POCKET COMPANION , OF USEFUL INFORMATION APPERTAINING TO^THEXUSE OF PITTSBURGH, PA. FOR ENGINEERS, ARCHITECTS AND BUILDERS, BY C. L. STROBEL, C. E. M.A.S. C. E. Electrotype Edition, Price $1.SO. WM. G. JOHNSTON & CO. PRINT. PITTSBURGH. Entered according to Act of Congress, in the year 1881, by CARNEGIE BROS. & CO. LIMITED, In the Office of the Librarian of Congress, at Washington. S3- PREFACE. THE present electrotype edition of the Pocket Companion is a new work throughout. It is intended to supply such special information and tables as, it was thought, would prove valuable to workers in wrought iron in general, and the patrons of the publishers, the firm of Carnegie Bros. & Co., Limited, in particular. The tables, with a few exceptions, were computed expressly for this work, and some of them are original in both matter and form. The author hopes that they will be found to possess the qualities of accuracy and reliability. Such of the tables a$ were not Calculated for this work were obtained from two or more works of presumably independent origin, which were compared for the detection of errors. The table of weight of a cubic foot of substances was derived mostly from Trautwine, while for the table of linear expansion of .substances by heat, Rankine is authority. The list of shapes rolled by the Union Iron Mills will be found increased in number, and some of the sections improved in form. All angle irons are now made with flanges of uniform thickness ; the range between the minimum and maximum weight for a number of the shapes has been increased, and a new and more rational system of numbering adopted. CONTENTS. PAGE. Lithographed Sections of Eyebeams, Shapes Nos. 1 to 13 1-4 " Sections of Deck Beams, Shapes Nos. 20 to 22 4 " Sections of Channel Bars, Shapes Nos. 25 to 45 5-8 " Section of Car Truck Channel, Shape No. 46 8 " Sections of Angles with Equal Legs, Shapes Nos. 50 to 63 9 " Sections of Angles with Unequal Legs, Shapes Nos. 65 to 76 10 " Sections of Square Root Angles, Shapes Nos. 80 to-93 .11 " Sections of Cover Angles, Shapes 95 and 96 . .12 " Section of Obtuse Angles, Shape No. 98 12 " Sections of Star Irons, Shapes Nos. 100 to 105 12 " Sections of Keystone Octagon Columns, Shapes Nos. 110 to 113 13 " Sections of Piper's Patent Rivetless Columns, Shapes Nos. 115 to 118 14 " Sections of Corrugated Columns, Shapes Nos. 120 and 121 15 Lithographed Sections of Patent Post Irons, PAGE. Shapes Nos. 125 and 126 15 " Sections of Half T's Shapes Nos. 127 and 128 15 " Sections of T Irons, Shapes Nos. 130 to 178 16-20 " Section of Roof Iron, Shape No. 180 20 " Sections of Hand Rails, Shapes Nos. 195 and 196 21 Sections of Grooved Irons, Shapes Nos. 200 to 209 21 Sections of Sash Irons, Shapes Nos. 215 to 221 22 " Sections of Fence Irons, Shapes Nos. 225 to 227 22 " Section of Beveled Flat, Shape No. 230 22 " Sections of Ice Slides, Shapes Nos. 231 and 232 '. .22 Section of Dove Tail, Shape No. 233 22 " Section of Z Iron, Shape No. 235 22 " Illustrations of Beams and their connections, and Girders 23 " Illustrations of Beam supporting Wall, of Sepa- rators, and of Fire-proof Floors 24 " Illustrations of Fire-proof and other Floors. . . .25 " " " Columns and Struts, and Dia- grams of Pratt and Whipple Trusses 26 " Sections of Additional Shapes 27-30 Explanation of Tables on Eyebeams 31, 32 ~~y[ " - PAGE. Tables on Eyebeams, giving Safe Load, Deflection and Proper Spacing 33-35 Explanation of Tables on the Properties of Beams, Chan- nels, Angles, Stars and Tees, also General Formulae on the Flexure of Beams. 56-61 Properties of Eye and Deck Beams 62, 63 " Channel Bars 64, 65 " " Angle Irons 66, 67 Angle Irons, weights corresponding to thicknesses varying by T V' 68 Properties of T Irons 69 " " Star Irons 69 Explanation of Table on Riveted Girders 70, 71 Table on Riveted Girders 72 Explanation of Tables on Columns and Struts 73-76 Keystone Octagon Columns, Thicknesses and corresponding Areas and Weights per foot 77 Piper's Patent Rivetless Columns, Thicknesses and correspond- ing Areas and Weights per foot .78 Ultimate Strength of Cast and Wrought Iron Columns 79 " " Wrought Iron Columns 80 Rectangular Timber Pillars 81 General Notes on Floors and Roofs 82-84 Corrugated and Galvanized Iron .' 85, 86 Illustration of Application of Tables on Flat Rolled Iron, and Decimal Parts of a Foot for each ^jth of an inch. . .87 Weights of Flat Rolled Iron per Lineal Foot. 1 88-93 Areas of Flat Rolled Iron 94-99 Decimal Parts of a Foot for each ^ of an inch 100-103 Weights and Areas of Square and Round Bars of Wrought Iron, and Circumferences of Round Bars 104-109 Sheet Iron, by Birmingham Gauge 110 " " American " , Ill VII PAGE. Areas and Circumferences of Circles 112-124 Weights of Rivets and Round-headed Bolts 125 Upset Screw Ends for Round and Square Bars 126, 127 Standard Screw Threads, Nuts and Bolt Heads, by Franklin- Institute Standard 128 Whitworth's Standard Screw Thread 129 Wood Screws, Tacks and Wrought Spikes 129 Sizes and Weights of Hot Pressed Square Nuts 130 " " Hexagon Nuts 131 Wrought Iron Welded Tubes, for Gas, Steam or Water 132 Explanation of Tables on Rivets and Pins 133, 134 Shearing and Bearing Value of Rivets 135 Maximum Bending Moments to be allowed on Pins 136 Bearing Value of Pins 137 Wooden Beams, Safe Load for 138 Explanation of Tables on Maximum Stresses in Pratt and Whipple Trusses. 139, 140 Maximum Stresses in Pratt or Single Quadrangular Trusses . . 141 " " Whipple or Double Quadrangular Trusses 142, 143 Natural Sines, Tangents and Secants 144-152 Logarithms of Numbers 153-155 Weight of a Cubic Foot of Substances 156-158 Window Glass, No. of Lights per Box 159 Linear Expansion of Substances by Heat .160 Mensuration 161-163 Weights and Measures, United States and British 164, 165 Comparative Tables of United States and French, and French and United States Measures 166, 167 Strength of Materials 168-170 Decimals of an Inch for each J ? th 171 Index 172-177 _ . > CARNEGIE BROTHERS & CO. PITTS BURG H, . 31 1 / 2 to45!bs. Ill LL 0> Cr'O 01 CARNEGIE BROTHERS & CO. LIMP PITTSBURGH, PA CARNEGIE BROTHERS . &, i.i M ITI-: ix to i w o ' fs ! 4dto6o'lbs. ~ ' ! .'-. -' 1 1 -VH 22 1 / 2 to30lbs. v PITTSBURGH, PA. If *F 1' :1 ie CARNEGIE BROTHERS & GO.LIM? PITTSBURGH, PA. CARNEGIE BROTHERS & CO. ANGLES WITH EQUAL LEGS. .. . 3.5to7,3 Ibs ', 0.9 to 18 Ibs. . 0,8tol,2lbs PITTSBURGH, PA. ANGLES WITH UNEQUAL LEGS. IS 1 ? 65. 13,9 to EGA IBs 10 CARNEGIE BROTHERS & CO.LIM?. SQUARE ROOT ANGLES. 11 PITTSBURGH, PA COVER ANGLES. N 9 6. B7to8.3lbs OBTUSE ANGLE .. 2,3 Ibs. CARNEGIE BROTHERS & CO.LIM^ KEYSTONE OCTAGON COLUMN. 13 PIPER'S PATENT RIVETLESS COLUMN. CARNEGIE BROTHERS & CO. CORRUGATED COLUMN. 127 4 3 4 Ibs. PITTSBURGH, PA. T IRON. 16 BROTHERS a CO. GValbs. PITTSBURGH, N" 1-1-5. 13,8 Ibs. Nir,o 9 1 /*lbs. 18 CARNEGIE BROTHERS & CO. X"159 I - S'/^lbs. ** NJ61. _ 6.6lbs. HI ?, ^r i PITTSBURGH, PA. & N< 2.9 Ibs 1.9 Ibs - 1 . 1,1 Ibs ,. 1 . x,it!ir 0, 75 Ibs. I ' CARNEGIE BROTHERS & CO. 'sro' a 2 I PITTSBURGH, PA. CARNEGIE BROTHERS & CO.LIM9 PITT S B U R G H, PA, O.6 h. I 1.2 Iv. O.6 Jti. ; Thnqmt-06 CAR.NEGIE BROTHERS & CO. LIMP l H H PRATT OR SINGLE QUADRANGULAR TRUSS. D J F i ITI-: i). ADDITIONAL SHAPES PITTSBURGH, PA. ADDITIONAL SHAPES CARNEGIE BROTHERS & CO. i.iMi'n-:i>. ADDITIONAL SHAPES. PITTSBURGH, PA. ADDITIONAL SHAPES CARNEGIE BROTHERS & CO. 1. 1 AH 'ri-: i). ADDITIONAL SHAPES. EXPLANATION OP TABLES ON UNION IRON MILLS' EYEBEAMS. Pages 33 to 55, inclusive. These tables are calculated for the lightest and heaviest weights to which each shape or size can be rolled, the term shape being meant to include the variable sections which are rolled in the same grooves by increasing or reducing the distance between the rolls. Each shape is designated by a single number. These tables give : I. In second column, the load which a beam will carry safely, distributed uniformly over its length, for the distances between supports, (or lengths of span,) given in first column ; II. In fifth to eleventh columns inclusive, the distances be- tween centers at which beams should be placed in floors, to carry safely loads of 100, 125, 150, 175, 200, 250 and 300 Ibs. per square foot (including the weight of the beams), for the distances between supports given in first column ; III. In third column, the deflection of the beams at center under these loads. IV. In fourth column, the weight of the beam itself, for a length equal to the distance between supports. To determine the load which a beam will carry exclusive of its own weight, the figures in fourth column must be subtracted from the figures in second column. It is assumed in these tables that proper provision is made for preventing the compression flanges of the beams from deflecting sideways. They should be held in position at distances not exceeding twenty times the width of flange, otherwise the strain allowed should be reduced. If the deflection of beams carrying plastered ceilings exceeds !^th of the distance between supports, or J^th of an inch per foot of this distance, there is danger of the ceiling cracking, as has been found by practical tests. This limit is indicated in the following tables by a cross line, beyond which the spans and loads must not be used for beams intended to carry plastered ceilings. It may generally be assumed, both for rolled and m a SB- built beams, that the above limit is not exceeded so long as the depth of beam is not greater than 2 ] f th of the distance between supports, or j inch per foot of this distance. Inasmuch as the carrying capacity of beams increases largely with their depth, and it is therefore economical to use the greatest depth of beam consistent with the other conditions to which it is necessary to conform, (as clear hight, etc.,) the above cases of extreme deflection will rarely be met with in practice. EXAMPLES OF APPLICATION OF TABLES. I. What size and weight of beam 19'-G" long in clear be- tween walls, and therefore say 20'-0" long between centers of supports, will be required to carry safely a uniformly distributed load of 15 tons, the weight of the beam included ? . Answer : A 15" beam, No. 1, heavy, 65 Ibs. per foot, will be sufficient, since the safe load, as per table, for 20 ; length ,= 16.38 1. It is evident, however, that a beam intermediate in weight between 50 Ibs. and 65 Ibs. can be used, to ascertain which, proceed as follows : The safe load for a 15" beam 50 Ibs. per foot = 14.12 t. Since therefore an increase in the carrying capacity of beam, of 2.26 1., (16.38 1. 14.12 1.,) requires an increase of its weight of 15 Ibs., (65 Ibs. 50 Ibs.,) therefore an increase of its carrying capacity of 0.88 t., (15t. 14.12 t.,) will require -||j- X 15 = 6 Ibs. increase of weight of beam., i. e., the beam should weigh 56 Ibs. per foot. II. A fire-proof floor 24'-6" in clear between walls, weighing, inclusive of beams, 70 Ibs. per square foot, (assumed,) is to be proportioned to carry an additional load of 130 Ibs. per square foot; what size and weight of beams will be required, and how far apart should they be placed ? Answer : The total load = 200 Ibs. per square foot, and the distance between supports = 25', z. e. 6" greater than the distance in clear between walls. By referring to tables, it will be seen that either light 12" beams weighing 42 Ibs. per foot, spaced 2.9 ft. between centers, or light 15" beams, 50 Ibs., spaced 5.8 ft. between centers, will answer the purpose, but since the 12" beams for this span and load are beyond the cross-line, they must not be used, if intended to carry a plastered ceiling. _ , _ S3 UNION IRON MILLS' 15-INCH EYEBEAM, No. 1, LIGHT, 50 LBS. PER FOOT. Depth, 15". Width of Flanges, 5.03". Thickness of Web, 0.47". Maximum fiber strain = 12000 1 bs. per square inch. g -U ti^s J3 la Proper distance, in feet, center to center s Js |lli jl i | J of b< jams, for Safe Loads of 8 5 -JfiS I-S ?5 100 125 150 175 200 250 200 " J_, . '&' j 5 M Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. .s & 1 ~-~ &o d-s ! 