UC-NRLF OSBORN'S TABLES. LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Class u SBORN'S TABLES OF MOMENTS OF INERTIA AND SQUARES OF RADII OF GYRATION TO WHICH HAVK BEEN ADDED TABLES OF THE WORKING STRENGTHS OF STEEL COLUMNS, THE WORKING STRENGTHS OF TIMBER BEAMS AND COLUMNS, STANDARD LOADS AND UNIT STRESSES, AND CONSTANTS FOR DETERMINING STRESSES IN SWING BRIDGES. OF THE UNIVERSITY FIFTH EDITION REVISED BY THE OSBORN ENGINEERING CO. 1905 COPYRIGHT, I9O5 BY THE OSBORN ENGINEERING COMPANY, CLEVELAND 1 PREFACE TO FIFTH EDITION. "Osborn's Tables" are now too well known among engineers and designers to require further introduction. The first edition, by Mr. Frank C. Osborn, appeared in 1886, and was followed in turn by three others in the next eight years. Since the publication of the fourth edition in 1894, the various mills have adopted uniform standards of shapes which nearly all varied somewhat from those used in the tables. This considerably decreased the usefulness of the tables as they then existed. Believing, however, that the work still fills a want among de- signing engineers, the present edition has been prepared. The tables of moments of inertia and squares of radii of gyration have all been completely refigured, using the present standard mill sec- tions and shapes, and combining them in accordance with present designing practice. It is believed that these tables will prove much more convenient than the earlier ones in this respect. The tables of > square root, swing bridges, rivets, web plates and timber beams, have alt been preserved in the present edition. Some of the other matter, now obsolete, has been omitted and instead there have been included tables of the safe working strengths of soft steel and medium steel columns, of standard loads and unit stresses for bridges, of timber columns and of bridge weights. There have also been included a few pages of historical and other statistics concerning the bridges of the world that it is hoped may prove of interest. Such information is not easily obtainable elsewhere. It is earnestly hoped that this new work may have the same kind reception and may prove as useful a companion to the design- ing engineer as have its preceding editions. THE OSBORN ENGINEERING COMPANY. CLEVELAND, MARCH, 1905. CONTENTS. Page Explanation 6 Moments of Inertia, Rectangles w Squares of Radii of Gyration, Two Angles 14 * " " " " " " and One Top Plate 18 MOMENTS OF INERTIA AND SQUARES OF RADII OF GYRATION : One Web Plate and Two Angles 20 One Web Plate, Two Angles and Top Plate .... 24 Two Web Plates, Two Angles* and Top Plate ... 26 Squares of Radii of Gyration, Four Angles 28 MOMENTS OF INERTIA AND SQUARES OF RADII AND GYRATION: One Web Plate and Four Angles 32 Two Web Plates and Four Angles 42 Two Web Plates, Two Side Plates and Four Angles . 50 Three I Beams 53 Two Channels and One Separating I Beam ... 54 Two Web Plates, Four Angles and Top Plate . . .58 Two Channels and One Top Plate 75 Two Web Plates, Two Side Plates, Four Angles and Top Plate 78 Two Web Plates, Four Angles, Top Plate and Horizontal Flange Plates 82 Two Web Plates, Two Side Plates, Four Angles, Top Plate, and Horizontal Flange Plates . . 84 Values of M. 86 Working Strengths of Soft Steel Columns . . 97 " " Medium Steel Columns . . . 100 Square Roots . . . 103 SWING BRIDGES; SHEARS AND MOMENTS: Three Points of Support, Single I,oads, Spans of Four to Twenty Panels . . . 112 to 127 Three Points of Support, Symmetrical Ioads, Spans of Six to Twenty Panels .... 12810141 Four Points of Support, Symmetrical Ioads, Spans of Seven to Nineteen Panels . . 142 to 153 Bearing and Shearing Values of Rivets per Foot Run 154 Safe Resistance Against Buckling of Girder Webs . . 155 Centrifugal Force in Per Cent, of Weight .... 156 Chords I,oaded Transversely . . . . . . 157 Portal Bracing 158 Camber 160 Iength of Flange Plates, Girders 162 Bending Moments for Various I^oads and Spans . . . 163 Capacity of Timber Beams : 800 Ibs. to 1500 Ibs. per square inch fibre strain 164 to 167 Timber, Safe Working Stresses 168 Timber Columns, Working Strengths . .... 168 Weights of Railway Bridges 169 Cooper's Standard goading for Railway Bridges . . .170 The Osborn Engineering Company's Standard leading for Electric Railway Bridges ... 171 The Osborn Engineering Company's Standard loading for Highway Bridges 172 Impact Formulae 173 Unit Stresses I73 Formulae for I and r^, Carnegie Shapes .... 174 Formulae for I and >-2, Usual Sections 175 Conventional Signs for Rivets . ..... 176 Bridges : Historical and Other Data 177 EXPLANATION. The shapes used in the following tables are those manufactured by the Carnegie Steel Co., Pittsburg Pa. The moments of inertia will not, however, vary materially for shapes of same size and weight made by other manufacturers. In all cases calculations have been based on the gross area, and if it is desired to use the sections as beams to resist direct bending f due allowance should be made for loss of section from rivet holes in tension flanges. The following example will illustrate the general method pur- sued in obtaining the moment of inertia and square of radius of gy- ration for sections composed of two plates and four angles riveted as shown on page 43: 2 plates 12 x 5^=6.00 sq. ins. 4 angles 3^ X 2% X % 8.44 Total, 14.44 sq. ins. -HI2 X 122= 72.OO X 5-34 2 =24o.7i 4 X 1.09 4.36 1=317.07 317.07 + 14.44=21. 96= ^2 The moment of inertia of the plates being y 1 ^ 6d3=^ !f Ad* in which =breadth, tf=depth, and A the area of the plates; and the moment of inertia of each angle being adi+i, in which a equals the area of the angle, d the distance of its center of gravity from the neutral axis of the section, and z, its moment of inertia about an axis through its own center of gravity parallel to that neutral axis. In the above example, 5.34 inches is the distance from center of gravity of angle to the neutral axis, and 1.09 is the moment of inertia of one angle about an axis through its center of gravity, as given in Carnegie's Pocket Companion. For trough-shaped sections it is convenient to first determine the position of the neutral axis, which is done as follows; Multiply the area of the top plate, top angles, webs and bottom angles, each by the distance of its center of gravity from the lower edge of web. Divide the sum of these products by the total area of the section, and the result will be the distance of the neutral axis above the lower edge of the web: Top plate 17 X %= 6.38 X 14-19= 90.53 2 top angles 3 X 3 X %== 4.22 X 13.11= 55.32 2 web plates 14 X ^=10.50 X 7.oo 73.50 2 hot. angles 4 X 3 X S A= 7.96 X 0.87=- 6.92 29.06 X 7.79=226.27 7.00 deduct, 29.06 X 0.792 6.38 X 7-i9 2 =3-9-S2 4.22 X 6.112=157.54 10.50-4-12X142=171.50 7.96 X 6.132=299.11 957-97 + 9-36 96733 - 17.99 1=949 34 r 2 =949.34-1- 29.06-32. 7 Find the moment of inertia of the section about an axis through the center of the web, as follows: Multiply the area of the top plate, top angles and bottom angles, each by the square of the dis- tance of its center of gravity from the center of web; add to these results the moment of inertia of the webs, which may be taken from the table on page 12, and the moment of inertia of each angle about an axis through its center of gravity. From the result sub- tract the product of the area of the section by the square of the distance from the neutral axis to the center of the web, and the result will be the required moment of inertia of the section about an axis through the center of gravity perpendicular to the web. The moment of inertia of the top plate about an axis through its center of gravity should, strictly speaking, be added to the above, but its value in the present instance is so small that the final result is not materially affected. A somewhat easier method, especially when the operation has to be performed without the aid of a slide rule is the following: X 7-I9329-S2 X 6.11-157.54 Top plate 17 X %= 6.38 X 7.19=45.87 2 top angles 3 X 3 X % 4.22 X 6.11=25.78 71-65 2 web plates 14 X ^=10.50 2 bot. angles 4 X 3 X ^8= 7.96 X 6.13=48.79 29.06 X 0.79=22.86 deduct, 29.06 X 0.792 171.50 X 6.13299.11 957-97 + 9.36 967.33 - 17-99 1=949-34 This plan avoids the use of squares in getting the moment of inertia and saves cne multiplication in getting the position of i he neutral axis. The word eccentricity is used in the tables to denote the dis- tance of the neutral axis of the section from the center of the web. In the calculation of these sections for moments of inertia sideways, the distance out to out of webs was assumed equal to the width of top plates, less twice the nominal length of leg of top angle. The table for two angles, page 14, is based on the assumption that the angles are attached to each other securely enough to act as one member; if the angles are not so connected, then the least value of r a for one angle should be used, and the column considered as two separate members. STRENGTH OF COLUMNS. By means of the table of values of the working strength of any column for which ri is known, can be readily obtained. EXAMPLE: Required the working strength of a medium steel column 18 feet long, square at both ends, made up as section 81 on page 61. The value of r"* is 37.0 and the area 38.72 square inches. Referring to the table of , look down the column headed r% until we come to 37.0; then in the same horizontal line, under 18, find 9 for the value of ; referring now to the tables of working strength of medium steel columns we find opposite 9 the working strength per square inch of 14479 Ibs. The total working strength of the column will then be: 14479 x 38.72 = 560626.82 Ibs. BEARING AND SHEARING VAI,UE OF RIVETS. This table is designed to facilitate the calculation of pitch and diameter of rivets uniting flanges and web at the ends of stringers and beams. Assuming the shear as acting in lines of 45 degrees the total stress is transferred from web to flanges in a distance equal to the effective depth of the stringer or beam. If, therefore, we divide the total stress by the effective depth of beam we will obtain the shear per vertical foot of beam or its equivalents, the shear per horizontal running foot of beam. Dividing this shear per foot run by the allowed unit stress for bearing or shearing we ob- tain the required bearing or shearing area of rivets to be provided for each running foot, and an inspection of the table will show at once the necessary pitch, size of rivet and thickness of web required to give this area. EXAMPLE: Given a stringer or beam with an effective depth of 3 feet and a shear at the end of 45,000 pounds. What pitch and diam- eter of rivet will be required to transmit the shear to the flanges without exceeding a bearing pressure of 12,000 pounds per square Inch or a shearing strain of 8,000 pounds per square inch on the rivets? 45,000 Ibs. -*- 3 = 15,000 Ibs. per foot run. *- 12,000 = 1.25 bearing area required. * 8,000 = 1.88 shearing area required. Referring now to the table we find that for a ft" web %" rivets would require a pitch of 3", giving a bearing area of 1.31 square inches and 2.41 square inches for single shear, or 4.81 for double shear. With a ^" web 3^" pitch would give the same bearing area and would give 2.06 square inches for single shear or 4.12 square inches for double shear. Using %" rivets, a %" web would require a pitch of 2%" giving 1.35 square inches for bearing and 2.12 square inches for single and 4.24 square inches for double shear. A -^" web would permit 3" pitch and give i 31 square inches for bearing and 1.77 square inches for single or 3.53 square inches for double shear. RESISTANCE OF GIRDER WEBS AGAINST BUCKLING. This table will indicate, when the shear per foot run is known, whether stiffeners are necessary or not. If stiffeners are required the table will show the proper clear distance between them. The application of the table will be illustrated by the following; EXAMPLE: Given a stringer or beam with an effective depth of 3 feet and a shear at the end of 45,000 pounds. Will stiffeners be required, and if so, how far apart should they be placed? The shear per foot run equals 45,000 Ibs. + 3 = 15,000 Ibs. Referring now to the table and assuming that a ft" web has been adopted we find that in the column headed "t equals %," that 15,000 falls between 14,360 and 16,500, corresponding to a spacing of stiffeners of 2 feet 6 inches and 2 feet 3 inches. This spacing being less than the clear vertical distance between horizontal angles in- dicates that stiffeners are necessary, and indicates, also, that the end stiffeners should be spaced apart a distance not exceeding 2 feet 3 inches. Should this shear be produced by a concentrated load on the girder, then this spacing of stiffeners should be made uniform from the end of the girder to the point of application of the load. If this shear is produced by a uniformly distributed load the total shear, and consequently the shear per foot run, diminishes toward the center of the girder and consequently the stiffeners may be spaced farther apart until the clear distance between them equals the clear vertical distance between the horizontal angles of the gir- der. When the table shows a distance apart between stiffeners greater than the distance apart of the flange angles, stiffeners will not be required to prevent buckling of the webs. By referring to the column headed "t equals y^" it appears that if a -^ web is used stiffeners would not be required, as their distance apart would just equal the clear vertical distance between flange angles. If a T 5 ^ web were used stiffeners would be required i foot and 9 inches apart in the clear. The several formulae in use have for the numerator constants varying from 8,000 to 15,000. 