJAi \ ^ t-Hi-Hi-H i-d-li-l tHiHi-H t-Hi-Ii-I rHrHrH i-Hr-lrH as i-H ■sqrf Ul. 7J1 CD I-H O UO C33 t-H C:3 00 CD C~ CD O CO CO in 00 C33 t- C33 CM CO O CO 00 <— 1 00 CT) >-H Tjl 03 CM in O 00 CD O 00 CD rHrHCq iHCMCM i-HCMCM iHOaCM rHOlCM COCMCM CMCMCd •y}Dii9Jig 1845 2067 2151 2188 2378 2585 2532 2770 3021 2898 3175 3222 3261 3582 3937 3638 4000 4408 4013 4427 4891 CO rH •sq7 wt -Ml CDC33CM i-HCDO m"*C33 iHCDOO CDI>-LO OCOCO -^0003 CDOOi-H C-C33CM O CM 00 O CO CO i-H -* 03 CM LO C!3 CM lO rHTHCvl i-Ht-HCM rH CM cm i-H CM CM rH CM CM i-H CM CO y-1 Cd CM M 1^ M •yfOiiMfg LOOCD t-COLO OOOOCO CO O 00 lOOin OOOOlO CM CO LO rH'SicM 00 CM 00 lO 03 in OOOOO Tfl CO CM C!3 CD lO CD CO 0030 O CM OOLOCO t--C33CNl O 00 t> 00 C- rH O rH CO rHi-HCM CO CM CO COCMCM COCICO COOOCO CO CO -"H CO ^ 'h'l ■M?7' •sijT- wi -111 CD03rH tH CD O 10 00 03 i-H 00 00 CD t~ LO O 00 CM ^ 00 CO lO t> O CD 00 rH CO CT3 rH I> (33 CM C- O 00 00 rH -sjl 00 rH 00 rni-ICM rHrHCM rH rH (N rH rH CM rH CM CM rH CM CO rH CO CM ■y)Bu3.t}g fo fuopiffaoQ 1585 1812 1886 2078 2286 2196 2427 2683 2508 2786 3092 2828 3152 3511 3158 3526 3940 3491 3910 4380 0 0 !^ Q M w H 'M '^n •'■'"^ ■sqq Ul -fjii lOCOrH OCOC33 in CO CJ3 rH CO 00 CD CO lO O CM CO t^i CO 00 TliCOCT) lO I> C33 LOOOO COCOrH CD 03 CM t- O CO D- O CO PilrHrH rH rH rH rHrHCM rH rH Cd rHrHCM rH CM CO rH CM CO •y!Gu9.i}g fo }U9l0lffMQ 1455 1685 1775 1735 1928 2133 2022 2256 2515 2313 2591 2902 2612 2937 3288 2918 3288 3706 3230 3651 4123 (T ■sqq Ul -JM lOC33rH OCD03 •<* CO 00 O CO 00 CD CD lO O CO CO C- 00 CO in 00 CO CO t- CT) in t> o moOrH coc33co cdc33cm rH rH rH rH rH rH rH rH rH rHrHCM rHrHCM rH rH Cd rHrHCM ■y)Su9.i)g fo JUdlO'lffdOQ 1326 1558 1648 1583 1530 1992 1848 2086 2348 2120 2400 2712 2396 2725 3087 2678 3052 3472 2995 3392 3867 Id "u-ll -^^d ■sqT Ul -JAi LOOOrH OCD03 TtlCOOO OCOI>- LO CD in 03 CM CO -^o-oo CM Tfl t> 00 LO [> CO CD 00 CO 03 -^Jf I> O 00 rH LOOOrH rHrHrH rH rH rH rH rH rH rH rH rH rH rH CO rH rH Cg rH rH CO ■yj6u9j.jg fo '/wpiffaoQ 1296 1432 1432 1630 1846 1675 1915 2178 1925 2207 2522 2180 2507 2876 2440 2816 3238 2706 3133 3612 'fitf 'uyj Md ■sqi in -JAi lOOO OlO CO OCO in CD C33CO CO c~ rHCO CM Tff coin 00 in coco CO C- t> r-l rH rH rH rH rH rH rH rH rH rH rH r-< r-i •y]Gu9.i)g fo f uapiffboQ 1056 1307 1282 1482 1502 1745 1730 2015 1962 2293 2200 2580 2445 2878 Id 'UVJ Md ■sqj ill -JAl lo o o in 03 00 O rH rH CM CO CM 00 r-l j-< 1-1 t-i i-i i-i •y)Su9.ifg fo }U9piff90J 940 1122 1330 1535 1746 1962 2185 ■Sdipuj Ul Maoj fo y)piAi COtMCM CO CM CO CM t>l> OOO 00 00 00 COCOCD r-li-lT-l CM CO CM tNICOCO CO CO CO COOOCO 00 CO CO OOOOCO 1 rHCMOO ■CO (330rH rHrHrH rHrHrH rHrHrH rH CM CM 128 STKENGTH AND WEIGHT OF PLATE GIRDERS. RIVETED > iC B J Ui To find the distributed safe load in net tons, divide the coeflficient on opposite page corresponding to the number below by the length of span in feet. To find the coefiicient of strength for a given load and span, multiply the uniformly distributed load in net tons by the span in feet between centres of supports. See opposite page for coefficients. Weights include stiffeners. Nv/mher oj Section. Width of Govev (-^ ) in Inches. Depth of yyeo (±s) in Inches. Thickness oj Web (V) in Inches. Size of Comer Angles in Inches. 1 12 18 o A o^2 ^ '8 2 12 18 ^2 5 X 31/^2 X q O 1 9 1 Q % 5 X 31/2 X % 4 12 21 0 i 0 ^ i /q 5 12 21 5 X 31/2 X 6 12 21 % 5 X 31/2 X % 7 12 24 % 5 X 31^ X % 8 12 24 % 5 X 3^ X 9 12 24 5 X 31/2 X % 10 12 27 % 5 X 31^ X % 11 12 27 ^ 12 12 27 % 5 X 31^ X % 13 12 30 % 5 X 31/2 X % 14 12 30 5 X 3 ^2 X 1^ 15 12 30 % 5 X 3^ X % 16 12 33 5 x-SHiX % 17 12 33 5 X 31^2 X ^ 18 12 33 5 X 33^ X % 19 12 36 5 X 31^ X % 20 12 36 21 12 36 % 5 X 31,^ X % 129 r-( (M CO IrtCO C— 00 03 O i-H (M 00'* in CD l> CO 1— ( tHi-H 1-Hi-H rHi-H i-Hi— I •ssriouj til Mpjif) fo ytcbff CD CD CDCD CD CD CD CD CD CD CD CD QQ OO t-(iH tHt-H .-HtH rHrM tH i-H >H i-H C5 C5 CM CM ■iq^ ill 7.11 t- CD lO 00 wcj caS c!ioa c9 55 wed ^acd oj bd c3cd ■y]Bu9.i)S CO rjt C- CD rH (N oa CM " O CO 05 CO (MO O 00 OLD O lO O t~ OO lO lO CO t> i-i c 05 1-1 I CM in CO CD t>- CDCO coc-a CD rH in C3> CD O cvi w cvioq ojco cd CO ca eg cm co oaco oj cm cmoo yf6ii3j)g< CD O CM 00 T-H CM LO l> roCM COCD 00 rH CMCM CMCO COCO CO- CMCO ca CM oacM •yiBudJi^ fo }U9%0lffM[) cDi> coo int- Oi-i t>o CMCM C3> Tt< in CD in tH i> tHCO 00i-( CMCD coo i-li-l CMCM CMCM CMCO COCO CO -"il in eg in CM 00 'dj O lO LO Ir- CJ> Cvi eg CM eg CO Id "^n •i^'^d ■H'l '111 fo fll9l0lffd0Q CM lO 00 tH 1-1 CM i-(D-- 005 Oi-H OOCO CDCO tHCDCMOCO " ^ O CD eg CM CM CD eg eg C53 1-1 i-lCM CMCM eg CM CMCM CMCM Cd cg cj cg CMCM lo t~ 00 eg t> lo I-i rH rH CM 05 rH CJ in CM eg CD 05 05 CO CO l> C~ rH CMCM CMCO COCO CO'* CD CO LO CM 1* CD 05 eg CM CM 7i>r 'w/T -^^d ■sqq m 7^11 O Cn 05 rH CO-* D- CD CDCO CD O l>i-H COCM 1-HrH rHCM rH CM rH CM CD 00 un 05 CJ> CO o ^ rH CM CM CM CO O O LO CD t> rH CD O) CM 05 CO •y)6u9J.7SI fo rUi'lOlff'M^) CD t~ CO lO eg 00 rH CM T* 10 D- Ol eg o OOCO coco cdlo ino cm lO lO lo CD CO O CO 00 LD CO CO CM CM CM CM •IjJ -tlirf J9d ■sqj in 7^11 •yiSu9U]ff fo ludioiffdoj lH rH 1-1 rH rHCM rHCM rHCM ^ CO COLO rH CD CDCD t-rH CX) CM 0500 CD'* eg rH eg rH cm CM in LO LO 00 t>0 CDCD 10 t- LOCO - -- 05 in [>(D O"* oorH cocg cmtji int- C-C5 oco rHrH r-\ rHCM CMCd ^ O LO t> CD rH 00 CO CO CO i-{t-\ cm cm fo fudioiffdOQ •SHyOUJ Ul I CD CD CD CD s9)v}j- M.10J foym-Ai •S'dyOUJ Ul I 00 00 rH rH .wpMO fo yidsff \ !N> <>3 CDCO CDCD CDCD CDCD CDCD Q CD QO rHrH rHrH rHrH r-i rHrH CM Cg N CM r~- O 00 coco CDCO rHrH .-icg cot}< cci CM eg eg 10 CD C~00 CO CO CO CO 05 O rH CM CO 00 CO eg CM CM eg in CD t~ 00 130 STRENGTH AND WEIGHT OF RIVETED PLATE GIRDERS. To find the distributed safe load in net tons, divide the coefficient on opposite page corresponding to tlie number below by the length of span in feet. To find the coefflcient of strength for a given load and span, multiply the uniformly distributed load in net tons by the span in feet between centres of supports. See opposite page for coefficients. f -A- r C-. D - J Number of Section. Width of Cover (A) ill Inches. Depth of Web (B) in Inches. Thickness of Web (C) in Inches. Width of (D) in Inches. Size of Corner Angles in Inches. 1 16 18 % 8 31/2 xZ\x % 2 16 18 8 3Vfi T TC «-> /2 i 0 /2 -i- ('2 3 16 21 % 8 3\ X 31^ X % 4 16 21 '2 8 0 /2 i 00 C3> 0 W 00;^ lO ffl th eg eg oa CM eg eg cn cni eg csi co co co co co co co I>I> OO coco CDCD ■^■'Jl !>■ t> OO COCO CD CD cgcg coco coco coco oaoq eg eg coco coco coco OO OO OO OO s*! cgw cgc^ oqoa cgoa oaoa oa eg oa oi eg oj c 0 0 CO M w H iH ■sqq Ul -JM cr>-^ 00 CD t-D- CJ5C-- CD LO LOCO 03 CO gj ror-i oico o oa to T-icD cv] CD CO t~ CO LO C33 g; r-i oa CO oa CO coco coco coco coco coco coco co-* 4375 4685 4930 5300 5555 5927 6073 6571 4687 4795 5381 5520 6047 6223 6385 6948 7638 7886 r-( •If •xirq Md ■sqj ill -fAi CDC- eg CT) OCD i-H o co'^ loco 03 co c33 050 t=-^ o5oa thco oto o4i --iLO egco cor- eg 05 eg 00 oa CO coco coco coco coco coco coco coco fo )U»piff'MQ 4043 4357 4561 4933 5150 5526 5632 6132 4333 4443 4960 5125 5610 5785 6252 6466 7110 7356 rH 7 J "ut'J Md ■sqq Ul -Ui 259 299 275 312 292 322 284 333 285 324 294 337 303 348 313 359 319 372 i •yj Bud Jig fo timotff-jq) 3712 4030 4193 4570 4746 5125 5195 5700 3985 4092 4589 4730 5170 5346 5745 5958 6587 6837 CO W 'uyj .idd ■sqj m -JAi oaco ojto CDCD oot> toco ;3cD CO CD oa c~- th t~- t-cg Sco o oa LO T-i CD oco i-H LO egco co c~- cooo Soa oaoa oaoa o5 eg cm oa oaoa oa cm eg oa •y)Su9U)g fo fudioiffaoj 2392 2723 2728 3116 3135 3525 3431 3908 2580 2695 3012 3158 3416 3597 3838 4128 4480 4737 ')jT "w?T -isd ■sq'j ill -JAl ^ 1-H CD C- CO CD 03 rH rH 1-H rH •yiBuaxis fo )U9}0iff90Q 2066 2362 2731 2991 •g Old- youj wi dMj fo'ymM •snyouj up MpxiQ fo niddd °° •Mquin^ uotjodg SS o3S3 S^ STRENGTH AND WEIGHT OF RIVETED PLATE GIRDERS. To find the distributed safe load in net tons, divide tlie coefficient on opposite page corresponding to the number below by the length of span in feet. To find the coefficient of strength for a given load and span, multiply the uniformly distributed load in net tons by the span in feet between centres of supports. See opposite page for coefficients. f- ■A- — -> r D - J Number of Section. WUth of Cover {A) in Inches. Depth of Web (B) in Inches. Thickness of Web (C) in Inches. Width of (D) in Inches. Size of Corner ncfles in Inches. 19 20 20 20 27 27 11 11 4 X 3^ X % 4 X 31/2 X ^2 21 22 20 20 30 30 \ 11 11 4 X 31^ X % 4 X 33/2 X 3^ 23 24 20 20 33 33 % \ 11 11 4 X 31^ X % 4 X 3^2 X 3^ 25 26 20 20 36 36 \ 11 11 4 X 3^ X % 4 X 3^ X 1^ 27 28 24 24 24 24 \ 13 13 5x4 X % 5x4 x'% 29 30 24 24 27 27 13 13 5x4 X % 5x4 X 1/2 31 32 24 24 30 30 13 13 5x4 X % 5x4 X 33 34 24 24 33 33 % \ 13 13 5x4 X % 5x4 x\ 35 36 24 24 36 36 % \ 13 13 5x4 X % 5x4 X ^ 133 t~CO O) O I-H CO CO in CD t~ 00 CD O I-H , coco ch-^ •^•^ ■^■^ m ID in ] MpMQ fo iiidud OO coco CDCD CDCD CCI Cq CDCD 03 0) OJ CO ' coco coco OOCO coco •>4<-^ coco cooo •s9you{ in mnij MaoQ fo utVlAi OO OO OO OO OO CDCD CDCD CDCD coco coco OOCO coco coco coco coco coco 1 THICKNESS OF COVER PLATES IN INCHES. •sqq ui 7J1 396 441 406 451 412 461 420 473 428 483 464 515 472 523 479 564 •i{]Bu9.iJS' fO)U9lOl(}hOQ 7227 7351 7977 8188 8988 9236 9611 9910 10446 10793 10341 10587 11076 11248 12033 12370 iH •sqi in -lAi 1-HCD i-H CD CDCD ■<**[>- COC~ CO'* rH CO OOCO c-rH OOCO OOCO O) o m coc6 ^O) ^CO co^* co^ coM< co'^ ■*in "Ul3u9JlQ fo fudioiffdO[) 6625 6798 7368 7581 8326 8575 8892 9191 9681 10020 9542 9791 10210 10510 11090 11439 iH '1J[ 'Uirj Md ■sqq in -jm 345 390 350 400 361 411 369 422 377 432 402 453 411 462 418 j 502 •y}Bu9U)g fo )U9iOlff90O 6071 6247 6760 7973 7670 7920 8182 8473 8896 9297 8752 9002 9343 9645 10151 10507 'td '"JT ■'^'^ •sqj ill •}Ai oin mm mm coco rnco coco Or-j c~co COCD coo cooo O) mo C-CO 0000 00 0 COCO coco cooo coco COT* CO-* COT* co^ •y)Bu9.i)g fo )U9ptff30Q 5518 5695 6152 6367 7001 7253 7453 7757 8351 8475 7947 8200 8478 8781 9225 9577 Id •'^'^ ■sqq VI -/Al T* CD CDCD OO 00 rH CD rH rH OJ CD O O rH 0)00 O)'* rHCD rHO CCl 00 CD O m coco coco COOO COOO COCO COCO CO'* CO-* •ytBuo^lg fo tU9lOlff90J 4972 5146 5545 5762 6340 6593 6736 7041 7348 7653 7151 7405 7613 7918 8293 8646 "Id "Wll ■'■^d •sqq m 7/11 03 ■<* -rn CO CD Tj< com om rnco cooo cdih CDrH t-CO 00 00 CD'* om rHCD rH O 00 rH CMco coco coco coco coco COCO coco COt* ur •yjSud.ilg fo fU3ldlffdOQ 4417 4597 4938 5157 5678 5935 6018 6325 6575 6932 6255 6610 6750 7057 7362 7720 "Id "uyr -'"^ •sqq ui 7yii cooo rHoo o) CD o o mo OrH OCO mo T* CO m CD mo coco oco coco co-^ rooo cd CO coco coco coco coco coco cvico coco •y)6u9.i)g fo )U9piff'90Q 3866 4047 4307 4553 5047 5277 5301 5560 5802 6161 5560 5817 5886 6195 6456 6792 Id "^n •'^'^ ■sqq ill 7^1 •y)Su9^)g fo )U9lOlff90Q S9)V)(I ■i^'iOQ fo'vmAi OO OO OO OO OO CDCD CDCD CDCD COCO coco COOO coco coco coco cooo cooo •sayouj up MpM f) fo nidsQ 1 OO coco CDCD CDCD COCO CDCD ^ffi COCO cow COCO COCO COCO T»*'* 1 OOO (DO iH od COT* m CD OOO go "-J*^ 1 COCO CO'* , foj- various dimensions of plates : TOTAL CONCENTRATED LOAD IN POUNDS, ALLOWING FOR A DISTRIBUTED LOAD OF ] 20 POUNDS PER SQUARE FOOT. Slzf- of Plate. 36 Inches Square. 42 Inches Square. 48 Inches Square. 54 Inches Square. 60 Inches Square. Thickness in I?iches. 2 Inches I>epfh of Buckle. 1 4 5 T5" 3 •g" 7 IS^ 1 2 4350 6500 9000 11700 14700 4200 6350 8800 11500 14400 4000 6100 8550 11200 14100 3800 5900 8300 10900 13800 3550 5600 8000 10(500 13400 2^ Inches Depth of Buckle. 1 i A 3 8 xV 1 2 4600 7000 9750 12750 16050 4500 6850 9550 12550 15850 4350 6650 9350 12350 15600 4200 6450 9100 12050 15300 4000 6250 8850 11750 15000 3 Inches Depth of Buckle. 1 ¥ 5 1 6 3 A 1 2" 4850 7350 10250 13550 17100 4750 7250 10150 13350 16900 4600 7050 9950 13150 16700 4450 6900 9750 12950 16450 4300 6700 9500 12700 16150 * Winkler, " Querconstructionen," Vienna, 1884. 148 The formula shows that the concentrated load and the total uniform load are independent of I. This, of course, is only correct as long as the buckled plate is not subject to local deformations, say within the limits given in the previous table. The total uniform load a buckled plate can carry, follows from the above formula as : P = 4:hht. If we assume k = 6,000 lbs. per square inch, we get the following : TOTAL UNIFORMLY DISTRIBUTED LOAD ON ANY SIZE PLATE OP GIVEN THICKNESS AND DEPTH OP BUCKLE. Depth of Buckle. 2 Inches. 2^ Inches. 3 Inches. Thickness of Plate in Inches. Total Loads in Pounds. 1 3 8 tV 1 2 12000 15000 18000 21000 24000 16000 18750 22500 26250 30000 18000 22500 27000 31500 36000 WEIGHT OP BUCKLED PLATES THREE FEET SQUARE. Thickness of Plate in Inches. Weight of One Plate in Pounds. Size and Weight o/T. Weight in Pounds per Square Foot of Floor. 3 T6 68 4x2 T = 20 1bs. 91 1 ¥ 92 4x 2 T = 20 " 12 5 1 6 114 4x3 T = 25 " 15 3 "8 139 4x3JT = 30 " 18 . 7 1 0 160 4x4 T = 35 " 22 1 2 184 4x4JT = 40 " 25 149 PENCOYD Z BAR FLOORING. No. 1. —15 K— 46-H -9 — ^ «- — l-8"-*i ^7- I ^ ^ !<- — 4-8-->i L -10- r 4 r — No. 3. -21--- 1^ — -i9'-->i -12 Divide the coefficient in last column, on the opposite page, by the span of the floor in feet. The quotient will be the safe load in net tons, evenly dis tributed, for each foot of width of floor. 150 PENCOYD Z BAR FLOORING. Section Number. Thickness of 2 -Sar*. Thickness of Plates. Weight in Pounds per Square Foot. Pesisiance per Foot of Width. Coefficient for Distributed Load in Net Tons, per Foot of Width. 1 '4 25.9 9.3 46.7 ^4 3/„ '8 31.0 12.0 60.0 1 ^4 36.1 14.7 73.7 1 \ 29.1 ■ 10.4 52.0 3/„ '8 34.2 12.9 64.5 2 '2 39.3 15.7 78.5 2 '8 ^4 32.3 11.4 57.2 2 '8 3/0 37.4 14.0 70.0 2 3/o 42.5 16.7 83.5 9 5, 32.1 14.3 71.5 2 t'^ 16 37.3 17.6 88.0 2 42.3 20.9 104.7 2 % 35.2 15.5 77.5 9 iSl 'a 7 T(T 40.3 18.8 94.0 9 3/ « 9 45.4 22.1 110.7 o £t 7 _5_ 38 4 16.6 83.2 9 7 rn 43.5 20.0 100.0 9 7 9. 48.6 23.3 116.5 o o 3/ /8 3/„ '8 39.3 20.3 101.7 q 3/ /8 l!^ T2 44.3 24.1 120.7 3 % % 49.5 28.1 140.5 3 % 42.4 21.7 108.7 3 47.5 25.4 127.0 3 % 52.6 29.4 147.0 3 \ % 45.5 23.1 115.5 3 \ 50.6 26.7 133.5 3 % 55.7 30.7 153.6 151 PENCOYD COBIttJGATED FLOORING. 152 PENCOYD CORRUGATED FLOORING. Sections Nos. 210 M and 260 M are extensively used for floors of bridges and buildings. No. 210 M is generally used in buildings; No. 260 M is used for bridge floors. The following table gives the weights and strengths of each section for different thicknesses : WEIGHT AND STRENGTH OF CORRUGATED FLOORING. Section Flange Thickness Inches. Web Thickness Inches. Weight in Pounds pcT Sgudve Pool. Hesisldnce per Foot of Width. Coefficient for Distributed Load in Net Tons, per Foot of Width. 210M \ 14.8 4.4 22.0 210M 5 re 5.5 27.5 210M % 21.9 6.6 33.0 7 rs 21 1.1 38.7 210M: \ % 29.1 8.9 44.4 260M 20.0 10.5 52.5 260M '8 '4 23.6 13 2 DD.U 260M 27.1 15.9 79.5 260M % \ 30.7 18.6 93.0 260M % 26.5 14.3 71.5 260M \ 30.1 17.0 85.0 260M % 1^ 33.7 19.7 98.5 260M \ 37.2 22.4 112.0 260M % % 29.4 15.3 76.5 260M \ % 32.9 18.1 90.5 260M % 36.5 20.9 104.5 260M % 40.1 23.7 118.5 The resistances and coefficients for distributed loads iu net tons are for each foot in width ; the latter for fibre stress of 15,000 pounds per square inch. To find the load for any span, divide the coefficient by the length of span in leet ; the quotient is the distributed load in net tons, which produces fibre stress on the material, as aforesaid. The following tables give safe loads for varying thickness of each section, based on the fibre stress aforesaid. 153 PENCOYD CORRUGATED FLOORING. Loads in pounds per square foot of floor for a fibre stress of lf),O0O pounds per square inch. The figures in small type under the load in pounds are the corresponding centre deflections in inches. Those to tlie right of the dark line are where the centre deflection exceeds part of the spun. Section No. 210 M. Weight of Mate- rial per Sg. Foot. 14.8 18.4 21.9 25.5 29.1 20.0 23.6 27.1 30.7 26.5 30.1 33.7 37.2 29.4 32.9 36.5 40.1 Span in feet. 6 7 8 9 10 11 12 13 14 15 16 1222 898 688 543 440 364 306 260 224 196 172 .15 .21 .28 .35 .43 .52 .62 .73 .84 .97 1.10 1528 1122 859 679 550 455 382 325 281 244 215 .15 .21 .28 .35 .43 .52 .62 .73 .84 .97 1.10 1833 1347 1031 815 660 545 458 391 337 293 258 .15 .21 .28 .35 .43 .52 .62 .73 .84 .97 1.10 2150 1579 1209 956 774 640 533 458 395 344 302 .15 .21 .28 .35 .43 .52 .62 .73 .84 .97 1.10 2467 1812 1388 1096 888 734 617 525 453 395 347 .15 .21 .28 .35 .43 .52 .62 .73 .84 .97 1.10 Section No. 260 M. 8 9 10 11 12 13 14 15 10 17 18 1641 1309 1050 868 729 621 536 467 410 363 324 .17 .22 .27 .32 .38 .45 .52 60 .68 .77 .86 2063 1630 1320 109 1 917 781 693 587 516 457 407 .16 .21 .26 .31 .37 .44 .51 .58 .65 .74 .83 2484 1963 1590 1314 1104 941 811 707 620 550 491 .16 .20 .25 .30 .35 .41 .48 .55 .62 .71 .80 2906 2296 I860 1537 1292 1 101 949 827 727 644 574 .15 .19 .24 .29 .34 .40 .47 .54 .61 .69 .77 2234 1765 1430 1182 993 846 730 638 559 495 441 .16 .20 .25 .30 .36 .43 .50 .57 .65 .73 .82 2656 2099 1700 1405 1181 1006 867 756 664 588 525 .16 .20 .24 .29 .35 .41 .48 .55 .63 .71 .79 3078 2432 1970 1628 1368 1166 1005 876 770 682 608 .15 .19 .24 .29 .34 .40 .46 .53 .60 .68 .76 3500 2765 2240 1851 1556 1325 1143 996 875 775 691 .15 .20 .23 .28 .33 .39 .46 .51 .58 .66 .74 2391 1889 1530 1264 1063 905 781 680 598 529 472 .16 .20 .24 .29 .35 .41 .48 M .63 .71 .79 2828 2235 1810 1496 1264 1071 923 804 707 626 559 .16 .20 .24 .29 .35 .41 .48 .55 .62 .70 .39 3266 2580 2090 1727 1451 1237 1066 929 816 723 645 .15 .19 .24 .29 .34 .40 .46 .53 .61 .69 .77 3703 2926 2370 1959 1646 1402 1209 1053 926 820 731 .14 .18 .23 .28 .33 .38 .44 .51 .58 .65 .73 1.54 PENCOYD CORRUGATED FLOORING. Loads iu pounds per square foot which cause a deflection equal to jj, of the span. Section No. 210 M. J3I SPAN IN FEET. 5 6 7 8 9 10 11 12 13 14 15 14.8 2460 1400 900 600 420 300 230 180 140 110 90 18.4 3000 1750 1100 740 520 380 290 220 170 140 110 21.9 3600 2120 1300 900 630 460 340 250 210 170 130 25.5 4200 2500 1570 1050 740 540 400 310 240 200 160 29.1 4800 2850 1800 1200 850 620 460 360 280 220 180 Section No. 260 M. SPAN IN FEET. 8 9 10 11 12 13 14 15 16 17 18 20.0 2420 1650 1200 880 680 540 430 350 290 240 200 23.6 3050 2200 1580 1200 910 710 570 460 380 310 260 27.1 3670 2650 1910 1450 1140 890 720 580 470 390 330 30.7 4650 3310 2350 1760 1380 1040 860 690 570 480 400 26.5 3300 2240 1630 1250 990 780 636 500 420 350 290 30.1 3920 2670 1940 1480 1170 950 770 620 510 430 360 33.7 4920 3280 2360 1790 1410 1140 910 750 620 510 430 37.2 5600 3980 2830 2220 1720 1330 1070 870 730 610 510 29.4 3830 2550 1840 1390 1090 860 690 550 460 390 320 32.9 4530 3220 2290 1720 1290 1010 810 660 540 460 380 36.5 5230 3720 2640 1990 1550 1210 970 780 640 540 450 40.1 5930 4210 3160 2350 1820 1410 1130 930 770 640 530 ^- i - 1 : ' i-'i '^S' !>: ' H 1 1 . A _ _ ^ 1 — L. BEAMS SUPPORTING BRICK WALLS. When the masonry alone, without any floor attachment, is supported, the load on the girder will vary according to several conditions. If the masonry is not thoroughly bonded throughout, or if great inflexibility is desired, it may be necessary to consider the whole mass of wall as sus- tained by the girder. If the wall has no openings, and the brick is laid with the usual bond, the material incumbent on the girder would be indicated by the dark line— height, one-fourth of the span. It is best to consider this as a triangle, whose height equals one- third of span, as in lower dotted line ; and as the weight of brick walls is nearly 10 lbs. per square foot for each inch of tliickness, from these data we find the bending stress on the beam to be the same as that caused by a distributed load, in pounds equal to 25 X square of span in feet X thickness of wal l i n inches . 9 And from the table of distributed loads suitable beams can be selected, with proper limitations, for deflection, if the spans are long, to avoid cracking of wall. If the wall has 156 openings as illustrated, it is necessary to consider the mass of brickwork, indicated by the upper course of dotted lines, as supijorted by the beams, which can be selected accord- ingly. It is usually best to use two or more beams bolted to- gether to give a better bearing or to insure lateral rigidity, and the following tables give suitable beams for solid brick walls properly bonded, selected to deflect less than of spans up to 10 feet, and -^^-^ of spans 15 to 20 feet. Particulars for separators for these beams can be found on page 257. Thickness nf Wall in Inches. SPANS IN FEET. 8 or 9 feet. 10 or 11 feet. n or 13 feet. U or 15 feet. 16 or 17 feet. 18 or 20 feet. 9 2-4^^ 2—7'' 2—8" 2—9" 2—12" NO.40B No. SOB No. 70 B No. SOB No. 90 B No. 120 B 13 2—%" 2—7^' 2— S^^ 2—9^^ 2—12^^ No. 40 B No. 60 B No. 70 B No. SOB No. 90 B No. 120 B 18 2—7^^ 2—8" 2—9^^ 2—10" 2—12^^ NO.50B No. 70 B No. SOB NO.90B No. 100 B No. 120 B 22 2—7^^ 2—8^^ 2—9^' 2—10^^ 2—12^^ NO.50B No. 70 B No. SOB NO.90B No. 100 B No. 120 B If beams are used to support the whole length of a wall, and the span exceeds 16 feet, the entire weight of the wall should be calculated as resting on the beam, as excessive deflection might push out the supports from under the beam and destroy the structure. If beams support flooring as well as weight of wall, the beam sections must be selected to take the additional load with deflection, as before stated. 157 STRUTS OF ROLLED SECTIONS. In the following consideration of struts of various sec- tions the least radius of gyration of the cross-section, around an axis through the centre of gravity, is assumed as the effective radius of the strut. The tables on pages 160 to 165 are the classified averages of an extensive series of ex- periments. The tables for destructive pressures represent the ultimate load at the point of failure. The greatest safe loads are the aforesaid crippling loads, divided by the factors of safety hereafter described. As is well known, the method of securing the ends of the struts exercises an important influence on their resistance to bending, as the member is held more or less rigidly in the direct line of thrust. In the general tables, struts are classified in four divisions, viz.: " Fixed Ended," " Flat Ended," "Hinged Ended," and " Round Ended." In the class of " fixed ends " the struts are supposed to ])e so rigidly attached at both ends to the contiguous parts of the structure that the attachment would not be severed if the member was subjected to the ultimate load. " Flat- ended " struts are supposed to have their ends flat and normal to the axis of length, but not rigidly attached to the adjoining parts. " Hinged ends " embrace the class which have both ends properly fitted Avith. pins, or ball and socket joints, of substantial dimensions as compared with the section of the strut ; the centres of these end joints being practically coincident with an axis passing through the centre of gravity of the section of the strut. "Round- ended " struts are those which have only central points of contact, such as balls or pins resting on flat plates, but still the centres of the balls or pins coincident with the proper axis of the strut. If in hinged-ended struts the balls or pins are of com- paratively insignificant diameter, it will be safest in such cases to consider the struts as round-ended. If there should be any serious deviation of the centres of 158 round or hinged ends from the proper axis of the strut, there will be a reduction of resistance that cannot be esti- mated without knowing the exact conditions. When the pins of hinged-end struts are of substantial diameter, well fitted, and exactly centered, experiment shows that the hinged-ended will be equally as strong as flat-ended struts. But a very slight inaccuracy of the center- ing rapidly reduces the resistance to lateral bending, and as it is almost impossible in practice to uniformly maintain the rigid accuracy required, it is considered best to allow for such inaccuracies to the extent given in the tables, which are the average of many experiments. It is considered good practice to increase the factors of safety as the length of the strut is increased, owing to the greater inability of the long struts to resist cross strains, etc. For similar reasons we consider it advisable to increase the factor of safety for hinged and round ends in a greater ratio than for fixed or flat ends. Presuming that one-third of the ultimate load would con- stitute the greatest safe load for the shortest struts, the following progressive factors of safety are adopted for the' increasing lengths. 3. 4" .01 - for flat and fixed ends. r 3 .015^ for hinged and round ends. I = length of strut. r = least radius of gyration. From the above we derive the following factors of safety : I r Fixed and Flat Ends. Hinged and Round Ends. I r Fixed and Flat Ends. Hinged and Round Ends. ± r Fixed and Flat Ends. Hinged and Rou7td Ends. 20 3.2 3.3 110 4.1 4.65 200 5.0 6.0 30 3.3 3.45 120 4.2 4.8 210 5.1 6.15 40 3.4 3.6 130 4.3 4.95 220 5.2 6.3 50 3.5 3.75 140 44 5.1 230 5.3 6.45 (50 3.6 3.9 150 4.5 5.25 240 5.4 6.6 70 3.7 4.05 160 4.6 5.4 250 5.5 6.75 80 3.8 4.2 170 4.7 5.55 260 5.6 6.9 90 3.9 4.35 180 4.8 5.7 270 5.7 7.05 100 4.0 4.5 190 4.9 5.85 280 5.8 7.2 159 STRUTS OF WROUGHT IRON OR EXTREME SOFT STEEL.— No. 1. Destructive pressure in pounds per square inch. Length. Least Radius of Gyration. Fixed Ends. Flat Ends. Hinged Ends. Round Ends. 20 46000 46000 46000 44000 30 43000 43000 43000 40250 40 40000 40000 40000 36500 50 38000 38000 38000 33500 60 36000 36000 36000 30500 70 34000 34000 33750 27750 80 32000 32000 31500 25000 90 31000 30900 29750 22750 100 30000 29800 28000 20500 110 29000 28050 26150 18500 120 28000 26300 24300 16500 130 26750 24900 22650 14650 140 25500 23500 21000 12800 150 24250 21750 18750 11150 160 23000 20000 16500 9500 170 21500 18400 14650 8500 180 20000 16800 12800 7500 190 18750 15650 11800 6750 200 17500 14500 10800 6000 210 16250 13600 9800 5500 220 15000 12700 8800 5000 230 14000 11950 8150 4650 240 13000 11200 7500 4300 250 12000 10500 7000 4050 260 11000 9800 6500 3800 270 10500 9150 6100 3500 280 10000 8500 5700 3200 290 9500 7850 5350 3000 300 9000 7200 5000 2800 310 8500 6600 4750 2650 320 8000 6000 4500 2500 330 7500 5550 4250 2300 340 7000 5100 4000 2100 350 6750 4700 3750 2000 360 6500 4300 3500 1900 370 6150 3900 3250 1800 380 5800 3500 3000 1700 390 5500 3250 2750 1600 400 5200 3000 2500 1500 160 STRUTS OF WROUGHT IRON OR EXTREME SOFT STEEL.— No. 2. Greatest safe load in pounds per square inch of cross-section for vertical struts Both ends are supposed to he secured as indicated at the head of each column It both ends are not secured alike, take a mean proportional between the values given tor the classes to which each end belongs. If the strut is hinged by any uncertain method, so'that the centres of pins and axis of strut mav not coincide, or the pins may be relatively small and Length. Flat Ends. Hinged Ends. Hound Ends. Least liadiiis uf Gyration. Fixed Ends. 20 14380 XriOOU 13940 13330 30 13030 13030 12460 1 ifi7n llO/U 40 11760 11760 11110 50 10860 10860 10130 oyou 60 10000 innnn 9230 7820 70 9190 9190 8330 DoOU 80 8420 8420 7500 oyou 90 7950 7920 6840 100 7500 6220 4560 110 7070 6840 5620 oyou 120 6670 6260 5060 130 6220 5790 4580 iiyou 140 5800 4120 2510 150 5390 4830 3570 160 5000 4350 3060 -I /DU 170 4570 3920 2640 lOoU 180 4170 oOUU 2250 1310 190 3830 3190 2020 liOU 200 3500 2900 1800 lUUU 210 3190 2670 1590 oyu 220 2880 1400 790 230 2640 2250 7on laj 240 2410 2070 1140 DOU 250 2180 1910 1040 600 260 1960 1750 940 550 270 1840 1610 870 500 280 1720 1460 790 440 290 1610 1330 730 410 300 1500 1200 670 370 310 1390 1080 620 350 320 1290 970 580 320 330 1190 880 540 290 340 1090 800 490 260 350 1040 720 450 240 360 980 650 420 230 370 920 580 380 210 380 850 510 340 200 390 800 470 310 80 400 740 430 280 70 161 STRUTS OF MEDIUM STEEL.— No. 3. Destructive pressure in poumls per square inch, for steel of uiediuui grade, tensile strength, about 70,000 lbs. per square inch. For extreme soft steel, use table No. 1. Length. Least Radius of Oyralion. Fixed Ends. 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 70000 51000 46000 44000 42000 40000 38000 36100 34200 33100 31900 30100 28200 26800 25300 23400 21400 19400 17900 16200 15000 14000 13000 12000 11000 10500 10000 9500 9000 Flat Ends. 70000 51000 46000 44000 42000 40000 38000 36000 34000 32000 30000 28000 26000 24000 22000 20000 18000 16200 14800 13600 12700 11950 11200 10500 9800 9150 8500 7850 7200 Hinged Ends. 70000 51000 46000 44000 42000 39700 37400 34700 31900 29800 27700 25500 23200 20700 18100 15900 13700 12200 11000 9800 8800 8100 7500 7000 6500 6100 5700 5330 5000 162 STRUTS OF MEDIUM STEEL.-No. 4. Greatest safe load for steel of medium grade, tensile strength about 70 000 lbs h or extreme soft steel, use table No. 2. o , . The figures are the working loads in pounds per square inch for vertical struts Both ends are supposed to be secured as indicated at the head of eacli column. If both ends are not secured alike, take a mean proportional between the values given for the classes to which each end belongs. If the strut is hinged by any uncertain method so that the centres of pins and axis ol strut may not coincide, or the pins may be relatively small and loosely titted, xt is best in such cases to consider the strut as " round ended " Length. Least Eadius (jf Gyration. 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 Fixed Ends. Flat Ends. 21900 15400 13500 12600 11700 10800 10000 9260 8550 8070 7590 7000 6410 5950 5500 4980 4460 3960 3580 3180 2880 2640 2410 2180 1960 1840 1720 1610 1500 21900 15400 13500 12600 11700 10800 10000 9230 8500 7800 7140 6510 5910 5330 4780 4250 3750 3310 2960 2670 2440 2250 2070 1910 1750 1610 1460 1330 1200 Hinged Ends. 21200 14800 12800 11700 10800 9800 8900 7980 7090 6410 5770 5150 4550 3940 3350 2860 2400 2080 1830 1590 1400 1250 1140 1040 940 860 790 720 670 Round Ends. 20300 13800 11600 10300 9130 8050 7070 6090 5200 4540 3920 3330 2780 2340 1920 1660 1410 1190 1020 890 790 720 650 600 550 500 440 410 370 163 STRUTS OF HARD STEEL.— No. 5. Destructive pressure in pounds per square itcli for hard steel, tensile strength about 100,000 lbs. For softer steel, see table No. 3. Lenglh. 1 Hoiuiil J^'iids, Least Radms of GyraUon. Fixed Ends. Flat Ends. 20 30 40 50 100000 74000 62000 60000 j 100000 /4UL)U 62000 60000 100000 /'iUUU 62000 60000 95600 56600 52900 60 70 80 90 58000 55500 53000 49900 58000 55500 53000 49700 58000 OOiUU 52200 47800 49100 45300 41400 36600 100 110 120 130 46800 44700 42600 39400 46500 43200 40000 36700 43700 4U4iUU 36900 33500 32000 25100 21600 140 150 160 170 36300 34200 32200 29800 33500 30700 28000 25500 29900 26500 23100 20300 18200 15700 13300 11800 180 190 200 210 27400 25100 22900 23000 21000 19000 17200 17500 15800 14100 12400 10300 9060 7860 6950 220 230 240 250 18300 16900 15500 14200 15500 14400 13400 12400 10700 9820 8960 8270 6100 5600 5140 4780 260 270 280 290 300 12900 12200 11400 10900 10600 11500 10600 9700 9000 8500 7630 7060 6500 6130 5890 4460 4050 3650 3440 3300 161 STRUTS OF HA.RD STEEL.