LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Ctes PROPERTIES OF STEEL SECTIONS A REFERENCE BOOK FOR STRUCTURAL ENGINEERS AND ARCHITECTS INCLUDING TABLES OF MOMENTS OF INERTIA AND RADII OF GYRATION OF BUILT SECTIONS, EXAMPLES OF SECTIONS SELECTED FROM MONUMENTAL STRUC- TURES, UNIT STRESSES, SAFE LOADS FOR COLUMNS, PLATE GIRDER DESIGN, DESIGN IN TIMBER, ETC., WITH ONLY SUFFICIENT TEXT TO EXPLAIN THEIR APPLICATION BY JOHN C. SAMPLE, C.E., M. ARCH. Architectural Engineer, New York NEW YORK McGRAW PUBLISHING COMPANY 114 LIBERTY STREET 1905 COPYRIGHT, 1905 BY THE McGRAW PUBLISHING COMPANY NEW YORK PREFACE THERE is a tendency at the present time to call for designs to be submitted on short notice. Should the design be properly made, it requires rapid and often laborious calculations. It is hoped the designer will be able to select directly from the tables here given such sections as will meet his special requirements, thus saving the energy ordinarily spent in preliminary figuring for more important parts of design. A portion of the material here presented was originally prepared for the author's own use as designer for a structural steel plant. When it was decided to publish the tables additional sections were included. The aim has been to cover the particular field as thoroughly as possible without producing too large a volume. It has not been considered to be within the scope of this book to treat the subjects involved from a theoretical standpoint, only sufficient text being presented to explain the ap- plication of the tables. All values have been calculated and checked independently, and may be relied upon as correct. Sufficient time has been taken in preparing these tables to permit the author to add such sections as are in use. He has aimed to confine himself to those sections which are necessary to good design and such shapes as are carried in stock by most large structural steel plants, it being the desire to avoid unnecessary refinements. Common usage will account for the appearance of some of these sections. Properties of patented sections are omitted. They may be obtained by applying to the manufacturer. Where possible all controverted points have been avoided. There is a diversity of practice as to how much the back to back of angles should exceed the width of the plate for plate girders and columns, the practice being about equally divided between \" and y. The author has used \" for all sections with less than 42" plates, since this is on the safe side for those using %". Where cover plates are not used, it is un- necessary to chip the web plate, and it is seldom necessary to chip where cover plates are used unless it be for very long web plates. It is not intended to recommend any particular set of specifications, or to present a text on design in steel. With the exception of the chapter giving safe loads of col- umns, the material is general and capable of being applied to any specification. The author acknowledges his gratitude to those who have assisted him in pro- ? iv PREFACE viding material for the chapter on Monumental Structures, pages 56 to 66. He will appreciate suggestions tending to add to the value of future editions of the book. Chapters will be revised at intervals determined by the advance in the particular subject. Special acknowledgment is due Mr. H. R. Bradley for carefully checking all the material. CONTENTS PAGE MOMENT OF INERTIA AND RADII OF GYRATION - Explanatory notes and examples of application i TABLE No. i Two angles, unequal legs, long legs outstanding 4 2 " equal legs 6 3 " unequal legs, short legs outstanding 8 4 " "Star Struts," equal legs 10 5 " unequal legs n 6 Four angles, Axis AA, unequal legs, long legs outstanding 12 7 " equal legs 14 8 unequal legs, short legs outstanding 16 9 Axis BB, unequal legs, long legs outstanding .... 17 10 " equal legs 20 11 " " unequal legs, short legs outstanding .... 22 12 Moment of Inertia of one plate, Axis AA 23 13 of one plate, Axis BB 24 14 of two cover plates for angle columns 26 15 " of two cover plates for zee-bar columns .... 28 1 6 Two Angles and one plate, T-shaped section 29 1 7 Four zee-bars and one plate 30 18 Two channels laced, flanges in 31 19 " " flanges outstanding 32 20 (flanges outstanding) and one beam 34 21 " " (flanges in) and one beam 38 22 Three beams, H-section 39 23 Two channels and two cover plates 40 24 " one cover plate 46 25 One channel and one plate 49 26 " and one angle 50 27 Four angles, one plate, and one channel 51 VALUES OF COLUMNS FROM LARGE BUILDINGS 28 List and properties of sections 54 Columns having one web plate 56 two web plates 57 three web plates 58 Miscellaneous types 59 vi CONTENTS PAGE VALUES OF TOP CHORDS FROM LARGE BRIDGES TABLE No. 29 List and properties of sections 55 Laced top and bottom, two webs 61 " three webs 62 " " four webs 63 Cover plate on top, two webs 63 four webs 64 Miscellaneous types 66 UNIT STRAINS - Strains under dynamic loads 67 Unit strains in compression members 68 Summary of compression formulae 70 30 Values from compression formulae, reduced to 16,000 base unit . . 72 Curves derived from compression formulae, reduced to 16,000 base unit 73 31 Values corresponding to compression formulae 74 Curves corresponding to compression formulas 75 Railroad bridge, highway bridge, and building specifications ... 76 SAFE LOADS FOR COLUMNS 32 Two angles 78 33 Four angles and an 8-inch plate 80 34 " and a 12-inch plate 81 35 and an i8-inch plate 82 36 and a 24-inch plate 83 .37 Two channels laced 84 STRESS DUE TO WEIGHT OF SECTION - 38 Extreme fiber stress due to weight of angles 86 39 AREA OF ONE PLATE 87 40 AREA IN SQUARE INCHES DEDUCTED FOR ONE HOLE 90 NET AREA OF ONE ANGLE 41 Deducting one, two, and three f-inch holes 91 42 " |-inch holes 92 43 " " " i-inch holes 93 NET VALUES OF SECTIONS 44 Net values of beams 94 45 " " channels 95 46 " " cover plates for beams and channels 96 CONTENTS VU PAGE PLATE GIRDERS Graphics in design of plate girders 97 Three examples illustrating application of tables 99 Resistance of web plate to bending stress 100 TABLE No 47 Moment of inertia of one web plate for plate girders 102 48 " " of four angles deducting one hole 103 49 " " " two holes 104 50 . " " " " three holes 105 51 " " of two cover plates, deducting two holes . . . 106 TIMBER COLUMNS, BEAMS, AND FLOORING General notes on strength of timber no 52 Safe working stresses for various timbers 113 53 Ultimate breaking stresses for various timbers 114 54 Safe loads for columns 115 55 " (uniformly distributed) for beams i inch thick .... 116 56 (uniformly distributed) for beams of various thickness . 117 57 Safe bending moments for beams in foot-pounds 119 58 Bending moments in foot-pounds for uniform loading 120 59 Thickness of flooring for uniform loading 121 General Notes Governing Tables THE shapes used in the tables throughout are manufactured by the Carnegie Steel Co. as given in the Pocket Companion for 1903. It has been the object to supple- ment the Pocket Companion and not to include any information given in it. The values of all sections except for net values of beams, channels, and cover plates, pages 94-96; net sections of angles, pages 91-93; and plate girders, pages 97-109, are based upon their gross area. Should it be required to use net sections in other cases, due allowance must be made for deductions by rivet holes. The following notation is used throughout : Areas of sections are square inches in cross-section. Weights of sections are pounds per lineal foot. Dimensions are in inches unless noted. L = unsupported or unbraced length in feet. / = unsupported or unbraced length in inches. x = unknown distance in feet to point in question. w = uniform load in pounds per lineal foot of span. W = total load in pounds. P = safe stress in pounds per square inch. B = bending moment in inch pounds. R = extreme fiber stress in pounds per square inch. b = thickness in inches. h = depth in inches. A = total area of cross-section in square inches. I moment of inertia. M r = moment of resistance in inch pounds. r = radius of gyration in inches. e = distance in inches of extreme fiber from neutral axis. b. to b. = back to back in inches. C = coefficient of strength for fiber stress of 16,000 pounds per square inch. 5 = section modulus. 5 and C are with neutral axis perpendicular to web at center. ix MOMENTS OF INERTIA AND RADII OF GYRATION OF COLUMNS AND STRUTS THE values of all sections in this chapter are based on the gross sections, no deduc- tions being made for rivet holes. Bending produces tension in one side of a column and increases the compression in the other, but the tension is only sufficient to reduce the compression, or in rare cases to produce a slight tension. Should such a case be possible that tension determines the section, where the member has a strut action it would be necessary to use the net values of the section. A column of such proportions should be selected as to be of nearly the same strength about both axes for the particular loading and bracing. Such relative values of /, r, and / should be examined as will show the column weakest. The application of the tables of Moments of Inertia and Radii of Gyration is shown by the following examples. The sections will be determined in accordance with the requirements of the New York Building Law. The allowable strain in pounds per square inch for compression members, P = 15,200 58 - . The ratio of - must not exceed 120. r In each example the unsupported length about both axes is 20 feet. To this maximum ratio of - = 120, corresponds the minimum value of r = = r 120 = 2.0. The minimum value of r may therefore be determined for this 1 20 ratio of - by pointing off one decimal place in the value of / in feet. By examination of the tables it is seen that a large number of sections have a value of r equal to or greater than 2.0 The sections used in the examples have values of r much greater than 2.0, and it is important to select such sections as will give the greatest value of r for a given area, provided the requirements or conditions will permit the use of such a section. Let A required area of column in square inches. W = total direct load in pounds. B = bending moment in inch pounds. P = safe load in pounds per square inch. e = distance in inches from the neutral axis to the ' extreme fiber on the side in which the bending produces compression. MOMENTS OF INERTIA AND RADII OF GYRATION The values of compound sections may be found by combining the values of ele- mentary parts. This is illustrated by a column shown in the accompanying figure, the values of which are tabulated below. The column is composed of four angles 6 X 4 X f > l8 i" b - to b., l n g kg 8 outstanding, an 18" X " web plate, and two 14" X i" cover plates. SECTION. AREA. TABLE. I ABOUT Axis AA. TABLE. I ABOUT Axis BB. 4 LL 6x4 x| i PL i8"Xi" 2 Pis. I4"X|" 23-44 Q.OO 17.50 6 12 13 206.13 .19 285.84 9 *3 14 1,566.08 243.00 *559- a 3 Totals 49-94 492.16 3.368-31 v/'- / 492.16 J 3368.31 Q n -\ A 3- I 4 49.94 V 49.94 The safe direct load for this column according to the New York Building Law for an unbraced length of 20 feet is W / l\ I 2 4 0\ = A 15,200 - 58-] = 49-94 i5. 200 - 5 8 ) = 5377 pounds. V r ) \ 3- I 4/ General form of Example i. This form is for direct loading only, i.e. the loading is balanced about any horizontal axis through the center of gravity of the column. This is a general case and applicable to all sections. The form becomes W W 15,200 50 - General form of Example 2. This form is for combined direct load with eccentric loading or bending. This is a general case and is applicable to all sections. The form becomes MOMENTS OF INERTIA AND RADII OF GYRATION W l Be A = Example i. Required a channel column capable of carrying a direct or balanced load of 230,000 pounds. To obtain the approximate area required, assume an allow- able strain of 12,000 pounds per square inch. 230,000 -^- 11,000 = 19.2 square inches. From the table 23 the area of two 10* 15-pound channels and two 12" x 1* plates = 20.92 ; the least r = 3.68. Applying the general form, W 230.000 230,000 A = _ . = _ - = ^ - = 20.2. / 240 11,400 15,200 58 - 15,200 58 r 3.68 The section assumed has an excessive area of .72 square inch, and is capable of being reduced by approximately that amount. Example 2. Required a channel column capable of carrying a balanced load of 200,000 pounds, and having in addition a bending of 120,000 inch pounds. To ob- tain the approximate area required, assume an allowable extreme fiber strain of 10,000 pounds per square inch for the direct load. 200,000 -j- 10,000 = 20.0 square inches. From the table 23 the area of two 10* 15-pound channels and two 12" x \" plates = 20.92 ; the least r = 3.68. Turn the column so it will most effectively resist the bending, by placing the axis AA parallel to the plane of bending force. The value of I about the axis AA = 464.8. Applying the general form, W 100,000 200,000 / A Be ( 2 4 o\ (^5,200- 58 -J- y ^5,200-58 j- 120,000 x 5-5 10,000 464.8 square inches required. The section assumed has an excessive area of .92 square inch and is capable of being reduced by approximately that amount. * NOTE : It will be seen by referring to the table of specifications under the chapter on Unit Strains that the practice varies ; some add the total extreme fiber stress due to bending, while others add | of the extreme fiber stress, to the direct stress. 3 TABLE 1 TWO ANGLES, UNEQUAL LEGS, SIZE. TOTAL SECTION. Axis BB. Axis AA. o" b. to b. f" b. to b. T y b. to b. Weight Area. I r I r I r I r 7X3ix f 49-8 14.62 12. l6 .91 i7 2 -34 3-43 187.21 3-58 189.79 3.60 *% 46.0 13.50 11.38 .92 158.20 3-42 171.84 3-57 174.20 3-59 x I 42.0 12.34 10.56 93 143.22 3-4i 155-55 3-55 !57- 6 9 3-57 x& 38.0 II. 18 9.72 93 129.06 3-40 140.14 3-54 142.06 3-56 x \ 34-0 10.00 8.82 94 114.83 3-39 124.67 3-53 126.38 3-55 x& 30.0 8.80 7.90 95 IOO.I2 3-37 108.68 3-5 1 110.17 3-54 o" b. to b. i" b. to b. T y b. to b. 6x 4 x i 47-2 13.88 *7-36 1. 12 109.07 2.80 116.50 2.90 118.43 2.92 xtt 43-6 12.82 16.22 J -I3 100.04 2-79 106.85 2.89 108.61 2.91 x I 40.0 11.72 15.04 -I3 90.44 2.78 96.57 2.87 98.16 2.89 x& 36.2 10.62 13.82 I.I4 81.43 2.77 86.93 2.86 88.36 2.88 x i 32.4 9.50 12.54 I-I5 72.42 2.76 77-30 2.85 78-56 2.88 x^ 28.6 8.36 1 1. 20 1.16 63.04 2-75 67.26 2.84 68.36 2.86 X f 24.6 7.22 9.80 1.17 54-n 2.74 57-73 2.83 58.67 2.85 5X3ix f 33-6 9.84 9.66 99 5 2 -5 2.31 56-83 2.40 57-96 2-43 x& 30.4 8.94 8.90 1. 00 47.29 2.30 5!-i9 2-39 52.20 2.42 x * 27.2 8.00 8.10 I.OI 42.02 2.29 45-47 2.38 46.37 2.41 x^ 24.0 7.06 7.26 1. 01 36-56 2.28 39-54 2-37 40.33 2-39 x I 20.8 6.10 6.36 1. 02 3 J -37 2.27 33-92 2.36 34-59 2.38 X& 17.4 5.12 5-44 1.03 26.14 2.26 28.26 2-35 28.81 2-37 4X3X& 24.6 7.24 5-32 .86 24.29 1.83 26.85 I -93 27-53 J -95 x * 22.2 6.50 4.84 .86 21.60 1.82 23.86 1.92 24.46 1.94 x& IQ.6 5-74 4-3 6 .87 18.74 1.81 20.70 1.90 21.21 1.92 x f 17.0 4.96 3-84 .88 16.05 i. 80 17.71 1.89 18.15 1.91 x& 14.2 4.18 3-30 .89 13.40 1.79 14.78 1.88 IS.I4 1.90 3X2JX \ 17.0 5.00 2.60 .72 9.16 I 3S 10.49 i-45 IO.84 1.47 x& 15.2 4.44 2.36 73 8.02 i-34 9.18 1.44 9-49 1.46 x I 13.2 3.84 2.08 74 6.86 i-34 7.84 i-43 8.10 1.45 x& II.O 3.24 i. 80 74 5- 6 4 1.32 6-45 1.41 6.66 i-43 x i Q.O 2.62 1.48 75 4-5 1 i-3i 5-i5 1.40 5-32 1.42 2$X2X f 10.6 3.10 1.02 58 3-96 *-*3 4-65 1.22 4.84 1.25 x& 9.0 2.62 .90 58 3-3 1. 12 3-87 1.22 4.03- 1.24 x t 7-4 2.12 74 59 2.62 I. II 3-07 1. 2O 3.20 1.23 x& 5-6 1.62 58 .60 1.96 1. 10 2.29 I.I9 2.38 1. 21 (4) UNIVERSITY I TABLE 1 (Continued} LONG LEGS OUTSTANDING Axis AA. V b. to b. f" b. to b. f ' b. to b. I" b. to b. i b. to b. I r I r I r I r i r 192.40 3.63 197.71 3-68 203.12 3-73 208.65 3-78 214.30 3-83 1 76.59 3-62 181.46 3-67 186.42 3-72 191.50 3-77 196.68 3-82 159-85 3-60 164.25 3-65 168.74 3-70 1 73-34 3-75 178.02 3-80 144.01 3-59 J 47-97 3-64 152.01 3-69 156.14 3-74 160.36 3-79 128.10 3-58 131.62 3-63 135-21 3-68 138.88 3-73 142.63 3-78 111.67 3-56 II4-73 3-6i 117.86 3-66 121.05 3-7i 124.32 3-76 |" b. to b. &" b. to b. \" b. to b. I" b. to b. " b. to b. 120.38 2-95 122.36 2-97 124-37 2-99 128.47 3-04 132.67 3-09 110.40 2-93 112. 21 2.96 114.05 2.98 117.80 3-03 121.65 3-o8 99-77 2.92 ICI.4I 2.94 103.07 2-97 106.45 3-oi 109.93 3-o6 89.80 2.91 91.27 2-93 92.76 2.96 95-8o 3-oo 98-93 3-05 79.84 2.90 81.15 2.92 82.47 2-95 85.16 2-99 87.94 3-04 69.47 2.88 70.60 2.91 7i-75 2-93 74.09 2.98 76.50 3-03 59.62 2.87 60.59 2.90 6i-57 2.92 63-57 2-97 65-63 3.02 59.12 2-45 60.29 2.48 61.48 2.50 63.91 2-55 66.43 2.60 53-24 2-44 54-29 2.46 55-36 2.49 57-55 2-54 59.81 2-59 47-29 2-43 48.22 2.46 49.16 2.48 51.11 2-53 S3-" 2.58 41.12 2.41 4L93 2-44 42.75 2.46 44-44 2.51 46.18 2-56 35-27 2.40 35-96 2-43 36.66 2.45 38.11 2.50 39.60 2-55 29.38 2.40 2 9-95 2.42 30-53 2-44 31-73 2.49 32.97 2-54 28.21 1.97 28.92 2.OO 29.63 2.02 31.11 2.07 32.64 2.12 25.07 1.96 25.69 1.99 26.33 2.OI 27-64 2.06 29.00 2. II 21.74 i-95 22.28 1.97 22.83 1-99 23-96 2.04 25.14 2.O9 18.60 1.94 19.06 1.96 19-53 I. 9 8 20.50 2.03 21.51 2.08 I5-52 J-93 15.90 J -95 16.29 1.97 17.10 2.02 J 7-93 2.07 II. 21 1.50 "59 J-5 2 11.97 1-55" 12.77 1. 60 13.61 1.6 5 9.8l i-49 10.14 i-5i 10.48 1-54 u. 18 i-59 11.91 1.64 8.38 1.48 8.66 1.50 8-94 i-53 9-54 1.58 10.16 1.6 3 6.89 1.46 7.12 1.48 7-35 i-5i 7.84 1.56 8.36 1.61 5-50 i-45 5-68 1.47 5-87 1.50 6.26 i-55 6.67 i. 60 5-03 1.27 5-23 1.30 5-44 1.32 5-87 1-38 6.32 i-43 4.19 1.26 4-35 1.29 4-52 J-3 1 4.88 1-36 5-26 1.42 3-33 1.25 3-46 1.28 3-59 1.30 3-88 i-35 4.18 1.40 2-47 1.24 2-57 1.26 2.67 1.28 2.88 i-33 3- 11 1.38 (5) TABLE 2 TWO ANGLES, SIZE. TOTAL SECTION. Axis BB. Axis AA. o" b. to b. f" b. to b. &" b. to b. Weight. Area. I r i r I r i r 8x8x1 102.0 30.00 177.96 2-44 346.47 3-40 374.i8 3-53 379-01 3-55 xtf 96.0 28.24 168.66 2-44 323.29 3.38 349.06 3-52 353-55 3-54 x 1 QO.O 26.46 159.16 2-45 301-58 338 325-53 3-5 1 329.70 3-53 xH 84.0 24.68 149.42 2.46 279.98 3-37 302.13 3-50 305-99 3-52 x f 77-8 22.88 139.48 2.47 258.42 3-36 278.79 3-49 282.34 3-5 1 x& 71.6 21. 06 129.28 2.48 235-9 3-35 254-41 3-48 257.63 3-5o x f 65.4 19.22 118.84 2-49 214.42 3-34 231.17 3-47 234.09 3-49 x& 59-0 17.36 108.18 2.50 192.97 3-33 207.97 3-46 210.58 3-48 x I 52.8 15.50 97.26 2-50 171.60 3-33 184.87 3-45 187.19 3-48 6x6x f 57-4 16.88 56-30 1.83 109.78 2-55 121.64 2.68 I2 3-73 2.71 x& 53-0 15.56 52-38 1-83 100.03 2-54 110.79 2.67 112.69 2.69 x I 48.4 14.22 48.32 1.84 90.88 2-53 100.60 2.66 102.32 2.68 x& 43-8 12.86 44-14 1.85 81.74 2.52 90.44 2.65 91.98 2.67 x * 39-2 11.50 39-82 1.86 72.28 2.51 79-93 2.64 81.28 2.66 x& 34-4 IO.I2 35-36 1.87 63-25 2-50 69.90 2.63 71.08 2-65 x f 29.6 8.72 30.78 1.88 54-23 2-49 59-9 2.62 60.91 2.64 o" b. to b. i" b. to b. &" b. to b. 4X4X f 31.4 9.22 13-32 i. 20 27.27 1.72 30-25 1.81 31.04 1.83 x& 28.6 8.36 12.24 1. 