10,000 has been adopted in the present case, partly because it will in ordinary cases give fair results and partly because in case it is desired to use another formula the pres- ent formula may be readily adapted to another constant by a ready percentage comparison. CENTRIFUGAL FORCE. This table shows, for various velocities and degrees of curva- ture, the amount of centrifugal force, expressed in the form of per cent, of weight. It will be found useful in determining the stresses in lateral bracing due to moving loads on bridges located on curves, and its application is as follows : Obtain in the usual manner the maximum shearing stresses in the various panels of the truss, due to the specified rolling load, and in the same manner as if the truss were on a tangent. Multiply these shearing stresses by the tabular coefficient corresponding to the degrees of curvature and desired velocity and the results will be the shearing stresses due to the centrifugal force. STRENGTH OF TIMBER BEAMS. The use of the tables of bending moments and capacities of timber beams will be, perhaps, best illustrated by the following : EXAMPLE : Required the size of joist to support a load of 100 Ibs. per square foot, the length of span being 18 feet, the joists to be spaced 2 feet center to center and the unit stress not to exceed 1000 Ibs. per square inch. Assume the weight of joists and flooring to be 20 Ibs. per square foot. From the table of bending moments we find For 20 Ibs. per square foot and 18 foot span, 1620 foot Ibs. " 100 " " 18 " 8100 Total bending moment = 9720 Referring now to the table of capacities for 1000 Ibs. fiber strain we find that 3" X 16", 3^" X 15" or 4" X 14" will answer the purpose, the 3" X 16* being the most economical in material. For other spacing of joists than 24 inches, obtain the load per lineal foot of joist and then select the corresponding bending mo- ments and proceed as above. If, in the above example, the spacing of joists was 18 inches instead of 24, the operation would be as fol- lows : 20 Ibs. per square foot X i % = 30 Ibs. per lineal foot, And 100 " X 1^=150 " For 30 Ibs. per lineal foot, and 18 ft. span the bending moment ...... = 1215 ft. Ibs. For 158 Ibs per lineal foot, and 18 foot span the bending moment ...... =6075 " Total bending moment = 7290 " This bending moment on the basis of 1000 Ibs. fiber strain, would call for joists i% n X 15", 3" X 14" or 4" X 12", the deepest one being the stiffest as well as the most economical in material. MOMENTS OF INERTIA. RE CTANGLES. Depth in Inches Width of Rectangle in Inches X ft 3 /8 T v ' y^ T 9 * # 3 0.56 0.70 0.84 0.98 1.13 1.27 1.41 4 1.33 1.67 2.00 2.33 2.67 3.00 3.33 5 2.60 3.26 3.91 4-56 5.21 5.86 6.51 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 8 10.67 13.33 16.00 18.67 21.33 24-00 26,67 9 15.19 18.98 22.78 26.58 30.38 34.17 37.97 10 20.83 26.04 31.25 36.46 41.67 46.87 52.08 12 36.00 45.00 54.00 63.00 72.00 81.00 90.00 13 45.77 57.21 68.66 80.10 91.54 102.98 114.43 14 57.17 71.46 85.75 100.04 114.33 128.63 142.92 15 70.31 87.89 105.47 123.05 140.63 158.20 175.78 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 18 121.50 151.88 182.25 212.63 243.00 273.38 303.75 20 166.67 208.33 250.00 291.67 333.33 375.00 416.67 21 192.94 241.17 289.41 337.64 385.88 434.11 482.34 22 221.83 277.29 332.75 388.21 443.67 499.13 554.58 23 253.48 316.85 380.22 443.59 506.96 570.33 633.70 24 288.00 360.00 432.00 504.00 576.00 648.00 720.00 25 325.52 406.90 488.28 569.66 651.04 732.42 813.80 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 32 682.67 853.33 1024.00 1194.67 1365.33 1536.00 1706.67 34 818.83 1023.54 1228.25 1432.96 1637.67 1842.38 2047.08 36 972.00 1215.00 1458.00 1701.00 1944.00 2187.00 2430.00 38 1143.17 1428.96 1714.75 2000.54 2286.33 2572.13 2857.92 . 40 1333.33 1666.67 2000.00 2333.33 2666.67 3000.00 3333.33 44 1774.67 2218.33 2662.00 3105.67 3549.33 3993.00 4436.67 46 2027.83 2534.79 3041.75 3548.71 4055.67 4562.63 5069.58 48 2304.00 2880.00 3456.00 4032.00 4608.00 5184.00 5760.00 50 2604.17 3255.21 3906.25 4557.29 5208.33 5859.38 6510.42 60 4500.00 5625.00 6750.00 7875.00 9000.00 10125.00 11250.00 MOMENTS OF INERTIA. RECTANGLES. (CONTINUED.) Width of Rectangle in Inches Depth in Inches u X 11 H it 1 1.55 1.69 1.83 1.97 2.11 2.25 3 3.67 4.00 4.33 4.67 5.00 5.33 4 7.16 7.81 8.46 9.11 9.77 10.42 5 12.38 13.50 14.63 15.75 16.88 18.00 6 19.65 21.44 23.22 25.01 26.80 28.58 7 29.33 32.00 34.67 37.33 40.00 42.67 8 41.77 45.56 49.36 53.16 56.95 60.75 9 57.29 62.50 67.71 72.92 78.13 83.33 10 99.00 108.00 117.00 126.00 135.00 144.00 12 125.87 137.31 148.75 160.20 171.64 183.08 13 157.21 171.50 185.79 200.08 214.38 228.67 14 193.36 210.94 228.52 246.09 263.67 281.25 15 234.67 256.00 277.33 298.67 320.00 341.33 16 281.47 307.06 332.65 358.24 383.83 409.42 17 334.13 364.50 394.88 425.25 455.63 486.00 18 458.33 500.00 541.67 583.33 625.00 666.67 20 530.58 578.81 627.05 675.28 723.52 77J..75 21 - 610.04 665.50 720.96 776.42 831.87 887.33 22 697.07 760.44 823.81 887.18 950.55 1013.92 23 792.00 864.00 936.00 1008.00 1080.00 1152.00 24 895.18 976.56 1057.94 1139.32 1220.70 1302.08 25 1006.96 1098.50 1190.04 1281.58 1373.13 1464.67 26 1127.67 1230.19 1332.70 1435.22 1537.73 1640.25 27 1257.67 1372.00 1486.33 1600.67 1715.00 1829.33 28 1397.29 1524-31 1651.34 1778.36 1905.39 2032.42 29 1546.88 1687.50 1828.13 1968.75 2109.38 2250.00 30 1877.33 2048.00 2218.67 2389.33 2560.00 2730.67 32 2251.79 2456.50 2661.21 2865.92 3070.63 3275.33 34 2673.00 2916.00 3159.00 3402.00 3645.00 3888.00 36 3143.71 3429.50 3715.29 4001.08 4286.88 4572.67 38 3666.67 4000.00 4333.33 4666.67 5000.00 5333.33 40 4880.33 5324.00 5767.67 6211.33 6655.00 7098.67 44 5576.54 6083.50 6590.46 7097.42 7604.38 8111.33 46 6336.00 6912.00 7488.00 8064.00 8640.00 9216.00 48 7161.46 7812.50 8463.54 9114.58 9765.63 10416.67 50 , 12375.00 13500.00 14625.00 15750.00 16875.00 18000.00 60 3 -HCO OOCO CT> CO r-l C^OOOO (MCDr*- COCO lOCO **-lOCD C>-OOQO ^-^-LO tHlO OOOO COr-ICO OIOO OCOO H rH COCO CMCOCO lOtOCD C3 CM CO OOOO COCO OOOOOO OOOOOO OOOOOO 4 00 OOO CT>CM OOC--iH OOIS-T-I OO -C~.^*- T-4H CMCM T-ICMC3 CMCOCM' iHr-HtH O 'I v t CTJ'd- C7)CO OOCMC7) ^1-OOf-l iHCDCD T-HCM t>~OO CDC~-C-- OO'i-lO IOIOCO 9 i * C-CM COC7> CDCDCM 1OOOO OOIOO C7>O IOIO OO-^-lO OiHCM CMCO-:!- 1 ? * cocs. 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CO CD OO CO OO CO CD O C~ CO CD CO CO CO ni Bojy ]T!)oj> o oa o oa oo o- LO oa ^*- LO t- CD 'd- rH 00 CD OO CD a- o o CO rH CD CD T-H oa o oa O3 LO C^- - O> rH JSJ oa oo oo c^~ OO CD CM LO d- CD 00 o co co t-- OO CD rH LO CO oo oa o 03 CD fo ssan 311 H^ ^x J .S 8 Jl 00 X to CO X 10 ^t CO X CO X CD M'juinij CD O rH (M CM CO CO CO CO -4- LO CO CO CO CD C-~ CO CO CO CO CD H CO "3- 3- TWO ANGLE CO o in in co c- co oo co CT> o o o ^*-^-^-^-^- ^"^'3-^-^t' in in in in CD co in in co co is- oocoTi-Lom ^-ioio'^-^*-<*-io cMoaodcocvi COCNJCNICOCV] oooocococnoo CO CO OO *ct- ^- ^i- OOOOOOOOOO IS-C--t~t--OO r-(i-tr--l-lTH OOOOCOOOO i-JOi-IC<3O C7>O-i-i coc-t lOtOCDtOCD -l-F-!r-1rH-H OOOOCDO^O} mT-Hcr>oooo oo o> o *-< co *" COCDCOCS-t~ lOCDCDCOCD CD CO UJ CO O- in LO CD CD CD THr-fr-lr-lT-lTH cocotocoto tninininco I-IHT-T-(T--I COOK^CO D--OOOOCDCD C^OOOCSJCOtD ^d-^J-^d-COCO in^t-st-OOOO O3rHT-HO CJ> OO oooooococo cococococo co co co co in in CMOCMOO, OO CNJOOCO-a-CXJ OCMOOCOOCO OiH-d-COCT) COCOCT>COCD inO>CM-ooir>co e-aooco eci oo a- in CD B ONE TOP PLATE. a ea g 1 .22 <=a ^ X S^ co*-oo cai>-'-n cococoo- ocococ^- CMoaca tNoaoa oooooooo tdioioio cococo cooooo cocooooo cocooocn .2 ea 0^*00 oocooo T-* oo c-- oo o)^*c oo CD CD CO OOOiO) COOOOOOJ -ICMO<- r-H^HOr-l CO CM LO r-ICDO t-IOOOO OOO-IOO3 J| x x x x H o. ^- o> oo r-t T-t H T-l -3 EE. as e bg -*! si JHCQ OO O rH CD CD OO CD lOCOC-O) ^Hcaoa r-tcaca lotoioio cocococo 3*- t-tOOO COOOCQ COIOOIO COOOLOO c-.e-.oo porn o)o>oo cooo-^-io II fr~t-O COIOO ^*-^-OO) COio tocoo oaoooo OT^I-IO^ 1-1 T-l -( T-l T-l TH ii X X X X ** TH t-t co oa M jk M 22 *0 J - g t-tc^co o>iOTH caiocoo coca COCOf rH CM CO T-lT-ICMOO 0)0)OTH CM CX! CM CM CM CM *< ^*- * CM CM OO OD fn CM CM CM CM CM CM coc>^t-a- caoacQoa TWO ANGLES. A 1 OOCOOO t-(MCD 0)CSIO>10 0)THC.CJt"VJt>i 1 cocoo coc-o me-o3c- OT-ICDO - ^ T-ITHT-I T-IT-IT-I cocococo oaoscMoa g 7 my Z J oooooo r-icMoa OOTHTH mioioio Pjj T-IOO co^i-m cooiino) cotooco if t^^ X^^ -^^^ -^^^ lId J M !S co co oo e- .iJ D c eg co eo XXX X en co co t- rHCMCO 5*-lOCO t- OO CD O i-tCMCO'S- 18 ^ 15- lOCOC^OT ^J-lOt~ OOCOCOCo. COCOOOT-I NLDO-O ,-ITHT-IT-I 10 in in LO oooocoo oooooocn t-trHrnoa 1 13- oo o in TH ^- CD in ^o tocncoco Oicomin e^-inosoo Oi-irHca oorHoa cr>HCNJca co cococo oacococo us: 1 s inoaoca cocs-or>- cocooca o-oooo- ^^in^* ocainc^- cr>mcj>co t*tnoaoo THCOt~-T-i ocacoo T-tcocs.T-1 oooooats- t- *t- CD r * 2 1 = x* m n x^" "" x^ x x O OO C7> O^ O CM ^ ,-H ^H 03 f 5=1. ^j-incDoo c^coinc^ 0000*4- OOCDTHCO co oo o oa u S si- COCNJCSICO 000000*1- oaoaoaoo cj-*d-int-- a oaoacaoa cooococo cocococo _J CL ll coc>-oc-- inoaooa oococ- CNJOOOD^ t^ots-co eno^t- ooo'coco o5Oi-c^ rHinoioa cacoo^-. Q. O 5-: H x^ x w x x x ^" CQ CO CO ^t" Id ^ IS COIOCVI,H COCOCOTH ^oco-^ cocaoo CDIS-^CO SB ~ in inmio csioacsjcsj cocococo co cococo ^^a-^ o 5 I oo ^^^m ca oacNioa co cococo cooococo ^^^^ . a (0 ~ => S3 ~^ 3 \N *o *^^ S^S^S3Sg^So;:^S u J** _i o ea ig^s^; s^^5 22SZ szzz ssss z < ' A 51 > N^- J t*-**-inco cMcvjoaco THTHIHCNJ OOOOTO OOOTCDO <4 : '*i : ! : ca cva'cvjoa cocococo oaoioaco co coco** o : P cDoooocj) Ot-iincn *-mooo *-ts.cQC^ ooooe-*- ^ T*-^i-^-'tf- cacaoaoa caoaoooo caoaoaoa cocococo 81 fgiiyj-j TH T-H H T-I oacMc>a<>a cvjoaoaoa cocococo cocococo 1 III THOOin cDinoo caoo**- ^1-00 oa* o o m co IS8 OQ -2 s;x O- OO OO O> 4 If * W CO CO S- X X X X X *r in in o to 8=5 THTHTHTH THoacacM oaoaoaoa csicNJoaco cocococo ONE PLATE TWO ANGLES. 1 k One Plate, Size in Inches TWO ANGLES Total Area, Square Inches AXIS A B Eccen- tricity Axis C D r 2 Size in Inches Thick- ness I r 2 i 6XX 2^X2 X 3.62 10.6 2.93 1.44 0.86 2 ft 4.12 11.1 2.69 1.55 0.95 3 3 X2J X 4.12 11.2 2.72 1.49 1.26 4 3^X2^ ft 5.06 12.3 2.43 1.66 2.00 5 6X# 2^X2 1 A 4.37 14.1 3.23 1.19 0.78 6 A 4.87 14.9 3.06 1.31 0.86 7 3 X2y 2 X 4.87 14.9 3.06 1.26 1.13 8 3^X2^ A 5.81 16.2 2.79 1.45 1.84 9 7X X 2^X2 1 A 3.87 16.3 4.21 l.2 0.80 10 T\ 4.37 17.2 3.94 1.76 0.89 11 3vy o / /Z \/ 4.37 17.1 3.91 1.70 1.19 12 3i/ 2 X2i/ 2 A 5.31 18.6 3.50 1.92 1.90 13 7X# 2^X2 X 4.75 21.8 4.59 1.32 0.72 14 A 5.25 22.9 4.36 1.47 0.80 15 3 X2# 2 5.25 22.8 4.34 1.42 1.05 16 3>X2i^ 6.19 25.1 4.05 1.64 1.73 17 8XX 2^X2 A 4.62 25.0 5.41 1.95 0.84 18 3 X2j 4.62 24.9 5.39 1.89 1.13 19 3^X2^ A 5.56 27.0 4.86 2.15 1.82 20 4 X3 H 6.96 29.4 4.22 2.29 2.56 21 8X^ 2%X2 ft 5.62 33.5 5.96 1.60 0.75 22 3 X2 ^ X 5.62 33.0 5.87 1.56 0.98 23 A 6.56 36.3 5.53 1.82 1.63 24 4 2 X3 2 H 7.96 39.1 4.91 2.01 2.35 25 9X X 3 X2^ X 4.87 34.4 7.06 2.07 1.07 26 3 >X2^ A 5.81 37.7 6.49 2.36 1.74 27 4 X3 3^ 7.21 40.4 5.60 2.56 2.47 28 TV 7.99 41.6 5.21 2.66 2.60 ONE PLATE. TWO ANGLES. (CONTINUED.) SO. One Plate, Size in Inches TWO ANGLES Total Area, Square Inches AXIS A B Eccen- tricity Axis CD r 2 Size in Inches Thick- ness I r 2 29 9X^ 3 X2% 1 A 6.00 46.0 7.67 1.68 0.92 30 3^X2^ T\ 6.94 50.5 7.28 1.98 1.54 31 4 X3 y% 8.34 54.5 6.53 2.21 2.24 32 7 9.12 56.2 6.16 2.33 2.39 33 lOXi^ 3 X2y 2 X 5.12 46.4 9.06 2.22 1.02 34 3^X2^ (L 6.06 50.7 8.37 2.56 1.67 35 4 X3 y% 7.46 54.1 7.25 2.81 2.38 36 A 8.24 57.6 6.99 2.93 2.52 37 lOX^ 3 X2y 2 l/ i 6.37 61.7 9.69 1.79 0.88 38 3 1^X2 y z 7.31 68.0 9.30 2.12 1.46 39 4 X3 y% 8.71 73.3 8.42 2.40 2.15 40 A 9.49 75.7 7.98 2.54 2.30 41 12X^ 3%X2% 5^ 6 56 84.6 12.90 2.91 1.54 42 4 X3 y% 7.96 90.9 11.42 3.25 2.24 43 5 X3 y% 8.72 95.2 10.92 3.48 3.89 44 5 X3^ y* 9.10 95.2 10.46 3.45 3.75 45 12X^ 3^X2^ fV 8.06 112.9 14.01 2.37 1.33 46 4 X3 2 ^ 9.46 122.0 12.90 2.74 1.98 47 5 X3 H 10.22 128.6 12.58 2.97 3.44 48 5 X3% 14 10.60 128.7 12.14 2.96 3.34 49 14X T 5 .I 3^X2^ A 7.94 152.9 19.26 2.85 1.31 50 4 X3 ^ 9.34 165.5 17.72 3.30 1.95 51 5 X3 y% 10.10 173.9 17.22 3.57 3.43 52 5 X3^ y* 10.48 173.9 16.59 3.57 3.31 53 14X^ 3^X2^ A 8.81 173.4 19.68 2.57 1.21 54 4 X3 ^8 10.21 188.4 18.45 3.02 1.83 55 5 X3 Ks 10.97 198.5 18.10 3.28 3.21 56 5 X3% Ks 11.35 198.5 17.49 3.30 3.12 ONE PLATE. T TWO ANGLES. No. One Plate, Size in Inches TWO ANGLES Total Area, Square Inches AXIS A B Eccen- tricity Axis CD r 2 Size in Inches Thick- ness I r 2 57 15x T 5 s 3X3 A 8.25 179.9 21.81 2.86 0.82 58 4X3 A 9.65 200.9 20.82 3.45 1.89 59 5X3 y% 10.41 210.8 20.25 3.74 3.32 60 5X3^ H 10.79 211.4 19.59 3.75 3.22 61 15X^ 3X3 A 9.19 204.3 22.23 2.57 0.77 62 4X3 3 A 10.59 228.2 21.55 3.15 1.77 63 5X3 y& 11.35 240.5 21.19 3.43 3.10 64 5X3^ 3 A 11.73 241.1 20.55 3.45 3.02 65 16x fV 4X3 3 A 9.96 240.0 24.10 3.60 1.83 66 5X3 y% 10.72 253.4 23.64 3.89 3.23 67 5X3^ 12.06 262.1 21.74 4.17 3.36 68 6X4 2 13.36 272.4 20.39 4.41 5.13 69 IQX3/ S 4X3 3 A 10.96 273.2 24.93 3.27 1.71 70 5X3 H 11.72 288.4 24.61 3.56 3.00 71 5X3^ 13.06 299.6 22.94 3.85 3.16 72 6X4 T 7 6 14.36 312.1 21.74 4.10 4.85 73 16X# 4X3 3 A 12.96 334.4 25.80 2.76 1.52 74 5X3 3 A 13.72 352.8 25.72 3.04 2.67 75 5X3^ y* 16.00 379.3 23.71 3.55 3.08 76 6X4 n 17.50 396.0 22.63 3.81 4.72 77 16X^ 4X3 JLJ 16.50 421.2 25.53 2.82 1.69 78 5X3 y* 17.50 443.4 25.34 3.11 2.86 79 5X3^ X 19.84 469.0 23.64 3.50 3.24 80 6X4 21.72 490.7 22.59 3.76 4.91 81 18X 5 4X3 N 10.59 333.9 31.53 3.85 1.73 82 5X3 H 11.35 351.7 30.99 4.18 3.05 83 5X3 % 12.69 365.3 28.79 4.52 3.19 84 6X4 1 13.99 381.2 27.25 4.80 4.90 ONE PLATE. TWO ANGLES. (CONTINUED.) No. One Plate, Size in Inches TWO ANGLES Total Area, Square Inches AXIS A B Eccen- tricity Axis CD r 2 Size in Inches Thick- ness I r 2 85 18X^ 4 X3 # 11.77 379.4 32.40 3.48 1.60 86 5 X3 H 12.47 399.4 32.03 3.81 2.83 87 5 X3% A 13.81 417.2 30.21 4.15 2.99 88 6 X4 15.11 434.7 28.77 4.45 3.48 89 18X^ 4 X3 % 15.50 499.2 32.21 3.43 1.71 90 5 X3 y* 16.50 526.7 31.92 3.75 2.98 91 5 X3^ % 17.00 527.9 31.05 3.81 2.91 92 6 X4 X 18.50 552.5 29.87 4.11 4.47 93 18X# 4 X3 H 19.21 617.5 32.15 3.37 1.82 94 5 X3 fa 20.47 651.2 '31.81 3.69 3.14 95 5 X3% ft 21.09 652.8 30.95 3.76 3.04 96 6 X4 22.97 682.7 29.72 4.07 4.65 97 2Qxy & 3y 2 X3y 2 H 12.46 496.9 39.88 3.58 1.04 98 5 X3} y* 13-60 537.4 39.51 4.10 2.60 99 6 X4 14.72 562.2 38.19 4.44 4.06 100 20Xi^ 3y 2 X3y 2 J /2 16.50 655.6 39.73 3.52 1.13 101 o X 3 ^2 y> 18.00 708.6 39.37 4.04 2.74 102 6 X4 y* 19.50 741.4 38.02 4.39 4.24 103 8 X6 23.52 795.9 33.84 4.90 8.04 104 20Xj^ 3y 2 X3i/ 2 y& 20.46 810.8 39.63 3.46 1.22 105 5 X3y 2 * 22.34 876.5 39.23 3.99 2.87 106 6 X4 24.22 918.4 37.92 4.34 4.41 107 8 X6 H 29.38 984.4 33.51 4.87 8.37 108 20X^ 3y 2 X3y 2 X 24.38 961.1 39.42 3.41 1.34 109 5 X3 V 2 X 26.62 1041.0 39.11 3.93 3.05 110 6 X4 28.88 1090.0 37.75 4.29 4.63 111 8 X6 X 34.88 1168.0 33.49 4.79 8.71 c ssssss mamcm TWO PLATES Ar--J|l --B TWO ANG LES 1 D Web Plate Top Plate TWO ANGLES Total AXIS ] LB Axis No. Size in Inches Size in Inches Size in Inches Area Square i l t I r 2 Eccen- tricity CD r 2 Inches 1 6X# ?x* 3X2#XX 5.87 14.8 2.52 1.98 2.J9 2 H y& 7.97 16.5 2.06 2.16 2.34 3 l /2 10.00 18.3 1.83 2.26 2.48 4 6X^g 8X^ 3X2%X% 7.87 22.1 2.81 2.00 2.80 5 y* H 10.09 24.2 2.44 2.16 2.95 6 * 12.25 26.5 2.17 2.27 3.10 7 7X^ 7X% 3X3 X T ff 7.06 22.9 3.24 2.23 1.95 8 H y?