-No. 6. Greatest safe load for hard steel, tensile strength about 100,000 lbs. l'"or soft steel, see table No. 4. The ligtires are the working loads in pounds per square inch for vertical struts. Hoth ends are supposed to be secured as indicated at the head of each ■column. If lioth ends are not secured alike, take a mean proportional between the vrilues given for the classes to which each end belongs. If the strut is hinged by any uncertain method, so that the centres of pins and axis of strut may not coincide, or the pins may be relatively small and loosely fitted, it is best in such cases to consider the strut as " round ended." - - Length. Flat Ends. Hinged Ends. Round Ends. Least Radius (if Gyration. Fixed Ends. 20 31200 31200 30 22400 22400 21400 20100 40 18200 18200 17200 15700 50 17100 17100 16000 14100 60 16100 16100 14900 12600 70 15000 15000 13600 11200 80 13900 13900 12400 9860 90 12800 12700 11000 8410 100 11700 11600 9710 71 in 110 10900 10500 8670 6130 120 10100 9520 7690 5230 130 9160 8530 6770 4360 140 8250 7610 5860 3570 150 7600 6820 5050 2990 160 7000 6090 4280 2460 170 6340 5420 3660 2130 180 5710 4790 3070 1810 190 5120 4280 2700 1550 200 4580 3800 2350 1310 210 3980 3370 2020 1130 220 3520 2980 1700 970 230 3190 2720 1500 870 240 2870 2480 1360 780 250 2580 2250 1220 710 260 2300 2050 1100 650 270 2240 1860 1000 570 280 1960 1670 900 510 290 1850 1520 830 470 300 1800 1420 780 440 16-5 ROLLED STRUCTURAL SHAPES AS STRUTS. The following tables of safe loads for rolled struts are derived from jirevious table No. 4, and from the columns given for flat-ended bearings. When steel of medium grade is used, say 65,000 pounds tensile strength or greater, the tables derived from No. 4 can be used, described as applicable to steel of medium grade. In all cases the strut is supposed to be vertical. In short struts this distinction is immaterial, but in long horizontal struts some allowance is necessary for the deflection due to weight. If the struts are rigidly connected at the ends to con- tiguous parts of a structure, the increase of resistance be- comes considerable in extremely long struts, and proper allowance can be made by using the columns for "Fixed Ends " in table No. 4. On the contrary, if the end bearing of the strut is to be of uncertain character or fit, it will be best to reduce the safe load to that in the columns for "Round Ends," in the same table. In these working tables the calculations are made to apply to the mean thick- nesses of each shape. Where more exact results are re- quired for thicknesses above or below the mean, the true radius of gyration of the section will be found on pages 188 to 216. But within the range of variation of thickness possible for any shape, the tables may be accepted as prac- tically correct. For I beams, table No. 7 applies to cases where the strut is braced in the direction of the flanges, so that failure could occur in the direction of the web only. For unbraced I struts use table No. 8. Likewise for channel bars used as struts, and braced to resist failure in the directions of the flanges, use table No. 9 same as for latticed channels. For a pair of latticed channels, which form a more perfect column than single rolled sections, the safe loads are given for various conditions of the end bearings, as described on pages 158 and 159. On the table No. 9 the distances D or d 166 for flanges inward or outward, respectively, make the radii of gyration equal for either direction of axis, parallel to web or to the flanges. Under each length of struts in the table, I represents the greatest distance apart in feet that centres of lateral bracing can be spaced, without allowing weakness in the individual channels. The distance I is obtained as shown in last ex- ample, that is, by making ^ = ^- ' I = length between bracing. L = total length of strut. r = least radius of gyration for a single channel. R = least radius of gyration for the whole section. It is customary to make I much shorter than given in the tables, the figures given being useful as a guide. If a column is composed of four angles, forming the corners of a square, and properly latticed as explained above, find the radius of gyration of the combined section, a,s described on page 186, and then the working resistance from tables Nos. 2 to 6, or the safe load can be ascertained approximately from table No. 16 on page 180 for square columns. When a pair of angles are tied together forming a single strut - take the greatest radius of gyration, around axis A B, in column No. IX, page 207, for a single angle as the least radius of gyration of the pair, and proceed as before described. < n B 167 PENCOYD I BEAMS AS STRUTS— No. 7. GREATEST SAFE LOAD IN POUNDS PEH SQUARE INCH OF SECTION FOR STEEL OF MEDIUM GRADE. For struts secured against failure in the direction of the flanges and liable to bend only in the direction of the web. Size of I Beam in Inches. LENGTH IN FEET. 10 12 14 16 I 18 I 20 I 22 j 24 Greatest safe load in pounds per square inch of section. 24^=9.35 18 r=6.85 15 r= 5.87 12 r=4.74 10 r= 3.97 9r=3.50 8 r= 3.16 7r=2.78 g r=2.33 5 r = 1.95 4r=1.58 3r=1.18 21400 19730 21680 18760 16710 15320 17640 14330 15220 21510 18000 15350 14370 13770 13130 12520 13360 13930jl266o|il560 129101163010320 11610 9890 8380 21430 ?n33n 18120 21010 18520 16390 iRnnn IDUUU 14720 14180 13440 14050 13220 12710 13370 12730 12260 12910 12390 11630 12510 11660 10920 11540 10630 9810 10490 9530 8610 9150 8060 7040 7010 5770 4640 19500 17780 1627oji5080 15040 14240 13960 13400 12910|12570 1230011660 11550 10970 1099010320 10180 9030 7750 6100 3620; 9510 8290 6950 5220 2860 1628015240 1433013810 1369o|l3260 1296012670 12190 11140 10370 9730 8870 7580 6190 4400 2370 11630 10600 9820 9150 8250 6910 5460 3650 2000 168 PENCOYD X BEAMS AS STRUTS.— No. 8. GREATEST SAFE LOADS IN POUNDS PER SQUARE INCH OF SECTION FOR STEEL OF MEDIUM GRADE. When struts are unsupported, or free to bend in the direction of the flanges, r = least radius of gyration for mean thickness of each shape. LENGTH IN FEET. o S Size of Beam in Incites. 4 6 1 « 10 12 14 16 18 20 22 Greatest safe load in pounds per square inch of section. 240B 24 r 1.33 14080 12320 10630 9210 7920 6740 5660 4650 3730 3010 200B cfJoiy 206B 20 )■ = l.io 1.27 1.38 13420 13800 14290 11590 12080 12480 9890 10350 10870 8380 8900 9460 7010 7580 8190 5770 6370 7030 4640 5260 5960 3620 4250 4970 2860 3350 4060 2370 2730 3260 ioUiJ 183B loD±> 18 r = r = 1.12 1.20 1.32 13150 13500 14040 11340 11700 12290 9560 10000 10580 8000 8500 9160 6600 7140 7870 5330 5910 6680 4180 4780 5590 3210 3750 4590 2570 2960 3670 2150 2440 2960 iour> 152B 154B 156B 15 r = r = r = 1.07 1.13 1.24 1.32 12970 13210 13670 14030 11080 11390 11940 12290 9250 9610 10210 10580 7660 8070 8730 9160 6230 6670 7390 7870 4940 5410 6180 6680 3780 4260 5060 5590 2900 3270 4040 4590 2360 2610 3180 3670 1960 2190 2600 2960 120B 122B 124B 125B 12 r = r = r = 1.00 1.09 1.19 1.24 12730 13050 13460 13670 10640 11180 11650 11940 8790 9380 9950 10210 7140 7800 8440 8730 5680 6380 7080 7390 4360 5100 5840 6180 3240 3940 4710 5060 2530 3020 3680 4040 2070 2440 2910 3180 1690 2030 2410 2600 lOOB 102 B 10 r = 0.94 1.03 12550 12830 10270 10820 8350 8990 6660 7370 5150 5920 3810 4620 2830 3460 2260 2680 1820 2200 1450 1810 90B 9 r = 0.87 12230 9780 7780 6030 4490 3200 2430 1940 1520 BOB 8 0.81 11770 9310 7240 5440 3860 2740 2130 1650 1250 70B 7 0.76 11430 8880 6740 4900 3330 2420 1870 1410 60B 63B 67B 6 r = r = 0.69 1.11 1.24 10870 13130 13670 8210 11290 11940 5960 9500 10210 4060 7930 8730 2710 6530 7390 2020 5250 6180 1490 4100 5060 3150 4040 2530 3180 2110 2600 SOB 5 0.63 103C0 7520 5200 3290 2280 1650 40B 4 0.57 9670 6740 4340 2660 1870 1270 SOB 3 0.52 9060 6000 3550 2240 1510 169 TABLE OF STRUTS.— No. 9. LATTICED CHANNEL STRUTS. GREATEST SAFE LOADS IN POUNDS PER SQUARE INCH OF SECTION FOR Q MEDIUM STECL. For a pair of braced channels, or for a single channel secured j from flexure in the direction of flanges and liable to fail only in A- ■ -|— B the direction of the web C D. I r in the marginal columns gives the radius of gyration for axis ■ A. B, or for either axis of the combined pair of channels. See D description, page 167. Size 0/ Channels 15 ins. r= 5.49 D=12AS d= 9.14 13 ins. r= 4.42 J>=10.13 d= 7.25 10 ins. ?•= 3.66 D= 8.55 d= 5.80 9 ins. r= 3.38 D= 7.90 d= 5.34 8 ins. r= 3.00 D= 7.08 rf= 4.62 7 ins. r= 2.60 D= 6.22 d= 3.85 6 ins. r= 2.24 I)= 5.44 d - 3.21 Condi- tion of Ends. Fixed. Flat. Hinged. Bound. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. LENGTH IN FEET. 14 20 Greatest safe load in pounds per square inch of section. 22000 22000 22000 22000 1.03 22000 22000 22000 22000 1.10 22000 22000 22000 22000 1.22 20810 20810 20100 19130 1.25 18880 18880 18170 16950 1.33 16570 16570 15900 14700 1.45 14860 14860 14200 13240 1.56 22000 22000 22000 22000 1.38 20520 20520 19810 18790 1.47 17440 17440 16740 15460: 1.63 16200 1 16200 15540 14390 1.67 14900 ! 149001 14240' 13270 : 1.78i 13930 13930 13260 12180' 1.94 13170 13170 12400 11140 2.06 20420 20420 19720 18670 1.72 16870 16870 16180 14940 1.84 14700 14700 14040 13070, 2.03 14170 ! 14170 13500 12470: 2.08i 13500 i 13500, 12800 11600 2.22 12870' 128701 12040 10700 2.42 12360 12360 11440 9900 2.58 ' 17430 17430 16740 15460 2.06 14760 14760 14090 13130 2.20 13590 13590 12900 11720 2.44 13190 13190 12430 : 11180' 2 50 12730 12730' 11870 104901 2.6G| 122201 12220 11300 9690 2.91 11340 11340 10380 8690 3.09 15280 15280 14630 13630 2.41 13770 13770 13100 11970 2.57 12890 12890 12060 10730' 2.85 i 12620 12620: 11720 10330, 2.92 12160 12160 11240 9630 3.11 11320 11320^ 10370 8650 3.39 10400 1O400 9390 7550 3.61 14250 14250 13600 12580; 2.761 13110 13110 12330 11060 2.94 12450 12450 11520 10010 3.25 12070 12070 11160 9530' 3.33 i 11370: 11370 10430 8720 3.55 10490 10490 9500 7670' 3.88j 9580 9560 ! 8380, 6510 4.12 13590 13590 12900 ll':20 :.10 12690 1 2690 11790 10400 im IIQO iiao 10920 9270 11280 llc80 10440 8730 375 lOBiO 10640 9680 7850 4 00 9770 9733 8620 6770 Am 8830 87')0 74:0 5520 4.j4 13080 13080 12300 11020 3.45 12310 12310 11390 9810 3.67 11220 11220 10280 8540 4.07 10720 10720 9770 7950 4.1: lOOOCi 10000 8900 7070 4.41 9100 9060 7780 5890 4..sr, 8210 8000 6610 4730 5.16 170 TABLE OF STRUTS.— No. 9. LATTICED CHANNEL STRUTS. GREATEST SAFE LOADS IN POUNDS PER SQUARE INCH OF SECTION FOR STEEL OF MEDIUM GRADE. The channels must be connected so as to insure unity of action, and separated not less tlian the distances D or d re- spectively given in inches in the margi- (ri> nal column. Figures in smaller type H ro- under each length represent the greatest distance apart in feet on each channel ^ that centres of lateral bracing should be placed. LENGTH IN FEET. Condi- tion of Ends. Size of Channels. 22 24 1 26 28 30 32 34 36 Greatest safe load in pounds per square inch of section. 1 ' I 1 1 12070 ! 11590 11220 10830 10450 10100 Fixed. 15 ins. 12070 11590 11220 10830 10450 iUlUU Flat. r= 5.49 11860 11520 11160 10690 10280 9810 9450 Qr\AC\ yu^u Hinged. Z>=12.48 10480 10010 9530 9030 8540 8060 7620 Round. d= 9.14 3.79 4.14 4.83 5.17 5.52' 5.86 6 19 18 ins. 11730 1 1 oftr* iiZDU 10760 9890 9490 9100 8710 Fixed. 11730 11260 10760 10320 9890 9470 9060 8660 Flat. r= 4.42 10830 10320 9780 9300 8770 8270 7780 7290 Hinged. Z)=10.13 9170 8590 7990 7470 6930 6400 5880 5400 Round. d= 7.25 4.04 4.41 4.77 5.14 5.51 5.87 6.24 6.61 10 ins. 10630 10110 9610 9130 8670 8310 8000 7690 Fixed. 10630 10110 9590 9100 8620 8160 7700 7270 Flat. r= 3.66 9670 9040 8420 7820 7240 6750 6320 5900 Hinged. D= 8.55 7840 7200 6560 5930 5350 4880 4450 4040 Round. d= 5.80 4.47 4.88 5.29 5.69 6.10 6.50 6.91 7.32 9 ins. 10150 9610 9100 8590 8240 7900 7550 7130 Fixed. 10150 9600 9060 8540 8040 7560 7090 6650 Flat. r= 3.38 9100 8420 7780 7140 6650 6180 5730 5290 Hinged. Z)= 7.90 7260 6560 5890 5250 4770 4320 3880 3460 Round. d= 5.34 4.58 5.00 5.42 5.85 6.25 6.67 7.09 7.50 9410 8830 8360 7970 7590 7120 6650 6230 Fixed. 8 ins. 9380 8790 8220 7670 7140 6630 6150 5680 Flat. r= 3.00 8160 7450 6820 6280 5770 5270 4790 4310 Hinged. D= 7.08 6290 5560 4940 4420 3920 3450 3000 2600 Round. d= 4.62 4.88 5.33 5.77 6.22 6.66 7.10 7.55 7.99 8480 8030 7590 7050 6500 6060 5640 5180 Fixed. 7 ins. 8390 7750 7140 6560 6000 5460 4950 4450 Flat. r= 2.60 6990 6360 5770 5200 4640 4080 3530 3050 Hinged. D= 6.22 5100 4490 3920 3380 2870 2440 2050 1760 Round. d= 3.85 5.33 5.81 6.30 6.78 7.27 7.75 8.23 8.72 7690 7090 6450 5950 5460 4910 4350 3850 Fixed. 6 ins. 7280 6600 5950 5330 4740 4180 3660 3210 Flat. r= 2.24 5910 5240 4590 3940 3320 2800 2330 2010 Hinged. V= 5.44 4050 3420 2820 2340 1900 1820 1360 1140 Round. d= 3.21 5.67 6.19 6.70 7.22 7.73 8.25 8.77 9.28 171 PENCOYI> CHANNELS AS STRUTS— No. lO. GREATEST SAFE LOADS IN POUNDS PER SQUARE INCH OF SECTION FOR STEEL OF MEDIUM GRADE. When struts are unsupported, or free to bend in the direction of the flanges. r = least radius of gyration for mean thickness of eaeli size. Section Number. 154C— 155C; 150C— 153G Size of Chan- nels in Inches. LENGTH IN FEET. 10 12 14 16 18 20 Greatest safe load in pounds per sq. in. of section. t5 r=1.03 19360 .90 13 r= .95 17160 12830 12380 123C— 124Cr= .951804012570 120C-122Cr= .7915320111630 128C .7014370:10970 10 102C— 104C r= .77il5150'll490 10820 8990 7370 5920 10000 8030 1034018430 6310 6740 4780 4620 3460 5240 3910 3470 2590 2900 1000— 101C|r= .71 9 92C— 93C 90C— 910 8 820— 840 r= .69 80C— 810 720— 740 700— 710 610— -631 60O 500— 520 40O— 420 30O— 320 >■= .62 7 r= .66 r= .58 6 .59 .54 5 .49 4 .45 .42 14470 14680 14130 14290 13670 14030 13340 13420 13010 12680 12380 12040 11050 11200 10670 10870 10210 10580 9790 9890 9310 8650 8030 7520 9150,7040 5220,3650 261012020 8300 8970 8400 8600 7980 8210 7400 6080 6840 6200 6420 5720 4180 5010 4300 4550 3790 2790 3440 2880 3060 2560 5960 5060 3190 4060:2710 2070 1540 24801 1920 2130 2250 1900 2020 5590 4490 7860 6880 7010 631013860 55003100 4640 4780 2590 4180 2280 3670 2760 221011590 2480 1940 2000 2400 1660 2020 1660 1390 1280 1840 1330 1400 1600 1710 1370 1490 2680 2070 2300 1560 1450 1250 2200 1660 1870 1320 172 PENCOYD Z BARS AS STRUTS.- ^fo. 11. GREATEST SAFE LOADS IN POUNDS PER SQUARE INCH OF SECTION FOR STEEL OF MEDIUM GRADE. Wlien struts are unsupported, or free to bend in the direction of the flanges. == least radius of gyration for mean thickness of each size. 1 LENGTH IN FEET. SfC. No. Size in Inches. 2 4 ! 6 1 8 10 1 12 1 14 1 16 18 Greatest safe load in poi imls per sq ill. f / section. 67Z r = .81 3^x6A'x3i%xi3 15590 11780 9310 7240 5440 386oj2740 2130 1650 64Z. r -= .81 3ftx6iVx3i"gx% 15590 11780 9310 7240 5440 3860 2710 2130 1650 61Z r = .83 3^x6,1^x3135X1^ 15950 11970 9480 7430 5540 4070 2890 2230 1750 56Z r = .72 314x5 X31/4XIJ 14680 11200 8600 6420 4550 3060 2250 1710 1250 54Z r = .74 3:5%x5Tl|;X3-3f5Xj!V 14790 11290 8700 6530 4670 3150 2310 1760 1300 51Z r=.75 3i/4x5,iijx3i/4X% 14900 11370 8790 6640 4780 3240 2360 1810 1360 47Z r= .66 3V4J5X3VH 14030 10580 7860 5590 3670 2480 1840 1320 44Z r== .65 3;^x4Jsx3g^xi/2 14080 10490 7750 5460 3550 2410 1770 1260 41Z r = .65 14080 11490 7750 5460 3550 2410 1770 1260 34Z r= .54 2Ux3^x2iixM 13010 9310 6310 3860 2400 1660 31Z r= .55 2iix3ijx2iixi\ 1309C 944C 645C 402C 248C 1720 173 PENCOYD ANGLES AS STRUTS.-No. 12. GREATEST SAFE LOAD IN POUNDS PER SQUARE INCH OF SECTION STEEL OF MEDIUM GRADE. r = least radius of gyration for mean tbickuess of each size. Size of Angle in Inches. LENGTH IN FEET. 2 1 ^ 1 « 1 ^ 1 1 1 1 1 j 20 Greatest safe load in pounds per square inch of section. 8 x8 r — i.oy 1536C )|l294C ) 1167( ) 1036C 919C ) 810( \ 709( ) 616C ) 5280 6 x6 r = i.iy 21750 1346C :il65C 995C ) 844C 708C 5840 471C 368C 1 2910 5 x5 f = .99 18710 'l270C 1058C 872C 7060 559C 4270| 317C 248C 2030 4 x4 * 7Q 15320 11630 9150 704C 5220 3650 2610 2020 1560 ^\ X 3^2 r = .69 14290 10880 8220 5980 4080 2700 2010 1 1480 3 x3 r = .59 13420 9890 7010 4640 2860 2000 1400 2\ X 2\ r ~ .55 13090 9440 6450 4020 2480 1720 2\, X 21/2 — - /in 12680 8650 5500 3100 1990 1280 2\ X 2\ r = .44 12290 7860 4590 2480 1570 2 x2 r= .39 11560 6950 3550 1970 1% X 1% r= .36 11130 6310 2960 1660 11/^ X 11/2 r= .28 9560 i 4180i 1800 11/4 X 11/4 r= .26 1 9060 3540,^ 1510 1 xl r= .21 7520| 228o| 174 PENCOYD TEES AS STRUTS— No. 13. GREATEST SAFE LOAD IN POUNDS PER SQUARE INCH OF SECTION FOR STEEL OF MEDIUM GRADE. r = least radius of gyration of each size. LENGTH IN FEET. Size of Tee ill Inches. 2 4 6 8 10 12 1 14 1 16 18 20 Greatest safe load in pounds per square inch of section. 4x4 r= .85 16280 12110 9640 7610 5840 4280 3040 2330 1840 1430 31/2 X 3^2 r= .73 14680 11200 8600 6420 4550 3060 2250 1710 1250 3x3 r= .62 13670 10210 7390 5060 3190 2210 1590 21/2 X 2V2 r = .54 13010 9310 6310 3860 2400 1660 2\ X 2\ r= .48 12600 8500 5330 2960 1910 1200 2x2 r= .41 11870 7330 3970 2170 1290 r= .36 11130 6310 2960 1660 X V^r, r= .32 10400 5330 2340 1200 114 X 134- r= .30 10000 4780 2070 1x1 r= .26 9060 3540 1510 175 COLUMNS OF ROUND AND SQUARE SECTION Experiments on columns of this class are not very com- plete, especially as denoting the comparative values for the various end conditions. The following tables, Nos. 14 to l(i, are derived partly from experiment on actual columns, ex- tended and completed by comparison with the experiments on rolled struts from which all our previous tables of strut resistances are derived. Table No. 4, page 163, is taken as the basis for the working values. On account of the more perfect symmetry of form possessed by round and square sections than the shapes for which this table was especially calculated, the safe loads per square inch of section are increased ten (10) per cent, for round columns, and five (5) per cent, for square columns. That is, the factors of safety previously given remain the same, the ultimate strength is supposed to be 10 and 5 per cent, respectively greater than the rolled struts. The tables are calculated for certain thicknesses, varying from I inch for 2-inch diameter up to | inch for 12-inch diameter, as marked in the margins. At the same place R represents the radius of gyration for the diameter and thickness given. When the thickness varies but a little from that given, the strength per square inch of section can be accepted as practically unchanged. But when the varia- tion becomes of importance, the radius of gyration corre- sponding to the altered thickness will have to be obtained, and the strength of the column then ascertained from table No. 4, as heretofore described. The following table gives the values of the radius of gyration for round and square columns from 2 to 12 inches diameter, and from j\ of an inch to 1 inch thick. Example for Round Column : What is the greatest safe load for a flat-ended round column 6 inches outer diameter, ^ inch thick, 8.64 square inches area, and 18 feet long, r = 1.95 :^ = 111 ? By table No. 4, the corresponding safe load = 7,730 lbs. + 10 per cent. = 8,500 lbs. per square inch of section, or 73,440 lbs. for the column. 176 No. 14. RADII OF GYRATION FOR ROUND COLUMNS. Outxide Diameter of Column in Inches. Thickness in Inches Varying by Tenths. .1 o .3 .4 .5 .6 .7 .8 .9 i.U Corresponding Radius of Gyration in Inches. 2 .67 .64 .61 .58 .56 .54 .52 .51 .50 .50 3 1.03 .99 .96 .93 .90 .88 .85 .83 .81 .79 4 1.38 1.35 1.31 1.28 1.25 1.22 1.19 1.16 1.14 1.12 5 1.73 1.70 1.66 1.63 1.60 1.57 1.54 1.51 1.48 1.46 6 2.08 2.05 2.02 1.98 1.95 1.92 1.89 1.86 1.83 1.80 7 2.43 2.40 2.36 2.33 2.30 2.27 2.24 2.21 2.18 2.15 8 2.79 2.76 2.72 2.69 2.66 2.62 2.59 2.56 2.53 2.50 9 3.15 3.11 3.08 3.04 3.01 2.97 2.94 2.91 2.88 2.85 10 3.51 3.47 3.44 3.40 3.37 3.33 3.30 3.27 3.23 3.20 11 3.86 3.82 3.79 3.75 3.72 3.68 3.65 3.62 3.58 3.55 12 4.21 4.18 4.15 4.11 4.08 4.04 4.01 3.97 3.94 3.90 RADII OF GYRATION FOR SQUARE COLUMNS. A cross ches. Thickness in Inches Varying by Tenths. lam. . in In .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 . a 1^ O Corresponding Radius of Gyration in Indies. 2 .78 .74 .71 .68 .65 .63 .61 .59 .58 .58 3 1.18 1.14 1.11 1.08 1.04 1.01 .98 .96 .93 .91 4 1.59 1.55 1.51 1.47 1.44 1.41 1.38 1.35 1.32 1.29 5 2.00 1.96 1.92 1.89 1.85 1.81 1.78 1.75 1.71 1.68 6 2.41 2.37 2.33 2.29 2.25 2.21 2.18 2.15 2.11 2.08 7 2.82 2.78 2.74 2.70 2.66 2.62 2.58 2.55 2.51 2.48 8 3.23 3.19 3.15 3.11 3.07 3.03 2.99 2.96 2.92 2.89 9 3.63 3.59 3.55 3.51 3.48 3.44 3.40 3.36 3.32 3.29 10 4.04 4.00 3.96 3.92 3.88 3.84 3.80 3.77 3.73 3.70 11 4.45 4.41 4.37 4.33 4.29 4.25 4.21 4.17 4.13 4.10 12 4.86 4.82 4.78 4.74 4.70 4.66 4.62 4.58 4.54 4.51 177 STEEL. COLUMNS.— No. 15. ROUND SECTION. GREATEST SAFE LOADS IN POUNDS FOR SQUARE INCH OF SECTION. MEDIUM STEEL. By this table for the same ratios of ~ the safe loads are increased 10 per cent, over the results obtained for previous tables, as given in table No. 4. Size of Column. 1 8 ins. Diameter. tliick. J? = 4.03 10 ins. Diameter. I" thiclj. 'R= 3.37 8 ins. Diameter, j" thiclc. 11= 2.G6 6 ins. Diameter. I' tliick. R = 2.00 6 ins. Diameter. %" thiols. 'r = 1,64 4 ins. Diameler. rl" thick. R= 1.33 .3 ins. I)iameler. Y^o" thick. R= 1.00 3 ins. Diameter. ^" thick. R = 0.G6 Condi- tion of Mids. Fixed. I^lat. Hinged, Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged Round. Fixed. Flat. Hinged, Round. Fixed. Flat. Hinged, Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged, ttou nd. Fixed. Flat. Hinged. Round. LENGTH IN FKET. I 8 I 10 I 12 I Greatest Safe Load in Pounds per Square Inch of Sealic 23000i23000|23000 20920 17050 15570 14630!14030 13590 23000 23000l23000:20920il7050:l5570 14630:14030 13590 23000 23000 23000,23000 23000,20140:16390 14810 13810 13090 12580 23000, 18760 15260 13670, 12450 11590| 10880 23000 23000 2281oll778o!l5570 14500 13870 13260!l2500 23000l23000 2281017780|15570|l4500l3870 13260112500 23000|23000 22030 23000 23000 20950 23000 23000 23000 23000 23000 23000 23000 23000 23000 23000 23000: 23000 23000 23000 23000 23000 20770 20770 19990 18650 15450 15450 14700 13530 23000 23000 23000 23000, 20770 20770 19990 18650 17350 17350 16630 15430 15490 15490 14740 13590 14000 14000 13060 11540 11640 11640 10570 8560 17040,1483011366012880 12260ill460 15780 13690:i2280;il340 10470,' 9580 18600 15490 18600 15490 17850 14740 16480 13590 15510 15510 14760 13610 14370 14370 13500 12090 13550 13550 12540 10820 11700 11700 10650 8640 8920 8650 7120: 5060 14250!l3550 12570 11690 10900 14250;i35501257011690:10900 13350125401156010630 9670 1191010820, 9690 8620 7650 14000 12870 11700,10670 14000 12870 11700 10660 13060:il880;i0650: 9390 1154010040: 8640 7350 6110 13060 13060 12080 11600! 10360 9280 11600|10340 9180 10520: 9000 7620 10270 8500: 69401 5550 11690:10170' 897o! 7940 1169010140, 8710! 7420 10630 8610 9720 9670 8190 6110 6780 6150 4640 2790 8760: 7180: 5920 6680 5120| 3900 8350 6850| 5590 7850 6250: 4790 6350: 4740| 3250 4310' 2860 1880 4810 4040 2580 1510 3230; 2290 2730 2020 1580 890 1090 630 9720 9670 8190 8500 8070 6550 4510 8730 7200 5140 7590 7050 5550 3560 6830 5910 6220: 5120 4710| 3560 2850j 2040 4280 3300 3560 2790 2230 1270 1760 1450 790 450 1620 910 J 78 STEEL COLUMNS.-No. 15. ROUND SECTION. GREATEST SAFE LOADS IN POUNDS PER SQUARE INCH OF SECTION FOR MEDIUM STEEL. The calculations are based on the thicknesses and radii of gyration marked under the diameters on marginal columns. See description. LENGTH IN FEET. 36 Condi- tion of Ends. Size of Column. 20 22 1 24 2G 28 30 32 34 Greatest Safe Load in Pounds per Square Inch of Section. 12930 ' 12350 'll750 1 11230 ! 10730 1 10240 1 9770 9340 9020 Fixed. 13 ins. l-_'930 12350 ! 11750 ' 11230 : 10710 10220 9730 9260 8800 Flat. Diameter 11940 11310 10700 10080 9450 8850 8260 7710 7260 Hinged. thick. lUiiU 9400 8690 8070 7410 6770 6180 ODoU Round. R= 4.03 11770 11150 10550 yyou yiou yu-iu oD /U 8280 7820 Fixed. 10 ins. 11770 11150 10540 9950 9370 oooU Q9Qn 7780 7290 Flat. Diameter. 10730 9990 9230 8520 7830 7300 6770 6270 5790 Hinged. 34 "thick. 7960 7180 6450 5750 5230 4730 Q7Qn o/OU Round. R= 3.37 10170 9460 8970 QA on o^yu /y4U 7350 DOOO 6380 5910 Fixed. 8 ins. 10130 9410 8710 8050 7420 OoiU 5660 5120 Flat. Diameter. 8760 7870 7180 6540 5920 5310 4710 4110 3560 Hinged. % " thick. 6680 5790 5120 4500 3900 QQg'' thick. Round. R = 0.66 179 STEEL COLUMNS.— No. 16. SQUARE SECTION. GREATEST SAFE LOADS IN POUNDS FOR SQUARE I N CH O F S ECTIO N FOR MEDIUM STEEL. By this table for the same ratios of — - the safe loads are increased 5 per cent, over the results obtained for previous tables, as given in table No. 4. Size of Column. 12 ins. Side. I" thick. iJ= 4.65 10 ins. Side. \" thick. B= 3.87 8 ins. Side. ^" thick. R = 3.07 6 ins. Side. I' thick. B = 2.30 6 ins. Side, i" thick. i2= 1.89 4 ins. Side. I" thick. R= 1.53 3 ins. Side, thick. i2= 1.15 !J ins. Side. I" thick. R= 0.77 Condi- tion of Ends. Fixed. Flat. Hinged, Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged, Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. LENGTH IN FEET. 14 IG Greatest safe load in pounds per square inch of section. 23000 2300o'2300o!22400'l8580 15960 1478o'l402o!l3490 23000|23000 2300012240018580 15960 14780 14020^13490 23000 23000 23000121650 17850 15240 14070 13240 12610 23000 23000|23000 20680;i651014190il2960 11950 11200 23000 23000:23000 23000 23000 23000 23000 23000 23000 23000 23000|23000 23000 23000 20220 23000 23000:20220 23000 2300019480 23000 23000 18120 23000 23000 23000 23000 23000 23000 23000 23000 23000 23000 22190 22190 21440 20470 15910 15910 15190 14140 19240 15960 1458013760 13260 12790 19240'15960 14580!l3760 1326012790 18510'l5240 13880;i2950 1232011820 17180 14190 12730j 1 1620| 108501 101 30 15870 14300 13450 12890 1205011320 15870:14300:i345012890 1205011320 15160il3580;i2570|ll93011090 10280 14120123501115010250, 9320 8410 23000 22190 15870 13960|l311012040 11080 10230 23000 22190 15870 1396013110!l2040 11080 10220 21440:i515013170 12120 1109010050 9010 20460141101187010550 9320 8130 7060 18850 14440 13190 11980 18850 14440 13190 11980 18110 13740112220 11000 167701255010720 9210 15840 13440 12030 10630 9420 15840 13440 12030 10630 9380 10820 10820 9740 7830 15130 12550 11070 1409011130 9300 13960 12040 13960 12040 13170 11090 10870 9320 12060 12060 11110 9350 9460 9420 8050 6070 10230 10220 9010 7060 7680 7190 5750 3830 9520; 7990, 7590 6020 4780: .3780 9810 8900 9780 8810 8490: 7330 6510 5350 8480 7630 8200 7130 6740: 5700 8760 8610 7140 7650 7150 5720 5160 3790 5970 5260 3780 2200 4320 3610 2290 1320 6440 5390 5840 4630 4390 2640 3150 1830 1300 9390 9390 8010 6030 8260 7890 6440 4490 6670 6130 4700 2860 427i; 3580 2260 3080 2300 26001 2020 1510j 1100 8501 630 1800 1530 830 460 180 STEEL COLUMNS.— No. 16. SQUARE SECTION. GREATEST SAFE LOADS IN POUNDS PER SQUARE INCH OF SECTION FOR MEDIUM STEEL. The calculations are based on the thicknesses and radii of gyration marked under the diameters in marginal columns. See previous description. LENGTH IN FEET. 20 22 24 26 28 30 32 34 36 Greatest safe load in pounds per square inch of section. Condi- tion of Ends. Size of C'olumn. 13150il26801211o|ll6401115o|l0720 10300 9900 1315012680 1211011640 11150 10720 10290l 9880 12160 11720'11160 10650 10140 9620 9100 8600 10610 10010 9400 8780 8220 7700 7160 6630 12090 11550 10970 12090 11550 10970 1115010530 9920 9380 8660 7990 10650 10650 9550 7610 8760 8610 7140 5160 7540 7030 5600 3680 5920 5200 3710 2150 3390 2840 1700 950 10030 10020 8770 6810 8230 7860 6410 4450 6750 6220 4800 2940 5090 4330 2880 1680 10450 9970 10450 9950 9300 8690 7360 6720 9440 8900 8500 9400 8810! 8230 8020' 7330 6770 6040 5350 4800 7650 7150 5720 3790 6130 5460 3990 2350 4250 3560 2240 1290 2780 2280 2370 2000 1320 1090 760 630 7000 6480 5050 3170 5500 4740 3260 1880 3590 2990 1820 1020 1920 1670 890 520 6440 5830 4390 2640 4800 4050 2630 1540 3040 2570 1480 830 1660 1370 740 420 9500 9460 8100 6110 8110 7690 6240 4290 5940 5220 3730 2170 4140 3460 2170 1240 2640 2260 1250 720 9040 8980 7520 5530 7650 7160 5730 3800 5390 4630 3160 1830 3620 3010 1840 1030 2270 1990 1080 620 8700 8530 7060 5080 7170 6660 5220 3330 4830 4070 2650 1550 3150: 2660 1550 870 1970 1740 930 540 Fixed. Flat. 8110 Hinged 6120 Round. 9510 9470 8390 8080 6620 4660 6690 6160 4730 2890 4270 3580 2260 1300 2810 2390 1330 770 1780 1500 810 450 Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Round. Fixed. Flat. Hinged. Rouud. 13 ins. Side. I" thick. -R= 4.65 10 ins. Side. I" thick. i2= 3.87 8 ins. Side. 5" thick. ! Jt = 3.07 6 ins. Side. I' thick. R = 2.30 5 ins. Side. I" thick. i2= 1.89 4 ins. Side. J" thick. R= 1.53 3 ins. Side. /b" thick. R= 1.15 % ins. Side. \" thick. R=o.n 181 MOMENTS OP INERTIA OF STANDARD SECTIONS. When not otherwise specified, the inertia is the greatest around centre of gravity, or for horizontal axis in figures. A — total area of section. <>!> I Beam Section. l-kh y s = taper of flange. l — K g. J bh^ — cP I cs^ I csP^ I, axis X y — + Ti + 9 + Channel Section. s = taper of flange. s r ■- b—t bW I, axis xy ~~ 12 —Ad\ d t X Deck Beam Section. s = taper of flange. a = area of bulb s o = m — TT ^^^^^ 9 I ^ I 1 t 3' 4^ , jw - k)B 64 12 m3 (6 — I) , ( 6 — , s{b — t) 0 ^ 3 36 2 * ~ b^ T, axis a;?/ 12:4 12 12 ("+3) 2^ 182 6 Tee Section. ^ _ic^ bd^ — {b — t) ^~ 3 J . fb^-{- (h — f) I, axis xy=-' ' — — '-^ d 12 _b p-ht jh^ -P) ~ 2 A J, '\, 'i \\ Angle Section. ^^tf_±bd^-ib-JHd^tZ_ For even or uneven angles, T ...i - 1 ib-d,)^+ hd,^- jh-f) {d,-t)\ '1/ For uneven angles. xy passes through centre of gravity parallel to ee. 2d'^ — 2{d — ty-\-t\b—(2d—^ y I axis xy = ^ <—-^. even angles. For A close approximation for the latter is the following : ^ I Ab^ \ I, axis a;?/ = 25 • For even angles. AhW I, axis xy = 13 {p-i^y^y For uneven angles. A close approximation for 7, axis xy is 4- '1 i \ \ I. axis xy X A in which o = long leg ; c = short leg ; A =area of angle ; i? is a constant which will vary with the ratio of length of legs as follows : Even Legs B = 12.75. Ratio of Legs 1 : B = 12.9. Ratio of Legs 1 : If =13.4 Ratio of Legs 1 : IJ 5 = 13.L Ratio of Legs 1 : 2 j5=13.7 = i> J • even and uneven angles. 183 a = O A • ^ O'" uneven angles. In uneven angles the distance from centre of gravity in direction of the long leg exceeds that in the direction of the short leg by half the difference in the length of the two legs. In angles and tees of equal legs and thickness d = l^-\-^t ^ nearly. Inertia of Compound Shapes. "The moment of inertia of any section about any axis is equal to the Jabout a parallel axis passing through its cen- tre of gravity + the area of the section multiplied by the square of the distance between the axes." By use of this rule, the moments of inertia or radii of gyra- tion of any single sections being known, corresponding val- ues can readily be obtained for any combination of these sections. /-f^ Example No. 1.— A combination of two 9^^ channels of 3.89 square inches ^ section, and two 12 X } plates as shown. i E C- '*^'"b Axis A B op Section. /for two channels, col. V, page 192, = 95.78 /for two plates = ^2 = .03125 1 6 (area of plates) X 4f ^ ^ 128.34375 i = 128.376 /for combined section ■= 224.155 whicli divided by area (13.78) gives 16.27 = or 4.03 radius of combined section. Axis C D. Find distance d = (.60) from page 193, then obtaining the distance (4.17) between axes CD and E F. 184 / for two channels around axis EF from col. VI, = 3.54 Area of channels X sq. of dist. = 7.78 X 4.17* = 135.286 i for two plates = = 72. I for combined section = 210.826 J, „ ,. /210.826 Kadius of gyration = .» I = o.yi By similar methods, inertia or radius of gyration for any combination of shapes can readily be obtained. Tpfe^^^^ Example No. 2. — A "built-up beam" com- '4 LIJ posed of: 4 anglea 3'' X 3'' X V'. f 2 plates 8^^ X -T~^B 1 plate 15'^ X Axis A B. Jof two8^^ X i plates = ^-^^X2= .167 + 8 (area) X 7f (sq. of distance d) = 480.5 J of one 15^^ X I plate _ 15^ X f ^ 12 I of four 3 X 3 X i angles = 4 X 1.25 = 5 00 + 5.76 (area) X 6.66^ (sq. of distance c^) =255.488 480.667 105.469 260.488 Inertia of combined section around A B = 846.624 [846.624 Radius of gyration . = 6.61 Radius of Gyration op Compound Shapes. In the case of a pair of any shape without a web the value of R can always be readily found without considering the moment of inertia. The radius of gyration for any section around an axis parallel to another axis passing through its centre of gravity is found as follows : 185 Let r = radius of gyration around axis through centre of gravity. R = radius of gyration around another axis paral- lel to above, d — distance between axis. R = y^d^ + r"^. When r is small, R may be taken as equal to d without material error. Thus, in the case of a pair of channels lat- ticed together, or a similar construction. Example No. 1. — Two 9^^ channels of 3.89 square inches sec- tion placed 5. 68^^ apart, required the radius of gyration around axis C D for combined section. Find in col. X, page 192, r = .67 and = 0.45. Find distance from base of channel to neutral axis, same page, = .60, this added to one half the distance between the two bars, 2.84^^ -- Z.W d, and d^ = 11.8336. Radius of gyration of the pair as placed = |eo"c ir A 1 c |/11.8336 + 0.45 = 3.505 The value of R for the whole section in relation to the axis A B is the same as for the single channel, to be found in the tables. Example No. 2. — Four 3^^ X 3^^ X angles placed as shown, form a column of 10 inches square ; required the radius of gyra- tion. Find in column VIII, page 207, r - .93 and = .8649. Find distance from side of angle to neutral axis, same page, = .84. Sub- tract this from half the width of col- umn = 5. — .84 = 4.16 = d or dis- tance between two axes, = 17.3056. Radius of gyration of four angles as placed = 1/17^3056 +^-8649 = 4.26. When the angles are large as compared with the outer dimensions of the combined section, the radius of gyration can be taken without serious error from the table of radii cf gyration for square columns, on page 177. u D 186 ELEMENTS OF PENCOYD STRUCTURAL SHAPES. In the following tables various fundamental properties of rolled sections are given, whereby the strength or stiffness of each can be readily determined. The calculations are made for all sections of I beams and channels, and for the least and greatest thickness of other shapes ; intermediate thicknesses of these can be approxi- mated by interpolation. Moments of Inertia for the sections are obtained as here- after described. Radius of Gyration equals \\ is used for deter- \ area mining the resistance of struts or columns. Moment of Resistance equals ^ j ?5?!?i?L_^ ^_ distance from axis to extrsme libres is used for determining transverse strength in beams, etc., as described on page 116. CoEFFiCENT FOR Safe Load is the calculated load in net tons, on a beam one foot between supports, that produces fibre strains of 16,000 lbs. per square inch. A corresponding load for any beam is found by dividing this coefficient by the length of span in feet. Coefficients for Deflection are found by the formulae on page 220, based on a modulus of elasticity of 28,000,000 lbs. They apply to beams one foot long, bearing one ton (2,000 lbs.) The deflection of any beam in inches is found by multiplying its coefficient by the load in net tons and by the cube of tlie length in feet. Maximum Load in Net Tons indicates the greatest load that a beam, however short, should carry, unless its web is reinforced, to prevent crippling. This load is obtained by the formula : X = 8 tons. xd i d = depth of beam. , I = thickness of web. ~t" 3000<^ l = d X secant 45° {P = 2(P). 