'S P J per per per per per per per 314!.s.s r^- s3 Us. Ibs. Its. Ibs. Ibs. Ibs. Ibs. & 3 . Jjg"^ ^ ,3 'G _g per per per per per par per tg:a.s.s ^ ai.fi, El.ft sq.ft. sq. ft. Bl.it s:q. ft. ^. ft 10 40.00 0.09 0.40 80.0 64.0 53.3 45.7 40.0 32.0 26.7 11 33.36 ! 0.11 0.44 66.1 52.9 44.1 37.8 33.1 26.4 22.0 12 33.33 0.13 0.48 55.6 44.4 37.0 31.7 27.8 22.2 18.5 13 30.77 0.16 0.52 47.3 37.9 31.6 27.1 23.7 18.9 15.8 14 28.57 0.18 0.56 40.3 32.6 27.2 23.3 20.4 16.3 13.6 15 28.67 0.21 0.60 35.6 28.4 23.7 20.3 17.8 14.2 11.9 16 25.00 0.24 O.C4 31.3 25.0 20.8 17.9 15.6 12.5 10.4 17 23.53 0.27 O.C8 27.7 22.1 18.5 15.8 j 13.8 11.1 9.2 18 22.22 0.30 0.72 24.7 19.8 16.5 14.1 12.3 9.9! 8.2 19 21.05 0.33 0.76 22.2 17.7 14.8 12.6 11.1 8.9 7.4 20 20.00 0.37 0.80 20.0 16.0 13.3 11.4 10.0 8.0 6.7 21 19.05 0.41 0.84 18.1 14.5 12.1 10.4 9.1 7.3 6.0 22 18.18 0.45 0.88 16.5 13.2 11.0 9.4 8.3 6.6 5.5 23 17.39 0.49 0.92 15.1 12.1 10.1 8.6 7.6 6.0 5.0 24 16.67 0.53 0.96 13.9 11.1 9.3 7.9 6.9 5.6 4.6 25 16.00 0.58 1.00 12.8 10.2 8.5 7.3 6.4 5.1 4.3 26 15.38 O.C2 1.C4 11.8 9.5 7.9 6.8 5.9 4.7 3.9 27 14.81 0.67 1.08 11.0 8.8 7.3 6.3 5.5 4.4 3.7 23 14.29 0.72 1.12 10.2 8.2 6.8! 5.8 j 5.1 4.1 3.4 29 13.79 0.78 i 1.16 9.5 7.6 6.3 5.4 4.8 3.8 3.2 30 13.33 0.83 1.20 8.9 7.1 5.9 5.1 4.4 3.6 3.0 31 12.90 0.89 1.24 8.3 6.6' 5.5 4.8 4.2 3.3 2.8 32 12.50 0.9511.28 7.8 6.2 5.2 ; 4.5 3.9 3.1 2.6 83 12.12 1.01 1.82 7.3 5.9^ 4.9 4.2 3.7 2.9 2.4 84 11.76 ! 1.07 1.36 6.9 5.5; 4.6; 3.9 3.5 2.8 2.3 35 11.43 1.13 1.40 6.5 5.2 ' 4.3 3.7 3.3 2.6 2.2 86 11.11 1.20 1.44 6.2 4.9; 4.1 3.5 3.1 2.5 2.1 37 10.81 1.26 1.43 5.8; 4.7 3.9, 3.3 2.9 2.3 1.9 ' 38 10.68 1.33 ! 1.52 5.5 i 4.4 3.7 3.2 2.8 2.2 1.8 39 '4 10.28 1.40 1.56 5.3 4.2 3.5 3.0 2.6' i 2.1 1.8 c f. UNION IRON MILLS 1 12-INCH EYEBEAM, No. 3, LIGHT, 42 LBS. PER FOOT. Depth, 12". Width of Flanges, 4.64". Thickness of Web, 0.51". Maximum fiber strain = 12000 Ibs. per square inch. CJ +3 li^s 1 o3 a Proper distance, in feet, center to center {I t. ^0 33 |1 JS of beams, for Safe Loads of fi ^ f=g <*-! 100 125 1 150 175 200 250 300 | 15 ili Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. a & If A per sq. ft. par sq. ft. per sq. ft. per sq.ft. per sq.ft. per sjft. 10 18.36 0.12 0.21 36.7 29.4 24.5 21.0 18.4 14.7 12.2 11 16.69 0.14 0.23 30.3 24.3 20.2 17.3 15.2 12.1 10.1 12 15.30 0.17 0.25 25.5 20.4 17.0 14.6 12.8 10.2 8.5 13 14.12 0.20 0.27 21.7 17.4 14.5 12.4 10.9 8.7 7.2 14 13.11 J0.23 0.29 18.7 15.0 12.5 10.7 9.4 7.5 6.2 15 12.24 0.26 0.32 16.3 13.1 10.9 9.3 8.2 6.5 5.4 16 11.48 0.30 0.34 14.4 11.5 9.6 8.2 7.2 5.7 4.8 17 10.80 0.33 0.36 12.7 10.2 8.5 7.3 6.4 5.1 4.2 18 10.20 i 0.37 0.38 11.3 9.1 7.6 6.5 5.7 4.5 3.8 19 9.66 0.42 0.40 10.2 8.1 6.8 5.8 5.1 4.1 3.4 20 9.18 0.46 0.42 9.2 7.3 6.1 5.2 4.6 3.7 3.1 21 8.74 0.51 0.44 8.3 6.7 5.5 4.8 4.2 3.3 2.8 22 8.35 0.56 0.46 7.6 6.1 5.0 4.3 3.8 3.0 2.5 23 7.98 0.61 0.48 6.9 5.6 4.6 4.0 3.5 2.8 2.3 24 7.65 0.68 0.50 6.4 5.1 4.2 3.6 3.2 2.6 2.1 25 7.34 0.72" 0.53 5.9 4.7 1 3.9 3.3 2.9 2.4 2.0 26 7.06 0.78 0.55 5.4 4.3 3.6 3.1 2.7 2.2 1.8 27 6.80 0.84 0.57 5.0 4.0 3.3 2.9 2.5 2.0 1.7 28 6.56 0.90 0.59 4.7 3.7 3.1 2.7 2.3 1.9 1.6 29 6.33 0.97 0.61 4.4 3.5 2.9 2.5 2.2 1.7 1.5 30 6.12 1.04 0.63 4.1 3.3 2.7 2.3 2.0 1.6 1.4 31 5.92 1.11 0.65 3.8 3.1 2.5 2.2 1.9 1.5 1.3 32 5.74 1.18 0.67 3.6 2.9 2.3 2.0 1.8 1.4 1.2 33 5.56 1.26 0.69 3.4 2.7 2.2 1.9 1.7 1.3 1.1 34 5.40 1.34 0,71 3.2 2.5 2.1 1.8 i.6 1.3 1.1 35 5.25 1.42 0.74 3.0 2.4 2.0 1.7 1.5 1.2 1.0 36 5.10 1.50 0.76 2.8 2.2 1.9 1.6 1.4 1.1 0.9 37 4.96 1.58 0.78 2.6 2.1 1.8 1.5 1.3 1.1 0.9 38 4.83 1.67 0.80 2.5 2.0 1.7 1.5 1.3 1.0 0.8 39 5r~~ 4.71 1.76 0.82 2.4 1.9 1.6 1.4 1.2 1.0 0.8 5 E UNION IRON MILLS' 12-INCH EYEBEAM, No. 3, HEAVY, 60 LBS. PER FOOT. Depth, 12". Width of Flanges, 5.09". Thickness of Web, 0.96". Maximum fiber strain = 12000 Ibs. per square inch. rt * || P 1 . 2 Proper distance, in feet, center to center | J bl fs of beams, for Safe Loads of 2 J I'-^si 1-2 1 -|2 "."3 ,3 = ^ 2 ~ 100 125 150 175 200 250 300 jf -ill If -* -a 01 Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. a 1 JI.2.S 1 ll per rq. ft. per sq. ft. per sq.ft. per sq. ft. per sq.ft. per sq.ft. per sq.ft. 10 22.68 0.12 0.30 45.4 36.3 30.2 25.9 22,7 18.1 15.1 11 20.62 0.14 0.33 37.5 30.0. 25.0 21.4 18.7 15.0 12.5 12 18.90 0.17 0.36 31.5 25.21 21.0 18.0 15.8 12.6 10.5 13 17.45 0.20 | 0.39 26.8 21.5 i 17.9 15.3 13.4 10.7 8.9 14 16.20 0.23 0.42 23.1 18.5 i 15.4 13.2 11.6 9.3 7.7 15 15.12 0.26 ! 0.45 20.2 16.1 ' 13.4 11.5 10.1 8.1 6.7 16 14.18 0.30 1 0.48 17.7 14.2 ! 11.8 10.1 8.9 7.1 5.9 17 13.34 0.33 ! 0.51 15.7 12.6 10.5 9.0 7.8 6.3 5.2 18 12.60 0.37 0.54 14.0 11.2 i 9.3 8.0 7.0 5.6 4.7 19 11.94 0.42 i 0.57 12.6 10.1 8.4 7.2 6.3 5.0 4.2 20 11.34 0.46 0.60 11.3 9.1 7.6 6.5 5.7 4.5 3.8 21 10.80 0.51 0.63 10.3 8.2 6.9 5.9 5.2 4.1 3.4 22 10.31 0.56 0.66 9.4 7.5 6.2 5.4 4.7 3.7 3.1 23 9.86 0.61 0.69 8.6 i 6.9 5.7 4.9 4.3 3.4 2.9 24 9.45 0.66 0.72 7.9 6.3 5.3 4.5 3.9 3.1 2.6 i 25 9.07 0.72 0.75 7.3 5.8 4.9 42 36 29 2.4 26 8.72 0.78 0.78 6.7 5.4 4.5 3^9 3^3 27 2.2 27 8.40 0.84 0.81 6.2 5.0 4.2 3.6 3.1 2.5 2.1 28 8.10 0.90 0.84 5.8 4.6 3.9 a.3 2.9 2.3 1.9 29 7.82 0.97 i 0.87 5.4 4.3 3.6 3.1 2.7 2.1 1.8 30 7.56 1.04 0.90 5.0 4.0 3.4 2.9 2.5 2.0 1.7 31 7.32 1.11 0.93 4.7 3.8 3.2 2.7 2.4 1.9 1.6 32 7.09 1.18 0.96 4.4 3.5 3.0 2.5 2.2 1.8 1.5 33 6.87 1.26 0.99 4.2 3.3 2.8 2.4 2,1 1.7 1.4 34 6.67 1.34 1.02 3.9 3.1 2.6 2.2 2.0 1.6 1.3 35 6.48 1.42 1.05 3.7 3.0 2.5 2.1 1.9 1.5 1.2 36 6.30 1.50 1.08 3.5 2.8 2.3 2.0 1.8 1.4 1.2 37 6.13 1.58 1.11 3.3 2.6 2.2 1.9 1.7 1.3 1.1 38 5.97 1.67 1.14 3.1 2.5 2.1 1.8 1.6 1.3 1.0 39 5.82 1.76 1.17 3.0 2.4 2.0 1.7 1.5 1.2 1.0 G B 38 * rz UNION IRON MILLS' 10K-INCH EYEBEAM, No. 4, LIGHT, 313-2 LBS. PER FOOT. Depth, 10K". Width of Flanges, 4.54" . Thickness of Web, 0.41". Maximum fiber strain = 12000 Ibs. per square inch. g -g l^?2 t3 ; A. Proper dis >tance, in feet, center to center 1 3 Ifli I of b< jams, for Safe Loads of 42" ?'"o (S -- 1 o . ( t 100 ' 125 150 175 ! 200 250 300 3 1 Ssi 1 j3 Ibs. i Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. s 1* =2^ bD <~ ifj per i per per per per per per ji^.s.s * sq. ft. j sq. ft. sq. ft. sq. ft. sq. ft. sq.ft. sq. ft. . 10 12.56 0.13 0.16 25.1 1 20.1 16.7 14.4 12.6 10.0 8.4 11 11.42 0.16 0.17 20.8 i 16.6 13.8 11.9 10.4 8.3 6.9 12 10.47 0.19 0.19 17.5 14.0 11.6 10.0 8.7 7.0 5.8 13 9.66 0.22 0.21 14.9 1 11.9 9.9 8.5 7.4 5.9 5.0 14 8.97 0.26 0.22 12.8 i 10,2 8.5 7.3 6.4 5.1 4.3 15 8.37 0.30 0.24 11.2; 8.9 7.4 6.4: 5.6- 4.5 3.7 16 7.85 0.34 0.25 9.8 i 7.8 6.5 5.6; 4.9 3.9 3.3 17 7.39 0.38 0.27 8.7' 7.0 5.8 5.0 4.3 3.5 2.9 18 6.98 0.43 0.28 7.8; 6.2 5.2 4.4 3.9 3.1 2.6 19 6.61 0.48 0.30 7.0; 5.6 4.6 4.0 3.5 2.8 2.3 20 6.28 0.53 0.32 6.3 5.0 4.2 3.6 3.1 2.5 2.1 21 5.98 0.58 0.33 5.7 4.6 3.8 3.3 2.8 2.3 1.9 88 5.71 0.64 0.35 5.2 4.2 3.5 3.0 2.6 .2.1 1.7 23 5.46 0.70 0.36 4.8 3.8 3.2 2.7 2.4 1.9 1.6 24 5.23 0.76 0.38 4.4 3.5 2.9 2.5 2.2 1.7 1.5 25 5.02 0.82 0.39 4.0 3.2 2.7 2.3 2.0 1.6 1.3 26 4.83 0.89 0.41 3.7 3.0 2.5 2.1 1.9 1.5 1.2 27 4.65 0.96 0.43 3.4 2.8 2.3 2.0 1.7 1.4 1.1 28 4.49 1.03 0.44 3.2; 2.6 2.1 1.8 1.6 1.3 1.1 29 4.33 1.11 0.46 3.0; 2.4 2.0 1.7; 1.5 1.2 1.0 30 4.19 1.19 0.47 2.8' 2.2 1.9 1,6: 1.4 1.1 .9 31 4.05 1.27 0.49 2.6; 2.1 1.7 1.5 1.3 1.0 .9 32 3.93 1.35 0.50 2.5 2.0 1.6 1.4 1.2 1.0 .8 33 3.81 1.44 0.52 2.3 1.8 1.5 1.3! 1.2 .9 .8 34 3.69 1.53 0.54 2.2; 1.7 1.4 1.2 1.1 .9 .7 35 3.59 1.62 0.55 2.1 1.6 1.4 1.2 1.0 .8 7 36 3.49 1.71 0.57 1.9; 1.6 1.3 1.1 1.0 .8 .6 37 3.39 1.80 0.58 1.8 1.5 1.2 1.1 ! .9 .7 .6 38 3.31 1.90 0.60 1.7; 1.4 1.2 1.0 , .9 .7 .6 39 '4 3.22 2.01 0.61 1.7! 1.3 1.1 .9 ; .8 .7 .6 H UNION IRON MILLS' 10^-INCH EYEBEAM, No. 4, HEAVY, 45 LBS. PER FOOT. Depth, 10}^". Width of Flanges, 4.92". Thickness of Web, 0.79". Maximum fiber strain = 12000 Ibs. pe r square inch. a ^ ti^s 1.9 ! ft i ^ - i :.- Proper distance, in feet, center to center 11 jj'gj^g of beams, for Safe Loads of i* if Jit's 1 a ** <*-. 175 100 125 ICO 200 250 300 *8fj|lf Hi Ibs. Ibs. : Ibs. Ibs. Ibs. Its. Ibs. Q w iirfr I 1 per apt per per sq. ft. i Eq. ft. per sq^lt. per Eq ft. La per Eq. ft. i 10 15.32 0.13 i 0.23 30.6 24.5 20.4 17.5 15,3 12.3 10.2 11 13.93 : 0.16 I 0.25 25.3 20.3 16.9 14.5 12.7 10.1 8.4 12 12.77 : 0.19 i 0.27 21.3 17.0 ! 14.2 12.2 10.6 8.5 7.1 13 11.78 ! 0.22 ! 0.29 18.1 14.5 12.1 10.4 9.1 1 7.2 6.0 14 10.94 1 0.26 j 0.32 15.6 12.5 10.4 8.9 7.8 6.3 5.2 15 10.21 !0.30 0.34 13.6 10.9 l 9.1 7.8 6.8 5.4 4.5 16 9.58 10.34 0.36 12.0 9.6 8.0 6.8 6.0 4.8 4.0 17 9.01 0.88 0.38 10.6 8.5 7.1 6.1 5.3 4.2 3.5 18 8.51 10.43 0.41 9.5 7.6 6.3 5.4 4.7 3.8 3.1 19 8.06 0.48 0.43 8.5 6.8 5.7 4.8 4.2 3.4 2.8 20 7.66 i 0.53 ! 0.45 7.7 6.1 5.1 4.4 3.8 3.1 2.5 21 7.30 iO.58 0.47 7.0 5.6 4.6 4.0 3.5 2.8 2.3 22 6.96 10.64 0.50 6.3 5.1: 4.2 3.6 3.2 2.5 2.1 23 6.66 I 0.70 : 0.52 5.8 4.6 3.9 3.3 2.9 2.3 1.9 24 6.38 0.76 0.54 5.3 4.2 3.6 3.0 2.7 2.1 1.8 25 6.13 1 0.82 i 0.56 4.9 3.9 3.3 2.8 2.5 1.9 1.6 26 5.89 0.89 0.59 4.5 3.6 3.0 2.6 2.3 1.8 1.5 27 5.67 0.96 ; 0.61 4.2 3.4 2.8 2.4 2.1 1.7 1.4 28 5.47 1.03 : 0.63 3.9 3.1 ! 2.6 2.2 2.0 1.6 1.3 29 5.28 1.11 0.65 3.6 2.9 2.4 2.1 1.8 1.5 I 1.2 30 5.11 1.19 ! 0.68 3.4 2.7 2.3 1.9 1.7 1.4 1.1 31 4.94 1.27 0.70 3.2 2.6 2.1 1.8 1.6 1.3 1.1 32 4.79 1.35 : 0.72 3.0 2.4 2.0 1.7 1.5 1.2 1.0 33 4.64 1.44 0.74 2.8 2.2! 1.9 1.6 1.4 1.1 .9 34 4.51 1.53 . 0.77 2.7 2.1 1.8 1.5 1.3 1.1 .9 35 4.38 1.62 0.79 2.5 2.0i 1.7 1.4 1.3 1.0 .8 36 4.26 1.71 ; 0.81 2.4 1.91 1.6 1.4 1.2 .9 .8 37 4.14 1.80 i 0.83 2.2 1.8 1.5 1.3 1.1 .9 .7 38 4.03 1.90 i 0.86 2.1 1.7, 1.4 1.2 1.1 .8 .7 39 3.93 2.01 ; 0.88 2.0 1.6; 1.3 1.2 1.0 .8 .7 1 i UNION IRON MILLS' 10-INCH EYEBEAM, No. 5, LIGHT, 30 LBS. PER FOOT. Depth, 10". Width of Flanges, 4.32". Thickness of Web, 0.32". Maximum fiber strain = 12000 Ibs. per square inch. II it*! -2^ i. b-9 fl Proper distance, in feet, center to center of beams, for Safe Loads of ft w i.s r 9 100 125 150 175 200 250 300 J & IJfl i'f ILs Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. s S sSH tS M per per per per per per per =3:3.2.2 ^~ sq.ft. sq.ft. sq.ft. sq.ft. sq.ft. sq.ft. sq.ft. 10 12.00 0,14 0.15 24.0 19.2 16.0 13.7 12.0 9.6 8.0 11 10.91 0.17 0.17 19.8 15.9 ! 13.2 11.3 9.9 7.9 6.6 12 10.00 0.20 0.18 16.7 13.3 ! 11.1 9.5 8.3 6.7 5.6 13 9.23 0.23 0.20 '14.2 11.4 9.5 8.1 7.1 5.7 4.7 14 8.57 0.27 0.21 12.2 9.8 8.2 7.0 6.1 4.9 4.1 15 8.00 0.31 0.23 10.7 .5 7.1 6.1 5.3 4.3 3.6 16 7.50 0.35 0.24 9.4 7.5 6.3 5.4 4.7 3.8 3.1 17 7.06 0.40 0.26 8.3 6.6 5.5 4.7 4.2 3.3 2.8 18 6.67 0.45 0.27 7.4 5.9 4.9 4.2 3.7 3.0 2.5 19 6.32 0.50 0.29 6.7 5.3 4.4 3.8 3.3 2.7 2.2 20 6.00 0.55 0.30 6.0 4.8 4.0 3.4 3.0 2.4 2.0 21 5.71 0.61 0.32 5.4 4.4 3.6 3.1 .2.7 2.2 1.8 22 5.45 0.67 0.33 5.0 4.0 3.3 2.8 2.5 2.0 1.7 23 5.22 0.73 0.35 4.5 ! 3.6 3.0 2.6 2.3 1.8 1.5 24 5.00 0.80 0.36 4.2 3.3 2.8 2.4 2.1 1.7 1.4 25 4.80 0.87 0.38 3.8 3.1 2.6 2.2 1.9 1.5 1.3 26 4.62 i 0.94 0.39 3.6 I 2.8 2.4 2.0 1.8 1.4 1.2 27 4.44 1.01 0.41 3.3 2.6 2.2 1*9 1.6 1.3 1.1 28 4.29 1 1.09 0.42 3.1 2.4 2.0 1.7 1.5 1.2 1.0 29 4.14 1.17 0.44 2.9 2.3 1.9 1.6 1.4 1.1 .9 30 4.00 1.25 0.45 2.7 2.1 1.8 1.5. 