21 24.48 1.71 27.14 i. 80 27.84 1.83 x i 25.6 7-50 II. 12 1.22 21.56 1.70 23-89 1.78 24.51 1.81 x& 22.6 6.62 9-94 1.23 18.85 1.69 20.87 1.78 21.41 i. 80 x f 19.6 5.72 8.72 1.23 16.15 1.68 17.87 1.77 18.33 1.79 x& I6. 4 4.80 7.42 1.24 13-44 1.67 14.86 1.76 15.24 1.78 3X3X \ 18.8 5.50 4-44 .90 9.20 1.29 10.56 I -39 10.93 1.41 x& 16.6 4.86 3-98 .91 8.00 1.28 9.19 I -37 9-5 1 1.40 x f 14.4 4.22 3-52 .91 6.86 1.28 7.87 J-37 8.14 !-39 x& 12.2 3.56 3-02 .92 5-7i 1.27 6-54 1.36 6-77 1.38 x i 9.8 2.88 2.48 93 4-51 1.25 5-i6 i-34 5-34 1.36 2iX2iX& 13-6 4.00 2.22 74 4-65 i. 08 5-5o 1.17 5-73 1.20 x f n.8 3-46 1.96 75 3-96 1.07 4.67 1.16 4.86 I.I 9 x& 10.0 2.94 1.70 76 3-3i i. 06 3-90 i*S 4.06 1.18 x i 8.2 2.38 1.40 77 2-63 1.05 3.10 1.14 3-23 1.16 x& 6.2 i. 80 1. 10 .78 1.96 1.04 2.30 MJ 2-39 "5 2X2Xfk 8.0 2.30 .84 .60 1.70 .86 2.08 .95 2.19 .98. x* 6.4 1.88 .70 .61 i-35 85 1.66 94 i-75 .96 x& 5-0 1.44 56 .62 1.03 85 1.26 93 1.32 .96 TABLE 2 (Continued*) EQUAL LEGS Axis AA. \" b. to b. f " b. to b. I" b. to b. I" b. to b. i" b. to b. I r I r 1 r I r I r 383-89 3-58 393-83 3.62 404.01 3-67 414.42 3-72 425-07 3.76 358-10 3-56 367-35 3-61 376.82 3-65 386.52 3-/0 396.43 3-75 333-93 3-55 342-53 3.60 35J-34 3- 6 4 360.36 3.69 369-58 3-74 309.90 3-54 317.86 3-59 326.02 3-63 334-37 3.68 342.91 3-73 285-93 3-54 293.26 3.58 300.76 3.63 308.44 3-67 3J6-3I 3-/2 260.91 3-5 2 267.57 3-56 274.40 3 .6l 281.39 3-66 288.55 3-7o 2 37-o5 3-5i 243.08 3.56 249.27 3 .60 255.60 3-65 262.08 3-69 213.24 3-50 218.64 3-55 224.18 3-59 229.86 3-64 235-67 3-68 189.54 3-5 J 94-33 3-54 199.24 3-59 204.27 3-63 209.42 3-68 125.86 2-73 130.21 2.78 134.69 2.82 J 39-30 2.87 144.05 2.92 114.62 2.71 118.57 2.76 122.64 2.81 126.84 2.86 131-15 2.90 104.07 2.71 107.64 2-75 m-33 2.80 ii5-i3 2.85 119.03 2.89 93-54 2.70 96.74 2-74 100.04 2-79 103.45 2.84 106.95 2.88 82.66 2.68 85-48 2-73 88.38 2-77 91.38 2.82 94-47 2.87 72.28 2.67 74-73 2.72 77-27 2.76 79.88 2.81 82.58 2.86 61.93 2.66 64.02 2.71 66.18 2-75 68.41 2.80 70.71 2-85 I" b. to b. T y b. to b. \" b. to b. f " b. to b. I" b. to b. i 31-85 1.86 32.67 1.88 33-52 1.91 35-26 1.96 37-07 2.01 28.57 1.85 29.30 1.87 30.06 1.90 31.62 i-94 33-24 1-99 25-15 1.83 2 5.79 1.85 26.46 1.88 27.83 !-93 29.26 1-97 21.96 1.82 22.52 1.84 23.10 1.87 24.29 1.92 25-54 I. 9 6 18.80 1.81 19.28 1.84 19.77 1.86 20.79 1.91 21.85 J -95 J 5- 6 3 i 80 16.02 1.83 16.43 1.85 17.27 1.90 18.15 1.94 11.31 i-43 11.70 1.46 12.10 1.48 12.93 J -53 13.81 1.58 9-83 1.42 10.17 i-45 10.52 i-47 11.24 1.52 I2.0O 1-57 8.42 1.41 8.71 1.44 9-00 1.46 9.62 *-5 x 10.27 1.56 7.00 1.40 7.24 i-43 7-49 i-45 8.00 1.50 8-54 !-55 5-5 2 1.38 5-7 1 1.41 5-90 i-43 6.31 1.48 6-73 1-53 5-96 1.22 6.21 J - 2 5 6.46 1.27 6-99 1.32 7-56 J -37 5-07 1. 21 5-27 1.23 5-49 1.26 5-94 i-3i 6.42 1.36 4-23 1.20 4.40 1.22 4-58 1.25 4.96 1.30 5-36 i-35 3-36 I.I 9 3-50 1. 21 3- 6 4 1.24 3-94 1.29 4-25 i-34 2-49 1.18 2-59 1.20 2.69 1.22 2.91 1.27 3-14 1.32 2.30 I.OO 2.42 ' 1-03 2-54 1.05 2.80 I.IO 3-07 1.16 1.84 99 !-93 1. 01 2.03 1.04 2-23 1.09 2-45 1.14 !-39 .98 1.46 I.OI !-53 1.03 1.68 i. 08 1.85 I-!3 (7) TABLE 3 TWO ANGLES, UNEQUAL SIZE. TOTAL SECTION. Axis BB. Axis AA. o" b. to b. i" b. to b. T y b. to b. Weight Area. I r I r i r i r 7X3^X f 49-8 14.62 71.98 2.22 23-23 1.26 28.51 1.40 29.49 1.42 x& 46.0 13.50 66.94 2.2 3 21.13 1.25 25.91 !-39 26.80 1.41 x f 42.0 12.34 61.72 2.24 18.86 1-24 23.09 J -37 23-87 i-39 x& 38.0 ii. 18 56.36 2.25 16.88 1.23 20.62 1.36 21.32 1.38 x i 34-0 10.00 50.82 2.25 14.90 1.22 18.18 i-35 18.79 1-37 x^ 30.0 8.80 45-12 2.26 12.85 1. 21 J 5-63 r -33 16.16 J -35 o" b. to b. \" b. to b. - t V' b. to b. 6x 4 x | 47-2 13.88 49.02 1.88 33-55 !-55 37-5i 1.64 38.57 1.67 xH 43-6 12.82 45-64 1.89 30.62 i-55 34-22 1.63 35-18 1.66 x 40.0 11.72 42.14 1.90 27.47 J -53 30.67 1.62 3 r -53 1.64 x& 36.2 10.62 38.52 1.90 24.65 1.52 27.50 1.61 28.26 1.63 x i 32.4 9.50 34.80 1.91 21.85 1.52 2 4-35 i. 60 25.02 1.62 xA 28.6 8.36 30.92 1.92 18.90 1.50 21.04 J -59 21.62 1.61 x I 24.6 7.22 26.94 i-93 16.18 1.50 17.99 1-58 18.48 i. 60 5X3^x f 33.6 9.84 24.06 1.56 18.54 !-37 21.03 1.46 21.70 i-49 x& 30.4 8.94 22.06 i-57 16.63 1.36 18.85 i-45 J 9-45 i-47 x i 27.2 8.00 19.98 1.58 14.72 1.36 16.67 1.44 17.19 1.47 x^ 24.0 7.06 17.80 i-59 12.73 i-34 J 4-39 i-43 14.84 i-45 x f 20.8 6.10 15-56 i. 60 10.87 i-34 12.28 1.42 12.66 i-44 x& 17.4 5.12 13.20 1.61 9-05 !-33 IO.2I 1.41 10.52 1-43 4X3X& 24.6 7.24 II. IO 1.24 io-55 1. 21 12. 2O 1-30 12.65 1.32 x i 22.2 6.50 IO.IO 1.25 9-3 2 1.20 10.77 1.29 ii. 16 J-3 1 x^ IQ.6 5.74 9.04 1.25 8.03 1.18 9.27 1.27 9.61 1.29 x I 17.0 4.96 7.92 1.26 6.86 1.18 7.90 1.26 8.19 1.28 x& 14.2 4.18 6.76 1.27 5-7i 1.17 6-57 1-25 6.81 1.28 3X2^X 1 17.0 5.00 4.16 .91 5-4i 1.04 6-43 LI3 6.71 1.16 x& I5.2 4.44 3-76 .92 4-73 1.03 5-6i 1. 12 5-85 *"*S x f 13.2 3.84 3-32 93 4.02 1.02 4.76 I. II 4.96 1.14 xA II.O 3-24 2.84 94 3-30 I.OI 3-9 1. 10 4.07 1. 12 x 1 9.0 2.62 2-34 95 2.62 1. 00 3-09 1.0 9 3-23 I. II 2^X2X | 10.6 3.10 1.82 77 2.06 .82 2.56 .91 2.70 93 x& 9.0 2.62 1.58 .78 1.72 .8l 2.13 .90 2.24 93 x i 7-4 2.12 1.30 .78 1.36 .80 1.68 .89 1.77 .91 x& 5-6 1.62 i. 02 79 I. CO 79 1.23 -87 1.30 .90 (8) TABLE 3 (Continued} LEGS, SHORT LEGS OUTSTANDING Axis AA. i" b. to b. " b. to b. \" b. to b. I" b. to b. i" b. to b. I r I r I r I r I r 3o-5 1.44 32.60 i-49 34.82 i-54 37.I5 i-59 39.60 i-55 27.72 i-43 29.62 1.48 31.64 i-53 33-76 1.58 35-98 1.63 24.69 1.41 26.39 1.46 28.18 i-5i 30.07 1-56 32.06 1.61 22.05 1.40 2 3-56 i-45 25.16 1.50 26.84 i-55 28.61 I.OO iQ-43 !-39 20.76 1.44 22.16 i-49 23-64 i-54 25.20 i-59 16.70 1-38 17-83 1.42 19.04 1.47 20.31 1.52 21.65 i-57 I" b. to b. A" t>- to b. i" b. to b. f " b. to b. f " b. to b. 39-66 1.69 40.77 1.71 41.91 1.74 44-27 1.79 46.74 1.84 36.17 1.68 37-iS 1.70 38.22 J-73 40-37 1.77 42.62 1.82 32.41 1.66 33-3i 1.69 34-24 1.71 36-16 1.76 38.18 1.80 29.05 1.65 29.85 1.68 30.68 1.70 32-39 i-75 34-19 1.79 25-7I 1.65 26.42 1.67 27-15 1.69 28.66 1.74 30.24 1.78 22.21 1.63 22.82 1-65 23-44 1.67 24.74 1.72 26.10 1.77 18.98 1.62 19.49 1.64 20.02 1.67 21-13 1.71 22.28 1.76 22.39 i-5i 23.10 *-53 23.83 1.56 25-34 1.60 26.94 1.65 20.06 1.50 20.70 1.52 21-35 i-55 22.70 i-59 24.12 1.64 17-74 1.49 18.29 i-5i 18.86 i-54 20.06 1.58 21.31 1-63 I 5-3 1.47 15-78 1.50 16.27 1.52 17.30 i-57 18.38 1.61 13-05 1.46 13.46 i-49 13.88 i-5i 14.75 . i-55 15.66 1.60 10.85 1.46 ii. 18 1.48 11.52 1.50 12.24 i-55 13.00 i-59 13.11 i-35 J 3-59 i-37 14.08 !-39 15.10 1.44 16.18 1.50 "57 i-33 11.99 1.36 12.42 1.38 I 3-3 2 i-43 14.28 1.48 9.96 1.32 10.32 i-34 10.69 1.36 11.46 1.41 12.28 1.46 8.48 -3 8-79 i-33 9.10 r -35 9.76 1.40 10.46 i-45 7-05 1.30 7-30 1.32 7-56 i-35 8.ii i-39 8.68 1.44 6-99 1.18 7.29 1. 21 7.60 1.23 8.24 1.28 8-93 i-34 6.10 1.17 6.36 1.20 6.62 1.22 7.19 1.27 7-78 1.32 5-i7 1.16 5-39 1.18 5-62 1. 21 6.09 1.26 6.60 i-3i 4.24 1.14 4-42 1.17 4.60 I.I 9 4-99 1.24 5-4i 1.29 3-36 i-i3 3-5o 1.16 3-65 1.18 3.96 1.23 4-29 1.28 2.85 .96 3.00 .98 3-i6 I.OI 3-49 '1.06 3-85 i. ii 2.36 95 2-49 97 2.62 I.OO 2.89 1.05 3-!9 1. 10 1.86 94 1.96 .96 2.06 99 2.28 1.04 2-5 1 1.09 x -37 .92 1.44 94 1.52 97 1.68 1.02 1.85 1.07 (9) TABLE 4 STAR STRUTS TWO ANGLES, EQUAL LEGS SIZE. TOTAL SECTION. Axis CC. Axis AA. Weight. Area. I r 8x8x1 102.0 30.00 282.50 3-7 x|| 96.0 28.24 268.02 3.08 x I 90.0 26.46 253-I4 3-9 XT! 84.0 24.68 237.87 3.10 For I and r about axis AA, see x f 77-8 22.88 222.2O 3.12 Table 2. XT$ 71.6 21. 06 206.12 3- J 3 x| 65.4 19.22 189.61 3-i4 x& 59-0 17.36 172.69 3.15 x * 52.8 15.50 I55-32 3-17 6x6x f 57-4 1 6.88 89.39 2.30 XTS 53-0 15.56 83-25 2.31 x f 48.4 14.22 76.89 2-33 X& 43-8 12.86 70.31 2-34 x * 39-2 11.50 63-49 2-35 XTS 34-4 10.12 56.44 2.36 x I 29.6 8.72 49.14 2-37 4X4X | 3L4 9.22 2I.O4 r . 5 , X& 28.6 8.36 19.40 1.52 x i 25-6 7.50 17.66 1.53 X T5 22.6 6.62 15.82 1.55 x I 19.6 5.72 13.89 1.56 x& 16.4 4.80 11.85 ^57 3X3X i 18.8 5.50 6-99 1.13 XTS 16.6 4.86 6.31 1.14 X | 14.4 4.22 5-59 1.15 Xfk 12.2 3.56 4.81 1.16 x 1 9.8 2.88 3-97 1.17 21X2JX& 13.6 4.00 3-49 93 x I u.8 3-46 3.11 95 x& 10.0 2-94 2.69 .96 x i 8.2 2.38 2.24 97 x& 6.2 i. 80 1.74 .98 2X2X& 8.0 2.30 1.32 .76 x i 6.4 1.88 1. 10 77 X* 5-0 1.44 .87 .78 (10) 4- ! \ TABLE 5 STAR STRUTS TWO ANGLES, UNEQUAL LEGS TOTAL SECTION. Axis CC. SIZE. AXES AA AND BB. Weight. Area. I r 6x 4 x f 40.0 11.72 48.97 2.04 x& 36.2 10.62 44.85 2.o6 X J 32.4 9-50 40-57 2.07 xA 28.6 8.36 36.13 2.08 x I 2 4 .6 7.22 3L52 2.09 For I and r about axis AA, see 4X3X \ 22.2 6.50 12.32 1.38 Table 3. x IQ.6 5-74 11.07 1-39 xf 17.0 4.96 9-74 1.40 For I and r about axis BB, see x& 14.2 4 .l8 8-33 I.4I Table i. 3X2JX& 15-2 4.44 4.90 1.0 5 x| 13.2 3.84 4-35 1. 06 x& II.O 3-24 3-75 1. 08 y 1 Q.O 2.62 3.10 1.00 (II) TABLE 6 , L. J r T UNEQUAL LEGS, Axis AA. SIZE. f " b. to b. A" b. to b. \" b. to b. Weight. Area. I r I r I r 7X3*X f 9Q.6 29.24 374-43 3-58 379-59 3.60 384.81 3-63 xH 92.0 27.00 343-67 3-57 348.40 3-59 353-19 3.62 x I 84.0 24.68 311.10 3-55 3I5-38 3-57 3J9-7 1 3-60 x& 76.0 22.36 280.28 3-54 284.13 3-56 288.02 3-59 x i 68.0 2O.OO 249.34 3-53 252-75 3-55 256.21 3-58 x& 60.0 17.60 217.36 3-5i 220.33 3-54 223-34 3-56 i" b. to b. T y b. to b. f " b. to b. 6X4X 94.4 27.76 233.01 2.90 236.86 2.92 240.77 2-95 xft 87.2 25.64 213.69 2.89 217.22 2.91 220.79 2-93 x I 80.0 23-44 I93-J4 2.87 196.31 2.89 J 99-54 2.92 x& 72.4 21.24 173.86 2.86 176.71 2.88 179.61 2.91 x i 64.8 19.00 . 154-59 2.85 157.12 2.88 159.69 2.90 x^ 57-2 16.72 134-53 2.84 136.72 2.86 i3 8 -95 2.88 x I 49.2 14.44 115.46 2.83 H7-33 2.85 119.24 2.87 5X3ix | 67.2 19.68 113.67 2.40 "5-93 2-43 118.23 2-45 x& 60.8 17.88 102.37 2 -39 104.41 2.42 106.48 2.44 x i 54-4 16.00 90.94 2.38 92.74 2.41 94-57 2-43 x^ 48.0 14.12 79.09 2-37 80.65 2-39 82.24 2.41 x I 41.6 12.20 67.84 2.36 69.18 2.38 7-54 2.40 x& 34-8 10.24 5 6 -5 2 2-35 57-63 2-37 58.75 2.40 4X3X& 49.2 14.48 53-7 i-93 55-5 !-95 56.43 1.97 x 1 44.4 13.00 47.72 1.92 48.92 i-94 50.14 1.96 x^ 39-2 11.48 4i-39 1.90 42.42 1.92 43-48 !-95 x f 34-0 9.92 35-42 1.89 36-30 1.91 37.20 1.94 x& 28.4 8.36 29.56 1.88 30.29 1.90 31.04 1-93 3X2^X i 34-0 IO.OO 20.98 i-45 21.69 1.47 22.42 1.50 x& 30.4 8.88 18.36 1.44 18.98 1.46 19.62 1.49 x I 26.4 7.68 15.68 i-43 16.21 i-45 l6 -75 1.48 x& 22. 6.48 12.89 1.41 J 3-33 i-43 J 3-77 1.46 x i 18.0 5-24 10.29 1.40 10.64 1.42 10.99 i-45 2^X2X | 21.2 6.20 9.29 1.22 9.67 1-25 10.06 1.27 x& 18.0 5.24 7-74 1.22 8.05 1.24 8-37 1.26 x i 14.8 4.24 6.15 1. 2O 6.40 1.23 6.65 1.25 x& II. 2 3.24 4-58 I.I 9 4-76 1. 21 4-95 1.24 (12) TABLE 6 {Continued) ANGLES, LACED LONG LEGS OUTSTANDING Axis AA. f " b. to b. i" b. to b. I" b. to b. i" b. to b. I r I r I r I r 395-41 3 .68 406.24 3-73 417-30 3-78 428.59 3-83 362.91 3-67 372-85 3-72 382.99 3-77 393-35 3.82 328.50 3-65 337-49 3-7 346.67 3-75 356-05 3-80 295.94 3- 6 4 304.02 3-69 312.29 3-74 320.72 3-79 263.24 3-63 270.42 3-68 277.76 3-73 285.26 3-78 229.46 3.61 235-7I 3-66 242.11 3-7i 248.64 3-76 A" b. to b. \" b. to b. 'f " b. to b. f " b. to b. 244-73 2-97 248.75 2.99 256.94 3-04 265-35 3-09 224.42 2.96 228.10 2.98 235-60 3-03 243-3 3.08 202.81 2.94 206.13 2-97 212.90 3.01 219.86 3.06 182.55 2 -93 185-53 2.96 191.61 3-oo 197.86 3-05 162.29 2.92 164.93 2-95 170-33 2 -99 I75-87 3-4 141.21 2.91 143-50 2-93 148.19 2.98 i53-oo 3-03 121.17 2.90 123.14 2.92 127.14 2-97 131.27 3-02 120.57 2.48 122.95 2.50 127.83 2-55 132-85 2.60 108.58 2.46 110.72 2.49 115.10' 2-54 119.63 2-59 96-43 2.46 98-33 2.48 102.21 2-53 106.22 2-58 83.86 2.44 85-5i 2.46 88.88 2.51 92-36 2.56 71.92 2-43 73-33 2-45 76.21 2.50 79.19 2-55 59-90 2.42 61.07 2.44 63.46 2-49 65-94 2-54 57.83 2.OO 59-27 2.02 62.22 2.07 65-29 2.12 51-38 1.99 52-65 2.01 55-27 2.06 57-99 2. II 44-5 6 1.97 45-66 1-99 47-93 2.04 50.29 2.09 38.12 I. 9 6 39.06 1.98 41.00 2-03 43.01 2.08 31.80 i-95 32-58 1.97 34-19 2.O2 35-87 2.07 2 3-i7 1.52 2 3-95 i-55 25-55 1. 60 27-23 1.65 20.28 i-5i 20.95 i-54 22.35 i-59 23.82 1.64 I7-3I 1.50 17.88 -53 19.08 1.58 20.33 1.6 3 14.23 1.48 14.70 -S" 15.68 1.56 16.72 1.61 11.36 1.47 "73 1.50 12.51 *5S J 3-33 i. 60 10.46 1.30 10.87 1.32 "73 1.38 12.64 1-43 8.71 1.29 9-5 1-31 9-76 1.36 10.52 1.42 6.91 1.28 7.19 1.30 7-75 i-35 8-35 1.40 5-14 1.26 5-35 1.28 5-77 i-33 6.21 1.38 (13) u r" n" TABLE 7 FOUR EQUAL Axis AA SIZE. TOTAL SECTION. i" b. to b. iV" b. to b. \" b. to b. Weight. Area. I r I r I r 8x8x1 204.0 6O.OO 748.37 3-53 758.oi 3-55 767.78 3-58 xtf 192.0 56.48 698.13 3-52 707.10 3-54 716.19 3-56 x I iSo.O 52.92 651-05 3-5 1 659.40 3-53 667.85 3-55 xif 168.0 49.36 604.26 3-5o 611.98 3-52 619.80 3-54 x 1 155.6 45.76 557-57 3-49 564.67 3.51 57I-87 3-54 xft 143.2 42.12 508.81 3-48 515-27 3-5 521.81 3-52 x f 130.8 38.44 462.33 3-47 468.18 3-49 474.10 3.51 x^ 118.0 34.72 4I5-93 3-46 421.17 3-48 426.47 3-5 x * 105.6 31.00 369-75 3-45 374-38 3-48 379.08 3-5 6x6x | 114.8 33.76 243.28 2.68 247.47 2.71 251.72 2-73 xft 106.0 3LI2 221.58 2.67 225.38 2.69 229.24 2.71 x f 96.8 28.44 201.21 2.66 204.64 2.68 208.14 2.71 x& 87.6 25.72 180.88 2.65 183.96 2.67 187.09 2.70 x 1 78.4 23.00 I59-85 2.64 162.56 2.66 165-31 2.68 Xik 68.8 20.24 139.80 2.63 142.16 2.65 144.56 2.67 x 1 59-2 17.44 119.80 2.62 121.81 2.64 123.86 2.66 $" b. to b. T y b. to b. |" b. to b. 4X4X f 62.8 18.44 60.50 1.81 62.08 1.83 63-69 1.86 x& 57-2 16.72 54.28 1.80 55.69 1.83 57-13 1.85 x i 51-2 15.00 47-79 1.78 49.02 1.81 50.29 1.83 x rV 45.2 13.24 41.74 1.78 42.82 i. 80 43-92 1.82 x f 39.2 11.44 35-75 1.77 36.66 1.79 37.60 r.8i x& 32.8 9.60 29.72 1.76 30.48 1.78 31-25 i. 80 3X3X i 37.6 11.00 21.12 i-39 21.86 1.41 22.62 i-43 X A 33-2 9.72 18.37 i-37 19.01 1.40 19.67 1.42 x f 28.8 8.44 15-73 1.37 16.28 1.39 16.84 1.41 x& 24.4 7.12 13.09 1.36 J3-54 1.38 14.00 1.40 x i 19.6 5.76 10.32 i-34 10.68 1.36 11.04 1.38 2jX2iX^ 27.2 8.00 10.99 1.17 n-45 1.20 n-93 1.22 x f 23.6 6.92 9 : 34 1.16 9-73 I.I9 10.13 1. 21 x& 20.0 5-88 7.80 MS 8.12 1.18 8.46 1.20 x i 16.4 4.76 6. 20 1.14 6-45 1.16 6.72 I.I9 x& I2. 4 3-60 4-59 1-13 4-78 I-I5 4-97 1.18 2X2X& 16.0 4.60 4.16 95 4-38 .98 4.61 I.OO x i 12.8 3.76 3-32 -94 3-49 .96 3-67 99 x& 10.0 2.88 2.51 93 2.64 .96 2-77 .98 (14) ANGLES, LACED LEGS TABLE 7 {Continued} Axis AA. | " b. to b. \" b. to b. I" b. to b. i" b. to b. I r I r i r i r 787.67 3-62 808.02 3-67 828.84 3-7 2 - 850.13 3-76 734-7 3-6i 753-65 3-65 773-03 3-70 792.87 3-75 685.06 3-6o 702.68 3-64 720.71 3-69 739-i6 3-74 635-73 3-59 652.04 3-63 668.74 3-68 685.82 3-73 586.52 3-58 601.52 3-63 616.89 3-67 632.61 3-72 535-M 3.56 548.79 3-6l 562.78 3-66 577-09 3-7o 486.17 3-56 498.53 3-60 511.20 3-65 524-17 3-69 437.28 3-55 448.37 3-59 459-72 3-64 471-35 3-68 388.66 3-54 398.48 3-59 408.53 3-63 418.84 3-68 260.42 2.78 269.38 2.82 278.60 2.87 288.10 2.92 237-M 2.76 245-29 2.81 253-67 2.86 262.31 2.90 215.29 2 -75 222.66 2.80 230.25 2-85 238.07 2.89 !93-49 2.74 20O.09 2 -79 206.89 2.84 213.90 2.88 I70-95 2-73 176.77 2-77 182.77 2.82 188.95 2.87 149.47 2.72 154-54 2.76 J 59-77 2.81 l6 5-i5 2.86 128.05 2.71 *32-37 2-75 136-83 2.80 141-43 2-85 T y b. to b. i" b. to b. |" b. to b. f " b. to b. 65-34 1.88 67.03 1.91 70-51 1.96 74.14 2.01 58.61 1.87 60.12 1.90 63.24 1.94 66.48 1-99 51-59 1.85 52-9 1 1.88 55-65 i-93 58-51 1.97 45-05 1.84 46.20 1.87 48.59 1.92 51.08 1.96 38.56 1.84 39-54 1.86 41.58 1.91 43-7 i-95 32-05 1.83 32.86 1-85 34-54 1.90 36-3 1.94 23.40 1.46 24.20 1.48 25.86 J-53 27.61 1.58 20.34 i-45 21.04 1.47 22.49 1.52 24.01 i-57 17.41 1.44 18.01 1.46 19.24 i-5i ^o-55 1.56 14.48 i-43 14.97 i-45 16.00 1.50 17.08 i-55 11.42 1.41 11.80 1-43 12. 6l 1.48 13.46 i-53 12.42 1-25 12.93 1.27 !3-99 1.32 15.11 !-37 IO -55 1.23 10.98 1.26 u.88 J-3 1 12.83 1-36 8.80 1.22 9.16 1.25 9.91 1.30 10.71 !-35 6-99 1. 21 7.28 1.24 7.87 1.29 8-51 i-34 5-J7 1.20 5-38 1.22 5-82 1.27 6.28 1.32 4.84 1.03 5-o8 1.05 5-59 I.IO 6.14 1.16 3-86 I.OI 4-05 1.04 4.46 1.09 4.90 1.14 2.91 I.OI 3-o6 1.0 3 3-36 i. 08 3-69 1-13 S 2 00 W PQ * M S" t^ t^- O . O <"O ** O VO VO Tf Tt ON Tj- ON M IT) M O ON 00 % od O ON t^ vO u-> ON co ^- ro f*5 * t/i oONvot^fO ONOOl>.vO^Ovorl- 10 Tf ^ PO fj ONOOt^.to O 00 l> vO vo JiL i X X X X X X xxxxxxx xxxxxx ^- HN X (16) TABLE 9 (Continued on pp. 18 and 19) POUR ANGLES, LACED UNEQUAL LEGS, LONG , LEGS OUTSTANDING SIZE. TOTAL SECTION. Axis ED. 7i" b. to b. 8" b. to b. iol" b. to b. Weight. Area. I r I r I r 7X3*x f xH x I x& x * 6x4 x I xft x I x& x * x& x } 5X3}X f x& x * x& x i x& 4x3 x& xi x^ x| xA 3X2JX i x& x I x* x i 9Q.6 92.0 84.0 76.0 68.0 60.0 94.4 87.2 80.0 72.4 64.8 57-2 49.2 67.2 60.8 54-4 48.0 41.6 34-8 49.2 44.4 39-2 34-0 28.4 34-0 30.4 26.4 22.0 18.0 29.24 27.OO 24.68 22.36 20.00 17.60 27.76 25-64 23.44 21.24 19.00 16.72 14.44 19.68 17.88 16.00 14.12 12.20 IO.24 14.48 13.00 11.48 9.92 8.36 10.00 8.88 7.68 6.48 5.24 266.85 249.83 233.00 214.03 194.06 174.20 3.02 3-4 3-07 3-9 3.12 3-!5 334-12 312.35 290.70 266.64 241.42 216.28 3.38 3-40 3-43 3-45 3-47 3-5 1 553-7 1 516.20 478-52 437.70 395-22 352-68 4-35 4-37 4.40 4.42 4-45 4-48 8V' b. to b. io" b. to b. 313-68 293.36 273.12 250.61 227.00 203.38 177.81 3-36 3.38 3-4i 3-43 3-46 3-49 3-5 1 488.93 456.12 423-15 387-30 349-95 312.45 272.51 4.20 4.22 4-25 4.27 4.29 4-32 4-34 7i" b. to b. 8}" b. to b. io". b. to b. 173.61 1 59-99 145-25 130-83 114.62 97-59 2-97 2.99 3.01 3-4 3-07 3-9 217.71 200.32 181.58 163.20 142.77 121.38 3-33 3-35 3-37 3-40 3-42 3-44 362.35 332.45 300.46 268.96 234.64 198.90 4-29 4-3 1 4-33 4.36 4-39 4.41 6" b. to b. 8i" b. to b. ioj" b. to b. 94.04 85.81 77-63 68.20 58-43 2-55 2-57 2.60 2.62 2.64 l6 5-95 150.82 135-64 118.68 101.26 3-39 3-4i 3-44 3-46 3-48 275.27 249.49 223.46 194.96 165.88 4-36 4-38 4.41 4-43 4-45 Si" b. to b. ~8i" b. to b. ioi" b. to b. 45.20 40.95 36.12 3i-37 25-85 2.13 2.15 2.17 2.20 2.22 119.11 107.07 93-73 80.50 65.87 3-45 3-47 3-49 3-52 3-55 196.61 176.25 153-86 I3L63 107.43 4-43 4-45 4-48 4oi 4-53 (17) L r j TABLE 9 {Continued) FOUR ANGLES, UNEQUAL LEGS, LONG Axis BB. SIZE. i2" b. to b. i Si" b. to b. i8" b. to b. 2ii" b. to b. Weight. Area. I r I r I r I r ' 7X3*X f 9Q.6 29.24 831.78 5-33 J 358-54 6.82 2016.88 8.31 2806.80 9.80 xft 92.0 27.00 774-os 5-35 1262.08 6.84 1871.60 8-33 2602.63 9.82 x I 84.0 24.68 715-69 5-39 1164.00 6.87 !7 2 3-37 8.36 2393.81 9-85 x& 76.0 22.36, 6 53-47 5-41 1060.98 6.89 1569.11 8.38 2177.86 9-87 x } 68.0 20.00 589.02 5.43 954-72 6.91 1410.42 8.40 1956.12 9^9 x& 60.0 17.60 524.28 5-46 847.68 6-94 1250.28 8-43 1732.08 9.92 12!" b. tob. 151" b. to b. i8i" b. to b. 2ii" b. to b. 6x 4 x J 94.4 27.76 741.27 5.i7 1223.88 6.64 1831.40 8.12 2563-85 9.61 xft 87.2 25.64 690.21 5.i9 II 37-5 6.66 1700.17 8.14 2378.22 9-63 x.f 80.0 23-44 638.56 5.22 1049.58 6.69 1566.08 8.17 2188.06 9.66 x& 72.4 21.24 583-35 5-24 957.06 6.71 1426.36 8.19 1991.24 9 .68 1 x i 64.8 19.00 526.08 5.26 861.52 6-73 1282.47 8.22 1788.91 9.70 xA 57-2 16.72 468.44 5- 2 9 765.14 6.76 1137.08 8.2 5 1584.25 9-73 x I 49.2 14.44 407.81 5-3i 664.91 6.79 987.00 8.27 1374.06 9-75 i2|" b. to b. i5i" b. to b. i8J" b. to b. 2ii"b..tob. 5 X 3*X | 67.2 19.68 546.36 5-27 896.17 6-75 1334-55 8.23 1861.48 9-73 x& 60.8 17.88 5oo-35 5-29 819.24 6-77 1218.59 8.26 1698.40 9-75 x 1 54-4 16.00 45 I 34 5-3 1 737-66 6.79 1095.98 8.28 1526.30 9-77 x^ 48.0 14.12 402.96 5-34 656.91 6.82 974.40 8. 