> 8.60 25.3 2.94 2.41 2.17 9 y* 10.75 27.8 2.59 2.54 2.32 10 7Xf BXJf 3X3 X T \ 9.19 33.9 3.69 2.22 2.51 11 / n 10.85 36.8 3.39 2.40 2.75 12 K % 13.13 40.2 3.06 2.53 2.90 13 8X14: 8Xi^ 3X3 X^ 7.56 32.8 4.34 2.57 2.28 14 H ^i 9.22 35.0 3.90 2.79 2.59 15 y*> 11.50 39.3 3.42 2.95 2.78 16 8X3^ 9X^ 3X3 X T \ 9.94 48.7 4.90 2.55 3.00 17 l /2 f^ 11.72 53.1 4.53 2.75 3.32 18 M 14.13 57.3 4.06 2.91 3.49 19 9X T 5 ? 9X^ 4X3 X^ 11.15 60 5.38 3.08 3.68 20 % % 13.81 65.3 4.73 3.27 3.98 21 H ft 16.40 69.3 4.23 3.41 4.19 22 9X^ lOXSXi 4X3 X^ 12 09 70.5 5.83 2.98 .13 23 I/ i 14.88 75.7 5.09 3.20 .49 24 H H 17.59 80.8 4.59 3.35 .75 25 10X T 5 5 lOX^j 4X3 X^g 11.84 81.6 6.89 3.41 .18 26 \/ r/ 14.63 86.9 5.94 3.65 .53 27 H ^ 17.34 92.1 5.31 3.81 .78 28 iox^ 12X^g 4X3 X^ 13.21 96.4 7.30 3.35 5.50 29 y* ^ 16.25 102.8 6.33 3.61 5.98 30 H 19.21 109.9 5.72 3.78 6.32 31 10X^ 12XJ 4X3 X^g 15.96 127.6 8.00 3.28 5.74 33 H % 19.00 135.8 7.15 3.52 6.13 33 3 2 % 21.96 143.4 6.53 3.70 6.42 24 TWO PLATES. TWO ANGLES. (CONTINUED.) No. Web Plate Size in Inches Top Plate Size in Inches TWO ANGLES Total Area Square Inches AXIS A B Eccen- tricity .17 Axis CD r 2 Size in Inches I r 2 34 12X-5 i2x y % 5X3 x^ 13.97 139.2 9.97 6.31 35 36 N X X ft 17.25 20.47 148.3 156.8 8.59 7.66 .46 .65 6.86 7.24 37 12X^ i4x y % 5X3^X^ 15.85 165.3 10.43 .03 7.64 38 39 40 I % ft 19.50 23.09 26.62 177.3 187.4 195.5 9.09 8.12 7.34 .33 .54 .70 8.29 8.76 9.13 41 12X> 14X1 5X3i^X^g 26.10 257.9 9.88 4.69 10.17 42 43 2 2 X ft 35.00 43.84 298.3 339.1 8.52 7.74 5.21 5.60 11.21 11.84 44 14XJ/6 i4x y % 6X3^X^ 17.34 255.9 14.76 4.63 8.39 45 46 47 n ft y* ft 21.25 25.10 28.87 273.7 287.7 299 12.88 11.46 10.36 5.00 5.25 5.44 9-13 9.68 10,11 48 14X^ 14X1 6x3^x^6 27.84 391.5 14.06 5.30 10.43 49 lj y t 37.00 442.7 11.96 5.90 11.49 50 2 ft 46.10 494.5 10.73 6.33 12.16 51 16X^ i4x y z 6X4 Xy 18.47 371.3 20.11 5.09 7.88 52 y* y* 22.50 395.9 17.60 5.53 8.64 53 54 9 y* 26.47 30.38 417.1 428.8 15.76 14.12 5.83 6.07 9.18 9.62 55 16Xi^ i 6X4 xy^ 29.22 563.2 19.28 5.82 9.94 56 1 K y* 38.50 634.1 16.50 6.50 11.05 57 2 ft 47.72 700.9 14.69 6.99 11.75 58 18X^ i4x y % 6X4 X^ 19.22 514.7 26.78 5.54 7.57 59 % K 23.25 550.9 23.70 6.06 8.36 60 61 ft X # M 27.22 31.13 575.3 601.4 21.15 19.30 6.43 6.69 8.92 9.38 62 18XJ 14X1 6X4 X^j 30.22 775.7 25.67 6.33 9.61 63 64 2 2 % 39.50 48.72 868.6 952.9 21.99 19.56 7.11 7.66 10.77 11.51 65 18X^6 14X1 6X4 X^ 32.47 920.8 28.36 5.89 9.01 66 67 2 y* ft 41.75 50.97 985.2 1134.1 23.60 22.25 6.73 7.33 10.26 11.07 c n : ir THREE PLATES. A-- 1 - --- j-~ M--B TWO ANGLES. 1 i 1 No. Two Web Plates, Size in Inches Top Plate, Size in Inches TWO ANGLES Total Area, Square Inches AXIS A. B. Eccen- tricity Axis C.D. r 2 Dis- tance Betw'n Webs Size in Inches Thick- ness I r 2 1 9XX 12XX 2^X2^ T\ 10.44 78.3 7.50 2.39 12.3 6.0" 2 12x tV 11.19 82.3 7.36 2.55 12.3 3 9XyV 12.32 96.5 7.84 2.31 12.3 4 12X/8 H 13.59 102.0 7.51 2.51 12.5 5 9X3/ 14.71 116.1 7.89 2.31 12.5 6 12X T5 A 16.00 121.8 7.61 2.48 12.7 7 9x iV 17.13 135.9 7.94 2.32 12.7 8 12x^2 i^ 18.38 141.7 7.71 2.45 12.9 9 9X K 19.50 155.7 7.98 2.31 13.0 10 10XX 12XV 2 ^X2^ tV 10.94 104.4 9.54 2.55 12.2 11 12X- 5 - 11.69 109.6 9.38 2.73 12.2 12 lOX^, 12.94 128.4 9.92 2.46 12.2 13 12X>/ 8 Z A 14.21 135.7 9.55 2.68 12.4 14 loxs/g' 15.46 154.3 9.98 2.46 12.4 15 12X-7-T- JL 16.75 162.0 9.68 2.64 12.6 16 10 X T ^ 18.00 180.5 10.0 2.46 12.6 17 12X^ 1^ 19.25 188.2 9.78 2.62 12.8 18 10X^ 20.50 206.6 10.1 2.46 12.9 19 10 X^ 14X* 3 X3 tV 12.06 109.0 9.04 2.71 16.7 7.0" 20 12.94 114.4 8.84 2.88 16.7 21 10X T\ 14.19 134.3 9.47 2.63 16.6 22 14X3^ N 15.72 141.8 9.02 2.84 16.9 23 ioxa^ 16.97 161.6 9.52 2.63 16.9 24 14X - 7 - J7 T 1 18.49 169.3 9.16 2.81 17.2 25 10X T 7 6 19.74 189.0 9.57 2.63 17.2 26 14X^ I/ 21.25 197.0 9.27 2.78 17.4 27 10X1^ 22.50 216.5 9.62 2.63 17.5 28 14X|^ H 25.47 232.3 9.12 2.89 17.9 29 12XX 15XX 3 X3 T 5 G 13.31 181.7 13.7 3.10 20.3 8.0" 30 14.25 190.7 13.4 3.31 20.1 31 12X T\ 15.75 223.4 14.2 2.99 20.1 32 15X^ 3 /8 17.35 236.0 13.6 3.25 20.3 THREE PLATES. TWO ANGLES. (CONTINUED.) No. ho \Veb Plates, Size in Inches Top Plate, Size in Inches TWO ANGLES Total Area, Square Inches AXIS A. B. Eccen- tricity Axis C. D. r 2 Dis- tance Betw'n Webs Size in Inches Thick- ness I r 2 33 12X3/8 15X3/6 3 X3 y% 18.85 268.6 14.3 2.99 20.4 8.0" 34 L5Xy' 7 -r rV 20.42 281.4 13.8 3.21 20.6 35 12X T% TV 21.92 313.8 14.3 2.99 20.7 36 15X1^ X 23.50 327.1 13.9 3.18 20.9 37 12X^ 25.00 359.4 14.4 2.99 21.0 38 15X|^ y* 28.10 385.2 13.7 3.31 21.4 39 14X i\ 16X T 5 r 3 X3 P 17.31 344.1 19.9 3.33 23.9 9.0" 40 16X3/8 18.97 363.7 19.2 3.63 24.2 41 14x^/8 20.72 413.4 20.0 3.33 24.3 42 16X-X TV 22.36 433.5 19.4 3.58 24.5 43 14X-C 24.11 482.9 20.0 3.32 24.6 44 16X^ y 2 25.75 503.5 19.6 3.55 24.8 45 14X^ 27.50 552.7 20.1 3.32 24.9 46 16XJ^ y% 30.72 592.6 19.3 3.70 25.2 47 14X^6 34.22 692.7 20.2 3.32 23.8 8.5'' 48 15X^ 18X T\ 3 X3 T\ 18.57 425.6 22.9 3.59 31.0 10.5" 49 18Xf| y& 20.35 449.9 22.1 3.92 31.2 50 15X3/8 22.22 511.4 23.0 3.59 31.4 51 l8X lV TV 23.99 536.2 22.4 3.87 31.6 52 15X- 7 ^ 25.87 597.3 23.1 3.59 31.7 53 18X^ /^ 27.63 622.8 22.5 3.83 31.9 54 15X^ 29.50 683.8 23.2 3.59 32.1 55 18X5^ $ 32.97 733.1 22.2 4.00 32.4 56 15X|^ 36.72 857.2 23.3 3 59 32.8 57 16X TG 20X T\ 3 /^ x3 K r, TS 20.43 524.0 25.6 3.93 37.7 11.5" 58 20X3/ 8 y* 22.46 553.3 24.6 4.28 38.0 59 16X3^ 24.46 629.6 25.7 3.93 38.1 60 20Xy 7 ^ JL 26.49 659.4 24.9 4.22 38.4 61 16X T T 28.49 735.2 25.8 3.93 38.5 62 20X^ X 30.50 765.9 25.1 4.18 38.7 63 16X^ 32.50 841.5 25.9 3.92 38.9 64 20X^3 M 36.46 901.2 24.7 4.36 39.3 65 16X^ 40.46 1055. 26.1 3.93 39.7 66 18X3/6 24X3/8 4 X4 H 28.22 909.1 32.1 4.52 55.0 14.0" 67 24X F6 A 30.62 951.7 31.1 4.86 55.3 68 18X^ 32.87 1062. 32.3 4.52 55.5 69 24X^ K 35.25 1106. 31.4 4.81 55.8 70 18X i/^ 37.50 1215. 32.4 4.53 56.0 71 24X| ^ 42.22 1300. 30.8 5.01 56.4 72^18X5^ 46.72 1523. 32.6 4.53 56.9 73 ' 24 XV ^ 51.38 1611. 31.4 4.92 57.3 0) u -J o rr D o OinCT) OO r-l CO d- C-- {\3 ^ OO5OO O O CT> i-IOOCT) ^OT * cn co ,H a- cn CD oq <* o 10 O> CT> CT> O CD CD OOOOOO O5OOOO CDCTJO5OO CT>CDCN1 COO3CD CO CO CO O50OOO COOt- OOOOOO OOOOOOOO r-t rH C3 CM C<] CMCs] CQCMCM 000000**- THtHrH THC3CNJ T-trH^l - OO OO - - - o ...... . . _ OO*-lOOOlOCOd-lOD~'3-CDOO J ) -^-jrt'-H . SJ xxx S g CM CM CM CM X X X X X CM CM CM OO OO TH rHi-OOT-l IOC31OO> C3CDC3CD COOCOIO CNJi-lOO CMCN3THO COCMCM^-I ^-^-COCVJ miDiOLo tomtoio loiomio IOIDIOIO C: J T-l OO OO C^ O* CT> OO OO C*~ O> CJ^ OO OO O O CT> G> CO CO CO CO CO COCOCO COCOCOCO ^a-^i-COCO -1 3C<1CM X x: | O t-l OOC-t-CD OOOOC~C^ COCOOOfc-. OOOOOO "^ 0> -COCOCO ^^COCO ^KJ-^CO lOlfJ^^ <= -i 00 O O O O> i-HOOO fHtHOO YH*-4iHO ft 2 1 4 - CD OO O> LO CO r t rH O LO CO O> O IO 1 OO | 3. 4 u j g _ X COT-IOD CQCO^-IO oaco-tj-io ooooooa oaoaoacQ cocococo ^^^i' ^~ comio^- o^*-ioi- cocoo-ac- OT-ICQCVJ oioorH mo>oH cofomco CMcaoaca caoacoco coco^i-^- CD co co to 2 s 5 * oaoto^- D--O>CJ>1 IOOOT-ICO c-cnca'^ co en oo m O>THIT>OO 5 ll OCXIT*-^- (OOOCQIO ^HIO^HCO WOOOOC- ^c-CT>T-i O^ t-cDiom^j- odo-cDccir) CDCDtDCOtD CDtOCDCDCO OO5OOC^ (NtHOOO OOCMr-lOO CdCMCNJOa C^CDCDIO OOOOOr-l cocoooca ^t- LO CO CO OO OO CO OO CDCCCDCO CX1CO^-CO COOOOOCO rHO-r- to CD CD to co a)O5o>ai cvjcaoaco ooomcx) oooooao CNI 03 CM lOIOlOIOlO COOOOOOOO O5OOIOO CMCOCDCOCD COCOCXICDO OOr-irOC-. OCOCDCDCO IOQOCNILO C~-OOO>O 30 FOUR ANGLES-CONTINUED. f=J W 23 j o I .3 1 s "1 .2 IN 5 1 CM ooaiooisi cooirHOO OOOOD-D^O- OOOOOOCOOO cxi CM O CT> 00 0- C7> C7) OO OO OO OO TH to co CD oo oo oomooooo o CM H o- oo en CM oo ca T-I o o c*. c^ c t>- t~ COCOCOt-tO CDLOTt-^*-CO CO TH ocooco'S- oamo^T-ico OOOOOOIXCO i-IOCDCDCX) ^i-i-<5i-^-'- co in * tO IT) tO IO LO ^J- COmiOil-*- OO>-- * C>- O IO CO OO CM CM TH oa 1-H ^1-THC^CMCD O*1-OIOO O 00 CM CO T-) eaoaoacMoa cooacocgoa CO CO CO CO OO CD-^rHC^-OJ 00*-OJCO CD CO CD LO IO C~-C^C>-CDCO e4 4 -a _ .2 J 2 a r2 s=s J M t 73 - C- ^H O * O> 00 CO ^HCNJOO-^-LO coooocaco ^*-'*-'^-*i-'*- CDCDOOO T-l -( iH CO rH C- * CO i-l CM 00 10 CO ^ OO-IOOOI> OOCOOC^O CDOtHC<3c5 comcoooo CO'*-^*-^-^*- C75O>C7>C7>O O) tO O CO OO OO O) t-l CM CO c^ o. oo oo oo ^ C7JCMOOOCO CDIOOOCOO t~OOCT>OTH OCNJOOtOt- OO OO CO OO O CO CD OO CD TH t-1 cl c> c^ 06 ^ OCDi-HOOCO THCDCDCOO5 COCDC--OOCT> OOCDOCMCO co co co oo oo oo oo en cr> OO CO C*- CM OO co *i- LO >- oo ^ C0l003d-C0 OOOOOCOCD Tj-^-incoo- LOCOOOCDO cocococooo oooooocxjcn ^*- OO CM CD CO rH TH CO * LO ^ COOOLOCDt?~ COOCNJO-O CMCMOO^-IO CM'i-mcDOO OOOOCOCOCO OO OO OO OO OO rH IO OO TH iH m CD o CM co CO CO t- C^ C^ o OCMC~-CDLO C75CMCMCDCO OOOOOOCDO t-COC-OOCT5 cMoaoaoaco c~-t>~c*-o-t^ ^- OO CD rH CD CM CM CO LO LO CO CO CO CO CO soipiq 9inbs nt UMJ pwi O^l-OrhCD 4-O*--c7> o>-iir>oooo *-o>oocs.'-i i-Hi-lT-ICNl rHrHOJCOOO ^- o * co co CM ** C- O> O OO OO CO OO CM CM CM CO CO f -*S | Ji.1 C^OOOOt-OT OOCMOCOCM OOC3^COir)(J> -|TH>-| i-Hr-ICMCMCNJ CM CO CM D-- TH C^ CD ^ 00 CO rH TH CM CM CO a x 11 **: ^^^^^ X X *i- *i- X X *i- CO HS*3^ X CO X CO jsquinyj C-~OOCT>OT-I O30o-ioco ^-^*-*l-tOm IDLOLOLOLO C>~ CO CD O 1 LO IO LO CO CD 1 A J FOUR ANGLES, c ps " 3= D ONE PLATE. I B 1 One Web FOUR ANGLES Total AXIS A. B. AXIS C. D. No. Plate, Size in Inches Size in Inches Thick- ness Area, Square Inches I r 2 I r 2 1 6X# 2^X2 y* 5.74 31.6 5.51 6.2 1.07 2 y% 7.70 42.9 5.57 9.3 1.21 3 3 X 2 \^ y* 6.74 36.2 5.37 10.3 1.53 4 9.18 48.9 5.33 15.7 1.71 5 3*^X2% *A 7.26 40.5 5.58 16.0 2.21 6 y* 9.94 55.1 5.54 24.2 2.43 7 y* 12.50 68.1 5.45 32.3 2.59 8 6X^ 2y 2 X2 H 8.45 45.1 5.34 10.1 1.19 9 3 X t yJ 9.93 51.2 5.15 16.8 1.69 10 3%X2% H 10.69 57.4 5.37 25.6 2.40 11 y* 13.25 70.4 5.31 34.2 2.58 12 7X>^ 2)^X2 & 5.99 45.8 7.64 6.2 1.03 13 # 7.95 62.1 7.81 9.3 1.17 14 3 X2% 6.99 52.4 7.50 10.3 1.47 15 y% 9.43 71.1 7.53 15.7 1.67 16 3yX2% 1 A 7.51 58.4 7.77 16.0 2.13 17 3/8 10.19 79.6 7.81 24.2 2.37 18 12.75 98.8 7.75 32.8 2.54 19 3^X3 T\ 9.47 69.4 7.32 20.1 2.13 20 y% 10.95 80.2 7.32 24.2 2.21 21 y 13.75 98.8 7.18 32.8 2.38 22 4 X3 J>_, 10.11 76.5 7.57 29.6 2.93 23 y% 11.67 88.2 7.56 35.4 3.03 24 y z 14.75 109.5 7.42 47.8 3.24 25 5 X3 J>^ 11.35 90.5 7.97 56.3 4.96 26 $/ 13.19 105.0 7.96 67.6 5.12 27 % 16.75 130.9 7.81 90.6 5.41 28 7X^/3 2^X2 *A 8.83 65.7 7.44 10.1 1.15 29 3 X2% */* 10.31 74.6 7.24 16.8 1.63 30 3 y, x 2 y H 11.07 83.2 7.52 25.6 2.32 31 13.63 102.4 7.51 34.2 2.51 FOUR ANGLES. ONE PLATE. (CONTINUED.) Ik One Web Plate, Size in Inches FOUR ANGLES Total Area, Square Inches AXIS A. B. AXIS t. 1). Size in Inches Thick- ness I r 2 I r 2 32 7X^ 3^X3 H 11.83 83.7 7.08 25.7 2.17 33 14.63 102.4 7.00 34.7 2.37 34 H 17.31 119.6 6.91 43.5 2.51 35 4 X3 y% 12.55 91.8 7.32 37.3 2.97 36 y* 15.63 113.1 7.24 50.1 3.21 37 $ 18.55 132.4 7.14 62.8 3.39 38 5 X3 y* 14.07 108.6 7.72 70.2 4.99 39 17.63 134.5 7.63 94.2 5.34 40 s /i 21.07 157.4 7.47 118.4 5.62 41 7x /4 3UX2U i/ 14.50 106.0 7.31 36.1 2.49 42 3y 2 x3 2 l /2 15.50 106.9 6.90 36.7 2.37 43 /& 18.18 123.1 6.77 46.2 2.54 44 4 X3 l /2 16.50 116.7 7.07 52.8 3.20 45 19.42 135.9 7.00 65.9 3.40 46 5 X3 I/ 18.50 138.0 7.46 97.9 5.29 47 >6 21.94 161.0 7.34 123.0 5.61 48 8X.X 2i4X2 % 6.24 62.9 10.1 6.2 0.99 49 a/ 8.20 85.3 10.4 9.3 1.12 50 3 X2^ \ 7.24 72.1 9.96 10.3 1.42 51 y% 9.68 97.9 10.1 15.7 1.62 52 3 lX2 l 7.76 80.0 10.3 16.0 2.06 53 y 10.44 109.2 10.5 24.2 2.32 54 y 13-00 135.9 10.5 32.3 2.49 55 56 3^X3 ii 9.72 11.20 95.6 110.5 9.83 9.87 20.1 24.2 2.07 2.16 57 ^2 14.00 136.8 9.77 32.8 2.34 58 4 X3 A 10.36 105.1 10.1 29.6 2.86 59 H 11.92 121.2 10.2 35.4 2.97 60 # 15.00 151.0 10.1 47.8 3.18 61 5 X3 11.60 123.5 10.6 56.3 4.86 62 y% 13.44 143.4 10.7 67.6 5.03 63 i/ 17.00 179.4 10.6 90.6 5.33 64 5 XZft Z A 14.20 143.7 10.1 67.9 4.78 65 i/ 18.00 179.6 9.98 91.0 5.06 66 /'Z H 15.68 164.9 10.5 115.6 7.37 67 >/2 20.00 208.6 10.4 153.9 7.69 68 sx^/g" 2^X2 y& 9.20 90.6 9.85 10.1 1.10 69 3 X2% y 10.68 103.3 9.67 16.8 1.57 70 3}4X2}4 H 11.44 114.6 10.0 25.6 2.24 71 14.00 141.2 10 1 34.2 2.45 33 L A J FOUR ANGLES, c pS" 1 -* ' SB D ONE PLATE. 