1.3 1.1 .9 31 3.87 1.33 0.47 2.5 2.0 1.7 1.4 1.2 1.0 .8 32 3.75 1.42 ! 0.48 2.3 1.9 1.6 1.3 1.2 .9 .8 33 3.64 1.51 : 0.50 2.2 1.8 1.5 1.3 1.1 .9 i .7 34 3.53 1.60 i 0.51 2.1 1.7 1.4 1.2 1.0 ; .8 .7 35 3.43 1.70 ! 0.53 2.0 1.6 1.3 1.1 1.0 .8 .7 36 3.33 1.80 0.54 1.9 1.5 1.2 1.1 .9 .7 .6 37 3.24 1.90:0.56 1.8 1.4 1.2 1.0 .9 .7 .6 38 3.16 2,01 i 0.57 1.7 1.3 1.1 .9 .8 .7 .6 39 3.08 2.11 0.59 1.6 1 1.3 1.1 .9 .8 .6 .5 R 1 ' ] UNION IRON r. MILLS' 10-INCH EYEBEAM, No. 5, HEAVY, 45 LBS. PER FOOT. Depth, 10". Width of Flanges, 4.77". Thickness of Web, 0.77". Maximum fiber strain = 12000 Ibs. per square inch. I! 1-ili J| Si Proper distance, of beams, in feet, center to center for Safe Loads of 1 if ft? 1-9 ?5 100 125 150 175 < 200 250 300 E, ,~'f3 t -=? i 5 M Ibs. Ibs. Ibs. Ibs. ! Ibs. Ibs. Ibs. .2 * ilL J I- 2 .|Fg per per per per per cg^.S.S 5 * cq. ft. Jft *fft. sq. ft. sq.ft. 10 15.00 0.14 i 0.23 30.0 24.0 20.0 17.1 ! 15.0 12.0 ! 10.0 11 13.64 0.17 i 0.25 24.8 19.8 16.5 14.2 !12.4 9.9 8.3 12 12.50 0.20 0.27 20.8 16.7 13.9 11.6 10.4 8.3 6.9 13 11.54 0.23 0.29 17.8 14.2 11.8 10.1 : 8.9 7.1 5.9 14 10.71 0.27 0.32 15.3 12.2 10.2 8.7 : 7.7 6.1 5.1 15 10.00 0.31 0.34 13.3 10.7 8.9 7.6 6.7 5.3 : 4.4 16 9.38 0.35 0.36 11.7 9.4 7.8 6.7 5.9 4.7 3.9 17 8.82 0.40 0.38 10.4 8.3 6.9 5.9 i 5.2 4 2 3.5 18 8.33 0.45 0.41 9.3 7.4 6.2 5.3 : 4.6 3.7 3.1 19 7.89 0.50 0.43 8.3: 6.6 5.5 4.7 i 4.2 3.3 2.8 20 7.50 0.55 0.45 7.5 6.0 5.0 4.3 1 3.8 3.0 2.5 21 7.14 0.61 0.47 6.8 5.4 4.5 3.9 3.4 2.7 2.3 22 6.82 0.67 0.50 6.2 5.0 4.1 3.5 i 3.1 2.5 2.1 23 6.52 0.73 0.52 5.7 4.5 3.8 3.2 2.8 2.3 1.9 24 6.25 0.80 0.54 5.2 4.1 3.5: 2.9 2.6 2.1 1.7 25 6.00 0.87 0.56 4.8 3.8 3.2 2.7 2.4 1.9 1.6 26 5.77 0.94 0.59 4.4 3.6 3.0 2.5 2.2! 1.8 1.5 27 5.56 1.01 0.61 4.1 i 3.3 2.8 2.4 2.1 1.6 1.4 28 5.36 1.09 0.63 3.8 3.1 2.6 2.2 1.9 1.5 1.3 29 5.17 1.17 0.65 3.6 2.9 2.4 2.0 1.8 1.4 1.2 30 5.00 1.25 0.68 3.3 2.7 2.2 1.9 1.7 1.3 1.1 31 4.84 1.33 0.70 3.1 2.5 2.1 1.8 1.6 1.2 1.0 32 4.69 1.42 0.72 2.9 2.3 1.9 1.7 1.5 1.2 1.0 33 4.55 1.51 0.74 2.8! 2.2 1.8 1.6 1.4 1.1 .9 34 4.41 1.60 0.77 2.6 2.1 1.7 1.5 1.3 1.0 .9 35 4.29 1.70 0.79 2.4 2.0 1.6 1.4 1.2 1.0 .8 36 4.17 1.80 0.81 2.3 1.9 1.5 1.3 1.2 .9 .8 37 4.05 1.90 0.83 2.2 1.8 1.5 1.3 1.1 .9 .7 38 3.95 2.01 0.86 2.1 1.7 1.4 1.2 1.0 .8 .7 39 3.85 2.11 0.88 2.0 1.6 1.3 1.1 1.0 .8 .7 SB UNION IRON MILLS' 9-INCH EYEBEAM, No. 6, LIGHT, 23^ LBS. PER FOOT. Depth, 9". Width of Flanges, 4.01". Thickness of Web, 0.26". Maximum fiber strain = 12000 Ibs. per square inch. a H-s ^?^ .2 "3 eft .* Proper distance, in feet, center to center II JlMs bl f of beams, for Safe Loads of if 35*5 la 5i 100 125 150 175 200 250 800 .2 a j=.o'| g iif fls Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. | Ibs. s S ll.s.s Ji Jj |f per sq. ft. per sq.ft. per sq.ft. per sq.ft. per sj.ft. per ! per sq. ft. j sq. ft. 10 8.68 0.15 0.12 17.4 13.9 11.6 9.9 i 8.7 6.9! 5.8 11 7.89 0.19 0.13 14.4 11.51 9.6 8.2| 7.2! 5.7 4.8 12 7.23 0.22 0.14 12.1 9.6 8.0 6.9 6.0 4.8 4.0 13 6.68 0.26 0.15 10.3 8.2 6.9 5.9! 5.1 4.1 3.4 14 6.20 0.30 0.16 8.9 7.1 5.9, 5.1 4.4 3.5 | 2.9 15 5.79 0.35 0.18 7.7 6.2 5.1 4.4 3.9 3.1 1 2.6 16 5.43 0.40 0.19 6.8 5.4 4.5 3.9 3.4 2.7 2.3 17 5.11 0.45 0.20 6.0 4.8 4.0 3.4 3.0 2.4 2.0 18 4.82 0.50 0.21 5.4 4.3 3.6 3.0 2.7 2.1 1.8 19 4.57 0.56 0.22 4.8 3.8 3.2 2.7 2.4 1.9 1.6 20 4.34 0.62 0.24 4.3 3.5 2.9 2.5 2.2 1.7 1.4 21 4.13 0.68 0.25 3.9 3.2 2.6 2.2 2.0 1.6 1.3 22 3.95 0.75 0.26 3.6 2.9 2.4 2.0 1.8, 1.4 1.2 23 3.77 0.82 0.27 3.3 2.6 2.2 i 1.9 1.6 1.3 1.1 24 3.62 0.89 0.28 3.0 2.4 2.0 1.7 1.5 1.2 1.0 25 3.47 0.96 0.29 2.8 2.2 1.9 1.6 1.4 1.1 .9 26 3.34 1.04 0.31 2.6 2.0 1.7 1.5 1.3 1.0 i .9 27 3.21 1.12 0.32 2.4 1.9 1.6 1.4 1.2 1.0 .8 28 3.10 1.20 0.33 2.2 1.8 1.5 1.3 1.1 .9 .7 29 2.99 1.29 0.34 2.1 1.6 1.4 1.2 1.0 .8 .7 30 2.89 1.39 0.35 1.9 1.5 1.3 1.1 1.0 .8 .6 31 2.80 1.48 0.36 1.8 1.4 1.2 1.0 .9 .7 .6 32 2.71 1.58 0.38 1.7 1.4 1.1 1.0 .9 .7 .6 33 2.63 1.68 0.39 1.6 1.3 i 1.1 .9 .8 .6 .5 34 2.55 1.78 0.40 1.5 1.2 1.0 .9 .8 .6 .5 35 2.48 1.89 0.41 1.4 1.1 .9 .8 .7 .6 .5 36 2.41 2.00 0.42 1.3 1.1 Q .y .8 .7 .5 .4 37 2.35 2.11 0.43 1.3 1.0 .8 .7 .6 .5 .4 38 2.28 2.22 0.45 1.2 1.0 .8 .7 .6 .5 .4 39 2.23 2.34 0.46 1.2 .9 .8 .7 .6 .5 .4 x? , ^ UNION IRON MILLS' 9-INCH EYEBEAM, No. 6, HEAVY, 33 LBS. PER FOOT. Depth, 9". Width of Flanges, 4.33". Thickness of Web, 0.58". Maximum fiber strain = 12000 1 bs. per square inch. rt -*s tif^l-i- .3 -J Proper distance, in feet, center to center 11 |j K.2 a^ of b earns, for Safe Loads of j.a i'^s f.a Ja t= ~ > g -2" ^3 "^ CM ng-S-gjO c4 "" * <*-! ICO 125 150 175 200 250 300 il ^* J;g'| | g-^" 2a w Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 3 f -*5 w feJD^* JJ sj per per per per per per per & = Eq. ft. sq.ft. sq. ft. sq. ft. sq.ft. sq. ft. sq. ft 10 10.40 0.15 0.17 20.8 16.6 13.9 11.9 10.4 8.3' 6.9 11 9.45 0.19 0.18 17.2 13.8 11.5 9.8 8.6 6.9: 5.7 12 8.67 0.22 0.20 14.5 11.6 9.6 8.3 7.2 5.8 I 4.8 13 8.00 0.26 0.22 12.3 9.8 8.2 7.0 6.2 4.9 4.1 14 7.43 0.30 0.23 10.6 8.5 7.1 6.1 5.3 4.2 3.5 15 6.93 0.35 0.25 9.2 7.4 6.2 5.3 4.6 3.7 3.1 16 6.50 0.40 0.26 8.1 6.5 5.4 4.6 4.1 3.3 2.7 17 6.12 0.45 0.28 7.2 5.8 4.8 4.1 3.6 2.9 2.4 18 5.78 0.50 0.30 6.4 5.1 4.3 3.7 3.2 2.6 2.1 19 5.47 0.56 0.31 5.8 4.6 3.8 3.3 '2.9 2.3 1.9 20 5.20 0.62 0.33 5.2 4.2 3.5 3.0 2.6 2.1 1.7 21 4.95 ! 0.68 0.35 4.7! 3.8 3.1 2.7 2.4 1.9 1.6 22 4.73 0.75 0.36 4.3 3.4 2.9 2.5 2.2 1.7 1.4 23 4.52 0.82 0.38 3.9 3.1 2.6 2.3 2.0 1.6 1.3 24 4.33 0.89 0.40 3.6 2.9 2.4 2.1 1.8 1.4 1.2 25 4.16 0.96' 0.41 3.3 2.7 2.2 1.9 1.7 1.3 1.1 26 4.00 1.04 0.43 3.1 2.5 2.1 1.8 1.5 1.2 1.0 27 3.85 1.12 0.45 2.9 2.3 1.9 1.6 1.4 1.1 .9 28 3.71 1.20 0.46 2.7i 2.1 1.8 1.5 1.3 1.1 .9 29 3.59 1.29 0.48 2.5 2.0 1.6 1.4 1.2 1.0 1 .8 30 v 3.47 1.39 0.50 2.3 1.8 1.5 1.3 1.2 .9 .8 31 3.35 1.48 0.51 2.2 1.7 1.4 1 2 1.1 .9 .7 32 3.25 ! 1.58 0.53 2.0 1.6 1.4 1.1 1.0 .8 .7 33 3.15 : 1.68 0.55 1.9 1.5 1.3 1.1 1.0 .8 .6 34 3.06 1.78 0.56 1.8 1.4 1.2 1.0 .9 .7 .6 35 2.97 1.89 0.58 1.7 1.4 1.1 1.0 .9 .7 .6 36 2.89 2.00 i 0.59 1.6 1.3 1.1 .9 .8 .6 .5 37 2.81 2.11 0.61 1.5 1.2 1.0 .9 .8 .6 t 38 2.74 2.22 0.63 1.4 1.21 1.0 .8 .7 .6 39 2.67 2.34 0.64 1.4 U .9 .8 .7 .5 .5 UNION IRON MILLS' 8-INCH EYEBEAM, No. 8, LIGHT, 22 LBS. PER FOOT. Depth, 8". Width of Flanges, 3.81 ". Thickness of Web, 0.31 ". Maximum fiber strain = 12000 Ibs. per square inch. | rf -,: Proper distance, in feet, center to center I * ills il 2 .3 |s of beams, for Safe Loads of tS ~ 5]f:3g 2 -a ""M ICO 125 150 175 200 250 300 j?'S f. - ij i ;2 Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 1 1* ~Z'B fl-2 J> J> j -|f 1 per per per per i per per j per 8 If -3-^4? ijjj 5 100 125 150 175 200 250 300 _i . '5 3 s Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. M e <*H W 00 .2 'S 5 per per per per per per ' per . wS^S.2.2 ^ sq. ft. sq. ft. sq. ft. sq. ft. sq.ft. sq.ft. sq. ft. 5 7.58 0.06 0.05 30.3 24.3 20.2 17.3 15.2 12.1 10.1 6 6.32 0.08 0.05 21.1 16.9 14.0 12.0 105 8.4 7.0 7 5.42 0.11 0.06 15.5 12.4 10.3 8.9 7.7 6.2 5.2 8 4.74 0.15 0.07 11.9 9.5 7.9 6.8 5.9 4.7 4.0 9 4.21 0.19 0.08 9.4 7.5 6.2 5.3 4.7 3.7 3.1 10 3.79 0.23 0.09 7.6 6.1 5.1 4.3 3.8 3.0 2.5 11 3.45 0.28 0.10 6.3 5.0 4.2 3.6 3.1 2.5 2.1 12 3.16 0.33 0.11 5.3 4.2 3.5 3.0 2.6 2.1 1.8 13 2.92 0.39 0.12 4.5 3.6 3.0 2.6 2.2 1.8 1.5 14 2.71 0.45 0.13 3.9 3.1 2.6 2.2 1.9 1.5 1.3 15 2.53 0.52 0.14 3.4 2.7 2.2 1.9 1.7 1.3 1.1 16 . 2.37 0.59 0.14 3.0 2.4 2.0 1.7 1.5 1.2 1.0 17 2.23 0.67 0.15 2.6 2.1 1.7 1.5 1.3 1.0 .9 18 2.11 0.75 0.16 2.3 1.9 1.6 1.3 1.2 .9 .8 19 2.00 0.83 0.17 2.1 1.7 1.4 1.2 1.1 .8 .7 20 1.90 0.92 0.18 1.9 1.5 1.3 1.1 1.0 .8 .6 21 1.81 1.01 | 0.19 1.7 1.4 1.1 1.0 .9 .7 .6 22 1.72 1.11 0.20 1.6 1.2 1.0 .9 .8 .6 .5 23 1.65 1.22 0.21 1.4 1.1 1.0 .8 .7 .6 .5 24 1.58 1.33 0.22 1.3 1.1 .9 .8 .7 .5 .4 25 1.52 1.45 0.23 1.2 1.0 .8 .7 .6 .5 .4 26 1.46 1.56 0.23 1.1 .9 .7 .6 .6 .4 .4 27 1.40 1.68 0.24 1.0 .81 .7 . .6 .5 .4 .3 28 1.35 1.81 0.25 1.0 .8 .6 .5 .5 .4 .3 29 1.31 1.95; 0.26 .9- .7 .6 .5 .5 .4 .3 1 y > UNION IRON MILLS' r. 5-INCH EYEBEAM, No. 11, LIGHT, 10 LBS. PER FOOT. Depth, 5". Width of Flanges, 2.73". Thickness of Web , 0.225". Maximum fiber strain = 12000 Ibs. per square inch. Distance between supports, in feet. Safe load, uniformlv distributed, (includ- ing weight of beam,) in tons of 2000 Ibs. F> i Daflection under this ^ load, in inches. a a j s~ -*. i |i 0.03 Proper distance, in feet, center to center of beams, for Safe Loads of 100 Ibs. per sq. ft. 15.8 125 Ibs. per Eft. 12.6 150 Ibs. & 175 Ibs. per sq. ft. 200 Ibs. per sj.ft. 7.9 250 Ibs. per sq. ft. 300 Ibs. per sq.ft. 5 3.95 10.5 9.0 6.3 5.3 6 3.29 0.10 0.03 11.0 8.8 7.3 6.3 5.5 4.4 3.7 7 2.82 ' 0.14 0.04 8.1 6.4 5.4 4.6 j 4.0 3.2 2.7 8 2.47 0.18 0.04 6.2 4.9 4.1 3.5! 3.1 2.5 2.1 9 2.20 ! 0.23 0.05 4.9 3.9 3.3 2.8 2.4 2.0 1.6 10 1.98 ; 0.28 0.05 4.0 3.2 2.6 2.3 2.0 1.6 1.3 11 1.80 0.34 0.06 3.3 2.6 2.2 1.9 1.7 1.3 I~U 12 1.65 0.40 0.06 2.8 2.2 1.8 1.6 1.4 1.1 .9 13 1.52 0.47 0.07 2.3 1.9 1.6 1.3 1.2 .9 .8 14 1.41 0.55 0.07 2.0 1.6 1.3 1.1 1.0 .8 .7 15 1.32 0.63 0.08 1.8 1.4 1.2 1.0 .9 ' .7 .6 16 1.24 0.71 0.08 1.6 1.2 1.0 .9 .8 .6 .5 17 1.16 0.80 0.09 1.4 1.1 .9 .8 .7 .5 .5 18 1.10 0.90 0.09 1.2 1.0 .8 .7 .6 .5 .4 19 1.04 1.00 0.10 1.1 i .9 .7 .6 .5 .4 .4 20 21 .99 .94 1.11 1.22 0.10 0.11 1.0 .9 .8 .7 .7 .6 .6 .5 .5 .4 A A A .3 .3 22 .90 1.34 0.11 .8 .7 .5 .5 .4 .3 .3 23 .86 1.47 0.12 .7 .6 .5 .4 .4 .3 .2 24 .82 1.60 0.12 .7 .5 .4 .4 .3 .3 .2 UNION IRON MILLS' 5-INCH EYEBEAM, No. 11, HEAVY, 13 LBS. PER FOOT. Depth, 5". Width of Flanges, 2.91". Thickness of Web, 0.405". Maximum fiber strain = 12000 Ibs. per square inch. Distance between supports, in feet. :pl ijl Deflection under this load, in inches. Weight of beam, in tons of 2000 Ibs. Proper distance, in feet, center to center of beams, for Safe Loads of 100 Ibs. par sq.ft. 125 Ibs. 150 Ibs. per sq.ft. 175 Ibs. per sq.ft. 200 Ibs. per sq.ft. 9.1 250 Ibs. per 7.3 300 Ibs. per sq. ft. 6.1 5 4.55 0.07 0.03 18.2 14.6 12.1 10.4 6 3.79 0.10 0.04 12.6 10.1 8.4 7.2 6.3 5.1 4.2 7 3.25 0.14 0.05 9.3 7.4 6.2 5.3 4.6 3.7 3.1 8 2.85 0.18 0.05 7.1 5.7 4.8 4.1 3.6 2.9 2.4 9 2.53 0.23 O.OG 5.6 4.5 3.7 3.2 2.8 2.2 1.9 10 2.28 0.28 0.07 4.6 ' 3.6 3.0 2.6 2.3 1.8 1.5 11 12' 13 2.07 1.90 1.75 0.34 0.40 0.47 0.07 0.08 0.08 3.8 3.2 2.7 3.0 2.5 2.2 2.5 2.1 1.8 2.1 1.8 1.5 1.9 1.6 1.3 1.5 1.3 1.1 1.3 1.1 .9 14 1.63 0.55 0.09 2.3 1.9 1.6 1.3 1.2 .9 .8 15 1.52 0.63 0.10 2.0 1.6 1.4 IwB 1.0 .8 .7 16 1.42 0.71 0.10 1.8 1.4 1.2 1.0 .9 .7 .6 17 1.34 0.80 0.11 1.6 1.3 1.0 .9 .8 .6 .5 18 1.26 0.90 0.12 1.4 1.1 .9! .8 .7 .6 .5 19 1.20 1.00 0.12 1.3 1.0 .8 .7 .6 .5 .4 20 1.14 1.11 0.13 1.1 .9 .8 .7 .6 .5 .4 21 1.08 1.22 0.14 1.0 .8 .7 .6 .5 .4 .3 22 1.03 1.34 0.14 .9 .8 .6 .5 .5 .4 .3 23 .99 1.47 0.15 .9 .7 .6 .5 .4 .3 .3 24 '4 .95 1.60 0.16 .8 .6 i .5 .5 .4 .3 .3 i UNION IRON MILLS 1 4-INCH EYEBEAM, No. 12, LIGHT, 8 LBS. PER FOOT. Depth, 4". Width of Flanges, 2.48". Thickness of Web, 0.23". Maximum fiber strain = 12000 Ibs. per square inch. jl II till fei 'a .2 ii i~~ Proper distance, in feet, center to center of beams, for Safe Loads of 100 Ibs. par sq. ft. 125 Ibs. per sq. ft. 150 Ibs. per sq.ft. 175 Ibs. per sj.ft. 200 Ibs. 250 Ibs. 300 Ibs. per sq.ft. I I 5 2.48 0.09 0.02 9.9 7.9 6.6 5.7 5.0 4.0 3.3 6 2.07 0.13 0.02 6.9 5.5 4.6 3.9 3.5 2.8 2.3 7 1.77 0.17 0.03 5.1 4.0 3.4 2.9 2.5 2.0 1.7 8 1.55 0.22 0.03 3.9 3.1 2.6 2.2 1.8 1.9 1.6 1.3 1.0 9 1.38 0.28 0.04 3.1 2.5 2.0 1.5 1.2 10 11 1.24 1.13 0.35 0.42 0.04 0.04 2.5 2.1 2.0 1.6 1.7 1.4 1.4 1.2 1.2 1.0 1.0 .8 .8 .7 12 1.03 0.50 0.05 1.7 1.4 1.1 1.0 .9 .7 .6 13 0.95 0.59 0.05 1.5 1.2 1.0 .8 .7 .6 .5 14 0.89 0.68 0.06 1.3 1.0 .8 .7 -6 .5 .4 15 0.83 0.78 0.06 1.1 .9 .7 .6 .6 .4 .4 16 0.78 0.89 0.06 1.0 .8 .6 .6 .5 .4 .3 17 0.78 1.01 0.07 .9 .7 .6 .5 .4 .3 .3 18 0.69 1.13 0.07 .8 .6 .5 .4 .4 .3 .3 19 0.65 1.26 0.08 .7 t .5 .4 .3 .3 .2 2 53 I UNION IRON MILLS' 4-INCH EYEBEAM, No. 12, HEAVY, 10 LBS. PER FOOT. Depth, 4". Width of Flanges, 2.63". Thickness of Web, 0.88". Maximum fiber strain = 12000 Ibs. per square inch. 5^-jj I a Proper distance, in feet, center to center Jl fill 1 of beams, for Safe Loads of If ^15 5-2 "o ,_ 100 125 150 175 200 250 300 ISff 'llf 3 Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. Ibs. 1 1* sill 1 || 5, per per sq.ft. sq.ft. per per per per sq. ft. sq. ft. sq. ft. j sq. ft. 5 2.80 0.09 0.03 11.2 9.0 7.5 6.4 5.6 4.5 3.7 6 2.33 0.13 0.03 7.8 6.2: 5.2 4.4 3.9 3.1 2.6 7 2.00 0.17 0.04 5.7 4.6 3.8 3.3 2.9 2.3 1.9 8 1.75 0.22 0.04 4.4 3.5 2.9 2.5 2.2 1.8 1.5 9 1.56 0.28 0.05 r 3.5 2.8 2.3| 2.0 1.7 1.4 1.2 10 1.40 0.35 0.05 2.8 2.2 1.9 1.6 1.4 1.1 .9 11 1.27 0.42 0.06 2.3 1.8 1.5 1.3 1.2 .9 .8 12 1.17 0.50 0.06 2.0 1.6 1.3 1.1 1.0 .8 .7 13 1.08 0.59 0.07 1.7 1.3 1.1 .9 .8 .7 .6 14 1.00 0.68 0.07 1.4- 1.1 1.0 .8 .7 .6 .5 1 15 0.93 10.78 0.08 1.2 1.0 .8 .7 .6 .5 .4 16 0.88 0.89 i 0.08 111 .9 .7 .6 .6 .4 .4 17 0.82 1.01 0.09 1.0 .8 .6 .6 .5 .4 .3 18 0.78 1.13 0.09 .9 .7 .6 .5 .4 .3 .3 19 0.74 1.26 0.10 ,8 .6 .5 .4 .4 .3 .3 54 UNION IRON MILLS' 3-INCH EYEBEAM, No. 13, LIGHT, 7 LBS. PER FOOT. Depth, 3". Width of Flanges, 2.32". Thickness of Web v 0.19". Maximum fiber strain = 12000 Ibs. per square inch. M J .3 1 M IT Safe load, uniformly distributed, (includ- ing weight of beam,) in tons of 2000 Ibs. P P 1 Deflection under this Q to 1 l<> a( i, in inches. a "s 5 S3 _ Pro 100 Ibs. per sq. ft. per dis of b 125 Ibs. 41 tance, earns, 150 Ibs. per sq.ft. 4.4 3.0 2.2 1.7 1.4 1.1 .9 .8 .6 .6 in fee forSa 175 Ibs. per 4. ft. , cente ? e Loa loo Ibs. per sq.ft. r to c< Is of 250 Ibs. per sq.ft. mter ~300 Ibs. per sq.ft. 5 6 1.65 1.37 0.02 0.02 6.6 4.6 5.3 3.7 3.8 2.6 3.3 2.3 2.6 1.8 T3 1.0 .8 .7 .5 .5 : 4 s 2.2 1.5 1.1 n \7 .5 .5 .4 .3 .3 7 8 9 10 11 12 13 14 1.18 1.03 0.92 0.82 0.75 0.69 0.63 0.59 0.23 0.29 0.37 0.46 0.56 0.67 0.78 0.91 0.02 0.03 0.03 0.04 0.04 0.04 0.05 0.05 3.4 2.6 2.0 1.6 1.4 1.2 1.0 .8 2.7 2.1 1.6 1.3 1.1 .9 .8 .7 1.9 1.5 1.2 .9 .8 .7 .6 .5 1.7 1.3 1.0 .8 i i UNION IRON MILLS' 3-INCH EYEBEAM, No. 13, HEAVY, 9 LBS. PER FOOT. Depth, 3". Width of Flanges, 2.52". Thickness of Web, 0.39". Maximum fiber strain = 12000 Ibs. per square inch. Distance between supports, in feet. Safe load, uniformly distributed, (includ- ing weight of beam,) in tons of 2000 Ibs. Ij a 11 a JJ ^5 ILi s* Proper di oft stance, in feet, center to center earns, for Safe Loads of 100 Ibs. per sq. ft. 125 Ibs. per sq. ft. 150 Ibs. per sq. ft. 175 Ibs. per sq.ft. 200 Ibs. per sq. ft. 3.8 2.6 1.9 1.5 1.2 .9 .8 .7 .6 .5 250 Ibs. per sq.ft. 300 Ibs. Sq P \ 5 6 1.89 1.57 0.12 0.17 0.02 0.03 7.6 5.2 3.9 3.0 2.3 1.9 1.6 1.3 1.1 1.0 6.0 4.2 5.0 3.5 4.3 3.0 3.0 2.1 2.5 1.7 7 8 9 10 11 12 13 . 14 1.35 1.18 1.05 0.94 0.86 0.79 0.73 0.67 0.23 0.29 0.37 0.46 0.56 0.67 0.78 0.91 0.03 0.04 0.04 0.05 0.05 0.05 0.06 0.06 3.1 2.4 1.9 1.5 1.2 1.1 .9 .8 2.6 2.0 1.6 1.3 1.0 .9 .7 .6 2.2 1.7 1.3 1.1 .9 .8 .6 .5 1.5 1.2 .9 .8 .6 .5 .4 .4 1.3 1.0 .8 .6 .5 .4 .4 .3 8 55 EXPLANATION OF TABLES ON THE PROPERTIES OF UNION IRON MILLS' EYE AND DECK BEAMS, CHANNEL BARS, ANGLE, STAR AND TEE IRONS. Pages 62 to 69, inclusive. The tables on I Beams, Deck Beams and Channel Bars are calculated for the minimum and maximum weight to which the various shapes can be rolled. The lithographed plates indicate the manner in which the enlargement of the section takes place, and column 7 in tables gives the increase of thickness of web for each pound increase of weight of beam or channel. The width of flanges is increased the same amount as the thickness of web. Angle Irons are increased in weight in the manner indicated by Fig. 4 on page 23, the size corresponding with the least thickness, and increasing somewhat with the increase of thick- ness, but some of the heavier weights of a few of the shapes are rolled in special finishing grooves, whereby the exact size is obtained for a thickness greater than the minimum. In the tables, for the sake of uniformity, it was assumed generally that the size corresponds with the least thickness only,, and the increase of weight is obtained in the manner indicated by the above mentioned Fig. 4, page 23. Beams, Channels and Angle Irons, may be rolled to any weight intermediate between the minimum and maximum weights given. Each shape of Star and T Iron, however, can be rolled to one weight only. Columns 11 and 13 in the tables for beams and channels give coefficients, by the help of which the safe uniformly distributed load for any beam or channel, and for any span length, can be readily and quickly determined. To do this, it is only necessary to divide the coefficient given by the span or distance between supports, in feet, and multiply by 1000. If the weight of the beam or channel is intermediate between the minimum and B 5g maximum weights given, add to the coefficient for the minimum weight, the value given in columns 12 or 14 (for one pound increase of weight) multiplied by the number of pounds the beam or channel is heavier than the minimum. If a beam or channel is to be selected, (as will usually be the case,) intended to carry a certain load for a length of span already determined on, it will be most convenient to ascertain the coefficient which this load and span will require, and refer to the table for a beam or channel having a coefficient as large as this. The coefficient is obtained by multiplying the load, in pounds uniformly distributed, by the span length in feet, and dividing by 1000. In case the load is not uniformly distributed, but is concen- trated at the middle of the beam or channel, multiply the load by 2, and then consider it as uniformly distributed. The deflec- tion will be y^jths of the deflection by this load. If the load is neither uniformly distributed nor concentrated at the middle, obtain the bending moment. This, multiplied by 0.008 will give the required coefficient. If the loads for which the beams or channels are to be pro- portioned, are quiescent, the coefficients for a fiber strain of 12000 Ibs. per square inch should be used ; but if moving loads are to be provided for, the coefficients fo*r 10000 Ibs. fiber strain should be taken. Inasmuch as the effects of impact may be very considerable, (the strains produced in an unyielding inelastic material by a load suddenly applied, being double those produced by the same load in a quiescent condition,) it will sometimes be advisable to use still smaller fiber strains than 10000. The co- efficients for these can readily be determined by proportion. Thus, for a fiber strain of 8000 Ibs. per square inch, the coefficient will equal the coefficient for 10000 Ibs. fiber strain multiplied by ^-ths. The table on the properties of Union Iron Mills' Angle Irons requires explanation only relative to the angles with unequal legs, to which the latter half of the table applies. It will be observed that two values are given, in the case of each angle, for the distance of center of gravity from outside of flange, the moment of inertia, the moment of resistance and the radius of 67 gyration of the section. The first or larger value invariably refers to a neutral axis parallel to the smaller flange, and to the distance between the center of gravity and the outside of this flange, and the second or smaller value to a neutral axis parallel to the larger flange, and to the distance between the center of gravity and the outside of this flange. For each position of the neutral axis there will be two moments of resistance, since the distance between the neutral axis and the extreme fibers has a different value on one side of the axis from what it has on the other. The moment of resistance given in table is the smaller of these two values, and the fiber strain calculated from it, will therefore give the larger of the two strains in extreme fibers, (since these strains are equal to the bending moment divided by the moment of resistance of the section). The left hand figures in each column refer to the minimum weight of angle, and the right hand figures to the maximum weight, throughout the table. The table on the properties of Union Iron Mills' T Irons is modeled after the foregoing, and will therefore scarcely require explanation. The horizontal portion of the T is called the flange and the vertical portion the stem. In the case of the neutral axis parallel to the flange, there will be two moments of resistance, and the least is given; but in the case of the neutral axis coincident with stem, there is only one moment of resistance. In calculating the table, the flange and stem of the T's were considered as rectangles of equal area as the actual section, and the figures given are therefore approximations only, though very close ones. No approximations have entered into the calculations of any of the other tables, and the figures given may be relied upon as accurate. The use of the radii of gyration will be explained in connec- tion with the table on the strength of wrought iron columns. The moment of resistance is used to determine the fiber strain in a beam or other shape iron subjected to bending or transverse strains, by simply dividing the same into the. bending moment, expressed in inch pounds.* The 15th column in 'the table on the Properties of Union Iron Mills' Channels, giving the distance of the center of gravity of 58 channels from outside of web, is used to obtain the radius of gyration for columns or struts consisting of two channels latticed, as represented by Fig. 1, page 26, in the case of the neutral axis passing through the center of the section parallel to the webs of the channels. This radius of gyration is equal to the square root of the distance between the center of gravity of the channel and the center of the section. EXAMPLES OF APPLICATION OF TABLES. I. What load, uniformly distributed, will a 10" beam 'carry, weighing 40 Ibs. per foot, and measuring 14 feet between sup- ports, allowing a fiber strain of 12000 Ibs. per square inch ? Answer : By table, C, for a 10" beam, 40 Ibs., = 240 -f 10 X 4 = 280, therefore L = )0 * 28 = 20 000 Ibs., including weight of beam. II. What beam will be required to carry 36000 Ibs., uniformly distributed over a span of 16 feet between supports, same fiber strain ? 