3 I !355-43 9.80 x f 41.6 12.20 350-9 1 5.36 571.06 6.84 846.10 8-33 1176.05 9.82 x& 34.8 10.24 296.90 5.38 482.29 6.86 7 J 3-77 8-35 991.32 9.84 i2i"b. tob. i Si" t>. to b. i8i" b. to b. 2ii" b. to b. 4x3 x& 49-2 14.48 413-56 5-34 675.28 6.83 1002.17 8-32 1394.21 9.81 x| 44.4 13.00 374-i6 5-36 609.92 6.85 904.17 8-34 1256.93 9-83 x^ 39-2 11.48 334-24 5-40 543-47 6.88 804-35 8-37 1116.89 9.86 x| 34-0 9.92 291.08 5-42 472.47 6.90 698.50 8-39 969.17 9.88 x& 28.4 8.36 247.23 5-44 400.59 6.92 59I-58 8.41 820.18 9.90 12!" b. to b. iSi" b. to b. i8i" b. to b. 3X2}X | 34-0 10.00 294.11 5-42 477.86 6.91 706.61 8.41 x& 30.4 8.88 263.18 5-44 426.88 6-93 630-55 8-43 x f 26.4 7.68 22 9'35 5-46 371-40 6-95 548.00 8-45 x& 22.0 6.48 I95-72 5-50 3*6.15 6-99 465-74 8.48 x i 18.0 5-24 159.46 5.52 257.16 7.01 378.44 8.50 (18) TABLE 9 {Continued) LACED LEGS OUTSTANDING Axis BB. 241" b. to b. 28i" b. to b. 32|" b. to b. 3 6i" b. to b. i r I r i r i r 3728.30 11.29 5161.64 13.29 6828.91 15.28 8730.09 17.28 3455- I 5 11.31 4780.85 I3-3 1 6322.55 X 5-30 8080.25 I7-30 3I75-3 H-34 4390-05 13-34 5802.24 '5-33 7411.87 17-33 2887.24 , 11.36 3989-58 I3-36 5270.81 X 5-3S 6730-92 17-35 2591.82 ! 11.38 3579-42 I3-38 4727-02 '5-37 6034.62 17-37 2293.08 ' 11.41 3164.28 i3-4i 4176.28 15.40 5329-08 17.40 24}" b. to b. 28}" b. to b. 32i" b. to b. 3 6i" b. to b. 3421.22 ii. 10 4758.70 13.09 6318.25 I 5-og 8099.89 17.08 3171-65 II. 12 4409.04 13.11 5851-55 15.11 7499.17 17.10 29J5-52 11.15 4049-55 I3-J4 537i-io !5-i4 6880.16 I7-I3 2651.70 11.17 3680.99 13.16 4880.20 15.16 6249-33 i7-!5 2380.86 11.19 3303- 1 2 13.18 4377-38 15.18 5603.64 17.17 2106.67 11.23 2920.26 13.22 3867.62 15.21 4948-73 17.20 1826.11 11.25 2529.91 13.24 3349-24 15-23 4284.08 17.22 24V b. to b. 28!" t>. to b. 2476.97 11.22 3435-39 13.21 2258.67 11.24 3130-85 13-23 2028.62 11.26 2810.38 !3- 2 5 1709.99 11.29 2491.59 13.28 1560.90 II. 3 I 2159-43 13-30 1314.96 n-33 1818.15 !3-3 2 24i" b. to b. 1851.42 11.31 i668.!8 "33 1481.09 11.36 1284.47 11.38 1066.40 11.40 (19) L- 1 -1 rT" i TABLE 10 FOUR ANGLES, EQUAL SIZE. "OTAL SECTION. Axis BB. i6|" b. to b. 18}" b. to b. 2i}" b. to b. Weight. Area. I r I r I r i r 8x8x i x& x I x x i xft x f x& x i 6x6x xtf x f x& x i x& x i 4X4X | x& x i xA x f x& 3X3X i x& x 1 x& x* 2^X2jX^ x| x& xl x 204.0 192.0 iSo.O 168.0 155-6 143.2 130.8 118.0 105.6 114.8 106.0 96.8 87.6 78.4 68.8 59-2 62.8 57-2 51-2 45-2 39-2 32.8 37-6 33-2 28.8 24.4 19.6 27.2 23.6 20.0 16.4 12.4 60.00 56.48 52.92 49.36 45-76 42.12 38.44 34-72 3I.OO 33.76 3LI2 28.44 25.72 23.00 20.24 17.44 18.44 16.72 15.00 13.24 11.44 9.60 11.00 9-72 8.44 7.12 5.76 8.00 6.92 5-88 4-76 3-60 1 *' 2430.38 2310.06 2179.25 2046.31 1909.89 1774-88 1630.76 1483.00 1332-95 6.36 6.40 6.42 6.44 6.46 6.49 6. 5 I 6-54 6.56 3093.72 2937-45 2768.94 2598.06 2423.00 2249-39 2065.16 1876.57 1685.44 7 .l8 7.21 7-23 7-25 7.28 7-3 1 7-33 7-35 7-37 4444.62 4214.18 39 6 8.37 37J9-77 3465-64 3212.88 2946.78 2674.96 2400.15 8.61 8.64 8.66 8.68 8.70 8-73 8.76 8.78 8.80 i2"b.tob. i Si" b. to b. 1 8}" b. to b. 21}" b. to b. 787.16 734-94 677.68 618.41 559-99 497.14 432.20 4-83 4.86 4.88 4.90 4-93 4.96 4-98 1265.98 1178.89 1084.96 988.15 892-53 790.88 686.26 6.12 6.15 6.18 6. 20 6.23 6.25 6.27 I933-9 2 1797.40 1651.91 1502.42 1354-48 1198.62 1038.64 7-57 7.60 7.62 7.64 7.67 7.70 7.72 2753-78 2555-95 2346.84 2132.43 1919.94 1697.43 1469.50 9-3 9.06 9.08 9.11 9.14 9.16 9.18 8J" b. to b. io" b. to b. 12}" b. to b. 194.82 .179.00 163.61 146.30 128.09 108.89 3- 2 5 3-27 3-3 S-S 2 3-35 3-37 306.39 280.75 255- 6 9 228.03 199.11 168.82 4.08 4.10 4-13 4-15 4.17 4.19 468.48 428.39 389.04 346.26 3Q I -73 255-32 5-4 5.06 5-09 5- 11 5-i4 5.16 . . . 6i"b.tob. 8i" b. to b. ioi" b. to b. 12}" b. to b. 68.09 61.18 54-05 46.37 38.41 2-49 2.51 2-53 2-55 2.58 121.17 108.43 95-37 81.48 67.12 3-32 3-34 3-36 3-38 3-4i 202.46 180.65 158.41 !34-95 110.72 4.29 4-3 1 4-33 4-35 4-38 35-75 272.31 238-34 202.66 165.84 5-27 5-29 5-3 1 5-33 5-37 5i"b.tob. 8}" b. to b. ioi" b. to b. 12$" b. to b. 35-49 3I-32 27.16 22.42 17.48 2. II 2.13 2-15 2.17 2. 2O 93-95 82.28 70.77 57-99 44.68 3-43 3-45 3-47 3-49 3-52 155-47 !35-77 116.46 95.16 73.01 4.41 4-43 4^-45 4-47 4-50 232-99 203.10 I 739 I 141.86 108.54 5-40 5-42 5-44 5.46 5-49 (20) TABLE 10 (Continued) LACED LEGS Axis BB. 2 4 J" b. tO b. 28i" b. to b. 32}" b. to b. 36i" b. to b. I r I r I r i r 6065.52 10.05 8646.72 12.00 11707.92 13-97 15249.12 15-94 5745-07 10.09 8181.61 12.04 11070.00 14.00 14410.23 15-97 5405-94 IO.II 7 6 93-!5 1 2. 06 10403.71 14.02 J3537-63 J 5-99 5o63-59 10.13 7200;88 1 2. 08 9733-05 14.04 12660.10 16.02 4714.20 10.15 6699.27 12. IO 9050.42 14.06 11767.65 16.04 43 6 5-9 2 10.18 6198.14 12.13 8367-32 14.09 10873.46 16.07 4001.38 10.20 5676.60 12.15 7659-33 14.12 9949-59 16.09 3629-59 IO.22 5 J 45-46 12.17 6939.10 14.14 9010.49 1 6. 1 1 3254.35 10.25 4610.29 12.20 6214.23 14.16 8066.17 16.13 24i" b. to b. 28i" b. to b. 32^" b. to b. 361" b. tob. 3725-56 I0.5O 5257-59 12.48 7059-7 14.46 9131.89 16.45 3454-54 10-54 4870.50 12.51 6535-42 14.49 8449.30 16.48 3 l6 9-75 10.56 4466.05 12-53 5989.86 I4-5 1 7741.20 16.50 2878.19 10.58 4052.56 I2 -55 5432-70 14-53 7018.59 16.52 2588.89 10.61 3641.83 12.58 4878.77 14.56 6299.71 l6 -55 2287.33 10.63 32I5-53 12.60 4305.66 J4-59 5557-7 1 l6 -57 1978.83 10.65 2780.02 12.63 3720.74 14.61 4800.97 16.59 i Si" b. to b. 18!" b. to b. 2ii" b. to b. 24}" b. tob. i 780.76 6.51 1176.02 7-99 1654.27 9-47 2215.49 10.96 712.55 6-53 1071.94 8.01 1506.58 9-49 2016.45 10.98 645-3 1 6.56 969.09 8.04 1360.36 9-5 2 1819.14 II.OI 573- 2 6 6.58 859.84 8.06 1206.00 9-54 1611.74 11.03 498.55 6.60 746.86 8.08 1046.64 9-56 J397-9 1 11.05 421.06 6.62 630.01 8.10 882.15 9-59 1177.50 11.07 i Si" b. to b. i8i" b. to b. 5 OI -93 6-75 747-62 8.24 446.25 6.78 663,93 8.27 389.88 6.80 579-40 8.29 330-93 6.82 49!- 2 3 8.31 270.13 6.85 400.33 8-34 (21) o 1 1 3 I Oi w o 5 ...4- ff JL XJ o Btf vO 00 HI Tt- vO ON vo vo t^. r^. t^- r^ VO VO vo VO vo vo ,0 8 vO 00 M co 10 00 O 1 M M ot cs cq w co vO vd vO vo vC5 vO vO xi M CO VO OO O 3- vo ON OO t-~ M ro M 4 v6 10 r- t^.- * ON co vo 00 MO O to ON co XJ V iHHt vO f/j CO vO ON cs co O O \O vo co ON O ON >O 4 OO vO cs vd O vo ^T O vo ON *H co CO M ON t^ CS ^- t-^ CO 4 t>- cvi M ON Tf- f^ 00 O O 00 M t CO O VO HI >o vo > ^ ^T C j C j CO CM ON X> ON M Tj- VO 00 M vO t^~ t^- t~> r^ OO XJ t^ ON O t- 2 s co CM W O 00 X CM w 10 X3 CO ON 00 vo t^ vO M O rf O t> t^ VO Tj- xi CO Tt- 00 ON vo t^ CO CO ON O ON CO H^t N PO h- 1 v6 C>i 9 co 00 f^ t^ t^ .J CO ON VO ^j- o ^L 2 ON M Tf O ON N Tt H (N CN . o t~- N W M ON O co ON M OO VO M CO VO M rtHi ^ VO Tj- CM O O CM 00 ON ON ON 00 vO HI ON t^ vo co HI TT fO CO CI C4 ^- O CO O CN C>l (N ,0 vO 00 ^ * \O ON t^ t^. . oo oo oo XJ N Tt t^ ON M 10 t^ W M M N CO CO CO xi vO 00 O co vo 00 o 6^ 6V ^ ON d\ ON p 6666666 o ON ON ON ON ON ON 4-* CQ XJ IO <* OO O . O O t^ O M CO O W M O 00 00 t^ vO rf u M CO vO 00 O CO CO co co co -^ Tj- XJ o to t^ O N 't CO O t^. t^ OO OO OO OO ON x> ON M co vO 00 O vo vO vO vO vo t^- 4* OO OU OQ CXJ OU OO CO XJ \O O IO N M l^ H* M "- 1 t^ N rt O ci 'O ^ W ^ rth* TJ- cs vo co vQ r^ co CM f^ M vo OO M Tt" M ON 00 vO * CO H rth* 00 co vo M OO O 1^ CO CO CO CM CS O M O ON CO t* vO fN C< M H M W M N XJ h t^- ON co 10 t>> O 00 CO ON ON ON O xi ON HH rf r-- ON CM ^~ +> vO vo vO vO O vO .0 VO N ON O W xi co 00 CO 00 vO O co 00 O . O Tf t~* CN t^ vO vo vo "tf- co M M tH M M xi o h CO O ON H co O M M H t^ t^. J>. CO to 10 10 10 vo vo -M XI *< t^- ON ON 1O M ~^- t^ vO ON vO N CO x> *. oo co vo O w CM r-~ vo CO O !> ON Th vo XJ f^ ON ^ ON t^ t^ H vO O ^f OO r^ r^ MO vO SO *T 1-t* 10 M vo 00 O - VO vo VO H-* N CO t-. 00 O CN t-~ CO ON vo M r^. CO rj- co co co CM CM . t^ O co vo t^ O N n ^ x> o vo O vo M3 vo t^- t~>. CO ON ON ON ON O ^- J X) vO vO Tj- (N O 1> Tf 00 00 O N O ^t vO CO O M fN fN I < O l> Tl- N O 1> t^. \n ro M o\ vo <* O\ JN vd 4 - O N Tj- 1> O O* 00 00 t^ vO V) - O ^ 00 M Tj- VO vo IO Tt" "t CO u N c/3 c ** 1 35 "* H5 "** H5 X X X X X X He* CO X t* ^ H Mioo .jo HN _| e*o X X X X X X 1 .doe jg He. tJg KM ^te X X X X X X PO X IO (22} TABLE 12 MOMENT OF INERTIA OF ONE PLATE ABOUT AXIS AA III J2* THICKNESS OF PLATE IN INCHES. i A 1 A i A i H i H 1 tt i 4 .01 .01 .02 03 .04 .06 .08 .11 .14 .18 .22 .27 33 5 .01 .01 .02 03 5 .07 .10 .14 .18 .22 .28 34 .42 6 .01 .02 3 .04 .06 .09 .12 .16 .21 .27 33 .41 5o 7 .01 .02 3 5 .07 .10 .14 .19 25 31 39 .48 58 8 .01 .02 .04 .06 .08 .12 .16 .22 .28 36 45 55 .67 9 .01 .02 .04 .06 .09 J 3 .18 .24 3 2 .40 50 .62 75 10 .01 03 .04 .07 .10 15 .20 27 35 45 56 .69 83 ii .01 3 05 .08 .11 .16 .22 3 39 49 .61 .76 .92 12 .02 3 5 .08 13 .18 .24 32 .42 54 .67 .82 I.OO 13 .02 03 .06 .09 .14 .19 .26 35 .46 .58 73 .89 i. 08 14 .02 .04 .o5 .10 i5 .21 .28 38 49 63 .78 .96 1.17 15 .02 .04 .07 .10 .16 .22 3 1 .41 53 .67 .84 1.03 1.25 16 .02 .04 .07 .11 i7 .24 33 43 56 72 .89 ' 1. 10 i-33 i7 .02 .04 .07 .12 .18 25 35 .46 .60 .76 95 1.17 1.42 18 .02 05 .08 J 3 .19 2 7 37 49 63 .80 I.OO 1.24 1.50 iQ .02 5 .08 J 3 .20 .28 39 5 1 .67 85 i. 06 1.30 1.58 20 3 5 .09 .14 .21 30 .41 54 .70 .89 1. 12 i-37 1.67 21 3 S .09 15 .22 31 43 57 74 94 I.I7 1.44 i-75 22 3 .06 .10 15 23 33 45 .60 77 .98 1.23 i-5i 1.83 23 3 .06 .10 .16 .24 34 47 . .62 .81 1.03 1.28 1.58 1.92 24 3 .06 .11 *7 25 36 49 65 .84 1.07 i-34 1-65 2.00 25 03 .06 .11 J 7 .26 37 Si .68 .88 1. 12 1.40 1.72 2.08 26 3 .07 .11 .18 2 7 39 53 .70 .91 i.z6 i-45 1.79 2.17 27 .04 .07 .12 .19 .28 .40 55 73 95 1. 21 i-5i 1-85 2.25 28 .04 .07 .12 .20 .29 .42 57 .76 .98 1.25 1.56 1.92 2-33 29 .04 .07 r 3 .20 30 43 59 79 1.02 I. 3 1.62 1.99 2.42 30 .04 .08 !3 .21 3 1 44 .61 .81 1.05 i-34 1.67 2.06 2.50 32 .04 .08 .14 .22 33 47 .65 .87 1. 12 1-43 1.79 2.20 2.67 34 .04 .09 !5 .24 35 5 .69 .92 1.20 1.52 1.90 2 -33 2.83 36 OS .09 .16 25 38 53 73 97 1.27 1.61 2.01 2.47 3.00 38 5 .10 *7 .27 .40 56 77 1.03 i-34 1.70 2.12 2.61 3-i7 40 5 .10 .18 .28 .42 59 .81 i. 08 1.41 1.79 2.23 2-75 3-33 42 OS .11 .18 .29 44 .62 85 1.14 1.48 1.88 2-34 2.88 3-5 44 .06 .11 .19 3 1 .46 65 .90 1.19 i-55 1.97 2.46 3.02 3-67 46 .06 .12 .20 32 .48 .68 94 1.25 1.62 2.06 2-57 3-i6 3-83 48 .06 .12 .21 33 5 7i .98 1.30 1.69 2.15 2.68 3-3 4.00 50 .07 !3 .22 35 52 74 I.O2 i-35 1.76 2.23 2.79 3-43 4.17 54 .07 .14 .24 38 56 .80 1. 10 1.46 1.90 2. 4 ! 3.01 3-7i 4-5 60 .08 15 .26 .42 63 .89 1.22 1.62 2. II 2.68 3-35 4.12 5.00 (23) B L^\DL^IL, 1O B MOMENT OF INERTIA OI ~o c ,; s' s THICKNESS OF PLATE IN INCHES SSc &<~ 4 fV t TV i A f 4 i-33 1.67 2.00 2-33 2.67 3-oo 3-33 5 2.60 3.26 3-9 1 4-56 5-21 5-86 6.51 6 4-5 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 2i-33 24.00 26.67 9 *5-*9 18.98 22.78 26.58 30-38 34-17 37-97 10 20.83 26.04 31-25 36.46 41.67 46.88 52.08 ii 2 7-73 34.66 41-59 48.53 55-46 62.39 69-32 12 36.00 45.00 54-00 63.00 72.00 8 1. oo 90.00 13 45-77 57-2i 68.66 80. 10 9i-54 102.98 114-43 14 57-17 71.46 85-75 100.04 IJ 4-33 128.63 142.92 15 70.31 87.89 105.47 123.05 140.63 158.20 175.78 16 85-33 106.67 128.00 M9-33 170.67 192.00 213.33 17 102.35 127.94 J53-53 179.12 204.71 230.30 255-89 18 121.50 151.88 182.25 212.63 243.00 273-38 303-75 iQ 142.90 178.62 214.34 250.07 285-79 321-52 357-24 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-n 482.34 22 221.83 277.29 332-75 388.21 443-67 499. J 3 554.58 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 3 2 5-52 406.90 488.28 569.66 651.04 732.42 813.80 26 366.17 457-7 1 549-25 640.79 732-33 823.88 915.42 27 410.06 512.58 615.09 717.61 820.13 922.64 1025.16 28 457-33 57I-67 686.00 800.33 914.67 1029.00 JI 43-33 29 508.10 635-13 762.16 889.18 1016.21 1143-23 1270.26 30 562.50 7 3-!3 843-75 984.38 1125.00 1265.63 1406.25 32 682.67 853.33 1024.00 1194.67 !3 6 5-33 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 ii43-i7 1428.96 I7U.75 2000.54 2286.33 2572-13 2857.92 40 1333-33 1666.67 2000.00 2333-33 2666.67 3000.00 3333-33 42 !543-5 1929.38 23I5-25 2701.13 3087.00 3472.88 3858-75 44 1774.67 2218.33 2662.OO 3105.67 3549-33 3993.00 4436.67 46 2027.83 2534.79 3 4L75 3548-7 1 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 54 3280.50 4100.63 4920.75 5740.88 6561.00 738i-i3 8201.25 60 4500.00 5625.00 6750.00 7875-00 9000.00 10125.00 11250.00 (24) TABLE 13 (Continued} ONE PLATE ABOUT AXIS BB THICKNESS OF PLATE IN INCHES. H 1 H i it ; I -h 3-67 4.00 4-33 4.67 5.00 ' 5-33 33 7.16 7.81 8.46 9.11 9-77 10.42 65 12.38 13-50 14.63 15-75 16.88 18.00 "3 19.65 21.44 23.22 25.01 26.80 28.58 1.79 29-33 32.00 34-67 37-33 40.00 42.67 2.67 41.77 45-56 49-36 53-i6 56.95 60.75 3.80 57- 2 9 62.50 67.71 72.92 78.13 83-33 5-2i 76.26 83.19 90.12 97-05 103.98 110.92 6-93 99.00 108.00 117.00 126.00 135-0 144.00 9.00 125.87 *37-3* 148.76 160.20 171.64 183.08 11.44 157.21 171.50 l8 5-79 200.08 214.38 228.67 14.29 193-36 210.94 228.52 246.09 263.67 281.25 17-58 234-67 256.00 277-33 298.67 320.00 341-33 21-33 281.47 307.06 332-65 358-24 383-83 409.42 25-59 334-13 364-5 394.88 425-25 455.63 486.00 30-38 392.96 428.69 464.41 500.14 535-86 57I-58 35-72 458-33 500.00 541-67 583-33 625.00 666.67 41.67. 530-58 578.81 627.05 675.28 723-52 771-75 48.23 610.04 665.50 720.96 776.42 831.88 887-33 55-46 697.07 760.44 823.81 887.18 950-55 1013.92 63-37 792.00 864.00 936.00 1008.00 1080.00 1152.00 72.00 895.18 976.56 1057.94 1139.32 1220.70 1302.08 81.38 1006.96 1098.50 1190.04 1281.58 I 373- I 3 1464.67 9J-54 1127.67 1230.19 J 332.7o 1435.22 1537-73 1640.25 102.52 1257.67 1372.00 1486.33 1600.67 1715.00 1829.33 "4-33 1397.29 I524-3 1 1651.34 1778.36 !905-39 2032.42 127.03 1546.88 1687.50 1828.13 1968.75 2109.38 2250.00 140.63 1877-33 2048.00 2218.67 2389-33 2560.00 | 2730.67 170.67 2251.79 2456.50 2661.21 2865.92 3070.63 | 3275.33 204.71 2673.00 2916.00 3159.00 3402.00 3645.00 3888.00 243.00 3 I 43-7 I 3429.50 3715.29 4001.08 4286.88 4572-67 285-79 3666.67 4000.00 4333-33 ! 4666.67 5000.00 5333-33 333-33 4244.63 4630.50 5016.38 5402.25 5/88.13 6174.00 385.88 4880.33 5324.00 5767-67 6211.33 6655.00 7098.67 443-67 5576.54 6083.50 6590.46 7097.42 7604.38 8111.33 506.96 6336.00 6912.00 7488.00 8064.00 8640.00 9216.00 576.oo 7161.46 7812.50 8463-54 9114.58 9765-63 10416.67 651.04 9021.38 9841.50 10661.63 11481.75 12301.88 13122.00 820.13 12375.00 13500.00 14625.00 15750.00 16875.00 18000.00 1125.00 (25) OQ I? NO NO NO NO NO NO NO II H O q ro HI co co HI 00 00 O ON vo O rt IO CO t^. CS ON t IO rt CO CS M pi co t^. !>. co co r^ u- O rt rt O NO NO HI HI CO CO M ON ON M HI OO NO 10 co cs ts 3 00* PJ VO M M IO t>- NO 6 HI rt ON NO NO ON vo t-- t^ ON rt rt VO CO ON t- vo rt CO CS HI in !>. NO rt CO M 00 CO O t> vo CS CO rt rf i *n CS ON VO CS vo ON VO oho ro O vo O 10 NO OO co * ON ON IO IO O HI NO CS HI CO HI M CS HI ON t^. 10 rt CO CS i 6 rt (N HI O rt CO t^< t^ NO ON NO ON NO NO CO CS CO t^ NO t^ ON O 00 NO rt CO CS Hi PJ vo PJ t^ ON CS IO CS r^ Hi t^ CS ON NO CO HI CS O CS IO M CS rt t> ON f>- VO rt CO CS M O VO l~- O OO ON M rt rt t^ M CO ON CS VO M t^ HI \O O O CS NO vN HI ON 00 O 00 CS cs t~s. cs t-^ co ON NO O l~- vo CS co co rt in NO CS 00 CO NO f^ 10 t~ rt O 1>- NO ON NO $ 1 \O VO * rt HI OO CO rt ON t^. ON NO vo OO 8 ON HI IO VO NO OO t^. NO rt CO CS M t O NO M rt vo CO CO CO O ON 00 NO NO t^ ON M rt O HI co NO 00 IN vo rt CO CS HI pi CO 00 10 co ON t^ 00 M HI O t^- NO NO NO 00 CS 00 10 l^ O rt t^ NO rt CO CS CS M IH HI HI HI NO HI NO O O O O cs O cs o CS CS CS CS CS CS CS CO co CO co 00 co 00 MM t cs cs CO O CO CO ON rt IO t^ CS NO CO CS o rt vo vo t~* HI to r* t~>- M CO rt vo O NO co q M CO OO NO CS HI NO rt 00 HI HI 00 rt ON rt i 5 10 t> NO NO vo co ON cs O NO cs CO t*- ON NO 9 vo O vo O NO cs ON ON r^ rt CS t-. CO 00 IO CO rt rt VO ON NO VO oo r^. NO vo t^ NO M 1/3 -<|tO it co co cs CO CO ON cs rt t^ Hi CO ON CS IO 00 NO 10 co cs cs M pi PJ rt t^ NO HI t-^ co t** O NO O cs rt r~ ON VO ON NO rt NO ON CO t^ IO rt CO CS M HI * NO HI O CO NO NO CO NO CS CO ON Hi CS CS 10 cs O ON co t^ cs NO vo rt cs cs HI H* _) o HI rt NO ON OO CO CS 9 00 00 00 00 co 00 co o rt CS ON i s > r^ CO rt vo ON CS VO O CS HI o 1 "* 10 pi PJ ON O O M CS rt 00 rt 00 ON CO ON O HI NO O NO rt NO O rt t^ NO rt CO CS CS M 8 ON rt ON rt CO M O ON O NO ON ON OO NO t** rt M O CO t^* CS NO IO rt CO CS HI M M ON 00 00 t^ rt ON CO rt CS rt O ON VO O ON t-* NO t- O 10 M VO rt CO CS CS HI HI H fc M 10 CO CS CS Hi ON O CO O HI cs co M cs co o ON rt ON rt HI t^. CO NO rt HI ON VO O NO 10 NO NO t-> OO CS rt CO CO t~-. M IO OO ON ON fl HS o PJ M HI CO * ON CS NO NO vo O M O ON NO 00 rt CS M rt t^. CS NO VO rt CO CS HI HI 00 H tvo NO O HI co vo OO t^. t^ HI VO HI rt CO CS CS HI HI 10 NO ON ON rt co co rt CO co NO CS t^. ON 00 CO CS CS rt OO co ON vo rt co CS HI HI o HI HI HI HI NO HI NO ON ON ON ON Hi rt NO g 00 00 CO 00 00 00 00 VO VO IO vo VO VO VO g NO NO NO NO HI NO HI cs cs cs w O t^ vo H o 00 t- NO ON NO ON CS NO t> CS HI IO CS OO HI O OO l- *>. M VO M NO rt CO CS CS HI H! NO M O NO O cs NO cs O ON O vo ON O ON rt CS CO rt CO rt ON 10 rt CO CS M HI 4 M t- rt CO rt NO O 00 CS IO ON rt VO CO NO !> r^ CO M NO (N oo rt CO CS CN) M HI 10 CS \O O vo rt M NO O co t > * O cs co cs i CO 00 co 00 rt O NO M OO NO co rt vo 10 IO rt ON 10 O CO ON r^. cs co vo *- NO NO OO * 10 O ** O O CS 10 ON O O rt O vo t^ NO co cs cs rt OO co ON vo rt CO CS HI HI 4 H M ON O CO NO M HI HI ro 00 CO rt CS NO t^ t^ 00 M NO CS 00 rt CO CS CS Hi M PJ* M cs cs O NO O ON co CS t-~ CS NO rt NO vo HI CS VO OO rt O t** rt CO CS M HI HI g 10 CO O co 10 M co CO rt NO t-. rt ON M o M M HI HI NO HI NO co co co co O CO vo O t^ IO CS O CO HI ON CS M O ON NO t^ O M|QO HI t^ CS IO NO CO O rt CS ON NO rt t^. t^ CS vo vo t- O vo M CO rt CO CS CS HI HI PJ M rt CO 00 ON CO O CS CS ON VO M O rt CO O HI rt 00 rt O t^- rt CO - cs rt 00 vo 00 CS VO ON *- HI CS g cs *- cs t^. co O NO M CO NO co rt vo vo vo NO M t^. CS CO M NO CO vo NO 00 HI 00 00 < ON CS rt NO t^ ON HI 10 00 ON ON O NO CO r^ ON cs NO CO ON NO CO CS CS HI Hi O HI CS O ON OO Cs M vo rt vo CO O NO NO O co NO O 10 HI 00 NO CO CS CS HI M IN 00 rt ON rt ON t^ CO ON Cs Hi OO HI M VO CS ON CO t^ CO O t^ VO O CS HI M M 1 ,,: .-t>* h H h J J * O PJ 00 Tt- M CO to O PJ 00 Tl- M 00 IO O PJ 00 Tf M 00 10 SHiV'I HO H1U1 I AY ^ >0 .-'; o ^ ^ ^ 1 ; M - M s w PQ 00^ O O t^ O -~piioo t^-OOMOMfN PO . 10 OOO O>- H-I Ooo O O 10^-0000 O\t^ro\O t>- 0 Tf O\M POlOtOPOOO O vooO O WOO POO ^ t>.O POO PO 8 MOO 10MOO IOPON too M O OOOM O <* PO Pi M M M O M PO to O M o pp oo PJ o q "^ o -* to O MT^-Ot^ 0-tOO POOOOOOMPOt^ to PO PO N M M s, PO PO MCIC^OO POOO ** P) O tOMOOO * ION O^O wooo t* Ttrfpopo - .f^. M M IO O O to 00 totoO r^-O O M O^fOfOf^^O IOOIOMOOO - *> O PO O l>. to Tf s 00* ^ M 00 O to O 3 00 PO CO POtOO toO M 1~N.P<00 i^. T}-M OO IOPOP1 sHivnd o B -* TABLE 15 MOMENT OP INERTIA OF TWO COVER PLATES FOR Z-BAR COLUMNS ABOUT AXIS BB Thickness of plate equals thickness of Z-bar 1 N N| |. THICKNESS OF COVER PLATES IN INCHES. h* "35 A i|* S^ O. a * d. I ^ | 1 I 8 i Q ^ rt 6 17 I2f 746.14 95-3 6 .1161.84 1380.70 1607.03 6 H 16 " 702.25 894.45 1093.50 1299.48 1512.50 6 if 15 .... 