187 ELEMENTS OF PENCOYD BEAMS. I. II. III. IV. V. VI. VII. VIII. Size in Inches. Section Number. Area in Square Inches. Weight per Fool in Pounds. Moments of Inertia. Square of Radius of Gyration. Axis A. B. Axis C. D. Axis A. B. Axis C. D. 24 240B 23.53 80 91 1 1 An AO fM. '±ci.ty± RQ 78 1 89 24 241B 24.99 85 9181 R7 AA -{A 87 8n 1 77 24 242 li 26.47 90 2356.76 54.38 89.07 2.06 24 243B 27.92 95 2427.03 55.93 86^93 2!oo 24 244B 29 42 100 2497.30 57.53 84.88 1.96 20 200B 19.10 65 1179 71 97 79 R1 7R 01. /D 1 20 201B 20.58 70 1 99Q nd. 9ft 87 f^Q 79 1 An 20 202B 22.04 75 1 977 71 OU.UO f^7 07 o/.y / 1 8R i.oO 20 203B 23.53 80 1404 39 98 9A RQ oy.oy 1 Rc^ i.OO 20 204B 25.01 85 A.'iDO.UO t^a in 1 R1 i.Ol 20 205B 26.47 90 IRfll 7"^ 41 88 t^R 78 00. lo 1 "^8 i.Oo 20 206B 27.95 95 1601.86 53.63 57.31 1.92 20 207B 29.42 loo 1649.55 55^57 56!07 l!89 18 180B 16.13 55 onn r\Pi ouy.uo 91 17 OU.lD 1 81 18 181B 17.64 60 OAQ QQ 99 99 1 9R 18 182B 19.12 65 ooy. lo 98 8n 1 99 18 183B 20.59 70 Q01 79 8n 98 AH flQ '±1 DO 1 An 18 184B 22.05 75 1AOO CO 81 R7 oi.D/ Afi AO 1 AA 18 185B 23.53 80 iUDo.o/ 88 1 9 45.19 1/11 1.41 18 186B 25.00 85 1149.62 44.18 45.98 1.77 18 187B 26.46 90 1187.99 46.03 44.90 1.74 15 150B 12.35 42 443.71 14.43 35.93 1.17 15 151B 13.23 45 460.30 14.97 34.79 1.13 15 152B 14.70 50 515.22 19.20 35.05 1.31 15 153B 16.17 55 542.84 20.34 33.57 1.26 15 154B 17.64 60 619.02 27.60 35.09 1.56 15 155B 19.11 65 646.58 29.13 33.83 1.52 15 156B 20.60 70 718.71 36.73 34.89 1.78 15 157B 22.05 75 745.99 38.64 33.83 1.75 15 158B 23.54 80 773.84 40.69 32.87 . 1.73 12 120B 9.27 31.5 218.71 9.45 23.59 1.02 12 121B 10.29 35.0 230.95 10.01 22.44 0.97 12 122B 11.77 40.0 274.68 14.26 23.34 1.21 12 123B 13.23 45.0 292.25 15.41 2209 1.16 12 124B 14.70 500 332.08 20.79 22.59 1.41 12 125B 16.17 55.0 368.06 25.12 22.76 1.55 12 126B 17.64 60.0 385.77 26.96 21.87 1.53 12 127B 19.12 65.0 403.48 28.93 21.10 1.51 188 IX. XI. XII. XIII. XIV. XV. IV. I. Radius of Gyration. Resist- ance. Coef.for Greatest Safe Load in Net Tons. Coefficient for Deflection. Max. Load in Net Tons. Weight per Foot in Lbs Size in In. A. B. C. D. Axis A. B. Distributed Load. Center Load. 9.47 1.35 176.0 938.4 .00000076 .00000122 37.9 80.0 2A 9.34 1.33 181.8 969.6 .00000073 .00000117 48.5 85.0 24 9.44 1.44 196.4 1047.4 .00000068 .00000109 48.3 90.0 24 9.32 1.41 202.3 1078.7 .00000066 .00000106 59.7 95.0 24 9.21 1.40 208.1 1109.9 .00000064 .00000103 71.7 100.0 24 7.86 1.20 1 1 p n iXo.U 629.2 .00000137 .00000217 37.1 65.0 20 7.73 1.18 122.9 655.5 .00000130 .00000209 49 1 7.61 1.17 127!8 681.5 .00000125 .00000200 61.5 75.0 20 7.73 1.28 140.4 749.0 .00000114 .00000183 60.3 80.0 20 7.62 1.27 145.3 775.0 .00000110 .00000176 73.1 85.0 20 7.53 1.26 150.2 800.9 .00000106 .00000171 86.8 90.0 20 7.57 1.39 160.2 864.1 .00000100 .00000160 79.3 95.0 20 7.49 1.37 165.0 889.8 .00000097 .00000155 92.4 100.0 20 7.08 1.14 QQ Q oy.y 479.4 .00000198 .00000317 32.8 55.0 18 6.94 1.12 503.6 .00000188 .00000302 45.3 60.0 18 6.82 1.10 98,9 527.3 .00000180 .00000288 00. 1 DO.U 1 Q 6.91 1.21 109! 1 581.8 .00000162 .00000261 57.2 70.0 18 6.81 1.20 113.7 606.5 .00000156 .00000250 70.9 75.0 18 6.72 1.19 118.2 630.2 .00000150 .00000241 84^2 80.0 18 6.78 1.33 127.7 689.9 .00000139 .00000223 76.0 85.0 18 6.70 1.32 132.0 712.9 .00000135 .00000216 89.1 90.0 18 5.99 1.08 59.2 315.5 .00000357 .00000578 23.8 42.0 15 5.90 1.06 61.4 327.3 .00000348 .00000557 31.2 45.0 15 5.92 1.14 68.7 366.4 .00000311 .00000498 35.1 50.0 15 5.79 1.12 72.4 386.0 .00000295 .00000472 48.1 55.0 15 5.92 1.25 82.5 440.2 .00000258 .00000414 44.7 60.0 15 5.82 1.23 86.2 459.8 .00000247 .00000397 57.8 65.0 15 5.91 1.33 95.8 511.1 .00000223 .00000357 54.9 70.0 15 5.82 1.32 99.5 530.5 .00000214 .00000344 68.0 75.0 15 5.73 1.32 103.2 550.3 .00000207 .00000331 81.3 80.0 15 4.86 1.01 36.5 194.4 .00000727 .00001172 17.8 31.5 12 4.74 0.99 38,5 205.3 .00000693 .00001110 26.6 35.0 12 4.83 1.10 45.8 244.2 .00000582 .00000933 26.1 40.0 12 4.70 1.08 48.7 259.8 .00000547 .00000877 39.2 45.0 12 4.75 1.19 55.4 295.2 .00000482 .00000772 40.1 50.0 12 4.77 1.25 61.3 327.2 .00000435 .00000697 40.9 55.0 12 4.68 1.24 64.3 342.9 .00000415 .00000665 54.2 60.0 12 4.59 1.23 67.3 358.7 .00000397 .00000635 67.2 65.0 12 189 I. II. III. IV. V- VI. VII. VIII. Size ill Inches. Section Number. Area in Square Inches. Weight Foot in Lbs. Moments of Inertia. Square of Radius of Gyration. Axis A.B. Axis CD. Axis A. B. Axis CD. 10 lOOB 7.34 25.00 123.07 6.81 0.93 10 lOlB 8.82 30.00 135.41 7.58 15.35 0.86 10 102B 10.27 35.00 163.14 11.19 15.89 1.09 1 n 11. /o An nn 175.48 12.36 14.93 1.05 9 90B 6.17 21.00 84.94 5.06 13.77 0.82 9 91B 7.34 25.00 92.83 5.60 12.65 0.76 9 92B 8.82 30.00 102.80 6.37 11.66 0.72 9 93B 10.30 35.00 112.76 7.25 10.95 0.70 8 SOB 5.29 18.00 57.36 3.72 10.84 0.70 8 BIB 6.03 20.50 61.29 4.02 10.16 0.67 8 82B 6.77 23.00 65.21 4.35 9.63 0.64 8 83B 7.50 25.50 69.14 4.70 9.22 0.63 7 70B 4.42 15.00 36.61 2.64 8.28 0.60 7 71B 5.15 17.50 39.58 2.90 7.69 0.56 7 72B 5.88 20.00 42 55 3 20 7.24 0.54 6 60B 3.60 12.25 22.09 1.83 6.14 0.51 6 61B 4.34 14.75 24.28 2.06 5.59 0.48 6 62J? 5.07 17.25 26.50 2.34 5.23 0.46 5 5313 9.49 32.30 51.79 11.66 5.46 1.23 to to 6 63B 10.99 37.40 56.29 13.78 5.12 1.25 6 67B 12.06 41.00 63.87 18.23 5.30 1.51 to to 6 67B 13.56 46.10 68.37 21.22 5.04 1.56 5 50B 2.87 9.75 12.12 1.21 4.22 0.42 5 51 B 3.60 12.25 13.66 1.42 3.79 0.40 5 52B 4.34 14.75 15.18 1.67 3.50 0.39 4 40B 2.20 7.50 5.90 0.76 2.68 0.34 4 41B 2.50 8.50 6.29 0.83 2.52 0.33 4 42B 2.79 9.50 6.68 0.91 2.39 0.33 4 43B 3.08 10.50 7.07 1.00 2.30 0.32 3 SOB 1.62 5.50 2.43 0.45 1.50 0.28 3 31 B 1.91 6.50 2.64 0.51 1.38 0.27 3 32B 2.20 7.50 2.87 0.59 1.30 0.27 190 ELEMENTS OF PENCOYD BEAMS. IX. 1 ^- XI. Resist- ance. XII. XIII. 1 XIV. XV. IV. I I. Radius of Gyration. Coef.for Greatent SafeLoa( Coefficient for Deflection. Load in Net Tons. ]Veight Foot in Lbs. Size in Ins. A-Xia A. B. A xis CD. Axis A. B. in Net Tons. DisiTibiited Load. (JenieT Load. 4.10 0.96 24.6 131.3 .0000129 .0000208 13.5 25.00 — 10 3.92 0.93 27.1 144.4 .0000118 .0000189 26.6 30.00 10 3.99 1.04 99 ft 1 HA n 1/4.U nnnnnQS nnnm "iS .U\J\J\J ±\JO 26.2 35.00 10 3.86 1.03 35.1 187.2 .0000091 .0000146 39.4 40.00 10 3.71 0.91 18.9 100.7 .0000185 .0000302 10.6 21.00 9 3.56 0.87 20.6 110.0 .0000172 .0000276 20.9 25.00 9 3 41 U.oO 22.8 1 91 ft .UUUUiOD .UUUUii49 QA 1 30.00 9 3^31 0.84 25!l 133.6 .0000142 .0000227 46.9 35.00 9 3.29 0.84 14.3 76 5 .0000275 .0000447 Q 7 a. / lO.UU g 3 19 15.3 8L7 .UUUUiiOi r\r\r\r\/\ 1 Q .UUUU4io 16.3 20.50 8 3.10 0.80 1 ft Q 87.0 .0000245 .0000393 22.9 23.00 8 3.04 0.79 17.3 92.2 .0000231 .0000371 29.4 25.50 8 2.88 0.78 10.5 55.8 .0000433 .0000700 8.6 15.00 7 9 77 \J. ID 11. 0 60.3 nnnri/in/i .UUUU4U'3: .UUuUd4o 15.1 17.50 7 2.69 0.74 12.2 64.8 .0000376 .0000603 21.6 20.00 7 2.48 0.71 7.4 39.3 .0000717 .0001161 6.9 12.25 6 2.36 0.69 8.1 43.2 .uuuuDoy .UUUiUOD 13.5 14.75 6 2^29 o!68 D Q O.O 47.1 .0000604 .0000968 19.9 17.25 6 2.34 1.11 17.3 92.1 .0000310 .0000495 21.9 32.30 6 2.26 1.12 18.8 100.1 .0000286 .0000456 34.6 to 37.40 6 2.30 1.23 21.3 113.6 .0000251 .0000401 28.5 41.00 6 2.25 1.25 22.8 121.6 .0000235 .0000375 40.7 to 46.10 6 2.05 0.65 4.9 25.9 .0001305 .0002115 5.5 9.75 5 1.95 0.63 5.5 29.1 .0001171 .0001877 12.1 12.25 5 1.87 0.62 6.1 32.4 .0001054 .0001689 18.4 14.75 5 1.64 0.58 3.0 15.7 .0002671 .0004346 4.1 7.50 4 1.59 0.57 3.2 16.8 .0002544 .0004076 6.7 8.50 4 1.55 0 57 3.3 17.8 .0002395 .0003838 9.2 9.50 4 1.52 0.57 3.5 18.9 .0002263 .0003627 11.7 10.50 4 1.23 0.53 1.6 8.6 .0006452 .0010552 2.7 5.50 3 1.17 0.52 1.8 9.4 .0006061 .0009713 5.3 6.50 3 1.14 0.52 1.9 10.2 .0005575 .0008934 7.8 7.50 3 191 ELEMENTS OF PENCOYD CHANNELS. I. Size in Ins. II. III. IV. V. 1 VI. VII. 1 VIII. IX. X Section Area Square Inches. Weight per Fool in Lbs. Moments of Inertia. Sqvareof Had. of G-y ration. Radius of Cryration. Axis A. B. Axis C. D. Axis A. B. Axis a D. Ans A.B. A xts 0. D. 15 150C 9.69 33.0 311.21 8.10 32.12 0.84 5.67 0.91 15 151(! 10.29 35.0 322.46 8.48 31.34 0.82 5.60 0.91 15 1520 11.76 40.0 350.02 9.38 29.76 0.80 5.46 0.89 15 1530 13.23 45.0 377.59 10.29 28.54 0.78 5.34 0.88 15 154C 14.70 50.0 442.29 15.87 30.09 1.08 5.49 1.04 15 155C 16.17 55.0 469.85 17.20 29.06 1.06 5.39 1.03 12 120C 6.02 20.5 129.27 3.90 21.47 0.65 4.63 0.81 12 1210 7.34 25.0 145.11 4.53 19.77 0.62 4.45 0.79 12 1220 8.82 30.0 162.83 5.20 18.46 0.59 4.30 0.77 12 1230 10.30 35.0 207.68 9.32 20.16 0.91 4.49 0.95 12 1240 11.76 40.0 225.25 10.49 19.15 0.89 4.38 0.95 12 1280 6.01 20.5 123.98 3.10 20.63 0.52 4.54 0.72 to to 12 1280 9.40 32.0 164.30 4.42 17.48 0.47 4.18 0.69 10 lOOO 4.41 15.0 67.11 2.28 15.22 0.52 3.90 0.72 10 1010 5.88 20.0 79.36 2.84 13.50 0.48 3.67 0.70 10 1020 7.36 25.0 100.11 4.39 13.60 0.60 3.69 0.77 10 1030 8.83 30.0 112.36 5.16 12.72 0.58 3.57 0.77 10 1040 10.29 35.0 124.61 5.99 12.11 0.58 3.48 0.76 9 900 3.89 13.25 47.89 1.77 12.31 0.45 3.51 0.67 9 910 4.41 15.00 51.35 1.95 11.64 0.44 3.41 0.67 9 920 5.88 20.00 66.97 3.19 11.39 0.54 3.38 0.74 9 930 7.35 25.00 76.93 3.89 10.47 0.53 3.24 0.73 8 80C 3.31 11.25 32.51 1.32 9.82 0.40 3.13 0.63 8 81(.' 4.04 13.75 36.43 1.55 9.02 0.38 3.00 0.62 8 820 4.78 16.25 44.00 2.33 9.21 0.49 3.03 0.70 8 830 5.51 18.75 47.93 2.65 8.70 0.48 2.95 0.69 8 840 6.25 21.25 51.85 2-97 8.30 0.48 2.88 0.69 192 ELEMENTS OF PENCOYD CHANNELS. A C— [i + A-T.-D I B XI. XII. XIII. XIV. XV. XVI. I. Dislance "d" from Bane to Ni' III nil A .ri,'i. Ilesist- Coef. for Greatest Safe Load ill Net Tons. Coefficient for Deflection. Max. Load in Net Tons. Size Ins. Axis A. B. Distributed Load. Center Load. 0.79 41.5 221.3 .00000514 .00000826 22.5 15 0.78 43.0 229.3 .00000496 .00000796 27.4 15 0.78 46.7 248.9 .00000457 .00000734 40.0 15 0.78 50.4 268.5 .00000424 .00000681 53.1 15 0.94 59.0 314.5 .00000362 .00000581 54.5 15 0.95 62.7 334.1 .00000340 .00000546 67.7 15 0.70 21.6 114.9 .00001237 .00001986 11.7 12 0.67 24.2 129.0 .00001103 .00001771 22 5 12 0.67 27.1 144.7 .00000983 .00001578 35.7 12 0.89 34.6 184.6 .00000770 .00001236 34.7 12 0.89 37.5 200.2 .00000710 .00001140 47.8 12 0.62 20.7 110.2 .00001290 .00002072 12.1 12 0.62 27.4 146.0 .00000974 .00001564 41.2 12 0.64 13.4 71.6 .00002384 .00003838 8.2 10 0.60 15.9 84.7 .00002016 .00003246 20.6 10 0.71 20.0 106.8 .00001598 .00002573 27.4 10 0.73 22.5 119.9 .00001424 .00002293 40.5 10 0.76 24.9 132.9 .00001284 .00002067 53.4 10 0.60 10.6 56.8 .00003341 .00005379 7,8 9 0.59 11.4 60.9 .00003116 .00005017 12.1 9 0.68 14.9 79.4 .00002389 .00003846 19.8 9 0.69 17.1 91.2 .00002080 .00003349 33.1 9 0.57 8.1 43.4 .00004921 .00007923 6.8 8 0.55 9.1 48.6 .00004392 .00007071 13.2 8 0.65 11.0 58.7 .00003636 .00005854 15.4 8 0.65 12.0 63.9 .00003338 .00005374 22.0 8 0.66 13.0 69.1 .00003086 .00004968 28.5 8 193 ELEMENTS OF PENCOYD CHANNELS. A B T X. III IV. V. VI. VII. VIII. IX. X. Size in Ins. Section No. Area in Square Inches. Weight Foot in Lbs. Moments of Inertia. Square of Had. of Gyration. Radius of Gyration. Axis A. B. Axis C. D. Axis A. B. Axis a D. Axis A. B. Axi.'i CD. 7 70C 2.86 9.75 21.37 0.98 i.4n 0.34 2.73 0.59 7 710 3.60 12.25 24.37 1.19 6.77 0.33 2.60 0.58 7 720 4.34 14.75 29.85 1.89 6.88 0.44 2.62 0.66 7 730 5.07 17.25 32.85 2.18 6.48 0.43 2.55 0.66 7 740 5.81 19.75 35.85 2.49 6.17 0.43 2.48 0.66 6 60O 2.35 8.00 13.07 0.69 5.56 0.29 2.36 0.54 6 610 3.09 10.50 16.23 1.08 5.25 0.35 2.29 0.59 6 620 3.82 13.00 18.43 1.32 4.83 0.35 2.20 0.59 6 630 4.56 15.50 20.64 1.57 4.53 0.34 2.13 0.59 5 50C 1.91 6.50 7.37 0.47 3.86 0.25 1.96 0.50 5 510 2.64 9.00 8.90 0.64 3.37 0.24 1.84 0.49 5 520 3.38 11.50 10.43 0.82 3.09 0.24 1.76 0.49 4 40O 1.54 5.25 3.74 0.32 2.43 0.21 1.56 0 45 4 410 1.84 6.25 4!l3 o!38 2!24 0^21 liso o!45 4 420 2.13 7.25 4.52 0.44 2.12 0.21 1.46 0.46 3 30O 1.18 4.00 1.61 0.20 1.36 0.17 1.17 0.41 3 310 1^47 5!oo 1.83 0.25 1.24 0.17 1.11 0.42 3 320 1.76 6.00 2.05 0.31 1.16 0.18 1.07 0.42 220 1.12 3.80 0.80 0.19 0.71 0.17 0.85 0.42 2 20O 0.87 2.90 0.48 0.08 0.55 0.10 0.74 0.31 2 20O 1.06 3.60 0.54 0.11 0.51 0.10 0.71 0.32 1% 170 0.33 1.13 0.15 0.01 0.46 0.03 0.67 0.16 194 ELEMENTS OF PENCOYD CHANNELS. c-R-^-L-i-.-n xr. XII. XIII. XIV. XV. XVI. I. Size in Inches. Dislan c "d" from Base to Neutral Axis. Resis- tance. ^'Oej.jov Greatest Safe Load in Net Tons. Coefficient for Deflection. Maxim. Load in Net Tons. A^B. Distributed Centre 0.54 6.1 .00007487 .00012054 0.0 7 0.52 7.0 37.1 .00006565 .00010570 13.2 7 0 62 8 5 45.5 .00005360 .00008630 16 0 7 0^63 9^4 50!l .00004870 .00007841 22^6 7 0.65 10.2 54.6 .00004463 .00007185 28.9 7 0 51 A A. 23 2 .00012242 .00019709 5.4 5 0.56 5.4 28!9 .00009858 .00015871 io!o 6 0.57 6.1 32.8 .00008681 .00013976 16.5 6 0.59 6.9 36.7 .00007752 .00012481 22.9 6 0.49 3.0 15.7 .U0Uo49o>5 4.6 5 0.48 3.6 19.0 .00017977 .00028943 11.1 5 0.50 4.2 22.3 10.7 5 0.46 1.9 10.0 .00042781 .00068877 4.1 4 0.45 2.1 11.0 .00038741 .00062373 6.7 4 0.46 2.3 12.1 .00035398 .00056991 9.2 4 0.43 1.1 5.7 .00099377 .00159997 3.0 3 0.43 1.2 6.5 .00087432 .00140765 5.5 3 0.45 1.4 7.3 .00078050 .00125660 8.0 3 0.47 0.7 3.8 .00200000 .00322000 4.3 2\ 0.36 0.5 2.6 .00333333 .00536666 3.3 2 0.37 0.5 2.9 .00296980 .00478138 4.8 2 0.18 0.2 0.9 .01066672 .01717342 1.0 1% 195 SEPARATION OF CHANNELS IN IiATTICEL> STRUTS. Tabulated distances " d" and " D" make radii of gyration the same for both axes. . For a Single § For a Single 1 C/iiuaiel. % Channel. e '■~ g s ■5 < 3 ^ 1^ ^ -9 II 150i ' \ 15 33.0 9.69 y.oy 1 9 7 9.75 2.86 4.26 6.42 151(' 15 35.0 10.29 9.49 1 O ftl iZ.Di n 1 12.25 3.60 4.03 6.11 152( ' 15 40.0 11.76 9.20 12.32 720 7 14.75 4.34 3.83 6.32 153(' 15 45.0 13.23 8.98 12.10 730 7 17.25 5.07 3.66 1 6.18 154(' 15 50.0 14.70 8.89 12.65 740 7 19.75 5.81 3.49 6.09 155C 15 55.0 16.17 8.68 12.48 60O 6 8.00 2.35 3.58 5.62 i2or; 12 20.5 6.02 7.73 10.52 610 6 10.50 3.09 3.31 5.55 121(J 12 '25.0 7.34 7.41 10.09 62(:; 6 13.00 3.82 3.09 5.37 122(] 12 30.0 8.82 7.11 9.79 630 6 15.50 4.56 2.91 5.27 1230 12 35.0 10.30 6.99 10.56 1240 12 40.0 11.76 6.76 10.33 50O 5 6.50 1.91 2.82 4.78 1280 12 ;20.5 6.01 7.73 10.21 510 5 9.00 2.64 2.58 4.50 1280 12 '32.0 1 9.40 7.00 9.49 520 5 11.50 3.38 2.37 4.37 lOOO 1 10 15.0 4.41 6.39 8.95 40O 4 5.25 1.54 2.06 3.90 lOlO 10 i20.0 5.88 6.01 8.42 410: 4 6.25 1.84 1.96 3.76 102(! 103O 10 !25.0 10 130.0 7.36 8.83 5.81 5.51 8.65 8.43 420 4 7.25 2.13 1.85 3.70 1040 10 135.0 10.29 5.27 8.31 30O 3 4.00 1.18 1.32 3.05 90O 910 913.25 9 15.00 3.89 4.41 5.68 5.52 8.08 7.88 310 320 3 3 5.00 6.00 1.47 1.76 1.21 1.09 2.93 2.89 92(J 9 120.00; 5.88 5.23 7.95 930 9 25.00 7.35 4.92 7.68 220 21 3.80 1.12 0.54 2.42 800 8 11.25. 3.31 5.00 7.28 20C 2 2.90 0.87 0.64 2 08 00 813.75 4.04 4.78 6.98 20O 2 3.60 1.06 0.54 2.02 820 8 16.25, 4.78 |4.60 7.20 830 840 8 8 18.75' 5.51 '21.25 6.25 1 1 4.43 4.27 7.03 6.91 170 1.1 1.13 0.33 j 0.94 1.66 196 ELEMENTS OF Z BAR COLUMNS. /= Mom. of Inertia. Y n : ( r c L Y i2=Rad. of Gyration. The Thicknesses of Web Plate and Z Bars are the same. Size (if 7j Bar in inches. 3i x6 z3i xj 3i»gX6J;X3iH;Xi' 3^ x6.^ x3i x% 3i x6" x3i x|»_ 3i-',jx6iVx3,96- x| 3J x6| x3g x}f 3i x6 x3!v X I 3-Sjx6,Vx3;9;xit1 3f x6i x3f X - 3^^(fX5 x3i%Xy'}, 3\ x5Jijx3i X ■■ 3,-^x5J x3i5gx-f« 3,f,x5 x3/^xi 3iIx5J x3Vix| 'i\xb xSi'x^ii 3r'^,x5Ji;x3j_5jx| 2|^x4^ x2 j"xi 21§x4Tijx2iix^; 3 x4J x3 X I 231x4 x23ixf^; 3:^;x4^x3,';x \ 3, 1x4 J x3;^^XiH. 3^x4 x3i^x I 3i x4-iijx3J x\l 3v'cx4i_x3j%^| 2;; x3 ~x2fn 2}ix3,Vx2'iixiS 2,1 x3J x2| X i 2':^ix3 x2|Jxit 2||^fgx2i|xJ 7'' TFe6 Plate. 'l'%"Face to Face. Area ofkX Bars and ] Plate. Axis A'A'. I. i2. I. 20.99 264.11 3.55 287.85 3.70 24.62 306.46 3.53 346.98 3.75 28.26 347.80 3.51 409.27 3.80 30.66 365.19 3.45 426.34'3.73 34.22402.96 3.43 489.21 3.78 37.81l440.31 3.41 555.79 3.83 39.81'448.24 3.36 562.39 3.76 43.21 481.03 3.34'628.18 3.81 46.77l514.64 3.32'699.1i:3.87 7" Weh Plal(i^%"Face to Face. 15.63193.88 3:52[147.41|3.07 18.83 231.00'3.50!l83.49!3.12 22.06 267.64 3.48:222.06'3.17 24.42 287.66'3.43'234.48'3.10 27.58,321.15'3.41:273.70 3.15 30.78 354.333.39 315.67 3.20 32.65,'364.87 3.34 320.05 3.13 35.81395.55 3.32,363.02 3.18 G" Wrb P/ale.r^%"Face to Face. 10.78,101.90,3.07 ^65.7112.47 13.52ll26.14 3.05 85.80|2.52 16.33|150.56 3.04 107.8712.57 18.47il66.03 3.00115.6212.50 21.24188.60 2.98 138.66i2.55 24.02 210.64 2.96ll63.07|2.60 25.95 221.78 2.92167.28:2.54 28.69 242.16 2.91I192.77I2.59 31.50,262.652.89,220.5112.64 6" mi) Plate.&-4"Faeeto Face. 9.26 84.7813.03 11.64 105.17 3.01 14.01 125.10 2.99 15.63 134.64 2.93 18.00153.14 2.92 31.741.85 41.891.90 53.4l!l.95 55.241.88 67.171 1.93 V'Weh Plate. «%" Fa ce to Fac e. Area ofiX Bars and 1 Plate. Axis XX. Axis YY. R. 21.36 337.09 3.97287.86 3.67 25.06 391.45 3.951346.99 3.72 28.76 444.60 3.93 409.29 3.77 31.22'469.13 3.88 426.36 3.69 34.841518,08 3.86 489.23 3.75 38.50 566.52 3.83 555.82 3.80 40.56 579.76 3.78 562.43 3.72 44.02:622.55 3.76 628.23 3.78 47.64;666.66^.74:699. 173.83 8" Weh Plate.?,yi"FacK to Face. 15.94 248.26 3.95 147.41|3:04 19.20 295.96 3.92 183.50 3.09 22.50 343.27 3.91 222.07,3.14 24.92 370.54 3.86 234.50 3.07 28.14'414.03 3.83 273.72 3.12 31.40457.20 3.81^315.69 3.17 33.341472.86 3.77;320.08 3.10 36.56j513.07_3.74 363.05l3.15 7' Weh Plate.nVi" Face to Face. 11.03134;7f 3.49, 65.79 2^44 13.83166.94 3.47i 85.80 2.49 16.71 199.42 3.45 107.87 2.54 18.90 220.65 3.42115.63 2.47 21.74 250.89 3,40138.67 2.52 24.58 280.45 3.38 163.08 2.58 26.58 296.36 3.34 167.30 2.51 29.37 323.88 3.32 192.80,2.56 32.25 351.59 3.30 220.55i2.61 V'Weh Pla,te.l\i" Face Face. 9.51 112.6513.44 11.95 139.88 3.42 14.39 166.56l3.40 16.06 180.30;3.35 18.50j205.32 3.33i 31.74 1.83 41.891.87 53.42 1.93 55.25 1.85 67.18 1.90 197 ELEMENTS OP PENCOYD Z BARS. c D 1 1 < Sec. Size in Inches. Area Wt. per Foot Moments of Inertia. Resistance. No. Sq. Ins. Axis Axis Axis Axis Axis Lbs. A. B. C. D. E. F. A . li C* D, - 30Z 2% X 3 X 2% X 34 1.94 6.60 2.81 2.61 0.59 1.9 1.0 31Z 2Ux3Tigx2UxA 2^/4x3±/8x2%x% 2.44 8.29 3.52 3.38 0.74 2.3 1.3 32Z 2.94 10.00 4.34 4.22 0.92 2.8 1.7 33Z 2^ix3 x2Hxi^ 3.25 11.15 4.20 4.24 0.95 2.8 1.7 34Z 2^x3^x2Hx|f 3.51 11.93 4.54 4.64 1.01 3.0 1.9 35Z 2§| X S^Jg X 2§| X 3.75 12.75 4.88 5.04 1.11 3.2 2.0 40Z 27/8 X 4 X 2% X 1/4 2.32 7.88 5.95 3.47 0.95 3.0 1.3 41Z 2Hx4A'X2iixA 3 X 41/8 X 3 X % 2.91 9.89 7.52 4.49 1.23 3.7 1.6 42Z 3.52 11.90 9.14 5.58 1.53 4.4 2.0 43Z 2^1x4 x2MxX 3.96 13.46 9.40 6.09 1.63 4.7 2.2 44Z 3^ X 4 Jg X StjIj X ±^ 33\x4l/8x3^^x^\ 4.56 15.50 10^92 7!21 l!94 5.4 2.6 45Z 5.16 17.54 12.40 8.40 2.27 6.0 3.0 46Z Sfg X 4 X 3^15 X % 5.55 18.80 12.11 8.73 2.32 6.1 3.2 '±1 /-J v3 /8 X * X 0^8 ^ TH 6.14 20.87 13.52 9.95 2.67 6.7 3.6 48Z 33^x41/8x3t^5x!^4 6.75 22.95 14.97 11.24 3.03 7.3 4.0 50Z 3Ax5 xSAxfg 31/4 X SiV X 31/4 X % 3j^x5l/8x3tVxT% 3.36 11.42 13.14 5.81 1.86 5.3 1.9 51Z 4.05 13.77 15.93 7.20 2.28 6.3 2.4 52Z *±* ID 16.15 18.76 8.67 2.75 7.3 2.8 53Z 3^'^ X 5 X 3^ X 1,42 5.23 17.78 19.03 8.77 2.76 7.6 3.0 54Z 3^«2 X X 3^^ X A 34ix5i/8x3Mx% 5.91 20.09 21.65 10.19 3.20 8.6 3.4 55Z 6.60 22.44 24.33 11.70 3.73 9.5 3.9 56Z 31/4 X 5 X 31/4 X U 6.96 23.66 23.68 11.37 3.59 9.5 3.9 57Z 3tV X S^ij X 3^ X ^/4 7.64 25.97 26.16 12.83 4.12 10.3 4.4 60Z 31/2 X 6 X 31,^ x % 4.59 15.61 25.32 9.11 3.11 8.4 2.8 61Z 3 A X X SX X 3%x6i/8x3%xi/2 5.39 18.32 29.80 10.95 3.74 9.8 3.3 62Z 6.19 21.05 34.36 12.87 4.37 11.2 3.8 63Z 31^ X 6 X 31/^ X A 3Ax6^x3AxS/8 3% X 61/8 X 3% X \l 6.68 22.71 34.64 12.59 4.37 11.6 3.9 64Z 7.46 25.36 38.86 14.42 4.92 12.8 4.4 65Z 8.25 28.05 43.18 16.34 5.66 14.1 5.0 66Z 3I/I2 X 6 X 31/2 X \ 3 A X 6Jf; X 3 A X U 3% X 6^8 X 3% X % 8.64 29.37 42.12 15.44 5.61 14.0 4.9 67Z 9.38 31.89 46.13 17.27 6.16 15.2 5.5 68Z 10.16 34.54 50.22 19.18 6.85 16.4 6.0 198 ELEMENTS OF PENCOYD Z BARS. Radii of Gyration. Coef. in Net Tons for Greatest Safe Load Dis. Coef. for Deflection About Axis A. B. Max. Load Sec. No. Axis A. B. Axis C. D. Least. Axis E. F. Mbre Stress 16,000 lbs. Fibre Stress n,000 lbs. Distrib- uted. Centre. in Net Tons. 1.20 1.20 1.21 1.16 1.18 l!20 0.55 0 55 0.56 10.0 12.3 14.'8 ■ 7.5 9 2 nil .0005694|. 0009167 .0004545.0007317 .0003687|. 0005937 5.5 7.2 9.0 30Z 31Z 32Z 1.13 1.14 1.14 1.14 1 15 1^16 0.54 0.54 0.55 14.9 16.0 17!o 11.2 12 0 12!8 .00038091.0006132 .00035241.0005674 .0003279.0005279 10 2 11.1 12.0 33Z 34Z 35Z 1.60 1.61 l!62 1.22 1 24 l!26 0.64 0 65 o!66 15.9 19.7 23.6 11.9 14 8 17!7 .0002689.0004329 .0002128;. 0003426 .0001750.0002817 6.8 9.1 11.5 40Z 41Z 42Z 1.54 1.55 1.55 1.24 1.27 1.28 0.64 0.65 0.66 25.1 28.7 32.1 18.8 21.5 24.1 .0001702 .0001465 .0001290 .0002740 .0002359 .0002077 13.3 15 6 17.9 43Z 44Z 45Z 1.48 1.48 1.49 1.26 1.27 1.29 0.65 0.66 0.67 32.3 35.5 38.7 24.2 26.6 29.0 .0001321 .0001183 .0001069 .0002127 .0001905 .0001721 19.5 21.8 24.3 46Z 47Z 48Z 1.98 1.98 1.99 1.32 1.33 1.35 0.74 0.75 0.76 28.0 33.6 39.1 21.0 25.2 29.3 .0001218 .0001005 .0000853 .0001961 .0001618 .0001373 10.7 13.5 16.4 50Z 51Z 52Z 1.91 1.91 1.92 1.30 1.31 1.33 0.73 0.74 0.75 40.6 45.6 50.6 30.5 34.2 38.0 .0000841 .0000739 .0000658 .0001354 .0001190 .0001059 18.8 21.6 24.5 53Z 54Z 55Z 1.84 1.85 1.28 1.30 0.72 0.73 50.5 55.1 37.9 41.3 .0000.676 .0000612 .0001088 .0000984 26.6 29.5 56Z 57Z 2.35 2.35 2.36 1.41 1.43 1.44 0.82 0.83 0.84 45.0 52.4 59.8 33.8 39.3 44.9 .0000632 .0000537 .0000466 .0001017 .0000864 .0000750 15.4 18.8 22.3 60Z 61Z 62Z 2.28 2.28 2.29 1.37 1.39 1.41 0.81 0.81 0.83 61.6 68.4 75.2 46.2 51.3 56.4 .0000462 .0000412 .0000370 .0000744 .0000663 .0000596 25.1 28.5 32.0 63Z 64Z 65Z 2.21 2.22 2.22 1.34 1..36 1.37 0.81 0.81 0.82 74.9 81.2 87.5 56.2 60.9 65.6 .0000380 .0000347 .0000319 .0000612 .0000559 .0000513 34.5 38.0 41.5 66Z 67Z 68Z 199 ELEMENTS OF PENCOYD DECK BEAMS. I. II. ni. IV. V. 1 YI. VII. 1 VIII. IX. X. Size in Ins. Section No. in Sq. Inches. Weight Foot in Lbs. Moments of Inertia. Square of Radius of Gyration. Radius of Gyration. Axis A. B. Axis CD. Axis A. B. Axis a D. Axis A. B. Axis CD. 11^2 HOD 9.51 32.2 179.33 6.36 18.86 0.67 4.34 0.82 11^ 116D 13.41 45.6 ID. let 0 61 4.09 0 78 10 lOOD 8.20 28.0 118.55 6.08 14.46 0.74 3.80 0.86 10 105]) 11.32 38.6 140. / / u.o / 3 59 0 82 9 90D 7.35 25.0 84.99 4.85 11.56 0.66 3.40 0.81 9 94D 9.60 32.6 100.68 5.78 10.49 0.60 3.24 0.77 8 BOD 6.17 21.0 57.75 3.58 9.36 0.58 3.06 0.76 8 85D 8.43 28.6 70.19 4.44 8.33 0.53 2.89 0.73 7 70D 5.32 18.0 36.99 2.56 6.95 0.48 2.64 0.69 7 75D 7.29 24.5 45.32 3.26 6.22 0.45 2.49 0.67 6 60D 4.27 14.5 21.83 1.62 5.11 0.38 2.26 0.62 6 64D 5.77 19.6 26.50 2.07 4.59 0.36 2.14 0.60 5 SOD 3.39 11.5 11.96 1.01 3.53 0.30 1.88 0.55 5 55D 4.64 15.8 14.64 1.29 3.16 0.28 1.78 0.53 200 ELEMENTS OF PENCOYD DECK BEAMS. XL XII. XIII. XIV. XV. XVI. XVII. XVIII II. I. Re- sist- ance. Add to Resist, for each Coef. Qreat. Safe Add to Prev's Coef.for Coefficient for De- flection. Max. Load Dist. "d" from Section No. Size in Axis A.B. Add' I Pound per Ft. Load in Net Tons. Add' I Pound per Ft. Distvib' d Load. Centre Load. in Net Tons. Base to Neut. Axis Ins, 27.9 36.0 0.60 0.60 148.7 191.9 3.22 3.22 .uuuuuoy .0000071 .UUUUi4o .0000114 24.3 59.7 5.07 5.27 llOU HOD 11^/2 20.7 26.4 0.54 0.54 110.5 140.8 2.86 2.86 .UUUUloiD .0000107 .0000172 20.4 48.2 4.28 4.48 lOOD lOOD 10 10 16.7 20.3 0.48 0.48 88.9 108.3 2.55 2.55 .0000188 .0000159 .0000303 .0000256 19.5 39.5 3.90 4.04 90D 90]) 9 9 12.8 16.0 0.43 0.43 68.1 85.5 2.28 2.28 .0000277 .0000228 .0000446 .0000367 16.2 36.1 3.48 3.62 801) 801) 8 8 9.3 11.8 0.38 0.38 49.8 62.9 2.02 2.02 .0000432 .0000352 .0000695 .0000568 15.1 32.3 3.04 3.16 70D 701) 7 7 6.4 8.1 0.32 0.32 34.3 43.0 1.69 1.69 .0000733 .0000604 .0001180 .0000972 12.0 25.1 2.61 2.71 60D 601) 6 6 4.3 5.4 0.26 0.26 22.9 28.9 1.39 1.39 .0001337 .0001093 .0002147 .0001755 10.7 21.4 2.22 2.30 50D SOD 5 5 201 ELEMENTS OF PENCOYD BULB A:NrGLES. A I 1 F D B I. II. in. IV. V, 1 1 VII VIII. 1 IX. 1 XI. Ixii. Ixiii Size, in Ins. See. No. Aret in Sq. Ins. t wt. per Foot in Lbs. Moments of Inertia. Square of Radius of Gyralio)i. Radius of Gyration. Axis A.B. .ixis a D Axis E.F Axis A.B. Axis C. D. Axis E.F Axis A.B Axis CD. Axis E.F. 10 lOOA 7.56 25.59 90.90 5.03 5.17 12.02 0-67 0.68 3.47 0.82 0.82 in inn A 9.28 31.55 111.10 6.81 7.29 11.97 0-73 0.79 3.46 0.86 0.89 9 90A 6.65! 22.61 65.51 4.40 4.38 9.85 0.66 0.66 3.14 0.81 0.81 9 90A 7.63 25.94 75.00 5.32 5.37 9.83 0.70 0.70 3.14 0.84 0.84 8 80A 5.71 19.41 44.92 3.59 3.16 7.87 0.63 0.55 2.81 0.79 0.74 8 BOA 7.07 24.04 54.64 4.86 4.67 7.73 0.69 0.66 2.78 0.83 0.81 7 70A 4.67 15.89 28.68 2.72 2.74 6.14 0.58 0.59 2.48 0.76 0.77 7 70A 5.64 19.18 34.42 3.53 3.27 6.10 0.63 0.58 2.47 0.79 0.76 6 60A 3.74 12.73 17.26 1.96 1.92 4.61 0.52 0.51 2.15 0.72 0.72 6 60A 5.61 19.07 25.66 4.03 3.11 4.57 0.72 0.55 2.14 0.85 0.74 5 50A 2.85 9.69 9.20 1.29 1.20 3.23 0.45 0.42 1.80 0.67 0.65 5 50A 3.79 12.89 12.44 1.95 1.74 3.28 0.51 0.46 1.81 0.72 0.68 ftl 202 i ELEMENTS OF PENCOYD BULB ANGLES. C B XIV. XV. XVI. XVII. XVIII. XIX. XX. XXI. XXII II. I. Me- sist- ance. Add to Resist, for Ooef. Great. Safe Add to XVI. for AddH PoxiTid per Ft. Coefficient for Deflection. Max. Load Dist. "d" from Dist. "i" from Sec. Size in Axis A. B. Add' I Pound per Ft. Load in Net Tons. Distrib'd Ij)ad. Centre Load. in Net Tous. Base to Neu, Axis. Base to Neu. Axis. No. Lis. 1R 9 10.^ 19.7 \J.OO 0.58 104.9 *^ in 3.10 .0000176 .0000144 .0000282 .0000231 ol.D 42.7 4 39 4.35 0.77 inn A lOOA in 10 12.9 14.8 0.56 0.56 68.8 78.7 2.99 2.99 .0000244 .0000213 .0000391 .0000342 28.3 34.6 3.92 3.92 0.69 0.74 90A 90A 9 9 9.9 11.9 0.43 0.43 52.7 63.2 2.28 2.28 .0000356 .0000293 .0000571 .0000448 24.0 31.7 3.45 3.39 0.69 0.74 80A 80A 8 8 7.2 8.6 0.43 0.43 38.5 46.0 2.27 2.27 .0000558 .0000465 .0000894 .0000745 19.0 24.8 3.03 3.01 0.66 0.72 70A 70A 7 7 5.1 7.5 0.38 0.38 27.2 40.1 2.05 2.05 .0000927 .0000624 .0001486 .0000999 14.5 25.1 2.61 2.59 0.64 0.77 60A 60A 6 6 3.2 4.4 0.35 0.35 17.2 23.3 1.89 1.89 .0001739 .0001286 .0002787 .0002061 10.7 16.1 2.15 2.15 0.60 0.69 50A 50A 5 5 203 ELEMENTS OF PENCOYD TEES. EVEN LEGS. C rh I I. II. III. IV. VI." VII. 1 VIII IX. X. XI. I. Sec. Size in Inches. Area in Wt. per Fool in Lbs. Moments of Inertia. Resist- ance. Radivs of Oyration. iHsl. "d" from Sec. No. Ins Axis A.B. Axis CD. Axis A.B. Axis CD. Axis A.B. Axis CD. Base toN. Axis. No. MOT MIT 4 x4 4 X 4 3.10 3.98 10.9 13.7 4.70 5.70 2.20 2.79 1.64 2.02 1.10 1.40 1.23 1.20 0.85 0.84 1.15 1.18 440T 441T 335T 3361^ 3\ X 3V.2 31/2 X 31,;^ 2.08 2.65 7.0 9.0 2.27 2.83 1.03 1.32 0.89 1.16 0.59 0.75 1.04 1.03 0.71 0.71 0.94 1.06 335T 336T 337T 330T 3\ X 3 1/., 3 X 3 " 3.24 1.91 11.0 6.5 3.61 1.57 1.75 0.75 1.49 0.74 1.00 0.50 1.05 0.91 0.73 0.62 1.07 0.87 337T 330T 331T 225T 3 X 3 2H2 X 2\ 2.27 1.47 7.7 5.0 1.82 0.79 0.89 0.38 0.86 0.44 0.60 0.30 0.89 0.73 0.62 0.51 0.88 0.69 331T 225T 226T 227T 2\ X 2\ 2\ X 2\ 1.71 1.94 5 8 6.6 0.95 1.08 0.48 0.56 0.55 0.63 0.38 0.45 0.75 0.75 0.53 0.54 0.76 0.79 226T 227'r 22Zr 223T 2\ X 21/4 2\ X 2\ 1,18 1.18 4.0 4.0 0.51 0.52 0.27 0.26 0.31 0.33 0.24 0.23 0.66 0.66 0.48 0 47 0.62 0.65 222T 223T 220T 117T 2 X 2 l\ X 1% 1.03 0.71 3.5 2.4 0.37 0.19 0.18 0.09 0.26 0.15 0.18 0.10 0.60 0.52 0.41 0.36 0.60 0.51 220T 117T 115T 112T 1"M> X 11/., II4 X II/4 0.59 0.44 2.0 1.5 0.12 0.07 0.06 0.04 0.12 0.09 0.08 0.06 0.45 0.40 0.32 0.30 0.47 a43 115T 112T HOT 1 X 1 0.29 1.0 0.03 0.02 0.05 0.04 0.32 0.26 0.38 HOT 204 ELEMENTS OF PENCOYD TEES. UNEVEN LEGS. I. II. III. IV. V. VI. VII. |viii IX. X. XI. IHsl. ' 'd' ' from loN. Axis. I. See. No. Size in Inches. Area in Sq. Wl. per Fool in Lbs. 3 foments of Inerlia. Itesisl- ance. Radius of Gyralion. No Axis A.B. Axis CD. Axis A.B. Axis CD. Axis A.B. Axis C D. ' 64'!' 6 X 4 5.12 17.4 6.56 9.33,2.19 3.11 1.13 1.35 1.00 64T 65T 6 X 5^4 11.58 39.0 28.68 18.75 8.19 6.25 1.57 1.27 i. /o uo± 53T 5 X 3V<> 4.95 17.0 5.29 5.47 2.17 2.19 1.03 1.05 1.06 53T 54T 5 x4 4.54 15.3 6.16 5.41 2.11 2.16 1.17 1.09 1.08 54T 42T 4 X 2 1.93 6.5 0.53 1.75 0.34 0.87! 0.52 0.95 U.1D *±Ci 1 43'r 4 X 3 2.67 9.0 l!99 2.10 0.90 1.05 0.87 0.89 0.78 43T 44'r 4 X 3 3.05 10.2 2.24 2 44 1.02 1.22!0.85 0.89 0.81 44T 45T 4 X 41/2 3.97 13.5 7.36 2^53 2.33 1.27 1.36 0.80 1.34 45T 38T 3Vo X 3 2.11 7.0 1.65 1.18 0.75 0.67 0.88 0.75 0.80 00 1 oyi- 3 V.> X 3 2.46 8.5 l'.91 1.41 0.88 0.81 0.88 0.75 0.83 39T 30T 3 X 1.20 4.0 0.18 0.60 0.16 0.40 0.39 0 71 0.36 ou 1 31T 3 X 2H2 1.46 5.0 0.78 0.60 0.42 0.4010.73 0.64 0.66 32T 3 X 2H2 1.76 6.0 0.93 0.74 0.51 0 49! 0.73 0.65 0.68 33'r 3 X 2\ 2.06 7.0 1.08 0.89 0.60 0,59 0.72 0.66 0.71 33T 34T 3 X 21/0 2.38 8.0 1.32 0.91 0.78 0.6110.74 0.62 0.80 34T 35T 3 X 3H^ 2.46 8.3 2.82 0.89 1.17 0.59 1.07 0.60 1.08 35T 36T 3 X 3H2 2.81 9.5 3.19 1.04 1.33 0.69 1.07 0.61 1.10 36T 28T 2% X 1\ 1.96 6.6 0.56 0.60 0.50 0.44 0.54 0.56 0.64 28T 29T 2\x2 2.14 7.2 0.82 0.61 0.66 0.44:0.62 0.54 0.75 29T 25T 2H2 X 11/4 0.97 3.3 0.10 0.33 0.11 0.26' 0.32 0.58 0.31 25T 261^ 2H2 X 2«/4 1.68 5.7 1.16 0.43 0.60 0.34 i 0.83 0.51 0.83 26T 27T 2 i,b X 3 1.76 6.0 1.48 0.44 0.71 0.3510.92 0.50 0.93 27^r 24T 21/4 X 1% 0.66 2.2 0.01 0.24 0.03 0.21 j 0.14 0.60 0.17 24T 20T 2 X ^% 0.60 2.0 0.01 0.17 003 0.17 0.14 0.53 0.17 20'r 22'r 2 X 1 Jg 0.62 2.0 0.04 0.16 0.05 0.16 0.24 0.51 0.23 22'r 21T 2 X 1 0.72 2.5 0.05 0.17 0 07 0.17:0.26 0.49 0.27 2i'r 23T 2 X 11/2 0.91 3.0 0.16 0.17 0.15 0.17 0.42 0.44 0.45 23T 17T 1% X IjVr 0.56 1.9 0.05 0.11 0.06 0.13 0.30 0.45 0.24 17T 18T 1=*4 X II4 1.04 3.5 0.12 0.21 0.14 0.24 0.35 0.45 0.40 18T 15T 1^/2 X 0.41 1.4 0.02 0.07 0.03 0.09 0.22 0 41 0.21 15T 12T 1^4 X -l e 0.35 1.2 0.02 0.03 0.03 0.05 0.24 1 0.30 0.22 12T 205 ELEMENTS OF PENCOYD ANGLES. I. II. III. IV. V. VI. VI r. VIII. Section Size in Thick- Weight per Fool Moments of Inertia. Number. Inches. ness. Sq. Ins. in Lbs. Axis A. B. A xis C. B. Axis E. F. 860A 868A 8 x6 8I4 X 6I/4 \ 1 6.75 13.29 23.0 45.6 44.38 85.34 21.73 41.67 12.04 24.76 730A 738A 7 X 3\ 1\ X Z\ \ 1 5.00 9.79 17.0 32,5 25.29 48.59 4.37 8.47 3.64 7.47 650A 659A QHy X 4 6^/8x4% % 3.80 9.48 12.9 31.9 16.83 42.40 5.03 12.91 3.29 9.28 640A 649A 6 x4 6% X 4% 1 G 3.61 9.01 12.2 29.4 13.48 33.95 4.91 12.47 3.04 8.57 630A 639A 6 X 3i/.> 6% X 37/8 % It 3.42 8.54 11.6 28.6 12.82 32.56 3.32 7.74 2.39 6.50 500A 504A 51/2 X 3"i/o| 5-'4 X 3\ % % 3.23 5.47 11.0 17.9 10.15 17.62 3.28 5.85 2.14 3.82 540A 546A 5 x4 3.23 6.35 11.0 21.3 8.13 15.65 4.65 8.74 2.50 4.95 510A 517A 5 X 31/2 51/4 X 3% 2.56 6.07 8.7 20.0 6.58 15.51 2.71 6.41 1.65 4.17 530A 537A 5 x3 53/4 X 31/4 4 2.40 5.69 8.2 18.7 6.27 14.75 1.75 4.18 1.20 3.05 450A 457A 41/2 X 3 ^\ X 31/4 2.25 5.32 7.7 17.4 4.72 11.04 1.72 4.07 1.10 2.96 410A 417A 4 X 31/2 41/4 X 3% 4 2.25 5.32 7.7 17.4 3.57 8.42 2.56 6.06 1.18 3.08 208 ELEMENTS OF PENCOYD ANGLES. IX. X, XI. XII. XIII. xrv. XV. I. Radius of Gyration. Resistance. Distance from Base to Neutral Axis. Section Axis A. B. Axis C. D. Axis K F. Axis A. B. Axis a n. d Number. 2.56 2.53 1.79 1.77 1.34 1.37 8.03 15.43 4.80 9.20 2.47 2.72 1.47 1.72 860A 868A 2.25 2.23 0.93 0.93 0.85 0.87 5.66 10.85 1.61 3.10 2.53 2.77 0.78 1.02 730A 738A 2.10 2.12 1.15 1.17 0.93 0.99 3.87 9.58 1.62 4.07 2.15 2.45 0.90 1.20 650A 659A 1.93 1,94 1.17 1.18 0.92 0.98 3.32 8.21 1.60 3.98 1.94 2.24 0.94 1.24 640A 649A 1.94 1.95 0.99 0.95 0.84 0.87 3.24 8.05 1.23 2.77 2.04 2.33 0.79 1.08 630A 639A 1.77 1.79 1.01 1.03 0.81 0.84 2.76 4,66 1.22 2.10 1.82 1.97 0.82 0.97 500 A 504A 1.59 1.57 1.20 1.17 0 88 0.88 ' 2.34 4.50 1.57 2.93 1.53 1.71 1.03 1.21 540A 546A 1.60 1.60 1.03 1.03 0.80 0.83 1.93 4,51 1.02 2.38 1.59 1.81 0.84 1.06 510A 517A 1.62 1.61 0.85 0.86 0.71 0.73 1.89 4.40 0.75 1.78 1.68 1.90 0.68 0.90 530A 537A 1.45 1.44 0.87 0.87 0.70 0.75 1.55 3.61' 0.75 1.76 1.46 1.69 0.71 0.94 450A 457A 1.26 1.26 1.07 1.07 0.72 0.76 1.27 2.95 1.00 2.33 1.18 1.40 0.93 1.15 410A 417A 209 ELEMENTS OF PENCOYD ANGLES. I. II. III. IV. V. VI. VII. VIII. Section Size in Thick- ^rea in Weight per Fool in Lbs. Moments of Inertia. Number. Inches. ness. /Sg. Ins. Axis A. B. 430A 4oOA 4 x3 AV -r "iljU 2.09 A Oft 7.1 ft 3.38 6.36 1.64 2.59 0.93 1.80 300A oUOA 31^x3 1.93 o.yo 6.6 1 9 Q 2.33 5.12 1.59 3.54 0.80 1,88 310A Ql /I A oi4A 31,^ X 2H2 Q3/ -w 03/ ^2 1.44 z.yo 4.9 Q A y.