1L 16 X 36000 K - c , . , Answer: C required = -^ = -^ = 576, which calls for a 15" beam, 52 Ibs. per foot. III. A light 4" X 3" angle iron, weighing 8.3 Ibs. per foot, spanning 4 feet, is loaded with 1000 Ibs. at center : what will be the maximum fiber strain if the 4 /; flange is in a vertical position ? Answer: By table, moment of resistance = 1.46. Bending moment = 12000 inch pounds. Therefore maximum fiber strain= 120 ^ Q = 8220 *lbs., occurring in the fibers furthest from the 1.46 neutral axis, i, e., at the end of the long flange. SPECIAL CASES OF LOADING. I. Beam loaded at a point distant "-a" feet from the left hand and "b" feet from the right hand support, by a single load P. 1 = length of beam between supports = a -|- b. 59 Maximum bending moment, neglecting dead weight of beam, occurs at point of application of the load and = I 2 P = load given in tables X 8ab Pressure or reaction at left hand support = P , and at right hand support == P -p II, Beam unsupported at one end and held horizontally at the other, 1 representing the length of beam from end to support. If loaded by a uniformly distributed load W : W 1 bending moment occurs at support and = ^ W= load given in tables X X and tne deflection = that of the tables X 2.4. If loaded with a single load P at its extremity : Maximum bending moment occurs at support and = PI. P = load given in tables X ^> an d the deflection that of tables X 3.2. GENERAL FORMULAE ON THE FLEXURE OF BEAMS OF ANY CROSS-SECTION. Let A = area of section, 1 = length of span, W = load, uniformly distributed, M = bending moment, d = depth of beam, out to out, n = distance of center of gravity of section, from top or from bottom, s = strain per square inch in extreme fibers of beam, either top or bottom, D = maximum deflection, I = moment of inertia of section, R = moment of resistance, r = radius of gyration, E = modulus of elasticity, (assumed = 2600QOOO for wrought iron in tables.) Then R = ~~r~ R 8 =T 8 Q w=- _ Win _ w i_ 81 8 R 5 Wl 3 for beam supported at both ends and uni- 384 El formly loaded, _ PI 3 for beam supported at both ends and loaded ~ 48 El by a single load P at middle, _ Wl 3 for beam held horizontally at one end only 8 El and uniformly loaded, PI 3 for beam held horizontally at one end only 3 El and loaded with a single load P at the other. VALUES OF / AND Jt FOR USUAL SECTIONS. 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The moments of inertia and resistance, and radii of gyration, in this table, are close approximations only. The table does not include all sizes manufactured. w | ij |J 111 f 3 s| :|| 5 1-1*5*1! all I'glJl |a gll sT m 1*1^1- II? 111 5 X3 13 3.90 ! 0.73 2.5 1.1 0.80 5.7 ! 2.3 1.21 5 X25 101* 3.08 0.58 1.4 0.71 0.66 4.6 i 1.8 1.21 -4)^X33-2 15 4.50 1 1.13 5.2 2.18 1.07 3.9 ; 1.7 0.93 4 X5 14 4.20 1.57 10.5 3.05 1.57 2.7 | 1.4 0.80 4 X4X 13j^ 4.05 i 1.37 7.8 2.48 1.39 2.7 1.4 0.82 4 X4 " 12 3.60 ! 1.18 5.4 i 1.91 1.22 2.6 1.3 0.84 4 X3 ^ 2.78 , 0.80 2.1 | 0.96 0.87 2.3 1.1 0.90 4 X%% ly 2 2.25 ; 0.62 1.1 : 0.60 0.70 2.0 1.0 0.93 4 X2 6K 1.95 l 0.46 0.54 0.35 0.53 1.8 1 0.91 0.96 3lX4 11) 3.38 1.24 5.15 i 1.87 1.23 1.8 1.00 0.72 3)^X3^ 10 8.00 ! 1.04 3.34 ! 1.36 1.05 1.6 0.93 0.73 3^X3 9>^ 2.78 | 0.85 2.14 1.00 0.88 1.6 0.93 0.77 3 X4 1214 3.68 ! 1.35 5.55 '12.10 1.24 1.8 ! 0.87 0.60 3 X3^' 11% 3.53 j 1.15 3.93 1.67 1.06 1.4 0.92 0.62 3 X3 7.6 2.28 i 0.90 1.89 0.90 0.91 0.94 0.63 0.64 3 X2> 6 1.80 ! 0.69 0.96 ; 0.53 0.73 0.77 0.51 0.66 2^X3 : 6^ 1.95 ! 0.96 1.66 0.81 0.93 0.50 0.40 0.51 2KX2%- 6.6 1.98 0.86 1.39 ! 0.74 0.84 0.55 0.44 0.53 2)^X2^ 5.4 1.62 0.75 0.91 0.43 0.75 0.46 0.37 ; 0.53 2^>Xl*4i 3 0.90 i 0.30 0.09 0.10 0.32 0.33 0.26 0.61 PROPERTIES OF UNION IRON MILLS' STAR IRONS. Size. Inches. Weight Thickness in \ Inertia Moment of Radius of perfoot. If^sat Area. | neutral ^ ; Resistance, Gyration, r Lb ? End and Root i Sq. In. ! +;,,.' M t. neutral ans neutral axis of Flange. | I ^ gravity as Before. as before. 4 X4 12 M T 9 u ! 3.60 , 2.32 1.16 0.81 3% X3^ 9 1 4 % I A 2.85 ; 1.49 0.85 0.72 3 X3 7 4 T 5 6-M i 2.18 0.82 0.55 0.61 2M X2^ 4 A -H I. 0.45 0.36 0.52 2 ><2 3^ 4 U'M 1.13 0.20 i 0.20 0.43 O &. 3 tV A > 0.69 i 0.065 0.087 0.31 . 69 ^ EXPLANATION OF TABLE ON RIVETED GIRDERS. Riveted girders are used in cases where rolled I Beams are insufficient to carry the load. On page 23 of the lithographed plates will be found illustrations of various forms of riveted girders. The sections with single webs are more economical than those with double webs (box girders), but the latter are stiffer laterally, and should always be used where the proportion of length of span to width of top flange is great and the girder is not held in position sideways. This proportion of length to width should not exceed twenty, without making provision for such increase by an addition of metal in the compression flange beyond that required by the table. The web of the girder must be made of such thickness that there will be no tendency to buckle, and that the vertical shearing stress per square inch will not exceed 9000 Ibs. This shearing stress is obtained by dividing half the load upon the girder by the web section. The first condition is attained when this 10000 shearing stress does not exceed d 2 in which d repre- h ~~^ sents the depth of web of girder and t its thickness, both in inches. Ordinarily this formula gives a lower strain per square inch than 9000 Ibs., so that both conditions are usually attained when the first is. Instead of increasing the thickness of the web, it may be stiffened also by means of vertical angle irons riveted to it at proper intervals. These should always be less than the depth of the girder, at least for the end panels, but towards the middle of the girder the stiffeners may be placed further apart or entirely omitted. Stiffeners ' should always be used at or near the supports, and at any other points where there is a concentration of heavy loads. The rivets should be ^", unless the girder is light, when $" may be sufficient. The spacing ought not to exceed 6" and should be closer for heavy flanges, but in all cases it should be close at the ends, say 3" for a distance of 18" to 24" at each end. The following table furnishes a ready means of determining the section of girder necessary to carry a certain load, for any span length from 10 to 39 feet, inclusive. It will be noticed that the table is calculated for an allowed fiber strain of 10000 Ibs. per square inch, while the tables on rolled beams are calculated for a fiber strain of 12000 Ibs. per square inch. This reduction in the allowed strain is intended to cover the loss in strength, (somewhat greater than the loss in sec- tion,) due to the rivet holes, and the riveted girders proportioned by this table, will be found to be of about the same strength as the rolled beams, proportioned by the tables applying to them. The transverse strength of the web is neglected in the table. The term flange, as applied to riveted girders, embraces all the metal in top or bottom of girder exclusive of web plate; or, in the case of a rolled beam or channel, with top and bottom plates, all the metal exclusive of web between fillets. Girders intended to carry plastering, should be limited in depth, out to out, to J T th of the span length or y 2 " per foot of this length, otherwise the deflection is liable to cause the plastering to crack. EXAMPLE OF APPLICATION OF TABLE. A 20 ;/ box girder is to carry a 13" brick wall equivalent to a weight of 30 tons over a space 20' in the clear. What size of girder is required? Answer : The value of the coefficient for 20' span and 20 /7 depth, as per table, = 300, and for 21' span and 20" depth = 315. The span, in this case, may be assumed at 20M5", and the coefficient therefore at 307. Consequently *, = 9.21 will be the area required in each flange. Making the top and bottom plates 12" X &"> = 4.5 sq. in., there remain 4.7 sq. in. for the two angles, = 8 Ibs. per foot apiece. Making the webs * 20" X X", the shearing stress = ~ g g ^ /2 = 3000 Ibs. per square inch, which is also safe against buckling, since 10000 10000 d 2 = (20) 2 = 3200 Ibs., allowed. h 3000 t 2 3000 (X) 2 71 RIVETED a GIRDERS. Coefficients for determining the area required in flanges, allow- ing 10000 Ibs. per square inch of gross section fiber strain : Multiply the load, in tons of 2000 Ibs., uniformly distributed, by the coefficient, and divide by 1000; the quotient will be the gross area, in square inches, required for each flange. |t| Depth of Girder, Out to Out of Web, in Inches. J3 S^ 12 14 i i ; &% ~ 16 18 20 22 24 26 28 30 32 34 36 10 250 214 188 167 150 136 125 115 107 100 94 88; 83 11 275 :236 206 183 165 150 138 127 118 110 103 97 92 12 300 |257 2251200 180 164 150 138 129 120 113 106 100 13 325 279 2441217 195 177 163 150 139 130 122:115 108 14 350 300 263 233 210 191 175 162 150 140 131 124 117 | 15 375 321 281 250 225 205 188 173 161 150 141 : 132 125 16 400 343 300 267:240 218 200 185 171 160 150 i 141 1 133 17 425 364 319 283 255 232 213 196 182 ! 170 159 150 ! 142 18 450 386 338 300 270 245 225 208 i 193 i 180 169 159 150 19 475 |407 356 317 285 259 238 219 204 190 178 168 158 20 500 429 375 333 300 273 250 231 214 200 188 176 167 21 525 450 394 350 315 286 263 242 225 210 197 185 175 22 550 471 413 "367 330 300 275 254 236 220 206 194 183 23 575 493 431 383 345 314 288 265 246 i 230 216 203 192 24 600 514 450 400 360 327 300 ,277 257 240 225 212 200 I 1 25 625 536 469 417 375 341 313 ! 288 268 250 : 234 221 208 26 650 557 488 433 390 355 325 300 279 260 ' 244 '229 217 27 675 579 506 450 405 368 338 312 289 j 270 253 238 i 225 28 700 600 525 467 420 382 350 323 300 280 263 247 233 29 725 621 544 483 435 395 363 335 311 290 272 256:242 30 750 643 563 500 450 409 : 375 346 321 300 281 265 250 31 775 664 581 517 465 423 388 358 332 310 291 274 258 32 800 686 600 533 480 436 400 369 343 320 300 282 267 33 825 707 619 550 495 450 413 381 : 354 330 309 291 275 34 850 729 638 567 510 464 425 392 364 340 319 300 283 35 875 750 656 583 525 l 477 438 404' 375 ' 350 ! 328 ' 309 : 292 36 900 771 675 600 540 491 450 415 386 360 338 318 300 37 925 793 694; 617 555 505' 463 427 396 370' 347 326 308 38 950 814 713! 633 570 518 475 438 407 380 856 335 317 39 r/,._. 975 836 731 650:585 532 488 450 418 390 366 344 325 72 COLUMNS AND STRUTS. Explanation of tables, pages 77 to 81, inclusive. The tables on Keystone Octagon and Piper's Patent Rivetless Columns give the areas and weights corresponding to different thicknesses of metal. Sections of these columns will be found 'on pages 13 and 14. As it is .impossible to repaint the inner surface of closed columns, or, at best, this is attended with much difficulty and expense, such columns should preferably be used only in the interior of buildings, where the changes in temperature are not considerable and the air is comparatively dry. In places exposed to the extremes of temperature and unprotected from the rain, the paint on the inner surface of the columns will, sooner or later, cease to be a protection to the iron from the moisture of the atmosphere, corrosion will set in, and, once begun, will continue as long as there is unoxidized metal left in the column. Figures 1, 3 and 4, on page 26, represent types of columns with open sections, which admit of repainting at any time, and are therefore suitable for out-door work. The table on the Ultimate Strength of Hollow Cylindrical Cast and Wrought Iron Columns gives the strains per square inch of section at which columns will fail, for various propor- tions of length of column to diameter. To facilitate the use of the table, the length (=1) is ex- pressed in feet, and the diameter ( = d ) in inches. The diameter to be assumed is the mean between the outside and inside diameters of the section. Wrought iron columns fail either by deflecting bodily out of the straight line, or by the buckling of the metal between rivets or other points of support. Both actions may take place at the same time, but if the latter occurs by itself, it is an indication that the rivet spacing or the thickness of metal is insufficient; provided, however, that the length of column is greater than twelve diameters, as columns of shorter length fail generally by the buckling of the metal. The rule has been deduced from actual experiments, that the distance between centers of _ rivets in columns should not exceed, in