658.36 838-55 1025.16 I2I8.27 1417.97 J 14 u .... 614.47 782.65 956.81 II 37-5 1323-44 5 i 14 iol 332.23 452.87 578.59 709.49 845-63 987.11 5 i 13 " 308.50 420.52 537-27 658.81 785-23 916.60 5 i 14 ioi 310.45 423-5 541-47 664.45 792.52 925-75 5 i 13 (1 288.27 393- 2 5 502.80 616.99 735-9 1 859-63 (28) "E 00 < < X < u "q q q^ vO 11 O t> w M q q 00 O Tf M t^ 1^ l^. t^ 00 to CO H, ! CO co CO co co H, 00 % C q q ON q\ - M Tf O O CO M CO M 1-4 O 00 r^ M to <*5 O co o *>. t^. o M d c> o co t^ 10 M ro to ro O fO CO ^ M IO CO Tf Tf CD M 00 00 t^. 00 Tf CO 1-4 O 00 to M M M Hi M co O O M Tf \O Hi d oo vd to M X ; 810 co C> CN 10 M O O O O CO \O <*5 HI CO HI HI M O t^ Tf M Cs rf Tf Tf CO 10 CO O CO vO vO vO to oc H V. M a, V 1-1 0, % CO CO co CO h co Tf Tf MOM to to to O "- M M IO VO IO >O to 10 to to t^ t-~ 00 00 IO to to to 4444 CO 00 \O vO O O 4444 Tf Tf 10 O r^ t^. t~- r^ co co co CO 10 O CO to vq > IO M 4 CN o to Tf to O ** vO C\ fO w f^ to to to M 00 Tj- O tO M M M to co M CO M O 00 CO \d d to O X^ CO O CO M M HI 00 co co to CO CO co M 10 VO 00 CN co HI o t>- HI HI _: < < - ~ r^ O Tf 10 q to d 06 n n M r<. O * t^- C^ tr> M O\ M 00 \O rO M M M Hi O M fO HI to O r^ CO to fO HI ON 8O C\ t>. to to oq 4 M d 06 O Tf O M .to C\ HI M Tf M O rO CO G*- cJ to CO Tf Tf CO M to O to t- Tf CO VO HI \O M CO to M M H4 HI -4 M C 1 - O M TJ- vq HI d 06 vd to n PQ r. 1 V r^ f*5 M O vO M O\ t^ O O 00 00 IO M O *^ M HI M O CO fO O rO t^ rf M O co co co co CO CO co co !>- O O Tf qv oc oq oq M M M M <* * < ^- a. urj CO c*5 ro ro u M -3- Tt M M M 4-^-4 to O r~ t^- ^t Tf Tj- Tf 4444 M CO fO Tf IO to to to ro ! < <; X / < U ro t^ 10 n M M VC H, CO fO rp M OJ IO > M M O CO t> M O O ON l^ *^ to O O vO M O d^ , O 00 I s - to t^ O >-> Tf M q to co c^ o< to od Tf Tf CO C w Tf Tf r^ Tf COO M O M OO' to 5 M W o. "o M M M "5. 00 M M M M _ CO O O M M f) rO co ro M M r*5 ^J- * Tt *<* CO <*5 *5 **5 CO Tf IO to oq oo oq oq cJ e! M M O O to to vO NO M M M M Tf 10 \O \O CO CO co co M M M M HH t^ M t^ \O M ro ro - ro CO O M M P- ro M d co M CO vO rO W M M HI Tf M O\ t^ o c\ >. o CO to vO t^- t-<. \O tO Tf CO f>" HI IO Tf CO CO M J2 M C t>. t-. 10 ro M |>. VO M M H M O M M M IO 'O l> ST S 8Tf 10 tO Tf 00 N CO M CN 00 M M 800 Tf O vQ CO t^ vO * o to 4 SHIONV dO VHHV (SON NOON OVOON o^-ooo ^^^N wio-; t^mroOIO vdlOTJ-r}- rfrOfON M M M M fed O H !i w< ox-r.,^* *c^^c*o HN^KW,^ HN^ntao,^ ^rtoo^H* XXX XXXX XXXX XXXX XXXX * X $ y * x * X < > co O ro co ro ro 10 CO O 01 Tt Tt ON O CN CN M *- > - n X "H rp co O O Tt Tt 10 10 ro co OI OI 10 Tt ON CO Tt T}- Tt T; oo' 06 c^ 6 M M IO 1^ I I Es - ON IO O ON O". O O MM MM ^ - ro co CO co IO CO M M co ro ro IO io t- 10 10 CO CO oi oi MM 1 * co M II oi M IO IO \O vO 10 10 O4 O OI O t^ r>. MO O O O O o! oi CO 00 MM Tt Tt *- gg M c: PQ - Ov ro 1 Tt 00 Tf CO 3 OJ o< o ON IO CO ro I M ON ON t- O^ Tt ro CN ro ro ro oi 5 o; " : z M X - 00 O 10 O CO Tt O Tt ^ N O H N ro ON ^ 10 Tt q 10 ro ON O ON 00 -t O t^ IO M OO MM Tt CO si i - ro co ro *>. oq co co o ^o M M ro ro M ON CO co CO M CO M Tt 10 00 O oi oi MM K* N * fV H * i i K ^% M X - t^. CO co oq" oq IO IO IO IO IO IO CO r^ O\ ON IO IO 00 00 M t t CN O oq oq ro ro 00 r- ro 01 t^ t^ oo oo ON CJN oi oi CO 00 Tt Tt r^ O oq oq o o 2 H M IO 00 ON $ vO*00 c O^ ^O 5 * 1 CO M CO 01 ON 10 Tt l CN O 00 Tt i S M Tt CO & Tt ro ro rO g co co 1^1 co ro ro ro a co co t/; X M ON ON 10 CO rto q io 00 10 CCiOC M 00 M 810 ro CO 04 t. Tt ON 10 6 >- *O 10 Tt ro r>. O io M O O oi r^. O) M MM 00 M Tt oq oi od r^. 00 ro Ol I I 4 | 1! s & 6V 06 co ro O ro Tt ON ON O Tt 10 ON M 6 CO CO 0) M MO O ro M 00 Tt Tt Oi M 00 0) 10 O 10 10 O) CN 4J - rO co 00 10 O t-~ ro co IO CO q q co ro ON IO ro ro ro O ro O Tt Tt 00 CO oi oi MM O ro t^ O IO IO OO OO (N Oi MM s 0) x oq oq C*T 00 O) ON O) OI ON M M M OO t> IO IO oi oi 00 00 O O ro ro CO CO oi oi O O ro ro MO ro n CO 00 O O M M CO CO Tt Tt O O ^ D CO 0Q * ro t^. 00 ON Tt CO 1 i>- oo Tt ro 0) ON 10 ro co Tt 04 00 Tt co co 1 IO ro IO Tt ON 10 Tt O ro ro ro ro 3 " ro ro ro oi a * x ff ON ON CN q 10 t^- M CO 10 CO N O 00 oq q Jod M 10 ^ t^. ON IO ON ; - 00 f^ O t^- M 0)' Tt ro -,-r | 00 n t^ ^vo 00 JN t^ so i | q-z jt qjd 3 d vo|| vo | I IO IO to io|| Tt Tt ro ro || Tt Tt ro ro (30) J TABLE 18 TWO CHANNELS LACED, FLANGES IN SIZE OF CHANNEL. TOTAL SECTION. Axis BB. Axis AA. ^ j7 . | Jc M i < io"b. tob. u" b. to b. i2"b. to b. I r I r I r r r 15 55 no 32.36 860.4 5-16 588.98 4-27 732.23 4-76 891.67 5-25 " 50 100 29.42 805.4 5- 2 3 54067 4.29 671.50 4 . 7 8 817.04 5-27 45 90 26.48 750.2 5.32 490.36 4.30 608.51 4-79 739-9 1 5.29 " 40 80 23.52 695.0 5-43 437.04 4-3 1 542.10 4.80 658-93 5.29 " 35 70 20.58 640.0 5.58 381.90 4-3 1 473-7 4.80 575-8o 5-29 " 33 66 19.80 625.2 5-62 366.73 4-30 454.96 4.79 553-09 5-29 9" b. to b. 10" b. to b. ii" b. tob. 12 40 80 23.52 394-0 4.09 348.97 3.85 443-71 4.34 550.20 4.84 M 35 70 20.58 358.6 4.17 309.91 3-88 393-39 4-37 487.15 4.87 it 30 60 17.64 3 2 3-4 4.28 268.23 3-9 340.08 4-39 420.75 4.88 " 25 50 14.70 288.0 4-43 223.79 3-90 283.65 4-39 350.86 4-89 if 20.5 4i 12.06 256.2 4.61 181.60 3.88 230.39 4-37 285.22 4.86 9" b. tob. 10" b. to b. n" b. tob. 10 25 50 14.70 182.0 3-52 228.10 3-94 288.81 4-43 356-87 4.93 M 20 40 11.76 I 57-4 3.66 183-75 3-95 232.44 4-45 287.02 4-94 15 30 8.92 133.8 3-87 I 37-57 3-93 174.24 4.42 215-37 4.91 8" b. to b. 9" b. to b. 10" b. to b. 9 20 40 11.76 121. 6 3-2i 142.05 3-48 185.15 3-97 234-13 4.46 M 15 30 8.82 101.8 3-40 106.46 3-47 138-74 3-97 !75-43 4.46 " 13.25 26.5 7.78 94-6 3-49 93-n 3-46 121.45 3-95 153-68 4-44 8" b. to b. 9" b. to b. 10" b. to b. 8 16.25 32.5 9.56 79.8 2.89 116.95 3-50 152-27 3-99 192.36 4-49 " 13.75 27-5 s.os 72.0 2.98 98.88 3-50 128.72 3-99 162.60 4.49 a 11.25 22.5 6.70 64.6 3-" 81.21 3-48 105.83 3-97 133-79 4-47 < < * X < ,0 O fj ,0 "a - s tovo O to r^. GO to PO T)- to \o vO O PO fO to ON ON M POfOPOPOPOrOCNCMCMCNCM MHM HMM OOM JD 5 X5 to t^ ON to n- to ooo ooo * Tf Tf Tt TJ- Tj- to to IO to to to IO to to to to to to to IO to to IO to to t I OO QO T)- POO CO PO O O ON N toO to GO M to rj- PO s CMtoQCMOPOOOCMM^f-MOM ON ^ Tj- ON to CM CM O to (N ON M M CM CM -sf to (N M ON M tO CM M Tj-toPOPO^fCMCMOOOCMO to ON tO Tt- rfo to ON to too OOOPOONMtOPOO rt- O to GNCQ tovo totoOto^h^POPOPOCM co W CM CM CM M V. Tj- ON to tO O OO rt M ON CM O to MM MM U2 o ,> ^ bo - O CO to to loco 00 to -5f Tt- to to\o C\ OO to ON O ^NO CM CM tototo tototo toto cOfOfO fOfOTO roro - M to W IO ON U^OO O O to -rf- to t^vO lO^'^-lO'^-fOfOCNl frjCSIM CNIMM CNIMM M CM CO O to 6 ^0^2- M ON to ON tovQ O JO S ,d "K ||| H ONOO 00 00 ON ONO vo VOOO OOtoQ ^rf\O OOM rj ONOO O \O IO to CM fO O OOM OOO OO - COCO to ro T)- * M ON O'O O CM lO M Tfrj-toeooNto MM-^-CMU^XOU-)toM\OO>fO ONOO fDtoMO PO Tf rOONtorD'^-'^- OO ONONCM ^-OO to O vo to rf fO fd OOONM TfOOMD OCMO torOONlOTl-toONM Tl- totoOOCNM ONCMCOtoCO ONOO CM O to ^ r^ VOOO ON^OIOMQ fOONTj-OtoCNU-)CM lOMQ CMQOO V OOOOOO OOM COIOCN tO-^-fDtOrJ-rOfOCM M e*)f*> co ,0 3 j=> "in - rovO CNONM toMOOtoM ONCNCM^COOO CMOOO CO -^-OtorofO XOCMOO vofO ^M Q\ "oCto ON to\o POrOPOCMCMCM CMCMMMM MM ,d 5 ,e V M \O to CO tot^t^OOO NO\O\O & B n IO to to CMCMCN CMCMCM CSCNCN MMM HH * ' MIOCMCOtoCN) CMfOCM torot^. TtO ^ O ONM M CO ONO CM to LOO **5 ^OO VO to to *(N CM ON to H 10 LO % M X Tf 10 VO O M CM TfrvO IOO 00 CMTtTl-OOONlH lOlOtoMCMCOOOONlO 1 1 ^1-^-CMOOCM OOTt-OCM O -^-00 OOOvOOOOvO Tj-TtCNivOCMOCOOO\O O tO O to O to ^tOO fOOO O CMtorOMMTJ-ONCMTf TfOO CM Tf O \O to T^- t>. VOQtOON^fCM ONtOCMOOtOOOtOfOCNOONto foO lOTj-Tj-rOfOCM MM 00 00 to\o OvO rorofOCMCN MMM MM SECTION. < M OS < SONOONOOO NOOTl-OvO OONvOMOONOOOe OOOO -TfOO vO O O O ro ^- "^ in moo in invo i> o io j> & t^cc t^moto \oNtovOMtoroOM (S ONVO roOOcoOCoT}-(S Tj-MOO MQOto o\00 vo oo t*if> tovo -^ in PO r^ j 1 XHOIHM oooooo ooooo ooo oomminin inininooo oo in OOOOO^O OOOOw OOO OOO (N^N O\^^vOM\OOOfOO M o o>oo t^vo oo t^vo m^in^co'^-fOtN COCNN ooo ao in HidHQ in^. v~s.~ fs v. >.>.. Ov.^. o\x. s. oo .. to,. ^ vo ^. m~ ^ (32) PQ H 3 oq oq oq co oc oq 06 od 06 od 06 od O -3- NO M PO 0* to PONO t^ ^f O NO PO O ^*" VO PO O 00 NO vo N o w M M M 00 00 00 00 00 00 NO O NO VO d O OO NO ^" PO oq oq oq oq oq oq t^- 1>. r>. r-. t>- IOION t^OO o6 6 HH M PO O t^. t^ O O ^t"NO *-i pooq q oq q -^t- r^- O O O NO ONO PO O ^ O O vo O NO PONO ^" C 00 O vo vo voO t>. Tf c ro\O vO vooO M o\O PO M O t>. vo vo\O t (N VOOO NO O VO fO Tf POOO O C\OO ^- N M f5 \& >* \O PO\O M POOCNON ONOW I^VOM M PO f>- vo\o 1-1 p^ d^od N d M vood w ON NMOOOOOOOt^. t^OO O t^ t^-OO t^ I s * M O OOO t^.NO t^NO VOTj-TfTj-PCM POCI vO m o t^vo inmm in in in in in in oinoinoinoininroinoinincofOM M ^t* ^O ^O W^CS^MMM f^ f^ M M M M M M 00 100000 tnvoiovomoooooo q oo o o oq 6 00 3 CO C4 (N M M M ON O 8 Tft^. OONlOUOVO O OlO ONONOH^iOO B3JV O\O OOOO OO (SCO Tf-00 OAOAOON OOMMinvO Tl-00 Tj-\O 00 N\O NOO ininininm inininininminin 1> vO Tj-rONMO (SMOONOO cONMOO\iHOO\OOI>00 omoin*^) oinom omo in^-^-'Oco TfcoroN N mTf^ in in inro omoindm oin 40#S 16" 23.52 8.75 BB AA 694.17 794.96 658-77 737-67 623-57 676.97 588.17 612.83 556.37 553-86 4-69 5.02 4.80 5-08 4-93 5- J 4 5-09 5-20 5-27 5- 2 5 773-07 837.63 737.67 780.33 702.47 7J9-63 667.07 655-50 635-27 596.52 4.80 5.00 4.91 5-05 5-4 5.10 5-20 5-15 5-37 5.20 853.56 880.30 818.16 823.00 782.96 762.30 747.56 698.17 7I5-76 639.19 4.90 4.98 5.01 5-3 5-i4 5-7 5-29 5-n 5-45 5-i5 935-64 922.96 900.24 865.67 865.04 804.97 829.64 740.83 797-84 681.86 4-99 4.96 5.10 5.00 5-23 5-4 5-38 5.08 5-53 5- 12 12" I 35#S 16" 20.58 9 BB AA BB AA IF] 30# S 16" 17.64 9.25 12" J 25#S 16" 14.70 9-5 BB AA !2"> 20.5 S 16" 1 2.O6 9-75 BB AA Thickness of Pis. i A I A Area of 2-14" Pis. 7.00 8.75 10.50 12.25 l*> 40# S 14" 23.52 6.75 BB AA 656.65 5 22 -39 621.25 488.13 4-64 4.14 4-75 4- 21 725.69 550.97 690.29 516.71 4.74 4-13 4-85 4.20 796.12 579-55 760.72 545- 2 9 4-83 4-13 4-95 4.19 867.94 608.13 832.54 573-88 4-93 4.12 5.04 4.18 12' > 3sn MT 20.58 7 BB AA (40) TABLE 23 TWO COVER PLATES A I B I 1 i 20.25 22.50 24-75 27x10 3i-5<> 36XM> i r . I r i r I r I r I 3167.40 ::,_ S( 3112.40 2072.35 3057-20 998-36 3002.00 ; 1 9.5 ' 2947-00 835-61 2932.20 1804-29 t 2087.03 1764.61 2032,03 1647.10 1976.83 1575-- 1 1921.63 1494-01 1866.63 1410.36 1851.83 1379-04 6.30 5-79 6.40 5-76 6.50 5.80 6.63 5-84 6.76 5-88 6.80 5-87 2234.42 1825.36 2179.42 707.85 2124.22 1633-86 2069.02 rr , : , : 2014.02 1471.11 1999.22 J439-79 6.38 5-77 6.48 5-74 6-59 5-78 6.71 '." 6.84 5-84 6.87 5-83 384.10 :-..'/ :: 2329.10 768.60 2273.90 694.61 2218.70 1615-51 2163-70 1531-86 2148.90 1500-54 6^6 5-75 5-7 1 6.66 5-75 6.78 5-79 6-91 5-8i 6-95 5 .8c 2536-09 946.86 2481-09 829-35 2425-89 1755-36 2370.69 1676-26 2315-69 ->; 6] 2300-89 1561.29 6.54 5-73 6-63 5-69 6-74 5-73 6.85 5-7^ 6.98 5-79 7.01 5-78 2847,03 2068.36 2792-03 950-85 --/ '\ 1876-86 2681.63 797 '/- 2626.63 1714.11 2611-83 ^:.-- 6.68 5-69 6-77 5-66 6-87 5-69 6.98 5-72 7.10 5-74 7-i4 5-73 6-81 5-66 6.90 5^3 7.00 s-66 7.1 5-68 7.22 5-7 7-25 :/-, & 1 & 1 1 i 18.00 20.00 22.00 24-00 28.00 ytjoo 1950.74 1241.18 1895.74 1157.62 1840.54 1110.45 1785-34 1059.23 i730'34 1004.19 I7IS-54 981.90 6.22 4.96 6-32 4-94 6.43 5.00 6.56 5-05 6.70 : - - 74 5-io 2081.75 1283.84 2026.75 1200.28 i97i-55 1153.11 1916.35 1101.89 1861.35 1046.85 1846.55 1024.56 & - :- 4-95 6.40 4-93 6-51 4-98 6.64 5-03 6-77 5-o8 5-07 ' --- 2214.80 ':-' r - 2159-80 1242.95 2104.60 "95-78 2049.40 ' : 44 ; '- 1994.40 co8( -: .... fa 1067.23 6.38 4-94 6.48 4.92 6-59 4-97 6.71 5-oi 6.84 . , , 5-5 2349-90 1365 iG 2294-90 1285.62 2239.70 1238.45 2184.50 3 : g J ; ; :::; r, 1I32-I9 2114.70 1109-90 6^6 +93 6-55 : ': 4-95 6.78 5-00 6-93 5-04 6-95 m 2626-30 1454-51 2571.30 1370-95 2 5 it ic 1323.78 2460.90 1272.56 2405 -^ 1217.52 2391-10 "95-23 6.60 4-91 6.69 4-89 6-80 4-93 6-91 4-97 7-04 5-01 7-07 2911^07 1539-84 2^56.07 I40.2S 2800-87 1409.11 2745-^ 1357-89 . 690 '' 7 1302-85 2675^87 12*0.56 6-73 4-89 6-82 4*7 6.92 4-91 7^>3 4-95 7-*5 4^98 7.19 1-97 i I tt 1 1 I 1 6.00 18.00 20.00 22.00 24.00 28-00 32-00 IOI 9-33 965.63 9 8 3-93 908-33 948.73 847-63 913-33 783-50 881.53 724-52 5.08 4-94 5-19 4-98 5-3* 5-02 5-45 S'5 5.60 5-o8 1104.65 1008.30 1069.25 "-;-'-- 890.30 998-65 826.17 966.85 767.19 :' 4 : 5 . 2 e 4-9< r : 5-00 5-53 S'3 5.67 5-05 ; ] : 6c 1050.96 ] : - ' : c II2I.OO 932-97 1085.60 868.83 1053.80 809.86 x ; : r 34 4-95 5-46 4^8 5-59 5-00 5-73 5-03 1280.21 1093.63 1244.81 1209.61 975-63 1174.21 911.50 1142.41 852.52 5-3 x ;,'. 5-43 4-93 5-52 4-96 5-66 4.98 5-79 15-00 1370.50 1136-30 i335-io : '. - ; '.<-. 1299-90 1018.30 1264.50 954-17 1232.70 895.19 5-37 4-89 1556-14 1221-63 1520.74 H64-33 1485-54 1103-63 1450-14 1039-5 1418-34 9*>.52 4-87 5-59 -:-'- 5-71 4^92 4-93 5-95 4-95 1748.67 1306.96 1713-27 1249.67 1678-07 1188-97 1642-67 1124-83 1610-87 1065.86 5-6i 4*5 5-7i flftft 4^92 W5 4^95 5-72 441 5-85 4^9* 5-8i 4.80 $-93 4^91 6-05 4^92 I & 1 tt f i I 14.00 15-75 17-50 19.25 21.00 24-50 28.00 941.17 636.72 905-77 602.46 5-oi 4-12 5-12 4.17 1015.82 665.30 980.42 631.04 5-09 4.12 5-i9 4.17 1091-90 693,88 1056.50 659-63 5-16 4-n 5-27 4.16 1169.44 722-47 1 134-04 688.21 5-23 4-n S-34 4-16 1248-44 75 lJ 5 1213^04 716.79 5-3 4-n 5-4 4-15 1410.88 808.22 1375-48 773-96 5-42 4-io 5-52 4-J4 1579-33 865.39 1543-93 831-13 5-54 4-M = .*4 4-34 (41) TABLE 23 (Co?itinued) TWO CHANNELS AND Thickness of Pis. i ft I ft Area of 2-14" Pis. 7.00 8.75 10.50 12.25 SECTION. AREA OF 2 [s B. TO B OF [S Axis. I r I r I r I r Channel. Plate. 12" ? 30#S 14" 17.64 7.25 BB AA 586.05 451.22 550-65 411.62 518-85 375-Q2 4.88 4.28 5-4 4-36 5-22 4.44 6 55-o9 479.80 619.69 440.20 587.89 403.60 4.98 4-26 5-14 4-33 5-32 4-40 725-52 508.39 690.12 468.79 658-32 432.18 5.08 4-25 5- 2 3 4-3 1 5-40 4-38 797-34 536-97 761.94 497-37 73- I 4 460.77 5.16 4.24 5-32 4-3 5-48 4-35 12"? 25^ S 14" 14.70 7-5 BB AA 12" / 20.5# ( 14" 1 2. 06 7-75 BB AA Thickness of Pis. 1 ft 1 7 TS Area of 2-14" Pis. 7.00 8.75 10.50 12.25 10" ? 25#S 14" 14.70 8 BB AA 365-89 434-89 341-29 383-58 317.69 332.I4 4.II 4.48 4.27 4-52 4-47 4.57 414.70 463.48 390.10 412.17 366.50 360.72 4.21 4-45 4-36 4.48 4-55 4-52 464.08 492.06 440.08 440-75 416.48 389-3I 4-29 4.42 4-45 4-45 4-63 4-48 5I5-83 520.64 49 I - 2 3 469-33 467.63 417.89 4-37 4.40 4-52 4.42 4.70 4.44 10" ? 20# $ 14* 11.76 3.25 BB AA 10" i5#S 14" 8.Q2 8.5 BB AA Thickness of Pis. 1 ft 1 ft Area of 2-12" Pis. 6.00 7-50 9.00 10.50 10"? 25! S 12" 14.70 6 BB AA 339.62 271-43 315-02 241.67 291.42 211.51 4-05 3.62 4.21 3- 6 9 4.42 3-77 381.46 289.43 356.86 259.67 333-26 229.51 4-i5 3.61 4-3 3-67 4-51 3-74 424.3 307-43 399.70 277.67 376.10 247-5 1 4-23 3.60 4-39 3-66 4-58 3-72 468.14 325-43 443-54 295.67 419.94 265-5! 4-3 1 3-59 4.46 3-64 4-65 3-7o 10" ? 20#S 12" 11.76 6.25 BB AA Vfl i5#S 12" 8.Q2 6.5 BB AA Thickness of Pis. | ft 1 ft Area of 2-12" Pis. 6.00 7-50 9.00 10.50 9 "/ 20#S 12" 11.76 6.25 BB AA 249.97 238-77 230.17 205.96 222.97 198.90 3-75 3-67 3-94 3-73 4.02 3-8o 284.26 256.77 264.46 223.96 257.26 216.90 3-84 3-65 4-03 3-7o 4.10 3-77 319.46 274.77 299.66 241.96 292.46 234-90 3-92 3-64 4.10 3-68 4.17 3-74 355-57 292.77 335-77 259.96 328.57 252.90 4.00 3-63 4.17 3-67 4.24 3-72 tfl i5#S 12" 8.82 6.5 BB AA 9V 13-25 S 12" 7.78 6.75 BB AA Thickness of Pis. i 1 ft Area of 2-11'' Pis. 5.50 6.88 8.25 9.63 gr'j 20#S II" 11.76 5.25 BB AA 239.28 181.53 219.48 J 57-75 212.28 J53-33 3-72 3-24 3-9 1 3-32 4.00 3-40 270.71 195.40 250.91 171.61 243-7 1 167.19 3.81 3-24 4.00 3-3i 4.08 3-38 302.97 209.26 283.17 185.48 275-97 181.05 f 3-89 3-23 4.07 3-30 4-15 3-36 336-07 223-13 316.27 J 99-34 309.07 194.92 3-96 3-23 4.14 3-29 4.21 3-35 9" > i5#S II" 8.82 5.50 BB AA 9V 13-25 S II" 7.78 5-75 BB AA Thickness of Pis. i 4 ft A Area of 2-12" Pis. 6.00 7.50 9.00 10.50 8"? 16.25 \ 12" 9.56 6.50 BB AA 181.92 214.04 3-42 3-7 1 209.42 232.04 3-5 3-6q 237.72 250.04 3-58 3-67 266.84 268.04 3-65 3.66 TABLE 23 (Continued) TWO COVER PLATES \ A | H f I 14.00 15-75 17.50 19.25 21.00 24.50 28.00 I r i r 5-32 4.22 5-47 4.27 5.62 4-3 2 I r i r I r I r I r 870-57 565-55 835-17 525-95 803.37 489.35 5- 2 5 4-23 5-39 4.28 5-55 4-33 945-22 594-14 909.82 554-54 878.02 517-93 1021.30 622.72 985.90 583-12 954.10 546.52 5-39 4.21 5-53 4.26 5.68 4-3 1098.84 651-3 1063.44 611.70 1031.64 575-Jo 5-46 4.20 5-60 4.24 5-74 4.29 1177.84 679.89 1142.44 640.29 1110.64 603.68 5-52 4.19 5.66 4-23 5 .8o 4.27 1340.28 5.64 1508.73 5.75 737.05 4.18 794-22 4.17 1304.88 5.77 1473-33 5-87 697.45 4.22 754.62! 4.20 1273.08 5.90 1441.53 6.00 660.85 4- 2 5 718.02 4.23 1 A I ft 1 14.00 15.75 17.50 19.25 21.00 568.17 549-23 543-57 497.92 5*9-97 446.47 4-45 4-37 4-59 4-40 4-76 4.41 621.71 577-8i 597- 11 526.50 573-51 475-o6 4-52 4-36 4.66 4-37 4.82 4-39 676.46 606.39 651.86 555-o8 628.26 503-64 4-58 4-34 4-72 4-36 4.88 4-37 732-45 634-98 707-85 583-67 684.25 532.22 4.64 4-32 4-78 4-34 4-93 4-35 789.69 663-56 765.09 612.25 741.49 560.81 4.70 4-3 1 4-83 4-32 4.98 4-33 | A 1 H I 12.00 13.50 15.00 16.50 18.00 S^-oo 343-43 488.40 3I3-67 464.80 283-51 4-38 3-59 4--S3 3-63 4.71 3-68 558.89 361-43 534-29 33!- 6 7 510.69 3 I -5 I 4-45 3-58 4.60 3-62 4-77 3-67 605.83 379-43 581-23 349-67 557-63 S^-S 1 4-5 2 3-57 4.66 3.61 4-83 3-65 653.82 397-43 629.22 367-67 605.62 337-5 1 4-58 3-57 4-72 3-6i 4.88 3-64 7 02.8 7 4I5-43 678.27 385-67 654.67 355-5 1 4.64 3.56 4-77 3-6o 4-93 3-63 i A f H 1 I2.0O 13-50 15.00 16.50 18.00 392.60 3 IO -77 372.8o 277.96 365.60 270.90 4.06 3-62 4-23 3-65 4-3 3-7 430-57 328.77 410.77 295.96 403-57 288.90 4-i3 3-6i 4.29 3-64 4-35 3-68 469.49 346.77 449.69 3 J 3-9 6 442.49 306.90 4.19 3=6o 4-34 3-63 4.41 3-67 509-37 364-77 489-57 33J-96 482.37 324.90 4-25 3-59 4.40 3.62 4.46 3-66 550.22 382.77 530-42 349.96 523-22 342.90 4-3 3-59 4-45 3-6i 4-51 3-65 \ A i H I 11.00 12.38 13.75 15.13 16.50 370.02 236.99 350.22 213.21 343-02 208.78 4-03 3-23 4.20 3-28 4-27 3-33^ 404.82 250.86 385.02 227.07 377-82 222.65 4.10 3.22 4.26 3-27 4-33 3-32 440.50 264.72 420.70 240.94 413-50 236.51 4.16 3-22 4-32 3-27 4.38 3-3 1 477.06 278.59 457.26 254.80 450.06 250.38 4.21 3.22 4-37 3-26 4-43 3-3 1 514-5 292-45 494.70 268.67 487.50 264.24 4-27 3-22 4-42 3-26 4-48 3-30 * A I 12.00 13-50 15.00 296.80 286.04 3-7i 3-64 327.60 304.04 3-77 3-63 359-25 322.04 3.82 3.62 (43) TABLE 23 (Continued} TWO CHANNELS AND Thickness of Pis. i TTT i Area of 2-12" Pis. 6.00 7.50 9.00 SECTION AREA OF 2 [s. B. TO B. OF[S. Axis. i r I r i r Channel. Plate. 8V 13-75 S 12" 8.08 6-75 BB AA 174.12 200.02 166.72 l8 5-97 3-52 3-77 3.62 3-83 201.62 2l8.02 194.22 203.97 3.60 3-74 3-70 3-79 229.92 236.02 222.52 221.97 3.67 3.72 3.76 3-76 8V 11.25 S 12" 6.70 7 BB AA Thickness of Pis. i T* f Area of 2-10" Pis. 5.00 6.25 7.^-0 8V 16.25 \ 10" 9.56 4.50 BB AA 164.90 120.50 157.10 114.23 149.70 107.72 3-37 2.88 3-47 2.96 3-58 3-03 187.82 130.91 l8o.02 124.64 172.62 Il8.I4 3-45 2.88 3-54 2-95 3-65 3.02 211.40 J 4i-33 203.60 i35-o6 196.20 128.55 3.52 2.88 3.61 2-94 3-72 3.01 8V 13-75 ) 10" 8.08 4-75 BB AA 8" ? 