1 B I One Web FOUR ANGLES Total AXIS A. B. AXIS 0. D. Plate, Area, No. Size in Inches Size in Inches Thick- ness Square Inches I r 2 I r 2 72 8X/8 3^X3 3/8 12.20 115.9 9.50 25.7 2.11 73 15.00 142.1 9:47 34'. 7 2.31 74 ft 17.68 166.4 9.41 43.5 2.46 75 4 X3 H 12.92 126.6 9.79 37.3 2.89 76 16.00 156.3 9.77 50.1 3.13 77 $ 18.92 183.5 9.70 62.8 3.32 78 5 X3 y~ 14.44 148.7 10.3 70.2 4.86 79 y*. 18.00 184.7 10.3 94.2 5.24 80 ft 21.44 217.1 10.1 118.4 5.52 81 X 3 5*2 H 15.20 149.0 9.80 70.6 4.64 82 19.00 185.0 9.74 94.7 4.99 83 22.68 218.3 9.63 118.2 5.21 84 6 X3% 16.68 170.3 10.2 119.3 7.15 85 y* 21.00 213.9 10.2 158.9 7.57 86 ft 25.20 252.4 10.0 198.5 7.88 87 29.24 286.5 9.80 240.6 8.23 88 8X*4 3>X2^ y* 15.00 146.6 9.77 36.1 2.41 89 3y 2 x3 2 y*. 16.00 147.4 9.21 36.7 2.29 90 18 68 171.7 9.19 46.2 2.47 91 4 X3 \/ 2 17.00 161.7 9.51 52.8 3.10 92 ft 19.92 188.8 9.48 65.9 3.31 93 5 X3 19.00 190.1 10.00 97.9 5.15 94 ft 22.44 222.4 9.91 123.0 5.48 95 5 X3^ 20.00 190.3 9.52 98.4 4.92 96 ft 23.68 223.7 9.44 123.0 5 19 97 X 3 5"2 22.00 219.2 9.97 164.2 7.46 98 y& 26.20 257.8 9.81 204.9 7.82 99 % 30.24 291.9 9.65 248.3 8.21 100 9X # 3 X2% % 7.49 95.5 12.7 10.3 1.38 101 y& 9.93 129.6 13.1 15.7 1 58 102 3*< 2 X2y 2 1 A- 8.01 105.5 13.2 16.0 2.00 103 H 10.69 144 13.5 24.2 2.25 104 y 2 13.25 179.5 13.6 32.3 2.44 34 FOUR ANGLES. ONE PLATE. (CONTINUED.) No. One Web Plate, Size in Inches FOUR ANGLES Total Area, Square Inches AXIS A. B. AXIS C. D. Size in Inches Thick- ness I r 2 I r 2 105 9X^ 3^X3 T 5 * 9.97 226.7 22.7 20.1 2.02 106 YO 11.45 146.5 12.8 24 2 2.12 107 I/ 14.25 181.7 12.8 32.8 2.30 108 4 X3 5 10.61 138.8 13.1 29.6 2.79 109 3 A 12.17 160.2 13.2 35.4 2.91 110 ^2 15.25 200.0 13.1 47.8 3.13 111 5 X3 A 11.85 162.2 13.7 56.3 4.75 112 i2 13.69 188.5 13.8 67.6 4.94 113 X 17.25 236.4 13-7 90.6 5.25 114 5 X3J 14.45 189.6 13.1 67.9 4.70 115 J^2 18.25 237.6 13.0 91.0 4.99 116 6 X 3 5*2 N 15.93 216.8 13.6 115.6 7.26 117 20.25 274.7 13.6 153.8 7.60 118 6 X4 A 16.69 217.8 13.1 115.4 6.91 119 X 21.25 274.3 12.9 154.5 7.27 120 9X2/6 3 X2|^ y* 11.06 137.2 12.4 16.8 1.52 121 3^X2/4 11.82 151.6 12.8 25.6 2.17 122 ' i/ 14.38 187.1 13.0 34.2 2.38 123 3^X3 y& 12.58 154.1 12.3 25.7 2.05 124 i/ 15.38 189.3 12.3 34.7 2.26 125 & 18.06 222 12.3 43.5 2.41 126 4 X3 H 13.30 167.8 12.6 37.3 2.81 127 16.38 207.6 12.7 50.1 3.06 128 X 19.30 244.1 12.7 62.8 3.26 129 5 X3 14.82 196.1 13.2 70.3 4.74 130 K 18.38 244.0 13.3 94.2 5.13 131 % 21.82 287.5 13.2 118.4 5.42 132 5 X3 *- y% 15.58 197.2 12.7 70.6 4.53 133 y> 19.38 245.2 12.7 94.7 4.89 134 *A 23.06 290.1 12.6 118.2 5.13 135 3/ 26.62 329.7 12.4 143.1 5.38 136 5*2 y 17.06 224.4 13.2 119.3 6.99 137 \/ 21.38 282.3 13.2 158.9 7.43 138 X 25.58 333.9 13.1 198.5 7.76 139 * 29.62 380.4 12.8 240.6 8.12 140 6 X4 17.78 225.4 12.7 119.3 6.71 141 l /2 22.38 281.9 12.6 159.7 7.14 142 26.82 335.1 12.5 199.6 7.44 143 */ 31.14 382.3 12.3 240.8 7.73 144 9X^ 3i^X2^ X 15.50 194.7 12.6 36.2 2.33 145 3^X3 16.50 196.9 11.9 36.7 2.22 146 ti 19.18' 229.6 12.0 46.2 2.41 35 L A J FOUR ANGLES. C ~? i J=^ D ONE PLATE. I B i No. One Web Plate, Size in Inches FOUR, ANGLES Total Area, Square Inches AXIS A. B. AXIS C. D. Size in Inches Thick- ness I r 2 I r 2 147 9X^ 4 X3 y z 17.50 215.2 12.3 52.8 3.02 148 ft 20.42 251.7 12.3 65.9 3.23 149 5 X3 Yz 19.50 251.6 12.9 97.9 5.02 150 ft 22.94 295.1 12.9 123.0 5.36 151 5 X 3 5*2 I/ 20.50 252.8 12.3 98.5 4.80 152 ft 24.18 297.7 12.3 123.0 5.09 153 y* 27.74 337.3 12.2 148.7 5.36 154 5 1 * 22.50 289.9 12.9 164.2 7.30 155 ft 26.70 341.5 12.8 206.2 7.72 156 X 30.74 388.0 12.6 248.3 8.08 157 6 X4 Yz 23.50 289.5 12.3 165.1 7.02 158 27.94 342.7 12.3 206.3 7.38 159 3 4 32.26 389.9 12.1 248.9 7.71 160 10x14: 3*/ 2 X2y 2 X 8.26 134.9 16.3 16.0 1.94 161 3 /8 10.94 184.2 16.8 24.2 2.21 162 Yz 13.50 229.7 17.0 32.3 2.39 163 3^X3 TV 10.22 162.7 15.9 20.1 1.97 164 H 11.70 188.2 16.1 24.2 2.07 165 Yz 14.50 233.9 16.1 32.8 2.26 166 4 X3 10.86 177.8 16.4 29.6 2.72 167 H 12.42 205.1 16.5 35.4 2.85 168 Yz 15.50 256.6 16.6 47.8 3.08 169 5 X3 _5 T 12.10 207.0 17.1 56.3 4.66 170 y^> 13.94 240.5 17.3 67.6 4.85 171 i/ 17.50 302.1 17.3 90.6 5.18 172 5 X3y 2 y% 14.70 242.7 16.5 67.9 4.62 173 \/ 2 18.50 304.7 16.5 91.0 4.92 174 6 X3J H 16.18 276.6 17.1 115.6 7.15 175 Yz 20.50 350.8 17.1 153.9 7.50 176 6 X4 16.94 278.4 16.4 115.4 6.81 177 Yz 21.50 351.4 16.4 154.5 7.19 178 IQXl/s 3^X2^ y* 12.19 194.6 16.0 25.6 2.10 179 Yz 14.75 240.1 16.3 34.2 2.32 FOUR ANGLES. ONE PLATE. (CONTINUED.) fb. One Web Plate, Size in Inches FOUR ANGLES Total Area, Square Inches AXIS A. B. AXIS C. D. Size in Inches Thick- ness I r 2 I r 2 180 lOX^g 3^X3 3/8 12.95 198.6 15.3 25.7 1.99 181 l /2 15.75 244.3 15.5 34.7 2.20 182 ft 18.43 286.7 15.6 43.5 2.36 183 4 X3 3/S 13.67 215.5 15.8 37.3 2.73 184 y* 16.75 267.0 15.9 50 1 2.99 185 ft 19.67 314.3 16.0 62.8 3.19 186 5 X3 3/8 15.19 250.9 16.5 70.3 4.62 187 i/ 18.75 312.5 16.7 94.2 5.03 188 ft 22.19 368.8 16.6 118.4 5.33 189 5 X3y 2 H 15.95 253.1 15.9 70.6 4.42 190 19.75 315.1 16.0 94.7 4.80 191 ft 23.43 373.3 15.9 118.2 5.05 192 6 X3^ f 8 17.43 287.0 16.5 119.3 6.85 193 21.75 361.3 16.6 158.9 7.31 194 ft 25.95 428.3 16.5 198.5 7.65 195 3 4 29.99 489.2 16.3 240.6 8.02 196 6 X4 18.19 288.8 15.9 119.3 6.56 197 y* 22.75 361.8 15.9 159.7 7.02 198 ft 27.19 430.8 15.8 199.6 7.34 199 u 31.51 492.7 15.6 240.8 7.64 200 10X^ 3^X2^ l /2 16.00 250.5 15.6 36.2 2.26 201 3^X3 y 2 17.00 254.7 15.0 36.7 2.16 202 ft 19.68 297.2 15.1 46.2 2.35 203 4 X3 y 18.00 277.4 15.4 52.8 2.93 204 ft 20.92 324.7 15.5 65.9 3.15 205 5 X3 y z 20.00 322.9 16.1 97.9 4.90 206 ft 23.44 379.2 16.2 123.0 5.25 207 5 X3*4 21.00 325.6 15.5 98.5 4.69 208 s2 24.68 383.7 15.6 123.0 4.98 209 6 X3% \/ 23.00 371.7 16.2 164.2 7.14 . 210 ft 27.20 438.6 16.1 206.1 7.58 211 H 31.24 499.6 16.0 248.3 7.95 212 6 X4 y^ 24.00 372.3 15.5 165.1 6.88 213 ft 28.44 441.2 15.5 206.3 7.25 214 32.76 503.1 15.4 248.9 7.60 215 12x14; 3}X2.^ % 8.76 206.4 23.6 16.0 1.83 216 11.44 281.1 24.6 24.2 2.11 217 y 2 14.00 350.4 25.0 32.3 2.31 218 3^X3 5 T T 10.72 250.3 23.4 20.2 1.88 219 3 /8 12.20 289.3 23.7 24.2 1.99 220 i 'V-z 15.00 359.8 24.0 32.8 2.19 37 1 A 1 FOUR ANGLES. C ==.-= D ONE PLATE. No. One Web Plate, Size in Indies FOUR ANGLES Total Area, Square Indies AXIS A. B. AXIS C, D. Size in Inches Thick- ness I r 2 I r 2 221 12X^ 4 X3 A 11.36 272.2 24.0 29.6 2.60 222 H 12.92 314.0 24.3 35.4 2.74 223 16.00 393:2 24.6 47.8 2.99 224 5 X3 T& 12.60 314.7 25.0 56.4 4.47 225 y& 14.44 365.5 25.3 67.6 4.68 226 y*. 18.00 459.7 25.5 90.6 5.03 227 5 ^3/^ y& 15.20 371.1 24.4 67.9 4.46 228 'A 19.00 466.8 24.6 91.0 4.79 229 6 X3J^ H 16.68 420.6 25.2 115.6 6.93 230 21.00 534.2 25.4 153.9 7.33 231 6 X4 Vt, 17.44 425.3 24.4 115.4 6.62 232 y* 22.00 538.0 24.5 154.6 7.03 233 12X^ 3^X2^ y% 12.94 299.1 23.1 25.7 1.98 234 l /2 15.50 368.4 23.8 34.2 2.21 235 3^X3 3/8 13.70 307.3 22.4 25.7 1.88 236 16.50 377.8 22.9 34.7 2.10 237 % 19.18 443.9 23.2 43.5 2.27 238 4 X3 y& 14.42 332,0 23.0 37.3 2.59 239 y* 17.50 411 2 23.5 50.2 2.87 240 $ 20.42 484.5 23.7 62.9 3.08 241 5 X3 H 15.94 383.5 24.1 70.3 4.41 242 19.50 477.7 24.5 94.3 4.83 243 fa 22.94 564.9 24.6 118.4 5.16 244 5 X3^ y* 16.70 389.1 23.3 70.6 4.23 245 20.50 484.8 23.6 94.7 4.62 246 fa 24.18 575.1 23.8 118.2 4.89 247 6 X3 1 y& 18.18 438.6 24.1 119.3 6.56 248 y* 22.50 552.2 24.5 158.9 7.06 249 fa 26.70 656.2 24.6 198.5 7.43 250 30.74 751.7 24.5 240.6 7.83 251 6 X4 y* 18.94 443.3 23.4 119.3 6.30 252 23.50 556.0 23.7 159.7 6.80 253 fa 27.94 663.1 23.7 '199.7 7.15 254 32.26 760.8 23.6 240.8 7.46 38 FOUR ANGLES. ONE PLATE. (CONTINUED.) No. One Web Plate, Size in Inches FOUR ANGLES Total Area, Square Inches AXIS A. B. AXIS C. D. Size in Inches Thick- ness I r 2 I r 2 255 12X^ 3^jX2^ y* 17.0 386.4 22.7 36.2 2.13 256 3^X3 % 18.0 395.8 22.0 36.7. 2.04 257 20.68 461.9 22.3 46.2 2.23 258 4 X3 \s 19.00 429.2 22.6 52.8 2.78 259 $ 21.92 502.5 22.9 66.0 3.01 260 5 X3 l /t 21.00 495.7 23.6 97.9 4.66 261 % 24.44 582.9 23.9 123.1 5.04 262 5 X3^ l /2 22.00 502.8 22.9 98.5 4.48 263 yk 25.68 593.1 23.1 123.0 4.79 264 6 X3j^ \/ 24.00 570.2 23.8 164.2 6-84 265 y* 28.20 674.2 23.9 206.1 7.31 266 *4 32.24 769.7 23.9 248.3 7.70 267 6 X4 % 25.00 574.0 23.0 165.1 6.60 268 % 29.44 681.1 23:i 206.3 7.01 269 & 33.76 778.8 23.1 248.9 7.37 270 14Xi^ 4 X3 TS" 11.86 389.3 32.8 29.6 2.49 271 If 13.42 448.7 33.4 35.4 2.64 272 16.50 561.8 34.0 47.8 2.90 273 5 X3 T 5 F 13.10 447.6 34.2 56.4 .30 274 3/ 14.94 519.4 34.8 67.6 .52 275 l /2 18.50 653.4 35.3 90 6 .90 276 5 X3^ y% 15.70 529.8 33.7 67.9 .32 277 19.50 666.8 34.2 91.0 .67 278 6 X3^ 3/8 17.18 598.0 34.8 115.6 6.73 279 21.50 759.4 35.3 153.9 7.16 280 6 X4 H 17.94 607.1 33.8 115.4 6.43 281 */2 22.50 768.6 34.2 154.6 6.87 282 14X^g 4 X3 f' 15.17 477.2 31.5 37.3 2.46 283 18.25 590.4 32.4 50.2 2.75 284 5^ 21.17 695.5 32.9 62.9 2.97 285 5 X3 y% 16.69 548.0 32.8 70.3 4.21 286 l /2 20.25 682 33.7 94.3 4.66 287 R/ 23.69 806.8 34.1 118.4 5.00 288 5 X3^ y% 17.45 558.4 32.0 70.6 4.04 289 % 21.25 695.3 32.7 94.7 4.46 290 24.93 825.4 33.1 118.2 4.74 291 6 X 3^ y% 18.93 626.6 33.1 119.4 6.30 292 y 23.25 788.0 33.9 158.9 6 84 293 e 27.45 937.6 34.2 198.5 7.23 294 \ 31.49 1075.9 34.2 240.6 7.64 295 6 X4 y% 19.69 635.6 32.3 119.4 6.06 296 y* 24.25 797.1 32.9 159.7 6.59 297 28.69 951.2 33.2 199.7 6.96 298 y* 33.01 1093.4 33.1 240,8 7.29 1 A J FOUR ANGLES c CS SJ D ONE PLATE - 1 B 1 No. One Web Plale, - Size in Inches FOUR ANGLES Total Are, Square Inches AXIS A. B. AXIS 0. I). Size in Inches Thick- ness I r 2 I r 2 2^9 14X^ 4 X3 Yz 20.00 618.9 31.0 52.9 2.64 300 y$> 22.92 724.1 31.6 66.0 2.88 301 5 X3 y> 22.00 710.6 32.3 98.0 4.45 302 y% 25.44 835.4 32.8 123.1 4.84 303 5 X3;^ K 23.00 723.9 31.5 98.5 4.28 304 y% 26.68 854.0 32.0 123.1 4.61 305 6 X3^ i /-> 25.00 816.5 32.7 164.3 6.57 306 H 29.20 966.2 33.1 206.1 7.06 307 33.24 1104.5 33.2 248.3 7.47 308 6 X4 H 26.00 825.7 31.8 165.1 6.35 309 ^8 30.44 979.8 32.2 206.3 6.78 310 3^ 34.76 1122.0 32.3 248.9 7.16 311 16X^" 5 X3 A 13.60 606.7 44.6 56.4 4.14 312 y& 15.44 703.1 45.5 67.6 4.38 313 i/. 19.00 884.1 46.5 90.6 4.77 314 5 X3^ y% 16.20 720.0 44.4 67.9 4.19 315 1 A 20.00 905.8 45.3 91.0 4.55 316 6 X3/4 ^8 17.68 809.8 45.8 115.6 6.54 317 l /t 22.00 1027.6 46.7 153.9 6.99 318 6 X4 y* 18.44 824.6 44.7 115.4 6.26 319 l /2 23.00 1043.9 45.4 154.6 6.72 320 16X^ 5 X3 H 17.44 745.8 42.8 70.3 4.03 321 y^ 21.00 926.7 44.1 94.3 4.49 322 y 24.44 1096.1 44.9 118.4 4.84 323 5 X3l y% 18.20 762.7 41.9 70.6 3.88 324 y z 22.00 948.5 43.1 94.8 4.31 325 y& 25.68 1125.5 43.8 118.3 4.61 326 6 X3^ y* 19.68 852.5 43.3 119.4 6.07 327 y* 24.00 1070.3 44.6 159.0 6.62 328 28.20 1273.7 45.2 198.5 7.04 329 */i 32.24 1463.0 45.4 240.6 7 46 330 6 X4 H 20.44 867.3 42.4 119.4 5.84 331 25.00 1086.6 43.5 159.7 6.39 332 ft 29.44 1296.8 44.1 199.7 6.78 333 H 33.76 1492.0 44.2 240.8 7.13 FOUR ANGLES. ONE PLATE. (CONTINUED.) One Web FOUR ANCLES Total AXIS A. B. AXIS C. D. No. Plate, Size in Inches Size in Incises Thick- ness Area, Square Inches I r 2 I r 2 334 IBXfl 5 X3 y* 23.00 969.4 42.1 98.0 4.28 335 H 26.44 1138.8 43.1 123.1 4.63 336 5 X3'/ 2 % 24.00 991.2 41.3 98.5 4.11 337 H 27.68 1168.1 42.2 123.1 4.45 338 6 X3^ l /2 26.00 1112.9 42.8 1,64.3 6.32 339 X 30.20 1316.3 43.6 206.1 6.83 340 X 34.24 1505.6 44.0 248.4 7.25 341 6 X4 y* 27.00 1129.3 41.8 165.2 6.12 342 H 31.44 1339.5 42.6 206.3 6.56 343 3 A 35.76 1534.7 42.9 248.9 6.96 344 18XX 6 X3^ ft 18.18 1057.0 58.1 115.6 6.36 345 % 22.50 1340.0 59.6 153.9 6.84 346 6 X4 ft 18.94 1079 57.0 115.4 6.09 347 X 23.50 1366.0 58.1 154.6 6.58 348 18X^ 6 X3^ y* 20.43 1118.0 54.7 119.4 5.84 349 X 24.75 1401. 56.6 159.0 6.42 350 H 28.95 1666. 57.6 198.5 6.86 351 X 32.99 1914. 58.0 240.7 7.29 352 6 X4 # 21.19 1140. 53.8 119.4 5.63 353 l /2 25.75 1426. 55.4 159.7 6 20 354 % 30.19 1701. 56.4 199.7 6.61 355 X 34.51 1958. 56.8 240.8 6.98 356 8 X6 % 33.79 1802. 53.3 368.9 10.9 357 % 40.51 2173. 53.7 468.7 11.6 358 K 46.51 2490. 53.4 563.1 12.1 359 ' 7 /$ 53.23 2838. 53.3 672.2 12.6 360 i 60.39 3192. 52.9 811.6 13.4 361 18X^ 6 X3> % 27.00 1462. 54.1 164.3 6.09 362 ft 31.20 1727. 55.4 206.2 6.61 363 ^ 35.24 1975. 56.1 248.4 7.05 364 6 X4 % 28.00 1487. 53.1 165.2 5.90 365 ft 32.44 1762. 54.3 206.4 6.36 366 % 36.76 2019. 54.9 249.0 6.77 367 8 X6 y* 36.04 1863. 51.7 377.8 10.5 368 % 42.76 2234. 52.3 479.9 11.2 369 X 48.76 2551. 52.3 576.7 11.8 370 7 /& 55.48 2899. 52.3 688.2 12.4 371 i 62.64 3253. 51.9 830.7 13.3 i r TWO PLATES. A | Ifi FOUR ANGLES. j| D!L Two Web FOUR ANGLES Total AXIS A. B. AXIS 0. D. No. Plates, Size in Inches Size in Inches Thick- ness Area, Square Inches I r 2 Out to Out of Webs I 1 8X X 2 X2 X 7.76 66.5 8.57 5.4 68.5 2 5_ 8.60 75.9 8.82 3 y 9.44 84.7 8.97 5.4 89.0 4 8x T 5 TiT 11.48 166. 14.5 15 jtf 12.68 187. 14.8 6.5 191. 16 lox rV 3 X2 \"i. r, i (> 12.73 177. 13.9 6.5 179. 17 13.93 198. 14.2 18 7 Ttf 15.13 219. 14.5 6.4 221. 19 10X^ 3 X2^ # 15.18 208. 13.7 6.5 213. 20 7 16.38 229. 14.0 21 I/ 17.50 248. 14.2 22 A 18.62 267. 14.3 6.3 268. 23 12X^ 3 X3 X 11.76 230. 19.6 8.1 235. 24 ij 13.12 265. 20.2 25 k 14.44 299. 20.7 8.1 305. 26 12X T 5 6 3 X3 A 14.62 283. 19.4 8.0 286. 27 fy& 15.94 317. 19.9 28 T 7 ^ 17.22 350. 20.3 29 s 18.50 382. 20.6 8.0 387. TWO PLATES. FOUR ANGLES. (CONTINUED.) No. Two Web Plates, Size in Inches FOUR ANCLES Total Area, Square Inches AXIS A. B. AXIS C. D. Size in Inches Thick- ness I r 2 Out to Out of Webs I 30 12X3/ 8 3 X3 H 17.44 335. 19.2 8.0 340. 31 A 18.72 368. 19.6 32 20.00 400. 20.0 33 9 21.24 430. 20.2 34 H 22.44 457. 20.4 7.9 464. 35 12X^ 3 X3 K 23.00 436. 18.9 8.0 445. 36 9 24.24 466. 19.2 37 >l 25.44 493. 19.4 7.9 502. 38 12X^ 3 X3 ft 28.44 529. 18.6 7.9 536. 39 12XX 3>X2J4 l 11.76 242. 