^ 1.81 3.93 0.78 1.76 0.45 1.01 316A oioA 3^x2 1.31 i.yy 4.5 D.O 1.66 2.55 0.41 0.65 0.30 0.45 325A 329A 3 x2i^ 3^4 X 2% 1.31 2.70 4.5 8.7 1.15 2.64 0.73 1.71 0.41 0.76 320 A 324A 3 x2 314 X 2^4 1.19 2.45 4.1 7.9 1.09 2.41 0.40 0.92 0.24 0.57 200 A 2O0A 2\ X 2 2}g-x2i!V 0.81 2.26 2.7 7.0 0.51 1.64 0.29 0.97 0.13 0.44 206 A 209A 21/4 X 11^ 0.67 1.38 2.3 4.4 0.35 0.73 0.12 0.29 0.08 0.18 215 \ ;:il8A 2 X 11/2 0.62 1.28 2.1 4.3 0.25 0.52 0.12 0.29 0.07 0.15 210 A 213A 2 XII4 2^ X ii^ 0.57 1.19 1.9 3.9 0.23 0.50 0.07 0.17 0.05 0.12 210 ELEMENTS OF PENCOYD ANGLES. IX. X. XI. XII. XIII. XIV. XV. I. Radius of Gyration. Resistance. Distance from Base to Neutral Axis. Section Axis A.B. Axis a D. Axis E. F. Axis A.B. Axis a D. d. I. Number. 1.27 1.25 0.89 0.80 0.67 0.67 1.23 2.33 0.73 1.16 1.26 1.40 0.76 0.90 430A 435A 1.10 1.13 0.91 0.95 0.64 0.69 0.95 2.00 0.73 1.53 1.06 1.25 0.81 1.00 300A 305A 1.12 1.15 0.74 0.77 0.56 0.59 0.76 1.58 0.41 0.88 1.11 1.26 0.61 0.76 310 A 314A 1.13 1.13 0.56 0.57 0.48 0.48 0.72 1.09 0.27 0.41 1.21 1.28 0.46 0.53 316A 318A 0.94 0.99 0.75 0.80 0.56 0.53 0.55 1.20 0.40 0.88 0.92 1.05 0.67 0.80 325A 329A 0.96 0.99 0.58 0.61 0.45 0.48 0.54 1,14 0.26 0.57 0.99 1.14 0.49 0.64 320A 324A 0.79 0.85 0.60 0.66 0.40 0.44 0.29 0.88 0.19 0.60 0.76 0.94 0.51 0.69 200A 205A 0.72 0.73 0.42 0.46 0.35 0.36 0.23 0.46 0.11 0.24 0.74 0.86 0.37 0.48 206A 209A 0.63 0.64 0.44 0.48 0.34 0.34 0.18 0.36 0.11 0.24 0.64 0.76 0.39 0.50 215A 218A 0.64 0.65 0.35 0.38 0.30 0.32 0.18 0.36 0.07 0.17 0.69 0.80 0.31 0.42 210A 213A 211 Width of Rectangle in Inches. i 1 i 1 6 4.50 5.63 6.75 7.88 9.00 10.13 11.25 7 7.15 8.93 10.72 12.51 14.29 16.08 17.86 g in Ri lU.D/ 1 ft nn 18.67 21.33 24.00 26.67 g 10. ly 1 Q QQ lo.yo OO HQ acx. IO 26.58 30.38 34.17 37.97 in OR r\A ^0.114 Q1 OR 36.46 41.67 46.87 52.08 11 27.73 34.66 41.59 48.53 55.46 62.39 69.32 12 36.00 45.00 54.00 63.00 72.00 81.00 90.00 1 Q io AR nn 40. / / R'7 01 ftQ ftft Do. DO 80.10 91.54 102.98 114.43 RH 1 n •71 /1ft QR IR 00. /D 100.04 114.33 128.63 142.92 1 R /U.ol <5/.oy 1 CiR Al 1U0.4/ 123.05 140.63 158.20 175.78 16 85.33 106.67 128.00 149.33 170.67 192.00 213.33 17 102.35 127.94 153.53 179.12 204.71 230.30 255.89 1 Q 1 01 c;n IZi.oU 1 Pil QQ 101. OO 212.63 243.00 0'70 OO ^/o.3o 303.75 1 Q 1/10 on 1 1Q ftO 250.07 285.79 321.52 357.24 1 ft'? IDD.D/ OnO QQ 250.00 291.67 666.66 375.00 416.67 21 192.94 m.n 289.41 337.64 385.88 434.11 482.34 22 221.83 277.29 332.75 388.21 443.67 499.13 554.58 OQ iSO oc;q yl Q QI ft Qc: OlD.OO QQO OO 443.59 506.96 570.33 633.70 ouU.UU /JQO OA 504.00 576.00 648.00 720.00 OR ylAft OA 4UD.yU ^QQ OQ 569.66 651.04 732.42 813.80 26 366.17 457.71 549.25 640.79 732.33 823.88 915.42 27 410.06 512.58 615.09 717.61 820.13 922.64 1025.16 28 457.33 571.67 686.00 800!33 914!67 1029^00 1143.33 29 508.10 635.13 762.16 889.18 1016.21 1143.23 1270.26 30 562.50 703.13 843.75 984.38 1125.00 1265.63 1406.25 31 620.65 775.81 930.97 1086.13 1241.30 1396.46 1551.62 32 682.67 853.33 1024.00 1194.67 1365.33 1536.00 1706.67 33 748.69 935.86 1123.03 1310.20 1497.38 1684.55 1871.72 34 818.83 1023.54 1228.25 1432.96 1637.67 1842.38 2047.08 35 893.23 1116.54 1339.84 1563.15 1786.46 2009.76 2233.07 36 972.00 1215.00 1458.00 1701.00 1944.00 2187.00 2430.00 37 1055.27 1319.09 1582.90 1846.72 2110.54 2374.35 2638.17 38 1143.17 1428.96 1714.75 2000.54 2286.33 2572.13 2857.92 39 1235.81 1544.77 1853.72 2162.67 2471.62 2780.58 3089.53 40 1333.33 1666.67 2000.00 2333.33 2666.67 3000.00 3333.33 217 ELEMENTS OF USUAL SECTIONS. Moments refer to horizontal axis as shown. This table is intended for convenient application where extreme accuracy is not Important. Some of the terms are only approximate ; those marked * are correct. Values for ra- dius of gyration in flanged beams apply to standard minimum sections only. A = area of section. Shape of Section. Moment of Inertia. Moment of Resistance. Distance of Base from Centre of Oravity. X/Cast Ttfidvus of Gyration. <- b" 1 ■ h bhi * 12 6 h 2 Least Side* 3.46 f,i * 12 0. 1 1 78/(3 * h * 3.46 5* — h* * 12 1 B* — h* * 6 B 2 ■./^ + 62* ' 12 - b- — B— 1 B 1 3G 6/l2 * 24 2 h The least of the two : A.orl* 4.24 4.9 .Ai hlfi * 12 > - h-p 2 2 662 + 666 1 _i_ 1,^2 * 36 (26 + 6i) ' 136 + 6,. 3 26 + 6i ■ - 1)— Am* 16 8 J) 2 D* 4 (»- D~ •» 0.0491 (D^ — d*)* 0.0982:^^-1^* T) 2 1 ,/(X>2 + d2)* 4 ^ 218 BENDING MOMENTS, DEFLECTIONS, ETC., W •= Total load. L = Length of beam. B = Modulus of elasticity. J = Moment of inertia. Form of Support and Load. Reactiovs A. B. Safe Load W. Bending Moment M. ^ — ' — T V «i 1 A^B^E 2 2 i>/max.= ""^^ 4 m s m _ -a, X — a.— ® i A- ^'^i ^ L B=Kd For vlT), M=^''^£ ^ For BD, i>/=ir^i 3/max. = I'J f'l. i I, 3 , l[ — ^ -J 1^ 1 i(> For^Z), W?. 16 For BI), .Vniax. - Tlx. ISU WL. 220 BENDING MOMENTS, DEFLECTIONS, ETC., FOR BEAMS OF UNIFORM SECTIONS. Tr= Total load. L = Length of beam. E = Modulus of elasticity. I = Moment of inertia. R = Resisting moment. K = Fibre stress, c = Distance from neutral axis to extreme fibres. Beam supported at both ends, 2 symmetrical loads. AC=EB = Distance from support to load. Draw trapezoid having CD = EF= J H'a. Ordinates give bending moments for corresponding positions on beam. Bending moment between loads = J Wa. Maximum deflection = ;3^^,(3 — 4a2). Draw (by 3, page 221) the triangles having vertices at C, D and E, the verti- cals representing bending moments for loads uA, and m-s, respectively. Extend FO to P, GD to R, and HE to S, making each long vertical equal to the sum of the bending moments corresponding to its position. That is, FP= FC + FI + FJ, GR= GD + GL+ GK. And HS ^ HE + HN + H3I. Verticals drawn from any point on the polygon, APRSB to AB, will repre- sent the bending moments at the corresponding points on the beam. 22G STRESSES IN SOME SIMPLE FORMS OF FRAMED STRUCTURES. Compression indicated by the sign — and by solid lines. Tension by the sign + and by dotted lines. When the prefix "stress" is used, the load borne by the member is indicated ; otherwise the length of the member is meant. Cranes. | Supported at the points A and B, maximum longitudinal stresses, due to weight W, suspended at the end. These stresses are modified by the position of the hoisting chain. D is the point where a line drawn from Cat right angles to A B will intersect the latter. Stress^ C= + ^XTf Stress B C= ^ X W A B " AB = — ^y. Win Fig. 2, or = + 4-5 X in Fig. 3. jA. B A B When point A is supported by inclined back stays as shown in Fig. 1, and when the back stay is in the plane of A B and W. Stress AE= + -^><.Wy. 45 > AB E B and a resulting compression ensues on AB = ^ ^ X V ^ ^ AB^^^ BE- 227 Cranes. Stress CD = — ^XW FIG. 4 AD " A C= + ^X W " E D = — stress D a Let w = the horizontal reaction at B B E Stress B E=-\- X if " AE=-\- -^-^ X (stress C D — and II are points where , lines drawn from D intersect ^ at right angles A C and ^ _B. X, Y and 2^ are the angles formed by extending the braces C B and B I) as indi- cated by dotted lines, iv = the horizontal reaction at B AC AB CE X W. Stress A C = + ~ X Tf . Stress (7 D = A D = — stress C Z> X or = — stress B D X " B D = Sine Y SineX Sine Y Sine Z 228 Roors. Iron roofs having a slope of 2 to 1, and trusses about 15 feet apart, will approximate in weight as follows per square foot of building area : Weight of material in frame, including truss and purhns, but not covering : Truss of 75 to 100 feet span, 8 to 10 pounds per sq. ft. " " 60 to 75 " 7 to 8 " under 50 " 5 to 7 " " " To this must be added the following weights of covering material per square foot of building area : Tin on V boards 4.5 pounds. Corrugated sheets. No. 20, galvanized .... 2.3 " No. 20, " on boards 6.7 Slate tV^ thick, on lY^ boards 11.0 " " " "1 " 7.6 " Felt and gravel . . . 9-11 " If plastered below rafters, add 10 The snow load will vary with the latitude from 10 pounds per square foot of building area for Baltimore and Cincin- nati to 30 pounds for Northern New England. In roofs with inclinations of 45 degrees or over the snow load can be neglected if no snow guards or other obstructions are attached. On slate roofs with a slope of 2 horizontal to 1 vertical, the snow will not accumulate to any material thickness. The normal wind load is usually computed by Button's formula = u sin a i-84 cos a - 1 where v/ = pressure due to wind normal to roof surface u = horizontal pressure of wind in pounds per square foot, qc = inclination of the roof to the horizontal in degrees. Taking the horizontal pressure at 30 pounds per square foot we derive the following normal pressure per square foot of roof surface : Inclination. Pressure. Inclination. Pressure. Inclination. Pressure. 5° 3.9 lbs. 25° 16.9 lbs. 45° 27.1 lbs. 10° 7.2 " 30° 19 9 " 50° 28.6 " 15° 10.5 " 35° 22.6 " 55° 29.7 " 20° 13.7 " 40° 25.1 " 60° 30.0 " 233 SHAFTING OF STEEL OR WROUGHT IRON. The resistance to shearing averages about j% of the tensile strength, i. e . about 40,000 lbs. for wrought iron, or 50,000 lbs. for soft steel, per square inch of section. The torsional resistance of any shaft can be determined, when the shearing resistance is known ; thus d = diameter of the shaft in inches. s — shearing strength in pounds per square inch. T= the torsional moment in inch-pounds ; that is, the force in pounds multiplied by the length in inches of the lever through which the force acts. Taking s at 40,000 and 50,000 lbs., respectively for iron and steel, and assuming that in machinery the working value should be between one-fourth and one-fifth of the ultimate strength— adopting the mean — makes the working resistance to shearing 9,000 lbs. per square inch for iron, and 11,200 lbs. per square inch for steel. Putting this in terms of the torsional moment and diameter, we derive from equa- tions a and h These formulte apply to shafts subject to twisting strains alone. In practice, however, such cases seldom occur, as shafts are generally subjected to combined bending and twisting strains. As there are no experimental data for T= .196 dh for round shafts, T=r ,28 cPs for square shafts. (a) T = 1760 d? for round iron shafts, r= 2200 d^ for round steel shafts, T— 2520 d? for square iron shafts, T— 3150 d^ for square steel shafts, (d) [e) if) 234 such a combination of forces, we have to rely on analysis, which gives the following : = iP + (/) M= bending moments in inch-pounds. (See page 220.) T ---= twisting T^— a new twisting moment which, substituted for T in equations g to k, will give the desired proportions for the shaft. In revolving shafts the longitudinal stress resulting from the bending action is continually changing from tension to compression, and vice versa. It is therefore advisable, for reasons given on page 22, to increase the factor of safety as the bending stress increases comparatively to the torsional stress. The following changes in factors of safety are recom- mended : Divisor in Formulce. RaHo ofMto T. Factor of Safety. (g) for Iron. (h) for Steel. if = .3 Tor less. ^ 1760 2200 M=.&T " 5 1570 1960 M= T 5J 1430 1790 M= greater than T, 6 1310 1640 HORSE-POWER. If it is desired to find the relations between horse-power and diameters of shafts, the elements of time and velocity have to be considered. Taking the horse-power HP at 628 X r X T'' 396,000 inch-lbs. per minute, we have HP— where V = revolutions per minute. y_ 63,057 HP (m) or in terms of the diameter by equation {d) we get for shafts of medium steel ^29 HP 235 The above will give the proper diameter of a shaft for transmitting any desired HP when the shaft is subjected to twisting stress alone ; but since, as previously stated, such a case seldom occurs, we must combine the bending and twisting stresses, for which a general rule will be given at the close of the subject. DEFLECTION OF SHAFTING. As the deflection of steel and iron is practically alike under similar conditions of dimensions and loads, and as shafting is usually determined by its transverse stiflfness rather than its ultimate strength, it follows that nearly the same dimensions should be used for steel that are found necessary for iron. For continuous line shafting used for transmitting power in shops, factories, etc., it is considered good practice to limit the deflection to a maximum of of an inch per foot of length. The weight of bare shafting in pounds= 2.6 cPl^ W, or when as fully loaded with pulleys as is customary in practice, and allowing 40 lbs. per inch of width for the vertical pull of the belts, experience shows the load in pounds to be about 13 dH=^W. Taking the modulus of transverse elasticity at 26,000,000 lbs., we can derive from the authoritative formulae the following: I = f 873^2 for bare shafts (p) I = fnbd^ for shafts carrying pulleys, etc., (r) which would be the maximum distance in feet between bear- ings for continuous shafting subjected to bending stress alone. If the length is fixed, and we desire the diameter of the shaft, we have, rw ^ \ 873 f'O^ bare shafting. (s) \T \ 175 shafting carrying pulleys, etc. {t) To apply the above to revolving shafting subjected to both twisting and bending stress, it is necessary to combine equa- tions {p) and (r) with equation (o). 236 But in shafting, with the same transmission of power, the torsional stress is inversely proportional to the velocity of rotation, while the bending stress will not be reduced in the same ratio. It is, therefore, impossible to write a formula covering the whole problem and sufficiently simple for prac- tical application, but the following rules are correct within the range of velocities usual in practice. WORKING FORMUL.^ FOR CONTINUOUS SHAFTING. For the diameter (d) in inches, and the maximum length [1) in feet between bearings of steel or iron shafting so pro- portioned as to deflect not more than of an inch per foot of length, allowance being made for the weakening effect of key seats, d = -^ ^^Y ^ fov bare shafts , (m) 3 /7Q J££* d = — y- for shafts carrying "pulleys, etc. , (y) I = f 720d2 for bare shafts, (w) I = if 140 for shafts carrying pulleys, etc., {x) The moment of resistance of round shafts for bending is one-half of the resistance for twisting strains. The resistances are simply and accurately expressed thus: V = ^ and T = ^ for sohd shafts. if = ^^=^\nd r^^i^'for hollow shafts. D being full diameter and A corresponding area, d is the internal diameter and a corresponding area. BELTING. When designing shafting, allow for the tension of belting, 50 lbs. per inch of width for single leather belt or its equiva- lent, or 80 lbs. per inch of width for double leather belt, or its equivalent of other material. 237 WORKING PROPORTIONS FOR COJfTINUOUS SHAFTING. MEDIUM STEEL,, Transmitting power, but subject to no bending action except its own weight. Diam- eter of S/iaft ii Inches. 3£ci'xi7num Safe Torsional Fuel Pounds. Revolutions per Minuie. Maximum Distance in Feet Between Bearings. 100 150 200 250 300 IIP IIP HP IIP HP 618 7 10 14 17 20 11.7 1% 786 9 13 17 21 26 12.4 982 11 16 21 26 32 13.0 1208 13 20 26 33 40 13.6 2 1467 16 24 32 40 48 14.2 21/8 1758 19 29 38 48 58 14.8 2\ 2088 23 34 46 57 68 15.4 2% 2457 27 40 54 67 80 16.0 2\ 2865 31 47 63 /o 16.5 , 2% 3896 42 62 83 102 124 17.6 3 4950 54 81 108 134 162 18.6 31/4 6293 69 103 137 172 206 19.7 3^ 7860 86 129 172 215 258 20.7 3% 9668 105 158 211 264 316 21.6 4 11733 128 192 256 320 384 22.6 238 WORKING PROl-ORTIOJVS FOR CONTINUOUS SHAFTING. MEDIUM STEEIi. Transmitting power, and subject to bending action of pulleys, belting, etc. Diam- eter of Shaft in Inches. Safe Torsional Moment in Foot- pounds. Revolutions per Minute. Maximum Distance m Feet Between Bearings. 100 150 200 250 300 HP HP HP HP HP IV2 618 5 7 10 12 14 6.8 1% 786 6 9 12 15 18 7.2 1\ 982 8 11 15 18 22 7.5 l\ 1208 9 14 19 23 28 7.9 2 1467 11 17 23 28 34 8.2 21/8 1758 14 21 27 34 42 8.6 21/4 2088 16 24 33 41 48 8.9 2«/8 2457 19 29 38 48 58 9.2 21/2 2865 00 00 Do 9.6 3896 24 36 48 60 72 10.2 4950 39 58 77 96 116 10.8 31/4 6293 49 74 98 123 148 11.4 31/2 7860 61 92 123 153 184 12.0 3% 9668 75 113 151 188 226 12.5 4 11733 91 137 183 228 274 13.1 DIAMETER IN INCHES FOR ROUND STEEL SHAFTS. PROPORTIONED FOR RESISTANCE TO TORSION, WITH THE LIMITATIONS DESCRIBED ON OPPOSITE PAGE. Torsional Moments in Foot Pounds. H. P. a; Diameter in Inches for Conditions Described. Torsional Moments in Foot Pounds. H. P. B. P. M. Diameter in Inches for Conditions Described. No. 1. No.Z. No. 3. No. 1. No. 2. No. 3. 500 .095 2.4 2.6 2.9 15000 2.855 5.7 6.2 6.8 600 .114 2.6 2.8 3.0 18000 3.425 6.0 6.5 7.1 800 .152 2.8 3.0 3.3 21000 3.996 6.2 6.7 7.4 1000 .190 2.9 3.2 3.5 25000 4.757 6.5 7.0 7.7 1200 .228 3.0 3.3 3.6 30000 5.709 6.8 7.4 8.1 1500 .2 3.2 3.5 3.8 35000 6.660 7.1 7.6 8.4 1800 .343 3.4 3.6 4.0 40000 7.612 7 Q l.o •7 Q / .y O. / 2100 .400 3.5 3.8 4.2 45000 8.563 7.5 8.1 9.0 2500 .476 3.7 3.9 4.3 50000 9.515 7.7 8.4 9.2 3000 .571 3.8 4.1 4.6 60000 11.418 8.1 8.7 9.6 4000 .761 4.1 4.4 4.9 70000 13.321 8.4 9.1 10.0 5000 .952 4.4 4.7 5.2 80000 15.224 8.7 9.4 10.3 6000 1.142 4.6 4.9 5.4 90000 17.127 9.0 9.7 10.6 8000 1.522 4.9 5.3 5.8 100000 19.029 9.2 9.9 10.9 10000 1.903 52 5.6 6.1 120000 22.835 9.6 10.4 11.4 12000 2.284 5.4 5.8 6.4 150000 28.544 10.2 11.0 12.1 240 TORSIONAL STIFFNESS OF SHAFTS Torsional elasticity is calculated from the following formula) X = Tl Ip X = length of arc of deflection, for a unit of length and unit radius. y= moment of torsion. I — length of shaft subject to torsion. fp = polar moment of inertia of cross-section, y*;! = modulus of torsional shear = of the modulus of elasticity or about 11,600,000 pounds for steel shafts. From this is obtained the angle of torsion in degrees Ffor each foot of length L for steel shafts of diameter "d" in inches: V= Ti for round shafts. 1661 a* 2m ^^"^^6 shafts. The amount of torsional yield or twist permissible is obtained by experience and depends on the service to which the shaft is subjected. The following is considered good ])ractice within the limits of length usual in ordinary practice : PERMISSIBLE TWIST PER FOOT OP LENGTH. No. 1. .10 degree for ordinary service, no violent fluctua- tions. No. 2. .075 degree with fluctuating loads, suddenly applied. No. 8. .050 degree when suddenly reversed under full load These give, when applied to the foregoing rule, for round steel shafts diameter d in inches for torsional moments T in inch pounds or for H. P. horse-power in foot pou nds per minute R. F. M. number of revolutions per minute No. 1. d = .278 ^ T= 4.4 ' ^• \ " \ R. F. M. No. Z. d = .33 ^ T= 5.23 ^ No. 2. d = .30 ^ r=4.75 H. F. R. F. M. The table on opposite page gives diameters for shafts corre- sponding to given torsion moments or power transmission, and for thetliree cases of limitation of twist described above. If the shaft is subjected to bending stress in addition to twisting, it should be reinforced as previously described. 241 PENCOYD TURNTABLES. The Pencoyd Slandard Turntable is entirely center bear- ing, resting on three hardened steel discs of sufficient diam- eter to distribute the pressure. The discs are placed in an (jil box, a steel casting, which is bolted to a cast-iron base. The pivot is made of cast-steel and fits between the two upper cross channels, through which pass the two sus- X)ending bolts. The lour end truck wheels, which simply steady the table in turning, are made of chilled cast-iron ; these wheels should always clear the circular track rail about one inch wlien the table is level and unloaded, as the engine and tender should be carried entirely on the centre discs. This turntable can be easily revolved by two men when loaded with the heaviest engine and tender. DIMENSIONS OF PENCOYD STANDARD TURNTABLES, IN FEET AND INCHES. A B 0 Size. Length of girder out to out. Diam. of pit. Diam. of circular track. Diam. of center discs. Depth from top chord angles to lop of center stone. Depth from top/ chord angles to top of circular track rait. Depth of Girder in center back to back of angles. Total weight in lbs. 50.0 50.8 47.8J 7" 3.9^ 4.6J 25200 55' 55.0 5.58 52.7i 7" 3.9| 2.U 4.6| 26800 55' heavy 55.0 55.8 52.7J 7" 3.0J 2.1^ 4.6J 28400 CO' 60.0 60.8 57.7 7" 3.9^ 2.U 4.6i ' 34000 60' heavy 60.0 60.8 57.7 7" 3.9^ 2.1J 5.0 J 37800 05' 65.0 65.8 62.6J 7" 3.9i 2.n 4.6i 36000 65' heavy 65.0 65.8 62.6^ 8" 3.9J 2.n 5.0J 39500 75' 75.0 75.8 72.61 9" 5.7i 3.01 5.0 61000 243 MAXIMUM BENDING MOMENTS ON PINS, With Extreme Fibre Strains Varying from 15,0C0 to 25,C00 Pounds per Square Inch. Diameter of Pin in inches. . Area of Pin in So Indies. Moments in Inch- Pounds for Fibre Strains of 15,000 lbs. per Sq, Inch. 20,000 lbs. per Sq. Inch. 22,000 lbs. per Sq. Inch. 25,000 lbs. per Sq. Jnch. 1 0.785 1470 1960 \ 2160 2450 1^/8 0.994 2100 2800 3080 3500 11/. 1 997 2880 3830 4220 4790 13/„ 1 AiV\ i.rtoO 3830 5100 6380 1\ 1.767 4970 6630 7290 8280 1% 2.074 6320 8430 9270 10500 7890 10500 11570 13200 17/ i'/8 9 7R1 9710 16200 2 3.142 11800 15700 17280 19600 21/8 3.547 14100 18800 20730 23600 91/. cs.y /o 16800 22400 24600 28000 93/ 19700 9ftQnn 32900 2\ 4.909 ZdUuU 30700 33700 38400 2% 5.412 35500 39000 44400 9-3/ 30300 40800 44900 51000 97/ 3'Sfinn 4R7nn r±D I\J\J E^i Qnn 58300 3 7.089 ononA o9o00 53000 58300 66300 31/8 7.670 44900 59900 65900 74900 ! "31/. 074 ft 9Qf! 50600 67400 74100 84300 3% ft QdA /oouu QQfinn ooUUU 94400 9.621 63100 84200 92600 105200 3% 10.321 70100 93500 102900 116900 1 q;5/ 04 77700 103500 113900 129400 1 Q7/ 1 1 TOO 85700 114200 1 9'iRnn li^jOOUU 142800 4 12.566 94200 125700 138200 157100 4^8 13.364 103400 137800 151600 172300 ! ^74 14. loo 113000 150700 165800 188400 4% 15.033 123300 164400 180800 205500 4^2 15.904 134200 178900 196800 223700 ^ '8 4% 16.800 145700 194300 213700 17^721 157800 210400 231500 263000 4% 18.665 170600 227500 250200 284400 5 19.635 184100 245400 270000 306800 51/8 20.629 198200 264300 290700 330400 51/4 21.648 213100 284100 312500 355200 5% 22.691 228700 304900 335400 381100 23.758 245000 326700 359300 408300 5% 5% 24.850 262100 349500 384400 436800 25.967 280000 373300 410300 466600 5% 27.109 298600 398200 438000 497700 214 MAXIMUM BENDING MOMENTS ON PINS, With Extreme Fibre Strains Varying from 15,000 to 25,000 Pounds per Square Inch. Area of Pin in Sg. Inches. 28.274 29.465 30.680 31.919 33.183 34.472 35.785 37.122 38.485 39.871 41.282 42.7] 8 44.179 45.664 47.173 48.707 50.265 51.849 53.456 55.088 56.745 58.426 60.132 61,862 63.617 65.397 67.201 69.029 70.882 72.760 74.662 76.590 78.54 82.52 86.59 90.76 95.03 99.40 103.87 113.10 Moments in Inch-Pounds for Fibre Strains of 15,000 lbs. per Sq Inch. 318100 338400 359500 381500 404400 428200 452900 478500 505100 532700 561200 590700 621300 652900 685500 719200 754000 789900 826900 865100 904400 944900 986500 1029400 1073500 1118900 1165500 1213400 1262600 1313100 1364900 1418100 1472600 1585900 1704700 1829400 1960100 2096800 2239700 2544700 20,000 lbs. per S q. Inch. 424100 451200 479400 508700 539200 570900 603900 638000 673500 710200 748200 787600 828400 870500 914000 958900 1005300 1053200 1102500 1153400 1205800 1259800 1315400 1372500 1431400 1491900 1554000 1617900 1683400 1750800 1819900 1890800 1963500 2114500 2273000 2439300 2613400 2795700 2986300 3392900 22,000 Ihs. per Sq. Inch. 466500 496300 527300 559600 593100 628000 664200 701800 740800 781200 823000 866300 911200 957500 1005300 1054800 1105800 1158500 1212800 1268800 1326400 1385800 1446900 1509800 1574500 1641100 1709400 1779600 1851800 1925900 2001900 2079900 2159900 2325900 2500200 2683200 2874800 3075400 3284800 3732200 25,000 lbs. per Sq. Inch. 530200 564000 599200 635900 674000 713700 754800 797500 841900 887800 935300 984500 1035400 1088100 1142500 1198700 1256600 1316500 1378200 1441800 1507300 1574800 1644200 1715700 1789200 1864800 1942500 2022300 2104300 2188500 2274900 2363500 2454400 2643100 2841200 3049100 3266800 3494800 3732800 4241200 245 STANDARD PINS AND NUTS FROM a " TO 9" DIAMETER. FIJV. 1^ 25£ 3}i MA 1^ 2.00 2.030 2.25 2.50 2.75 3.00 3.25 3.50 2.280 2.530 2.780 3.030 3.280 0.030 0.030 0.030 0.030 0.030 0.030 3.530 0.030 Screw. NUT. it. _^ 1% 1% 2^6 2^6 4^ 3K 3% 4^6 5Mg §■ WASHER.] 2% 2% 2% 2>s' 3% 3% 4 4}i 4M 4Jf 5 5 5}£ 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 ,771 ,022 273 ,524 ,775 ,026 277 ,528 779 030 021 022 023 3% 0.024 3}^ 025 02 6 027 028 029 030 3]^i 2% 2% 3^6 3% 45^6 4J^c 4^6 5?^ 5% 5X 7 7 7 3% 3% 55^1 5 7 7 7 8 14 3Vz 1 1 1 1 7 7 7 7 2^ 7X 8 sms 8?:i|8 9 6.28 6.53 6.78 7. 03 7.28 7.53 7.78 8. 03 8.28 8.53 8.78 9. 03 0.030 6 0.030 5 0.030 5J^2 0.030 5>i 0.030 6 0.030 6 0.0306^ 0.030j63i 0.030 7 "■ 0.030 7 0.030 7K 0.030 7>^ 4% 4% 5% 5% 6M6 6% 6% 7^6 7M 7M 8M 9J^ 1 1 11 8% 8i?4 10% 10% 1 1 11 11% 11% 12% 12% 12 12 13J^ 13^ 17 17 9% 10% 10% 10% 11>^ llj^ 11% 12% I3}i 13% 14 6% e% 6%. "!% 7?i 7% 7Ju 8% 8?,; 8% 8% Note. — To f)btain pri]) G of pin, add ^5 e.xtra for each bar packed together with the proper additional amount giveu above in the table. 246 STANDARD COTTER PINS FROM 1" TO 31" DIAMETER. ■Length over all M •» •- Length under Head L ■» Diameter of Pin. Diameter of Pin Hole, Play in Pin Hole. Diameter of Head H. 1 Thickness of Head 1 T. Length L under Head equal to. Letigth over all equal to. Size of Colter a 1 Diameter of Pin 1 1.00 1.03 0.03 l\ \ G+ % G+ % 4xi| 1 1^4 1.25 1.28 0.03 1^ G+ % G+ \ 1^4 1.50 1.53 0.03 1% \ G+ % G + 1 IV2 l\ 1.75 1.78 0.03 2 \ G+ % G + 1 1% 2 2.00 2.03 0.03 2% % G+ G + 114 |x3 2 2\ 2.25 2.28 0.03 2% % i^i G+ % G + 1\ |x3i 214 2\ 2.50 2.53 0.03 2^8 % G + 1% G + II/2 21^ 2% 2.75 2.78 0.03 31/8 % G + 1% G + li^ 2% 3 3.00 3.03 0.03 3^2 \ G + 1% G + \% ix5 3 3^4 3.25 3.28 0.03 3% \ G + 1% G + 1% ix5 314 3^ 3.50 3.53 0.03 4 G + 1% G +2^/8 ^x6 31;i2 3% 3.75 3.78 0.03 G + 1% G +21/8 .fx6 334 247 PENCOYD STEEL SLEEVE NUTS. U. S. standard Thread. L— -4"- Round Bars. Diam. Area \ % 1 1^8 1^4 1% 1^2 1% 1% 1% 2 2\ 2% 2H2 2% 2% 2^/8 3 3^8 3\ 3% 3% 0.307 0.442 0.601 0.785 0.994 1.227 1.485 1.767 2.074 2.405 2.761 3.142 3.547 3.976 4.430 4.909 5.412 5.940 6.492 7.069 7.670 8.296 8.946 10.320, Square Bars, Side. Area. \ % 1 IVa 1% 11/2 1% 1\ 1^/8 2 21/8 2\ 2% 2\ 2% 2\ 2\ 3 Size of 1 x4 0.563 \\ X 4 0.766 \\ X 4 l%x4 1.000 1\ X 4 1.266 l%x 41;^ 13/4X41;^ 1.56317/8x43^ 1.891 2 X 5 2%x5 2.250 21/4 X 5 2.641 2% X 51^ 3.063-2]^ X 5^ 2% X 51^ 3.516|234 X 6 4.000 27/8 X 6 4.516 3 x6 31/8 X 6^2 5.063 31/4 X 6^ 3% X 7 5.641 31/2 X 7 6.250 3% X 8 33/4 X 8 6.891 37/8 X 8 7.563,4 X 8 8.266 41/4 X 9 9.OO0I41/2 X 9 1^ 1% 1% 2 2 2\ 2\ 2\ 2\ 2\ 2% 3 3 31/4 33/4 3^ 31/2 3% 33/4 4 4 41/4 A\ 4^2 ^\ 4% 5 7 7 8^2 8^2 9 9 91/2 91/^ 10 10 10^2 101/2 11 11 ll\ n\ 12 12 121^ 121/2 13 13 13^2 14 A. 1% 1% 2 2 2% 2% 23/4 234 3^8 3^8 31/2 31/2 37/8 37/8 414 4^4 4% 4% 5 5 5% 5% 534 534 61/8 61/8 61/2 6^k OS'S B. 1% 1% 2i\ ^f, 2\ 2\ 3t^ 3i\ 3% 3% 4iiir 4,^ 41,^ 41/2 4H 5% 5% 61/8 61/8 6H 7^8 71/8 7A 1^8 11/8 1% 1% 1% 1% 1% 1^/8 21/8 21/8 2% 2% 2% 2% 27/8 27/8 3^8 31/8 3% 3% 3% 3% 37/8 37/8 41/8 4^8 43/8 434 Lhs. ^4 \ % % IB \ % 1 1 1^8 31/2 4 41^ 61^2 8 8I/2 10 11 14 15 18 19 22 23 27 28 34 35 39 40 45 47 52 55 65 75 248 PENCOYD STEEL CLEVISES. Proportioned According to Pencoyd Specifications. Distance JTcan be made to suit connections.— All dimensions in inches. Size of Clevis. SqUQ/TC Bod. B. Pin. P. Upset. U. Dia- meter of Clevis. D. Fork. F. Nut. N. Width. W. Thick- ness. T. Weight in Pounds. 1 1% 11^x4 31/2 l\ r\ 1% 2 114 X 4 31,^ 1\ 1% r\ 9 ^\ 2 11/8 X 4 31/2 1% 1% 1% 41/2 21/4 I'^/g X 4i/£2 41/0 2 2 2 % 1^/8 2ii«2 1% X 41/2 41/2 2 2 2 1 121,^ 41/0 1 2? 11/2X4 41/2 2 2 2 4I/2 21/2 114x4 41/2 2 2 2 % 5 214 2x5 5 2% 214 214 5 2% 1^/8 X 41^ 5 214 214 214 14 5 2% 1% X 41^ 5 214 214 214 5 1 3 11/2X4 5 21/4 2\ 214 % 5% '8 21/2 23/q X 51jb 51/2 217^2 2\ 21^ 5% 1^/2 2»4 214 X 5 51^ 21,^ 2\ 21/2 19 5% 1% 3 2x5 51^ 21^ 2\ 21/^ 314 1% X 41/2 51/2 21^ 2\ 21^ % 6 1% 2\ 21^ X 51,^ 6 2% 2% 234 % 6 1% 3 2% X 51/2 6 2% 2% 2% ^4 25 6 l^k 314 214 X 5 6 2% 2\ 2% 6 1% 31,42 2x5 6 2% 2\ 2'i4 •^4 I'^/s 3 2% X 6 e\ 3 3 3 6V2 314 21;^ X 51/2 6H2 3 3 3 % 30 1% 3% 2% X 51/2 6\ 3 3 3 1^/2 3% 214 X 5 6^2 3 3 3 % 7 2 3 27/8 X 6 7 314 314 314 > 7 1% 3\ 2\ X 6 7 314 314 314 39 7 1% 3% 21^ X 51^ 7 314 314 314 7 1% 4 2% X 51/2 7 314 314 314 % 7^ 214 3 314 X 6I/2 31^ 31/2 31/2 1 1\ 21/8 31/2 3x6 7^ 31^ 3% 31;^ 1 491/2 1\ 2 4 27/8 X 6 7^ 31/2 31^ 3I/2 1 7^ F/8 414 2»4 X 6 7^ 31,^ 31^ 31^ 1 The size of pin given for each combination of bar and clevis is the maxi- mum size allowed, and cannot be increased, but may be decreased. 249 PENCOYD STEEL EYE BARS. w Width of Bar. t Minimum Thickness of Bar. D Diameler of Head. d Diameter of Largest Pin. Additional Length of Bar Beyond Centre of Eye Required to Form One Head. 3" 3" 4'' 4" 5" 5'' 6'' 6' 7'' 7' 8'' 8'' 8" 9'' 9' \" %" \" \" \" 1" %" 1" %" w 1" 7" 8" 9^2" IV-b" I21/2" 131/2" I41/2" 16" 17" 17" 18" I8I/2" 3" 37/8" 41/8" 5^" 4|i" 5U" 51/2" 6i%" 6U" 7i/2" 6" 7" 71/2" r 3" r b\" V 71/2" r 10' 1' 9" 2' 0%" r 11" 2' 2V4" 2' 2%" 2' 7«4" 2' 2%" 2' 6' 2' 9%" 9'' lO'' 10' 10" 12" 12" 12" Note. — Pencoyd eye bars are hydraulic forged, and are guaranteed to develop the full strength of the bar, under conditions given in the above table, when tested to destruction. The maximum sizes of pins given in the above table allow an excess in sectional area of head on line " ss " over that of the body of the bar of 33 per cent, for diameters of pins, not larger than the width of the bar, and 36 per cent, for pins of larger diameter than the width of the bar ; the thickness of eye being the same as ihe thickncf^s of the body of the bar, or not exceeding the same by more than of an inch. The steel manufactured by us for the use of eye bars is open hearth steel, and will be furnished of such quality as to satisfy the demands of engineers. 250 soMjgl to (jjcn ooLO lOo t>io mm fo p/Upjii |S| T-H(M oico co^ Tum (oc^ ^^Vl(J r^u^ ^to|3= co)a5^ Hto,® Lom moj cob-- t>00 f-^"HA CO Tj< m mm m co co t> ■}9sd/j I MfppV MdipV9.ll/X fo Mqmnji^ •pvguyj; fo looy; fo 'pns-iyx fom-afo iHi-l r-li-l iHi-H ifHtH 00 05 tH oq ... [> CO m CO m CO 00 O O CO I-H CO f\n ^ T*1 CO mm CD CO CD i> CO oi t> oa C» CT> 03 D- CD C» OJ 00 iH OC CO CO m t> p CO CO CO S tea m CD CO CO CI> 05 ■pv9H mnw.ixvjff' J MfppY i^rf- OO co^c5- ij-^r m^m;^ mm T-(iH OO oa oa c~i> oacg cdoa ojoa Max. Diam. of Head, with Max. Pin allowed. Pin d >^ Bs^ <^ coco mm mm coco c-t- Head D tjitgi toitsi i-rrf H~T-f~ T-Ti-T it coco OO oa oa t~ t- T-l rH rH 1-1 i-H i-t tH iH •pvdfi Mfppv coco t-- 1> 05 CD T-lrH oa oa ^?H JhJh tH^H ^HrH Oa OJ Min. Diam. of Head, with Max. Pin allowed. tgDJD cSlxSw l!g)J^ H--eHti> 5: t ,^H~ Hr^H-l iH^lH^ r^r-r4r^ COCO •<^< mm coco Head D; ts)^ jfJti ^-S? r^f^ ■^'"C ?_?^ i> t> c:3 OJ 1— 1 rH COCO coco iH iH I— 1 rH T— 1 1— 1 Thickness of Bar. ^ rH rH iH rH rH rH iH rH rH i— 1 OO OO OO OO OO I-l rH rH rH rH rH rH rH S =>• 3 ft K| COCO mm cdcd c-- [> 251 ALLOW AJfCE FOR UPSETS ON SQUARE AND ROUND STEEL BARS. —■6" «•! In. Sound Bars. 1 iVs 1% 1% 1% r% 1% 2 2>i 2^4 2% 2K 2?^ 2% 3 SVh 3\ 3Vs 3§^10 0.307 0.442 0.601 0.785 0.994 1.227 1.485 Lbs. 1.04 41436.8 1.50 3% 24.4 2.04 5 48.3 2.67143/^34.7 3.38!3% 30.3 4.18:3%!23.5 5.05,3K'17.4 1.767 6.01i4''j^'30.3 2.074 7.05 4i/4[27.8 2.405 8.184 25.7 2.761 9.39 4i^'23.9 3.142 10.68 3%il8.3 3.547 12.06 3'J^ 17.1 3.97613.52 4^4 28.5 4.430 15.O7I43422.6 4.90916.69:43421.3 5.412 18.401434 20.3 5.940 20.20j4^|19.3 6.492 22.07 514I25. 9 7. 069124. 03151^122. 2 7.670l26.08i5Vii21.3 8.296 28.20 4?^!20. 7 8.94630.42 6 26.6 .32 :35. 09,434 23.6 Size of Upset. In. In. %4 1 4 1%4 1KI4 1%!4 1>^!4 1^4 434 1 1!4 4^2 1%434 ' 5 231^5 234 5 2%5H2 23^53^2 2% 53^ 2 25^46 - 2% 6 6 33^ 634 2 3H 63$ 2 3% 7 3 k, 7 3->^8 3%I8 1"^ Sq. In. 731 0.420 .837 0.550 940 0.694 065 0.891 .I6O1 1.057 284 389 .490, 615 712 837 .962 .087 175 300 .425 ,550 629 754 879 004 100 225 317 442 43i!9 3. 434i9 i4. 1.295 1.515 1.744 2.049 2.302 2.651 3.023 3.410 3.716 4.155 4.619 5.107 5.430 5.957 6.510 7.088 7.548 8.170 8.641 9.305 567i 9.9935: 798ill.33 028112.75 7 7 6 6 53^ 5 5 434 13' 43$ 15 Lbs 23^ 334 4 534 6 7K 10 1134 33^34 334 38 33^50 334 50 33465 334 65 334 334 3 3 2% 2% Square Bars. In. ?4 0.563 % 0.766 1.000 1% 1.266 1341.563 1% 1.891 2^45 234 6 2% 6 2% 7 2%8 1.9133420.6 2.60 4 3.404 1342.250 7.65 4% 34 1^^2.641 8.98 45^29. 1^3.06310.41 434 21 1% 3.516 11.95 53^ 31 4. 