11.25 S 10" 6.70 5 BB AA Thickness of Pis. i S i Area of 2-10" Pis. 5.00 6.25 7.50 T'\ 14-75 S 10" 8.68 4-75 BB AA 120.13 117.97 114.13 110.06 107.93 100.94 2.96 2.94 3.06 3-0 3.18 3-7 138.00 128.39 132.00 120.48 125.80 111.36 3-4 2-93 3- J 3 2.99 3-24 3-05 i5 6 -47 138.80 150-47 130.90 144.27 121.77 3-n 2-93 3.20 2.98 3-3 1 3-4 Ti 12.25 $ 10" 7.20 5 BB AA 7*1 9.75 S 10" 5.70 5-25 BB AA Thickness of Pis. i 5 $ Area of 2-0" Pis. 4. co 5.63 6.75 r l 14.75 s 9" 8.68 3-75 BB AA IJ 3-55 83-59 I0 7-55 78.77 101.35 73.00 2.94 2.52 3-3 2-59 3-i5 2.68 129.64 91.18 123.64 86.36 117.44 80.59 3.01 2.52 3.10 2-59 3-22 2.67 146.26 98.78 140.26 93-96 134.06 88.19 3.08 2-53 3-!7 2.60 3.28 2.66 7V 12.25 S 9" 7.20 4 BB AA 7V 9-75 S 9" 5.70 4.25 BB AA Thickness of Pis. T 5 * f Area of 2-10" Pis. 5-00 6.25 7.50 6V I3# S 10" 7.64 5 BB AA 83-45 JI 3-35 79-05 103.89 74-85 93-87 2 -57 2-99 2.66 3-5 2-77 3.10 96.91 123.76 92-51 114.31 88.31 104.29 2.64 2.98 2-73 3-03 2.83 3.08 110.89 134.18 106.49 I2 4-73 102.29 114.70 2.71 2.98 2-79 3.02 2.89 3.06 6V io.5# S 10" 6.18 5.25 BB AA 6V 8#$ 10" 4.76 5-5 BB AA Thickness of Pis. \ 1 Area of 2-8" Pis. 4.00 5-00 6.00 6V I3#S 8" 7.64 3 BB AA 73.68 54-55 69.28 51.08 65.08 47.19 2.52 2.16 2.61 2.24 2-73 2.32 84.45 59.89 80.05 56.41 75-85 52.53 2-58 2.18 2.68 2.25 2-79 2-32 95-63 65.22 91.23 6i.75 87-03 57.86 2.65 2.19 2.74 2.25 2.84 2-32 6V io.5# S 6V 8#j 8" 6.18 3-25 BB AA 8" 4.76 3-5 BB AA (44) TABLE 23 (Concluded) TWO COVER PLATES T'S i fV i 10.50 12.00 13.50 15.00 I r I r I r I r 259.04 254.02 251.64 239-97 3-73 3-7o 3-82 3-74 289.00 272.02 281.60 257-97 3-79 3-68 3-88 3-7i 319.80 290.02 312.40 275-97 3-85 3.67 3-93 3-70 351.45 3.90 308.02 3.65 344.05 3.98 293-97 3-68 TV i A f 8.75 10.00 H.25 12.50 235- 6 7 I 5 I -75 227.87 145.48 220.47 I38-97 3-59 2.88 3-68 2-94 3-78 3.00 260.63 162.16 252-83 155-89 245-43 149-39 3-65 2.88 3-74 2-94 3-83 2-99 286.30 172.58 278.50 166.31 271.10 159.80 3-7i 2.88 3-8o 2-93 3-89 2.98 312.68 3.76 183.00 2.88 304.88 3.85 176.73 2.93 297.48 3.94 170.22 2.98 TV ^ T* 8.75 10.00 11.25 !75-54 149.22 169.54 141.31 163-34 132.19 3- J 7 2-93 3-26 2.98 3-36 3-02 195-23 159.64 189.23 151-73 183-03 142.61 3-23 2.92 3-32 2-97 3-4i 3.01 215-55 170.05 209-55 162.15 203-35 153-02 3-29 2.92 3-37 2.96 3-46 3-oo TV i s 7.88 9.00 10.13 163-43 106.37 J57-43 iQi-55 I 5 I - 2 3 95-78 3-M 2-53 3-23 2.60 3-34 2.66 181.15 113.96 *75-*S 109.14 168.95 103.38 3-20 2-54 3-29 2.60 3-39 2-65 J 99-43 121.56 193-43 116.74 187.23 110.97 3.26 2-54 3-34 2.60 3-44 *.6 5 TV * T 9 * 8.75 IO.OO 11.25 1 2 5-39 144.60 120.99 I35-M 116.79 125.12 2-77 2-97 2.85 3.01 2-94 3-4 140.43 155-01 136.03 145-56 131-83 135-54 2.82 2.96 2.90 3-oo 2-99 3-3 156.02 165.43 151.62 J 55-98 147.42 J 45-95 2.87 2.96 2-95 2-99 3-3 3.02 Tff \ S 7.OO 8.00 9.00 107.23 70-55 102.83 67.08 98.63 63.20 2.71 2.20 2-79 2.26 2.90 2.32 119.27 75-89 114.87 72.41 110.67 68.53 2.76 2. 2O 2.8 5 2.26 2.94 2.32 I 3 I -74 81.22 127.34 77-75 123.14 73.86 2.81 2.21 2.90 2.26 2-99 2-32 (45) S13NNVH3 HO ox -a NOIXDHg HO vany 1VXOJ, S1HNNVHQ HO a ox -a NOIXDHg HO VHHy 1VXOJ, MCS MCI (NNCStNMM ON NW^-O xxxxxx xxxxxx xxxxxx OOONOOON ON^ONTJ- ONTfON'"*- t^ OO MvOt^Tj- OOO^ Mvo OO\ONONC^ON Tj-fpfOrOrOrO MMHM WM'HMMM cici(NcJcN v> NNM NNM OOOOO \OvOvOOOOOOO ^-Ov^OOOfC N1>NVOMVO OOOOO XXX X XXXXXX XXXXXX XXXX <00 00 O M .00 O N ONTfONTt ONTfO (46) w J PQ < H TWO CHANNELS AND ONE COVER PLATE B X - 00 g. o -9 v> CO Tj- NO VO NO ON O co^-^-t^M ^ MC CO co 4 IO o 4- vo co ^ vo CO ^" vo TI-IONO ^VONO ^-vo NO - r^. VO q 00 q cc IO 'JC 1 g\ 1^ P. NOlOOOOVOPOMON VOONM O POCS COO cT O w O\ *"- ^O cs 00 00 O 00 O fO UEti c? 5 tn X - NO M -si I 1 c 00 ^* O ^ W O^ SN ScO^C^g OO" S ^ PO o *) o CO CO CO PO PO CO PO COPOCOPOPOPOPOPO - oo ft 2* M 5c ^0 IH vo CNJ TJ- ON VO CO vo M PO M CO 00-<1-POMTJ-ONl-lt^ u 2 o M g ^ -i co VO NO NO NO t^ 00 fO O 00 t^N t^M\o *-* vno in M M (N oo o\o (S &*1 MM X rr;- X Tf ~ A X NM X *e X N CN) O OO NO vo ** NO NO IO VO VO VO O O ONOOOOOC t^-t ^ co co co co CO CO TtTj-POPOPOPOPOPO PO - 00 IO VO CO NO PO O CS ON ON CNI M t^ rf NO 00 PO- PO 00 ONCSNO VO 8: o' o 6 M O NO M ON vo O rj- Tj- vo 'sj- vo NO ONNO WOO VOCNINO Tf ^ 8 S S o? cT c?^ c . CO 4 M ? ? ON ^ ** l^- w rj- S Tt- 10 M CO * TfCNCMOO O CNI ON g S13NNVH3 HO a ox -a K o M in m in in in in in in in in in in (S t 00 ro 00 g. o\ 5. N f.^ s R S O M M (S O M M M N N N N romtnvOOOOO O> O, X X "t X NO X (N X X vO X X X X X X N Tj- vO N * vo xxxxxxxx ^vooo ^VOQO ^vo x 00 1 CHANNELS. ^ m M M 5 2 m f~ 5 2 in po M in- ^ o- m.- s ,,d, a 00 s 5 00 s ^ Ov - ^ O> 3 ^ 2 - - o - (47) S1HNNVHO HO a ox -a NOIXDHg HO vaay -ivxoj, S1HNNVH3 HO a ox -a NOIXDHg HO V3HV IVXOJ, ^OtHMOONOWO M MMQsMvOOOu->M Tt-^-Tj-^-tf-TtTfTt 00 O ^f O Tf . IO VO VO IO IO to VO to to to tO IO MO <-O OO CO -+* H* 05|o8 c*io c*o c*c * csloo * nice crtoo c*e ccloo fcloo XXXXXXXXX XXXXXX XXXXXX vOOOO^OOOOvOOOO OOOMOOON OOONOOON l> , IQ in - - in - .. (48) TABLE 25 ONE CHANNEL AND ONE PLATE G EQUALS GAUGE OF CHANNEL CHANNEL. M H 5 1 5 * O AREA OF SEC- TION. Axis AA. Axis BB. G s be e I r e' I r 9 13.25 8x | 6.89 2.04 8405 3-5 94 18.77 1.6 5 if " " 8x& 6.39 1.82 80.31 3-55 .91 16.00 I. 5 8 " M 8x* 5.89 i-57 75-56 3-58 .87 13.22 1.50 c 8 11.25 8x | 6.35 1.98 60.08 3-o8 .89 18.05 1.6 9 I* " " 8x& 5.85 1.78 57-05 3.12 .86 i5-3i 1.62 1 " 8xi 5-35 J-54 53-62 3.i7 .83 I2 -57 i-53 " 7 9-75 8xA 5-35 1.71 38. 9 2 2.70 .88 14.97 1.67 "1 " 11 8x i 4-85 1.49 36.55- 2.74 .84 12.23 J -59 u " 7X^ 5-04 i-59 37-66 2-73 -85 10.52 i-45 tf " 7X J 4.60 1.38 35-36 2-77 .81 8.67 i-37 . " 6 8 7Xtk 4-57 i-5i 24-37 2.31 .81 10.05 1.48 I* " u 7X i 4-13 1.32 22.86 2-35 -77 8.22 1.41 11 u 6x i 3-88 1. 21 21.99 2.38 75 5-54 i.ig (49) TABLE 26 ONE CHANNEL AND ONE ANGLE LONG LEG OF ANGLE PERPENDICULAR TO WEB OF CHANNEL BACK OF ANGLE FLUSH WITH FLANGE OF CHANNEL CHANNEL. SIZE OF ANGLE. TOTAL AREA. Axis BB. Axis A A. J o Q 1 e' I r e r 12 (i 20.5 tt 5X3ix& 4x3 x& 8.59 8.12 1-54 1-35 178.67 172.37 4-5 6 4.61 + .02 + .20 19.97 13.28 1.52 1.28 10 en 15 5X3ix& 4x3 x& 7.02 6-55 1.52 *-3S 97-77 94.13 3-73 3-79 -17 + .0 3 16.98 10.81 I. 5 6 1.28 9 13-25 u 5X3jXfk 4x3 xA 6.45 5.98 i-45 -3 70.70 67.97 3-3 1 3-37 -.26 -5 15.82 9.89 T -57 1.29 8 11.25 4x3 x^ 3X2^X i 5-44 4.66 1.24 .94 47.46 43-55 2-95 3.06 -!3 + .16 9-5 4-58 1.29 99 7 9.75 4x3 x^ 3X2JX i 4.94 4.16 1.16 .89 31.80 29.08 2-54 2.64 .22 + .0 9 8.29 4-05 1.30 99 6 n 8 4x3 x& 3X2JX i 4-47 3.69 1.05 83 20.23 18-37 2.13 2.23 -3 1 + .01 7-59 3-59 1.30 99 (50) A TABLE 27 FOUR ANGLES, ONE PLATE, AND ONE CHANNEL Back to back of Angles = width of Plate + i" L indicates long leg of Angles " E " in contact with channel S indicates short leg of Angles " E " in contact with channel SIZE OF PLATE. SIZE OF ANGLES " C." SIZE OF ANGLES "E." CHANNEL. TOTAL AREA. Axis AA. Axis BB. H ~2 "5; e < JB Q. (5 4 c I r I r e 3 6x| 6x6 x| 6x6 x| 15 33 60.84 528.62 2 -95 12785.41 14.50 15.64 36xj 6x6 x 6x6 x$ 15 33 SO.QO 478.29 3-07 10759.02 14.54 15.08 3 6x| 6x6 x| 6x6 x| 15 33 40.8 4 432.5 6 3-25 8625.16 J4-53 14.23 30X| 6x6 xf 6x6 xf i.S 33 57-09 528.50 3-4 8389.78 12.12 12.97 30x4 6x6 xi 6x6 xl 15 33 47-90 478.22 3-16 7074.84 12.15 12.48 3ox| 6x6 x| 6x6 xf 15 33 38.59 43 2 -54 3-35 5682.11 12.14 n-75 30X| 6x4 x| 6x4 x| 15 33 52.09 526.11 3-i8 7841-38 12.27 12.73 L 30XJ 6x4 x 6x4 xi 15 33 43.90 477.85 3-30 6618.33 12.28 12.20 L 3ox| 6x4 xf 6x4 xf 15 33 35-59 43L97 3-48 53 2 7-84 12.23 !*-43 L 24Xi 6x4 x| 6x4 xj 15 33 40.90 477-7 8 3-42 3997-7 1 9.89 9.69 L 2 4 Xf 6x4 xf 6x4 xf 15 33 33-34 43J-94 3-6o 3224.18 9-83 9.04 L 24X| 5X3M 5X3ixi 12 20.5 34.03 196.38 2.40 3I93-45 9-69 10.51 S 2 4 Xf 5X3ix| 5X3ixf 12 20.5 27.23 176.53 2-55 2572.07 9.72 9.98 S 2 4 Xt 6x4 x 4x3 xj 12 20.5 34.03 237-I4 2.64 3387-15 9.98 11.28 L 2 4 Xf 6x4 xf 4x3 xf 12 20.5 27.21 206.43 2-75 2738.78 10.03 10.71 L 21X5 6x4 xj 6x4 x^ 15 33 39.40 477-75 3-48 2958.90 8.67 8.46 L 2lXf 6x4 x| 6x4 xf 15 33 32.22 43J-93 3-66 2389.51 8.61 7.88 L 2IX 5X3M 5X3M 12 20.5 32.53 I 9 6 -35 2.46 2348.64 8.50 9.20 S 2lXf 5X3ixf 5X3ixf 12 20.5 26.11 176.51 2.60 l8 95-95 8.52 8.72 S 2IXJ 6x4 x 4x3 xi 12 20.5 32.53 237.11 2.70 2505-38 8.78 9.87 L 2lXf 6x4 x| 4x3 xf 12 20.5 26.09 206.41 2.81 2029.79 8.82 9-36 L i8x 6x4 xj 6x4 x 15 33 37.90 477-72 3-55 2091.22 7-43 7-25 L i8xf 6x4 xf 6x4 xf 15 33 31.09 431.92 3-73 1691.84 7.38 6.75 L i8xi 6x4 x* 4x3 xj 10 15 29.46 161.98 2-34 1626.05 7-43 8-95 S i8xf 6x4 x| 4x3 xf 10 15 23-39 135-08 2.40 1315.82 7-50 8-57 S i5Xi 6x4 xi 4x3 x| 10 15 27.96 161.94 2.41 1070.58 6.19 7-5 S iSXf 6x4 x| 4x3 xf 10 IS 22.27 j i35- 7 2.46 870.01 6.25 7.17 S (51) SECTIONS OF COLUMNS, SECTIONS OF TOP CHORDS, Selected from some of the Largest Buildings and Bridges in the United States The values of the sections covered by the tables on Moments of Inertia and Radii of Gyration are suitable for structures of ordinary proportions. The variety of ways in which standard shapes are used to compose sec- tions of monumental structures, has made it necessary to treat this class separately. The sections here given are selected from some of the largest buildings and bridges in the United States. The types show what is customary as well as what can be done when circumstances and condi- tions demand it. It is necessary to be acquainted with these conditions in order to compare intelligently the values of these sections. They are classified and tabulated here in order to more readily serve as a guide in the design of new structures. (53) 33 Tf XO CO ON ON xo co vo CO co 00 M xo ^ co t^. XO Tj- -fr ^ CO Tf 4 1 * t- vo t- * vO xo t^ ON 00 ON h- 1 3- 2 M XO CO co o o 00 xo O 00 M CO o | M M 3- 0, CO 00 M O 00 t^ 00 co XO vo 10 ON Tj- IO vO VO^ | 10 i> |8 ro N V? M ON ON 00 00 ro vO W H M M VO M O IO IO 00 g fcfc *0 (N g 1> M 00 M IO ON ON * p^ p^ ^^ ^ ^ =y y U U ^- N 2, 3, "o "o U U . "^ 15 s ' ,0 (U ' ^ Web Plates ^J :| ^ o M o be C is '3 PS c M C 5 :| . . ILand Title Building, Philadelphia Columns having Two & c ^ c .2 ll r* bB 61 3 b w II '3 || w ^ c W g "^ -3 rt O PH O IWanamaker Building, New York Adams Building, Chicago .... Columns having Three mers' Bank Building, Pittsburg umn i Waldorf-Astoria Hotel, K 6 6 6 66 (54) s O o WJ f * n tM S o S S ^ s s i a CM S o * a fc w J on < I- PQ M HI S3 6 o\ M H]* cc 5 HI C4 - 4 M oq" M" o\ o co to co 6 6v M M M O vO co O ON ON co M 00 4 4 co O" O\ to 3 - M O NO vo vO vO W C4 NO M & to 1 1 M O O 04 10 O 8 S 8,5- M r^ O t^. C1 vO -* OO C* M ^O ^O SN 3- ON vO S co to o \O N CO ,,3 M N O O * co r** O O Ov Tj- 00 ON to rf 10 \ ON O O M M M Ht " H HI *>. OO O\ HI CO O M O to H M M M O O co ON I M vgvg cTS- to to O ON M vo M OO to ^t ON ON to o o 00 00 vo c^lcol Tj- CO CO H in ** M in in oo o 0- - "; in o ** ** 5 B 1 M f^ M SO t^ M H M 00 11^ f^ M fS PO VO ** OV M M M- - . 8 sa B in o vO vO 00 C4 W ro ! ,_. ADAMS BUILDING, CHICAGO 3 - i3"[ 5# 6 Pis. - 18" x i" 2 Pis. - \2\" x |" FARMERS' BANE BUILDING, PITTSBURG 6 Pis. - i 3 "x \" 8IJ.-6" x 4" X I" 2 Pis. - 24" x \\" 4 Pis. - 24" X f" COLUMN 1, WALDORF-ASTORIA HOTEL, NEW YORE 4- 15" [* 55# 2 Pis. - i 4 \" xf" 6 Pis. - 20" x |" (58) SECTIONS OF COLUMNS M* * ^v A , 1! =i ^if* COLUMN (b), IVINS BUILDING, NEW YORK 3 Web Pis. -24" xH" 4 Cover Pis. - 28" X H" 8|-6"x6"xH" COLUMN 280.WALDORF-ASTORIA HOTEL, NEW YORK 10 Pis. - 32$" X |" 4 Pis. - 36" X I" 4t!-6"X4"xH" 8ll -6"x 3 i"xf" COLUMN (a), ILLINOIS STEEL COMPANY, CHICAGO (59) SECTIONS OF COLUMNS COLUMN (b), ILLINOIS STEEL CO., CHICAGO (60) SECTIONS OF BRIDGE CHORDS WILLIAMSBURQ BRIDGE, NEW YORK 300-FOOT SPAN, BOONE VIADUCT, BOONE, IOWA 4 [*_ _ 6 /r x 4" X I" 4 LS. - 6" X 4" X T V 2 Pis. - 30" X f" 2 Pis. - 1 8" X |" PANTHER HOLLOW STEEL ARCH, PITTSBURG SECTIONS OF BRIDGE CHORDS INTERNATIONAL BRIDGE, BUFFALO 4[i 6" x 6" x f " 2 Pis. 40" x \" 2 Pis. - 27 Y f x I" 2 PIS. - tf" X T y MONONGAHELA BRIDGE, PITTSBURG 4 li. - 8" x 8" x i" 2 Pis. 2O" X l" 2 pis. - 3 6- x 3r y NIAGARA CANTI- LEVER BRIDGE, NIAGARA FALLS SECTIONS OF BRIDGE CHORDS MEMPHIS BRIDGE, MEMPHIS, TENN. 81s. - 6" X4" X |" 8 Pis. - 30" x H" -^l //f ; //* j. /** .^V- THEBES BRIDGE, THEBES, ILL. NEW OMAHA BRIDGE, OMAHA, NEB. 1 PL - 28" x \" 2 Pis. - i8"x i" 2 PIS. - 10" X f" 2 Pis. - 5" x f " (63) SECTIONS OF BRIDGE CHORDS //* CAIRO BRIDGE, CAIRO, KENTUCKY INTERNATIONAL BRIDGE, BUFFALO 1 -. /-S" /-S SIXTH STREET BRIDGE, PITTSBURG LoceJ (64) SECTIONS OF BRIDGE CHORDS BELLEFONTAINE BRIDGE, ALTON, ILLINOIS _ iJf MONONGAHELA RIVER BRIDGE, PITTSBURG RANKIN BRIDGE, RANKIN, PA. SECTIONS OF BRIDGE CHORDS - I" ' ROOF TRUSS, WALDORF-AS- TORIA HOTEL, NEW YORK I2 |_s__6"x 4"X \" ioPls.-29j // x f" 2 Pis. - 3 6""x J" EADS BRIDGE, ST. LOUIS (66) UNIT STRAINS The following data on unit strains, pages 67, 68, 69, 70, 71, and 73, is taken from Bulletin No. 41 of the American Railway Engineering and Maintenance of Way Association, published in 1903. STRAINS UNDER DYNAMIC LOADS The subject of unit strains in iron and steel structures is, as said before, so closely related to the quality and strength of material used, and the loading which the struc- ture has to carry, that the three must be studied together. The quality and strength of material to be used in the structure is well known from the numerous tests made on both specimens and full-sized structural members in the last fifty years, during which period iron and steel have been used for struc- tures of various kinds. The load which the structure may have to carry during its service is, c n the con- trary, more or less an assumption at the time the structure is designed. If this is a railroad bridge, we assume that it shall carry a load represented by a typical train. The static load applied on the bridge from this typical train may closely represent the static load of the heaviest actual train passing over the bridge when in service, but we are still in doubt how much this static load should be increased to closely represent the dynamic load from the moving train. It is on the question how to provide for this dynamic load of the moving train that the engineers who design bridges differ, and there is a wide field for the investi- gator to determine by experiments and observation what the relations are between the static train load and the load produced by the moving train for various lengths of spans and for the various members of the bridge. Such investigation, if carefully made and of sufficient extent, would be of great value to both the designers ajid the purchasers of bridges. The Committee is now making some investigations in this direction in connection with the subject of impact. Two distinct methods are used to provide for the excess of the dynamic load above the assumed static load. The first method, which we may say has been used ever since bridge designing became a science, and which is still adhered to by many engi- neers, is to vary the unit strains in the different members of the structure according to some rule.. Some engineers vary the unit strains according to the relation between (6?) UNIT STRAINS live and dead load, or total load and dead load; some use different fixed unit strain for the different members of the structure; and some use different unit strains for live load and for dead load. The second method, which has lately found favor with and has been adopted by many of the American engineers, is to use a constant unit strain for the same grade of material and provide for the dynamic effect of the load by increasing the static live- load strains according to impact formulas. This last method seems to be the most rational, as it treats the dynamic increment of the load as a load, and not as a decreased strength of material. It has been thoroughly demonstrated, by experiments, that when a piece of iron or steel is strained above its elastic limit, but below its ultimate strength, it will finally break if the strain is repeated a sufficient number of times, and that the nearer this strain is kept to the elastic limit, the larger is the number of repetitions of the strain that are required to break the piece, and that when this repeated strain is close above the elastic limit, the number of repetitions required to break the piece rapidly ap- proaches infinity. It is therefore reasonable to assume that a piece strained below the elastic limit will stand any number of repetitions of the strain without being in- jured or reduced in strength. If, therefore, all the possible strains with their dynamic increment to which the various members of the structure will probably be subjected are found, and if such perfect workmanship is possible that each piece in a member is strained equally per unit with every other piece in the same member, and the material is free from defects, then it would be safe to use a unit strain equal to that required to strain the member up to the elastic limit. The material may have defects not discovered by the in- spection and the workmanship is not perfect. The pieces forming the member will, therefore, not be equally strained in the finished structure. Some pieces may have to be stretched considerably before other pieces take any of the strain. How much additional section should be allowed for these defects in material and workmanship depends on the care taken in the manufacturing at mills and shops, and on the thoroughness of inspection. If the section is increased seventy-five per cent., it seems reasonable to assume that these defects have been provided for very liberally. This would give an allowable unit strain equal to four-sevenths of the elastic limit. UNIT STRAINS IN COMPRESSION MEMBERS There is much diversity of opinion in regard to unit strains for compression mem- bers. Numerous tests have been made, the results plotted on diagrams, and formulas (68) UNIT STRAINS devised to agree as closely as possible with the average of the results of tests. Most of these formulas, when reduced to the same base unit, follow each other closely within the limits for length of member divided by least radius of gyration of cross-section of member that are used in good designing. The attached diagram (page 73) gives the allowed unit strains, derived from some well-known formulas for the various relations of "1 over r," reduced to a base unit strain of 16,000 pounds per square inch. The straight-line formula, first proposed by Thomas H. Johnson, and used, among others, by Theodore Cooper in his specifications, is very simple, and gives values that are no doubt as close to the actual conditions as any of the other more complicated formulas, within the limits for the relation "1 over r" used in good designing. This formula discourages inexperienced designers from using long and flimsy compression members, which they are very apt to do when they use a formula which will allow comparatively high unit strains for high values of the relation "1 over r." The earlier formulas always made a distinction between members with pin end connections and members with riveted end connections, but the later formulas make no such distinction. A member with pin end connections is not as rigid as a member with riveted end connections; but, on the contrary, pin connections do not transmit the secondary bending strains, caused by the deflection of the structure, to their member as much as riveted connections. It seems, therefore, as if the advantage of stiffness in a member with riveted end connections is, at least to some extent, counterbalanced by the dis- advantage of transmitted bending strains, and that there is practically no difference in strength between the two members, if of same section but with the above difference in end connection. Our knowledge is still limited in regard to the effects of alternating and com- bined strains. As the members subject to these strains are very few in an ordinary structure, we can afford to be liberal with material in proportioning them. The large number of bridges are of so short spans that the lateral and sway bracing should be proportioned to resist the effect of the swinging and swaying of the trains rather than the effect of the wind pressure. The term "wind bracing" is misleading, except for long spans. There is no reason why the unit strains allowed on these parts of the structure should be different from those previously given. (69) SUMMARY OF COMPRESSION FORMULAE From Bulletin No. 41 of the American Railway Engineering and Maintenance of Way Association A Gordon 's Formula. Square bearing. 