20.6 8.0 248. 40 5 TtT 13.12 280. 21.4 41 H 14.44 317. 22.0 42 A 15.72 352. 22.4 7.9 355. 43 12x iV 3J4X2J4 A 14.62 298. 20.4 7.9 301. 44 y* 15.94 335. 21.0 45 T'*T 17.22 370. 21.5 46 18.50 404. 21.9 7.9 412. 47 12X^/8 3J4X2I4 N 17.44 353. 20.2 7.9 358. 48 A 18.72 388. 20.7 49 20.00 422. 21.1 50 22.44 485. 21.6 7.7 486. 51 12XJ4 3^X2^ 14 23.00 458. 19.9 7.8 459. 52 9,. 24.24 490. 20.2 53 ^ 25.44 521. 20.5 7.8 532. 54 12X# 314x214 # 28.44 557. 19.6 7.8 566. 55 14X T\ 3J4 X3 > A 17.11 455. 26.6 9.4 461. 56 ft 18.67 510. 27.3 57 20.23 564. 27.9 56 ^ 21.75 616. 28.3 9.4 626. 59 14X3/8" 314x314 r^ 20.42 539. 26.4 9.4 549. 60 A 21.98 592. 26.9 61 23.50 645. 27.4 62 ^ 26.42 743. 28.1 9.3 753. 63 14X^ 3^X3^ y z 27.00 702. 26.0 9.3 710. 64 _9 28.48 752. 26.4 65 ^ 29 92 800. 26.7 9.3 815. ~ii c sr TWO PLATES. A f 1-6 FOUR ANGLES. J DJL No. Two Web Plates, Size in Inches FOUR ANGLES Total Area, Square Inches AXIS A. B. AXIS C. D. Size in Inches Thick- ness I r 2 Out to Out of Webs I 66 14XJ* 3^X3^ % 33.42 857. 25.7 9.2 857. 67 14X3^ 314x3% X 34.00 816. 24.0 9.3 822. 68 A 35. 4b 866. 24.4 69 A 36.92 914. 24.8 9.3 927. 70 14 X A 4 X3 A 17.11 475. 27.8 9.2 482. 71 3/ 18.67 534. 28.6 72 JL 20.23 593. 29.3 73 l /2 21.75 648. 29.8 9.2 650. 74 14X3^ 4 X3 N 20.42 563. 27.6 9.2 563. 75 A 21.98 622. 28.3 76 23.50 676. 28.8 77 M 26.42 781. 29.6 9.2 796. 78 14Xl 4 X3 y 2 27.00 733. 27.2 9.2 742. 79 A 28.48 787. 27.6 80 H 29.92 838. 28.0 9.1 841. 81 14X# 4 X3 >8 33.42 896. 26.8 9.1 897. 82 14X34 4 X3 14 34.00 848. 24.9 9.2 852. 83 A 35.48 901. 25.4 84 H 36.92 953. 25.8 9.2 966. 85 15X T7 3^X3^ & 17.74 540. 30.4 10.2 549. 86 & 19.30 605. 31.4 87 A 20.86 668. 32.0 88 22.38 729. 32.6 10.2 737. 89 15X3/ 8 3y 2 X3y 2 Hi 21.17' 640. 30.2 10.1 642. 90 T% 22.73 703. 30.9 91 i 24.25 765. 31.5 92 y& 27.17 880. 32.4 10.1 885. 93 15X^ 3^X3^ y* 28.00 835. ' 29.8 10.1 846. 94 A 29 48 894. 30.3 95 H 30.92 951... 30.7 10.1 965. TWO PLATES. FOUR ANGLES. (CONTINUED.) No. Two Web Plates, Size in Inches FOUR ANGLES Total Area, Square Inches . AXIS A. B. AXIS C. D. Size in Inches Thick- ness I r 2 Out to Out of Webs I 96 15X^ j 3/ 2 X3% X 34.67 1021. 29.4 10.0 1023. 97 15X3/ 3 14 X3 l /t i 35.50 976. 27 5 10.1 992. 98 Tfi 36.98 1035. 28.0 99 & 38.42 1091. 28.4 10.1 1111. 100 15X^6 3^X3^ 39.25 1046. 26.6 10.1 1059. 101 9 40.73 1105. 27.1 102 ft 42.17 1162. 27.5 10.1 1179. 103 15X& 4 X3 A 17.74 562. 31.7 10.1 571. 104 H 19.30 631. 32.7 105 A 20.86 700. 33.5 106 X 22.38 764. 34.1 10.1 774. 107 15X3/6 4 X3 y^ 21.17 667. 31.5 10.0 668. 108 7 22.73 735. 32.3 109 X 24.25 799. 33.0 110 ft 27.17 922. 33.9 10.0 931. 111 15X^4 4 X3 X 28.00 869. 31.1 10.0 880. 112 29.48 932. 31.6 113 II 30.92 993. 32.1 10.0 1009. 114 15X# 4 X3 X 34.67 1063. 30.7 9.9 1064. 115 15X3^ 4 X3 X 35.50 1010. 28.5 10.0 1022. 116 36.98 1073. 29.0 117 X 38.42 1133. 29.5 10.0 1151. 118 15X^5 4 X3 y* 39.25 1080. 27.5 10.0 1089. 119 40.73 1143. 28.1 120 ft 42.17 1203. 28.5 10.0 1218. 121 16X3/ 3^X3^ y* 21.92 752. 34.3 10.9 758. 122 j 23.48 825. 35.1 123 y 25.00 897. 35.9 124 ft 27.92 1031. 36.9 10.9 1032. 125 16Xi^ 3%X3]4 X 29.00 982. 33.9 10.9 998. 126 A 30.48 1051. 34.5 127 ft 31.92 1117. 35.0 10.9 1133. 128 16X^ 3y 2 X3% ft 35.92 1200. 33.5 10.8 1210. 129 16X3^ 3*4X3% y* 37.00 1155. 31.2 10.8 1165. 130 A 38.48 1220. 31.7 131 ft 39.92 1285. 32.2 10.8 1295. 132 16XJ 3)4X3% X 41.00 1240. 30.2 10.8 1250. 133 A 42.48 1305. 30.8 134 43.92 1375. 31.3 10.8 1380. 45 1? F TWO PLATES. A-f-j 1-6 FOUR ANGLES. J b L No. Two Web Plates, Size in Inches FOUR ANGLES Total Area, Square Inches AXIS A. B. AXIS C. D. Size in Inches Thick- ness I r 2 Out to Out of Webs I 135 16X1 3^X3^ # 45.00 1325. 29.4 10.8 1330. 136 T7T 46.48 1390. 30.0 137 H 47.92 1460. 30.4 10.8 1460. 138 16X^ 4 X3 3 /s 21.92 780. 35.6 10.8 785. 139 TE 23.48 860. 36.6 140 tt 25.00 935. 37.4 141 H 27.92 1075. 38.6 10.8 10SO. 142 16X^ 4 X3 y* 29.00 1020. 35.1 10.8 1035. 143 JL 30.48 1090. 35.8 144 H 31.92 1160. 36.4 10.8 1180. 145 16X^ 4 X3 # 35.92 1245. 34.7 10.7 1250. 146 16X ^ 4 X3 Yi 37.00 1190. 32.2 10.7 1195'. 147 JL 38.48 1265. 32.8 148 8 39.92 1335. 33.4 10.7 1335. 149 16X^ 4 X3 y* 41.00 1275. 31.1 10.7 1275. 150 A 42.48 1350. 31.7 151 H 43.92 1420. 32.3 10.7 1420. 152 16X1 4 X3 % 45.00 1360. 30.2 10.8 1380. 153 Yff 46.48 1435. 30.8 154 )l 47.92 1505. 31.4 10.8 1525. 155 18X^ 3^X3^ /8 23.42 1010. 43.1 12.4 1015. 156 1 7 J 24.98 1105. 44.2 157 26.50 1200. 45.2 158 ^ 29.42 1375. 46.8 12.6 1398.' 159 18X^ 3^X3^ ^ 31.00 1320. 42.6 12.4 1335. 160 T7) 32.48 1410. 43 4 161 33.92 1495. 44.1 12.4 1505, 46 TWO PLATES. FOUR ANGLES. (CONTINUED.) Two Web FOUR ANGLES Total AXIS A. B. AXIS C. D. No. Plates, Size in Inches Size in Inches Thick- ness Area, Square Inches I r 2 Out to Out of Webs I 162 iQxfy 3%X3% # 38.42 1620. 42.1 12.3 1620. 163 18X%( 3^X3^ yt 40.00 1565. 39.1 12.2 1565. 164 T 9 ^ 4X4 i/ 87.00 5235. 60.2 16.3 5285. 220 A 88.72 5425. 61.2 221 90.44 5620. 62.2 16.4 5675. 222 27X y 2 4X4 ^ 42.00 3940. 93.8 18.8 3960. 223 T'ff 43.72 4190. 95.8 224 fl 45.44 4445 97.8 19.0 4460. 225 27X ft 4X4 5/8 52.19 4855. 93.0 18.8 4900. 4 S TWO PLATES. FOUR ANGLES. (CONTINUED.) No. Two Web Plates, Size in Inches FOUR ANGLES Total Area, Square Inches AXIS A. B. AXIS 0, D. Size in Inches Thick- ness I r 2 Ont to Out of Webs I 226 27 X ^ 4X4 X 55.50 4760. 85.8 18.4 4790. 227 T5 57.22 5010. 87.6 228 ft 58.94 5265. 89.3 18.6 5295. 229 27X1 4X4 X 69.00 5580. 80.9 18.2 5605. 230 T 9 * 70.72 5830. 82.4 231 X 72.44 6085. 84.0 18.4 6125. 232 27X1*4 4X4 X 85.94 6905. 80.3 18.3 6920. 233 27X1% 4x4 ft 99.44 7725. 77.7 18.3 7745. 234 27X y 2 6X6 y* 50.00 4935. 98.7 18.4 4965. 235 ft 55.44 5675. 102.4 236 X 60.76 6390. 105.2 237 65.96 7080. 107.4 18.5 7090. 238 27X ft 6X6 ft 62.19 6085. 97.9 18.3 6100. 239 67.51 6800. 100.7 240 % 72.71 7495. 103.1 241 i 77.75 8155. 104.9 18.4 8190. 242 27X % 6X6 ft 68.94 6495. 94.2 18.2 6515. 243 H 74.26 7210. 97.1 244 X 79.46 7905. 99.5 245 i 84.50 8565. 101.3 18.3 8595. 246 27X 7/% 6X6 * 75.69 6905. 91.3 18.1 6910. 247 81.01 7620. 94.1 248 y* 86.21 8315. 96.4 249 i 91.25 8975. 98.3 18.3 9065. 250 27X1 6X6 ft 82.44 7315. 88.8 18.1 7355. 251 87.76 8030. 91.5 252 #* 92.96 8725. 93.8 253 i 98.00 9385. 95.8 18.2 9425. 254 27X1^ 6X6 ft 95.94 8135. 84.8 18.1 8195. 255 101.26 8850. 87.4 256 y* 106.46 9545. 89.6 257 i 111.50 10205. 91.5 18.2 10280. 258 27X1*4 6X6 ft 109.44 8955. 81.8 18.1 8995. 259 3^ 114.76 9670. 84.3 260 r 119.96 10365. 86.4 261 1 125.00 11025. 88.2 18.2 11090. 49 c FOUR PLATES. A-|j j-jj-B FOUR ANGLES. b Two Web Two Side FOUR ANGLES ' Total AXIS A. B. Out to Out IV Plates, Plates, Area, of Webs no. Size in Size in Size in Thick- Square 2 for Inches Inches Inches ness Inches . Equal I 1 18X# 10^X3/ 8 3^X3^ 38.88 1392 35.8 11.3 2 % 41.50 1417 34.1 3 ;Hi H 43.38 1514 34.9 4 46.00 1538 33.4 5 H /8 51.55 1739 33.7 11.0 6 18X3/ lO^XSxg 3^X3^ H 47.88 1635 34.1 11.4 7 y t 50.50 1660 32.9 8 % 53.13 1684 31.7 9 ^ 50.80 1812 35.7 10 y* 53.42 1836 34.4 11 N 56.05 1861 33.2 11.0 12 21X^ 12^X3/8 4X4 M 45.38 2219 48.9 13.2 13 y* 48.50 2260 46.6 14 3/1 N 48.82 2506 51.3, 15 y* 51.94 2546 49.0 16 H 55.07 2587 47.0 12.8 17 21X# 12%X3/ & 4X4 M 50.63 2412 *47.6 13.2 18 l /t 53.75 2453 45.6 19 f6 56.88 2493 43.8 20 . N H 54.07 2699 49.9 21 57.19 2739 47.9 22 # 60.32 2780 46.1 12.8 23 21X34 12^X3/8 4X4 % 55.88 2605 46.6 13.3 24 y* 59.00 2646 44.8 25 $ 62.13 2686 43.2 26 ^i 65.25 2727 41.8 27 H H 59.32 2892 48.8 FOUR PLATES. FOUR ANGLES. (CONTINUED.) Two Web Two Side FOUR ANGLES Total AXIS A. B. Out to Out ft Plates, Plates, Area, oHVeks HO. Size in Size in Size in Thick- Square _2 for Inches Inches Inches ness Inches r Equal I 28 21X3^ 12J*X# 4X4 ft 62.44 2932 47.0 29 ft 65.57 2973 45.3 30 68.69 3014 43.9 12.6 31 21X^ I2y 2 xy 2 4X4 ft 67.69 3125 46.2 13.1 32 ft 70.82 3166 44.7 33 U 73.94 3206 43.4 34 21X1 i2y 2 xy 2 4X4 y 2 69.50 3032 43.6 35 ft 72.63 3072 42.3 36 l /2 ft 72.94 3318 45.5 37 ft 76.07 3359 44.2 13.0 38 24X^ i5y 2 x3/ & 4X4 1 A 50.63 3163 62.5 15.1 39 y 2 54.50 3241 59.5 40 ft ft 61.82 3706 60.0 41 24X^j i5y 2 X3/z 4X4 l /2 56.63 3451 60.9 15.1 42 y* 60.50 3529 58.3 43 ft 64.38 3606 56.0 44 ft 63.94 3916 61.2 45 ft 67.82 3994 58.9 14.7 46 24X3^ 15%X3/z 4X4 Y2 62.63 3739 59.7 15.2 47 l /2 66.50 3817 57.4 43 ft 70.38 3894 55.3 49 ft 66.07 4126 62.5 50 24x34; I5y 2 x% 4X4 ft 69.94 4204 60.1 51 ft 73.82 4282 58.0 14.8 52 24XJ/ S I5y 2 xy 2 4X4 I A 72.50 4105 56.6 14.9 53 ft 76.38 4182 54.8 54 ft 75.94 4492 59.2 c FOUR PLATES. A-Jj- jj-B FOUR ANGLES. D Two Web Two Side FOUR ANGLES Total AXIS A. B. Out to Out Plates, Plates. 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Top Plate, Size in Inches Total Area, Square Inches Eccen- tricit) AXIS A. B. AXIS C. D. I Depth in Inches Lbs. per Foot I r 2 i 5 6.5 4.0 8X14: 5.90 0.89 23.9 4.05 35.8 2 6.0 10x34: 6.40 1.03 25.3 3.95 69.3 3 9.0 4.0 8 x^ 7.30 0.72 27.8 3.81 44.6 4 6.0 7.80 0.84 29.5 3.78 86.3 5 11.5 3 5 8X34: 8.76 0.60 31.5 3.59 46.8 6 5.5 10x14: 9.26 0.71 33.4 3.61 94.2 7 6 8.0 6.0. 10x14: 7.26 1.08 42.0 5.79 81.1 8 8.0 12x34: 7.76 1.21 44.0 5 67 134.5 9 10.5 5.5 8.68 0.90 47.6 5.48 88.0 10 7.5 12x14: 9.18 1.02 49.9 5 44 149.6 11 13.0 5.5 10x34: 10.14 0.77 53.0 5.23 104.5 12 7.5 12X^ 10.64 88 55.7 5.23 177.2 13 15.5 5.0 10x3^ 11.62 0.67 58.2 5.01 108.0 14 7.0 12x14: 12.12 0.77 61.1 5.04 187.9 15 7 9.75, 5.5 10X# 8.20 1.11 65.1 7.93 84.7 16 7.5 12x34: 8.70 1.25 68.1 7.82 143.2 17 12-25 5.5 9.70 0.93 72.8 7.51 100.6 18 7.5 12X# 10.20 1.07 76.2 7.47 170.1 19 14.75 5.0 ioxy 11.18 0.81 79.9 7.15 103.6 20 7.0 11.68 0.93 83.7 7.17 180.1 21 17.25 5.0 10x14: 12.64 0.72 86.8 6.86 118.7 22 7.0 12x14: 13.14 0.83 90.8 6.91 206.0 23 19.75 4.5 10x14: 14.12 0.64 93.5 6.62 117.8 24 6.5 12x34: 14.62 0.74 97.8 6.69 210.4 25 8 11.25 5.0 10x14: 9.20 1.12 95.6 10.4 86.9 26 7.0 13X34: 9.70 1.28 100.0 10.3 150.0 27 13.75 5.0 iox 14: 10.58 0.97 104.5 9.88 99.4 28 7.0 12x^4: 11.08 1.12 109.2 9.86 172.1 29 16.25 5.0 lOXyV 12.69 1.03 120.6 9.50 118.9 30 7.0 12X T 5 6' 13.31 1.17 126.4 9.49 205,8 31 18.75 4.5 10X3^ 14.77 1.06 136.7 9.26 122.7 32 6.5 12X^ 15.52 1.21 143.7 9.26 218.6 33 21.25 4.5 lOxS/e' 16.25 0.97 146.2 9.00 136.4 34 6.5 12X3/8 17.00 1.11 153.7 9.04 242.6 75 TWO CHANNELS. ONE PLATE. (CONTINUED.) No. TWO CHANNELS Dist, b.tob. Top Plato, Size in Inches Total Area, Square Inches Eccen- tricity AXIS A. B. AXIS e. D. i Depth in Inches Lbs. per Fool I r 2 35 9 13.25 7.0 12X X 10.78 1.29 140.9 13.1 170.8 36 9.0 14X% 11.28 1.44 146.3 13.0 263.6 37 15.0 7.0 12x14: 11.82 1.17 149.7 12-7 187.5 38 9.0 14XX 12.32 1.31 155.4 12.6 289.6 39 20.0 6.5 15.51 1.13 183.3 11.8 222.9 40 8.5 14X T 5 r 16.14 1.26 190.8 11.8 351.3 41 25.0 6.0 12X3/6 19.20 1.10 217.2 11.3 252.1 42 8.0 14X^-6 19.95 1.23 226.5 11.4 404.8 43 10 15.0 6.5 12Xi^ 11.92 1.29 192.8 16.2 175.5 44 8.5 14X X 12.42 1.44 199.8 16 1 275.0 45 20.0 6.5 12X T 5 ^ 15.51 1.25 233.0 15.0 225.8 46 8.5 14 X 5 16.14 1.40 242.3 15.0 354.8 47 10.5 16X T 5 ^ 16.76 1.54 250.7 15.0 516.1 48 25.0 6.0 12X^| 19.20 1.22 274.8 14.3 253.4 49 8.0 14X^8 19.95 1.37 286.2 14.4 406.3 50 10.0 lex^g" 20.70 1.50 296.8 14.3 599.1 51 12 20.5 8.0 14x14: 15.56 1.38 358.0 23.0 331.9 52 25.0 7.5 14XX 18.20 1.18 394.1 21.7 354.4 53 7.5 14X-A- 19.08 1.41 415.9 21.8 368.7 54 7.5 14X^| 19.95 1-63 436.2 21.9 383.0 55 9.5 16X S T 19.70 1.56 429.4 21.8 548.8 56 9.5 16X^| 20.70 1.79 44*1.2 21.3 570.2 57 11.5 18X^6 21.45 1.95 465.2 21.7 798.5 58 30.0 7.5 14 X T\ 22.02 1.22 456.4 20.7 427.6 59 7.5 14X^ 22.89 1.42 478.4 20.9 441.9 60 7.5 14X T 7 7 r 23.77 1.60 499.4 21.0 456.2 61 9.5 16X T 5 OOLO CMOOOCMr-l CO*-I**-CO**- CDCMOCOCM < XI - 1 LOOOOCOOO OOtDOOOLO CMCOCT>C-.O> to Id J= j & OTHCDOC-- >* oo c. -i T-I co^j-coo5*- CMCMCMCOCM COCMCOOOCM T-tCMi-HCMCXJ rf S 2 a; oc i C^COOOLOCTJ OOti-OC^O OOC005COLO DC HM E rJ tOOTOiT-icM cotocooooa oooooc^o D O h. 3 j IL^J I j J CO CO CO XXX IO LO ID M| go 1 1 * ** . 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UJ^WCDC- oococa u coo) o IOOOCOOCM cr>'^^-cr> - S s "*-CO OS tOOOCOOOC^. ^-IC^-CO^l- Z. ^- ii-J tOlO CD IO CO CD CD t>- CD CO CO E~- ff s ^ XX X X X o E -i * IO IO CO Ik OS DO jl **** ^*^x . x M-i ol {- o S3 Size in Inches CO -*- * *1- CO XX X XX CO <*- Tf ^*- 10 D < ll gi H * X * *** PS S 2= f ^ ^5, ^ CO CO CO (0 .S XX X Ul ^ CO CO CO < !i X X X X X Q. | i s o O ca co co z * JM ,-H ^ ^-1 ^H ,H u H ^HS^HS ^HS^Hs ^ ,- u c cs XX X CO 1 r J oa 03 ca s 1 1 s ^ i-| XX X oo o 1-1 H oa oa * rH oa CO *- lOCD^OOO 84 t- o- t~- *a- ^> <^- co 3- t-l ^1- OO oo to CO O i-H SCn CO CO T-t OQ oo e* * 00 T-I -l .H rH O3 -( CO OO O> 10 00 00 C-- CO C>- T-I O O O 000 O O O o o o o o o o o o o o CSJ CO C-~ CO CM CM O O> CO ^1 00 CM <> CO CO CO CO CO CO CO CO CO CO e- co c^ C^ CD C- OO 00 OO fr- OO OO 00 CO T*- O Oi C7) tO OO IO OO -* t-i co *- LO 10 IO CM C-- a- LO 10 rH tO OO CM LO to 10 10 co co OO r-t CM * 10 CO 00 00 0- CO LO CO 05 CO * -^ CO IO CO C- 0- OO -< f- 10 C-. *- CM o c> 10 O. CO CO * O OO OO T-I OO CO OO C- C- 00 00 03 oa o c- oo CM CM IO O> CO * (^ C> CNJ CO OO OO (J> C7> O) CO O IO * LO OO oo LO oi CO C- 00 CM ** O CM CD LO c^ -^ -^ OO OO O CD O Oi O ^t X to ^x>t X CO ^^: >t X X CO D- ^ ^ X CO >3OS X co ^x X X co t- *3OS ^2C* ^ ^:^^ ^ ^ X ^ ^ ^^^: .^ OO X ID ^ CO X 10 ^ CO ** X X 10 co ^ OO X IO ^ CD X to * CD * X X LO CO 3W5 3^ * ^^ ^ ^x -^ CO X ^ OO X, CD X ^ CO X OO X ^ 00 X OO X $ 00 ^ OO X ^ 00 ^ CD X ^ 00 \NSJO ~\l/*X X ^ CO ^^ X * OO ^ ^ X X X OO OO ^ ^ X ^ * s^^ X ^- X ^^^5t X X a? co co ** X CM ^ X - .