000113.60 4?4 27 23^4.51615.35 4^20 234 5.063 17.22 53^28.6 4.30 434 19.7 5.31 434 31.1 6.43 4% 21.7 ,641 19.18163^ 33. E 1.250121.25163430.7 . 891123. 43!6% 35 .563 25.71'6 266^28.10:8 9.000130.60,734 41 16.3 29.5 .0 25.1 37.0 .7 252 M'cT .'0 rH(>)(M (SNCO (OCOCO ■^■^■^ TfiOiO IQIOCO ui w j fo OOffiO rHrHCq CO W ® t- CO (Mwco cococo cococo eccoco CQWiM cococo cococo cococo PoOO) O-i^ NM^ W^t^ NNcq cococo cococo cococo ao^^ Sco^" u5tot- «« eqcgcN wcoco cococo cococo 10 S t- 00 0)0 cqcqcg (MCQCo CO CO CO CO CO CO coo rHNcb O w Cq CO ^ CO CO CO CO CO CO OS O -H « CO w CO CO CO CO CO CO*''*' locot- ««« -( « (M (M 0) ffit-^CO oo^ (MCOCO S^t- cocoa Ot^n ^S'lD t^oiffl O^HN ,-lrHrH rH « 0) « t-cD(0 do-H tH tH H rH i-H »H »H 03 cq co'<* CQOlOl oicqN ^<«oi «'«co mcora ■^uiS Sjoto 253 STANDARD FRAMIJfG OF PENCOYD BEAMS AND CH ANNEXES. 24" 2 2 -9- -0- — .->--H-© 4- -0 ^1 >t- 2 Angles 4" x '6^' x t'^" x 18". 20 2" 2" i<— >i i< -> 'ft 1 \ 1 1 1 ■ U- ■4- 2 Angles 4" x 31/2" x ^" x 15". 2" 2" i I I ! I 1 ■l-f 18' ■3: 2^2 -•i -0- ,0. -4- 6 15' 2 2 I.— >i i<— .1 2^22^" |>- \ 1 1 i 1 1 ■|-r- 0], 02^ 46 2 Angles 4" x 3^^" x ^" x 15". 2 Angles 6" x x ,%" x Vd%". 254 CONNECTIONS FOR BEAMS OF DIFFERENT DEPTHS. (Framing Opposite.) 15" I and 12" I. i boo ] boo i^i I t ^^.'J 12" I and 10" I. o o o b o o o 6 10" I and 9" I. 15" I and 10" I. O 0(g) ( ( O 0( oe- o o o'd 15" I and 9" I. o 0( ( ( O 0( o-o o o do 15" I and 8" I. 15" I and 7" I i boo t)0 o ■A 12" I and 9" I. d^^ lO O do 12" I and 8" I. 0( o o do Oi/tUfbrlieaui/& 12" I and 7" I. j¥o}55i. 12" I and 6" I. 10" I and 8" I. 9" I and 8" I. o o dd o o d'd 10" I and 7" I. 9" I and 7" I. 8" I and 7" I. o o<^ ddc Sei-bach. %' bo-ol-.--, ^1 ' ro; 10" I and 6" I. 9" I and 6" I. 8" I and 6" I. o qc ddc 1" I and 6" I. 256 STANDARD ANGLE CONNECTIONS. The connections illustrated on preceding pages are propor- tioned, for a load uniformly distributed over a minimum length of span as given below : Size of Beams. Section Number. Minimum Safe Span in Feet. Size of Beams. Section Number. Minimum Safe Span in Feet. Size of Beams. Section Number. ^ Minimum Safe Span in Feet. 24 240B 19.0 20 203B 17.5 12 124B 12.0 8 80B 5.0 20 200B 16.0 12 122B 9.0 7 70B 40 18 183B 16.0 12 120 B 7.5 6 67B 6.0 18 180B 14.0 10 102B 8.5 5 50B 4.5 15 156B 14.5 10 lOOB 7.0 4 40B 3.0 15 154B 12.0 9 90 B 5.5 3 SOB 2.0 15 152B 10.0 All holes ii". All rivets f. When beams frame opposite each other into another beam or girder with web thickness less than y\^^, tiie above given minimum lengths of spans ought to be increased in the pro- portion of the web thickness to -i^^^. These connections are based on shearing strains of 10,000 pounds per square inch, and bearing strains of 20,000 pounds per square inch, when the length of attached beams corre- spond to the foregoing table, and extreme fibre stress of 16,000 pounds per square inch at beam flanges. STANDARD SPACING of RIVETS THROUGH FLANGES OF 2j ^^R COLUMNS. Size of Z Bar. a. b. c. d. e. 6 inch. 71/4 2 4I/4 5 " 10 &k 13/4 4 4 " 5I/I2 1% 3 1^4 3 " 4% 1^'2 2V2 1^/8 KIVETS 8/4 INCH, 260 CO O Ah CO H M o H Q 0 J?; I-l 12000 9840 11250 9190 10500 Ht< 8530 1 9750 6750 7880 9000 6190 7220 8250 4690 5630 6560 7500 O O O o to c- o o o O lO o CO 00 LO Cd o UO CD O o o o o CO CO Tt< C35 lO C3> lO oq 00 CO lO Single Shear at 6,000 Lbs. 660 1180 184(1 o o o LO rH tH CO CO 1> (Nl CO Ttf Area Square Inches. Tt< CO CO 00 CO O CO CD T-H 1-4 LO i-H 05 O T*l O 00 rH »— 1 00 CD t> un o LO o uo o t; O LO i> o CO LO CD I> CO O ^ -4^ ^ ^ JO , o o olo o o rH 00 ■<+( IrH 00 LO CO COloQ CO t- rH rH eg |C?3 CO CO Single Shear at 7,500 Pounds. Q p O O O O 00 O O rH rH CJ) 00 TfH 00 00 LO 00 rH eg 00 Ttl lD Area in Square Inches,' ^ CO 00 00 CO O CO CO rH rH lO rH O ■'^^ O CDO rH rH CO T# CO C- i Inches. Decimal. tp O lO O lO o E:; o oa LO t- o 00 LO CD 00 O r-i ■Fraction. -jyi ^ JO _j p III .9 fl ° 3 Z « CO w 9 ^ 5 =s ^ o "It! a c3 cs 264 Q I?; P o Ph M SO H H P £ 0 q ^ o fq ft I-H CO Inch. 22000 Square . 18050 20630 nds per 16840 19250 1 o 15640 17880 li e 12380 14440 16500 in Inch 11340 13240 15130 of Plate 8600 10320 12040 13750 '.knesses 7740 9280 10840 12380 ent Thit 55001 o 00 CO CD 8250 9630 11000 ■ Differ o 6020 7220 8430 9630 ilue for M~ 3090 4130 5160 6190 7220 8250 is: •i 2580 j o |4300 5160 6020 o 00 00 CD Bea: 2060 2750 3440 4130 4810 O O LO LO Single at 11,000 Lbs. 1210 o CD 1— 1 3370 4860 6610 8640 ?; a Ch ) H .1104 .1963 .3068 .4418 .6013 .7854 •hes. Decimal. LO l> CO o o LO lO oq CO o lO LO o 00 l.OCO 1 Inc Fraction. 1C~ 265 U. S. STANDARD SCREW THREADS. □n 8 c Ins. Threads per Inch. °£ Width of Flat. Area of Bolt Body in Sq. Inches. Ins. Ins. 1 4 20 .185 .0062 .049 -5^ Iff 18 .240 .0074 .077 3. 8 16 .294 .0078 .110 ts 14 !344 .0089 .150 •A 10 13 .400 .0096 .196 12 .454 .0104 .249 5. 11 .507 .0113 .307 10 !620 .0125 .442 t 9 .731 .0138 .601 1 8 .837 .0156 .785 ■■-8 7. .940 .0178 .994 7 l!065 .0178 1.227 If 6 1.160 .0208 1.485 li 6 1.284 .0208 1.767 l| 5i 1.389 .0227 2.074 l| 5' l'.491 .0250 2.405 5 1.616 .0250 2.761 2 41 1.712 .0277 3.142 Ah 1.962 .0277 3.976 2\ 4' 2!l76 .0312 4.909 2| 4 2.426 .0312 5.940 3 3^ 2.629 .0357 7.069 3i 3 J 2.879 .0357 8.296 31, 3i 3.100 .0384 9.621 3| 3 3.317 .0413 11.045 4 3 3.567 .0413 12.566 4i 2| 3.798 .0435 14.186 4.V 2| 4.028 .0454 15.904 4| 2| 4.256 .0476 17.721 5 2i 4.480 .0500 19.635 5i 2i 4.730 .0500 21.648 5| 2| 4.953 .0526 23.758 5J 2| 5.203 .0526 25.967 6 21 5.423 .0555 28.274 .027 .045 .068 .093 .126 .162 .202 .302 .420 .550 .694 .893 1.057, 1.295 1.515 1.746 2.051 2.302 3.023 3.719 4.620 5.428 6.510 7.548 8.641 9.963 11.329 12.753 14.226 15.7631 17.572 19.267 21.262 23.098 Ins. 11 m 2 2^ 2f 2A 2H 4§ 5 5t 5| Qi 61 6| 75 42 1 If ii% If lit 21 2A 2i 2H 2J 3fff 3A 3fl 4tl' 63:1 Ins. Ifi 1* m 2| 2M 3-A 3M 3f 4i^- ^ 5| mm 8pil0t| gp xij 8ino,^i2| 9J;10M12e 1^ Ins. iS ■'■ff4 m li m 2,V 2JI 2f| 33^ 3?| 3f 3^i 4 m 4|ji 51 6 71: 266 WEIGHTS OF BOLTS PER HUNDRED SQUARE HEADS AND NUTS. Dimensions in Inches. Diameter. % % % % 1 1^8 1^4 1% 1^2 Length. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. r\ 2 9.7 10.5 11.3 20.4 21.3 22.4 37.0 37.9 39.9 58.0 60.8 63.2 97.7 145 2\ 2V2 2\ 12.1 12.9 13.7 23.6 25.0 26.4 42.0 44.4 46.2 66.0 69.0 72.1 101.6 105.6 109.7 149 153 158 3 31/2 4 14.5 16.1 17.7 27.8 30.6 33.4 48.3 52.5 56.7 75.2 81.4 87.6 113.8 122.0 130.2 163 174 185 240 253 267 309 325 342 350 370 390 480 500 520 41/2 5 19.2 20.7 22.2 36.2 39.0 41.8 60.9 65.1 69.2 93.8 100.0 106.1 138.4 146.4 154.9 196 207 218 281 295 309 359 376 394 410 430 450 545 570 595 6 61/^ 7 23.7 25.2 26.7 44.6 47.4 50.2 73.4 77.6 81.8 112.2 118.3 124.4 163.2 171.5 179.8 229 240 251 323 337 351 412 430 448 470 490 510 620 645 670 71;, 8 9 28.2 29.7 33.1 53.1 56.0 61.5 86.0 90.0 98.0 130.5 136.6 148.8 187.1 195.4 212.0 262 273 295 365 379 407 466 484 518 530 550 590 695 725 775 10 11 12 36.5 40.0 43.5 67.0 72.5 78.0 106.3 114.6 122.9 161.0 173.2 184.4 229.0 246.0 263.0 317 339 361 435 463 491 552 586 620 630 670 710 825 875 925 Additional per Inch. Increase in Length 3.1 5.5 8.7 12.5 17.0 22.2 28.1 34.8 42.0 50.0 Amount to be deducted f rom weights in table if Hexagon Heads and Nuts are ^ised. 1.2 3.6 5.3 12.0 15.0 21.0 31.0 42.0 50.0 64.0 267 WEIGHT OF BRIDGE RIVETS PER 100. This Table also Applies to Button-headed Bolts. IJzameiGT of Rivet in % ^2 % 34 % 1 Inches. Length of Rivet Un- der Head in Inches. Weight Weight Weight Weight Weight Weight Weight Weight in Rounds. in Rounds. in Rounds. Jrounas. J. O UTidS, JrOUnttS. 1)4 5.7 12.8 22.0 29.3 43.9 66.6 93.3 127.1 1% 6.1 13.5 23.1 30.9 46.1 69.4 96.9 131.5 6.5 14.2 24.1 32.4 48.2 72.1 100.4 135.8 1^ 6.9 14.8 25.2 34.0 50.3 74.9 103.9 140.2 1% 7.3 15.5 26.3 35.5 52.5 77.7 107.4 144.5 li^ 7.7 16.2 27.4 37.1 54,6 80.5 110.9 148.9 2 8.0 16.9 28.5 38.7 56,7 83.3 1 14.5 153.2 2V 8.4 17.6 29.6 40. 2 58.8 86.0 1 18. 0 157.5 Z\i 8.8 18.3 30.7 41.8 61.0 88.8 121.5 161.9 2% 9.2 19.0 31.7 43.3 63.1 91.6 125.0 166.2 2>i 9.6 19.7 32.8 44.9 65.2 94.4 128.5 170.6 2% 10.0 20.4 33.9 46.5 67.4 97.2 132.1 174.9 2% 10.4 21.1 35.0 48. 0 69.5 99.9 135.6 179.3 2.% 10.8 21.8 36.1 49.6 71.6 102.7 139.1 183.6 3 1 1.2 22.5 37.2 51.1 73.7 105.5 142.6 188. 0 3}i 1 1.6 23.2 38.3 52.7 75.9 108.3 146.1 192.3 3/^ 1 1.9 23.9 39.3 54.3 78. 0 111.1 149.7 196.7 CO 12.3 24.6 40.4 55.8 80.1 113.8 153.1 201.0 12.7 25.3 41.5 57.4 82.3 1 16.6 156.7 205.4 3% 13.1 26.0 42.6 58.9 84.4 1 19.4 160.2 209.7 05 13.5 26.7 43.7 60.5 86.5 122.2 163.7 214.1 3Ji 13.9 27.4 44.8 62.1 88.6 125. 0 167.3 218.4 4 14.3 28.1 45.9 63.6 90.8 127.8 170.8 222.8 4X 14.7 28.7 46.9 65.2 92.9 130.5 174,3 227. 1 4>4' 15.1 29.4 48.0 66.7 95.0 133.3 177,8 231.4 4?^ 15.5 30.1 49.1 68.3 97.2 136.1 181.3 235.8 4k 15.8 30.8 50.2 69.9 99.3 138.9 184.9 240. 1 16.2 31.5 51.3 71.4 101.4 141.7 188.4 244,5 4?i' 16.6 32.2 52.4 73.0 103.5 144.4 19 1.9 248.8 4J^ 17.0 32.9 53.3 74.5 105.7 147.2 195.4 253.2 5 17.4 33.6 54.5 76.1 107.8 150.0 198.9 257.5 18.2 35.0 56.7 79.2 112.1 155.6 206. 0 266.2 19.0 36.4 58.9 82.3 116.3 161.1 213.1 274.9 5?i 19.7 37.8 61.1 85.5 120.6 166.7 220.1 283.6 6 20.5 39.2 63.2 88.6 124.8 172.2 227.1 292.3 7 23.6 44.7 71.9 101.1 142, 0 194.5 255.3 327. 1 8 26.8 50.3 80.6 1 13.7 158.9 216,7 283.4 361.9 9 29.9 55.9 89.3 126.2 175.9 239.0 31 1.6 396.6 10 33.0 61.4 98. 0 138.7 193.0 261.2 339.7 431.4 12 39.3 72.5 1 15.4 163.7 227.0 305. 7 367.9 501.0 WKIGHT OF TWO (2) BIVET HEADS IN POUNDS. % % % % 1 1^4 Before driving.. After driving.... .037 .032 .116 .082 .222 .147 .273 .246 .453 .369 .78 .545 1.16 .746 1.67 1.02 WEIGHT OF BODY PER INCH OF I,ENGTH IN POUNDS. % % % \ % 1 1^8 IV4 Before driving.. .03 1 .056 .087 .125 .170 .223 .282 .348 268 PENCOYD SPECIFICATIONS FOR RAILROAD BRIDGES. Material —1. All structures to be wholly of rolled steel (cast- ings of iron or steel will be permitted only in machinery for draw-bridges). Live Load.— 2. They shall be designed to carry, in addition to tlieir own weight and that of the floor, a moving load for each track, consisting of two engines coupled at the head of a uniformly distributed train load, placed so as to give the greatest strain in each part of the structure. This load will be such as specified by the Railroad Company and represented on a diagram accompany- ing the specifications. Dead Load. — 3. In determining the weight of the structure for the purpose of calculating strains, tlie weight of timber shall be assumed at 4i pounds per foot B.M., and the weight of rails, spikes, and joints at 100 pounds per lineal foot of track. Wind Pressure. — 4. The wind pressure shall be assumed acting in either direction horizontally : First. At 30 pounds per square foot on the exposed surface of all trusses and tlie floor as seen in elevation, in addition to a train of 10 feet average height, beginning 2 feet 6 inches above base of rail, moving across the bridge. Second. At 50 pounds per square foot on the exposed surface of all trusses and the floor system. The greatest result shall be assumed in proportioning the parts. 5. For determining the requisite anchorage for the loaded struc- ture, the train shall be assumed to weigh 800 pounds per lineal foot. Momentum of Train. — 6. For longitudinal bracing of trestle towers and similar structures, the momentum produced by sud- denly stopping the train shall be considered, the coefficient of friction of wheels sliding upon the rails being assumed as 0.2. Centrifugal Force of Train. — 7. When the structure is on a curve, the additional effects due to the centrifugal force of as many trains as there are tracks, shall be considered and calculated by the following formula : C= 0.02 WD for a curvature up to 5 degrees, C = centrifugal force in pounds, where W= weight of train in pounds, D = degree of curvature. The coefficient for centrifugal force (0.02) shall be reduced 0.001 for every degree of curvature above 5 degrees. PROPORTION OF PARTS. Effect of Impact. — 8. In proportioning the members of the structures, the effects of impact and vibration shall be considered and added to the maximum strains resulting from the above mentioned engine and train loads. The effect of impact is to be determined by the following formula : I^S '^^3Qo) (See Table, page 278.) 269 J= impact to he added to tlie live-load strain. ;S' = calculated maximum live-load strain, where i = length of loaded distance in feet which produces tlic maximum strain in member. Permissible Tensile Strains.— 9. All parts of the structure slui 1 1 he so proportioned that the sum of the maximum loads, to.iietlicr with the impact, shall not cause the tensile strain to exceed : On soft steel, 15,000 pounds per square inch. On medium steel, 17,000 pounds per square inch. 10. The same limiting unit strains shall also be used for mem- bers strained by wind pressure, centrifugal force, or momentum of train. Permissible Compressive Strains.— 11. For compression mem bers, these permissible strains of 15,000 and 17,000 pounds pci' square inch, shall be reduced in proportion to the ratio of t lie length to the least radius of gyration of the section by the follow - ing formulae : For soft steel, = 1 + 13,500r2 For medium steel, p = ^^'^^^ 1 ■ ^ ll,000r2 = permissible working strain per square inch in compression. I = length of piece in inches, centre to centre of connection. r = least radius of gyration of the section in inches. (See Table.) 12. No compression member, however, shall have a length exceeding 100 times its least radius of gyration, excepting those for wind bracing, which may have a length not exceeding 120 times the least radius of gyration. Alternate Strains.— 13. Members subject to alternate strains of tension and compression, shall be so proportioned that the total sectional area is equal to the sum of areas required for each strain . Combined Strains.— 14. In case the maximum strains in chords of bridges, or posts of trestle towers, due to wind and centrifugal force, added to the maximum strains due to vertical loading, (in- cluding impact), shall exceed the following limits : On soft steel, 19,000 pounds per square inch. On medium steel, 21,000 pounds per square inch, properly re- duced for compression, addition must be made to such mem'bers until these limits are not exceeded. 15. Should the strains be reversed in any possible case, proper provision must be made for such strains in the opposite direction. Transverse Loading of Tension or Compression Members. — 16. When the floor system rests directly on the top or bottom chord, the latter must be so proportioned that the algebraic sum of the strains per square inch on the outer tibre, resulting from 270 the direct compression or tension, and three-fourths of the maxi- mum bending moment (the chord being considered as a beam of one panel length, supported at the ends), shall not exceed the before-mentioned limiting strains in tension or compression, the proper amount of impact being added to each kind of loading. 17. Tlie bending moment at panel points shall be assumed equal to that in the centre, but in opposite direction. 18. All other members which are subject to direct strain in addition to bending moment are to be similarly calculated. Shearing and Bearing Strains. — 19. The shearing strain on rivets, bolts, or pins, per square inch of section, shall not exceed 11,000 pounds for soft steel, and 12,000 pounds for medium steel ; and the pressure upon the bearing surface of the projected semi- intrados (diameter X thickness) of the rivet, bolt, or pin-hole, shall not exceed 22,000 pounds per square inch for soft steel, and 24,000 pounds for medium steel. 20. In case of field riveting by hand, the number of rivets thus found shall be increased 25 per cent. Bending Strains on Pins.— 21. The bending strain on the ex- treme fibre of pins shall not exceed 22,000 pounds per square inch for soft steel, and 25,000 pounds per square inch for medium steel, when the centres of bearings of the strained members are taken as the points of application of the strains. 22. Net sections must be used in all cases in calculating tension members, and, in deducting rivet-holes they must be taken i of an inch larger than the size of the rivets. Plate Girders.— 23. No allowance shall be made for the web in calculating the flange sections of plate girders. The compressed flange shall have the same sectional area as the tension flange ; but the unsupported length of flange shall not exceed twelve times its width. 24. In calculating shearing strains and bearmg strams on web rivets of plate girders, the whole of the shear acting on the side of the panel next the abutment is to be considered as being trans- ferred into the flange angles in a distance equal to the depth of tliG girder. 25. The shearing strain in web plates shall not exceed 9,000 pounds per square inch for soft steel, and 10,000 pounds per square inch for medium steel ; but no web plate shall be less than i of an inch in thickness. 26. The web shall have stiffeners riveted on both sides, with a close bearing against upper and lower flange angles at the ends and inner edges of bearing plates, and at all points of local and concentrated loads, and also, when the thickness of the web is less than ^ of the unsupported distance between flange angles, at points throughout the length of the girder, generally not farther apart than the depth of the full web plate, with a maxi- mum limit of 5 feet. GENERAL DESCRIPTION. Clearance.— 27. On straight line a clear section shall be provided to conform to given requirements. The width must be increased so as to allow the same minimum clearance on curves and on double track. 271 Spacing of Trusses— 28. The width between centres of trusses shall in no case be less than of the span between centres of end pins. Spacing of Stringers— 29. The floor stringers shall be placed generally 8 feet between centres for single track, and 6i feet for double track bridges, the standard distance between centres of tracks being 13 feet. Wooden Floor.— 30. The floor shall consist of cross-ties 8 inches by 8 inches if the stringers are placed 6i feet between centres, and 8 inches by 10 inches if the stringers are 8 feet between centres. They shall be spaced with openings not exceeding 6 inches, and shall be notched down ^ inch, and have a full and even Ijearincc on stringers. 31. Every fifth tie shall be fastened to the stringer by a ^-inch bolt. 32. In case of deck bridges, with ties resting on the upper chord, when the distance between centres of trusses exceeds 8 feet, the ties are to be proportioned to carry the maximum wheel load distributed over three ties, the fibre strain on the timber not to exceed 1,000 pounds per square inch. Plate Girders.— 33. Deck-plate girders shall be spaced generally 6i feet between centres. 34. In through-plate girders, the floor stringers shall be spaced 6i feet between centres. Guard Eails.— 35. There shall be guard timbers 6 inches by 8 inches on each side of each track, with their inner faces not less than 3 feet 3 inches from centre of track. They shall be notched 1 inch over every tie, and shall be fastened to every third tie and at each splice by a 1-inch bolt. Splices shall be over floor timbers with half-and-balf joints of 4 inches lap. 36. The floor timbers and guards must be continued over piers and abutments. 37. On curves the outer rails shall be elevated as may be required. Strain Sheets. — 38. Complete strain sheets, showing sectional areas and dimensions of all the parts, will be submitted with every proposal. DETAILS OF CONSTRUCTION. Adjustable Members.— 39. Adjustable members in any parts of structures shall preferably be avoided. Lateral and Sway Bracing. — 40. All lateral and sway bracing shall be made of shapes which can resist tension as well as com- pression. Portals. — 41. All through spans with top lateral bracing shall have portals at each end of span, connected rigidly to end-posts. They shall be as deep as the specified head room will allow, and provision shall be made in the end-posts for the bending strain produced by the wind pressure. Diagonal Bracing.^2. Deck bridges shall have diagonal braces at each panel of sufficient strength to carry half the maximum strain-increment due to wind and centrifugal force. Pony Trusses. — 43. Pony trusses and through plate girders shall be stayed by knee braces or gusset plates at the ends, and at each floor beam or transverse strut. 272 Floor Beam Connections. — 44. All floor beams in through bridges sliall be riveted between the posts, above or below the pin. Expansion Rollers. — 45. All bridges exceeding 100 feet in length shall have at one end nests of turned friction rollers, running be- tween planed surfaces. Rollers shall not be less than 3 inches in diameter ; and the pressure per lineal inch of roller, including impact, shall not exceed 1200 Vd for steel rollers between steel surfaces (r2 = diameter of roller in inches). Friction Plates. — 46. For bridges less than 100 feet in length, one end shall be free to move upon planed surfaces. Truss Bridges. — 47. Single-track bridges shall have lower chord end panels stiffened, and all through spans stiff and vertical sus- penders. Temperature. — 48. Provision shall be made for a free expansion and contraction of all parts, corresponding to a variation of 150 degrees Fahrenheit in temperature. Bed Plates. — 49. Bed plates shall be so proportioned that the pressure upon masonry (including impact) will not exceed 400 ])()unds per square inch. Web Splices.— 50. Web plates of girders must be spliced at all j (lints by a plate on each side of the web, capable of transmitting tlie full sliearing strain through splice rivets. Rivets. — 51. The pitch of rivets, in the direction of the strain, shall never exceed 6 inches, nor 16 times the thickness of the tliinnest outside plate connected, and not more than 30 times that thickness at right angles to the strain. 52. At the ends of compression members the pitch shall not exceed four diameters of the rivet, for a length equal to twice the width of the member. 53. The distance from the edge of any piece to the centre of a rivet-hole must not be less than li times the diameter of the rivet, nor exceed 8 times the thickness of the plate ; and the distance between centres of rivet-holes shall not be less than 3 diameters of the livet. Tie Plates. — 54. All segments of compression members con- nected by latticing only, shall have tie plates placed as near the ends as practicable. They shall have a length of not less than the greatest depth or width of the member, and a thickness not less than of the distance between the rivets connecting them to the compressed members. Lacing. — 55. Single lattice bars shall have a thickness of not less than and double bars connected by a rivet at the inter- section of not less than ^«of the distance between the rivets con- necting them to the member ; and their width shall be : For 15-inch channels, or built sections ) „, . , /7 . , . . \ with 3i- and 4-inch angles. j ^4 ^ches (i-mch rivets) . For 12- and 10-inch channels, or built | oi • i • i • j. \ sections with 3-inch angles. ) "^^^^^'^ (5""^^^^ ^^^^^^s) . For 9- and 8-inch channels, or built jo- i • i, • j. \ sections with 2Mnch angles. } ^ "^ches (g-inch nvets) . 56. The distance between connections of the lattice bars shall not exceed 8 times the least width of the segments connected. Pin Plates. — 57. All pin-holes shall be re-enforced by additional material when necessary, so as not to exceed the allowed pressure 273 on the pins. These re-enforcing plates must contain enough rivets to transfer the proportion of pressure wliich comes upon tliem, and at least one plate on each side shall extend not less than G inches beyond the edge of the tie plate. Joints. — 58. All joints in riveted work, whether in tension or compression members, must be fully spliced. Pin connection, in riveted tension members shall have a section through the pin- hole 25 per cent, in excess of the net section of the body of thr member. The section back of the pin-hole shall be at least 0.75 of the section through the pin-hole. The sections of compression chords shall be connected at the abutting ends by splices sufficient to hold them truly in position . Least Thickness of Material. — 59. For main members and their connections, no material shall be used less than ft of an inch thick : and for laterals and their connections, not less than ^ of an inch thick except for lining or tilling vacant spaces. Eye-bar Heads. — 60. The heads of eye-bars shall not be less in strength than the body of the bar. Symmetrical Sections. — 61. All sections shall preferably hv made symmetrical, and the pins placed in the hue of the neutral axis. Camber. — 62. All truss bridges with parallel chords shall be given a camber, by making the panel lengths of the top chord longer than those of the bottom chord in the proportion of i of an inch to every 10 feet. Nuts. — 63. All nuts must be of hexagonal shape. WORKMANSHIP. Riveted Work. — 64. All riveted work shall be punched accu- rately with holes of i^ich larger than the size of the rivet; and when the pieces forming one built member are put together, the holes must be truly opposite ; no drifting to distort the metal will be allowed ; if the hole must be enlarged to admit the rivet, it must be reamed. 65. All holes for field rivets, excepting those in connections for lateral and sway bracing, shall be accurately drilled to an iron templet, or reamed while the connecting parts are temporarily put together. Planing and Reaming. — 66. In medium steel over f of an incli thick all sheared edges shall be planed, and all holes shall lie drilled or reamed to a diameter of i of an inch larger tlian the punched holes, so as to remove all the sheared surface of the metal. 67. The rivet heads must be of approved hemispherical shape, and of a uniform size for the same size rivets throughout the work. They must be full and neatly finished throughout tlie work and concentric with the rivet-hole. 68. All rivets when driven must completely fill the holes, the heads be in full contact with the surface, or countersunk when so required. 69. Wherever possible, all rivets shall be machine-driven. Power riveters shall be direct-acting machines, worked by steam, hydraulic pressure, or compressed air, and capable of holding on to the rivet when upsetting is completed. 274 70. When members are connected by bolts which transmit sliearing strains, the holes must be reamed parallel, and the bolts turned to a driving fit. 71. The several pieces forming one built member must fit closely together, and when riveted shall be free from twists, bends, or open joints. 72. All portions of the work exposed to view shall be neatly finished. 73. All surfaces in contact shall be painted before they are put together. Forged Work.— 74. The heads of eye-bars shall be made by up- setting, rolling, or forging-into shape. Welds in the body of the l)ar will not be allowed. Eye-bars.— 75. The bars must be perfectly straight before boring. 76. The holes shall be in the centre of the head and on the centre line of the bar. 77. All eye-bars shall be annealed. Machine Work. — 78. All abutting surfaces in compression members shall be truly faced to even bearings, so that they shall be in such contact throughout, as may be obtained by such means. 79. The ends of floor girders shall be faced true and square. 80. Pin-holes shall be bored truly parallel with one another and at right angles to the axis of the member unless otlierwise .shown in drawings ; and in pieces not adjustable for length, no variation of more than 3^ of an inch will be allowed in the length between centres of pin-poles. 81. Bars which are to be placed side by side in the structure shall be bored at the same temperature, and shall be of such equal length that, upon being piled on each other, the pins shall pass through the holes at both ends at the same time without driving. 82. All pins shall be accurately turned to a gauge, and shall be straight and smooth. _ , . , , i „ u 1 ^ 83. The clearance between pm and pm-hole shall be ^ of an inch for all lateral pins ; and for truss pins the clearance shall be 7^(5 of an inch for pins 8J inches in diameter, which amount shall be gradually increased to ^ of an inch for pins 6 inches in diameter and over. 84. All pins shall be supplied with steel pilot nuts, for use dur- ing erection. . 85. All workmanship shall be first class in every particular. STEEL. Process of Manufacture.— 86. All steel must be made by the Open Hearth process, and if by acid process, shall contain not more than .08 per cent, of phosphorus, and if by basic process, not more than .05 per cent, of phosphorus, and must be uniform in character for each specified kind. Finish.— 87. The finished bars, plates, and shapes must be free from injurious seams, flaws, or cracks, and have a clean, smooth finish. . „,,.., 1 Test Pieces.— 88. The tensile strength, limit of elasticity and ductility, shall be determined from a standard test-piece cut from the finished material, of at least i square inch section . All broken samples must show a silky fracture of uniform color. 275 89. Every finished piece of steel shall be stamped with the blow number identifying the melt. 90. Steel shall be of two grades : soft and medium. Soft Steel. — 91. Soft steel shall have an ultimate strength of 50,000 to 60,000 pounds per square inch, elastic limit of one-halt ultimate strength, and a minimum elongation of 26 per cent, in 8 inches. This steel must bend double to close contact, without sign of fracture on the outside. Medium Steel. — 92. Medium steel sh&W have an ultimate strengtli, when tested in samples of the dimensions above stated, of 60,000 to 70,000 pounds per square inch ; an elastic limit of not less than one-half the ultimate strength, and a minimum elongation of 22 per cent, in 8 inches. 93. Tliis steel must stand bending 180 degrees around a 2-inch pin without cracking on the convex surface, either cold, hot, or after being heated to a cherry red and cooled in water of 00 de- grees Fahrenheit. 94. Full-sized eye-bars must elongate 10 per cent, in a gauged length of 10 feet, and break in the body of the bar. Pin Steel. — 95. Pins made of either of the above-mentioned grades of steel shall, on specimen test-pieces cut from finished material, fill the requirements of the grade of steel from which it is rolled, excepting the elongation, which shall be decreased 5 per cent, from that specified. 96. Punched rivet-holes, pitched two diameters from a sheared edge, must stand drifting until the diameter is one- third larger than the original hole, without cracking the metal. 97. All rivets will be made of soft steel, and the steel for riv^ets must bend double to close contact without cracking. 98. The slabs for rolling plates shall be hammered or rolled from ingots of at least twice their cross-section. 99. Pins up to 7 inches diameter shall be rolled. 100. Pins exceeding 7 inches diameter shall be forged under a steel hammer striking a blow of at least 5 tons. The blooms to be used for this purpose shall have at least three times the sec- tional area of the finished pins. 101. A variation in cross-section or weight of rolled material of more than 2i per cent, from that specified, may be cause for rejection. Steel Castings. — 102. Steel castings shall be made of Open Hearth steel containing from to per cent, carbon and not over per cent, of phosphorus, and shall be practically free from blow holes. Cast Iron. — 103. Except where chilled iron is specified, all cast- ings shall be of tough, gray iron, free from injurious cold shuts or blow holes, true to pattern, and of workmanlike finish. Test bars 1 inch square, loaded in middle between supports 12 inches apart, shall bear 2,500 pounds or over, and deflect .15 of an inch before rupture. Timber. — 104. The timber shall be strictly first-class white pine. Southern yellow pine, or white oak bridge timber ; sawed true and out of wind, full size, free from wind shakes, large or loose knots, decayed or sapwood, wormholes or other defects impair- ing its strength or durability. 276 PAINTING. 105. All iron work before leaving the shop shall be thoroughly cleaned from all loose scale and rust, and be given one good coat- ing of pui'e boiled linseed oil, well worked into all joints and open spaces. 106. In riveted work, the surfaces coming in contact shall each be painted before being riveted together. 107. Pieces which are not accessible for painting after erection shall have two coats of paint. 108. The paint shall be of a good quality of iron ore paint, mixed with pure linseed oil, or such as may be specified in con- tract. 