50000 B " 1 J2 I + 36000 "B Gordon 's Formula. Pin and square bearing. 50000 i + 24000 C Gordon 's Formula. Pin bearing. 50000 i + 18000 r 2 D American Bridge Co. Standard specifications railway bridges. 15000 13500 r* Boston & Maine R. R. Standard specifications riveted members. 8700 10000 i + 28000 r 2 Boston & Maine R. R. Standard specifications pin members. 14000 G J- B. Johnson's Formula. Riveted ends. H J. B. Johnson's Formula. Pin ends. (70) SUMMARY OF COMPRESSION FORMULA (Continued) From Bulletin No. 41 of the American Railway Engineering and Maintenance of Way Association I Max von Leber's Formula. In Bulletin of European Railway Congress. P, = o.oi - r J Cooper's Formula. Chord segments. Live load strains. 10000 - 45 - K Cooper's Formula. Posts of through bridges. Live load strains. P a = 8500-45^ L Cooper's Formula. Posts of deck bridges. Live load strains. Pi = 9000 40 - M Formula recommended by the Committee on Iron and Steel Structures. P t = 16000 - 70- P = Base unit strains in Ibs. per square inch. PI = Allowable unit strains in Ibs. per square inch. 1 = Unsupported length in inches, r = Least radius of gyration in inches. E = Modulus of elasticity = 29,000,000. f = Elastic limit = 28,000. a = Values given in table in Boston & Maine R. R. speci- fications for metal bridges, 1896. s = Factor of safety. (71) w j n * JO O O O PO NO ON CNI to rf CO PO 8 to NO CN! to OO M to rf PO PO 1 CM s O ON SNC^ 00 M oo oo R. NO CO t- t^ NO I CO CM CO NO 2 8 ON CM PO PO O O ON C0_ CM IH M JO O O O tO W NO M H CO rf NO to rf PO CNI 0^ M CM 8" | o O O CM 00 CM PO ON 00 o o PO 00 tO NO rf .ON 00 ON to rf O rf 80 to % ct JO to ^ M rf -' JO O O OO NO rf CM CN! to OO M IO rf PO PO 8 CM M I O rf (N CM to ON Jc/0 o OO OO N8 rf ro O t^* \O ON to O 00 10 rf if PO PO CM O CO NO CM IH M JO O O O to PO IH PO to PO PO rf rf CO O) *H ON ON CM CO rf CO 00 Jo O) t- NO RNO* !>. NO NO O to NO" NO 8,2 to to CM PO 10 PO to to H JNO NO CO rf to to to to to to CO) CO PO O O ON NO M t CO PO 00 CM M CM M M R Q\ vQ M \Q O ON M ! ON 00 si CO t- O NO to to to to o PO to ON LO OOO ON NO CM rf rf rf ia PO PO O CO PO CM a CM M CO CO PO rf 8 8" V CO NO 8 NO ON * O O O O O CM > CM ON t^ ON 00 !> rf M PO PO PO PO PO t O O to to 00 rf NO NO Jo <"O t*> IO Q Jo o o o 00 to O PO to to to rf O O PO tO NO PO CM O to O < 8 N| ON 00 O O t^. t^ PO NO^ Jo CM I/J >a to rf rf r?^ (J JO O O O M to rf ON ON NO CM NO to to to rf to o ro ro & 10 Jo PO 00 I- CM to O ON IH to IO (N CO t^ M M S s. NO tO ^O ON \J~> rt pa JO O O O CO rf CM O IO to to IO 1 O O CO | n PO % ON rf CM NO IH O ON O PO ON o M 28 1 1 CO t^ NO IH CM 00 t^ NO O O ro O \o ^ < Jo o o o NO CM H CM ON 00 NO PO to to to to i 0_ f ON NO to O CO CO O CM OO to ON CM M CO ON ^ & 5 o o o o to to 00 CM 00 co CO rf ON ON 00 00 ON 00 ON to 1 - 00000 M o * ^- to to O O O O O O O O O O O O O NO O - t~^ NO O VO O O 10 O 10 O vo O NO M t^ 10 10 * Tf CO O O O O O O vo O vo O vo O (N 00 fO ON Tf O CO - o o o o o M NO OO CO t^- NO * (N O 00 5- 2 g.^ SN NO 't M ON NO O O NO PO M ON ON O o o o o o o O ON NO 1-1 ^t" O ON ON ON OO r*- NO NO NO NO 00000 10 10 ro ON Tf r^ NO 1O rO . to fO vO IO VO IO VO O t^ CO ON O M PO M ON t^- NO "^ (S VO Tf Tj- rj- Tt rt fc O O O 10 NO ON NO M O ON O N *> PO - *O *- O ^O NO ON * ^t PO PO PO K O O O O O >O O ** ^ vo O O 00 NO PO PO PO O M \O M M M HI O O O CNI M o rt- CO >O M \O w \O ON ON OO OO t> 000000 Tj- M W VO O t^ 00 * ro M ON O Tf o o o o o "t 00 ON Tf M ON t^* t^* ON (N ON t^ to ro O O O O O O N rt ON NO Tt" Cl NO M OO NO vo O VO M O O O O O O ON OO O OO O t*- M N CO O ON ON 00 NO XO Tj- -^ Tj- Tf O O O O O CO 00 ro to fO M N 000000 M ON ON CO t^ VO OO M NO CN ON t^- >-) rh N M ON 00 CN] (N CN CN) M M <5 O O O O O O NO xo 00 00 O 00 TJ- t^ 00 O ON ON 00 t o o o o o t^ \O M IO M *> * O -^ 00 NO IO rl- N O O O ro M O) ro r-^. M Tj- t^ O fO ON t^ vo rj- M 000000 t^. - PO ON O O ON t> NO rf PO PO vB Reg & 00000 O M (S CO Tf O O O O O O WO t^ 00 ON O (74) CURVES CORRESPONDING TO FORMULA ON PAGES 70 AND 71 1 I I 5 * 1 1 s ^ * > sfujs 41 un 9/qoMO/iy I I (75) RAILROAD BRIDGE SPECIFICATIONS NAME. H < M >< GRADE OF STEEL. ELASTIC LIMIT. SAFE TENSION. SAFE COMPRESSION. SAFE STRESS COMBINEUJ American Bridge Co. Theodore Cooper The Osborn Eng. Co. *A.R.E. &M.ofW.A. Pennsylvania R.R. N.Y.C. & H.R. R.R. Missouri Pacific I9OO I9OI 1903 1903 I9OI I9O2 I9O2 52000-62000 60000-70000 540OO-62OOO 60000-67000 52OOO-62OOO 60000-70000 55000-65000 52000-62000 56000-64000 52000-62000 60000-70000 * Ult. JUlt. 32000 35000 28000 28000 33000 $Ult. 15000 17000 Variable 15000 17000 16000 15000 L.L. - 8000 D.L. 16000 15000 {15000 17000 D+f B D+B D+IB D+B P P 13500^ iiooor Straight line-Variable ( i 5000 i 7000 \ P P L X ' 36ooor 2 ' 36ooor 2 16000 70- r 15000 il * 13500- f 8000 16000 il P H P I iSooor 2 iSocior 2 17000-80- D = direct stress in pounds per square inch. B = extreme fiber stress in pounds per square inch. L.L. = live load. D.L. = dead load. * American Railway Engineering and Maintenance of Way Association (76) HIGHWAY BRIDGE SPECIFICATIONS NAME. K M GRADE OF STEEL. "" ELASTIC LIMIT. SAFE TENSION. SAFE COMPRESSION. SAFE STRESS COMBINED. American Bridge Co. 1901 52000-62000 60000-70000 i Ult. 15000 17000 {1 5000 1 7000 D+l B P P I 35 oor2 ' nooor 2 Theodore Cooper 1901 54000-62000 60000-68000 iUl, Variable Straight line-Variable D + B The Osborn Eng. Co. I9OI 52000-62000 60000-70000 32000 35000 2OOOO 22000 f 20000 22OOO D + B < P P I 36ooor 2 ] 36000^ BUILDING SPECIFICATIONS NAME. o5 <: H > GRADE OF STEEL. ELASTIC 1 LIMIT. 1 SAFE TENSION. SAFB COMPRESSION. SAFB STRESS COMBINED^ Charles Evan Fowler I9OI 55000-65000 iuit. 15000 I 12500 41.7- . . . C. C. Schneider 1904 55006-65000 28000 16000 16000 70 - D+$B New York Bldg. Law l8 99 54000-64000 32000 16000 15200-58 - - Chicago Bldg. Law 1903 . . . 15000 15000 reduced . . . D = direct stress in pounds per square inch. B = extreme fiber stress in pounds per square inch. L.L. = live load. D.L. = dead load. (77) TABLE 32 SAFE LOADS OF TWO ANGLES T Short legs outstanding Safe Loads are based on the New York Building Law Formula, P 15200 58 - Safe Loads given are total safe loads in thousand pounds For sections to the left of the heavy line - is less xiian iao LEAST. r TOTAL AREA. SIZE OF ANGLES. b. TO b. OF ANGLES. UNBRACED SPAN IN FEET. 4 5 6 7 8 9 10 I.4Q 14.62 7X3X f 1 194.9 188.1 181.2 174.4 167.6 160.8 J53-9 1.48 13.50 xtt f 179.8 J 73-5 167.1 160.8 154-4 148.1 141.7 I. 4 6 12.34 x f 1 164.0 158.2 !5 2 -3 146.4 140.5 134.6 128.7 1.40 II.lS xA 1 147.7 142.1 136.6 131.0 125-5 119.9 114-3 1-39 10.00 x i i 132.0 127.0 I22.O 116.9 111.9 106.9 101.9 1-35 8.80 xA A 115.6 in. i 106.5 IO2.O 97-5 92.9 88.4 1.79 13.88 6x4 x f f 189.4 184.0 178.6 J 73-2 167.8 162.4 I 57- 1.77 12.82 x& f 174.7 169.7 164.6 159.6 J54-5 J 49-5 144-5 1.76 11.72 x f 1 159.6 !55- !5o-3 J 4S-7 141.1 136.4 131.8 1.70 10.62 xA \ 144.0 139-7 !35-3 131.0 126.6 122.3 118.0 1.69 9-50 x i i 128.8 124.8 120.9 117.0 113.1 109.2 I0 5-3 1.65 8.36 xA A 113.0 109.5 105.9 102.4 98.9 95-3 91.8 1.62 7.22 x f 1 97-3 94.2 91.1 88.0 84.9 81.8 78.7 1.56 9.84 5X3^X f 1 132.0 127.6 123.2 "118.8 114.4 IIO.I I0 5-7 1-55 8.94 xA i 119.8 115.8 iii.8 107.8 103.8 99-8 95-8 1.54 8.00 x * } 167.1 I0 3-S 99-9 9 6 -3 9 2 .7 89.1 85-4 1.50 7.06 x& A 94.2 90.9 87.6 ' 84-4 81.1 77-8 74-5 1.46 6.10 x I 1 81.1 78.2 75-3 72.4 69-5 66.6 63.6 1-43 5.12 xA A 67.9 65-4 62.9 60.4 57-9 55-4 52-9 1.24 7-24 4x3 XA A 93-8 89.7 85-7 81.6 77-5 73-5 69.4 1.25 6.50 x i i 84-3 80.7 77.1 73-5 69.8 66.2 62.6 1.25 5-74 xA A 74-5 7i-3 68.1 64.9 61.7 58.5 55-3 1.26 4.96 x f 1 64.4 61.7 59- 56.2 53-5 50-7 48.0 1.27 4.18 xA A 54-4 52.1 49.8 47-5 45-2 42.9 40.6 .91 5.00 3X2^X \ \ 60.7 5 6 -9 53-i 49.2 45-4 41.6 37-8 .92 4-44 x^ A 54-1 5-7 47-3 44.0 40.6 37-3 33-9 93 3.84 x f 1 46.9 44.0 41.1 38-3 35-4 32-5 29.6 94 3.24 xA A 39-7 37-3 34-9 3 2 -5 30.1 27.7 25-3 95 2.62 x \ A 32.1 30.2 28.3 26.4 24-5 22.5 20.6 77 3.10 2$X2X f 1 35-9 33-i 30.3 27-5 24.7 21.9 19.1 .78 2.62 x^ A 30-5 28.1 25.8 23-5 21. 1 18.8 16.5 .78 2.12 x i A 24.7 22.8 20.9 19.0 I7.I 15.2 13.3 79 1.62 XA \ 18.9 J 7-5 16.1 14.6 I3.'2 n.8 10.4 (78) TABLE 32 (Continued} AS COLUMNS OR STRUTS Short legs outstanding Safe Loads are based on the New York Building Law Formula, P 15300 58 - Safe Loads given are total safe loads in thousand pounds For sections to the left of the heavy line - is less than 120 UNBRACED SPAN IN FEET. II 12 14 16 18 20 22 24 26 28 30 147.1 140.3 126.6 113.0 99-3 85.6 72.0 58-3 44-7 135-4 129.0 116.3 103.6 90.9 7 8.2 65.5 52.8 40.1 I22.Q II7.O 105.2 93-4 81.7 69.9 58.1 46.4 34-6 108.8 103.2 92.1 81.0 69.9 58.8 47-7 36.5 25-4 96.9 91.9 81.9 71.9 61.9 51-9 41.8 31,8 21.8 83-9 79-3 70.2 61.2 52-1 43-o 34-o 24.9 15.8 151.6 146.2 r 35-4 124.6 113.8 103.0 92.2 81.4 70.7 59-9 49.1 J39-4 134-4 124-3 114.2 104.1 94-o 84.0 73-9 63.8 53-7 43-6 127.2 122.5 "3-3 104.0 94-7 85-4 76.2 66.9 57-6 48.4 39-i 113.6 109.3 100.6 91.9 83.2 74-5 6 5-9 57-2 48.5 39-8 3i-i 101.4 97-4 89.6 81.8 74-o 66.1 58.3 5-5 42.7 34-8 27.0 88.3 84.8 77-7 70.7 63.6 56-5 49-5 42.4 35-4 28.3 21-3 75-6 72-5 66.3 60. i 53-9 47-6 41.4 35-2 29.0 22.8 16.6 101.3 96.9 88.1 79-3 7o-5 61.8 53-o 44.2 35-4 91.7 87.7 79-7 71.7 63.6 55-6 47-6 39-6 3i-5 81.8 78.2 71.0 63.8 56.5 49-3 42.1 34-8 27-6 7*-3- 68.0 61.4 54-9 48.3 41.8 35-2 28.7 22.1 60.7 57-8 52-0 46.2 40.4 34-6 28.7 22.9 I 7 .I 50-4 47-9 42.9 38.0 33-o 28.0 23.0 18.0 13.0 65-4 61.3 53-2 45-o 3 6 -9 28.8 59-o 55-4 48.1 40.9 33-7 26.4 52-1 48.9 42.5 36-1 29.7 23-3 45-3 42.5 37-o 31.6 26.1 20.6 38-3 36.1 31-S 26.9 22.3 17.7 33-9 30.1 22.5 30.6 27.2 20.5 26.8 23-9 18.1 22.9 20.5 J 5-7 18.7 16.8 12.9 (79) cn H 3 PL, g 5 CO ^ , nO ^S fl i-^ vo vo M co oo r~- 04 vo to Tj- vo TJ- oc Tt ON vO V M ON vO Tj- CM CM CM CM MH M VO O\ O\ M 01 Tj- ON rt CM O 00 00 vo ON co M 00 10 CM O t^ 10 CO CM CM CM CM HI M CM CO rj- M CM M CM ON vC CO M 06 O co CM ON t^ Tf M ON vO CO CM M CM CM M M ON t- 00 O M t^ rt rt CM VO CO vQ Tf o N O W t> tf O O N ^ w oo vo PC O r^. fO fO d CS VO CO M CM M HI M M M O M ro o M -^- r^ vo 00 HI vo vo t^ H > iS __ N t>. M t>. M M ^0 W O VO rf M- oo PO CO CO CM CM CM HH ON O H vO CM 00 CO M ON VO * M CM CM H HI M H 5 vo * ^ *;- ON q M q vO co t^ *> co O ON 00 co 00 O M t>. Tj- M t^. 1O CM ON VO CM O t^. VO CM O vo CO M ON Tf VO t^ M CM O CM O ON IO CO ON O ro O ON *^ vO ON CM VO ^ s 5 * ^ r? O Tf CO CM HI 00 vo rf CM O . H XO 10 O * VO CM & 2 * to 00 ON H 00 Tj- O O PO ON t^- fj O t^. Tj- CM rf t^ ON t^ Tf CM ON VO CO t^ M ON t^ vQ 00 t^. * CM O 00 CO VO O\ ON Tf VO t^ ^- OO co O t> t^. ts. ^- ON 00 M CM ro vo vo t^ fO ON IH 1^ Tf O *> * O ^" HI OO O CM CO OO vo CM O t^ '^f T^- t^. VO CM O ON t'* vo co M M O 00 Tf ON t^- M CO HI O ON ON 00 ON ^ Tf CM co M M M M CM CM CO OO ^J" CM 00 VO M 00 Tf M rj- f5 ro ro CM CM CM CM 00 VO VO VO t^ ON vo co O l>- Tf CM CM CM CM M M M T}- HI OO VO 800 vo co HI . HI M HI HI VO t^ M 00 ON O 00 t^. ON co O OO O O CM Tf VO 00 o M ON 00 O 00 ON Tf 00 CM OO VO M OO VO M ON Tfr M M M CM ON vO rf M 00 vo ON M t^ CO ON o ON vo n- M ON r}- ro fO 00 * rf CO t^ VO CM 00 CM CM ON vo OO CO a CO ON vO CM ON vo CM Tf CO CO CO CM CM CM O t Tt HI 00 VO M ON t^ ^ CM t* M 1^ T}- M OO ^ N OO t^. t^- t^ vo vO vO 00 VO CM 00 VO CO CM CM CM HI M M ON vO co O *>. t>. t^ t^ t^ O < 4 CM CM CM CM CM CM CM CM CM CM CM CM M HI M HI HI B x CO vO \O M CM O t> VO t^ O vO O CM CM 0X Q IH M t^ 10 ON 00 Tt ON vo VO Tj- -^ HI Tf HI CO t^ VO CM CO <; ~ VO VO CO VO VO HI ON vO co M 00 vo * M ^^ O OO co O t- CM M ON OO t^ VO ON CM Tt t^ O VO vo rf CO CO S. co * CO HI CM HI CM PQ CO ' * ' co 2 00 CM 00 * "* * vO O t^ ON co O CO t^ VO M t>. t^. CM CO vO ON 00 t^ *> 00 vo O 00 O CM HI CO VO VO TJ- M o t^ in S % 17 c8* NO* CO 01 0) CM 01 HI M 10 1^ VO 01 HI VO CO " ON PO ON "* HI HI d Tf- M CO vo PO O t- PO PO Ol Ol O O HI to O O- CO NO vo 00 00 * ON CO O t^ O M CO HI vo 00 rj- PO 01 NO PO O O rt HI 00 PO PO PO 01 01 01 HI 00 00 ON -^- HI NO CO O CO NO * M Ol Ol HI HI HI HI vo 01 PO PO HI O CO N OO Tj- CO CO PO K M H f co 01 PO co vo PO CO rf Ol CO vo CM ON NO PO * t^ 01 NO VO Ol O t^- to Ol fa NO vo 00 00 r^ NO ON t^ co OO t- NO ON M HI ^t t^ M z O VO CO *> HI t-^ PO O NO PO Ov I s ** PO O $ CO . Ol O O- CO t>. NO Tf HI ON HI HI HI M NO OO Ol Tf d t^> Tf HI OO PO t^ CO to ON ON PO ON ^ 4- u vo d vo d vo ON '*' d 00 to HI 00 Tt HI HI Tf CO PO Tf VO Ov to PO O t^- ^ CO t^ ^- M ON ON t^ vo CO O M ^J* TJ- \o O 4 s ** ^O OO 10 VO HI VO PO PO ON ^ HI t>* P M XO t-t PO ON W to C^ ON oi O O O O ON O * HI 00 to 01 10 M OO Tf O 00 vo PO M HI vO IH IN- O^ 00 t*** O\ Tf 6 M \6 00 M Tj- co O r*- O \d to O r^ rt HI oo to t^ 00 NO Tj- H, d PO co" ^f d HI ON VO Tf 01 _ t^ Qx M 10 t^ M 01 ON O HI CO ON HI t^ t^ NO ^l- M M rf GO O\ ^t" 10 t^ O t^ t"* VO PO HI ON HI t^ VO Ol ON to ON Hi VO O to HI O *"** VO Ol NO PO M Th CO t- Tf O t* 01 vO ^J- t^ Tf O Ov 00 *^ O M PO t CO HI O PO vo NO HI OO rf HI t- PO vO VO 01 ON t^^ ^ 01 CO O 01 Ov NO t > * ON Ol vo O 01 O CO VO PO HI O PO t^ HI 00 NO t^ ^ Tf M VO oo to O HI M 0> PO NO NO CO ON ON O r>. 01 ON ^ HI r^. ^f ^ ^* CO PO PO 01 Ol rj- CO ON NO PO ON CO Ov NO PO O NO PO Ol Ol Ol Ol HI to t>. O co vo PO M ON NO PO (M Ol HI HI HI . \O vo VQ \o vo vo to t> to 01 oo NO co HI i-i i-i o O O O *^ co HI 00 t^ NO NO NO to 8 r^ Tf Tf vo O ON ON t^ CO HI vo O 01 01 *"* vo NO ^" ON vO O CO Tj- ON to NO O co ^ to 3- t NO Ol co < \0 vo PO vo vo M ON NO PO HI 00 vO rj- HI Ol Ol Ol HI HI M HI CO 00 PO *^ 01 HI o co t^ to ON 01 ^ t^ O to to rj- co CO HI . Tj- Tf * r^* . M w 00 ON oq ON CO ON 9 t^ HI NO VO OO ^ HI M Ol to PO O ^ CO O 10 -^f "O M O CO co PO Qs O^ O^ NO NO Tf 00 PO to M 01 o 01 < ON O 00 VO CO HI HI 3- CO 01 vo ON PO O \O W CO 10 Tf M rO t^** cs \O O ^" to NO t^ to 01 CO ^t* ON ^ ON \O 10 10 -^ ^ PO U 2 rt & S - 00 C ro ON *>- ro M (X) v PO P PI PI O4 M H -2 00 Pl co O H t^ J p * 10 t^ ro vo co PI 10 M ON 10 CO O J CO CO t 10 00 O O l^ * 00 -* ON VO ro 1 P) PI P) M M M NO M fc *5 Tf- *5 ON f) OO u MO 00 M CO 1>- ^ C T}- QS r> n Q\ \r> p TJ- ro ro ro N d C 1 -> CO M M OO l^ t^ H M 6 06 od 06 i ^t r- * ro P< PI P) M M Ov t>- 00 00 ro O C . Tl- 10 vO 10 Tt ro It M 00 00 O O fD rj- u \O M O ^ l-l t^. P 1 Tf ^ ro fO f5 M P -> PI ON t- ^ P4 O > P) t^. to P) O 1 . O ro P) P) Pt HI M XO O\ fO 00 Tt- rO T t- 10 o H cs o oo P* M M 00 O t^ ON 00 f ro 00 >0 O vO M < ro P P) P) P4 M M (N 00 00 * O C Js VO ^ O ON t^ Tf O M Tf C\ ON Tt 10 CS C M uo M t^ rf O V" uo rf- rj- CO ro CO c > Tf \O O M ON vo M 00 l ro ro w P Pi M rt- ro 00 00 ro O f rf ro ON vo ro M < l CN ON C4 . M (N ro o O\ Qs N t>- M CO f LO vo fO vo vo M c vo ro M oO O Tf H O4 M * ' * * r^ M O PJ ro O r>- O u O ON 00 ro Tf t>~ P ~> O ON 00 PI in Tf ro 10 ON O ro vo X . oo 10 ro O ro 00 P O \O ^t ro M O 00. j O VO IO 00 O ro O ^ c*3 f) N C* M ! N O O ^- \O O"> M ro t>- Ov "4" *^- M ro CO 10 O 00 TT M Tj- CO f5 PO N N N r^ r> to O O vo 10 06 06 ON t^. f> w CO NO *5 W 1-1 M M z t^ IO OO M W **> CO * C i "2 pa M O O\ * 00 00 00 TJ- 6\ cJ 06 M d 6 00 O * d 00 <* O 00 00 O N ON NO M 6^ NO PO ON O M O t>. fO Ov w vo fO (i M t^. vO 00 r- ON * ON rO t^ TT CO 10 M O 10 rj- rt f> rf) fO NO rf M ro vo i t^- CN| O NO CS OO ro ro CO M W M * * ON CO NO M * * ON NO NO M M o o t- *> o * NO O t- O t^ PO CO 10 10 * * fO rO M \O M Hi M M O rt Ct CO rf O Tf CO fO N W W . IH M NO NO M CO NO rj- ^- co PO **J N d M CO CO VO CO O ON ON CO 00 00 CO < f !/> ON ON ON 00 00 00 * M O *5 ** M CO fO M t^- CO co Tj- ON CO ON vo O NO NO < NO NO ro O vo M ON NO **5 M OO NO * M & I/} O 00 ro M t^. ro ^- ^- co ro ff) N N * OA 00 ^t M Is. ro oq q w - NO in to co to to to nfco r^rt in TJ- to M O r^. ON w co m od r>- r>- O in $. ^ ?? rj- CO CO N! M co M O ON 00 NO 00 O HI fO 6 ON & CO* t^- NO VO Tt tO M m t^ ON M to NO in rj- T}- CO 8 in O vn O w in t~ O *o O ^o O vo c* in t^ O w O m O vn O in t^ O w m m o vn o vn t^. O $<%<% O OO in to O in co - M m oo m to o oo m CS NO O tO t^ to O 00 vo fO M m oo cs NO H r^. NO \O in in co to co to to Tj- CO CO NO NO vo CM W W ! \O in m TJ- rj- ON ON 00 00 *- O to m oo O in M t^. to o to m oo O to NO N oo in M m oo O fO vn t^ to o NO N oo O to vn oo 00 vn M i>- co C* N M M W O O ON ON ON 00 00 00 t- t^ NO NO NO in in in TJ- co w O t^ ^- HI oo m ON 00 NO in rj- M co in w ON to M O ON 00 NO fO O NO CO \O m <* to M O t^ * M oo M M M M M H* 8 in O m O t^ m N o in O *o O vo O in O vn O in O vn o vo cs o r*- vn w m O oo ON O w O oo O m M CO Tj- VO NO to M ON t^- in 00 ON O HI co CO M O 00 NO ^- m NO co ON rj- -i o oo m to o oo co t^. NO m co m co O oo m - NO IO ^f fO to to to to to 00 00 ON O O cs M d d 6\ to to to to cs CO ON 10 HI CO HI IH CS fO fO CO t- NO vo 1 ^- cs cs cs cs cs -3- O NO fO ON TJ- VO VO NO NO CO CS M O ON CS CS CS CS M 8 fO vo 00 O H CS fO IO to vo CO O to NO t^ 00 O HI VO 00 O fO 10 cs to 10 NO r^ OO O to vo OO 00 O Hi (N to vo rt fO CS HI to to to to to O ON CO 00 t^- to cs cs cs cs NO IO ^ tO CS CS NO NO vo cs cs cs cs cs Ti" tO CS HI HI CS CS CS CS CM O ON 00 t^ t^ to cs cs cs cs 10 O vo O vo CS VO t^ O CS NO IO TJ- "t CO CS CS 00 00 !> NO VO * O HI to ^ vo vo 00 HI rj- f^ ^ ^^ 8 Z> ^~ to cs cs HI fO Tf VO NO CO NO O\ cs vo CO O ON ON CO I~- ON O HI to Tl- HJ VO CO M rl- 1> NO IO IO ^t MM 800 10 fO O CO t~^ HI IO oo 10 to o oo OO CS NO O to M M O ON VO tO O CO vo !>. HI IO OO CS CO 00 !> NO NO to o co io to NO O to r- M VO vo ^ fO to PLATE. HS O * 00 HI vo VO ON to OO CS cs HI M d d ON fO NO O Tj- NO HI 10 O Tj- ON ON 00 CO t^. 