the line of stress, sixteen times the thickness of metal of the parts joined, and that the distance between rivets or other points of support at right angles to the line of stress, should not exceed thirty times the thickness of metal. The table on the Ultimate Strength of Wrought Iron Columns gives the strain per square inch of section at which columns will fail, for various proportions of length, in feet, to least radius of gyration, in inches. This table should be used for columns and struts which are not cylindrical, such as those represented by Figures 1, 2, 3, 4 and 5, on page 26. If the column or strut is a single rolled beam, channel or other shape, the radius of gyration will be found in the foregoing tables on the properties of Union Iron Mills' Beams, Channels, etc. If the column is composed of two channels latticed, as represented by Fig. 1, on page 26, the channels are usually placed far enough apart so that the column will be weakest in the direction of the webs, i. e., with neutral axis at right angles to the webs; for which case the radius of gyration of the column section is the same as that of the single channel. But if the radius of gyration is wanted for the neutral axis through center of section parallel with web, obtain first the distance between center of gravity of channel and center of section, by the help of column 15 in table on the properties of Union Iron Mills' Channel Bars; the square root of this distance will be the radius of gyration of the section. For a column section consisting of two channels with a beam between them, as in Fig. 3, on page 26, it is necessary to obtain first the moment of inertia of the section, whence the radius of gyration is found as the square root of the quotient of the moment of inertia divided by the area of the section. This moment of inertia, for a neutral axis through center of beam coincident with web, is equal to the sum of the moments of inertia of the beam and channels, as per tables on the properties of these shapes. The moment of inertia with neutral axis through center at right angles to web of beam, is found by adding the moment of inertia of the beam for this position of the axis, as per tables, to the product of the area of both channels multiplied by the square m of the distance of the center of gravity of the channel from the center of the section. The moment of inertia, thus obtained, is approximate, being too small by the value of the moment of inertia of the channels with reference to a neutral axis through their centers of gravity parallel to the web, but the error is small and on the safe side. For a section composed of three beams, as represented by Fig. 4, page 26, the correction for this approximation can be made, since the moments of inertia of beams with reference to an axis through their centers of gravity parallel to (coincident with) web is given in table for beams. In all other respects, proceed for this form of section as in the previous case. If two channels are connected by means of two plates instead of a beam, as shown by Fig. 2, on page 26, the moment of inertia of the plates must be obtained instead of the beam. This moment 'of inertia, for a neutral axis through center of section perpendicular to the plates, is equal to the cube of the width of plate multiplied, by T ^th of the thicknesses of the two plates added; and for a neutral axis parallel to plates, is equal to the area of the two plates multiplied by the square of the distance between the center of the plate and the center of the section. A column is square bearing when it has square ends which butt against or are firmly connected with an immovable surface, such as the floor of a building; it is pin and sqttare bearing when one end only is square bearing and the other presses against a close fitting pin, and it is pin bearing when.both ends are thus pin-jointed, (for example, the posts in pin-connected bridges.) With regard to the table on the Safe Resistance of Wooden Pillars, it should be said that comprehensive tests establishing the constants to be used in the formula have not been made to date, but it is believed that the values given in table err on the side of safety. EXAMPLES OF APPLICATION OF TABLES. I. W T hat is the ultimate strength of a square bearing 10" octagon column, ^" thick and 20' long? Answer : The area of a 10" X YZ" column, as per table on page 77, is 21.3 square inches. The mean diameter is 10", very 75 1 20 nearly, so that ~-r-= -v = 2, for which the ultimate strength, as per table on page 79, = 33560 Ibs. per square inch. Conse- quently the ultimate strength of the column = 33560 Ibs. X 21.3 = 714800 Ibs. The safe resistance for quiescent loads would be = X X 714800 = 178700 Ibs., and for moving loads = i X 714800 = 143000 Ibs. II. Required the ultimate strength of a 30 Ib. 10" beam used in the form of a strut, riveted at its ends so as to be firmly fixed, and measuring 10' between the points where it is held in position. By reference to table on page 64, the least radius of gyration of a 30 Ib. 10" beam is found to be = 0.94, (neutral axis coincident with web,) so that ==-_ g = 10.6, for which the ultimate strength, as per table on page 80, =27600 Ibs. per square inch. The area of the beam being = 9 square inches, its ultimate strength will, therefore, = 9 X 27600 = 248400 Ibs. III. What is the radius of gyration of a column section composed of two 9", 18 Ib. channels, and a 6", 13>^ Ib. beam, riveted together in the manner shown by Fig. 3, on page 26 ? Answer, if neutral axis coincident with web of beam : Moment of inertia of beam ^= 2.0 " channels = 129.6 " " " section = 131.6 Area of section = 14.85 square inches. .Therefore radius of 131.6 gyration = ~\, Answer, if neutral axis at right angles to web of beam : Moment of inertia of beam = - - . - 24.5. Moment of inertia of channels = area of channels X distance of center of gravity from center of section squared = 10.8 square inches X 3.68 = - - 146.3 Moment of inertia of section = .... 170.8 Therefore radius of gyration = y / "TToc' == 3.39. ^ v v or 3- ~* KEYSTONE OCTAGON COLUMNS. Thicknesses and Corresponding Areas and "Weights per Foot. ^Wa | ** HS* ** -B* , 1 i 4 ! CON OC5 001> C0 1010 i> o co NI> coca coco oco t>o HiH NN NCO ij iH 00 1C N O t> 05Oi OrH NN CO ^ C01> 00 05 i 3 CD & l>0i NO OOiH COCO H^uj t^-QO 05rH NCO rH iHtH 1 {d t** 00 05 C^ rH C^3 CO ^^ rH N NCO CO ^H ^ IO ft CO COO COCO 05 N rH CO N t^ N C** CO 1Q t^* 00 ^^ rH CO ^H CO 3 O 00 Hi* N OOlO N05 CON O5 CD 00 05rH CO^ COOO 05iH iH rHrH rHrH rH N ! 1* CO COO OOUD N05 CO^ N 05CO NO5 CON 05 CD CO CO"* O1O CO1> I>00 I> 0000 0000 0000 0005 05 rHCO IOI> 05rH COIO rHrH rH rH rH N NN o iH 1 sis 05 00 00 00 t^ t** ^Q c^ co if^j rHCO* IO1> 05 rH CO'lO t>05 rHrH rH rH rH N NN NN j* I>10 COrH 00 CO* ^N OOO v$\Q C01> l>00 O5O rHrH rH i 1 rH ii N Sw COS T^CO OOrH COCO OOO COlO rHrH rH N NN NCO COCO sswnpiqj; | -ex 2 ^ <* ** ** 77 ULTIMATE STRENGTH OF HOLLOW CYLINDRICAL CAST AND WROUGHT IRON COLUMNS, For different proportions of length in feet ( = 1 ) To least diameter in inches (= d). Ultimate Strength in Ibs. per square inch = Cast Iron. Wrought Iron. Square Bearing : Pin & Square : Pin Bearing : Square Bearing : Pin & Square : Pin Bearing : 80000 80000 80000 40000 40000 40000 (121 ) 2 1 , 3(12 1) 2 (1! I 2 M600 d 2 '40 21) 2 (12 1) 2 (12 1) 2 (12 1) 2 "^800 ( Od 2 "^OOOd 2 '20004^ ' 1500 d 2 To obtain Safe Resistance : For quiescent loads (buildings) divide bjr{ J f ^oughTiron. For moving- loads (bridges) divide by < ? r r ?' ' (5 for wrought iron. Cast Iron. "Wrought Iron. 1 Ultimate Strength in Lbs. per sq. in. Ultimate Strength in Lbs. per sq.in. Square. Pin and p . Square. ; Pm ' Square. Pin and Square. Pin. 1.0 ' 67800 62990 58820 38170 37310 36500 1.1 65690 - 60300 55730 37800 36790 35840 1.2 63530 57600 52690 37410 36240 35140 1.3 61340 54930 49740 37000 35660 34420 1.4 59140 52310 46900 36560 35050 33670 1.5 56940 49770 44200 36100 34420 32890 1.6 54760 47300 41630 35620 33770 32110 1.7 52620 44940 39210 35130 33110 31320 1.8 ' 50530 42670 36930 34620 32430 30510 1.9 48490 40510 34790 34090 31750 29710 2.0 48510 38460 32790 33560 31060 28900 2.1 44600 38520 30920 38010 30360 28100 2.2 42750 34680 29180 32460 29660 27310 2.3 40980 32940 27540 31900 28970 25530 2.4 39280 31310 28030 31340 28270 25760 2.5 1 37650 29770 24620 30770 27590 25000 2.6 ! 38090 28320 23300 30200 26900 24260 2.7 34600 26950 22070 29630 26230 23530 2.8 33180 25670 20930 29060 25570 22820 2.9 31820 24460 19 860 28500 24910 22130 3.0 30530 23320 18870 27930 24270 21460 3.1 29310 22250 i 17940 27370 23640 20810 3.2 28140 21250 17070 26820 23020 20170 3.3 27030 20300 ! 16260 26270 22420 19560 , 3.4 25970 19410 15500 25730 21830 18960 , 79 ULTIMATE STRENGTH OF WROUGHT IRON COLUMNS, For different proportions of length in feet ( = 1 ) To least radius of gyration in inches (= r). Ultimate Strength in Ibs. per square inch = Column Square Bearing : 40000 , (121)* 36000 r 2 Column Pin and Square Bearing 40000 (121)*." 24000 r 2 " Column Pin Bearing : 40000 14 IJL 18000 r 2 To obtain Safe Resistance : For quiescent loads, as in buildings, divide by 4. For moving loads, as in bridges, divide by 5. Ultimate Strength in Lbs. Ultimate Strength in Lbs. 1 per square inch. 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 38610 33430 38230 38030 37820 37590 37360 37120 38870 36620 36360 36090 35820 35540 35260 34970 34870 34370 34060 33750 33440 33130 32810 32490 32170 37950 37680 37400 37110 36810 36500 36170 35840 35500 35140 34780 34420 34050 33670 33280 32890 32500 32110 31710 31310 80910 30510 30110 29710 29310 37310 36970 36610 36240 35860 35460 35050 34640 34210 33770 33330 32890 32440 31980 31520 31060 30590 30130 29670 29200 28740 28270 27820 27360 26910 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 per square inch. Square. Square!' Pin. 31850 28900 26460 31520 28500 26010 31190 28100 25570 30870 27700 25130 30540 ; 27310 24700 30210 : 26920 : 24270 29880 26530 ' 23850 29550 26140 23430 29230 ; 25760 i 23030 28900 ; 25370 | 22620 28570 ! 