-I CNJ 00 <- CM 72 I + 1 + I + ' 36ooor 2 24000 r 2 iSooor* Where : S = Working strengths in Ibs. per square inch. L = Length in feet. / = Length in inches. r Least radius of gyration in inches. WORKING STRENGTHS WORKING STRENGTHS L 2 Lbs. per Sq. In. L 2 Lbs. per Sq. In. r 2 Square Pin and Square Pin r 2 Square Pin and Square Pin l 14940 14910 14881 26 13587 12976 12417 2 14881 14822 14764 27 13538 12909 12336 3 14822 14735 14649 28 13489 12843 12255 4 14764 14649 14535 29 13441 12777 12175 5 14706 14563 14423 30 13393 12712 12097 6 14648 14479 14313 31 13345 12648 12019 7 14591 14396 14205 32 13298 12584 11943 8 14535 14313 14098 33 13251 12521 11867 9 14479 14232 13992 34 13204 12459 11793 10 14423 14151 13889 35 13157 12397 11719 11 14368 14071 13787 36 13112 12336 11646 12 14313 13992 13686 37 13066 12275 11574 13f 14259 13915 13587 38 13021 12215 11503 14 15205 13838 13489 39 12976 12155 11433 15 14151 13761 13393 40 12931 12097 11364 16 14098 13686 13298 41 12887 12039 11295 17 14045 13612 13204 42 12843 11981 11228 18 13992 13538 13112 43 12799 11924 11161 19 13940 13465 13021 44 12755 11867 11095 20 13889 13393 12931 45 12712 11811 11030 21 13838 13322 12843 46 12669 11756 10965 22 13787 13251 12755 47 12626 11700 10901 23 13736 13181 12669 48 12583 11646 10838 24 13686 13112 12584 49 12542 11592 10776 25 13637 13044 12500 50 12500 11538 10714 WORKING STRENGTHS OF MEDIUM STEEL COLUMNS. (CONTINUED.) L 2 WORKING STRENGTHS Lbs. per Sq. Inch. L 2 WORKING STRENGTHS Lbs. per Sq. Inch. r 2 Square Pin and Square Pin r 2 Square Pin and Square Pin 51 1245.9 11486 10653 86 11161 9894 8886 52 12417 11433 10593 87 11128 9855 8844 53 12376 11381 10534 88 11095 9817 8803 54 12336 11329 10475 89 11062 9779 8762 55 12295 11278 10417 90 11030 9740 8721 56 12255 11227 10359 91 10997 9702 8680 57 12215 11177 10302 92 10965 9665 8640 58 12176 11128 10246 93 10933 9628 8601 59 12136 11078 10190 94 10901 9591 8562 60 12097 11030 10135 95 10870 9554 8523 61 12058 10981 10081 96 10838 9518 8484 62 12019 10933 10027 97 10807 9482 8446 63 11981 10886 9974 98 10776 9446 8408 64 11943 10838 9921 99 10745 9410 8370 65 11905 10791 9869 100 10714 9375 8333 66 11867 10745 9817 101 10684 9340 8297 67 11830 10699 9766 102 10653 9305 8260 68 11793 10653 9715 103 10623 9271 8224 69 11756 10608 9665 104 10593 9237 8188 70 11719 10563 9615 105 10563 9202 8152 71 11682 10519 9566 106 10534 9169 8117 72 11646 10475 9518 107 10504 9135 8082 73 11610 10431 9470 108 10475 9102 8047 74 11574 10388 9422 109 10446 9069 8013 75 11538 10345 9375 110 10417 9036 7979 76 11503 10302 9329 111 10388 9003 7945 77 11468 10260 9282 112 10359 8971 7911 78 11433 10218 9236 113 10330 8930 7878 79 11398 10176 9191 114 10302 8907 7845 80 11364 10135 9146 115 10274 8876 7812 81 11329 10094 9102 116 10246 8844 7780 82 11295 10053 9058 117 10218 8813 7748 83 11261 10013 9014 118 10190 8782 7716 84 11227 9973 8971 119 10163 8751 7685 85 11194 9934 8928 120 10135 8721 7653 WORKING STRENGTHS OF MEDIUM STEEL COLUMNS. (CONTINUED.) WORKING STRENGTHS WORKING STRENGTHS L 2 Lbs. per Sq. Inch. L 2 Lbs. per Sq. Inch. r* Square Pin and Square Pin r 2 Square Pin and Square Pin 121 10108 8691 7622 180 8721 7212 6143 122 10081 8661 7591 185 8621 7109 6048 123 10054 8631 7560 190 8523 7010 5952 124 10027 8601 7530 195 8427 6912 5859 125 10000 8571 7500 200 8333 6818 5769 126 9974 8542 7470 205 8242 6726 5682 127 9947 8513 7440 210 8152 6637 5597 128 9921 8484 7411 215 8064 6550 5515 129 9894 8456 7382 220 7979 6465 5435 130 9868 8427 7353 ?25 7895 6383 5357 131 9843 8399 7324 230 7812 6303 5282 132 9817 8370 7296 235 7732 6224 5208 133 9791 8343 7268 240 7653 6148 5137 134 9766 8315 7239 245 7575 6073 5067 135 9740 8287 7212 250 7500 6000 5000 136 9715 8260 7184 255 7426 5929 4934 137 9690 8233 7157 260 7353 5859 4870 138 9665 8206 7129 265 7281 5791 4808 139 9640 8179 7102 270 7212 5725 4747 140 9615 8152 7076 275 7143 5660 4668 141 9591 8126 7049 280 7076 5597 4630 142 9566 8099 7023 285* 7010 5535 4573 143 9542 8073 6996 290 6945 5475 4518 144 9518 8047 6970 295 6881 5415 4464 145 9494 8021 6945 300 6818 5357 4412 146 9470 7996 6919 310 6696 5245 4311 147 9446 7970 6893 320 6579 5137 4214 148 9422 7945 6868 330 6465 5034 4121 149 9399 7919 6843 340 6356 4934 4032 150 9375 7895 6818 350 6250 4839 3947 155 9259 7772 6696 360 6147 4747 3866 160 9146 7653 6579 370 6048 4658 3788 165 9036 7538 6465 380 5952 4573 3713 170 8929 7426 6356 390 5859 4491 3641 175 8823 7317 6250 400 5769 4412 3572 TABLE OF SQUARE ROOTS. IN. Roots Nos. Roots Nos. Roots Nos. Roots Nos. Roots i 1.00 51 7.14 101 10.05 151 12.29 201 14.18 2 1.41 52 7.21 102 10.10 152 12.33 202 14 21 3 1.73 53 7.28 103 10.15 153 12.37 203 14.25 4 2.00 54 7.35 104 10 20 154 12.41 204 14.28 5 2.24 55 7.42 105 10.25 155 12.45 205 14.32 6 2.45 56 7.48 106 10.30 156 12.49 206 14.35 . 7 2.65 57 7.55 107 10.34 157 12.53 207 14.39 8 2.83 58 762 108 10.39 158 12.57 208 14.42 9 3.00 59 7.68 109 10.44 159 12.61 209 14.46 10 3.16 60 7.75 110 10.49 160 12.65 210 14.49 11 3.32 61 7.81 111 10.54 161 12.69 211 14.53 12 3.46 62 7.87 112 10.58 162 12.73 212 14.56 13 3.61 63 7.94 113 10.63 163 12.77 213 14.59 14 3.74 64 8.00 114 10.68 164 12 81 214 14.63 15 3.87 65 8.06 115 10.72 165 12.85 215 14.66 16 4.00 66 8.12 116 10.77 166 12.88 216 14.70 17 4 12 67 8.19 117 10.82 167 12.92 217 1473 18 4.24 68 825 118 10.86 168 12.96 218 14.76 19 4.36 69 831 119 10.91 169 13.00 219 14.80 20 4.47 70 8.37 120 10.95 170 13.04 220 14.83 21 4.58 71 843 121 11.00 171 13.08 221 14.87 22 4.69 72 8.49 122 11.05 172 13.11 222 14.90 23 4.80 73 8.54 123 11.09 173 13.15 223 14.93 24 4.90 74 8.60 124 11.14 174 13.19 224 14.97 25 5.00 75 8.66 125 11.18 175 13.23 225 1500 26 5.10 76 8.72 126 11.22 176 13.27 226 15.03 27 5.20 77 8.77 127 11.27 177 13.30 227 15.07 28 5.29 78 8.83 128 11.31 178 13.34 228 15.10 29 5.39 79 8.89 129 11.36 179 13.38 229 15.13 30 5.48 80 8.94 130 11.40 180 13.42 230 15.17 31 5.57 81 9.00 131 11.45 181 13.45 231 15.20 32 5.66 82 9.06 132 11.49 182 13-49 232 15.23 33 574 83 9.11 133 11.53 183 1353 233 1526 34 5.83 84 9.17 134 11.58 184 13 56 234 1530 35 5.92 85 9.22 135 11.62 185 13.60 235 15.33 36 600 86 9.27 136 11.66 186 13.64 236 15.36 37 608 87 9.33 137 11.70 187 1367 237 1539 38 6 16 88 9.38 138 11.75 188 13.71 238 1543 39 624 89 943 139 11.79 189 1375 239 15.46 40 632 90 9.49 140 11.83 190 13 78 240 1549 41 640 91 954 141 11.87 191 1382 241 15.52 42 6.48 92 9.59 142 1192 192 13.86 242 15.56 43 656 93 964 143 11.96 193 13.89 243 15.59 44 663 94 9.70 144 1200 194 1393 244 15.62 45 6.71 95 9.75 145 12.04 195 13.96 245 15.65 46 678 96 980 146 12.08 196 14.00 246 1568 47 686 97 9.85 147 12.12 197 14.04 247 15.72 48 6.93 98 9.90 148 12.17 198 14.07 248 15.75 49 700 99 9 95 149 12 21 199 14.11 249 15.78 50 7.C7 100 10.00 150 12.25 200 14.14 250 15.81 103 TABLE OF SQUARE ROOTS. Nos. Roots Nos. Roots Nos. Roots Nos. Roots Nos. Roots 251 15.84 301 17.35 351 18.73 401 2002 451 21.24 252 1587 302 1738 352 18.76 402 2005 452 21.26 253 15.91 303 17.41 353 13.79 403 20.07 453 21.28 254 1594 304 1744 354 18.81 404 20 10 454 21.31 255 1597 305 17.46 355 18.84 405 20.12 455 21.33 256 1600 306 17.49 356 18.87 406 20.15 456 21 35 257 1603 307 17.52 357 18.89 407 80.17 457 21.33 258 16.06 308 17.55 358 1392 408 20.20 458 21 40 259 16.09 309 17.58 359 18.95 409 20.22 459 21 42 260 16.12 310 17.61 360 18.97 410 20.25 460 21.45 261 1616 311 1764 361 19.00 411 20.27 461 21.47 262 16 19 312 17.66 362 19.03 412 2030 462 21.49 263 16.22 313 1769 363 19.05 413 20.32 463 21 52 264 1625 314 17.72 364 19.08 414 20.35 464 21 54 265 16.28 315 17.75 365 19.10 415 20.37 465 21 55 266 1631 316 17.78 366 19.13 416 2040 466 21.59 267 1634 3i7 17.80 3S7 19.16 417 20.42 467 21.61 268 16.37 318 17.83 368 19.18 418 20.45 468 21.63 269 16.40 319 17.86 369 19.21 419 20.47 469 21.66 270 16.43 320 17.89 370 19.24 420 20.49 470 21.68 271 16.46 321 17.92 371 19.26 421 20.52 471 21.70 272 16.49 322 17.94 372 1929 422 20.54 472 21 73 273 16.52 323 17.97 373 19.31 423 20.57 473 21.75 274 1655 324 18.00 374 19.34 424 2059 474 21 77 275 16.58 325 18.03 375 19.36 425 20.62 475 21.79 276 16.61 326 18.06 376 19.39 426 2064 476 21.82 277 1664 327 18.08 377 19.42 427 20.66 477 21.84 278 16.67 328 18.11 378 19.44 428 20.69 478 21.86 279 16.70 329 18.14 379 19.47 429 20.71 479 21.89 280 16.73 330 18.17 380 19.49 430 20.74 480 21.91 281 15.76 331 18.19 381 19.52 431 20.76 481 21.93 282 13.79 332 1822 382 19.54 432 20.78 482 21.95 283 16 82 333 18.25 383 1957 433 20.81 483 21.98 284 1685 334 18.28 384 19.60 434 20.83 484 2200 285 16.88 335 18.30 385 19.62 435 20.86 485 22.02 286 1691 336 1833 386 19.65 436 20.88 486 22.05 237 1694 337 1836 387 19.67 437 20.90 487 22.07 288 16.97 333 18.38 388 19.70 438 20.93 438 2209 289 17.00 339 18.41 389 19.72 439 20.95 489 22.11 290 17.03 340 1844 390 19.75 440 2098 490 22.14 291 17.06 341 18.47 391 19.77 441 21.00 491 22.16 292 17.09 342 1849 392 19.80 442 21.02 492 22.18 293 17.12 343 18.52 393 19.82 443 21.05 493 22.20 294 17.15 344 18.55 394 19.85 444 21.07 494 22.23 295 17.18 345 18.57 395 19.87 445 21.10 495 22.25 296 17.20 346 18.60 396 19.90 446 21.12 496 22.27 297 17.23 347 18.63 397 19.92 447 21.14 497 22.29 298 17.26 348 13.65 398 19.95 448 21.17 498 22.32 299 17.29 349 18.68 399 19.97 449 21.19 499 22.34 300 17.32 350 18.71 400 20.00 450 21.21 500 22.36 104 TABLE OF SQUARE ROOTS. Nos. Roots Nos. Roots Nos. Roots Nos. Roots Nos. Roots 501 22.38 551 23.47 601 24.52 651 25.51 701 26.43 502 22.41 552 23.49 602 24.54 652 25.53 702 26.50 503 22.43 553 23.52 603 24.56 653 25.55 703 26.51 504 22.45 554 23.54 604 24.58 654 25.57 704 26.53 505 22.47 555 23.56 605 24.60 655 25.59 705 2655 506 22.49 556 23.58 606 24.62 656 25.61 706 26.57 507 22.52 557 23.60 607 24.64 657 2563 707 2659 508 22.54 553 23.62 608 24.66 658 25.65 708 2661 509 2256 559 23.64 609 24.68 659 25.67 709 26.63 510 22.58 560 23.66 610 24.70 660 2569 710 2665 511 22.61 561 2369 611 24.72 661 25.71 711 2668 512 22.63 562 23.71 612 24.74 662 25.73 712 2668 513 2265 563 23.73 613 24.76 663 25.75 713 2670 514 22.67 564 23.75 614 24 78 664 25.77 714 26.72 515 22.69 565 23.77 615 24.80 665 . 25.79 715 26.74 516 2272 566 23.79 616 24.82 666 25.81 716 26.76 517 22 74 567 23.81 617 24.84 667 25.83 717 26.78 518 22.76 568 23 83 618 24.86 668 25.85 718 25.80 519 22.78 569 23.85 619 2488 669 25.87 719 26.81 520 22.80 570 23.87 620 2490 670 25.88 720 26.83 521 22 83 571 23.90 621 24.92 671 25.90 721 26.85 522 22.85 572 23.92 622 24.94 672 25.92 722 26.87 523 22 87 573 23.94 623 24.96 673 2594 723 2689 524 22.89 574 2396 624 24.98 674 25.96 724 26.91 525 22.91 575 23.98 625 25.00 675 25.98 725 26.93 526 22.93 576 24.00 626 25.02 676 26.00 726 26.94 527 22.96 577 24.02 627 25.04 677 26.02 727 26.96 528 22.98 578 2404 628 25.06 678 2604 728 26.98 529 23.00 579 24.06 629 2508 679 26.06 729 27.00 530 2302 580 24.08 630 25.10 680 2608 730 27.02 531 23.04 581 24.10 631 25.12 681 26 10 731 27.04 532 23.07 582 24.12 632 25.14 682 2612 732 27.06 533 23.09 583 24.15 633 25.16 683 26.13 733 27.07 534 23.11 584 24.17 634 25.18 684 26 15 734 2709 535 23.13 585 24.19 635 25.20 685 26.17 735 2711 536 23.15 586 24.21 636 25.22 686 26.19 736 27.13 537 2317 537 24.23 637 25.24 687 2621 737 27.15 533 23.19 588 24.25 633 2526 688 2623 738 27.17 539 23.22 589 24.27 639 2528 689 26.25 739 2718 540 23.24 590 24.29 .640 2530 690 26.27 740 27.20 541 23.26 591 24.31 641 25.32 691 2629 741 27.22 542 23.28 592 24.33 642 '25.34 692 2631 742 27.24 543 23.30 593 24.35 643 25.36 693 2632 743 27.26 544 2332 594 24 37 644 2538 694 26.34 744 27.28 545 2335 595 24.39 645 25.40 695 26-36 745 27.29 546 2337 596 24.41 646 2542 696 26.38 746 27.31 547 2339 597 2443 647 2544 697 2640 747 27.33 548 2341 598 24.45 648 25.46 698 26.42 748 2735 549 23.43 599 24.47 649 2548 699 2644 749 2737 550 23.45 600 24 49 '650 2550 700 26.46 750 27.39 105 TABLE OF SQUARE ROOTS. I* Roots Nos. Roots Nos. R.MltS Sos. Roots Nos. Roots 751 27.40 801 28.30 851 29.17 901 30.02 951 30.84 752 27.42 802 2832 852 29.19 902 30.03 952 30.85 753 27.44 803 28.34 853 29.21 903 30.05 953 30.87 754 27.46 804 28.35 854 29.22 904 30.07 954 30.89 755 27.48 805 28.37 855 29.24 905 30.08 955 30.90 756 27.50 806 28.39 856 29.26 906 30.10 956 30.92 757 27.51 807 28.41 857 29.27 907 30.12 957 30.94 758 27.53 808 28.43 858 29.29 908 30.13 958 30.95 759 27.55 809 28.44 859 29.31 909 30.15 959 30.97 760 27.57 810 28.46 860 29.33 910 30.17 960 30.98 761 27.59 811 28.48 861 29.34 911 30.18 961 31.00 762 27.60 812 28.50 862 2936 912 30.20 962 31.02 763 2762 813 28.51 863 2938 913 30.22 963 31.03 764 27.64 814 28.53 864 29.39 914 30.23 964 31.05 765 27.66 815 28.55 865 29.41 915 30.25 965 31.06 766 27.68 816 28.57 866 29.43 916 30.27 966 31.08 767 27.69 817 28.58 867 29.44 917 30.28 967 31.10 768 27.71 818 2860 868 29.46 918 30.30 968 31.11 769 27.73 819 28.62 869 29.48 919 30.32 969 31.13 770 27.75 820 28.64 870 29.50 920 30.33 970 31.14 771 27.77 821 28.65 871 29.51 921 30.35 971 31.16 772 27 78 822 28.67 872 29.53 922 30.36 972 31.18 773 27.80 823 28.69 873 29.55 923 30.38 973 31.19 774 27.82 824 28.71 874 29.56 924 30.40 974 31.21 775 27.84 825 28.72 875 29.58 925 30 A 1 975 31.22 776 27.86 826 28.74 876 29.60 926 30.43 976 31.24 777 27.87 827 28.76 877 29.61 927 30.45 977 31.26 778 27.89 828 28.77 878 29.63 928 30.46 978 31.27 V79 27.91 829 28.79 879 29.65 929 30.48 979 31.29 780 27.93 830 28.81 880 29.66 930 30.50 980 31.30 781 27.95 831 28.83 881 29.6 931 30.51 981 31.32 782 27.96 832 28.84 882 29.70 932 3053 982 31.34 783 27.98 833 28.86 883 29.72 933 30.55 983 31.35 784 2800 834 28.88 884 29.73 934 30.56 984 31.37 785 28.02 835 28.90 885 29.75 935 30.58 985 31.38 786 28.04 836 28.91 886 29.77 936 30.59 986 31.40 787 28.05 837 28.93 887 29.78 