00 M 10 ON to 00 fO l> M NO NO NO vo vo ^i- NO O ^ 00 HI O vo ON to OO ^- to cs cs M s | H ooooo O vo O vo O OOOOO vo O vo O 10 80 O vo O vo O OOOOO vo O vo O vo 2 M ON ON 00 00 r^ t^. NO NO 10 VO ^J" ^" to to CS CS HI HI O O O NO to ON vo vo O NO H l> M oo "tf- O NO to 00 * O vo to ON vo HI OO M NO CS OO fO - O vo O vo O vo cs O t^ vo vo O vo O vo cs o t^ vo cs O ON ON ON ON M 00 00 oo CO t^ t^ t^ t-~. NO NO NO NO IO IO IO -JO O HI CO -3- 10 10 fO M ON !> NO 00 ON O M 10 fO HI O 00 fO * vo NO CO NO TJ- CS O CO ON O HI to "^ NO IO fO HI ON "h t- t- J^VO NO NO NO NO NO vo VO vo IO VO ^~ * * Tl- Tj- CO Hw 800 10 to o CO t^ NO IO 00 vo to O 00 to cs HI O 00 10 fO O 00 10 t^ NO VO fO CS fO O 00 vo to HI O CO t^ NO HS O ^ CO HI IO ON to NO O ^ - M HI O O ON CO HI IO ON fO CO OO t^ NO NO NO O * 00 HI vo vo Tt CO fO I JlVIjI JO o o\ oo t^ NO IO ^- CO (S M O ON 00 IN vO IO Tf CO N M N N . CO CO ON CO t^- NO 10 8 to \O PO ON tO HI q M M to 4 PO PI M ^ ? ON 00 O NO PO IO IO NO t^. NO 10 # VO M *T co CO 04 ? t^. co HOC O PO to CO 10 NO r- oo r-^ NO* to Tf CO 10 00 O PO M CN CO 10 NO co CN M d ON vo CO t^ 00 O co to '<% O co IO NO VO CO t^ CO 5 3 CO t^ t^ NO to Tf PO CN) M 32 10 Tf CO M PJ Tf \O 00 NO 10 Tf PO 8 CO ON 00 NO to Tf M PO VO t>- ON PO HI HI CO 2^28 NO O VO Tf PI Tf PO HI NO oo NO 5- 8 CN M O ON 00 co t^ NO IO Tf Tf CO P* M ** 1 10 O 10 CN \o r^ to Tf co P 8 CN to O 10 O to PJ 10 t>. O PI M d ON ON 00 10 10 t^ 810 o CN IO 10 810 IN O to 10 r^ NO to % 2* t^ NO NO 10 Tf CO CO CN IH 32 10 NO 00 ON r* O co NO 8 M PO Tf VO NO CO NO ON P IO 00 ON OO HI O HI PO 10 00 HI Tf IO NO t^ O CO ON PO NO PI 10 Tf ^ CO M CO CO o to t^ 10 CN 8 vo O to O 10 O to 8to O to 8VO t^ O to 10 CN ON PO NO HI * tO NO OO ON t> If) PO HI 8 M CO Tf VO NO 00 NO Tf CN Q S8# O M PO IO CO HI ON 10 \O r^ 10 CO ON CO HI J CO co co co co PI CN CN O) CN HI HI HI IH M H. O 00 10 co 10 CO PI M 8 00 10 CO O 00 00 t^ NO 10 PO to co CN HI 800 vo 00 f^ CO NO 2> oo t^ NC M in ^f CO . ro O OO CO ON O rO vo 00 O NO M OO VO O HI M M PO vo 00 O M t^- PO O PO PO Tf VO M 35 ON t^ vO * in M t^ ro M H N fO N O ON ON IO M >O M CO Tt Tf t^- vO vo fO N 00 Tf O vo vo vO *- - w M rr> ro W ON vO ro 01 vO w vO Tf Tj- VO VO ON VO fO O O vo O vo O vo r^- t^ t^. ^ M CO ON Tf ON ro ^- 00 00 ON rf M OO vo OO PO t-- CS ON M M M M 35 PO O O N * oo ~ O M M VO 00 M Tf w 10 O rf M fO Tf Tt VO ON . IH vo r^. t^ OO CO N VO OO M a^i- co PO ON ON O $ M u 2 *o O 00 t^ vO PO t^ M vo O O M M vo Th ro ro ON fO !> M M M W KJ Tj- rj- CO t- vO vo O Tf 00 IN vo vo vo vO ^ PO O) M vo o n- oo vo *> t-- t- O ON 00 00 PX vo ON PO CO 00 00 ON w _3 X a. - M Tf OO M 00 M rl- r^ - ON 0000 t-. M Tj- OO M Tt VQ 00 M rf 00 M M ro vo OO M (Nl (N CO ro PO PO OO N vo ON ON rO (N W M M O O ON O- !- o o o o 8 s M J? ^? M M N Ol W N (N ro PO PO PO PO rt- Tf Tf Tf 4* vOtnr--.ro M PO *f vO 00 ^f ON 10 t^ ON O N M VO N 00 t vo r^. 00 PO ON r|- O O M ro vo VO M ^. PO VO 00 ON M 00 Tf ON vo M TJ- vo t-~ fi M PO vo t^ M (N ro "> I] . 39 tooooo oooo ooooo oooo 8 ooo oooo ooo ooo ooo oooo ooo ooo t~N.(N\OO MvoeqrooOOvo ^-NOOO OONO"3-roONOO ^NMO ON OO t^* *> IO l^i ^O ^ rO f^O fO CN) H rt 1O I^Tt O-^-. to \0 t-CO M H N ro -t w 10VONO CN^OONt-OfOt-OO^rt Z c/2 ^^^NS lo ^5^^^ HOO QNOOOOi>-OOt^t^t^.\OiOiOiO b O | Joooo ooooo oooo ooooo M 10 OO OfOoO<^0 10 to 10 TJ- VOIO to 10 J o M M M" M CN ^- ffi o 8Q o 8888 Q\ s. N. M -^ %. >+ t^- s* S. - ^t* % >* N* H M---- &*'*'*'* 8 M^ 10 cs O OO 5 | ro ro Tt* M l/> O Q M M M M SH-IOH * HHXHWIVIQ XHAI>I HO aHxawviQ J. OIOO1OO OtOOlOO OOOOOOO OOvOvOOOO M M moio omoio looiooiootoN ^- O . 00 10 qjdaa rt 5 * * 5 (S,---- M M (94) TABLE 45 NET VALUES OF CHANNELS. ABOUT AXIS BB Deducting one hole in top flange and one hole in bottom flange, using standard gauge and maximum size rivet CHANNEL. li s. DEDUCT FOR HOLES. NET VALUBS OF CHANNEL Depth. Weight. I C s I C S 15 55 1 I 56.6 80400 7-5 373-6 53 I 5 49-9 M 50 " " " " " 346.1 492300 46.2 " 45 11 " H " " 3 l8 -5 453100 42-5 " 40 " M 59.1 84100 7-9 288.4 410100 38.4 II 35 " " " " " 260.9 370900 34-8 " 33 " " n " " 253-5 360400 33-8 12 40 I 27-3 48500 4-5 169.7 301700 28.3 M 35 " " " M " 152.0 270300 25-4 " 30 " " " " 11 134-4 238900 22.4 " 25 " u " " " 116.7 207600 19.5 " 20.50 u " " " u 100.8 179300 16.9 10 25 f I 15.2 32400 3-o 75-8 161700 15.2 " 20 " " 17.5 37300 3-5 61.2 130700 12.2 " 15 " " " u " 49-4 105400 9-9 9 20 f 1 12.2 28900 2 -7 48.6 115200 10.8 " 15 " " I3.I 31100 2.9 37-8 89400 8.4 " I3-25 " M M " " . 34-2 81100 7-6 8 16.25 f 1 9-5 25400 2.4 30-4 81000 7-6 " 13-75 " " " " " 26.5 70600 6.6 " 11.25 " " M " " 22.8 60700 5-7 7 14-75 f f 5-7 17400 1.6 21.5 65400 6.2 M 12.25 " " " " " I8. 5 56300 5-3 " 9-75 " " u " M 15-4 49400 4-4 6 13 f f 4.1 14700 i-4 13.2 46900 4-4 " 10.50 " " M " " n.o 39100 3-6 " 8 " " " " u 8.9 3 I 5 2.9 (95) Q \ TABLE 46 NET VALUES OF COVER PLATES About axis BB. The value of d is such that the plates may be used as cover plates for beams and channels l J LMETER RIVET. 1 LMETER I HOLES. I NET AREA OF NET VALUE OF M w H LMETER 1 RIVET. I LMETER 1 HOLES. 1 AREA OF NET VALUE OF CflPM Q P PLATES. PLATES. I C/20H 14,280,000 6, 12,960,000 11,400,000 9,600,000 7.560,000 5,2oO,000 II, 2 760,000 PLATE GIRDERS Compute the moment at the center of the span from equation (a) which for this point reduces to B = -| wl?. Conditions of design will give the depth of girder from which the value of e is obtained, whence / = ~ may be computed. K The curve, in connection with the tables for plate girders may now be made the basis of further determinations as follows, see Fig. 2. Draw the radial line xx repre- senting I above determined, to a convenient scale. In a similar manner draw yy to rep- resent half the span to a convenient scale. Proceed as in the following case in which the required moment of inertia at the center of the girder is 97,000, and the span 480 inches. Uniform Loading (i) Assume that no part of the web acts as flange, and a girder depth of 60 J inches back to back of flange angles. From table No. 49 the value of four 8 X 8 X f angles, 6oJ inches back to back, is 31,384, which leaves 65,616 to be provided for in cover plates. From table No. 51 for two 20-inch cover plates on angles 6oJ inches back to back, the nearest value is 65,677 for two i| inch plates. This can be made up of six 20 X f-inch plates, three on top and three on bottom. From the same table the value of two 20 X f-inch plates is 21,017,* and two 20 X i^-inch plates is 42,903^ Fig. 3- * It is seen from the tables that the value of two plates ij inches thick is greater than twice the value of two f-inch plates with the same distance back to back, since the value of e is greater for the thicker plates; the values should therefore be taken as the value of two plates of the total thickness of each flange plate. (99) PLATE GIRDERS Represent these values to scale on the line xx and draw lines parallel to RS until they intersect the curve RAS. From these points of intersection draw vertical lines to intersect yy, from which the length of the cover plates may be scaled. The cover plates shown in the figures are allowed to extend beyond this point 18 inches. This distance is an arbitrary figure, and will depend on the distance required to develop the plate, and the inclination of the curve. The web plate and stiffener angles are not considered in this example, as the tables give values for flanges only. The required girder is therefore made up of four angles, 8 X 8 X f , 6o inches back to back, and six cover plates, 20 X f inches as flanges. (2) Assume the same conditions as in example (i), except that J of the 60 X f inch web plate is considered as flange. See Fig. 3. From table No. 47, the value of a 60 X inch plate with 8X8 inch flange angles is 8801; the value of four 8 X 8 X J inch flange angles 60 J inches back to back is 31,384; as given in example (i), the re- Fig. 4- mainder of 56,460 is made up of cover plates in the same manner as in example (i). Lines are drawn from xx to " CL of Girder " parallel to RS', from this line all lines parallel to the line representing the value of the web until they intersect the curve RAS; the remainder of the operation is the same as in example (i). (100) PLATE GIRDERS Concentrated Loading (3) Assume a girder of 480 inches span, supporting two concentrated loads, re- quiring a moment of inertia shown in Fig. 4 and bounded by the lines RBS. The uniform load diagram is bounded by the lines RCS. Combining these diagrams by adding the ordinates, for example, AD = CD + BD, the diagram RAS is obtained. By laying off to scale on a vertical line 57" the values of flange angles and cover plates and drawing lines parallel to RDS, the length of the cover plates is deter- mined as shown in the figure. RESISTANCE OF WEB PLATE TO BENDING STRESS B Fig. 5- The general formula for moment of resistance is M r = RI -f- e. This equation becomes M r = RAh+6foT the rectangle shown ; where h = depth of web in inches and A = area of section in square inches = bh. Therefore the resistance of a web plate to bending is equivalent to a flange of ^ of the area of the web concentrated at each edge of the web plate. If it be assumed that an equivalent to \ of the web be cut away for rivets, the equa- tion takes the form M r = RAh-~ 8, or its resistance is equivalent to a flange of J of the area of the web concentrated at each edge of the web plate. The assumption is made in the discussion above that there is no shearing stress in the web, and hence is only applicable at the center of plate girders carrying uniform loads where the web plate is fully spliced. The following table, giving moment of inertia of web plates, is based on of the area of the web plate as effective flange at the center of gravity of each pair of flange angles. (101) -f TABLE 47 a MOMENT OF INERTIA OF ONE WEB PLATE FOR PLATE GIRDERS ABOUT AXIS BB | of area of web considered as effective flange at center of gravity of each pair of flange angles Long leg of angles outstanding FLANGE ANGLES. THICKNESS OF WEB IN INCHES. H Ed * h X H JL M Q Size. Back to Back. 1 A I A i A I H ! I i 4X3X^ i8i ' 78 97 117 136 156 J 75 195 214 234 273 312 18 24i I 9 2 240 289 337 385 433 481 529 577 673 770 24 " 30| 385 481 577 673 770 866 962 1058 "54 1347 1539 30 " 361 675 844 1013 1182 J 35i 1520 1688 1857 2026 2364 2701 36 5X3ix^ 18! 7 6 96 "5 J 34 J 53 172 191 210 229 268 306 18 " 24i IQO 237 285 332 379 427 474 522 569 664 759 24 3oi 38o 476 57i 666 761 856 95i 1046 1141 J 33 2 1522 30 36i 669 836 1004 1171 1338 1506 1673 1840 2007 2342 2677 36 " 421 1089 1362 1631 1906 2178 245 1 2723 2995 3268 3812 4357 42 6X4X 241 1 86 232 279 325 372 418 465 511 558 651 744 24 " 301 375 468 562 656 749 843 937 1030 1124 1311 1498 30 36i 66 1 826 99 1 1156 1321 1486 1652 1817 1982 2312 2642 36 u 42i 1077 J 347 1616 1886 2155 2424 2694 2963 3 2 32 377i 43 10 42 48 1623 2029 2435 2840 3246 3 6 52 4058 4463 4869 5681 6492 48 6x6x& 24i 163 203 244 285 325 366 407 447 488 569 651 24 H 301 337 422 506 59i 675 759 844 928 IOI2 1181 !35 30 U 36i 606 758 909 1061 1213 i3 6 4 1516 1667 1819 2122 2425 36 (( 42i 1002 I2 53 !53 1754 2005 2255 2506 2756 3007 3508 4009 42 11 4 8i I5 2 4 !95 2286 2667 3048 3429 3810 4191 4572 5335 6097 48 541 22OI 2752 3302 3853 4403 4953 5504 6054 6604 775 8806 54 u 6o 3054 3818 4582 5345 6109 6873 7636 8400 9163 10691 12218 60 fi 721 5369 6711 8053 9395 I0 737 12079 13421 14764 l6lo6 18790 21474 72 8x8x 42i 945 1181 1417 l6 53 1889 2125 2362 2598 2834 33o6 3779 42 u 48^ 1448 1810 2172 2534 2896 3258 3620 3982 4344 5068 5792 48 " 54* 2104 2630 3156 3683 4209 4735 5261 5787 6 3 J 3 73 6 5 8417 54 it 60^ 2934 3667 4401 5J34 5867 6601 7334 8068 8801 10268 IJ 735 60 (( 72* 5!93 6491 7789 9087 10386 11684 12982 14280 15578 18175 20771 72 (102) TABLE 48 B -JiL MOMENT OF INERTIA OF FOUR ANGLES ABOUT AXIS BB DEDUCTING ONE HOLE FROM EACH ANGLE One 3" hole deducted for angles less than f" thick One \" hole deducted for angles over T y thick Long legs of angles outstanding SIZE OF ANGLES. TOTAL SECTION. BACK TO BACK OF ANGLES IN INCHES. Gross Weight Net Area. i8i 24i 3oi 36* 42* 48} 54* 6oi 72* 4X3X& 28.4 7.28 5i6 947 1409 2202 x I 34-0 8.60 607 i"5 1777 2595 x& 39-2 9.96 699 1286 2053 3098 x * 44.4 11.24 783 1444 2307 3372 x& 49.2 12.52 868 1602 2562 3747 5X3ix& 34-8 9.16 640 1177 1880 2748 3827 x I 41.6 10.88 756 !393 2227 3256 4536 x& 48.0 12.60 871 1608 2571 3762 5243 x * 54-4 14.24 977 1807 2894 4236 5908 x& 60.8 15.92 1087 2013 3226 4725 6 59i x i 67.2 17.16 1166 2162 3467 5081 7091 6x4x1 49.2 13.12 1661 2660 3894 5432 7I 4 8 x& 57-2 15.20 . . 1917 3072 4501 6280 8267 x 1 64.8 17.24 2163 3470 5087 7102 9352 x& 72.4 19.28 2410 3869 5 6 75 7926 I044I x f 80.0 20.92 . . 2605 4186 6144 8583 II309 xM 87.2 22.88 . . 2834 4559 6695 9359 12337 x I 94-4 24.76 . . 3055 4919 7228 10108 J 3327 C6x 4 x | 49.2 13.12 . 1415 2 335 349i 4946 6584 =3 Xfg 57-2 15.20 . . 1632 2696 4034 57i8 7614 I x \ 64.8 17.24 . . 1840 344 4558 6465 8612 1 x& 72.4 19.28 2050 3393 4984 7214 9613 x f 80.0 20.92 . 2216 3672 554 7812 10413 1 XH 87.2 22.88 . . 2409 3897 5996 8517 "357 t x f 94.4 24.76 2596 43 11 6472 9197 12268 6x6 x f 59-2 16.12 1834 2993 4442 6261 8302 10634 13256 J 937i x^ 68.8 18.72 2121 3565 5 X 46 7255 9624 12329 !537 2 22469 x i 78.4 21:24 . . 2 397 3919 5824 8214 10899 13967 17417 25463 x& 87.6 23.76 . . 2666 43 6 4 6490 9160 12160 15587 19442 28434 x I 96.8 25.92 . . 2897 4747 7064 9973 13242 16978 21180 30984 xH 106.0 28.36 1 . . 3157 5178 7709 10889 14462 18546 23140 3386o x i 114.8 30.76 . . 3405 595 1 833 "773 !5 6 43 20067 25045 36661 8x8 x \ 105. 6 2O.24. 10817 14424 18^7 23217 341 jc xA v^^.vx 118.0 "y * et ^ 22.76 I2OQ3 16130 x/0 / 207^7 O 1 2CQ74 O^ J 38776 ' lo x no 8 O'*'. / v 5C Q2 ^^"yo I 3232 i?6?; / / 22724 ^OV /T- 28430 o / 41810 XN 8 Xtt A ^VJ.VJ 143.2 oo.y^ 79.76 i *-o*o* 14468 / 00 19309 *"*( **+ 2481:9 "~"tjy 3III7 4^7^9 ' N 16 x 1 ^O ** i.6 OV*O X ' 42.76 KJ667 yo y 20918 *T OV 2694O O / 33731 T^O / 0V 49622 4 Xtt OO " 168.0 T.^* / ^^ 46.12 3 I 16861 22520 2QOOQ OOl O A 36328 ^34^7 16 X i 180.0 if W. i ^ 4 0.4.O 18021 24076 y^^v 31021 O"v)^ W 3881:1; Ootj / C.7IQO ^* 8 x4| 102 o ^.y .i^.vj C2 72 ' 10180 m^prfu 2c64<; 33O5I J^^JJ 4I4O^ / A y'-' 5ooco ^16 X I A vy ^ . w 204.0 O-^* /* 56.00 . . iy i OF FLANGE Is n IN INCHES. Two |" holes deducted for plates less than f " thick " i'' " " " " over T V' thick If 4 one-inch holes are deducted, use values of plates 2 inches less in width THICKNESS OF PLATE IN INCHES. \ A f Aj_T_j_5_LJ tt * = 3.63 4-53 5.44 6.34 7.25 8.16 8-75 9-63 10.50 i8i 24i 3oi 310 544 843 39 683 1058 472 824 1275 554 967 1494 637 IIIO 1714 722 1256 1936 780 J 354 2086 863 J 497 2304 948 1641 2523 10 IO 2 HZ 20 20 M (1 BACK TO BACK OF FLANGES [s_ IN INCHES. THICKNESS OF PLATE IN INCHES. i A i A 4 A f H 1 tt A = 7oT 42* 48 -V 54i 6oi 724 = 9-13 11.41 13.69 15.97 18.25 20.53 22.50 24.75 27.00 29.25 339 4169 5422 6838 8419 12074 3812 5227 6794 8567 10546 15118 4590 6290 8174 10304 12681 18173 5374 7360 956i 12049 14825 21238 6162 8436 i955 13802 16977 243 1 4 6956 95 J 9 12356 15563 I 9 I 39 27400 7649 10462 T 3575 17094 21017 30079 8443 11542 14971 18846 23167 33 J 44 9242 12628 16374 20606 25324 36219 10046 13720 17784 22374 27491 39304 22 22 A = = 10.13 12.66 .15.19 17.72 20.25 22.78 25.00 27.50 30.00 32.50 36i 424 48i 54i 6o 72i 337 2 4626 6016 7588 9342 13397 4230 5800 7539 9506 11701 16775 5093 6980 9070 11434 14071 20165 5963 8167 10609 i337o 16449 23566 6838 9361 12156 I S3 I S 18838 26979 7719 10562 13710 17268 21236 30403 8499 11624 15084 18993 23353 3342i 938i 12824 16635 20940 25741 36827 10269 14031 18193 22896 28138 40243 1163 15244 19760 24860 30546 43672 24 A = =11.13 13-91 16.69 19.47 22.25 25.03 27.50 30.25 33-00 35-75 2 4 u M 36* 42* 484 544 604 72^ 3705 5083 6610 8337 10264 14720 4648 6372 8284 10445 12857 18432 5596 7669 9966 12563 15460 22156 655 1 8974 11657 14690 18074 25893 75 J 3 10286 !335 6 16827 20699 29643 8481 11605 15064 18974 2 3334 334o6 9349 12787 16592 20892 25688 36763 10319 14107 18298 23034 38315 40509 11296 J 5434 20013 25185 30952 44268 12279 16769 21736 27346 336oo 48039 26 A = 30.00 33-00 36.00 39-00 26 42i 48^ 544 604 72i 13949 18101 22792 28023 40106 15389 19962 25128 30889 44192 16837 21832 27475 33766 48292 18293 23712 29832 36655 52406 : 28 38 ( A = 32.50 35-75 39-00 42.25 424 484 54i 604 72^ 15112 19609 24691 3035 8 43448 16671 21625 27222 33463 47874 18240 23651 29764 36580 5 2 3 l6 19817 25688 32318 39709 56773 32 A = I 37.50 41.25 45-00 48.75 32 (( 424 48| 54i 6o 72* J 7437 22626 28490 35029 50132 19236 24952 31410 38611 55240 21046 27290 34344 42207 60365 22866 29639 37290 45818 65507 (108) TABLE 51 (Continue TWO COVER PLATES TWO HOLES FROM EACH PLATE d = distance back to back of flange angles A = net area of two plates Two J" holes deducted for plates less than f" thick " i" " " " " over T V thick If 4 one-inch holes are deducted use values of plates a inches less in width THICKNESS OF PLATE IN INCHES. I \ if I 1| ii if ii if if i* 2 31.50 33-75 36.00 40.50 45.00 49.50 54.00 58.50 63.00 67.50 72.0O 10856 14818 19201 24150 29666 42400 11671 15923 20625 25934 31851 45507 12491 !734 22056 27726 34044 48624 14148 19274 24939 3 J 333 38456 54889 15827 21540 27851 34972 42903 61196 17527 23831 30792 38644 47387 67545 19250 26147 33761 42347 5*905 73937 20994 28489 36760 46083 56460 80372 22761 30857 39788 49852 61050 86849 24550 3325 1 42845 53653 65677 93368 26362 35671 4593 1 57487 70339 9993 1 35-00 37.50 40.00 45-00 50.00 55-00 60.00 65.00 70.00 75.00 80.00 12062 16465 21334 26833 3 2 9 6 3 47111 12968 17692 22916 28815 35390 50563 ^879 18926 24506 30806 37826 54026 15720 21416 27710 34814 42729 60987 17585 2 3933 30945 38858 47670 67995 19475 26478 34213 42937 52652 7505 21388 29052 375*2 47052 57672 82152 23327 31655 40844 51203 62733 89302 25290 34286 44208 55391 67833 96498 27278 36946 47605 59614 72974 103742 29291 39634 5 I0 34 63874 78i54 111034 38.50 41.25 44.00 49.50 55-00 60.50 66.00 7L50 77.00 82.50 88.00 13268 18111 23467 295 i 7 36259 51823 14265 19461 25208 3 l6 97 38929 556i9 45-00 15267 20819 26957 33887 41609 59429 17292 23557 30481 38296 47001 67086 19344 26326 34040 42744 52437 74795 21422 29126 37634 47231 57917 82555 23527 3*958 41264 51758 63440 90368 25659 34820 44928 56324 69006 98232 27818 37714 48629 60930 74616 106148 30005 40640 52337 65576 80271 114116 32227 43605 56145 70269 85977 122145 42.00 48.00 54.00 60.00 66.00 72.00 78.00 84.00 90.00 96.00 J 975 8 25601 32200 39555 56534 21230 27499 34578 42467 60676 22711 29407 36967 4539 1 64831 25699 33252 41777 5 I2 74 73i85 28719 37 J 34 46629 57204 8i594 3*774 41055 5 J 525 63182 90060 34863 45 OI 5 56463 69207 98583 37985 49013 6i444 75279 107162 4U43 53050 66469 81400 115798 44334 57125 7*537 87568 124490 4756i 61241 76649 93785 133241 45.50 48.75 52.00 58.50 65.00 7L50 78.00 84.50 91.00 97.50 104.00 21404 27734 34883 42852 61245 22999 