25000 ' 22220 28250 I 24630 21830 27920 i 24260 21440 27600 1 23890 21060 27270 I 23530 20690 26950 23170 20330 26640 22820 19960 26320 26000 25690 25380 25070 24770 24470 24170 22470 22130 21800 21460 21130 20810 20490 20180 19610 19270 18930 18590 18260 17940 17620 17310 80 ^ ULTIMATE STRENGTH OF RECTANGULAR TIMBER PILLARS, WELL SEASONED, For different proportions of length in feet (= 1) To least diameter or side in inches (= d). Ultimate Strength in Ibs. per square inch = Pillar Pillar Pillar Square Bearing: Pin and Square Bearing : Pin Bearing: 5600 5600 5600 (121)' " 550 d^ 1.5(121)* 1 , (121) 2 550 d^ 275 The above formula for Square Bearing Pillars is based upon Lemande's experiments on French oak, and agrees fairly with Hodgkinson's formula for French oak pillars of 30 diameters and over. The strength of pillars of French oak, Red deal and Dantzig oak, is given by Hodgkinson as proportional to the ratio, 6.9: 7.8: 10.95. It is believed the above formulae for French oak and the fol- lowing table calculated from them, will also apply to American white pine of best quality. Green timber has only about half the strength of dry. To obtain the Safe Resistance, divide by 6. Ultimate Strength in Lbs. Ultimate Strength in Lbs. 1 per square inch. 1 per square inch. T Square. Pin and Square. Pin. d Square. Pin and Square. Pin. 1.0 4440 - 4020 3680 2.5 2120 1620 1310 1.1 4250 3800 3430 2.6 2020 1530 1230 1.2 4070 3580 3190 2.7 1930 1450 1160 1.3 3880 3370 2970 2.8 1830 1370 1100 1.4 3700 3160 2760 2.9 1750 1300 1040 1.5 3520 2970 2570 3.0 1670 1230 980 1.6 3350 2790 2390 3.1 1590 1170 930 1.7 3190 2620 2230 3.2 1520 1120 880 1.8 3040 2470 2080 3.3 1450 1060 840 1.9 2890 2320 1940 3.4 1390 1010 790 2.0 2740 2180 1810 3.5 1330 960 760 2.1 2600 2050 1690 3.6 1270 920 720 2.2 2470 1930 1580 3.7 1220 880 690 2.3 2350 1820 1490 3.8 1170 840 650 2.4 2230 1720 1400 3.9 1120 800 620 81 GENERAL NOTES ON FLOORS and ROOFS. On page 23 will be found examples of floor joists and their connections. When two beams are placed side by side, as in Fig. 1, they should be connected together by means of bolts and cast-iron separators, fitted closely between the flanges of the beams. The office of these separators is to hold in position the compression flange of the beams, preventing side deflection or buckling, and to firmly unite the two beams, so that they will act in unison. Separators should be used near the supports and at distances of five or six feet. They are shown by Figs. 2 and 3, on page 24. Their weight will range from 19 Ibs. for the heavy 15" beams, to 5 Ibs. for 6" beams. Figures 1, 2 and 3 show the methods of connecting beams with each other. In Figs. 1 and 2 the lighter beam is coped into the heavier one, the weight being carried by the lower flange of the latter. The angle with which the webs are connected, serves only to hold the beams in position, in this case. In Fig. 3 the load of the smaller beams is transferred to the larger by means of angles riveted to the webs, and in case this is not sufficient, an angle may be riveted to the web of the larger 'beam underneath the smaller, as shown, to assist in carrying the load. Figures 5, 6, 7, 8, 9 and 10, on page 23, are illustrations of various forms of girders, such as it is often necessary to use in the front of buildings, to carry walls, or in the interior, to support the joists. Where these girders rest upon the wall, cast or wrought- iron bed plates should be used, to distribute the pressure over a greater surface, and thereby prevent the crushing of the brick directly under the girder. In some cases a tough, large size stone will answer without the plates, but where the pressure is heavy, both plates and stone should be used. Figs. 5, 6, 9 and 10, are illustrations. On page 24, Fig. 1, is represented a girder composed of two beams, carrying a brick wall, in position. In case of failure of the girder, only a part of the wall above it would drop down, the line of rupture for brick-work making an angle of about 30 with the vertical, called the angle of repose. The weight to be 82 " carried by the girder may, therefore, be considered to be only that part of the wall between the lines of rupture, provided, that in building the wall, the center of the girder was supported tem- porarily with a wooden prop, preventing deflection. Several courses should, however, be laid before this is done. If /= the clear span of girder, and h = the hight of wall above it, the superficial area of the trapezoid between the lines of rupture, is expressed by h (2 1 1.2 h), but deductions must, of course, be made for windows or other openings in the wall, if there are any. In order to be entirely on the safe side, and also for the sake of simplicity, the weight of wall between vertical lines directly over the girder, is frequently adopted as the load to be carried by it. Weight of Brick-ivork per Superficial Foot, for a 9" wall = 84 Ibs., 13" wall = 121 Ibs., 18" wall = 168 Ibs., one cubic foot weighing 112 Ibs. There are various fire-proof floors in use; one of the most common is that represented by Fig. 1, on page 23. Four-inch brick arches are built between beams spaced not over 5 feet apart, and tied together by rods %" to 1" diameter, at intervals of 4' to 6', so as to take the thrust of the arches off the walls. Tee or angle irons are inserted in the wall, so as to hold it firmly in line between the points held by the rods. The top of the arches is leveled off with concrete, allowing space, however, for wooden strips, to which the floor timber is nailed. The plastering for ceiling usually covers the arches only, so that the ceiling will appear curved and show the lower flanges of the iron beams. A convenient device for centering the arches is shown in Fig. 4. The centers are suspended by iron hooks from the lower flanges of the beams, and can be moved forward and back, and removed at pleasure. Figure 4, on page 24, and Fig. 3, on page 25, are examples of flush, plastered ceilings, the laths in the latter case being held by light castings. Fig. 3, on page 24, is an example of an iron ceiling, composed of sheet iron pressed to suitable form, laid upon the lower flanges of the beams; . and Figs. 2 and 5 are _ illustrations of corrugated iron ceilings. Both are open to the objection that the condensed moisture of the air will collect upon the iron and fall into the rooms below. Particularly is this the case in rooms filled with people, and such ceilings should, therefore, be restricted in their use, or the iron should be covered in such manner from below, that the access of the air is effectually cut off, as by plastering. The weight of a fire-proof floor, consisting of four-inch brick arches between beams, with concrete filling above the arches and flooring, will generally average about 70 Ibs. per square foot, exclusive of the weight of the beams. The following are average weights of some other constructions, and the usual assumptions made for superimposed load: Iron roof of 100 feet span, with corrugated iron laid directly upon purlins, will weigh Approximately, - - - - - - -10 Ibs. ^ sq. ft. If boarded, add 3 " For lathed and plastered ceiling, allow - - 10 " " For snow and vertical component of wind force, allow 30 For superimposed load on Floors of dwellings, assume - - - 60 " " " " churches, theaters and ball rooms, 125 " " " " warehouses, - 250 " " Weight of snow, freshly fallen, - - 5 to 12 " cub. ft. " " saturated, (slush,) - 40 " " Crowd of people, closely packed, - 80 " sq. ft. Wind pressure (violent hurricane,) - 50 " " Rule for finding the sectional area of a bar of wrought iron, given the weight per foot : Multiply by 3 and divide by 10. Rule for finding the weight per foot, given the area : Divide by 3 and multiply by 10. 84 CORRUGATED AND GALVANIZED IRON. Corrugated Iron is used for roofs and sides of buildings. It is usually laid directly upon the purlins in roofs, and held in place by means of clips of hoop iron, which encircle the purlin and are placed in distances of about twelve inches apart. Special care must be taken that the projecting edges of the corrugated iron, at the -eaves and gable ends, of the roof, are well secured, other- wise the wind will loosen the sheets and fold them up. The corrugations are made of various sizes ; the smaller present a more pleasing appearance to the eye, while the larger are stiffer and will span a greater distance, thereby permitting the purlins to be placed further apart. The sizes of sheets generally used for both roofing and siding, are No. 20 and 22. The corrugated iron which will be described in the following, is manufactured by the Keystone Bridge Company, of Pittsburgh. It is of medium size, presenting both a good appearance and being of sufficient strength for usual requirements. By one corrugation is meant the double curve between corre- sponding points, and by depth of corrugation, the greatest deviation from the straight line, measured between the concave surfaces of the corrugated sheet. The Keystone Bridge Company's corrugations are 2.425" long, measured on the straight line ; they require a length of iron of 2.725 /; to make one corrugation, and the depth of corrugation is |4". One corrugation is allowed for lap in the width of the sheet and ft" in the length, for the usual pitch of roof of two to one. Sheets can be corrugated of any length not exceeding ten feet. The most advantageous width is 30^ /; , which (allowing y 2 " for irregularities) will make eleven corrugations = 30", or, making allowance for laps, will cover 24^" of the surface of the roof. By actual trial it was found that corrugated iron No. 20, spanning 6 feet, will begin to give a permanent deflection for a load of 30 Ibs. per square foot, and that it will collapse with a load of 60 Ibs. per square foot. The distance between centers of -purlins should therefore not exceed 6 feet, and, preferably, be less than this. KEYSTONE BRIDGE CO.'S CORRUGATED IRON. The following table is calculated for sheets 3C y^ 11 wide before corrugating. I J^ Weight per Square of 100 square feet, || when laid, allowing 6" lap in length and or one corrugation in width of .O.SJf JSJ3 Jjp 2 jjjf'l she 4 et for sheet lengths of: 'Ijf3 Lbs. Lbs. 5' 6' 7' 8' 9' 10' LbT 16 .065 2.61 3.28 365 358 353 350 348 346 2.95 18 .049 1.97 2.48 275 270 267 264 262 261 2.31 20 .035 1.40 1.76 196 192 190 188 186 185 1.74 22 .028 1.12 1.41 156 154 152 150 149 148 1.46 24 .022 .88 1.11 123 121 119 118 117 117 1.22 26 .018 .72 .91 101 99 97 97 96 95 1.06 RESULTS OF TEST of a corrugated sheet No. 20, 2/_0" wide, 6'-0" long between supports, loaded uniformly with fire clay. Load per Square Foot. Lbs. Deflection at Center under Load. Inches. Permanent Deflection, Load Removed. 5 /2 10 X 15 1 20 1 25 1 30 ] H % 35 2 Vt Yz 40 2 1 /o K' 45 3/2 ] -/& 50 4 ] Y* 55 C # Not Noted. 60 Broke Down. " a 86 ILLUSTRATION OF APPLICATION OP TABLES ON FLAT ROLLED IRON. Pages 88 to 99, inclusive. What is .the weight per foot of a bar 5" X IjV' in section? Answer : In the column for 5" width, and in the line for 1 j 1 ^" thickness, will be found the value 17.71, which is the weight desired. What thickness of 4^" bar will be required to give an area of 5.3 square inches? Answer: In the column for 4^" width will be found 5.34, which is the area nearest to that required ; the corresponding thickness being IfV ' tne ^ ar should be 4^" X W- ILLUSTRATION OF APPLICATION OP TABLES ON DECIMAL PARTS OP A FOOT FOR EACH th OP AN INCH. Pages 1OO to 1O3, inclusive. What is the value of 5' 7^ \" , expressed in feet and decimals of a foot? Answer : 5.5977; found by looking in column for 7", and in line for \\". What is the value of 11.6838', expressed in feet, inches and fractions of an inch? Answer: The value nearest to the decimal .6833, to be found in table, is .6836, which is = 8$f ", therefore 11.6838' = 11' 8JJ", nearly. 87 WEIGHTS OF FLAT ROLLED IRON PER LINEAL FOOT. For Thicknesses from -y^ in. to 2 in. and Widths from 1 in. to 12% In. Iron weighing 480 Ibs. per cubic foot. Thickness in Inches. 1" i //] IK" 2" 2)i" 2K" 2fc" 12" * .208 .260 .313 .365 .417 .469 .521 .573 2.50 .417 .521 .625 .729 .833 .938 1.04 . 1:15 5.00 A .625 .781 .938 1.09 1.25 1.41 1.56 1.72 7.50 i .833 1.04 1.25 1.46 1.67 1.88 2.08 2.29 10.00 TS 1.04 1.30 1.56 1.82 2.08 2.34 2.60 2.86 12.50 f 1.25 1.56 1.88 2.19 2.50 2.81 3.13 3.44 15.00 A 1.46 1.82- 2.19 2.55 2.92 3.28 3.65 4.01 17.50 I 1.67 2.08 2.50 2.92 3.33 3.75 4.17 4.58 20.00 j\ 1.88 2.34 2.81 3.28 3.75 4.22 4.69 5.16 22.50 1 2.08 2.60 3.13 3.65 4.17 4.69 5.21 5.73 25.00 e 2.29 2.86 3.44 4.01 4.58 5.16 5.73 6.30 27.50 2.50 3.13 3.75 4.38 5.00 5.63 6.25 6.88 30.00 it 2.71 3.39 ! 