937 30.61 987 31.42 788 28.07 838 28.95 888 29.80 938 30.63 988 31.43 789 28.09 839 2897 889 29.82 939 3064 989 31.45 790 28.11 840 28.98 890 29.83 940 30.66 990 31.46 791 28.12 841 29.00 891 29.85 941 30.68 991 31.48 792 28.14 842 29.02 892 29.87 942 30.69 992 31.50 793 28.16 843 29.03 893 29.88 943 30.71 993 31.51 794 28.18 844 29.05 894 29.90 944 30.72 994 31.53 795 28.20 845 29.07 895 29.92 945 30.74 995 31.54 796 28.21 846 29.09 896 2993 946 30.76 996 3156 797 28.23 847 29.10 897 29.95 947 30.77 997 31.58 798 28.25 848 29.12 898 29.97 948 3079 998 31.59 799 28.27 849 29.14 899 29.98 949 3081 999 31.61 800 28.28 850 29.15 900 30.00 950 30.82 1000 31.62 106 TABLE OF SQUARE ROOTS. to. Roots Nos. Root* Sos. Roots Nos. Rjoik Nos. Roots 1001 31.64 1051 32.42 1101 33.18 1151 33.93 1201 34.66 1002 31.65 1052 3243 1102 33.20 1152 33.94 1202 34.67 1003 31.67 1053 32.45 1103 3321 1153 33.96 1203 34.68 1004 31.69 1054 32.47 1104 33.23 1154 33.97 1204 34.70 1005 31.70 1055 32.48 1105 33.24 1155 33.99 1205 34.71 1006 31.72 1056 32.50 1106 33.26 1156 34.00 1206 34.73 1007 31.73 1057 32.51 1107 33.27 1157 34.01 1207 34.74 1008 31.75 1058 32.53 1108 33.29 1158 34.03 1208 34.76 1009 31.76 1059 32.54 1109 33.30 1159 34.04 1209 34.77 1010 31.78 1060 32.56 1110 33.32 1160 34.06 1210 34.79 1011 31.80 1061 32.57 1111 33.33 1161 34.07 1211 34.80 1012 31.81 1062 32.59 1112 33.35 1162 34.09 1212 34.81 1013 31.83 1063 32.60 1113 33.36 1163 34.10 1213 34.83 1014 31.84 1064 32.62 1114 33.38 1164 34.12 1214 34.84 1015 31.86 1065 32.63 1115 33.39 1165 34.13 1215 34.86 1016 31.87 1066 3265 1116 33.41 1166 34.15 1216 34.87 1017 31.89 1067 32.66 1117 33.42 1167 34.16 1217 34.89 1018 31.91 1068 3268 1118 33.44 1168 34.18 1218 34.90 1019 31.92 1069 32.70 1119 33.45 1169 34 19 1219 34.91 1020 31.94 1070 32.71 1120 33.47 1170 34.21 1220 34.93 1021 31.95 1071 32.73 1121 33.48 1171 34.22 1221 34.94 1022 31 97 1072 32.74 1122 33.50 1172 34.23 1222 3496 1023 31.98 1073 3276 1123 33.51 1173 34.25 1223 34.97 1024 32.00 1074 32.77 1124 33.53 1174 34.26 1224 34.99 1025 32.02 1075 32.79 1125 33.54 1175 34.28 1225 35.00 1026 32.03 1076 32.80 1126 33.56 1176 34.29 1226 35.01 1027 32.05 1077 32.82 1127 33.57 1177 34.31 1227 3503 1028 32.06 1078 32.83 1128 33.59 1178 34.32 1228 35.04 1029 32.08 1079 32.85 1129 33.60 1179 34.34 1229 35.06 1030 32.09 1080 32.86 1130 33.62 1180 34.35 1230 35.07 1031 32.11 1081 32.88 1131 33.63 1181 34.37 1231 35.09 1032 32.12 1082 32.89 1132 33.65 1182 34.38 1232 35.10 1033 32.14 1083 32.91 1133 33.66 1183 34.39 1233 35.11 1034 32.16 1084 32.92 1134 33.67 1184 34.41 1234 35.13 1035 32.17 1085 32.94 1135 33.69 1185 34.42 1235 35.14 1036 32.19 1086 32.95 1136 33.70 1186 34.44 1236 35.16 1037 32.20 1087 32.97 1137 33.72 1187 34.45 1237 35.17 1038 32.22 1088 32.98 1138 33.73 1188 34.47 1238 35.19 1039 32.23 1089 3300 1139 33.75 1189 3448 1239 35.20 '1040 32.25 1090 33.02 1140 33.76 1190 34.50 1240 35.21 1041 32.26 1091 33.03 1141 33.78 1191 34.51 1241 35.23 1042 32.28 1092 33.05 1142 3379 1192 34.53 1242 35.24 1043 32.30 1093 33.06 1143 33.81 1193 34.54 1243 35.26 1044 32.31 1094 33.08 1144 33.82 1194 34.55 1244 35.27 1045 32.33 1095 33.09 1145 33.84 1195 34.57 1245 35.28 1046 32.34 1096 33.11 1146 33.85 1196 34.58 1246 3530 1047 32.36 1097 33.12 1147 33.87 1197 34.60 1247 35.31 1048 32.37 1098 33.14 1148 3388 1198 34.61 1248 35.33 1049 32.39 1099 33.15 1149 3390 1199 3463 1249 35.34 1050 32.40 1100 33 17 1150 33.91 1200 34.61 1250 35.36 107 TABLE OF SQUARE ROOTS Hos. Roots N *- 0> *- o in m o d o o o + 1 4-1 4- * to to -* o . . C7> O H ^ ^ ^o *n T ? do d + 1 4- A** J z o / 5 H f O 1 H oo oo 00 00 to to to o t- o oo in ^ 3 o o i- CO - *f TJ- oo o ca . ^ 2j w u m o to . in \gr ^^ **<* o o d d 1 n g 1 1 - 1 1 e< 1 M to * o JH i2 O CT> O CT) O *Q N^ *1- O . ^- o m ^ c^- oa o *>* CNJ CM OJ CM .. o o o o III! ' T ' " H H g Vi in CM LO oo CO CO CO ff 0-00 CO OO O co oo o W o o" o o + + 1 1 do T-i + 1 + CO r-* OO ^~ *1- C>- O !- CD C- CO CO O c> 10 CM OO -H O O O O O + + 1 1 00 T-i + 1 + / ^0 < ^ CO T-I 00 *- c~ o / OO CO O / fc ^0 CNJ 10 OO TH O J- J 2 8 dodo 1 1 + + do T-i + 1 + 3 ^-jH T-I CM CM i co o O- Ul W M oo 10 10 oo ** oo oo * o o o o co o CD . CM T-H d < !>- 00 * oo o _ ^ *- fr- CO O oo _ o ^3 Vj o o o o " 3 W 1 1 1 1 1 UJ *J Z <0 pS c^ ^_i co ^. i-H ^t- CO CO 2g ^ -^ tl- 05 tS. <* CM ^1- C~- CO OO CM LO CO CO I M d o d d 1 + 1 1 o o o o + 1+1 x g P4 \ II W 00 T-I 00 T3- 3- 0- > II < w C/2 " CT> ^1~ CT> C*-- 10 CM o o dodo CO CO O OO T-I O do T-i a + + 1 1 + 1 + ! ^^^^ ' ' ' l i; g ^ T p " "* ^ ^ 1 f g 3 i 1 rr lO 00 00 10 f co c>- ca ca c- co . (N. . \i CNJ co co co co ca OO f f f f f f T H C>- rH O * 00 C- IS. ^- en o o 00 rH CO CO 00 rH . CO tO O ^ ^v CO OO CO rH rH rH to o o o o o p o 4-4- 4- 1 T 1 rH O CSI 4- 1 4- ' rH co oo ca T- en 10 10 A * ^ CD CO 00 CD 10 to co o s *^ to -a- rH o o o ca ca 10 / jpijfjpffj rH O rH 4- 1 4- s "** * * en a- ea oo to rH LO IO O 10 en oo to o en to co o ^4 I O O O rH ^ CO ca ca 10 u '*> < f f f +?? rH O rH 4-'T 4- ' a o i c*. oo ^- oo t- 00 w ^^ tO OO rH rH 00 tO co o N frt co to en en to co en . 10 **1 J rH O CD tO O O 5~ 7"! ** . < 4- 4- 4- + + + 4- 4- Ed < en * eg ca * o> o o *N * ^ CO IO OO O O O .CD LO 09 . ^ ^ f f f f f f " T T H "* UJ ^ w en ^t- co ca ^- tr> 00 00 O O Z "crt ^r o en to oo o> 10 to co LO LO ^ ^- ^- o o cu o o co oo en 10 C-- ^- 10 LO " ^ ^J CO a- rn O O O IO LO C>- C3 \ c W : f ??f f f ?f ?? \ < -a 03 rH tO 00 CM * CD CD O tO OO CD LO to 10 o CO CO c c> CO ^- rH O O ca CM LO = 0000 + T + : i & ^ 5 i 5 J ^ w di o v -y s^ c^^j 1^ 3 -1 X M 1 115 A 3 . . o - w G a .2 1 < i OOOOHCOIOC^ o o o 00 C^ CO O >-i o oa V llSsISIl oa o oooooooo in ca s CMxt-lDOOOOOO O -0 OOOOOOOO 1 1 1 1 i 1 i 1 T -7 Isssliil 00 00 00 ca cvj oo TH C-- CQ CM 1 TO O O 1 1 4- I 1 1 1 .H 0^-1 1 + 1 g rt 1 OJ-tf-COr-IOOOO TO O O O O O 1 ++ 1 1 1 1 ca CQ o o CO CO O 6- O tO tO + T +T w g 5^0WC^OT5 00 00 O O a- * oo 05 in cs) CM TO +++ 1 1 1 1 O f-t + 1 +1 s^ss^^s^ 00 o o o O- CO O . oooooooo + + + + 1 I 1 1 iH CM . + 1 + I 4 ii i 1 < a 4 4 1 * B5 116 oooooooo ^caoococooooQ**- s dodooooo< 1 1 ! 1 1 1 1 I o CO 00 O ocDr-ir-ioooooocr> o o o -s3 ^* _^ OOOQIOO30OOOTH oo ca o / OOOOOOOO + + + + 1 1 1 1 O iH co<7) 00 N 00 * J E z ? Or-idodddd + + + + 1 1 1 1 tf- CO O 03 CO + J + a 2 j O , * O O LOT-tooac^-ooo^" 00 * -0 t-lOOOt-IOOOO dddddddo + + + + 1 1 1 1 C CO Q T-l d oj + 1 + \ ' H 5 ^ P 00 IO C- O O 0* 0) 10 do T-! d + 1+1 - 00>O^OCOO>0)t>-^- a- t<- to (o T?????T?T i-i d TH d + 1+1 H^?TT?TT 10 IO O CO <> O H CO IO ca o c-a + 1 + ' N 5 Q 1 jl 1 I 118 S*SSS2 c~. oo 1 1 1 1 1 1 1 1 1 1 *- ' | ,-1 00 in CT> o s ooooainoo*--a-oocx 1 1 + + + 1 1 1 1 1 + 1 ? a / i ir~Tr r -i~ 7 T-t 0> H ^ SwSS^ in ^- o. " oooooooooo CO i-< * ,. + + + + + Mill + 1 + **< H j ^ W '" . IU O co oo o* ^ o> ^ oo ^ c, c. D * (T> fa . J Q oocc>ac-oor-jcaoaoa,-i ^- o in dd^nodooooo +++++ 1 1 1 1 1 CO rH o ^ 2 ^ 0000,-iooooaoooo^ao C~- O3 O 03 D>- i ^ z o^odoo ooo o CO O * + 1 + 8 a>CT>o^-ocoa>o>c^? CO CD O pOs c^tn^-ca T-*OOOOO t-i co in oooooooooo ca o oo + 1 + ^S . .< ^: 1 * Q 1 *>f ^Ml^-i u Q .C>.COCOOooco**-cM OOOOOOOTHOO*3-COOO oooooooooooo r-1 OO c^ cj 10-51- cvj d 4- 1 r-tr-i(T<^*-cn^ej -HTHOC)OOC^C>.OOCOOtH^H oa^t-coc^ooaicDooc^tOTj-ca oooooooooooo + ^ + 4- + + + + + + + + ^ T-l 0~ ^ : : : SHEAR IN PANEL : OOvHCDOOCS3-^-C^C^DtS.CDlO o-LOi-tcoO'-iinooCTJoococo T-icoLOcoaoa)OOoooo Toooooododod i 1 1 1 1 1 1 1 1 1 I !>. 10 -0 . . CO CO '1 ' ! i ! OOrH000(M-C-COC^CDm e^int-Hcoocomoocnootooo -1001010000000000 oooooooooooo i 1 1 II + 1 1 1 1 1 1 r- 1 rH O CS1 O CM 4-14-1 *}*./ J * J, * I | ** A 14 PANELS ALL EQUAL. NOTE : Shear in panel ab = reaction at a. > OOt-HCOOOOOCDC^C^COC^-CDm O~LOt-tCDC7>OOir>OOCT>OOC>OO t-tcomiOT-iooooooo oooooooooooo 1 1 1 1 ++ 1 1 1 1 1 I * r-t CD O5 CO ^- TH D- IO IO CO ^- OO CO o -H d o + 1+1 "8 oo.-!*3-cNiaoiots.c-.tr>ts.eDm e--ioooc>ocr)oomooo)coc)co T-HOO^J-OOr-tOOOOOOO o iddddddddo'dd ! 1 4- + 4-4- 1 1 II 1 1 o is. 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To proportion chord sections which are subjected to a bending load in addition to direct compression let M = the bending moment in inch pounds, C = direct compression due to position as a truss member, A = required area of section, I = moment of inertia of section, d = distance from neutral axis to extreme top fibre; then Q = Direct compression per square inch, A. Mflf - compression per square inch in extreme fibre due to bending. y _ C + M^ = resultant fibre 6tress ..... (j) A 1 But I = A r 2 , and substituting in equation (i), /= + M-4- from which A AH _ C r 2 + M d If the specified unit stresses for bending, live and dead loads have different values, then let, ft = unit stress for transverse load, /i = unit stress for live load, /d = unit stress for dead load, then M d At = -f j ~ area required for bending, Cl Al = -r- = area required for live load stress, Ad= 7- = area required for dead load stress, yd and A = At + Ai + Ad =total area required. 157 A A. E \ w r i ^<^y x X ^ PORTAL BRACING. .a ^X^<1> t i ^^^ ^^^te, Direct stresses and T bending moments due 1 I * c * to a load W applied at B; assuming the reac- i Fig. I. tions at C and D to be 1 equal to ^W, and as- 1 suming that the mem- i ^W ^LL bers AD and BC are [ ) 2 ( * 2 free to rotate at C and A B W ^* \ ^ . i* ^^^ ^ -X 11 In Fig. i AB and EF i -^^C^ are struts and AF and 1 v t -^x xX *^ ^ SN *S S ^ i. ^^^ ^^^. EB tensions members. *E In Fig. 2 AB and EF are tension members 1 d Fig.2. and AF and EB are I struts. i I In Fig. 3 all mem- i__ W W bers are struts. [ 32 ( ^^^^^^ ^^ s Let a, b, c, d and e A Kd->^c-*^d^ represent the length of the several mem- bers as indicated in Figs, i, 2 and 3, and F i- ly^ V 1 / o \ // \ F let the + sign repre- \ sent a compressive i Fig. 3. stress and the sign ^ tensile stress : then 1 r r*? < r*2" 158 Fig. i. Stress AB = + W (^ + i ) B F has no direct stress, but B F C and AED are both subjected to bending moments, varying uniform- ly from M = O at A, B, C and D to M = ^L? at F and E. Fig. 2. Stress AB = - W ^ BFC = - W A E has no direct stress, but AED and BFC are both subjected to bending moments, varying uniform- ly from M = O at A, B, C and D to Fig. 3. Stress BH = + W (~ b + i ) \& ft Bending moments at E and F = -^ 159 CAMBER. Theoretically a truss should have just sufficient camber to bring the joints of the compression chords to a true square bearing when the truss is fully loaded. The most perfect way of accomplishing this is to calcu- late the lengths of the various members in the position they are expected to assume when the truss is fully loaded; then calculate the stresses in the web members for the same condition of loading; calculate the elonga- tions of the various tension members and the shortening of the compression members due to the stresses under full load and the actual sections used; then diminish the lengths of the tension members and increase the lengths of the compression members by these amounts. While this method accomplishes the desired pur- pose, it does not give directly the amount of camber which the truss will assume when erected and unloaded. This, however, may be calculated if desired. A shorter method, and the one more generally used, is as follows: Assume the amount of camber to be given to the truss; that is, the versed sine of the camber curve of the chord; then assume the chords to be arcs of concentric circles and the posts to be intercepts of radii. Knowing the length of bottom chord panel and the depth of truss, the length of top chord panel and the length of diagonal members may be readily obtained. Let c camber desired d depth of truss / = length of span n = number of panels in truss i increase of top chord panel over bottom chord panel, all values being expressed in inches or all in feet. 1 60 Then: In all ordinary cases 4C 2 is small in comparison with the other values in the formula and may be neglected; the formula then becomes Scd l -~fo in which ^may be expressed in inches, d and /in feet, and the value i will be in inches. Having now the length of top and bottom chord panels the diagonal may be computed as the hypothe- nuse of a right angled triangle of which one side is the depth of truss and the other a mean of the top and bot- tom chord panel lengths. 161 LENGTH OF FLANGE PLATES, PLATE GIRDERS. I The lengths of flange plates for girders with par- allel flanges may be readily obtained analytically, as follows; let a l = area of first flange plate a 2 area of first and second plate a,= area of first, second and third plate a t = total area of flange x x = length of first flange plate x 2 = length of second flange plate x 3 = length of third flange plate / = length of span. 