29791 3746o 46006 65732 24604 31858 40048 49 J 74 70234 27840 36023 45258 55548 79284 3i"3 40229 505*5 61971 88394 34422 44476 558i8 68447 97565 37768 48766 61168 74974 106798 4H5 1 53097 66564 81552 116092 44571 57470 72007 88183 125447 48029 61886 77498 94865 134864 5*524 66344 83036 101600 144344 52.50 56.25 60.00 67.50 75.00 82.50 90.00 97.50 105.00 112.50 120.00 24697 32001 40250 49444 70667 26538 34374 43223 53084 75844 28389 36759 46209 56739 81039 32123 41565 52221 64093 91481 35899 46418 58287 7^05 101993 397 i 7 5^9 64405 78977 H2575 43578 56268 70578 86508 123228 47481 61265 76805 94099 I 3395 2 51428 66311 83085 101749 144746 55417 71406 89420 109459 155613 5945 7655 95810 117230 166550 (109) TIMBER COLUMNS, BEAMS, AND FLOORING STRENGTH OF TIMBER The following data on strength of timber, pages no to 114, are taken from the Report of a Committee of the American International Associa- tion of Railway Superintendents of Bridges and Buildings on " Strength of Bridge and Trestle Timbers." The report was made in 1895. The test data at hand and the summary of criticisms of leading authorities seem to indicate the general correctness of the following conclusions: (1) Of all structural materials used for bridges and trestles, timber is the most variable as to the properties and strength of the different pieces classed as belonging to the same species; hence it is impossible to establish close and reliable limits for each species. (2) The various names applied to one and the same species in different parts of the country lead to great confusion in classifying or applying results of tests. (3) Variations in strength are generally directly proportional to the density or weight of timber. (4) As a rule, a reduction of moisture is accompanied by an increase in strength; in other words, seasoned lumber is stronger than green lumber. (5) Structures should be, in general, designed for the strength of green or moder- ately seasoned lumber of average quality and not for a high grade of well-seasoned material. (6) Age and use do not destroy the strength of timber unless decay or season check- ing takes place. (7) Timber, unlike materials of a more homogeneous nature, as iron and steel, has no well-defined limit of elasticity. As a rule, it can be strained very near to the breaking point without serious injury, which accounts for the continuous use of many timber structures with the material strained far beyond the usually accepted safe limits. On the other hand, sudden and frequently inexplicable failures of individual sticks at very low limits are liable to occur. (8) Knots, even when sound and tight, are one of the most objectionable features of timber, both for beams and struts. The full-size tests of every experimenter have demonstrated not only that beams break at knots, but that invariably timber struts will fail at a knot or owing to the proximity of a knot, by reducing the effective area of the stick and causing curly and cross-grained fibers, thus exploding the old prac- tical view that sound and tight knots are not detrimental to timber in compression. (no) TIMBER COLUMNS, BEAMS, AND FLOORING (9) Excepting in top logs of a tree or very small and young timber, the heart wood is, as a rule, not as strong as the material farther away from the heart. This becomes more generally apparent, in practice, in large sticks with considerable heart wood cut from old trees in which the heart has begun to decay or been wind shaken. Beams cut from such material frequently season check along middle of beam and fail by longitudinal shearing. (10) Top logs are not as strong as butt logs, provided the latter have sound timber. (n) The results of compression tests are more uniform and vary less for one spe- cies of timber than any other kind of test; hence, if only one kind of test can be made, it would seem that a compressive test will furnish the most reliable comparative results. (12) Long timber columns generally fail by lateral deflection or "buckling" when the length exceeds the least cross-sectional dimensions of the stick by 20; in other words, when the column is longer than 20 diameters. In practice the unit stress for all columns over 15 diameters should be reduced in accordance with the various rules and formulae established for long columns. (13) Uneven end bearings and eccentric loading of columns produce more serious disturbances than are usually assumed. (14) The tests of full-size long compound columns, composed of several sticks bolted and fastened together at intervals, show essentially the same ultimate unit resistance for the compound column as each component stick would have if consid- ered as a column by itself. (15) More attention should be given in practice to the proper proportioning of bearing areas; in other words, the compressive bearing resistance of timber with and across grain, especially the latter, owing to the tendency of an excessive crushing stress across grain to indent the timber, thereby destroying the fiber and increasing the liability to speedy decay, especially when exposed to the weather and the con- tinual working produced by moving loads. The aim of your committee has been to examine the conflicting test data at hand, attributing the proper degree of importance to the various results and recommenda- tions, and then to establish a set of units that can be accepted as fair average values, as far as known to-day, for the ordinary quality of each species of timber and corre- sponding to the usual conditions and sizes of timbers encountered in practice. The difficulties of executing such a task successfully can not be overrated, owing to the m eagerness and frequently the indefiniteness of the available test data, and especially the great range of physical properties in different sticks of the same general species, not only due to the locality where it is grown, but also to the condition of the timber as regards the percentage of moisture, degree of seasoning, physical characteristics, grain, texture, proportion of hard and soft fibers, presence of knots, etc., all of which affect the question of strength. (in) TIMBER COLUMNS, BEAMS, AND FLOORING Your committee recommends, upon the basis of the test data at hand at the present time, the average units for the ultimate breaking stresses of the principal timbers used in bridge and trestle constructions shown in the accompanying table. Attention should also be called to the necessity of examining the resistance of a beam to longitudinal shearing along the neutral axis, as beams under transverse load- ing frequently fail by longitudinal shearing in the place of transverse rupture. In addition to the ultimate breaking unit stress the designer of a timber structure has to establish the safe allowable unit stress for the species of timber to be used. This will vary for each particular class of structures and individual conditions. The selec- tion of the proper "factor of safety" is largely a question of personal judgment and experience, and offers the best opportunity for the display of analytical and practical ability on the part of the designer. It is difficult to give specific rules. The following are some of the controlling questions to be considered: The class of structure, whether temporary or permanent, and the nature of the oading, whether dead or live : if live, then whether the application of the load is accompanied by severe dynamic shocks and pounding of the structure. Whether the assumed loading for calculations is the absolute maximum, rarely to be applied in practice, or a possibility that may frequently take place. Prolonged heavy, steady loading, and also alternate tensile and compressive stresses in the same place will call for lower averages. Information as to whether the assumed breaking stresses are based on full-size or small-size tests, or only on interpolated values, averaged from tests of similar species of timber, is valuable in order to attribute the proper degree of importance to recommended average values. The class of timber to be used and its condition and quality. Finally, the particular kind of strain the stick is to be sub- jected to and its position in the structure with regard to its importance and the possible damage that might be caused by its failure. In order to present something definite on this subject, your committee presents the accompanying table, showing the average safe allowable working unit stresses for the principal bridge and trestle timbers, prepared to meet the average conditions existing in railroad timber structures, the units being based upon the ultimate break- ing unit stresses recommended by your committee and the following factors of safety, Tension with and across grain 10 Compression with grain 5 Compression across grain 4 Transverse rupture, extreme fiber stress 6 Transverse rupture, modulus of elasticity 2 Shearing with and across grain 4 (112) s 03 < 10 t* M O 1 o w . I w" ,,- W S5 8 2 * ^ o 1 5.S Modulu Elastici el s-i IS MMM oo ooooo 'oooooooo OO OOOOO .OOOOOOioO t^ N MOOOOOt^ OOt^\OOOCOOt^OO cu CX is U . a 2 . " _c S g S ^ ffl < H J* fc P? O W W 3 I w H M sj 03 O t> l'| I I S3 81 W W W Q H O M M g W RSE RE. b2 <5 ^ 635 - Since P' is less than P, the column is safe. TABLE 55 SAFE LOADS (UNIFORMLY DISTRIBUTED) FOR BEAMS 1" THICK Based on extreme fiber stress of 100O pounds per square inch. The table is for total uniform loads in pounds, for beams one inch thick. The values are for an actual depth of \ inch less than the nominal depth, or a 4-inch beam is reduced to 3! inches deep. IB tfL NOMINAL DEPTH OF BEAM. 4 5 6 7 8 9 10 12 14 16 18 20 22 24 4 391 627 918 1265 1668 2127 2640 3835 5268 6891 8752 10835 I3J4 1 15668 5 3*3 Soi 735 IOI2 1334 1701 2112 3068- 4201 55i2 7000 8668 10512 I2 535 6 260 418 612 844 III2 1418 1760 2557 35i2 4594 5834 7224 8760 10446 7 223 358 5 2 5 723 953 1215 1508 2191 3001 3937 5001 6191 759 8953 8 195 3i3 459 633 834 1063 1320 1918 2634 3446 4375 54i8 6570 7834 9 174 279 408 563 741 944 H73 1704 2341 3 6 3 3889 4815 5840 6964 10 156 251 367 5 06 667 851 1056 *534 2IOO 2756 35 4334 5256 6267 ii 142 228 334 460 607 774 9 60 J 394 1910 2505 3182 3940 4778 5698 12 130 209 306 422 556 709 880 1278 I75 6 2297 2917 3612 4380 5 22 3 13 1 20 i93 283 389 5 T 3 654 812 1180 1616 2120 2692 3333 4043 4821 14 112 179 262 362 477 608 754 I0 95 1500 1968 2500 395 3754 4477 15 IO4 167 245 338 445 567 704 4023 1400 1838 2333 2889 3504 4178 16 9 8 r 57 230 3 l6 417 532 660 959 W7 1723 2188 2709 3285 39*7 17 147 216 2 9 8 393 500 621 902 1236 l62I 2059 2549 3092 3687 18 i39 204 28l 37i 472 587 852 1170 1531 1944 2408 2920 3482 i9 132 J 93 266 35 1 448 556 807 1106 145 I 1842 2281 2767 3299 20 125 184 253 334 425 528 767 io54 1378 J 75 2167 2628 3*34 21 . . J 75 241 3i8 405 53 730 IOOO 1312 1667 2063 2503 2984 22 167 230 303 387 480 697 955 1253 !59 J 1970 2389 2849 23 160 220 290 37 459 667 917 1198 1522 1884 2286 2724 24 . . i53 211 278 354 440 639 878 1149 1458 1806 2190 2611 25 203 267 340 423 614 840 IIO3 1400 J 734 2IO2 2507 26 IQC 2C7 327 406 CQO 808 Io6o 1 34.6 1667 2O22 241 1 27 A VO l8 7 j 1 247 o / 315 39i jy^ 5 68 780 1021 L o i t w 1296 1605 1947 **T* * 2321 28 181 2 3 8 34 377 548 75 984 1250 1548 1877 2238 2O 23O 2Q3 364. C2Q 724. Q^O I 2O7 I4Q4. 1812 2164 -r 30 ^o w 222 *7J 283 O^"r 352 o y 5 11 / ^f 700 yj** 919 *\j 1 1167 "T^VT- 1444 !7S 2 2089 To obtain the safe load concentrated at the center of beam, divide the safe load given in the above table by two. (116) u go W | 1-3 X? 5 2 9 H its < H il 2 s * ^" o a P "g S S 5 S-2 B I! ps 2 II |Is 5 h| IH |S SIS' 3 H 5 a = ^ - = O jg 4J 43 - s si ^-^s squ o 3 Jq II aj * ^ *> p vC 0000000 HI ft Tf IO H- M O O * PO H. 10 POOO 10 CD 1-1 O O* O O O O O vO ^00 t^ "* f^vO 10 M OO *> t^-\O O 8,8 2 5-8 t^ rf H. 00 O 10 10 * * OO OC O p*"iOO PT5 HI O 00 O Tj- -^- Tf PO PO 00000 Tj- 1- O t^- *^ 10 Tf PO (N HI HI O W N N ff. O O O O H* O t^ t^ 10 HI O 10 P NO vo *^ - vO O O OO rr> rj- o t^ HI OO 10 ts O 00000 00 H. o w O 00 r-~ 10 1- PO &8,88* O O O O O t^ -t fO t^. t^.NO 10 10 M t* o o o o o o o r- rr 00 rj- r>. NO M M r*500 * O OvO O O 10 f^ IO ^C H4 O O O O O O W H, PO OOO t^O 10 O O O O O o o POOO PO o o o o o 00 * O vO . O - "5 10 o m -" O OO ^j- -*J-vO HI OO O ^ W HI o o o o o 00 O vO t^OO OOO t^.O IO 2 s a 10 ^ PO PO e* So o o o t^ PO OvO W HI HI O O n O O O O 00 W -t O O t^ * 10 w ^\C t^ \c TJ-OO N H. o OOC O O O fO Cs rj- O t>- 00 !> t> t-~O o o o o o Tj- M CO O PO NO NO 10 10 10 8g<8>8^ 10 Tf ^t * * O O O O 10 rJ-00 00 N O O O O O N IO C\ ^*" O O IO HI OC IO ,8^N8 : t-. N 00 ro C4 HI O OOO t t^ NO o \o 10 o IO IO ^J- ^ CD (S O O Tt t^ w 10 o N f*5 O f^. H. t^ N O S ^2 g,R s>8,8 2 ; M HI HI M PO PO PO PO ^t OO rO ^-U) W W oo ao N fS M 000000 M M Tt 10 M O O PO M toe to . !>. t>- OOOOOOO OOOOO OO'OO M o "*3" O O PO *** ^* O PO to Tf O O PO O to to O x^*O x^* O PO t^- P^ tooO POOt^-to-^- W M O O OOOOO PO- O M t^ to fO M o OOO 000 OOOO _MoroioOt^r^-r^- lOO lOMOOlON Ot^-tOfO OOOOO Tfotocso OOO t^-O to O O to 10 to OOOOOOO OOOOO OOOOO OOOOO OOOOO o tooo toco to N N ooo t^ to ooo M o 1-1 IOMOOM ^too ^000 tOO^Ot^-r^-O rf W O OOO O CO to ^O W M O OOO t^t--OOO OOOOOOO OOOOO OOOOO OOOOO OOOO OO.O ~ -*-- ~ - "SO ^J- P^ O O **** O to ^i" PO n M O O O ^ O OOO OOOOOOO OOOOO OOOOO OOOOO OOOOO MMt^MO^oOOTt-OOO 0-O'^'O - ^OOPOOt^toMOOOOioPON MIOMOOIO^N MOO OOO *" **- t^O O O lOlOlOtO '^^fTj-'rt-TJ- POMNMMMM MM 00 OOOOO o o -t w o o o O O^OPOTJ-\O O M O ^ 00 OO MNrOTf MMMMM MMMM O t^ CO ON . M T^- ON vo NO t^ t>- \o t^ r^ co o i N 00 M rt NO t- Tf CO M CO N NO PO M VO VO NO NO GO ON O t* O fO vo NO PD NO ON CO <* t> O fO ON vo ro ^ ^- vo O O t-^ vO NO M Tj- t^ ON vo w l-~ w - M N . t^ vO NO vo vo rt M to * vo ON w ro M M M (H M W m -os HHd f NI SSHMiS H3H -Id 3K3M.L -X3 3HVS JO VO O O O O l> ^ 00 O M N 5 c C M ll 12 S " lh 111 i! 1 J!S1 111 153 It! ^i "c -I* -S3 =0.13 N il! 2 S3 g ? - s Sis U 181 2. * ^2 ill 8 C "Ij -55 1* !J E-S5 1 S * ha Hi Hi i b S 8.8 .^5* l^l 1 ts s 5B (119) BENDING MOMENTS IN FOOT-POUNDS For the following uniform loads, the joists being spaced 24 inches centers LOAD IN POUNDS PER SQUARH FOOT. | O in (S O fO O O O co O 8O toO O O to to CM O O O CM M HI CM CO "3- tOO CO O co O co O O O too IO O to CM O M M M JcO O co O O toO Q OO O CNJ to H M CM CM CM CO O co O co O toO O O to CM O O O t*>- O COO ON CM CO CO CO CO O co O co O too O O to CM to O to CM CM to ON CM O Tf T)- Tf to IO (N JO to o to o to o CM OO "^ CM O O HI M CM CO ^J- IO O O to O to O to O CM TfOO CM O t^-CO ON M JO O to O to O Tj- CM O O CM TJ-O OO O M H M M CM O O to O to O to O CM TfOO CM CM CM CM CM CO JO O O O to O to O ^t CM O O COO ON CM to CO co CO * * m r^ O to M oo to co M M (N CM CO -^ ON t^ Tj- CM CO CO tOOO IOO t^OO ON 8^ to TJ- O "t t> ON O CM O M t^- IO M CM Tj- to t^ Tf 10 "Sf O * ON *^ Tt- O Tj- CM M M CM CO ON M CO 10 I-* M CM CM CM CM tO Tt" O ^ tr- t^* ON O ON t^ tOOO CO t^ co ON M rfO s CM CO CO CO CO & 00 00 O co to rj- O co to O ON COOO ^ O t^. H H CM CO CO to ^ CO CO rf * too t^co too o oo o CO to CO O 00 M to O O CM CO IO 00 O 00 O 00 CO to CO O CO to M oo o rj- O 00 ON M CO O CO O CO O to co O co to co co T*- to r^ to t^- ON M co in CM M OO CM CO O CO CM IO t^ M to O to M M M CM CM CO 00 CM CO t^ 10 CM M O CO CO CM OO O O M CM IO ON O M CM OO IO CM HI HI CM "3-O CO O to O to O to O O CM O . ij- CM O to too t^oo O CM OO CO CM O CO O to to IO CO ON O Hi CM o o o o o CM OO OO CM O to too CO O CO ^ toO 00 m O ON IO ON O ON IO O O r~- M O HI t^ CO ^O ON CM IOOO M M H CM t^ H O CM CM CM CO CO ^T JON 10 ON O M f^O O ^J- O *> to * toO O t^ ON to ON O ON CM O ONOO 00 ON ON O M to ON O ON to t*>-O O O *> O O r>- r^-oo CM CO ^ tOO o O 00 O CO O CO O CO CO CO to CM H to CM TJ-O OO HI Tj- t^. M M M 00 O 00 O 00 HI CM 10 CO CO HI to ON ^ ON CM CM CM CO CO O 00 O CO O oo to t>- M o Tf O O co O T}" IO tOO t~* 00 O 00 O 00 t^OO ON O O O 00 O 00 O CO to CM M to M CM CO ^ to s O to O to O to O Tf t^ ^- COO M O CM CO to t^ ON CM to to O to O to M o co ^ r-. OO M to ON co M CM CM CM CO O to O to O co ^ ^ toO to O to O to M O co rt t> O CM, ONO co O t^ t^OO ON O to O to O ^ COO HI O Hi ON r>*O to O O HI CM co in O CO O CO O co O CO O CO O CO O co O co O CO O CO O CO O co O co O CM CO ^O 00 O CM M M M M CM CM CM CM O O to O CO CO Tf- ^t to to O O CM CO too O t^- r^* 00 ON ON M M * O O O O O O O M CM co "tvO 00 O O M ^- ONO to CM T}-O ON CM M M M M CM O O O ON <* M O toco CM O O CM CM CO CO Tt- 00000 HI T!r ONO to TtoO CM r^. CM TJ- ^- to too O O O ON *t HI O *> CM OO ^J" O O t^- 1>-CO O^ a O 00 O 00 O 00 O CM OO r^O OO O to M M CN CO ^"O t^- 00 O 00 O CO O 00 O r^oo ON O CM ^f O O 00 O 00 O CM O co O O M -l t-t M H CM to O to O to O CM rfOO CM CM CM CM CM CO O to O to O 00 *t CM O O COO ON CM to CO co CO ^ rr m O "3" to rj- O ^ to O ON COOO "^ O f^ M M CM co co * O ^ to TJ- to rj- co co Tj- O Tf to rj- O O 00 M to O s O fNi co to "3- to TJ- O ^f to HI co o TJ- O CO ON HI CO to Tf O * to CO CO ^ to t^ to !> ON HI CO Id MI rj- mvo i^oo o\ o M (S ro -3- in vO t^CX) O\ O M N fOTj-m VO i>00 & O (120) TABLE 59 THICKNESS OP WOOD FLOORING Based on a safe extreme fiber stress of 1000 pounds per square inch, the flooring assumed in simple spans. To the thickness given below add \" to obtain the nominal thickness. ll * UNIFORM LOAD IN POUNDS PER SQUARE FOOT. 15 20 25 30 40 50 60 70 75 80 100 I2 5 ISO 175 200 250 12 .11 12 .14 15 J7 .19 .21 2 3 .24 2 5 .27 3i 34 36 39 43 16 .14 .16 .18 .20 23 .26 .28 3 1 32 33 37 .41 45 .48 5 2 58 18 .16 .18 .21 2 3 .26 .29 3 2 34 36 37 .41 .46 50 54 58 65 24 .21 25 .27 3 35 39 .42 .46 47 49 55 .61 .67 7 2 77 87 30 .27 3 1 34 38 43 .48 53 57 59 .61 .68 77 .84 .91 97 i. 08 36 32 37 .41 45 5 2 .58 .64 .69 7i 73 .82 92 I.OI 1.09 1.16 1.30 42 37 43 .48 53 .61 .68 74 .80 83 .86 .96 1.07 1.17 1.27 1.36 1.52 48 .42 49 55 .60 .69 77 85 .92 95 .98 I.IO 1.22 i-34 i-45 !-55 i-73 60 53 .61 .68 75 87 97 i. 06 I - I 5 1.19 1.22 i-37 !-53 1.68 1.81 1.94 2.17 72 .64 73 .82 .90 1.04 1.16 1.27 I -37 1.42 1.47 1.64 1.84 2.OI 2.17 2.32 2.60 84 74 .86 .96 1.05 1. 21 1.36 1.48 i. 60 1.66 I. 7 I 1.92 2.14 2-35 2.54 2.71 3-03 96 85 .98 I.IO 1.20 I -39, !-55 1.70 1.83 1.90 1.96 2.19 2-45 2.68 2.90 3.10 3-46 To obtain the required thickness for loads concentrated at center of span, divide the concen- trated load per foot of' width of flooring by one-half of the span in feet ; the resulting value is the equivalent uniform load in pounds per square foot. The above values were obtained from the following formula: Let h = thickness of flooring in inches, w = uniform load in pounds per square foot, / = simple span in inches, R = safe extreme fiber stress in pounds per square inch = 1000 in above table. Then h = (121) THIS BOOK IS DUE ON THE LAST BATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL. BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. MAY 17 1933 APR JANOI 2003 LD 21-50m-8,'32 ^w YC 13412