109. After the structure is erected, the iron work shall be thoroughly and evenly painted with two additional coats of paint, mixed with pure linseed oil, of such color as may be selected. 110. Pins, pin holes, screw threads, and other finished surfaces shall be coated with white lead and tallow before being shipped from the shop. Inspection. — 111. All facilities for inspection of material and workmanship shall be furnished by the contractor to competent inspectors, and the engineer and his inspectors shall be allowed free access to any part of the works in which any portion of tlie material is made. 112. The contractor shall furnish, without charge, such speci- mens (prepared) of the several kinds of material to be used as may be required to determine their character. lis. Pull-sized parts of the structure may be tested at the option of the purchaser; but, if tested to destruction, such material shall be paid for at cost, less its scrap value, if it proves satis- factory. 114. If it does not stand the specified tests, it will be considered rejected material, and be solely at the cost of the contractor, unless he is not responsible for the design of the work. C. C. Schneider, Chief Engineer. 277 COEFFICIENTS OF IMPACT. L. 300 L. — 300 L. 300 L. L. 300 L + 300 L + 300 L + 300 L + 300 L + 300 5 0.984 31 0.906 57 0.840 83 0.783 145 0.674 6 0.980 32 0.904 58 0.838 84 0.781 150 0.667 7 0.977 33 0.901 59 0.836 85 0.779 155 0.659 8 0.974 34 0.898 60 0.833 86 Q.lll 160 0.652 9 0.971 35 0.896 61 0.831 87 165 0.645 10 0.968 36 0.893 62 0.829 88 0.773 170 0.638 11 0.965 37 0.890 63 0.826 89 0.771 175 0.632 12 0.962 38 0.888 64 0.824 90 0.769 180 0.625 13 0.958 39 0.885 65 0.822 91 0.767 185 0.619 14 0.955 40 0.882 66 0.820 92 0.765 190 0.612 15 0.952 41 0.880 67 0.817 93 0.763 195 0.606 16 0.949 42 0.877 68 0.815 94 0.761 200 0.600 17 0.946 43 0.875 69 0.813 95 0.759 210 0,588 18 0.943 44 0.872 70 0.811 96 0.758 220 0.577 19 0.940 45 0.870 71 0.809 97 0.756 230 0.566 20 0.937 46 0.867 72 0.806 98 0.754 240 0.556 21 0.935 47 0.865 73 0.804 99 0.752 250 0.546 22 0.932 48 0.862 74 0.802 100 0.750 260 0.536 23 0.929 49 0.860 75 0.800 105 0.741 270 0.526 24 0.926 50 0.857 76 0.798 110 0.732 280 0.517 25 0.923 Ri Ol 0 855 77 u. /yo iiO U. 1^0 290 0.508 26 0.920 52 0.852 78 0.794 120 0.714 300 0.500 27 0.917 53 0.850 79 0.792 125 0.706 400 0.429 28 0.915 54 0.847 80 0.789 130 0.698 500 0.375 29 0.912 55 0.845 81 0.787 135 0.690 600 0.333 30 0.909 56 0.843 82 0,785 140 0,682 PERMISSIBLE COMPRESSIVE STRAINS. p = strain allowed in pounds per square inch ; I = length ; r = least radius of gyration (both in inches). FORMULA. FORMULA. FORMULA. / Soft Steel. Med. Steel. I Soft Steel. Med. Steel. l_ Soft Steel. Med. Steel. r 15,000 17,000 r 15,000 '"^13,5C0)2 17,000 r 15,000 P= -pT' 1 + 17.000 P=— 72 " '"""iTioou^ ^"''iS.SOOrS ^"^11,000)2 ^'^II.OOOjS' ^13,500r2 10 14900 16850 50 I 12660 13850 90 9370 9790 12 14840 16780 52 12500 13650 92 9220 9610 14 14780 16710 54 12340 13440 94 9060 9420 16 14720 16610 56 12180 13230 96 8910 9240 18 14650 16510 58 12010 13020 98 8760 9080 20 14560 16410 60 11840 12810 100 8610 8910 22 14480 16290 62 11670 12600 102 8470 8740 24 14400 16150 64 11500 12390 104 8320 8570 26 14280 16020 66 11340 12180 106 8180 8410 28 14180 15870 68 11140 11970 108 8050 8250 30 14070 15710 70 11010 11760 110 7900 8100 32 13940 15550 72 10840 11550 112 7780 7940 34 13810 15380 74 10670 11350 114 7640 7790 36 13690 15210 76 10500 11150 116 7510 7650 38 13550 15030 78 10340 10950 118 7380 7500 40 13420 14840 80 10180 10750 120 7260 7360 42 13270 14650 82 10010 10550 44 13120 14460 84 9850 10350 46 12960 14260 86 9690 10160 48 12820 14060 88 9530 9970 279 APPENDIX. The following jiages contain some tables in frequent use by Engineers; also the physical properties of materials used in construction, not the product of the works. These tables have been carefully compiled and corrected to conform to the latest knowledge on the respective sub- jects. All the materials described hereafter, otfer a wide range of resistance to stress in any direction ; and the tables for strengths indicate averages of reliable data. In cases where two values are given, they belong to materials that vary considerably in quality ; the figures applying to averages of the superior and inferior qualities respectively. The tables for timber, see page 284, have been principally derived from experiments made under the direction of the Division of Forestry, U. S. Government testing machine at Watertown, and the Massachusetts Institute of Technology. For stones and other minerals, the U. S. Government tests are used, supplemented by other authoritative data. For the alloys, the results of experiments made at the Stephen's Institute for the U. S. Board for testing metals are used. The strength and elasticity of the copper alloys are very sensitive and subject to rapid fluctuation, due to minute changes of proportions and improper treatment in prepara- tion. The figures given indicate a probable average, and individual cases may vary widely from them. The results of many tests made at Pencoyd have been used to complete missing data or check statements that did not seem consistent. When usual working loads are given, they accord with common practice under ordinary conditions, and in all cases are sufl[iciently low to embrace material not obviously unfit for use. 280 CAST-IRON. Foundry Metals. The gray irons, ordinarily used for castings, are usually graded in this section as Nos. 1 and 2 foundry, and No. 3, or gray forge,* these classifications being determined by fracture at the furnace. Grades of higher number, which run mottled or white in frac- ture, are too hard for ordinary tool cutting, and are only used for exceptional purposes in the foundry. By chemical analysis the gray irons are distinguished from the white by larger proportions of silicon and graphitic carbon in the former, while the latter grades contain more combined carbon. There is usually associated with the iron, small proportions of manganese, sulphur, phosphorus, and sometimes other elements, which vary in amount and influence, according to the ores from which the metal is derived. Characteeistics of Foundry Irons. No. 1. Softest grade, used for small castings, or mixed with large proportions. of scrap for larger castings. In the pig, it shows a dark, open grain and rough fracture, and the free graphite is discernible. Tensile strength is low, the iron turns soft, and the cuttings separating in coarse fragments. No. 2. Harder, and higher tensile strength than No. 1, and better adapted for large castings ; bears a less proportion of scrap in mixture. The fracture is not as rough as No. 1, and shows a mixed, large and small dark grain ; it turns harder, separating in finer fi-agments than No. 1. No 3, or gray forge. Harder, and higher tensile strength, but more brittle than No. 2. Adapted for large castings requiring hard surfaces. Not adapted for small castings, in which it is apt to run white ; will not usually bear any admixture of scrap. The grain is close, small and light gray, and sometimes shows white points, when approaching No. 4, or mottled in grade. Cast-iron is quite variable in strength, especially in tensile re- sistance. In ordinary foundry iron, the tensile strength per square inch of section will vary from 14,000 to 20,000 pounds ; and refined iron of high grade is known to run between 30,000 and 40,000 pounds tensile strength. The elastic limit and modulus of elasticity are not distinctly defined, as some permanent set can be observed under working loads. For practical purposes in ordinary iron the elastic limit can be called about 6,000 pounds, and the modulus of elasticity 1 0,000,000 pounds per square inch of section. Under compression, when not accompanied with bending strains, ordinary cast-iron will bear from 90,000 to 130,000 pounds per square inch, usually assumed at an average of 100,000 pounds. In test bars, cast 1 inch square of a fair quality of foundry iron for machinery castings, the tensile strength should be about 1(),000 pounds per square inch of section, and the same bars tested I transversely, between supports 12 inches apart, and load in mid- ille should endure 2,500 pounds and deflect 0.15 inches. *In some places this is subdivided, giving another grade of No. 3 Foundry Iron. 281 The shrinkage in casting will vary from .05 to .12 inches per foot of length. General average = .08 inches. Specific gravity averages 7.2. Weight per cubic inch, .26 pounds, or per cubic foot = 450 pounds. PHYSICAL PROPERTIES OP TIMBER. The physical properties of timber, given hereafter, are derived largely from the recent experiments of the Forestry Division, U. S. Department of Agriculture, which form the most complett' and systematic series on record. The following general con- clusions seem to be demonstrated : 1. That bleeding (the experiments were made on long leaf yellow pine) has no material effect on the strength of timber, the flexibility is slightly increased, but the bled timber will probably endure exposure to the weather as well as the other. 2. That moisture reduces the strength of timber, whether that moisture be the sap, or water absorbed after seasoning. In gen- eral, seasoned timber, or with not more than 12 per cent, moisture, is from 75 per cent, to 100 per cent, stronger than green tmiber. 3. When artificially dried, timber contains a uniform percent- age of moisture throughout, a condition requiring months or even years to attain in air-dried heavy timber. Wlien kiln-dried at usual temperatures, wood shows no loss of strength compared with air-dried timber of the same percentage of moisture. The effect of very high temperatures and pressures (as used in vulcanizing) is lower strengths than when air-dried. 4. Large timbers are equal in strength per square inch of sec- tion, tested every way, to small timbers, provided they are equally sound and contain the same percentage of moisture. 5. The tests seem to indicate that the strength of woods of uni- form structure increases with the specific gravity irrespective of species, i. e., in general, the heaviest wood is the strongest. Oak seems not to belong to the list of woods to which this general remark applies. The data on properties of timbers, given on page 284, must be used with considerable judgment and caution. Seasoned wood will gain weight, to the extent of 5 to 15 per cent., if exposed to the weather and this excess will be reduced if the wood is kept a week in a warm dry place. . . Some of the individual tests made 1)y the IT. S. Forestry Divi- sion varied considerably from the mean values given in the table. In the case of tension tests, which varied most from the average, a few were as low as 25 per cent., while others reached 190 per cent, of the mean. The elastic limit given in connection with the data from the U. S. Forestry Division, is the relative elastic limit suggested by Professor Johnson, as there is no definite "elastic limit" m timber similar to that in some metals. This relative elastic hmit is taken where the rate of deflection is 50 per cent, more than it is under initial loads. Modulus of ultimate bending is extreme fibre stress on beam at rupture. The modulus of elastic bending is the (iluc stress when the rate of deflection is increased 50 per cent. Thu nnnlulus of elasticity is derived from transverse tests. 282 WOODEN BEAMS AND PILLARS. The table on page 286 gives the safe loads in pounds, uni- formly distributed for rectangular wooden beams 1 inch thick, and is based on the experiments of the U. S. Forestry Division. As short beams have been found by experiment to fail by longitudinal shearing, the shorter lengths, marked with a star, have been calculated to resist this action. The working values of the sliearing resistance per square inch being taken for well-seasoned sound timber as follows : Hemlock, 80 pounds ; spruce, white pine and yellow pine (Southern), 120 pounds ; oak, 200 pounds. The values in ' the table calculated for cross-bending, are based on the fol- lowing extreme fibre stresses per square inch. Hemlock, 750 pounds ; white pine or spruce, 900 pounds ; oak, 1200 pounds ; yellow pine, 1500 pounds. The table on page 287 gives the concentrated central loads, and is also computed from the foregoing data. PILLARS. The formulfe heretofore proposed for resistance of the wooden pillars, are not sustained by the results of recent experiments, such as those made in 1882 at the Watertown Arsenal. These were on white and yellow pine, partly seasoned, and indicate the following average breaking loads in pounds per sq. inch of section for the given ratios of length to thickness. Jiatio of Length of Thickness. Yellow Pine White Pine Hemlock . . 4400 2450 2200 4275 2150 4100 2300 2050 25 35 3875 3fi00 3275 2n00 2475 2130 1760 2190 20.i0 1890 1700! 1490 1320,1090 1950 1800,170011530,1340 1190 OiiO 1480 910 820 The table given on page 288 for wooden pillars, is based on the above, corrected for seasoning, and taking one-eighth of the mean breaking loads as the safe working loads. Tests made of two or three sticks bolted and keyed together, showed that they did not behave like a sohd pillar, but as if the sev- eral timbers acted independently. Composite wooden pillars should be treated as an aggregation of independent members. 283 PHYSICAL PROPERTIES OF WOOD. Seasoned timber, moisture 12 per cent, and under. Stresses given in pounds per square inch. NA ME OF MA TER I A L . Ash (American) Birch Box . Cedar (White) Cedar (American Red) . , Chestnut Cottonwood (see Poplar) Douglas Spruce (Oregon Pine) Fir Gum Hemlock* Hiclcory (American) average Lignum Vitse Mahogany (Spanish) Maple Oregon Pine (see Douglas Spruce) . . . Oak (Red) Oak (Black or Yellow) Oak (White) Oak (Live) Pine (Southern Yellow, long leafed) . . Pine (Cuban) Pine (Loblolly) Pine (White) Poplar Spruce (Northern) Spruce Pine (Pinus glabra of So. States) Walnut (Black) • Ultim. Rensi. to Tension. 17000 15000 20000 10800 11500 13000 13000 8700 19600 11800 14900 11150 10250 10000 13600 13000 13000 13000 10000 7000 11000 12000 10500 Ultim. Resist, to Comp. Length. 7200 10300 5200 6000 5300 5700 7100 5700 9500 9900 8200 7150 7200 7300 8500 10400 8000 8700 7400 5400 5000 6000 7300 Ultim. Ultim. Resist. Resist. to to Comp. Shear Cross. L'gtJi. 1900 1100 700 400 800, 1400 2700 1800 2300 1800 2200 1260 1200 1150 700 1200 7500 2500 500 1300 400 1100 500 1100 1100 1000 835 770 800 400 400 800 Weight in Pounds per Cubic Foot of other Woods. Cherry Cork . Ebony . 42. 15.6 76.1 ♦Individual tests of Hemlock seem to indicate a wood equal to White Pine, 284 PHYSICAL. PROPERTIES OF WOOD. Seasoned timber, moisture 12 per cent, and under. Stresses given in pounds per square inch. Ultim. I Resist. to Shear. Cross. 6280 5600 Bla.r()nzc, ]\IcUi2i'n/nGS6 (ctist) " ' " (rolled) " Phosphor .... 100000 26800 35500 33000 30000 30000 37000 43000 49000 24000 34500 31760 21500 68900 71200 100000 47700 95000 75000 52000 48000 65000 79000 75000 117400 -LOUUUU 63000 52000 39000 24000 30000 36000 42000 48000 62400 43500 30200 60000 20000 16000 10000 9100 16400 16900 '22000 *17700 80000 21500 18.0 14.0 13.7 12.4 14.0 12.2 11.6 12.5 14.5 15.8 .282 .319 .318 !317 322 .316 .310 .308 .304 Tobin (rolled) . . 79400 175000 41900 55400 .296 " wire annealed. . . Iron Cast ( See page 281 ) . . ' ' wire annealed .... " " hard drawn . . " wrgt., rolled bars . . " " plates . 24800 32600 39800 45000 75000 50000 50000 36000 8000 25000 27000 30000 30000 18.0 18.0 26.0 29.0 29.0 Lead Steel (See page 18) ... . Tin Zinc (cast) 2050 3500 5400 7350 6400 1100 1670 4050 0.85 4.6 * This was true elastic limit, the " yield point " or "apparent elastic limit " given by drop of beam was at 38,640 pounds. 289 PHYSICAL PROPERTIES OF MATERIALS OF MASONRY, ETC. All stresses given in pounds per square inch. For working stresses seep. 291. MATERIAL. Brick, Flatwise Paving. {max. min. Paving Brick, Phila. Specifications. Red Shale Yellow Fire Clay f max. \ min. Hard Building Soft " Concretes, 1 month old, of following com- position : Cement mortar, 1 of natural cem., 2 of sand Natural Cement Mortar and Furnace Siag " " " " Sandstone. . " " " " Limestone*.. " " " " Granite . . " " " " Trap . . . Cement Mortar, 1 of Portland cem.,2of sand Porlland Cement Mortar and Furnace Slag' " " " " Sandstone. " " " " Limestone*, " " " " Granite . . " " " " Trap . . . " {Z^. Limestone jmax ( mm, Marble Sandstone \ ) mm, Slate Trap XJllim. Crush. Siren gth 20800 f 9090 \ 18000 f 8000 t 10000 18400 3800 250 to 500 24450 12000 22300 ZOOO 20000 4650 18750 4100 22000 Trans- verse Strength 3100 1350 f 5000 1 6000 / 5800 t 6200 1250 300 Modx.lus of Elas'y. 400COOO 200COOO 400C000 2000000 Concretes aft er 6 months wii; be about 4 times, and at the if 1 year will be 6 to 7 times as string as at the end ot the first month. 2700 900 2500 150 2850 150 2350 350 1300C000 162(000 800(000 33£000 1355C000 250(000 281E000 27(000 700(000 W'ght 150 125 100 109 120 136 142 142 147 134 137 153 159 159 164 164 158 170 139 174 170 WEIGHT IN POUNDS PER CUBIC FOOT OF SUBSTANCES. Name of Substance. Asphaltum Clay, potter's dry " in lump, loose Earth, com. loam, dry, loose . " " " " rammed Flint Glass, common window. . . Gneiss Gypsum " (plasterof Paris gr'd). Ivory Pounds. 87 119 63 72- 80 90-100 162 157 168 142 60 114 Name of Substance- Lime, quick, of ord. lime,stoLe " " ground, loose Lime, quick, gro.,well shakeo Mica Mud, dry, close " wet, fluid Quartz, common, pure . . . Salt, Syracuse, N. Y Sand, dry and loose " perfectly wet Shales, red or black Pounds. 95 53 75 183 80-100 104—120 165 45 90—106 118-129 162 * It is claimed that the use of limestone for the body of concrete ii attended with corrosion of the imbedded iron and it is obviously unfit for tire- proofing. 290 FOUNDATIONS. The bearing power of soils varies widely with their nature and condition. Rock may sustain from 18 to 180 tons per square foot. Compact gravel and coarse sand well cemented, of considerable thickiiess, not liable to be carried away by water, can be loaded with 8 to 10 tons per square foot, while the stiff varieties of dry clay will safely support 4 to 6 tons per square foot. In general, however, the building laws of different localities will limit the pressure on the different soils. The table below gives the requirements of a few cities. Bearing Makrial. Phila\N. Y.\ Chic.\ Buff.\ Mil. Solid natural earth of dry clay . . . Clay moderately dry Clay soft. (Confined) Gravel and coarse sand well cemented Gravel and sand Clay and sand Dry sand. (Confined) Dimension stone, beds dressed io^ uniform surface, cement, mortar V joints under V. J Concrete, (see page 290) Rubble stone work in cement mortar Common brick laid in lime mortar . Common brick laid in cement mortar Hard burned brick in lime mortar Hard burned brick in cement mortar First-class briclc work in Portland \ cement mortar J Hard brick in lime and cement) mortar mixed J Load Net Tons per Sg. Ft. 15 12 15 Piles. Philadelphia small end 5" head 12" spaced not over 30" centre to centre ... New York small end 5" spaced not \ over 30" centre to centre . . . / Chicago Buffalo small end 6" spaced not) over 36^^ centre to centre . . . . j Load Net Tons per Pile. 20 20 25 25 For Bearing Plates, see page 110. 291 PILES. The driving requirements for piles in municipal work will lie given in the local building laws, as also are the dimensions, load- ing and spacing as given on the preceding page. Their degree of stability under these conditions can be determined from the fol- lowing formulae : i=load in net tons, TF= weight of hammer in net tons, w = weight of hammer in pounds, if == fall of hammer in feet, A = fallof hammer in inches, p = penetration in inches, due to last fall. L^^HXwX. 026 (Trautwine.) p + 1 As a factor, Trautwine recommends that for piles thoroughly driven in firm soils, one-half of the above load be taken, in river mud or marsh (piles not driven to rock-bottom), the safe load be restricted to one-sixth of i. i=^_^ (Sanders.) p X.8 This formula applies to a pile driven until its penetration is small and nearly equal for successive blows. j^^ 2XwXH (Wellington.) p + 1 GRILLAGE BEAMS. Safe loads on Pencoyd I beams used in a grillage for foundations of walls or columns : Considering the lower course, i< — L- — the supporting pressure from the soil is taken as uniformly dis- tributed on the beams over the iim ■ — -w— I span S, while the load carried by I I the foundation is taken as uni- i< S >' formly distributed on beams over the span L. The maximum bend- ing moment is then J W {S— L) where W is the total load on the foundation. To find the safe load that a beam will carry as a grillage beam, it is only necessary to refer to the tables of safe load on pages 30 to 95, and take the safe load the beam will carry for a span {8— L) . Example. —Sup-pose a load of 500 net tons carried on a soil that will support safely 2 tons per square foot, the area required for the foundation will be 250 square feet. Taking the base of the column as 4 feet 6 inches square, 5 beams can be placed side by side in this width and permit of concrete being rammed between them. Then each beam will be loaded with 83 tons. The soil area covered by foundation will be a square of 16 feet side, hence (S— L) is 16 — 4i = Hi feet. Now, on page 31, of safe loads of I beams, we find that a 24 inch I beam, 85 pounds, will carry 84 tons. In the same way the beams in the lo^er course are found to be 16 — 15 inch I beams, 50 pounds. PAINT. The covering property of paint depends on the smoothness or absorbing power of the surface painted; also on the fluidity of the paint. Ordinarily one gallon of paint, consisting of finely ground pigment and linseed oil, covers about 600 square feet of metallic surface one coat, or 350 square feet with two coats. If the surface is very smooth and non-absorbent, or the paint is thinned with turpentine or naptha, the paint may spread over more surface to the extent of 50 per cent. If the contrary conditions exist, the surface covered may be diminished one-half. The volume of the mixed paint usually ex- ceeds the volume of oil used from 20 to 75 per cent , according to the kind of pigment used. AVERAGE SURFACE COVERED PER GALLON OF PAINT. Paint. Volume of Oil. Lhs. of Pig- ment. Volume and Square Feet. Weight of Paint. 1 Coat. 600 630 630 500 360 515 875 2 C'ts. Iron Oxide (powdered) " " (ground in oil) Red Lead (powdered) . . White Lead (g'rd in oil) . Graphite (ground in oil) . Black Asphalt Linseed oil (no pigment) . 1 gal. 1 " 1 " 1 " 1 " 1 " (turp.) 8.00 24.75 22.40 25.00 12.50 17.25 Gals. Lbs. 1.2=16.00 2.6=32.75 1.4=30.40 1.7=33.00 2.0=20.50 4.0=30.00 350 375 375 300 215 310 Light structural work will average about 250 square feet, and heavy structural work about 150 square feet of surface per net ton of metal. The cost of painting with oxide of iron or similar material, based upon paint costing 50 cents per gallon, labor at shops, $1.50 per day, and at erec- tion, f2.00 per day, will average : COST PER NET TON. Light Work. Heavy Work. One Coat at Shop : Cost of paint per net ton of steel . . Cost of labor per net ton of steel . Total $0.27 0.18 $0.45 $0.18 0.12 $0.30 Tivo Coats after Erection: Cost of paint per net ton of steel .... Cost of labor per net ton of steel 80.45 0.90 $0.30 0.60 1.35 $1.80 $1.20 Coating with tar at 300° F. requires 1 gallon of tar per 220 square feet of surface covered. The average cost, based upon tar at 10 cents per gallon and labor at $1.50 per day. Is as follows : lAght Work, Heavy Work. Cost of tar per net ton of steel . . $0.12 0.68 10.80 f0.07 0.38 $0.45 Cost of labor, etc., per net ton of steel . . . . 293 CRANE CHAINS. DIMENSION. SPECIAL CRANE. CRANE. Size of Chain. Inches. -5 .■§ §1 ■i ^11 s; 1^ g § e O || § ^ . |l e e O \ f f| i| i 1 2 i IJ l| 1932 2898 4186 5796 3864 5796 8372 11592 1288 1932 2790 3864 1680 2520 3640 5040 3360 5040 7280 10080 1120 1680 2427 3360 I 1 IM IM 2i 3i% 44 5 m ii 2^ 2J- 7728 9660 11914 14490 15456 19320 23828 28980 5182 6440 7942 9660 6720 8400 10360 12600 13440 16800 20720 25200 4480 5600 6907 8400 1 it 1 m 2M 5J 8 9 2i 2f4 2|- 3t^ 17388 20286 22484 25872 34776 40572 44968 51744 11592 13524 14989 17248 15120 17640 20440 23520 30240 35280 40880 47040 10080 11760 13627 15680 1 ii^ 2iS 211 3^^ lift 12i 13?, 3i 3A 3| 3?- 29568 33264 37576 41888 59136 66538 75152 83776 19712 22176 25050 27925 26880 30240 34160 38080 53760 60480 68320 76160 17920 20160 22773 25387 IJ If it^ 3-^ 3^1 3| 3^^ 3|i 16 16i ISA 19A 2lT'(y 4J 4| 4i% 46200 50512 55748 60368 66528 92400 101024 111496 120736 133056 30800 33674 37165 40245 44352 42000 45920 50680 54880 60480 84000 91840 101360 109760 120960 28000 30613 33787 36587 40320 The distance from centre of one link to centre of next is equal to the inside length of link, but in practice j", inch is allowed for weld. This is approxi- mate, and where exactness is required, chain should be made so. For Chain Sheaves. — The diameter, if possible, should be not less than . twenty times the diameter of ch.iin used. Example— Yor 1-inch chain use 20-inch sheaves. 294 WROUGHT IRON TUBES. Hydraulic Tubing. Ordinary Gas or Water Pipe. Extra. Double Extra. Nominal Diameter. Outside Diameter. Thickness. Inside Diameter. Internal Area. External Area. Weight per Foot. Threads per Inch. j Thickness. Inside Diamster. Thickness. Inside Diameter. \ .40 .07 .27 .06 .13 .2A 27 .10 .20 \ .54 .09 .36 .10 .23 .42 18 .12 .29 % .67 .09 .49 .19 .36 .56 18 .13 .42 .22 .23 \ .84 .11 .62 .30 .55 .84 14 .15 •54 .29 .24 \ 1.05 .11 .82 .53 .87 1.12 14 .16 .73 .31 .42 1 1.31 .13 1.05 .86 1.36 1.67 ll\ .18 .95 .36 .58 1.66 .14 1.38 1.49 2.15 2.24 .19 1.27 .38 .88 1.90 .15 1.61 2.03 2.84 2.68 ll\ .20 1.49 .40 1.08 2 2.37 .15 2.07 3.35 4.48 3.61 11^2 .22 1.93 .44 1.49 2\ 2.87 .20 2.47 4.78 6.49 5.74 8 .28 2.31 .56 1.75 3 3.50 .22 3.07 7.38 9.62 7.54 8 .30 2.89 .60 2.28 4.00 .23 3.55 9.89 12,57 9.00 8 .32 3.35 .64 2.71 4 . 4.50 .24 4.03 12.73 15.90 10.66 8 .34 3.81 .68 3.13 41/2 5.00 .25 4.51 15.96 19.64 12.34 8 .35 4.25 .72 3.56 5 5.56 .26 5.05 19.99 24.30 14.50 8 .37 4.81 .75 4.06 6 6.63 .28 6.07 28.88 34.47 18.76 8 .44 5.75 .87 4.87 7 7.63 .30 7.02 38.73 45.66 23.27 8 .50 6.62 .84 6.06 8 8.63 .32 7.98 50.03 58.43 28.18 8 .56 7.50 .87 6.87 9 9.63 .34 8.94 62.73 73.72 33.70 8 10 10.75 .36 10.02 78.84 90.76 40.06 8 12 12.75 .38 12.00 113.09 49.00 8 13 14.00 .38 13.25 53.92 8 14 15.00 .38 14.25 57.89 8 Note — Above 15 inches the outside diameters are the nominal size. All dimensions given in inches, all weights in pounds. 295 CORRUGATED IROX 2^ " PITCH. V. s. Standard Gauge. . Weight of 100 Square Feet in Pounds. ickness Sheet Inches Loose Sheets. Galvanized Iron Laid, Adding for Laps — for Sheet Lengths of: g -s Black. Galvann ized. 5' 6' 7' 8' 9' 10' 20 22 24 26 .0375 .0313 .025 .0188 167 139 111 83 184 156 128 101 210 178 146 115 208 176 145 114 207 176 144 114 206 175 143 113 206 174 143 113 205 174 143 113 Note. — If material is to be painted add 2 pounds to the above weights of 100 square feet. This table is based on galvanized corrugated sheets 27" wide and deep, 234" centre to centre of corrugation. Before corrugating, sheets are 30" wide. TABLE OF SAFE AND CRIPPI-ING r,OAI>S IN POUNDS PER SQUARE FOOT. Safe Load. Elastic Limit. Crippling Load. U.S. Standar Gauge. Span in Feet. Span in Feet. Span in Feet. 3 4 5 6 3 4 5 6 3 4 5 6 20 22 24 26 59 48 37 31 44 36 28 23 36 29 22 18 30 24 19 16 . 89 71 56 44 67 54 42 34 54 43 34 27 45 36 28 23 134 107 84 69 100 80 63 52 80 64 51 41 67 54 42 34 Formula : W= Crippling load in pounds per square foot. / = Thickness of metal in inches. W = 98000 t b d 6 = Centre to centre of corrugation in inches. I d = Depth of corrugation in inches. I = Length of span in inches. 296 WEIGHT OF ROLLED SHEETS. Calculations based on Specific Gravity of 7.85. No. of Gauge. Birmingham Wire Gauge and English Standard Gauge. American (B. & S.) Wire Gauge. New U, S. Standard Gauge, 1873. Thickness in Inches. Weight per Sq. Ft. Thickness in Inches. Weight per Sq. Ft. Thickness in Inches. JVciffht p€T Sq. Ft. 0000 000 00 0 .454 .425 .380 .340 18.52 17.34 15.50 13.87 .460 .410 .365 .325 18.76 16.72 14.88 13.26 .406 .375 .344 .313 16.58 15.30 14.03 12.75 1 2 3 4 .300 .284 .259 .238 12.24 11.59 10.56 9.71 .289 .258 .229 .204 11.80 10.52 9.36 8.33 .281 .266 .250 .234 11.48 10.84 10.20 9.56 5 6 7 8 .220 .203 .180 .165 8.98 8.28 7.34 6.73 .182 .162 .144 .129 7.42 6.61 5.88 5.24 .219 .203 .188 .172 8.93 8.29 7.65 7.01 9 10 11 12 .148 .134 .120 .109 6.04 5.47 4.89 4.44 .114 .102 .091 .081 4.66 4.15 3.70 3.29 .156 .141 .125 .109 6.38 5.74 5.10 4.46 13 14 15 16 .095 .083 .072 .065 3.87 3.38 2.94 2.65 .072 .064 .057 .051 2.93 2.61 2.32 2.07 .094 .078 .070 .063 3.83 3.19 2.87 2.55 17 18 19 20 .058 .049 .042 .035 2.37 1.99 1.71 1.42 .045 .040 .036 .032 1.84 1.64 1.46 1.30 .056 .050 .044 .038 2.30 2.04 1.79 1.53 21 22 23 24 .032 .028 .025 !022 1.30 1.14 1.02 o!898 .028 .025 .020 1.16 1.03 0.821 .034 .031 .025 1.40 1.28 1.10 1.02 25 26 27 28 .020 .018 .016 .014 0.816 0.734 0.653 0.571 .018 .016 .014 .013 0.729 0.651 0.581 0.515 .022 .019 .017 .016 0.89 0.77 0.70 0.64 29 30 31 32 .013 .012 .010 .009 0.531 0.489 0.408 0.367 .011 .010 .009 .008 0.459 0.409 0.364 0.324 .014 .013 .011 .010 0.57 0.51 0.45 0.41 33 34 35 36 .008 .007 .005 .004 0.326 0.286 0.204 0.162 .007 .006 .006 .005 0.288 0.257 0.228 0.204 .009 .009 .008 .007 0.38 0.35 0.32 0.29 297 WEIGHT OF STEEI. PI.ATE. Pounds per Lineal Foot. THICKNESS IN INCHES. ■m Inches. % 12 2.55 5.10 7.65 10.20 12.75 15.30 17.85 20.40 13 2.76 5.52 8.29 11.05 13.81 16.57 19.34 22.10 14 2.98 5.95 8.92 11.90 14.87 17.85 20.83 23.80 15 3.19 6.37 9.57 12.75 15.94 19.12 22.32 25.50 16 3.40 6.80 10.20 13.60 17.00 20.40 23.80 27.20 17 3.61 7.22 10.84 14.45 18.06 21.67 25.28 28.91 18 3.82 7.65 11.47 15.30 19.12 22.95 26.77 30.60 19 4.04 8.08 12.11 16.15 20.18 24.22 28.26 32.29 20 4.25 8.50 12.75 17.00 21.25 25.50 29.75 34.00 21 4.47 8.92 13.39 17.85 22.32 26.77 31.24 35.70 22 4.67 9.35 14.02 18.70 23.38 28.05 32.72 37.40 23 4.88 9.77 14.67 19.55 24.44 29.32 34.21 39.11 24 5.10 10.20 15.30 20.40 25.50 30.60 35.70 40.80 25 5.31 10.63 15.93 21.25 26.56 31.87 37.19 42.49 26 5.53 11.05 16.57 22.10 27.62 33.15 38.68 44.20 27 5.74 11.47 17.22 22.95 28.69 34.42 40.17 45.90 28 5.95 11.90 17.85 23.80 29.75 35.70 41.65 47.60 29 6.16 12.32 18.49 24.65 30.81 36.97 43.13 49.31 30 6.37 12.75 19.12 25.50 31.87 38.25 44.62 51.00 32 6.80 13.60 20.40 27.20 34.00 40.80 47.60 54.40 34 7.22 14.45 21.67 28.90 36.13 43.35 50.57 57.79 36 7.65 15.30 22.95 30.60 38.25 45.90 53.55 61.20 38 8.08 16.15 24.22 32.30 40.38 48.45 56.53 64.61 40 8.50 17.00 25.50 34.00 42.50 51.00 59.50 67.99 42 8.92 17.85 26.77 35.70 44.62 53.55 62.47 71.40 44 9.35 18.70 28.05 37.40 46.76 56.10 65.45 74.81 46 9.77 19.55 29.32 39.10 48.88 58.65 68.42 78.19 48 10.20 20.40 30.60 40.80 51.00 61.20 71.40 81.60 50 10.63 21.25 31.87 42.49 53.12 63.75 74.37 85.00 52 11.05 22.10 33.15 44.20 55.25 66.30 77.35 88.39 54 11.47 22.95 34.42 45.90 57.37 68.85 80.32 91.80 56 11.90 23.80 35.70 47.59 59.50 71.40 83.29 95.20 58 12.32 24.65 36.97 49.30 61.63 73.95 86.27 98.59 60 12.75 25.50 38.25 51.00 63.75 76.50 89.25 102.00 298 WEIGHT OF STEEt. PLATE. Pounds per Lineal Foot. THICKNESS IN INCHES. % % % il 1 in Inches. 22.95 25.50 28.05 30.60 33.15 35.70 38.25 40.80 12 24.87 27.62 30.38 33.15 35.91 38.68 41.44 44.20 13 26.77 29.75 32.72 35.70 38.68 41.65 44.62 47.60 14 28.69 31.87 35.07 38.25 41.44 44.62 47.82 51.00 15 30.60 34.00 37.40 40.80 44.20 47.60 51.00 54.40 16 32.52 36.13 39.74 43.35 46.97 50.59 54.19 57.80 17 34.42 38.25 42.07 45.90 49.72 53.55 57.37 61.20 18 36.34 40.37 44.41 48.45 52.48 56.52 60.56 64.60 19 38.25 42.50 46.75 51.00 55.25 59.50 63.75 68.00 20 40.17 44.62 49.09 53.55 58.02 62.47 66.94 71.40 21 42.07 46.75 51.43 56.10 60.77 65.45 70.12 74.80 22 43.99 48.88 53.76 58.65 63.55 68.43 73.32 78.20 23 45.90 51.00 56.10 61.20 66.30 71.40 76.50 81.60 24 47.81 53.12 58.43 63.75 69.05 74.37 79.68 85.00 25 49.72 55.25 60.77 66.30 71.83 77.35 82.87 88.40 26 51.64 57.37 63.12 68.85 74.59 80.32 86.07 91.80 27 53.55 59.50 65.45 71.40 77.36 83.29 89.25 95.20 28 55.47 61.63 67.79 73.95 80.12 86.28 92.44 98.60 29 57.37 63.75 70.12 76.50 82.87 89.25 95.62 102.00 30 61.20 68.00 74.80 81.60 88.40 95.20 102.00 108.80 32 65.02 72.25 79.47 86.70 93.92 101.14 108.38 115.60 34 68.85 76.50 84.15 91.80 99.45 107.10 114.75 122.40 36 72.67 80.75 88.83 96.90 104.98 113.02 121.13 129.20 38 76.50 85.00 93.49 102.00 110.50 119.03 127.50 136.00 4U 80.32 89.25 98.17 107.10 116.03 124.95 133.88 142.80 42 84.15 93.50 102.85 112.20 121.55 130.90 140.25 149.60 44 87.97 97.75 107.53 117.3Q 127.08 136.85 146.63 156.40 46 91.80 102.00 112.20 122.40 132.60 142.80 153.00 163.20 48 95.63 106.25 116.88 127.50 138.13 148.75 159.38 170.00 50 99.45 110.47 121.55 132.60 143.65 154.70 165.75 176.80 52 103.33 114.75 126.23 137.70 149.18 160.65 172.13 183.60 54 107.10 119.00 130.90 142.80 154.70 166.60 178.50 190.40 56 110.93 123.25 135.58 147.90 160.23 172.55 184.88 197.20 58 114.75 127.50 140.25 153.00 165.75 178.50 191.25 204.00 60 299 FliAT BARS. SECTIONAL AKEAS AND WEIGHTS PER liINEAL, FOOT. iV" Thick. 