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Train of 74-ton Coal Cars. Weight of Car = 38,000 Ibs. Rated Capacity = 100,000 ' 10% Overload = 10,000 " Total Load = 148,000 " Axle " = 37,000 " J II 1 r )( 3 G )( ) ( )( *\ r L) (, 2 5 o 19 o 50 8 LIVE LOAD "B." Train of 62-ton Coal Cars. Weight of Car = 36,000 Ibs. Rated Capacity = 80,000 " 10% Overload = 8,000 " Total Load = 124,000 " Axle " = 31,000 " LIVE LOAD "C." Train of 46-ton Flat Cars Same wheel spacing as for 62-ton Coal Cars. Weight of Car = 26,000 Ibs. Rated Capacity = 60,000 " 10 % Overload = 6,000 " Total Load Axle = 92,000 = 23,000 \ I ) C ) < ^ C ) ( 1 C ) ( 1 6'o* i6'o" 6'o" 12' o f 6'o" l6'o" 6' o" LIVE LOAD "D." Train of 4O-ton Motors. Axle Load = 20,000 Ibs. NOTE. Live Load "A" should be used for roads designed for heavy coal traffic, etc. Live Losd "B" " " " " to carry occasional coal cars. Live Load "C" " " " " " " ordinary freight traffic, but not cars of over 60,000 Ibs capacity This excludes coal traffic. Live Load "D" should be used for roads designed for passenger and ex- press traffic only 171 THE OSBORN ENGINEERING COMPANY'S STANDARD LIVE LOADS FOR HIGHWAY BRIDGES. UNIFORM UVE lyOADS For country bridges carrying heavy traffic, and for city bridges : for spans up to 150 feet long, 100 Ibs. per square foot of roadway and 80 Ibs. per square foot of sidewalks. For spans over 150 feet long, 80 Ibs. per square foot of both roadway and sidewalks. For country bridges carrying ordinary or very light traffic: for spans up to 150 feet long, 80 Ibs. per square foot of both roadway and sidewalks. For spans over 150 feet long, 60 Ibs. per square foot of both roadway and sidewalks. CONCENTRATED UVE I,OADS. For country bridges carrying heavy traffic, and for city bridges: a steam road roller weighing 35,000 Ibs., arranged as follows: 15 ooo Ibs. on forward roll and 10,000 Ibs. on each rear roll; axles eleven feet apart, forward roll four feet face, rear rolls each twenty inches face, rear rolls five feet center to center. For country bridges carrying ordinary traffic: a steam road roller weighing 21,000 Ibs., arranged as follows: 9,000 Ibs. on for- ward roll and 6,000 Ibs. on each rear roll; axles eleven feet apart, forward roll four feet face, rear rolls each twenty inches face, rear rolls five feet center to center. For country bridges carrying very light traffic: a single horse roller weighing 12,000 Ibs., the roll five feet face; or a wagon load of io,ooq Ibs. on two axles eight feet apart, wheels five feet gauge. Unit stresses may be increased twenty-five per cent, for the road rollers, but concentrated loads should not be considered as distrib- uted over two or more stringers, except when such distribution un- questionably occurs. If a paved floor of sufficient width be used, the rollers should be considered when turned at right angles to the axis of the bridge. If the structure is to be designed for the present or future ac- commodation of electric railways, suitable concentrations should be selected from page 171, and the structure proportioned for these concentrations also. 172 IMPACT FORMULAE. THEOSBORN ENGINEERING CO. where I Impact. "L, = Maximum live load stress. D = Dead load stress. THE AMERICAN BRIDGE CO. - L + 300 Where I =* Impact. S = Maximum live load stress. 1. = length in feet of loaded distance which produces maximum stress in member. THE OSBORN ENGINEERING COMPANY'S STANDARD UNIT STRESSES Pounds per Square Inch NATURE OF STRESS For Railroad Bridges For Electric Railway Bridges For Highway Bridges TENSION Wrought Iron, 13,000 15,000 18,000 Soft Steel, 15,000 17,000 20,000 Medium Steel, 17,000 19,000 22,000 COMPRESSION Values of C in formulae at bottom of page, Wrought Iron, 13,000 15,000 18,000 Soft Steel, 15,000 17,000 20,000 Medium Steel, 17,000 19,000 22.000 Values of ~ in the formulae below should not exceed: for main members, 100 100 125 for subordinate members, 120 120 150 BENDING Pins, closely packed, medium steel, 25,000 25,000 25,000 BEARING Pins, medium steel, 22,000 24,000 24,000 Rivets, rivet steel, 20,000 22,000 22,000 SHEARING Pins, medium steel, 11,000 12,000 12,000 Rivets, rivet steel, 10,000 11,000 11,000 Webs of plate girders, soft steel, " " " medium steel, 9,000 10,000 10,000 11,000 10,000 11,000 COMPRESSION FORMULAE: Square Bearing. 12500 Soft Steel, 8 = Pin and Square Bearing 12500 1 + 1 + / 2 Medium Steel, S = 15000 24000 r 2 15000 36000 r* 18000 r 2 S= Working strength in Ibs. per sq. in.; /= length in inches ; r = least radius of gyration in inches. 173 VALUES OF MOMENTS OF INERTIA FOR STANDARD SHAPES OF THE CARNEGIE STEEL COMPANY. I = Moment of Inertia neutral axis parallel to flange. I/= " " - " we b. j Area A=dt-f-(s-}-y)2z. I 4 )]. Area=A-dt+(s+y)z. t*)]-Ax 2 . 1 8c(h ^) 3 ]. I'= T V[d(b4-c) 3 2hc 3 6hcb 2 ]. "T 1 t)t. 2(h+b) l-x)-(b-t)(x-t)]. 174 VALUES OF I (Moment of Inertia) AND S (Section Modulus) FOR USUAL SECTIONS. bh 3 ~" 12 ' bh 3 "36' bh 2 bh 2 . 12 =0.0491 d 4 . 32 =0.0982 d -"--A'A 1= 1=0.0491 I _b / n 3 +bn /3 -(b-b / )a 3 _____ _ 0.0982 (d 3 - Min.= . n I=- bh 3 -2b'b/ 3 12 x x Denotes position of neutral axis. 175 CONVENTIONAL SIGNS FOR BRIDGE RIVETS. Shop. Field. Two Full Heads. Countersunk Inside and Chipped. Countersunk Outside and Chipped. Countersunk Both Sides and Chipped. Inside. Outside. Both Sides. (DO ODOqp Flattened to y%" high or Countersunk and not Chipped. Flattened to Flattened to The foundation of the above system is the diagonal cross to represent a countersink, the blackened circle for a field rivet, and the verticle stroke to indicate a flattened head. The position of the cross with respect to the circle (inside, outside or both sides) indi- cates the location of the countersink, and the number and position of the verticle strokes indicate the height and position of the flat- tened heads. Any combination of field, countersunk and flattened head rivets liable to occur may be readily indicated by the proper combination of the above signs. 176 BRIDGES. SOME HISTORICAL AND OTHER INTERESTING DATA. HISTORICAL. Ancient bridges are known to have existed in China, Assyria and India long before the Christian Eta. Stone bridges, built of slabs on piers, were built by the Greeks. The origin of the arch may be traced back to the Chaldeans and Assyrians. Crude arches of brick have been found in ruins of Thebes, probably built about 2900 B. C. The Romans, however, were probably the first to use the arch understandingly, about the second century B. C. The first bridge in the United States, so far as known, was a pile trestle, built in 1660, across Charles River, near Boston. A noted long wooden span was the bridge "Colossus." 340' 3%" long, built by lyouis Wernwag , about 1812, at Philadelphia, on the site of the present Callowhill bridge. The first iron bridge in the world was built over the Severn River at Ironbridge, England, in 1779. It was a cast iron arch of 100' 6" span and 40' rise. The next was the "Buildwas Bridge," a similar structure, built over the same river by Telford in 1796; span 130', rise 17'. The firs,t iron railway bridge was built in 1823, for the Stockton and Darlington Railway, over the Gaundless River, a tributary of the Wear River, in England, a cast iron trestle consisting of four spans i a' 6" each. The first plate girders were made in England in 1846, by Fair- bairn, from designs by Stephenson. They had cast iron flanges. The first bridge across the Mississippi River was a suspension bridge, built 1855, at Minneapolis, 620' span. There are now forty- six bridges across that river. Suspension bridges are said to have been built in China over 2000 years ago. Such structures were built in Europe as early as 1615. The first chain bridge in England was a foot bridge of 70' span built about 1741, over Tees River. The first chain bridge in the United States was built by Finlay, in 1796, over Jacob's Creek, near Uniontown, Pa. The first wire suspension bridge in the United States was built in 1816, over the Schuylkill River, in Philadelphia. 177 The first suspension bridge over the Niagara River was built by Charles Kllet, in 1848. The only railway suspension bridge in the world was built by Roebling at Niagara, in 1855. Wooden cantilever bridges were built by the Assyrians as early as 2000 B. C. The first cantilever bridge of importance to be built in the United States was the Kentucky River Bridge, built by C. Shaler Smith, in 1877. Total length, 1125'; being three equal spans of 375'. The second was the Minnehaha Bridge over the Mississippi River at St. Paul, built in 1880, with center span of 324'. The third was the Niagara cantilever, built in 1883, with center span of 420'. The Romans built cement arches ; remains of them still exist. Since their times the earliest was a concrete arch of 31' span, built by John C. Goodrich in 1871, in Prospect Park, Brooklyn, known as the Cleftridge Bridge. Reinforced concrete was first used by Monier in 1876. The first reinforced concrete bridge in the United States was built according to the Ransome system, in 1889, at Golden Gate Park, San Francisco. Span 20'. EVOLUTION OF TYPES IN THE UNITED STATES. The first known patent for a bridge was granted to Chas. W. Prale, Jan. 2, 1797. Patents were also granted to Timothy Palmer, Dec. 17, 1797 to Thomas Pope, April 18, 1807 ; to lyouis Wernwag, and several others; but the Patent Office records were burned in 1836 and could not be restored. The first patent for a truss bridge was granted to Theodore Burr, in 1817. The designs consisted of trusses reinforced with wood arches. Three noted names connected with early bridge building in the United States are Theodore Burr, Timothy Palmer and I,ouis Wernwag. Ithiel Towne patented the lattice girder bridge in 1820. I^ong patented his types in 1830 and 1839. The first iron truss bridge was patented in 1833, by Augustus Canfield. The first one built was over the Erie Canal at Frankfort, N. Y., in 1840, by Earl Trumbull. It was a combination of cast iron segments and suspension rods, with an anchored top chord in tension. Wm. Howe patented his type in 1840. Squire Whipple built his first bridge in 1840. It was a bow- string truss with cast iron compression members and wrought iron tension members. He secured a patent on the type April 24, 1841. 178 Thos. W. and Caleb Pratt patented the Pratt truss April 4, 1841. Wendell Bollman's first bridge was built over the Potomac River at Harper's Ferry, in 1852. It was a 124' span. Albert Tfink built a three span bridge over the Monongahela River in 1852. The first pin connected span was built by John W. Murphy in 1859, over a canal at Phillipsburg, N. J. It was a 165' span and was called a "Whipple-Murphy" bridge. The first bridge in which wrought iron was used for both tension and compression members was built by Murphy over the Iehigh River, at Mauchchunk, for the I^ehigh Valley R. R. The first riveted lattice girders were built in 1859 for the New York Central R. R., by Howard Carroll. S. S. Post built the first bridge of his type in 1865, for the Erie R. R., at Washingtonville. In 1874, James B. Hades built the Mississippi River Bridge at St. L,ouis. It consists of three trussed arches, one of 520' and two of 502' span. THE LONGEST BRIDGE STRUCTURES. Congest wooden structure a pile trestle across Iake Pontchar- train, near New Orleans, l,a., 21 miles long. Congest metal structure the Tay Viaduct, Scotland, 10,800 feet long, iron lattice girders. The bridge across the St. I^awrence River at Montreal has a total length of 8,791 feet. Longest masonry structure the I^ion Bridge in China, across an arm of the Yellow Sea, 22,968 feet long, composed of 300 arches. THE HIGHEST BRIDGE STRUCTURES. Name Country Length, Feet Height, Feet St. Giustina Switzerland 197 460 Garabit France 1852 406 Du Viaur France 1508 382 Stoney Creek British Columbia 336 340 Loa Bolivia 800 336 Pecos River United States 2180 328 Gokteik Burmah 2260 320 Kinzna United States 2052 302 179 C8 C3 1 1 2 22 M jf F I I I ca >->,>>->> w 1 F "rt ^ rt E JS * cc a *; CB .75 "S a "S o: rt.^.TJ cd c8 * *^^^JX s? * * * *~2 >>2 g >.>> :d " ** rt ea -^ 2222 ^ *0 ^'y'y "*y 44M ^ *bo')2')2 2 o2 "Si2 2'S)'M r"Hoq-H-N iS25* w-Hs55 ^"o ^cc^^. Q^ ,-1 ^H rt r-H v^XJS CO z _ * c~ . c~ C> O CD CO O> ^ cc CO CO ScOOOCOaSoQ SoOOO ^ "ca CJJ 2 Q or Q UI T3 h h h co E h 09 UJ J Q. o .2 o z u LL 6 5 SU f*.wwi*, ||t|gf 2 "3 o o o d o Ji IS 2 2 "S 2 a] C5OOOQO H o z _J u I t-i *- cfl V fi -5 >_ S FHE LONGEST 1 .3 u | UI O CO ' SOME U. 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D. < a a en cd c ^ M o cd ^^ tl ''^ s. ^ ** ^^il u w.2.5 Z iilli! Z a 2 So 2 * a-g - o^ 181 A V o v il A a &3 * >*. C-w o ca O W ^7i rt iii 1 g fr O-co C CO | 8 f g * 8 E JS c 8**"* *gS g t> ^3 _^_ tt cc CJ ^ w a^l - aj-J >iij^ ji "o 5 5 g'o S Ji i JJ JJ ^"0 a ^> i >" ,-. ^ z^ cd 05 O t; O O O *J cS a g a a a ^-j {-*Q<2 E UJ uWuuuHS 2 & 1 1 X s 5 a 1 -- * 8"1 QtU. c^oo cooo Be _i Ui 11 au- *f OO CD ^ CD CO *1- od TJ^ o eo" oi ' is 1 M .^ c-oooo UJ . J* Q 5 S result of diligent sea at some errors may Id greatly appreciat r notable structures c 5 4J * 3 C B UJ to A ** O fl _l CO d i ^"a S g bo ^ U C V] ti ** ^ bfl g J3 .2 +- a o O O B U i * 5&11 a b M g .2.2 g S^-gia 32 oa^^fc Z UJ i o _J j|!|| Wa& ILl g 'S |||S v bo w -2 .C a > .tJ g^ 3 o E S a -s o .2S g | "I'l K Z S oSg a ^ o N a g^ Z ill* 3 S25 g g 3fi3AS SS!IM>I ^ 'a -2 182 THE OSBORN ENGINEERING CO. (INCORPORATED) OSBORN BUILDING CLEVELAND CONSULTING ENGINEERS CIVII, MECHANICAL ELECTRICAL STRUCTURAL PLANS, SPECIFICATIONS, SUPERINTENDENCE OF CONSTRUCTION BRIDGES, BUILDINGS, MANUFACTURING PLANTS OF ALL KINDS, CONCRETE AND CONCRETE-STEEL CONSTRUCTION, INSPECTION AND TESTS OF MATERIAL. 183 THE OSBORN ENGINEERING CO.'S General Specifications for Highway Bridge Superstructures (1902) Price 25 cents General Specifications for Railroad Bridge Superstructures (1903) Price 25 cents General Specifications for Electric Railway Bridge Superstructures (1903) Price 25 cents Or the three Specifications sent post paid for 60 cents or THI UNIVERSITY IUFORH\, W. R. SMELLIE PRINTING CO. *%4 CLEVELAND, OHIO ETURNTO: CIRCULATION DEPARTMENT 198 Main Stacks )AN PERIOD 1 Home Use 2 3 4 5 6 .L BOOKS MAY BE RECALLED AFTER 7 DAYS. newals and Recharges may be made 4 days prior to the due date, oks may be renewed by calling 642-3405. JE AS STAMPED BELOW. JAN 02 20| RM NO. DD6 UNIVERSITY OF CALIFORNIA, BERKELEY \A 5-02 Berkeley, California 94720-6000 YA 06580 UNIVERSITY OF CALIFORNIA LIBRARY