1 1% 1^/4 1% 1^2 1% 1% 1^/8 2 2^8 2\ 2% 21/2 2% 2% 2% 3 31/4 31/2 3% 4 41/2 4% 5 514 51/2 5^4 6 61/, 7 9 10 11 12 Lbs. per Fool. .213 .239 .266 .292 .319 .345 .372 .399 .425 .452 .478 .505 .531 .558 .584 .611 .638 .691 .744 .797 .850 .903 .956 1.01 1.06 1.12 1.17 1.22 1.28 1.38 1.49 1.70 1.91 2.13 2.34 2.55 .063 .070 .078 .086 .094 .102 .109 .117 .125 .133 .141 .148 .156 .164 .172 .180 .188 .203 .219 .234 .250 .266 .281 .297 .313 .328 .344 .359 .375 .406 .438 .500 .563 .625 .688 .750 i/s" Thick. Lbs. per Fool. .425 .478 .531 .584 .638 .691 .744 .797 .850 .903 .956 1.01 .297 1.06 1.11 1.17 1.22 .313 .328 .344 .359 1.28 1.38 1.49 1.59 .375 .406 .438 .469 1.70 1.81 1.91 2.02 .500 .531 .563 .594 2.12 2.23 2.34 2.44 .625 .656 .688 .719 2.55 2.76 2.98 3.40 .750 .813 .875 1.00 3.83 4.25 4.67 5.10 1.13 1.25 1.38 1.50 ^" Thick. 3.51 3.67 3.83 4.14 4.46 5.10 5.74 6.38 7.01 7.65 Lbs. per Foot. Area in Sq. Jns, 1 1 0 ly .Do7 1 QQ .717 .211 .797 .234 .877 .^01 1.04 .305 1.12 .328 1.20 .352 1.28 .0/0 1.35 .398 1.43 .422 1.51 .445 1.59 .469 1.67 .492 1.75 .516 1.83 .539 1.91 .563 2.07 .609 2.23 .656 2.39 .703 2.55 .750 2.71 .797 2.87 .844 3.03 .891 3.19 .938 3.35 .984 1.03 1.08 1.13 1.22 1.31 1.50 1.69 1.88 2.06 2.25 300 FLAT BARS. SECTIONAIi AREAS AND WEIGHTS PER LINEAIi FOOT. s . I/4" Thick. ^" Thick. %" Thick. Width i Inches Lbs. per Fool. Area in Sq. Im. IM Lbs. per Foot. Area in Sq. Im. Lbs. per Foot. Area in Sq. Ins. ^1 S| 1 1^8 }^ 1% .850 .956 1 OR 1.17 .250 .281 .Oio .2AA 1.06 1.20 1.46 .313 .352 '5Q1 .430 1.28 1.43 1.75 .375 .422 469 !516 1 11/8 114 1% 11/2 1% 1% 1% 1.28 1.38 1 1.69 .375 .406 438 !469 1.59 1.73 1.86 l!99 .469 .508 547 '.586 1.91 2.07 A. 2.39 .563 .609 .656 !703 1^ 1% 1% 1^/8 2 2\ 2% 1.70 1.81 1 Q1 X . u 1 2.02 .500 .531 563 !594 2.12 2.26 2.39 2.52 .625 .664 703 !742 2.55 2.71 2 87 3!03 .750 .797 .844 .891 2 21/8 214 2% 21/2 2% 2^8 2.12 2.23 2.34 2^44 .625 .656 688 !719 2.66 2.79 2.92 3!06 .781 .820 859 !898 3.19 3.35 3 51 3;67 .938 .984 1.03 l!08 21,^ 2% 2% 2% 3 31/4 3V2 3«4 2.55 2.76 3.19 .750 .813 .0/0 .938 3.19 3.45 0, i 4a 3.99 .938 1.02 1 HQ 1.17 3.83 4.14 'x.'xO 4.78 1.13 1.22 1 31 l!41 3 314 31^ 3% 4 41/4 41/2 434 3.40 3.61 0 < 00 4.04 1.00 1.06 1 T5 1.19 4.25 4.52 5.05 1.25 1.33 1.48 6.10 6.42 ti ■ 1 % 6.06 1.50 1.59 1 fiQ i.oy 1.78 4 414 41/2 434 5 514 51^ 534 4.25 4.46 4.67 4.89 1.25 1.31 1.38 1.44 5.31 5.58 5.84 6.11 1.56 1.64 1.72 1.80 6.38 6.69 7.01 7.33 1.88 1.97 2.06 2.16 5 5V4 51,^ 5% 6 61^ 7 8 5.10 5.53 5.95 6.80 1.50 1.63 1.75 2.00 6.38 6.91 7.44 8.50 1.88 2.03 2.19 2.50 7.65 8.29 8.93 10.20 2.25 2.44 2.63 3.00 6 61/^ 7 8 9 10 11 12 7.65 8.50 9.35 10.20 2.25 2.50 2.75 3.00 9.56 10.63 11.69 12.76 2.81 3.13 3.44 3.75 11.48 12.75 14.03 16.30 3.38 3.75 4.13 4.50 9 10 11 12 301 FliAT BARS. SECTIONAIi AREAS AND WEIGHTS PER lilNEAI, FOOT. Thick. \" Thick. "i^s Thick. ■i ^ Lbs. per Area in Lbs. per Area in Lbs. per Area in n Fool. Sq. Jus. Foot Sq. Ins. Fool. Sq. Ins. mmm 1 mni It 1 ^ I 1.49 .438 1.70 .500 1.92 .563 '8 1.67 .492 1.91 .563 2.15 .633 ■■• '8 1.86 .547 2.12 .625 2.39 .703 1% 2.05 .602 2.34 .688 2.63 .773 1% -I. /2 2.23 .656 2.55 .750 2.87 .844 ^'U^ -i^ 2.42 .711 2.76 .813 3.11 .914 1*78 13/4 2.60 .766 2.98 .875 3.35 .984 13/, 1^/8 2.79 .820 3.19 .938 3.57 1.05 1% 2 2.98 .875 3.40 1.00 3.83 1.13 0 Ci 3.16 .930 3.61 1.06 4.08 1.20 3% 6.38 6.91 7.44 7.97 1.88 2.03 2.19 2.34 7.02 7.60 Q 1 Q 0. 1 0 8.76 2.06 2.23 0 /II 2.58 7.65 8.29 o.ao 9.67 2.25 2.44 2 63 2'.81 3 31/4 31^2 334 4 41/4 41/2 43/4 8.50 9.03 10.09 2.50 2.66 2.81 2.97 9.35 9.93 10.52 11.11 2.75 2.92 3.09 3.27 10.20 10.84 12.12 3.00 3.19 0.00 3.56 4 414 41/2 434 5 51/4 51/2 10.63 11.16 11 69 12!22 3.13 3.28 3.44 3!59 11.69 12.27 12.85 13^44 3.44 3.61 3.78 3!95 12.75 13.39 14 03 14.67 3.75 3.94 4.13 4.31 5 514 51/2 534 6 6I/2 7 8 12.75 13.81 14.87 17.00 3.75 4.06 4.38 5.00 14.03 15.20 16.36 18.70 4.13 4.47 4.81 5.50 15.30 16.58 17.85 20.40 4.50 4.88 5.25 6.00 6 6I/2 7 8 9 10 11 12 19.13 21.26 23.38 25.60 5.63 6.25 6.88 7.50 21.04 23,38 25.71 28.06 6.19 6.88 7.56 8.25 22.95 26.60 28.05 30.60 6.75 7.50 8.25 9.00 9 10 11 12 303 FLAT BARS. SECTIONAIi AREAS AND WEIGHTS PER L,INEAIi FOOT. s %" Thick. Thick. s Inches. 7/6s. per Fool. Area in Sg. Ins. Lbs. per Foot. Area in Sq. Ins. Lbs. per Foot. Area in Sq. Ins. 1 1^/8 J- 14. 1% 2.76 3.11 3.45 3.80 .813 .914 1.02 1.12 2.98 3.35 3.72 4.09 .875 .984 1.09 1.20 3.19 3.60 3.99 4.39 .938 1.06 1.17 1.29 1 1% 1^4 1% 1^ 1% 1^/1 ± /4 1^/8 4.14 4.49 4.83 5.18 1.22 1.32 1.42 1.52 4.46 4.83 5.21 5.58 1.31 1.42 1.53 1.64 4.78 5.18 5.58 5.98 1.41 1.52 1.64 1.76 IV2 1% 1% 1% 2 2% 2\ 2% 5.53 5.88 6.21 6.56 1.63 1.73 1.83 1.93 5.95 6.32 6.69 7.07 1.75 1.86 1.97 2.08 6.38 6.77 7.17 7.57 1.88 1.99 2.11 2.23 2 21/8 2\ 2% 2\ 2% J* 27/8 6.91 7.25 7.60 7.95 2.03 2.13 2.23 2.34 7.44 7.81 8.18 8.55 2.19 2.30 2.41 2.52 7.97 8.36 8.77 9.17 2.34 2.46 2.58 2.70 2^ 2% 23/4 2% 3 31/4 " /2 3\ 8.29 8.98 9.67 10.36 2.44 2.64 2.84 3.05 8.93 9.67 10.41 11.16 2.63 2.84 3.06 3.28 9.57 10.36 11.16 11.95 2.81 3.05 3.28 3.52 3 31/4 31/^ 3% 4 41/4 41/, 4^/4 11.05 11.74 12.43 13.12 3.25 3.45 3.66 3.86 11.90 12.64 13.39 14.13 3.50 3.72 3.94 4.16 12.75 13.65 14.34 15.14 3.75 3.98 4.22 4.45 4 41/4 41^ 434 5 51/4 5% 13.81 14.50 15.19 15.88 4.06 4.27 4.47 4.67 14.87 16.62 16.36 17.11 4.38 4.59 4.81 5.03 15.94 16.74 17.53 18.33 4.69 4.92 5.16 5.39 5 51/4 51/2 534 6 6I/2 7 8 16.58 17.95 19.34 22.10 4.88 5.28 5.69 6.50 17.85 19.34 20.83 23.80 5.25 5.69 6.13 7.00 19.13 20.72 22.32 26.80 5.63 6.09 6.56 7.50 6 6^ 7 8 9 10 11 12 24.86 27.62 30.39 33.15 7.31 8.13 8.94 9.75 26.78 29.75 32.72 36.70 7.88 8.75 9.63 10.50 28.69 31.88 35.06 38.25 8.44 9.38 10.31 11.25 9 10 11 12 304 T FLAT BARS. SECTIONAIi AREAS AND WEIGHTS PER LINEAIj FOOT. a , I" Thick. Thick. 1^^" Thick. .a Wid/h i Inches. Lbs. per Fool. Area in Lbs. per Fool. Area in Sq. Jus. 1 Lbs. per Fool. Area in Sf^, Ins, II 1 IVs 1 1/< 1% 3.40 3.83 4.25 4.67 1.00 1.13 1.25 1.38 3.61 4.08 4.52 4.97 1.06 1.20 1.33 1.46 4.04 4.56 5.05 5.55 1.19 1.34 1.48 1.63 1 1^8 114 1% IH2 1% 14 l'/8 5.10 5.53 5.95 6.38 1.50 1.63 1.75 1.88 5.42 5.87 6.32 6.77 1.59 1.73 1.86 1.99 6.06 6.56 7.07 7.57 1.78 1.93 2.08 2.23 IM2 1% 2 2i,(s 91/, 2'-'/8 6.80 7.23 7.65 8.08 2.00 2.13 2.25 2.38 7.22 7.68 8.13 8.58 2.13 2.26 2.39 2.52 8.08 8.58 9,09 9.59 2.38 2.52 2.67 2.82 2 2V8 214 2% 2I/0 2™; ^ 4 2^/8 8.50 8.93 9.35 9.77 2.50 2.63 2.75 2.88 9.03 9.49 9.93 10.38 2.66 2.79 2.92 3.05 10.10 10.60 11.11 11.61 2.97 3.12 3.27 3.41 2^2, 2% 2% 2% 3 3^4 10.20 11.05 11.90 12.75 3.00 3.25 3.50 3.75 10.84 11.74 12.65 13.55 3.19 3.45 3.72 3.98 12.12 13.12 14.13 15.14 3.56 3.86 4.16 4.45 3 314 3% 4 414 4i,4> 434 13.60 14.45 15.30 16.15 4.00 4.25 4.50 4.75 14.45 15.35 16.26 17.16 4.25 4.52 4.78 5.05 16.15 17.16 18.17 19.18 4.75 5.05 5.34 5.64 4 434 434 5 5';, '0% 17.00 17.85 18.70 19.55 5.00 5.25 5.50 5.75 18.06 18.96 19,87 20.77 5.31 5.58 5.84 6.11 20.19 21.20 22,21 23.22 5.94 6.23 6.53 6.83 5 514 53^2 534 6 61/:, 7 " & 20.40 22.10 23.80 27.20 6.00 6.50 7.00 8.00 21.68 23.48 25.29 28.90 6.38 6.91 7.44 8.50 24.23 26.24 28.26 32.30 7.13 7.72 8.31 9.50 6 6I/2 7 8 9 10 11 12 30.60 34.00 37.40 40.80 9.00 10.00 11.00 12.00 32.52 36.13 39.74 43.35 9.56 10.63 11.69 12.75 36.34 40.38 44.41 48.45 10.69 11.88 13.06 14.25 9* 10 11 12 305 ROUND AND SQUARE BARS. Sectional area in inches X 3.4 = weight per lineal foot in pounds. •.kness ameier nches. Weight per Lineal Foot in Pounds. Area of^in Thickness or Diameter in Inches. Weight per Lineal Foot in Founds. Area of ^ i n o Round 0 Square ■ Sq. Ins. Round • Square ■ Sq. Ins. 0 1 1 6 .010 .013 .0031 2 iV 10.68 11.36 13.60 14.46 3,1416 3.3410 1/8 .042 .094 .053 .119 .0123 .0276 ^8 3 IS 12.06 12.78 15.35 16.27 3.5466 3.7583 \ .167 .261 .212 .332 .0491 .0767 13.51 14.28 17.22 18.19 3.976] 4,2000 % .375 .511 ' .478 .651 .1104 .1503 % 16.06 16.86 19.18 20.20 4,4301 4,6664 .667 .844 .850 1.076 .1963 .2485 16.69 17.53 21.25 22.33 4.9087 5.1572 % U 1.043 1.261 1.328 1.607 .3068 .3712 % \h 18.40 19.29 23.43 24.66 5.4119 5.6727 3/4 it 1.502 1.762 1.912 2.245 .4418 .5185 % i'i 20.20 21.12 25.71 26.90 5.9396 6.2126 li Iff 2.044 2.347 2.603 2.989 .6013 .6903 % ii 22.07 23.04 28.10 29.33 6,4918 6.7771 1 2.670 3.014 3.400 3.838 .7854 .8866 3 24.01 26.04 30.60 31.88 7,0686 7.3662 ^8 3 IB 3.379 3.766 4.303 4.795 .9940 1.1075 26.08 27.13 33.20 34.55 7.6699 •7.9798 \ 4.173 4.600 5.312 5.857 1.2272 1.3530 \ 28.20 29.30 35.91 37.31 8,2958 8.6179 % 5.049 5.518 6.428 7.026 1.4849 1.6230 % 30.41 31.55 38.73 40.18 8.9462 9,2806 \ 6.008 6.620 7.650 8.301 1,7671 1.9175 32.71 33.89 41.65 43.15 9.6211 9,9678 % u 7.051 7.604 8.978 9.682 2.0739 2.2365 % \\ 35.09 36.31 44.68 46.24 10.321 10,680 if 8.178 8.773 10.41 11.17 2.4053 2.5802 \ \i 37.55 38.81 47.82 49.42 11.045 11.416 % 9.388 10.024 11.95 12.76 2.7612 2.9483 % 40.10 41.40 51.05 52.71 11,793 12.177 306 ROUND AND SQUARE BARS. Sectional area in inches x 3.4 = weight per lineal foot in pounds. Thickness or Diameter in Inches. ]Vei(;ht per Lineal Foot in Pounds. Area of<§)in Thickness or Diameter in Inches. Weight per Lineal Foot in Pounds. Area of ® in Round w Square Sq. Ins. Pound V Square H Sq. Ins. 4 1 1(1 42.72 44.07 54.39 56.11 12.566 12.962 6 ^. 96.1 98.1 122.4 126.0 28.274 Op pec ^/h 3 IS 45.44 46.83 57.85 59.62 13.364 13.772 \ IB 100.2 102.2 127.6 130.2 29.465 oU.uoy ^4 ^5 10 48.23 49.66 61.41 63.23 14.186 14.607 \ 104.3 106.4 132.8 135.5 30.680 pi 9QP '8 "ii; 51.11 52.58 65.08 66.95 15.033 15.466 % 108.5 110.7 138.2 140.9 31.919 pO CHp % 54.07 65.59 68.85 70.78 15.904 16.349 ^2 112.8 115.0 143.6 146.6 33.183 pp 004 % 57.12 58.67 72.72 74.70 16.800 17.257 % 117.2 119.4 149.2 152.1 34.472 35 125 % 1 s 1 11 60.25 61.84 76.71 78.74 17.721 18.190 % 121.7 123.9 154.9 167.8 35.785 PR Ac:r\ % 15 63.46 65.10 80.80 82.89 18.665 19.147 14 Iff 126.2 128.5 160.7 163.6 37.122 P7 pfin 5 66.76 68.44 85.00 87.14 19.635 20.129 7 tV 130.9 133.2 166.6 169.6 38.485 PQ 17c oy.i /o 3 1 0 70.13 71.86 89.30 91.49 20.629 21.135 1/8 IB 135.6 137.9 172.6 175.6 39.87] \ IB 73.60 75.37 93.72 95.96 21.648 22.166 14 5 16 140.4 142.8 178.7 181.8 41.282 % -ll' 77.15 78.95 98.22 100.5 22.691 23.221 . % Iff 145.2 147.7 184.9 188.1 42.718 43.445 1/2 I'ti 80.77 82.62 102.8 105.2 23.758 24.301 % Iff 150.2 152.7 191.3 194.4 44.179 44.918 % 84.48 86.38 107.6 110.0 24.850 25.406 % ii 165.2 157.8 197.7 200.9 45.664 46.415 1 IT 88.29 90.22 112.4 114.9 25.967 26.535 % 14 10 160.3 163.0 204.2 207.6 47.173 47.937 % 14 1 5 92.16 94.14 117.4 119.9 27.109 27.688 % 165.6 168.2 210.8 214.2 48.707 49.483 307 AREAS OF CIRCLES. Diameters increasing by eighths. No. No. +0. No.+Ys No.+}( No.+% iVb.-l-K No.W^ No.Ws 0 0.00000 0.01227 0.04909 nil HiR U. iiUTO 0.19635 0.30680 0.44179 n QXW QO U.bUio^:! 1 0.78540 0.99402 1.2272 1 AUA.CI i . HOT-y 1.7671 2.0739 2.4053 2 . 7612 2 3.1416 3.5466 3.9761 A AQni 4.9087 5.4119 5.9: 96 6.4918 3 7.oe 86 7.6699 8.2958 Q O . jnQO 9.6211 10.321 11.045 11 . 793 4 12.566 13.364 14.186 15.904 16. E 00 17.721 18 . 665 5 19.635 20.629 21.648 00 fiQ1 23.758 24.850 25.967 27 . 109 6 28.274 29.465 30. ( 80 Q1Q 33.183 34.472 35.785 37 122 7 38.485 39.871 41.282 42.718 44.179 45.664 47.173 48 ; 707 8 50.265 51. E 49 53.456 55.088 56.745 58.426 60.132 61.862 9 63.617 65.397 67.201 by . u. 71 683 49 689 30 695 13 30 706 86 712 76 718 69 / ^4 . 64 730 62 736 62 742 64 /48 . 69 31 754 77 760 87 766 99 773 . 14 779 31 785 51 791 73 32 804 25 810 54 816 86 823 . 21 829 58 835 97 842 39 848 . 83 33 855 30 861 79 868 31 874 . 85 881 41 888 00 894 62 901 . 26 34 907 92 914 61 921 32 bzo . Ub 934 82 941 61 948 42 955 . 25 35 962 11 969 00 975 91 989 80 996 78 1003.8 1010.8 36 1017.9 1025.0 1032.1 1039 . 2 1046.3 1053.5 1060.7 1068 . 0 37 1075.2 1082.5 108< 3.8 1097.1 1104.5 1111.8 1119.2 1126.7 38 1134.1 1141.6 1149.1 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 1684.9 1643.9 1652.9 46 1661.9 1670.9 1680.0 1689.1 1698.2 1707.4 1716.5 1725.7 47 1734.9 1744.2 1753.5 1762.7 1772.1 1781.4 1790.8 1800.1 48 1809.6 1819.0 1828.5 1837.9 1847.5 1857.0 1866.5 1876.1 49 1885.7 1895.4 1905.0 1914.7 1924.4 1934.2 1943.9 1953.7 308 AREAS OF CIRCLES. Diameters increasing by eighths. No. No. +0. No.-{-y^ No.+Yi No A-M No Nf) 4-7/, 50 1963.5 1973.3 1983.2 1993.1 2003.0 2012.9 2022.8 2032.8 51 2042.8 2052.8 2062.9 2073.0 2083.1 2093.2 2103.3 2113.5 52 2123.7 2133.9 2144.2 2154.5 2164.8 2175.1 2185.4 2195.8 53 2206.2 2216.6 2227.0 2237.5 2248.0 2258.5 2269.1 2279.6 54 2290.2 2300.8 2311.5 2322.1 2332.8 2343.5 2354.3 2365.0 55 2375.8 2386.6 2397.5 2408.3 2419.2 2430.1 2441.1 2452.0 55 2463.0 2474.0 2485.0 2496.1 2507.2 2518.3 2529.4 2540.6 57 2551.8 2563.0 2574.2 2585.4 2596.7 2608.0 2619.4 2630.7 Do OC^AO 1 ^O'l-^ . i 2653 . 5 2676 . 4 fD RECIPROCAI.S OF NOS. FROM 1 TO 1000. No. No. = Circum. = Diam. Area. Square. Cube. Square Itoot. Cube Root. Log. 1000 X Recip. 1 3.142 0 7854 1 1 1 0000 1 0000 0 00000 1500 000 2 6.283 3 1416 4 8 1 4142 1 2599 0 30103 500 000 3 9.425 7 0686 9 27 1 7321 1 4422 0 47712 333 333 4 12.566 12 5664 16 64 2 0000 1 5874 0 60206 350 000 5 15.708 19 6350 25 125 2 ^ 71 nn u £;qqq7 Dyoy/ Tin nnn uuu 6 18.850 28 2743 36 216 2 4495 1 8171 0 77815 166 667 7 21.991 38 4845 49 343 2 6458 1 9129 0 84510 'A2 857 8 25.133 50 2655 64 512 2 8284 2 0000 0 90309 125 000 9 28 . 274 63 6173 81 729 3 0000 2 0801 0 95424 :ii 111 10 31 416 78 5398 100 1000 o o 2 IOtt nnnnn uuuuu -UU nnn uuu 11 34.558 95 0332 121 1331 3 3166 2 2240 1 04139 90 9091 12 37.699 113 097 144 1728 3 4641 2 2894 1 07918 83 3333 13 40.841 132 732 169 2197 3 6056 2 3513 1 11394 76 9231 14 43.982 153 938 196 2744 3 7417 2 4101 1 14613 71 4286 15 47 . 124 715 225 3375 Q O 0/oU 0 1 17609 p.p. P.PJPS? 16 50.265 201 062 256 4096 4 0000 2 5198 1 20412 62 5000 17 53.407 226 980 289 4913 4 1231 2 5713 1 23045 58 8235 18 56.549 254 469 324 5832 4 2426 2 6207 1 25527 55 5556 19 59 . 690 283 529 361 6859 4 3589 2 6684 1 27875 52 6316 20 62 . 832 314 159 400 8000 4721 2 71 dil / iff 1 30103 50 nnnn uuuu 21 65.973 346 361 441 9261 4 5826 2 7589 1 32222 47 6190 22 69.115 380 133 484 10648 4 6904 2 8020 1 34242 45 4545 23 72.257 415 476 529 12167 4 7958 2 8439 1 36173 43 4783 24 75 . 398 452 389 576 13824 4 8990 2 8845 1 38021 41 6667 25 78 540 625 15625 5 0000 0 1 40 nnnn 26 81.681 530 929 676 17576 5 0990 2 9625 1 41497 38 4615 27 84.823 572 555 729 19683 5 1962 3 0000 1 43136 37 0370 28 87.965 615 752 784 21952 5 2915 3 0366 1 44716 35 7143 29 91 . 106 660 520 841 24389 5 3852 3 0723 1 46240 34 4828 94 248 /Uo C50o 07nnn 5 4772 3 1 n70 1 47712 33 3333 31 97.389 754 768 961 29791 5 5678 3 1414 1 49136 32 2581 32 100.531 804 248 1024 32768 5 6569 3 1748 1 50515 31 2500 33 103.673 855 299 1089 35937 5 7446 3 2075 1 51851 30 3030 34 106.814 907 920 1156 39304 5 8310 3 2396 1 53148 29 4118 oO 962 113 1225 5 9161 3 2711 1 54407 28 5714 36 113.097 1017 88 1296 46656 6 0000 3 3019 1 55630 27 7778 37 116.239 1075 21 1369 50653 6 0828 3 3322 1 56820 27 0270 38 119.381 1134 11 1444 54872 6 1644 3 3620 1 57978 26 3158 39 100 coo 1194 59 1521 59319 6 2450 3 3912 1 59106 25 6410 40 125.66 1256 64 1600 64000 6 3246 3 4200 1 60206 25 0000 41 128.81 1320 25 1681 68921 6 4031 3 4482 1 61278 24 3902 42 131.95 1385 44 1764 74088 6 4807 3 4760 1 62325 23 8095 43 135.09 1452 20 1849 79507 6 5574 3 5034 1 63347 23 2558 44 138.23 1520 53 1936 85184 6 6332 3 5303 1 64345 22 7273 45 141.37 1590 43 2025 91125 6 7082 3 5569 1 65321 22 2222 48 144.51 1661 90 2116 97336 6 7823 3 5830 1 66276 21 7391 47 147.65 1734 94 2209 103823 6 8557 3 6088 1 67210 21 2766 48 150.80 1809 56 2304 110592 6 9282 3 6342 1 68124 20 8333 49 153.94 1885 74 2401 117649 7 0000 3 6593 1 69020 20 4082 310 CIRCUMFERENCES, CIRCUI-AR AREAS, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, liOGARITHMS, AND RECIPROCATES OF NOS. FROM 1 TO 1000. No. Nn.= Diam. Square. Cube. Square Root. Cube Hoot. Log. 1000 X Recip. Circum. Area. 50 1 F^7 RO 2500 l^OUUU 7 . 0711 3 6840 69897 20 0000 51 1 fin 22 2042 82 2601 132651 7 . 1414 3 7084 70757 19 6078 52 ioo oD 2123 72 2704 1 A OCOQ 7.2111 3 7325 71600 19 2308 53 ou 2206 1Q its 2809 148877 7 2801 3 7563 72428 18 8679 54 169 65 2290 22 2916 157464 7.3485 3 7798 1 73239 18 5185 55 179 i/ £i 7Q 2375 83 3025 ibuo/O 7 A1 0.0 3 8030 1 74036 18 1818 56 i/0 QQ yo 2463 01 3136 175616 7 . 4833 3 8259 74819 17 8571 57 1 7Q 07 2551 76 3249 185193 7 . 5498 3 8485 75587 17 5439 58 21 2642 08 3364 195112 7 6158 3 8709 76343 17 2414 59 185 35 2733 97 3481 205379 7; 6811 3 8930 1 77085 16 9492 60 ic5o OU 2827 43 3600 1 . 1 4b0 3 9149 77815 16 6667 61 191 64 2922 47 3721 OOCQQ1 7 Q1 09 3 9365 78533 16 3934 62 7R /o 3019 07 3844 7 Q740 3 9579 79239 16 1290 63 197 92 3117 25 3969 250047 7 9373 3 9791 1 79934 15 8730 64 201 06 3216 99 4096 262144 8.0000 4 0000 1 80618 15 6250 65 204 20 3318 31 - 48 u .3333 .3385 .34375 4 4M6 4>8 la 32 .5833 .5885 .59375 7 2| .8333 .8385 .84375 10 lOMe 10>s .0990 .1042 .109375 15^e 64 .3490 .3542 .359375 4M6 4Me II .5990 .6042 .609375 7h VMe (54 .8490 .8542 .859375 IOMg 1 0^4 lOMc I .1146 . 1 198 .1250 1% IKe 1 .3646 .3698 .3750 4% 4^6 t .6146 .6 198 .6250 2% 1 .8646 .8698 .8750 lo;^ .1302 .1354 .140625 1% 64 .3802 .3854 .390625 4M6 4?^ 4% 41 64 .6302 .6354 .640625 .8802 .8854 .890625 IOMg lOJa 10%c .1458 . 1510 .15625 IX 1% IJe 11 .3958 .4010 .40625 4?^ If 21 32 .6458 .6510 .65625 2 a 32 .8958 .9010 .90625 10% 10% 10^8 11 04 .1615 .1667 .171875 1% 2 2 Me 2-1 04 .41 14 .4167 .421875 4% 5 5Me II .6615 .6667 .671875 8 8Me 64 .9115 .9167 .921875 10% 1 1 IIMg .1771 .1823 .1875 2M0 2/4 .4271 .4323 .4375 5V 5M6 5/4 11 16 .6771 .6823 .6875 SMe 8)i .9271 •9323 .9375 IIJb IIMg 11>4 13 t;4 .1927 .1979 .203125 2^6 2% 2Ke .4427 .4479 .453125 SMe 5% 5Kg u .6927 .6979 .703125 SMe 8% SKe .9427 .9479 .953125 IIMg 11% IIMg .2083 .2135 .21875 2}i 2!Ke 2^ IS 32 .4583 .4635 .46875 5)2 M .7083 .7135 .71875 8X SMe 8^ §1 32 .9583 .9635 .96875 llJi IIMg ll^s' if .2240 .2292 .234375 2% 2% 2% §4^ .4740 .4792 .484375 5% 53/ 5% 47. 64 .7240 .7292 .734375 8% 8^ 8% £a 64 .9740 .9792 .984375 11%-G 11% 1 1 'Xg 1 4 .2395 .2448 .2500 2% 2% 3 .4896 .4948 .5000 5% 5% 6 1 .7396 .7448 .7500 8% 8% 9 1 .9896 .9948 1.0000 1 1J< 11% 12 330 NATURAL TRIGONOMETRICAL FUNCTIONS. Beg. Min. Sine. Vers. Cos. Cose- cant. Tang. Co- tang. Se- cant. onn. Co- sine. Min. Deg. 0 0 OOOOO 1.0000|/n:/i». .00000 Infin. 1.0000 .00000 1.0000 90 10 .00291 .99709 343.77 .00291 343.77 1.0000 .00000 .99999 50 20 .00582 .99418 171.89 .00582 171.88 1.0000 .00002 .99998 40 30 .00873 .99127 114.59 .00873 114.59 1.0000 .00004 .99996 30 40 .01163 .98836 85.946 .01164 85.940 1.0001 .00007 .99993 20 50 .01454 .98546 68.757 .01454 68.750 1.0001 .00010 .99989 10 1 0 '01745 .98255 57.299 .01745 57.290 1.0001 .00015 .99985 89 10 .02036 .97964149.114 .02036 49.104 1.0002 .00021 .99979 50 20 .02327 .97673 42.976 .02327 42.964 1.0003 .00027 .99973 40 30 .02618 .97382 38.201 .02618 38.188 1.0003 .00034 .99966 30 40 .02908 .97091 34.382 .02910 34.368 1.0004 .00042 .99958 20 50 .03199 .96801 31.257 .03201 31.2411.0005 .00051 .99949 10 jj 0 .03490 96510 28.654 .03492 28.6361.0006 .00061 .99939 88 10 .03781 96219 26.450 .03783126.432 1.0007 .00071 .99928 50 20 .04071 .95929 24.562 .04075 24.5421.0008 .00083 .99917 40 30 .04362 .95638 22.925 .04366 22.9041.0009 .00095 .99905 30 40 .04652 .95347 21.494 . 04657 21.4701.0011 .00108 .99892 20 50 .0'4943 .95057 20.230 .04949 20.2051.0012 .00122 .99878 10 3 0 .05234 . 94766 19.107 .05241 19.081 1.0014 .00137 .99863 87 10 .05524 94476 18^103 .05532 18.0751.0015 .00153 .99847 50 20 .05814 .94185 17.198 .05824 17.1691.0017 .00169 .99831 40 30 .06105 .93895 16.380 .06116 16.3501.0019 .00186 .99813 30 40 .06395 .93605 15.637 .06408 15.6051.0020 .00205 .99795 20 50 .06685 .93314 14.958 .06700 14.9241.0022 .00224 .99776 10 4 0 06976 93024 14.335 .06993 14.3011.0024 .00243 .99756 86 10 .07266 92734 13! 763 .07285 13.7271.0026 .00264 .99736 50 20 .07556 .92444 13.235 .07577 13.1971.0029 .00286 .99714 40 30 .07846 .92154 12.745 .07870 12.7061.0031 .00308 .99692 30 40 .08136 .91864 12.291 .08163 12.2501.0033 .00331 .99668 20 50 .08426 .91574 11.868 .08456 11.8261.0036 .00356 .99644 10 5 0 08715 .91284 11.474 .08749 11.4301.0038 .00380 .99619 85 10 .09005 ! 90995 11.104 .09042 11.059 1.0041 .00406 .99594 50 20 .09295 90705 10 758 .09335 10.712 1.0043 .00433 .99567 40 30 .09584 .90415 10.433 .09629 10.385 1.0046 .00460 .99540 30 40 .09874 .90126 10.127 .09922 10.078 1.0049 .00489 .99511 20 50 .10163 .89836 9.8391 .10216 9.7882 1.0052 .00518 .99482 10 C 0 . 10453 .89547 9.5668 .10510 9.5144 1.0055 .00548 .99452 84 10 .10742 .89258 9.3092 .10805 9.2553 1.0058 .00579 .99421 50 20 .11031 .88969 9.0651 .11099 9.0098 1.0061 .00110 .99390 40 30 .11320 .88680 8.8337 .11393:8.7769 1.0065 .00643 .99357 30 40 .11609 .88391 8.6138 .11688 8.5555 1.0068 .00676 .99324 20 50 .11898 .88102 8.4046 .11983 8.3449 1.0071 .00710 .99290 10 7 Q .12187 .87813 8.2055 .12278 8.1443 1.0075 00745 99255 83 10 12476 .87524 8.0156 .12574 7.9530 1.0079 .00781 .99219 50 20 .12764 .87236 7.8344 .12869i7.7703 1.0082 .00818 .99182 40 30 .13053 .86947 7.6613 .13165:7.5957 1.0086 .00855 .99144 30 40 .13341 .86659 7.4957 . 1346117. 4287il. 0090 .00894 .99106 20 50 .13629 .86371 7.3372 .13757|7. 2687:1. 0094 .00933 .99067 10 8 0 .13917 .86083 7.1853 .14054 7.11541.0098 .00973 .99027 83 10 .14205 .85795 7.0396 .143516.96821.0102 .01014 .98986 50 20 .14493 .85507 6.8998 .14648 6.82691.0107 .01056 .98944 40 30 .14781 .85219 6.7655 .14945 6.69111.0111 .01098 .98901 30 40 .15068 .84931 6.6363 .15243,6.56051.0115 .01142 .98858 20 50 .15356 .84644 6.5121 .1554016.4348 1.0120 .01186 .98814 10 81 9 0 .15643 .84356 6.3924 .15838 6.31371.0125 .01231 .98769 Co- i^ers. Se- Co- Cose- Vers. Sine. sine. Sin. cant. tang. 1 gent. cant. Cos. 331 NATURAL TRIGONOMETRICAL FUNCTIONS. Beg. Min. Sine. Vers. Cos. Cose- cant. Tang. Co- tang. Se- cant. Vers Sin. Co- Min. Deg. 9 0 .15643 .84356 6.3924 .15838 6.3137 1.0125 .01231 .98769 81 10 .15931 .84069 6.2772 .16137 6.1970 1.0129 .01277 .98723 50 20 .16218 .83782 6.1661 .16435 6.0844 1.0134 .01324 .98676 40 30 .16505 .83495 6.0588 .16734 5.9758 1.0139 .01371 .98628 30 40 .16791 .83208 5.9554 .17033 5.8708 1.0144 .01420 .98580 20 50 .17078 .82922 5.8554 .17333 5.7694 1.0149 .01469 .98531 10 10 0 .17365 .82635 5.7588 .17633 5.6713 1.0154 .01519 .98481 80 10 .17651 .82349 5.6653 .17933 5.576411.0159 .01570 .98430 50 20 .17937 .82062 5.5749 .18233 5.4845 1.0165 .01622 .98378 40 30 .18223 .81776 5.4874 .18534 5.3955 1.0170 .01674 .98325 30 40 .18509 .81490 5.4026 .18835 5.3093 1.0176 .01728 .98272 20 50 .18795 .81205 5.3205 .19136 5.2257 1.0181 .01782 .98218 10 11 0 .19081 .80919 5.2408 .19438 5.1445 1.0187 .01837 .98163 79 10 .19366 .80634 5.1636 .19740 5.0658 1.0193 .01893 .98107 50 20 .19652 .80348 5.0886 .20042 4.9894 1.0199 .01950 .98050 40 30 .19937 .80063 5.0158 .20345 4.9151 1.0205 .02007 .97992 30 40 .20222 .79778 4.9452 .20648 4.8430 1.0211 .02066 .97934 20 50 .20506 .79493 4.8765 .20952 4.7728 1.0217 .02125 .97875 10 12 0 .20791 .79209 4.8097 .21256 4.7046 1.0223 .02185 .97815 78 10 .21076 .78924 4.7448 .21560 4.6382 1.0230 .02246 .97754 50 20 .21360 .78640 4.6817 .21864 4.5736 1.0236 .02308 .97692 40 30 .21644 .78356 4.6202 .22169 4.5107 1.0243 .02370 .97630 30 40 .21928 .78072 4.5604 .22475 4.4494 1-0249 .02434 .97566 20 50 .22211 .77788 4.5021 .22781 4.3897 1.0256 .02498 .97502 10 13 0 .22495 .77505 4.4454 .23087 4.3315 1.0263 .02563 .97437 77 10 .22778 .77221 4.3901 .23393 4.2747 1.0270 .02629 .97371 50 20 .23061 .76938 4.3362 .23700 4.2193 1.0277 .02695 .97304 40 30 .23344 .76655 4.2836 .24008 4.1653 1.0284 .02763 .97237 30 40 .23627 .76373 4.2324 .24316 4.1127 1.0291 .02831 .97169 20 50 .23910 .76090 4.1824 .24624 4.0611 1.0299 .02900 .97099 10 14 0 .24192 .75808 4.1336 .24933 4.0108 1.0306 .02970 .97029 76 10 .24474 .75526 4.0859 .25242 3.9616 1.0314 .03041 .96959 50 20 .24756 .75244 4.0394 .25552 3.9136 1.0321 .03113 .96887 40 30 .25038 .74962 3.9939 .25862 3.8667 1.0329 .03185 .96815 30 40 .25319 .74680 3.9495 .26172 3.8208 1.0337 .03258 .96741 20 50 .25601 .74399 3.9051 .26483 3.7759 1.0345 .03332 .96667 10 15 0 .25882 .74118 3.8637 .26795 3.7320 1.0353 .03407 .96592 75 10 .26163 .73837 3.8222 .27107 3.6891 1.0361 .03483 .96517 50 20 .26443 .73556 3.7816 .27419 3.6470 1.0369 .03560 .96440 40 30 .26724 .73276 3.7420 .27732 3.6059 1.0377 .03637 .96363 30 40 .27004 .72996 3.7031 .28046 3.5656 1.0386 .03715 .96285 20 50 .27284 .72716 3.6651 .28360 3.5261 1.0394 .03794 .96206 10 16 0 .27564 .72436 3.6279 .28674 3.4874 1.0403 .03874 .96126 74 10 .27843 .72157 3.5915 .28990 3.4495 1.0412 .03954 .96045 50 20 .28122 .71877 3.5559 .29305 3.4124 1.0420 .04036 .95964 40 30 .28401 .71608 3.5209 .29621 3.3759 1.0429 .04118 .95882 30 40 .28680 .713203.4867 .29938 3.3402 1.0438 .04201 .95799 20 50 .28959 .710413.4532 .30255 3.3052 1.0448 .04285 .95715 10 17 0 .29237 .70763 3.4203 .30573 3.2708 1.0457 .04369 .95630 73 10 .29515 .70485'3.3881 .30891 3.2371 1.0466 .04455 .95545 50 20 .29793 .7020713.3565 .3121013.2041 1.0476 .04541 .95459 40 30 .30070 .69929:3.3255 .3153013.1716 1.0485 .04628 .95372 30 40 .30348 .69652:3.2951 .31850:3.1397 1.0495 .04716 .95284 20 50 .30625 .69375!3.2653 .321713.1084 1.0505 .04805 .95195 10 18 .30902 .69098 3.2361 .32492 3.0777 1.0515 .04894 .95106 73 Co- Vers. Se- Co- Tan- Cose- Vers. sine. Sin. cant. tang. gent. cant. Cos. Sine. NATURAL TRIGONOMETRICAL FUNCTIONS. Deg. Min. 18 19 30 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 69098:3.2361 68822 ■3.2074 68545 3.1792 68269 3.1515 67994 3.1244^. 677183. 09771. 67443 1 3. 0715! 67168 3.0458i 668943.0206 66619; 2. 9957 66345!2.9713 66071! 2. 9474 65798^2.9238 655252.9006 65252 2.8778 64979 2.8554 64707:2.8334 6^435 2.8117 ,64163;2.7904 ,63892 2.7694 ,63621 '2. 7488 ,63350 2.7285 ,63079 2.7085: .62809^2.6388; ,62539-2.6695 .6227012.6504 .6200012.6316 .6173212.6131 .6146312.5949 .32492 .32814 .33136 33459 3.07771.0515 . 3.04751.0525 . 3.01781.0535 2.9600 1.0555L 2.93191.0566;. 2.9042 1.0576^ 2.8770:i.0587:. 2.8502:1.0598!. 35412^2.8239:1.0608!. 35739 2.79801.0619 .33783 .34108 .34433 .34758 .35085 .36068 .36397 .36727 .37057 .37388 .37720 .38053 38386 38720 1.0630] 1.0642 1.0653! 1.0664! 1.0676 1.0688 1.0699 1.0711 1.0723 .39055!2. 5605 1.0736 2.7725 2.7475 2.7228 2.6985 2.6746 2.6511 2.6279 2 . 6051 :2 . 5826 39391! 2. 5386 1.0748 Vers. Cose- ^ Co- Se- Stne. cbs_ cant. lang. cant. 30902 ,31178 ,31454 ,317301 ,32006! ,32282' ,32557: ,32832! 33106' ,33381 ,33655 33928 ,34202! ,34475! ,34748 ,35021' ,35293: ,35565 ,35837! ,36108! ,36379' ,35550! ,36921j ,37191! .37461! .37730 .37999 .38268 .33537 .33805 .39073 .39341 .39608 .39875 .40141 .40408 .40674 .40939 .41204 .41469 .41734 .41998 .42262 .42525 .42788 .43051 .43313 .43575 .43837 .44098 .44359 .44620 Vers. Sin. ,04894 05076 Co- sine. .95106 .95015 94924 1.0545 ;05i68\ 94832 05260!. 94740 05354!. 94646 054481.94552 05543!. 94457 05639! .94361 .61195 .60927 .60559 .60392 .60125 .59858 .59592 .59326 .59061 .58795 .58531 .58266 .58002 .57738 .57475 .57212 .56949 .56424 .56163 .55902 .55641 55380 ,45140 45399 Co- 2.5770; 2.5593' 2.5419 2.5247 2.5078 2.4912 2.4748 2.4586 2.4426 2.4269 2.4114 2.3961 2.3811 2.3662 2.3515 2.3371 2.3228 2.3087 2.2949 2.2812 2.2676 2.2543 2.2411 39727 40065 40403 40741 41081 41421 41762 42105 ,42447 ,42791 ,43136 .43481 .43827 .44175 .44523 .44872 . 45222 .45573 .45924 .46277 .46631 .46985 .47341 .47697 2.5171 2.4960 2.4751 2.4545 2.4342 2.4142 2.3945 :2.3750 2.3558 2.3369 2.3183 2.2998 2.2817 2 . 2637 2.2460 2.2286 2.2113 05736' 05833 05932 .06031 .06131 .06231 .06333 .06435 .06538 .06642 .06747 .06852 06958 07065 .94264 .94167 .94068 .93969 .93869 .93769 .93667 .93565 .93462 .93358 .93253 .93148 .93042 92935 Min. Deg. 1-0760 1.07731.07173!. 92827 1.0785 1.0798 1.0811 1.0824 1.0837 1.0850 1.0864 1.0877 1.0891 1.0904 1.0918 1.0932 1.0946 1.0961 .07282 .07391 .07501 .07612 .07724 .07836 .07949 .08178 .08294 .08410 .08527 ,08645 .92718 .92609 .92499 .92388 .92276 .92164 .92050 .91936 .91822 .91706 .91590 .91472 91354 1.09891 1.1004' 1.1019 1.1034 1.1049 1.1064 1.1079 1.1095 55120:2.2282 ,548602.2153 .54601 Vers. Sin. 2.2027 Se- cant. 2.1943 2.1775 2.1609 2.1445 2.1283 2.1123 2.0965 .48055:2.0809, .48414 2.06551.1110 .48773!2. 05031. 1126 .49134!2.0352!l.ll42 .49495!2. 0204:1.1158 . 498582. 0057!1. 1174 . 50222:1. 9912!l. 1190 .50587!l.9768!l.l207 .50952 1.9626jl. 1223 Co- Tan- Cose- tang. I gent. ! cant. .08764 .91236 1.0975 . 08884 .91116 .09004 .09125 .09247 .09369 .09492 .09617 .09741 .09867 .09993 .10121 .10248 .10377 .10506 .10637 .10768 .10899 Vers. Cos. .90996 .90875 .90753 .90631 .90507 .90383 .90258 .90133 .90006 .89879 .89751 .89623 .89493 .89363 .89232 .89101 Sine. 333 NATURAL TRIGONOMETRICAL FUNCTIONS. Deg. Min. Sine. Vers. Cos. Cose- cant. Tang. Co- tang. Se- cant. Vers. Sin. a- sine. Min. neg. 37 0 .45399 .54601 2.2027 .50952 1.9626 1.1223 .10899 .89101 .88968 63 10 .45658 .54342 2.1902 .51319 1.9486 1.1240 .11032 50 20 .45917 .54083 2.17781.51687 1.9347 1.1257 .11165 .88835 40 30 .46175 .53825 2.16571.52057 1.9210 1.1274 .112991.88701 30 40 .46433 .53567 2.15361.524271.9074 1.1291 .11434'. 88566 20 50 .46690 .53310 2.1418 .527981.8940 1.1308 .11569 .88431 10 S8 0 .46947 .53053 2.13001.531711.8807 1.1326 .117051.88295 63 10 .47204 .52796 2.11851.535451.8676 1.1343 .11842 .88158 .88020 50 20 .47460 .52540 2.1070 .539191.8546 1.1361 .11980 40 30 .47716 .52284 2.0957 .542951.8418 1.1379 .121181.87882 30 40 .47971 .52029 2.0846 .54673 1.8291 1.1397 .12257 .87742 20 50 .48226 .51774 2.0735 .55051 1.8165 1.1415 .123971.87603 10 39 0 .48481 .51519 2.0627 .55431 1.8040 1.1433 .125381.87462 61 10 .48735 .51265 2.0519 .55812 1.7917 1.1452 .12679 .87320 50 20 .48989 .49242 .51011 2.0413 .56194 1.7795 1.1471 .12821 .87178 40 30 .5075812.0308 .56577 1.7675 1.1489 .12964 .87035 30 40 .49495 .50505:2.0204 .56962 1.7555 1.1508 .13108 .86892 20 50 .49748 .50252:2.0101 .57348 1.7437 1.1528 .13252 .86748 10 30 0 .50000 .5000012.0000 .57735 1.7320 1.1547 .13397 .86602 60 10 .50252 .4974811.9900 .58123 1.7205 1.1566 .13543 .86457 50 40 20 .50503 .494971.9801 .58513 1.7090 1.1586L 13690. 86310 30 .50754 .492461.9703 .58904 1.6977 1.1606 . 13837 i. 86163 30 40 .51004 .489961.9606 .592971.6864 1.1626 .13985!. 86015 20 50 .51254 .487461.9510 .596911.6753 1.1646 .141341.85866 10 31 0 .51504 .48496 1.9416 . 60086 1 . 6643 1.1666 .14283 .85717 59 10 .51753 .48247 1.9322 . 60483 1 . 6534 1.1687 .14433L 85566 50 20 .52002 .47998 1.9230 .60881 1 . 6425 1.1707 .14584:. 85416 40 30 .52250 .47750 1.9139 .61280 1.6318 1.1728 .14736!. 85264 30 40 .52498 .47502 1.9048 .616811.6212 1.1749 .14888 .85112 20 33 50 .52745 .47255 1.8959 .6208311.6107 1.1770 .15041;. 84959 10 0 .52992 .47008 1.8871 .624871 .6003 1.1792 .15195 .84805 58 10 .53238 .46762il.8783 .628921 .59001.1813 .15350. 84650 50 20 .53484 .465161.8697 .632991 .5798 1.1835 .15505 .84495 40 30 .53730 .45270 1.8611 . 63707! 1 .5697 1.1857 .15661 .34339 30 40 .53975 .46025j 1.8527 .64117 1 .5596 1.1879 .158171.84182 20 33 50 .54220 .457801.8443 .64528 1 .5497 1.1901 .15975 .34025 10 0 .54464 .455361.8361 .64941 1 .5399 1.1924 .16133:. 33867! 57 10 .54708 .452921.8279 .65355 1 .5301 1.1946 .16292. 33708 50 20 .54951 .450491.8198 .65771 1 .5204 1.1969 .16451 .83549 40 30 .55194 .448061.8118 .66188 1.510811.1992 .16611 .33388 30 40 .55436 .445641.8039 .66608 1 .50131.2015 . 16772 .33228 20 50 .55678 .443221.7960 .67028 1 .49191.2039 .16934 .33066 10 34 0 .55919 .440811.7883 .67451 1.48261.2062 .17096 .32904 56 10 .56160 .438401.7806 . 67875 1.4733|l.2086 .17259 .32741 50 20 .56401 .435991.7730 .68301 1.46411.2110 .17423 .32577 40 30 .56641 .43359 1.7655 .68728 1.45501.2134 .17587 .82413 30 40 .56880 .43120 1.7581 .69157 1.4460ll.2158 .17752^.82247 20 35 50 R71 1 Q .42881 1.7507 .69588 1.43701.2183 .17918 .82082 10 0 .57358 .42642 1.7434 .70021 1.4281 '1.2208 .18085 .81915 55 10 .57596 .42404 1.7362 .70455 1.41931.2233 .182521 .81748 50 20 .57833 .42167 1.7291 .70891 1.4106,1.2258 .18420 .81580 40 30 .58070 .41930 1.7220 .71329 1.40191.2283 .18588 81411 30 40 .58307 .41693 1.7151 .71769 1.39331.2309 .18758 81242 20 36 50 .58543 .41457 1.7081 .72211 1.38481.2335 .18928 .81072 10 0 .58778 .41221 1.7013 .72654 1.37641.2361 .19098!. 80902 54 Co- Vers. Se- Co- Tan- Cose- Vers. Sine. sine. Sin. cant. tang. gent. ! cant. Cos. 1 334 NATURAL TRIGONOMETRICAL FUNCTIONS. Deg. Min. 36 37 Vers. I Cose- ~ Cb- Se- Vers. Cb- , „ Sine. Cos. cant. ^'^'^9- lang. cant. Sin. sine. M'^'^- ^^3- .726541.3764 .731001.3680 63832 . 64056' . ,64279!. ,64501|. ,647231. ,64945 . ,65166!. ,65386 . ,65806 , ,65825 , ,66044'. .65262 , .66479:, .66697! .669131 .67129! .67344: .67553; .67773; .679871, .68200' .68412 .686241 .63835:, .69045:, .69256;, .69465!, .69675' 73547 73996 74447 74900 75355 75812 76271 76733 77196 77661 78128 78598 79070 79543 80020 1.3597 1.3514 1.3432 1.3351 1.3270 3190 1.3111 3032 1.2954 2876 1.2799 1.2723 1.2647 1.2572 1.2497 1.2423 1.2349 1.2276 1.2203 1.2131 1.2059 1 1.1917 1.1847 1.1778 1.1708 1.1640 1.1571 1.1504 1.1436 1.1369 1.1303 1.1237 1.1171 1.1106 1.1041 1.0977 1.0913 1.0849 1.0786 1.0724 1.0661 1.0599 1.0538 1.0476 1.0416 1.0355 1.029511.3941 .97699:1. 0235;i. 3980 .98270! 1.0176! 1.4020 .98843! 1.0117; 1.4060 .99420 1.0058' 1.4101 1.0000,1.4142 Tan- Cose- gent. i cant. .95451 .95569 97133 1.2361 1.2387 1.2413 1.2440 1.2467 1.2494 1.2521 1.2549 1.2577 1.2605 1.2633 1.2661 1.2690 1.2719 1.2748 1.2778 1.2807 1.2837 1. 1. 1.2929 1.2960 1.2991 1.3022 1.3054 1. 1.3118 1.3151 1.3184 1.3217 1.3250 1.3284 1.3318 1.3352 1.3386 1.3421 1.3456 1.3492 1.3527 1.3563 1.3600 1.3636 1.3673 1.3710 1.3748 1.3786 1.3824 1.3863 1.3902 .19098 .19270 .19442 .19614 .19788 .19962 .20136 .20312 .20488 .20665 .20842 .21020 .21199 .21378 .21558 .21739 .21921 .22103 .22285 .22469 .22653 .22837 .23023 .23209 .23395 .23583 .23771 .23959 .24149' .24338 .24529 .24720 .24912 .25104 .25297 .25491 .25685 .25880 .26076 .26272 .26469 .26666 .26865 .27063 .27263 .27462 .27663 .27864 .28066 .28268 .28471 .28675 .28879 .29084 .29289 Vers. Cos. .80902 .80730 .80558 .80386 .802121 .80038 .79863 .79688 .79512 .79335 .79158 .78980 .78801 .78622 .78441 .78261 .78079 .77897 .77715 .77531 .77347 .77162 .76977 .76791 .76604 .76417 .76229 .76041 .75851 .75661 .75471 .75280 .75088 .74895 .74702 .74509 .74314 .74119 .73924 .73728 .73531 .73333 .73135 .72937 .72737 .72537 .72337 .72136 .71934 .71732 .71529 .71325 .71121 .70916 .70711 Sine. 335 Trigonometrical Functions. D L/iI Let angle y1 0 F be denoted by C. ~y OA = radius R. Sine C=FQ /\\ Cosine OG / \ Tangent C=AI / \ Cotangent C = D L / \ Secant C = 01 / C ' Cosecant G= 0 L O Gr ''^ Versed sine C=GA ' Coversedsine C= D K Trigonometrical JCquivalents. Sine = \/ 1 — COS.'* Cos. = \/ 1 — sin.2 Sine = COS. -r- Cotang. Cos. = sin. -T- Tang. Tang. = 1-4- Cotang. Cos. = sine X Cotang Cosec. = 1 Sine. Tang. = Sine Cosine. Secant = 1 -r- Cos. Cotang. = Cosine -i- Sine. Vers. = Rad. — Cos. (Rad.)'-' = Sin.2 _^ CQg;2 Covers. = Rad. — Sine! (Secant)'^ = Radius'-' + Tang.'-* Cotang = 1 Tang. Right Angled Triangles. Sin. A=- Tang. Sec. A c ° h b Cos. A=- Cot. A = ~ Cosec. A =- 336 Given. a, c a, b A, a A, h A, c A, B, a A , a, h a, h, C a, h, c A,B,C,a A, b, c a, b, c Re- quired. A,B, A, B,c B, b,c B, a, c B, a, 6 Sin bB b B A — . A ! I Area Area Area Formula:. in.^ = ^;cos.^ = |; 6 = -y/ (c + a) (c— a) Tang. -J = I ; cot. B^^;g = ^ «2 4. 52 B = 90° — A;b=^aX cot. A; c= ^ i? = 90° — .1 ; a = 6 X tang. A ; c sin. A b COS. A 90° — A; a = cX sin. A;b = cX cos. A Oblique Angled Triangles. B b = a Sin. B = sin. B sin. A b sin. A i?Tang. I U - B) - ^) tang. j M +^) a + Let 6^ = i (a+6+c); sin. s — b){s — c). s {s — a) ' sin 4 —9.V 8 (g — ") (s — fc) (s — c) be Area : sin. J? sin. C 2 sin. A Area = 4 & x c X sin. ^. Area = ^r{7^^if{r-^bj{s~^^^^ where s 337 MENSURATION. Triangle, Area = base X k perpendicular height. Parallelograni, Area = base X perpendicular height. Trapezoid, Area = J sum of parallel sides X perpendicular height. Area of an Irregular Plane Surface. Divide the surface into any number of parallel strips of equiil widths, "d" take the middle ordinates h^, h^, etc. rule). d X ^h-\-^(a- hu) (PonceletV II. Area = dx2/i+y^2 (8a+/i.— 9/ii)+ ^1, (86+/in-i— 9//,,^ (Francke's rule). III. Area = d X 2/i 2 is symbol for sum of. Circle. Circumference = 3. 1416 X diameter. Length of an arc = diameter X number of degrees in arc X 0.0087266. Ch 0 rd of arc^CZ>= v/ U"— [D-'lh] = 2s/E'—XR^^'' Chord of J Arc = i y^cS^ + AK^ VWyTh __ - - 4- Diameter 4 ' /i - Versedsine h = J {I)—^/D'^ — CD''-) or nearly R Area circle = .7854 (diam.) Area Sector ADFCA = ^} X arc DFC = 8.1416 X i?^ X an gle I ) AC i n degrees 360 Area Segment CDFC= ^ [arc DFC X R — CD (R — /«)] Sphere. Sphere, Surface = 12 5664 R' = 3.1416 D^ Sphere, Volume = 4.189 R'^ Splierical Sector, Surface = 1.5708 (4/i + CD) Spherical Sector, Volume = 2. 0944 R% = 2.0914 R!" X tR± Vr:^ — ^^^ 338 Spherical Zone, Surface = 6.2832 x B X h =^ 0.7854 iClf + 4/i2) Spherical Zone, Volume = 3.1416 [R — ^s h) = 3.1416/1^ V— 81 --'V ELLIPSE. — approxi- mately, where D is major axis and cl the minor axis. Area ellipse = .7854 D X d. Ellipsoid surface = 2.22 d "j/D^ + d'^ volumes 0.5231 D d^ PARABOLA. Area of parabola = f area of circumscribing rectangle. Paraboloid volume = 1.5707 X altitude X square of radius of base. CYLINDER. Convex surface = 3.1416 X diam. of base X altitude. Entire " = 3.1416 X diam. of base X altitude + 1.5708 X [diam.^]. Volume = 0.7854 diam.^ X altitude. CONE. Convex surface = circumference of base X i slant height. Volume = area of base X ^ altitude. Ffustrum of Right Cone. Convex surface = 1.5708 X slant height of frustrum X Hinn of diam. of bases. Volume = 0.2618 X altitude X [square of diam. of lovs'er l)ase + square of diam. of upper base + product of 2 diameters.] PRISM. Convex surface = perimeter of base X altitude. Volume area of base X altitude. PYRAMID. Convex surface regular pyramid — perimeter of base X J slant height. Volume = area base X \ altitude. Frustrum of a Regular Pyramid. Convex surface = ^ slant height X sum of perimeters of hases. Volume = -3- altitude X [sum of areas of 2 bases 4- square root of pi'oduct of tlie 2 bases.] 339 ELECTRICAL FORMUL-ffl. Standards of Measubement. The centimeter, gramme, and second are the units of space, mass and time. Unit of velocity = space -j- time = 1 cm. in 1 second. Unit of acceleration = change of 1 unit of velocity in 1 second. Acceleration, due to gravity at Paris, = 981 centime- ters in one second. Unit of force = 1 dyne = yh gm- = .000002247 pounds. A dyne is that force which, acting on a mass of 1 gm. dur- ing 1 second, will give it a velocity of 1 cm. per second. Unit of work 1 erg = 1 dyne-centimeter = .0000000- 7373 foot-pounds. Unit of power = 1 watt = 10 million ergs per second. 1 watt = jl^ of 1 h. p. = .00134 h. p. C. G. S. Unit of magnetism = the quantity wliich attracts or repels an equal quantity at a centimeter's distance with the force of 1 dyne. C. G. S. Unit of electrical current = the current which, flowing through a length of 1 centimeter of wire, acts with a force of 1 dyne ui)on a unit of magnetism distant 1 centi- meter from every point of the wire. Practical Units. Ampere— the unit of current strength, represented by C. Volt — the unit of electro-motive force, represented by JE. Ohm — the unit of resistance, represented by R. Coulomb— the unit of quantity. 7\mpere-hour = 3600 coulombs = represented by Q^. Watt — the unit of power — volt-ampere = P. Joule — the unit of work = volt-coulomb = W. Farad — the unit of capacity, represented by K, the one- millionth of the Farad, or micro-farad, is the usual unit. Henry— the unit of induction. The following formulte give the relation between these units : i = 1 second, T=l hour. C Q= a, Q' ^ CT, |, QE,P= CE. By combination the following formulae are derived : Q = ^t,K= ^^t, W= CEt = ^i= C'Et = Pt, A it 340 The relation between the practical units and the C. G. S. Units is : 1 Ampere 1 Yolt 1 Ohm 1 Coulomb 1 Farad 1 Volt-coulomb 1 Watt (volt-ampere) = 10-1 C. G. S. Units. = 108 = 109 = 10-9 = 10^ = 10' Equivalents of Wokk. Work = Power X Time. 1 Volt coulomb = 1 Watt (volt-ampere) per second. (Joule) = .737324 foot-pounds. = .101937 Kilogrammeters. = .00134059 H. P. per second. = .000022343 IT. P. per minute. 1 Foot-pound = 1.35626 Volt-coulombs. 1 Kilogrammeter = 9.81 " " 1 H. P. per second = 745.941 " " 1 H. P. per min. = 44756.47 " " Equivalents of Power. Power = Work Time' 1 Watt = 1 Volt-coulomb per second. = .00134059 Horse-power. (Volt-anipere) = .737324 foot-pounds per second. 1 Horse-power 1 Foot-lb. per sec. : 1 Foot-lb. per min. 44.23944 2654.3664 745.941 1.35626 .0226043 minute. " " hour. Watts (Volt-amperes) 341 DIMENSIONS, WEIGHT AND RESISTANCE OF BARE COPPER WIRE. B S Go/ugc Diam. in Mils 1 Mil =.001" Area in Circ. Mils d\ Wt,o/ 1000 Feel in Lbs. Lenglh in Feel of 1 Lb. Re Ohms per 1000 Feet. listant Ohms per Mile. e @ C8° F. Feel. 1 Ohm i; ■ Lbs. Current in Amperes. Ex- \con- posed. cea'd 4—0 460.000 211600 00 640.5 1.561 .049 .258 20440*. 00764 345 X / o 3-0 409.642167806 43 508.0 1.969 .062 .326 16210 .01215 290 145 2—0 364.796133077 66 402.8 2.482 .078 .411 12850.01931 245 120 0 324.861 105535 50 319.5 3 130 .098 .518 inann ir^nTi luyuu .uou / ± 210 100 1 289.296 83693 67 253.3 3.947 .124 .653 1 8083 .04883 17"=; 1/0 2 257.626 66371 31 200.9 4.977 .156 .824 6410 .07765 73 3 229.422 52634 37 159.3 6,276 .197 1.039 5084.1235 125 60 4 204.307 41741 32 .2481.309 110 50 5 181.941 33102 37 100.2 9.980 .3131.652 3197.3122 yu 45 6 162.022 26251 37 79.56 12.58 .394 2.083 2535 .4963 OU OO 7 144.285 20818 35 63.02 15.87 .497 2.626 2011 .7892 65 30 8 128.490 16510 64 49 98 90 m ^u.u± .627 3.311 55 25 9 114.434 13093 75 39.63 25.23 .7914.175 12651.995 48 20 10 101.897 10383 02 31.43 31.82 .9975.127 1003 3.173 40 17 11 90.743 8234 11 24.93 40.12 1.257 6.637 795.3 5.045 35 15 12 80.808 6529 95 19.77 50.59 1.586 8.374 630.78.022 30 13 13 71.962 5178 58 15.68 63.79 1.99910.56 500.112.76 25 10 14 64.084 4106 72 14.43 80.44 2.52l'l3.31 396.6'20.28 22 8 15 57.069 3256 88 9.86 101.4 3.179 16.79 314.5 32.25 19 7 16 50.821 2582 74 7.82 127.9 4.009:21.17 249.451.28 16 6 17 45.257 2048 39 6.20 161.3 5.055 26.69 197.8 81.53 14 5 18 40.303 1624 30 4.92 203.4 6.374133.66 156.9129.6 12 5 19 35.890 1288 13 3.90 256.5 8.038,42.41 124.4 206.1 11 4 20 31.961 1022 53 3.09 323.4 10.1453.54 98.66 327.8 9 3 CAPACITY OF CABIiES. A rea in Circular Mils. Amperes. Area in Circular Mils. Amperes. Open. Concealed. Open. Concealed. 200000 300 200 1200000 1145 715 300000 405 270 1300000 1215 755 400000 500 335 1400000 1285 795 500000 595 395 1500000 1355 835 600000 680 445 1600000 1425 875 700000 765 495 1700000 1490 910 800000 845 540 1800000 1555 945 900000 925 585 1900000 1620 980 1000000 1000 630 2000000 1680 1015 1100000 1075 675 342 AVOIRDUPOIS OR COMMERCIAL WEIGHTS. Ch-oss Ton. Cwts. Pounds. Ounces. 1 20 2240 35840 1 112 1792 1 16 LONG MEASURE. Miles. Rods. Yai'ds. Feet. ]n chits. 1 320 1760 5280 ();3:u;o 1 5.5 16.5 198 1 3 3() 1 12 SQUARE MEASURE. iSq. Miles. Acres. Sq. Rods. Sq. Yards. Sq. Feet. Sq. Inches. 1 640 102400 3097600 27878400 1 100 4840 43560 6272640 1 30.25 272.25 39204 1 9 1296 1 144 CUBIC MEASURE. Cubic Yard. Cubic Feet, Cubic Inches. Slnick Bushel. Wine Gallon. 1 27 46656 21 .7005 201.974 1 1728 0.8036 7.4805 0.0461 1.2445 2150.42 1 9.3092 0.1337 231. 0.1074 1.0 1 heaped bushel = li struck bushel. 1 cord of wood — a pile 4X4x8 feet = 128 cubic feet. 1 perch of masonry = 161 X U X 1 foot = 24| " LIQUID MEASURE. Barrel. Gallons. Quarts. Pints. Gills. 1 31.5 126 252 1008 1 4 8 32 1 2 8 1 4 343 METRIC SYSTEM. LINEAR MEASURE. MEASURE OF SURFACE. Denomination. Abbr. Value. Denomination. Abbr. Value. Myriameter 10000 meters Sq. Kilometer km2 1000000 m.' Kilometer km. 1000 " Hektar lia. 10000 m.2 Hectometer 100 " Are a 100 ni.2 Dekameter 10 " f Centare 1 m.2 Meter m. 1 " ( Square Meter m.' 1 m.2 Decimeter dm. .1 " Sq. Decimeter dm.2 .01 m.2 Centimeter cm. .01 " Sq. Centime'r m.2 .0001 m.2 Millimeter mm. .001 " Sq. Millimeter mm. 2 .000001 m.2 MW A flTTK TPS! OE VOLUME. 3IEASURES OF MASS f Kiloliter 1000 liters ("Millier 1000 kilos < Stere s. < Tonntau (Cubic Meter m.3 (Metric Ton ' t'. ' Hectoliter hi. 100 Quintal 100 " Dekaliter dal 10 Myriagram 10 " f Cubic Decimeter dm .3 1 " / Kilogram kg" 1000 grams \ Liter 1. 1 " IKilo Deciliter dl. .1 " Hectogram 100 " Centiliter cl. .01 " Dekagram 10 " f Cubic Centimeter cmS. .001 Gram g- 1 " ( Milliliter ml. .001 liter Decigram <3g. eg. .1 " Cubic Millimeter mm.3 .000001 " Centigram .01 " Microliter .001 m. 1. Milligram nig. .001 " Microgram y- .001 ni. g. METRIC CONVERSION TABLE. Millimeters X .03937 = inches. (( 25.4 I ( Centimeters X .3937 n (( 2.54 « Meters X 39.87 = " (Act (1 X 3.281 = feet. (( X 1.094 = yards. Kilometers X .621 = miles. 1.6093 a ii X 3280.7 = feet. Square Millimeters X .00155 = square inches. 645.1 (< (( Square Centimeters X .155 (( Cl 6.451 a (( Square Meters X 10.764 " feet. 344 Metric Conversion Table — Continued. Square Kilometers II ek tares Cubic Centimeters Meters Liters Hectoliters X 247.1 = acres. X 2.471 = acres. 16.383 = cubic inches. -r- 3.69 = fluid drachms. -T- 29.57 = fluid ounce. X 35.315 = cubic feet. X 1.308 = cubic yards. X 264.2 = gallons (231 cu. in.). X 61.022 = cubic inches (Act of Con- gress). 33.84 = fluid ounce (U. S. Phar.). 2642 = gallons (231 cu. in.). X X 3.7 -7- 28.316 = cubic feet X 3.531 X 2.84 X .131 X 26.42 X 15.432 bushels (2150.42 cu. in.), cubic yards. gallons (231 cu. in.). <^^rams X 15.432 = grains (Act of Congress). X 981 = dynes. " (water) — 29.57 = fluid ounces. " -T- 28.35 = ounces avoirdupois. " per cu. cent, -f- 27.7 = pounds per cubic inches. Joule X .7373 = foot-pounds. Kilograms X 2.2046 = pounds. " X 35.3 = ounce, avoirdupois. -T- 907.2 = tons (2000 lbs.). " per sq. cent. X 14.223 = pounds per sq. in. Kilogrammeters X 7.233 foot-pounds. Kilograms per lineal meter X .672 = pounds per lineal ft. " " square " X .205 = poundspersquareft, " " cubic " X .062 = pounds per cubic ft. ' ' " cheval-vapeurX 2.235 = lbs. per H. P. Kilo-watts W^atts (I (-alorie Cheval-vapeur ( I )eg. Centigrade Francs Cravity, Paris X 1.34 = horse-power, -j- 746 = " X .7373 = foot-pounds per second. X 3.968 = B. T. U. X .9863 = horse-power. X 1.8) -f 32 = degrees Fahrenheit. X .193 = dollars. = 980.94 centimeters per second. 1 Admiralty knot = ] .853 kilometers. 1 Atmosphere is the pressure of a column of 76 centime- ters of mercury at the temperature of melting ice at Paris, where it is equal to 1.0333 kilos on a square centimeter. 345 O M H Em © o :^ !1h 1:^ LD O LO CD eg c~- O O 1-1 03 CD i-l CD T-H CO C~ t- CO CD CD CO O O LO O LD CD CD t> C- CO CD LO tn CO O) (3) O CD LO lD CD CD CD tH CD tH r-H LO CO Cvj CO CO CO T)< CO ^tO^CO '^O i-H OJ CO LO i-H CO CO I— I Cv] CO CO O CO 00 CO T}< CD CO CO CJ cq O CJ LD Od t>- O] LO 05 eg CD ■51; LO uq CO LO CX> C5^ CD t- 00 O O CO CD O ^ -51; Tj( LO LD^lXI CM lD~ LO CM O C~- LD CO .-I CO CO CO l> T-H LO O CO CO CO CO LO 1> CD rH eg CM - a> o CM CO eg 00 LO O CD i-l i> LO l> 00 t- LO CO 00 CO o eg CO LO I> 00 05 o o o ~ CD CM (35 CD LO t- 00 O C3> !>• LO C33 CD CO o CM eg CM eg CO O t> LO CM LO LO CD C- CO 00 I-l cn 00 O CO lO CO i> t> CO a> o o o o O O --I CM lO T( 00 CO 05 [> T-l rH eg CM CO p C) C) C3 CO O LO o eg LO t> o .-I l> CO o CO CO LO 00 t> CD lO o o o o LO O LO O CM LO l> O CD eg 00 LO lO CD CD I> o o o o LO O LO eg LO t~ o I-l t- CO o 00 00 CD O 346 INDEX. PAGE ALLOWANCE for eye, square and round bars 253 for upsets on round and square bars 252 ALLOYS and other metals, physical properties of 289 ANGLES as beams, approximate rule for strength of 113 as struts , 174 dimensions and weights of 8-11 elements and properties of 206-211 greatest safe loads as beams 100-105 length of legs of, corresponding to given areas 1 moments of inertia 20G-211 radii of gyration 206-211 radii of gyration of two, back to back 212-216 rivet spacing in 261 ANGLES, BULB, elements and properties of 202-203 weights and dimensions of 12 ANGLE COVERS, weights of 13 A XLES, open hearth steel .... 16 RARS, sizes 15 l!AR, weights and areas of round and square 306-307 BEAMS. Bulb, or deck section 12 approximate rules for strength of 113 dimensions and weights 12 elements and properties of 200 moments of inertia 200 radii of gyration 200 tables of safe loads and deflections 107 I Beam Sections. approximate rules for strength of 113 dimensions and weights 2-4 elements and properties of 188-191 floor 28 greatest safe load 30-95 lateral strength of 146 limits of deflection 27 maximum load in tons 188-191 moments of inertia 188-191 properties and elements of 188-191 proportions of 2-4 radii of gyration 188-191 BEAMS— I Beam Sections. page safe loads and deHftctions 30-95 spacing and deflection of 27 supports and connections for 110 weight of floor per square foot 28-29 BEAMS, of angle and tee sections 123 stresses on, due to impact 122 subjected to compound stresses 118-121 supporting brick walls 156-157 supporting irregular loads 116 with fixed ends 25 without lateral supports 23 wooden 283-286-287 BEAMS AS STRUTS 168-169 BELTING 237 BENDING and compression beams subjected to both ....... 118-121 BENDING, bearing and shearing values for pins 244-245 BENDING moments for beams 220-226 BENDING, resistance to 24 BOLTS AND NUTS, weight of 267 BOLT IRON, sizes 15 BRICK ARCHES for floors 141 arches, tie rods for 146 walls, beams for supporting 156-157 BRIDGE RIVETS, shearing and bearing values of 264-265 weight of 268 BRIDGES, specifications for railroad 269 BUCKLED PLATES 147-149 greatest safe loads for 148 BULB ANGLES, elements and properties of 202-203 moments of inertia 202-203 radii of gyration 202-203 weight of 12 BULB BEAMS (see Beams). CANTILEVER BEAMS 114-115 CAST IRON 281 CHANNELS. approximate rule for strength of . ... 113 as struts 170-172 dimensions aud weights of 5-6 elements and properties of . . 192-195 greatest safe loads, and .^pacing 9i6-08 moments of inertia 192-105 proportions of 5-6 radii of gyratiou 192-195 separation of, in latticed struts 196 struts 166-167 ii PAGE CITICLES, areas and circumfereuces of 308-309 CLEVISES, dimensions of 249 • dimensions of square rods and pins for 253 COLUMNS. iireproofing and bases of ' 142-143 greatest safe load for round 178-179 " " " square 180-181 moments of inertia of Z bar 197 ' radii of gyration for round and square 177 Zbar 197 COMPOUND STRESSES, beams subjected to 118-121 CONNECTIONS, angle 260 CONTINUOUS BEAMS 25 CONTINUOUS shafting, working formuUe for . 237 CONTINUOUS GIRDERS, reactions for 138 CONNECTIONS, floor beams to columns 258-259 ; COPUER WIRE, dimensions, weight and resistance 842 CORRUGATED FLOORING 152-155 loads per square foot 154-155 weight and strength of 153 CORRUGATED IRON 296 COTTERPINS 247 CRANE STRESSES 227-228 CUBES of numbers 310-329 : CUBE ROOTS of numbers 310-329 DECIMAL equivalents for vulgar fractions 330 ; DECK BEAMS (see Beams). DEFLECTION of beams 24-27 ' limits of 27 tables of, for channel bars 192-195 " " " deck beams 200-201 " " " I beams 30-95 ; " " " Z bars 198-199 tables of, for corrugated flooring sections 154 DEFLECTION of shafting 236 ' DESTRUCTIVE pressures for iron and steel struts, tables of . . 160-1G5 : DIMENSIONS of allowance for upsets on round and square bars . . 252 of bolts 266-267 , " channels 5-6 " clevises , 249 " eye bars 250 " pins and nuts 246 " rivet shanks to form heads , 263 ' " screw threads 266 " separators ' 257 " sleeve nuts 248 " tees 14 iil DIMENSIONS. PAGE of working, for continuous sbafting 238-239 " Z bars 7 DUCTILITY, iron and steel 18-19 ELASTICITY of wrought iron and steel 19 ELECTRICAL formula; 340-341 ELEMENTS of structural shapes 182 of angles 206-211 " bulb angles 202-203 " channels 192-195 " deck beams 20tV201 " I beams 188-191 " tees 204-205 " usual sections 218-219 " Z bars 198-199 '' Z bar columns 197 EXPANSION, by heat 21 EYE BARS, dimensions of 250 FACTORS of safety for beams 22-23 " " " " shafting 235 " " " " struts 159 FIRE PROOF FLOORS 139-141-144-145 FIXED-ENDED steel or iron struts . . . . , 158 FLAT BAR IRON, approximate rule for beams of 112 FLAT-ENDED steel or iron struts 158 FLATS, sizes of rolled 15 FLEXURE (see Deflection) 24 FLOOR BEAMS 28 lateral strength of 14(') rule for weight of 28 spacing of ' 30-95 weight per square foot 29 FLOORING, fireproof 139-145 FLOORING, proportioned for evenly distributed load 145 corrugated, table of weight and strength 153-155 " " " causing deflection of of span 155 trough-shaped sections for bridges and buildings 153 Zbar 150-151 FLUCTUATING loads, limitations for safe loads 22 FOIlMULiE, approximate, for rolled beams 111-113 for unsymmetrically loaded beams 110 tables of, for beams of various sections 112 FOUNDATIONS AND MASONRY 291 FRACTIONS of an inch expressed in decimals 330 FRAMING, of I beams and channels 254-255 iv PAGH GIRDERS, coefficient of strength, rule for determining 12G reactions for continuous 138 riveted 125 rule to find safe loads 126 strength and weight for tables 127-137 stresses of trussed • • 229 supports and connections for 110 GYRATION, radii of 187 angles 206-211 bulb angles 202-203 channels 192-195 deck beams 200-201 formulae for various sections 218-219 I beams 188-191 round columns 177 square " 177 tees 204-205 two angles back to back 212-216 Z bars 198-199 HALF-ROUND BAR IRON, sizes 15 HKADS of rivets, dimensions of shank required to form 263 HINGE-ENDED steel or iron struts 158 HORSE POWER of shafting 235 I BEAMS (see Beams). IMPACT, stresses on beams due to 122 INERTIA, moments of 182-186 angles 20li-211 bulb angles 202-203 channels . • 192-195 combined sections 184-18G deck beams 200-201 formula) for various sections 218-219 I beams • 188-191 rectangles 217 tees 204-205 Z bars 198-199 Z bar columns 197 INTRODUCTION to appendix 280 IRON, corrugated 296 LATERAL STRENGTH OF FLOOR BEAMS 145 LATERAL supports, beams without 23 LATTICED channel struts, safe loads 170-171 " " " separation of 196 LATTICING for channel struts 167 LIMIT of safe loads for beams 22 LOADS (see Safe Loads). page character of 22 LOGARITHMS OF NUMBERS 310-329 MASONRY, physical properties of materials of 290 MASONRY AND FOUNDATIONS 291 MENSURATION , 338-339 METRIC CONVERSION TABLES 344 METRIC SYSTEM 344 MISCELLANEOUS SHAPES 14 MODULUS OF ELASTICITY 19 NUMBERS, squares, cubes, etc., of 310-329 NUTS and pins, sizes of 246 NUTS, sleeve, sizes of 248 FAINTING 293 PHYSICAL PROPERTIES of alloys and othermetals 289 of materials of masonry 290 of timber 284-285 PILLARS, and wooden beams 288 PINS AND NUTS, table of dimensions 246 PINS, shearing, bending and bearing values of 244-245 PRESSURE, destructive, tables of lGO-165 PROPERTIES and elements of angles 200-211 bulb angles 202-203 channels 192-195 f" ^-V bean s 200-201 Deaiu. ... 188-191 Z bars 198-199 Z bar columns 197 PROPORTIONS of bolts 2GG channels 5-6 clevises 249 eye bars 250 I beams 2-4 pins and nuts 246 rivets 263 rivet shank to form head 263 round and square bars to make upset 253 screw threads 266 separators 257 sleeve nuts 248 working, for continuous shafting 236-239 RADIUS of GYRATION of angles 206-211 bulb angles 202-203 channels 192-195 vi RADIUS of GYRATION. page deck beams 200-201 formulae for various sections 218-219 I beams 188-191 round columns 177 square " 177 tees 204-205 two angles back to back 212-216 Z bars 198-199 RAILROAD BRIDGES, specifications for 269-279 REACTIONS for continuous girders 138 RECIPROCALS of numbers 310-329 RECTANGLES, moments of inertia of 217 RESILIENCE of steel 20 RESISTANCE of copper wire 342 RIVETS, proportions of sbank to farm head 263 shearing and bearing value of 264-205 sizes 15 weights of bridge 268 RIVET SPACING in angles 261 RIVETED GIRDERS 124-137 coefficient of strength, rule for determining 124-137 rule to find safe loads 126 strength and weight of, tables 127-137 ROOFS 233 ROOF STRESSES 230-232 ROUND BARS, approximate rule for beams of .■ 112 sizes 15 weights and areas 306-307 ROUND COLUMNS, table of greatest safe loads 178-179 " " radii of gyration for 177 ROUND-ENDED steel or iron struts 158 RULES, approximate, for moments of inertia 218-219 for beams, bearing irregular loads 116 " lateral strength of I beams 145 " " " " channels 146 " radii of gyration 218-219 " shafting 234-235 " thrust of brick arches 145 " weight of rolled steel 21 " weight of steel in floor beams 28 SAFE LOADS, coefficient for 22 SAFE LOADS, greatest for angles 100-105 beams • 22 channels 96-99 corrugated flooring 153-155 deck beams 107 vii SAFE LOADS. page I beams 30-95 steel struts, tables of 160-165 tees 108-109 Z bars 106 SAFE LOADS, limits of, for beams 22 " " for struts, of angles, table of 174 channels 170-172 I beams 168-169 tees 175 Z bars 173 SAFE LOADS, round columns 178-179 square columns 180-181 square pillars 288 wooden beams 286-287 SCREW THREADS, table of standard 266 SEPARATORS, table of standard 257 SEPARATION OF CHANNELS, in latticed struts 196 SHAFTING, deflection of 236 horse-power of ... 236 iron or steel 23-1 rules for determining sizes and lengths 234-235 sizes rolled (see also Rounds) 15 stiffness of 240-241 working formulae for continuous 237 " proportions for continuous 238-239 SHANKS required to form head of rivets 263 SHAPES, miscellaneous, dimensions and weights 14 SHEARING, strength of iron and steel 234 SHEARING, bending and bearing values of pins 244-245 and bearing values of bridge rivets 204-265 SLEEVE-NUTS, sizes of ... - 218 SPACING floor beams of I beam sections 30-95 SPECIAL ANGLES, weights of 12 SPECIFIC GRAVITY, iron and steel 21 SPECIFICATIONS for railroad bridges 269-279 SQUARE BARS, sizes 15 weights and areas of 306-307 SQUARE ROOT ANGLES, weights of 12 SQUARE ROOTS, cube roots of numbers 310-329 SQUARE PILLARS, safe loads of 288 SQUARES AND CUBES of numbers •. . . . 310-329 STEEL, analysis of 18 columns, round and square • . 178-181 ductility 18 elasticity of rolled 18 elastic limit 18 expansion by heat 21 viii PAGE STEEI. for beams 17 " shafting 17 " struts 166 STEEIj, modulus of elasticity 19 physical properties of open hearth basic 18 resilience of 20 resistance to shearing • 234 " " torsion 234 shafting 234 sizes of bar 15 specilic gravity 21 strength of 17-18 " " in compression 18 " " " torsion . 234 structural 17 struts 158-165 tensile and compression tests 18-158 weight and area of round and square bar 306-307 " of sheets of rolled 297 " per lineal foot of bar 300-305 STEEL BEAMS (see Beams). deflection of 24 greatest safe loads for angles 100-105 channels 96-99 corrugated floors 153-155 deck beams 107 I beams 3O-95 tees 108-109 Z bars 106 STRIDNGTH OF STEEL in tension 18 in shearing 234 STRESSES in framed structures 227-232 on beams due to impact 122 STRUCTURAL STEEL 17 STRUTS, factors of safety for I59 fixed, flat, hinged, round 158 rolled 158 tables of destructive pressures for 160-162-164 STRUTS, tables of greatest safe loads for 161-163-165 angles I74 channels 170-172 I beams 168-169 STRUTS, tables of greatest safe loads of tees 175 Z bars 173 SUProRTS and connections for beams and girders 110 TABLE OF PHYSICAL PROPERTIES OF WOODS 284-285 ix VMIE TEES, approximate rule for strength of, as beams II3 as struts, tables of greatest safe loads 175 dimensions and weights of 14 elements of even-legged 204 " " uneven-legged 205 greatest safe loads ] 08-109 moments of inertia 204-205 radii of gyration 204-205 TENSION 18 of belting 237 THREADS, sizes of standard screw threads 266 TIE RODS for brick arches • 145 TIMBER, physical properties of 28 1-285 TORSIONAL STRENGTH 234 TRIGONOMETRICAL FUNCTIONS 336 TRIGONOMETRY 336-337 TUBES, wrought iron 295 TURNTABLES, dimensions and weights 242-243 ULTIMATE LOADS FOR STRUTS 160-162-164 UNITED STATES MEASURES 343 WEIGHTS OF ANGLES 8-11 bar flats 300-305 bars, round and square 306-307 bolts and nuts 267 bridge rivets 268 bulb angles , , 13 channels 5-6 deck beams 13 flooring, corrugated 153 floor-beams 28-29 I beams 2-4 rivet heads ■ 268 rolled sheets 297 tees 14 Z bars 7 WOODS, table of physical properties of 281-285 WOODEN BEAMS AND PILLARS 288 WOODEN BEAMS, safe loads of 280-2X7 WROUGHT IRON TUBES 295 Z BARS, approxiraate rule for strength of, as beams 113 as struts, tables of greatest safe loads 173 columns 197 dimensions and weights 7 elements and properties of 19S-199 flooring 15U-151 safe loads 100 PLATES OF STEEL SECTIONS. 77te dijn^nsjloTuf beforuj fx> the lea.vt ,seaf/o//^9. Several •'fecfio/is- orbeajns an/^l (^ui7aieL<^ are r o//e^l, w/iicJ} a/-r not s/wwn in- lit?>of/rap/u?. Sorn^. poj-f/eulars- o/ t/,rsr will be fbuM/l in. t/i^ taAies, or definite itLlorr/ia fion ^*•m be /lirn/.i/iefl (t/opl/^a/j/?/v. Plate No. 5. All wei]^Ms ^iven in pounds per foot. Plate No. 7. All weights ftiveii in pounds per foot Plate-N'o.9. AllAvei^ts given in pounds per foot. Plate No lG. All weights given in pounds per foot No. wgt. 100 C-15 LBS. 101 C-20 , No. W^t. 90 0-13.25 LBS. 91 C-isoo , Plate iNo.I7. All weights given, in pounds per foot. Plate No. 18. All weights given in pounds per foot. JOT. C .22to3l" > . 87 ^ , J No.w^t. I7C-I.I3 <- 1.09' >• No.Wgt 20 C-2.9 21 0-3« No. Wgt. 22 C-3.8 »■-— V.-U"— ■» No.Wgt. 30 C-4.0 31 C-S.0 32 C-6.0 No. wgi. 50 C-6.S 51 C-90 52 C-M.s No. W|t •40 C-5.25 41 C-6.25' 42 C-7.2S J*' r--i40'- !.«" No.wgt, 60 C-8.0 No. wgt. 61 C-105 62 C-13.0 63 C-I5.S -CI Plate No. 19. All weights given in pounds per foot. 5 V4"' No. too D WT. 28.0 TO 38 .6 LBS. No. 115 0 WT.J2.2 TO 45.6 LBS. Hi" No. 90 D WT.25jOT0 32£ lbs. 1315 ¥ Plate No. 23. All wei^ehts ^iven in poxuids per foot , f 3- i J No. 441 T WT. 13.7 LBS. No.440 T WT.10.9 Les No. 33 1 T WT.7. 7 LBS. No.330 T WT.6.S LBS. ^-----^zw- I No. 1 12 T. 2* WT. 1.5 LBS No. 117 T WT. 2.+ LBS. "Sno.iiot 2" ' ij WT.I.O LBS. ; No.223 T WT 4.0 LBS. N0.22OT WT.3.S LBS. PlcLte yo.24. N0.64T. WT.17.4 LBS. All weights given in poixnds per foot. N0.45T WT.13.5 LBS. 11 N0.54T WT, 1S.3 LBS. Si- No. 53 T WT. 17.0 LBS. N0.43T WT. 9 .0 LBS. » 4.. cnzx If' N0.44T WT.10.2 LBS. Plate No. 25. i All weights given in poimds per foot. "t. - .-3- . f i J 1' ' 2 No.36 T WT. 9.5 LBS. y. 16 -3- 5- 8 No.34 T WT. 8.0 LBS. No. 32 T WT. 6.0 LBS. No.33 T WT.7 O LBS. z'r No.SOT j WT. 4.0 LBS. ! Plate No. 28. All weights given in pounds per foot '/Vtoy«" Nos.330Ato336 A WT. 4.9 TO II . S NOS.275A to 279 A 4/ WT.4.5 TO 8.6 NO8.250 Ato255A .^jvv- WT. 3.1 TO 7. a No8. 225 A fo 228 A WT. 1.2 TO 3 . S Nos.125 A tot27 A WT. I .0 TO 2.0 Noft.no A foil 2 A WT. 0 . e TO I . 5 Plate No. 29. All weights given in pounds per foot , + \ jk^'*. "to I ' Nos.864-Ato868A / WT.33.8 TO 45.6 / / Nos.860Ato863A / / WT.23.0 TO 31.7 / / ***■* / iXOS. /OUMTO /JOA/ / WT. 17.0 TO 32.5// / Nos.650Ato659A WT. 12.9 TO 31.9 // Nos.640Ato649A / WT. 12. 2 TO 29.4. / y • • • » * / yr ^ \ / V' * • • Nos.630Ato639A WT.11.6 T0 28.6 / Nos.SOOAto 504 a WT. II.O TO 17.9 , Nos. 54-0 A TO 546 A WT.Il.O TO 21.3 Plate JSIo. 31 All weigtlits given in pounds per foot Plate No. 33. All wei^Ms given m pouncLs per foot. 3 3/2 6" evs' Nos. 66-67-68 Z . WTS. 29.+-3I.9-345 Nos. 63-64-65 Z WTS. 237-25.4-28.0 Nos. 60-61-62 Z WTS. IS.6 -18.3-21.0 3% 3^16 3^ . I' 4b- 5" Nos. 56-57 Z WTS 23.7-26.0 Nos 53-54-55 Z Nos. 50-51-52 Z WTS. 17.8-20.1-22.4 WTS II.+-I33-I6.I Nos. 46-47-48 Z WTS. 188-209-22.9 2% Nos. 43-44-45 Z WTS. 13.5-15.5-17.5 Nos. 40-41-42 Z WTS. 79-99-119 3" 3V6" Nos. 33-34-35 Z WTS. II.I-II.9-I2.7 Nos. 30-31-32 Z WTS. 6.6-a3-IOO Plate No.34. Trough. STnaped Sections for C orru,^ ate d Floor in^ All weights given in pounds per foot. ^ -6- i 6" WT. PER SQ rOOT 14. B TO 29 I LBS. Plate No. 35. METHOD OF INCREASING SECTIONAL AREAS. Cross hatched portions represent the minimxim sectioTis and the hlank portions the added areas.. ELEMENTS OF PENCOYD TEES. Since going to press one new Tee, section No. 46 T, has been added and No. 45 T has been altered. The sections, weights and properties of these are given below : 1^ 4" ^ ST- ^ N0.45T WT. 14. 6 LBS. No.46T WT. 15.8 LBS, I. Seciion Number. 46 T 45 T n. Size in Inches. 4Vx3V 4"x4^ III. Area in Square Inches. 4.65 4.29 IV. Weight in Pounds per Fool. 15.8 14.6 V. vr. Moments of Inertia. Axis A. B. Axis a D. 4.93 3.67 7.87 2.80 vn. vni. Resistance. Axis A. B. Axis C. D. 2.05 1.63 2.50 1.40 IX. X. Itadius of Gyration. Axis A. B. Axis a D. 1.03 0.89 1.37 0.81 XI. Distance "d" Base to Neutral Axis. Coefficient of Safe Load Axis A. B. in Net Tons. 1.11 10.91 1.37 13.39 SAFE IiOAI> IN NET TONS UNIFORMLY DISTRIBUTED. Fibre stress 16,000 lbs. per square inches. Section No. 46T 45T Size Flange by Stem Inches. 43,^2x31^ 4 x4i42 per Foot in Lbs. 15.8 14.6 LENGTH OF SPAN IN FEET. 10 11 12 13 Safe Load in Net Tons. 512.18 1.82 1.561.37 1.21 1.090.99 0.91 )2.68 2.23 1.911.67 1.49 1.341.22 1.12 0.84 1.03 PlaLteNo.35.