4.06 4.74 5.42 6.09 6.77 7.45 32.50 2.92 3.65 4.38 5.10 5.83 6.56 7.29 8.02 35.00 it 3.13 3.91 4.69 5.47 6.25 '7.03 7.81 8.59 37.50 1 3.33 4.17 5.00 5.83 6.67 7.50 8.33 9.17 40.00 i-V 3.54 4.43 5.31 6.20 7.08 7.97 8.85 9.74 42.50 li- 3.75 4.69 5.63 6.56 7.50 8.44 9.38 10.31 45.00 ly 3 ^ 3.96 4.95 5.94 6.93 I 7.92 8.91 9.90 10.89 47.50 H 4.17 5.21 6.25 7.29 8.33 9.38 10.42 11.46 50.00 IA 4.37 5.47 i 6.56 7.66 1 8.75 9.84 10.94 12.03 52.50 4.58 5.73 6.88 8.02 9.17 10.31 11.46 12.60 55.00 IJZg. 4.79 5.99 7.19 8.39 9.58 10.78 11.98 13.18 57.50 11 5.00 6.25 7.50 8.75 10.00 11.25 12.50 13.75 60.00 1 T 9 ^ 5.21 6.51 7.81 9.11 ! 10.42 11.72 13.02 14.32 62.50 If 5.42 6.77 8.13 9.48 10.83 12.19 13.54 14.90 65.00 ift 5.63 7.03 8.44 9.84 111.25 12.66 14.06 15.47 67.50 If 5.83 7.29 8.75 10.21 111.67 13.13 14.58 16.04 70.00 113 6.04 7.55 9.06 10.57 12.08 13.59 15.10 16.61 72.50 1? 6.25 7.81 9.38 10.94 12.50 (14.06 15.63 17.19 75.00 6.46 8.07 9.69 11.30 12.92 14.53 16.15 17.76 77.50 2 6.67 8.33 10.00 11.67 13.33 15.00 16.67 18.33 80.00 '4 j i WEIGHTS OF FLAT ROLLED IRON PER LINEAL FOOT. (CONTINUED.) Thickness in Inches. 3" 3K" 3^" g3/// 4// 4H 4K" 12" 625 .677 .729 .781 .833 .885 .938 .990 2.50 ? 1.25 1.35 1.46 1.56 1.67 1.77 1.88 1.98 5.00 A 1.88 2.03 2.19 2.34 2.50 2.66 2.81 2.97 7.50 i 2.50 2.71 2.92 3.13 3.33 3.54 3.75 3.96 10.00 _5_ 3.13 3.39 3.65 3.91 4.17 4.43 4.69 4.95 12.50 3. 3.75 4.06 4.38 4.69 5.00 5.31 5.63 5.94 15.00 ^ 4.38 4.74 5.10 5.47 5.83 6.20 6.56 6.93 17.50 \ 6 5.00 5.42 5.83 6.25 6.67 7.08 7.50 7.92 20.00 Ar I 5.63 6.09 6.56 7.03 7.50 7.97 8.44 8.91 22.50 f 6.25 6.77 7.29 7.81 8.33 8.85 9.38 9.90 25.00 H 6.88 7.45 8.02 8.59 9.17 9.74 10.31 10.89 27.50 7.50 8.13 8.75 9.38 110.00 10.63 11.25 11.88 30.00 it 8.13 8.80 9.48 10.16 10.83 11.51 12.19 12.86 32.50 1 8.75 9.48 10.21 10.94 11.67 12.40 13.13 13.85 35.00 It 9.38 10.16 10.94 11.72 12.50 13.28 14.06 14.84 37.50 1 10.00 10.83 11.67 12.50 13.33 14.17 15.00 15.83 40.00 JTC 10.63 11.51 12.40 13.28 14.17 15.05 15.94 16.82 42.50 l 1 ! 11.25 12.19 13.13 14.06 15.00 15.94 16.88 17.81 45.00 11.88 12.86 13.85 14.84 15.83 16.82 17.81 18.80 47.50 H 12.50 13.54 14.58 15.63 16.67 17.71 18.75 19.79 50.00 i JL 13.13 14.22 15.31 16.41 17.50 18.59 19.69 20.78 52.50 f 13.75 14.90 16.04 17.19 18.33 19.48 20.63 21.77 55.00 T V .14.38 15.57 16.77 17.97 19.17 20.36 21.56 22.76 57.50 .V 15.00 16.25 17.50 18.75 20.00 21.25 22.50 23.75 60.00 A 15.63 16.93 18.23 19.53 20.83 22.14 23.44 24.74 '62.50 4 16,25 17.60 18.96 20.31 21.67 23.02 24.38 25.73 65.00 m 16,88 18.28 19.69 21.09 22.50 123.91 25.31 26.72 67.50 1 f 17.50 18.96 20.42 21.88 23.33 J24.79 26.25 27.71 70.00 Hf 18.13 19.64 21.15 |22.66 24.17 25.68 27.19 28.70 72.50 1 1 18.75 '20.31 21.88 23.44 25.00 26.56 i28.13 29.69 75.00 U| 19.38 ;20.99 22.60 24.22 25.83 27.45 J29.06 30.68 77.50 2 20.00 21.67 23.33 25.00 26.7 28.33 ! 30.00 31.67 80.00 WEIGHTS OP FLAT ROLLED IRON PER LINEAL FOOT. (CONTINUED.) Thickness in Inches. 5" 6 m 5K" 6" 6* 6X 6X 12" Te" 1.04 1.09 1.15 1.20 1.25 1.30 i 1.35 1.41 2.50 2.08 2.19 2.29J 2.40 2.50 2.60 2.71 2.81 5.00 A 3.13 3.28 3.44 3.59 3.75 3.91 4.06 4.22 7.50 V 4.17 4.38 4.58 4.79 5.00 5.21 5.42 5.63 10.00 T 5 6 5.21 5.47 5.73 5.99 6.25 6.51 6.77 7.03 12.50 6.25 6.56 6.88 7.19 7.50 7.81 8.13 8.44 15.00 ft 7.29 7.66 8.02 8.39 8.75 9.11 9.48 9.84 17.50 i 8.33 8.75 9.17 9.58 10.00 10.42 10.83 11.25 20.00 T 9 * 9.38 9.84 10.31 10.78 11.25 11.72 12.19 12.63 22.50 5. 10.42 10.94 11.46 11.98 12.50 13.02 13.54 14.06 25.00 ft 11.46 12.03 12.60 '13.18 13.75 14.32 14.90 15.47 27.50 3 4 12.50 13.13 13.75 14.38 15.00 15.63 16.25 16.88 30.00 M 13.54 14.22 14.90 15.57 16.25 16.93 17.60 18.28 32.50 14.58 15.31 16.04 16.77 17.50 18.23 18.96 19.69 35.00 it 15.63 16.41 17.19 17.97 18.75 19.53 j 20.31 21.09 37.50 1 16.67 17.50 18.33:19.17 20.00 20.83 21.67 22.50 40.00 ! T V 17.71 18.59 19.48 ' 20.33 21.25 22.14 23.02 23.91 42.50 1| 18.75 19.69 20.63 jgl.56 22.50 j 23.44 24.38 25.31 45.00 19.79 20.78 21.77 1 22.76 23.75 24.74 25.73 1 26.72 47.50 1? 20.83 21.88 22.92123.96 5.00 26.04 27.08 28.13 50.00 IJL 21.88 22.97 24.03 25.1 6 ! 26.25 27.34 28.44 29.53 52.50 If 22.92 24.06 25.21 26.35 ; 27.50 28.65 29.79 30.94 55.00 4 23.96 25.16 26.35 27.55 28.75 29.95 31.15 32.34 57.50 U 25.00 26.25 27.50 28.75 30.00 31.25 32.50 33.75 60.00 1 T ^ 26.04 27.34 28.65 29.95 31.25 32.55 33.85 35.16 62.50 H 27.08 28.44 29.79 31.15 32.50 33.85 35.21 86.56 65.00 m 28.13 29.53 30.94 : 32.34 33.75 35.16 : 36.56 37.97 67.50 if 29.17 30.63 i 32.08 33.54 35.00 36.43 37.92 39.38 70.00 Ht 30.21 31.72 33.23 84.74 36.25 37.73 39.27 40.78 72.50 i? 31.25 32.81 34.38 35.94 37.50 39.08 40.63 42.19 75.00 lit 32.29 33.91 35.52 37.14 38.75 40.36 41. 98! 43.59 77.50 2 i 33.33 35.00 36.67 38.33 40.00 41.67 43.33 45.00 80.00 WEIGHTS OF FLAT ROLLED IRON PER LINEAL FOOT. . (CONTINUED.) Thickness in Inches. 1" 7M" 7 l o" 7%" 8" 8X W 12" T6 1.46 1.51 1.56; 1.61 1.67 1.72 1.77 1.82 2.50 2.92 3.02 3.13; 3.23 3:33 3.44 3.54 3.65 5.00 A 4.38 4.53 4.69 4.84 5.00 5.16 5.31 5.47 7.50 f* 5.83 6.04 6.25 6.46 6.67 6.88 7.08 7.29 10.00 jV 7.29 7.55 7.81 8.07 8.33 8.59 8.85 9.11 12.50 8.75 9.06 9.38! 9.69 10.00 10.31 10.63 10.94 15.00 i 10.21 10.57 i 10.94 11.30 11.67 12.03 12.40 12.76 17.50 i 11.67 12.08 12.50 12.92 13.33 13.75 14.17 14.58 20.00 Kl 13.13 13.59 14.06 14.53 15.00 15.47 15.94 16.41 22.50 V 14.58 15.10 15.63 16.15 16.67 17.19 17.71 18.23 25.00 A 16.04 16.61 17.19 17.76 18.33 18.91 19.48 20.05 27.50 i 17.50 18.13 18.75 19.38 20.00 i 20.63 21.25 21.88 30.00 It 18.96 19.64 20.31 20.99 21.67 22.34 23.02 23.70 32.50 7 20.42 21.15 21.88 22.60 23.33 24.06 24.79 25.52 35.00 ff 21.88 22.66 23.44 24.22 25.00 25.78 26.56 27.34 37.50 i 23.33 24.17 25.00 25.83 26.67 27.50 28.33 29.17 40.00 IT* 24.79 25.68 26.56^7.45 28.33 29.22 30.10 30.99 42.50 1? 26.25 27.19 28.13 29.06 30.00 30.94 31.88 32.81 45.00 27.71 28.70 i 29.69 30.68 31.67 32.66 33.65 34.64 47.50 H 29.17 30.21 i 31.25 32.29 33.38 34.38 35.42 36.46 50.00 IA 30.62 31.72 32.81 33.91 35.00 36.09 37.19 38.28 52.50 1 -^ 32.08 33.23 34.38 35.52 3C.67 1 37.81 38.96 40.10 55.00 l- 7 r 33.54 34.74 35.94 37.14 38.33 39.53 40.73 41 93 57.50 H 35.00 36.25 37.50 38.75 40.00 41.25 42.50 4^.75 ^ A .00 JJL 36.46 ! 37.76 39.06 40.36 41.67 42.97 44.27 45.57 62.50 i.f 37.92 39.27 40.63 41.98 43.33 44.69 146.04 47.40 65.00 39.38 '40.78 42,19 43.59 ' 45.00 46.41 47.81 49.22 67.50 If" 140.83 42.29 43.75 45.21 46.67 48.13 49.58 51.04 70.00 lif 42.29 43.80 45.31 46.82 48.33 49.84 51.35 52.86 72.50 1 i 43.75! 45.31 46.88 48.44 50.00 51.56 53.13 54.69 75.00 HI 45.21 I 46.82 i 48.44 50.05 51.67 53.28 54.90 56.51 77.50 2 46.67 48.33 ! 50.00 51.67 i 53.33 55.00 56.67 53.33 80.00 3 ~Ti WEIGHTS OP PLAT ROLLED IRON PEK LINEAL FOOT. (CONTINUED.) Thickness in Inches. 9" \9%" &A" 9%" 10" 1-,_ i 18.33 18.75 19.17 19.58 20.00 20.42 20.83 21.25 |.g A 20.63 ! 21.09 ' 21.56 22.03 22.50 22.97 23.44 23.91 || f 22.92 23.44 23.96 24.48 25.00 25.52 26.04 26.58 - "^ 4-1 125.21 25.78! 26.35 26.93 27.50 28.07 28.65 29.22 i| J I 127.50 28.13 28.75 29.38 30.00 30.63 31.25 31.88 j .* i* 29.79 30.47 31.15 31.82 32.50 33.18 33.85 34.53 ** 1 32.08 32.81 i 33.54 34.27 35.00 35.73 36.46 37.19 I J 44 34.38 35.18 35.94 36.72 37.50 38.28 39.06 39.84 3s 1 ' 38.67 ; 37.50 | 38.33 39.17 40.00 40.83 41.67 42.50 |-s |V 38.96 39.84 40.73 41.61 42.50 43.39 44.27 45.16 |x 1? 41.25 42.19 43.13 44.06 45.00 45.94 46.88 47.81 I 3 * Ij 3 r 43.54 44.53 45.52 46.51 47.50 48.49 49.48 50.47 ^\? 1 1. 45.83 46.88 47.92 48.96 50.00 51.04 52.08 53.13 Sis g^ 1 T 5 - 48.13 49.22 50.31 51.41 52.50 53.59 54.69 55.78 tiu If 50.42 51.56 i 52.71 53.85 55.00 56.15 57.29 58.44 H 52.71 53.91 1 55.10 56.30 57.50 58.70 59.90 61.09 So 5 ? 1? 55.00 56.25 57.50 58.75 60'.00 61.25 62.50 63.75 38 1 9 57.29 58.59 59.90 61.20 62.50 63.80 65.10 66.41 IsS H 59.58 60.94 62.29 63.65 65.00 66.35 67.71 69.06 ^ g- 61.88 63.28 64.69 66.09 67.50 68.91 70.31 71.72 " & + if 64.17 65.63 67.08 68.54 70.00 71.46 72.92 74.38 S f oo Ht 66.46 67.97 69.48 70.99 72.50 74.01 75.52 77.03 f rt B if 68.75 70.31 71.88 73.44 75.00 76.56 78.13 79.69 jgJS lit ,71.04 72.66 74.27 75.89 77.50 79.11 80.73 82.34 *" M x 2 73.33 75.00 76.67 78.33 80.00 81.67 83.33 85.00 '^ ~ f 93 1 a AREAS OP PLAT ROLLED IRON, For Thicknesses from T ^ in. to 2 in. and Widths from 1 in. to 12% in. Thickness 2K" 2K" in Inches. ~\." l/^ ;/ IV" \y n 2" 2^ 12" TV .063 .078 .094 .109 .125 .141 .156 .172 .750 f .125 .156 .188 .219 .250 .281 .313 .344 1.50 A .188 .234 .281 .328 .375 .422 .469 .516 2.25 i .250 .313 .375 .438 .500 .563, .625 .688 3.00 iV -313 .391 .469 .547 .625 .703 .781 .859 3.75 f i .375 .469 .563 .656 .750 .844 .938 1.03 4.50 A -438 .547 .656 .766 .875 .984 1.09 1.20 5.25 i i .500 .625 .750 .875 1.00 1.13 1.25 1.38 6.00 T V .563 .703 .844 .984 1.13 1.27 1.41 1.55 6.75 f ; .625 .781 .938 1.09 1.25 1.41 1.56 1.72 7.50 -}-;, .688 .859 1.03 1.20 1.38 1.55 1.72 1.89 8.25 f .750 .938 1.13 1.31 1.50 1.69 1.88 2.06 9.00 it ' -813 1.02 1.22 1.42 1.63 1.83 2.03 2.23 9.75 1 .875 1.09 1.31 1.53 1.75 1.97 2.19 2.41 10.50 f| .938 1.17 1.41 1.64 1.88 2.11 2.34 2.58 11.25 1 1.00 1.25 1.50 jl.75 2.00 2.25 2.50 2.75 12.00 IrV 1-06 1.33 1.59 il.86 2.13 2.39 2.66 2.92 12.75 H 1.13 1.41 1.69 1.97 2.25 2.53 2.81 3.09 13.50 1.48 1.78 2.08 2.38 2.67 2.97 3.27 14.25 if 1JB5 1.56 1.88 2.19 2.50 2.81 3.13 3.44 15.00 I_P T ! i 31 1.64 1.97 2.30 2.63 2.95 3.28 3.61 15.75 If 1.38 1.72 2.06 2.41 2.75 3.09 3.44 3.78 16.50 IjV ! !- 44 1.80 2.16 2.52 2.88 3.23 3.59 3.95 17.25 1 1 1.50 1.88 2.25 2.63 3.00 3.38 3.75 4.13 18.00 IT? 1.56 1.95 2.34 2.73 3.13 3.52 3.91 4.30 18.75 If 1.63 2,03 2.44 2.84 3.25 3.66 4.06 4.47 19.50 144 1.69 2.11 2.53 2.95 3.38 3.80 4.22 4.64 20.25 If 1.75 2.19 i 2.63 3.05 3.50 3.94 4.38 4.81 21.00 lit 1.81 2.27 2.72 3.17 3.63 4.08 4.53 4.98 21.75 H 1.88 2.34 2.81 3.28 3.75 4.22 4.69 5.16 22.50 VH 1.94 2.42 2.91 3.39 3.88 4.36 4.84 5.33 23.25 2 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 24.00 i , j tir AREAS OP PLAT ROLLED IRON. (CONTINUED.) Thickness in Inches. 8" SH" m m 4" 4V w 4%" 12" A .188 .203 .219 .234 .250 .266 .281 .297 .750 .375 .406 .438 .469 .500 .531 .563 .594 1.50 ft .563 .609 .656 .703 .750 .797 .844 .891 2.25 .750 .813 .875 .938 1.00 1.06 1.13 1.19 3.00 Jj .938 1.02 1.09 1.17 1.25 1.33 1.41 1.48 3.75 3. 1.13 1.22 1.31 Ml 1.50 1.59 1.69 1.78 4.50 1 1.31 1.42 1.53 1.64 1.75 1.86 1.97 2.08 5.25 i 1.50 1.63 1.75 1.88 2.00 2.13. 2.25 2.38 6.00 _ 9 ^ 1.69 1.83 1.97 2.11 2.25 2.39 2.53 2.67 6.75 T 1.88 2.03 2.19 2.34, 2.50 2.66 2.81 2.97 7.50 ft 2.06 2.23 2.41 2.58 2.75 2.92 3.09 3.27 8.25 2.25 2.44 2.63 2.81 3.00 3.19 3.38 3.56 9.00 if 2.44 2.64 2.84 3.05 3.25 3.45 3.66 3.86 9.75 2.63 2,84 3.06 3.28 3.50 3.72 3.94 4.16 10.50 A 2.81 3.05 3.28 3.52 3.75 8.98 4.22 4.45 11.25 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 12.00 i y ,y 3.19 3.45 3.72 3.98 4.25 4.52 4.78 5.05 12.75 i i 3.38 3.66 3.94 4.22 4.50 4.78 5.06 5.34 13.50 4 3.56 3.86 4.16 4.45 4.75 5.05 5.34 5.64 14.25 u 3.75 4.06 4.38 4.69 5.00 5.31 5.63 5.94 15.00 IA 3.94 4.27 4.59 4.92 5.25 5.58 5.91 6.23 15.75 l 1 ! 4.13 4.47 4.81 5.16 5.50 5.84 6.19 6.53 16.50 4.31 4.67 5.03 5.39 5.75 6.11 6.47 6.83 17.25 if 4.50 4.88 5.25 5.63 6.00 6.38 6.75 7.13 18.00 l- 9 - 4.69 5.08 5.47 5.86 6.25 6.64 7.03 7.42 18.75 1.1 4.88 5.28 5.69 6.09 6.50 6.91 7.31 7.72 19.50 5.06 5.48 5.91 6.33 6.75 7.17 7.59 8.02 20.25 i? 5.25 5.69 6.13 6.56 7.00 7.44 7.88 8.31 21.00 lit 5.44 5.89 6.34 6.80 7.25 7.70 8.16 8.61 21.75 11 5.63 6.09 6.56 7.03 7.50 7.97 8.44 8.91 22.50 1ft 5.81. 6.30 6.78 7.27 7.75 8.23 8.72 9.20 23.25 2 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 24.00 AREAS OF PLAT ROLLED IRON. (CONTINUED.) Thickness in Inches. 5" 5* 5K w 6" w ey, 6^ 12" .313 .328 .344 .359 .375 .391 .406 .422 .750 1 .625 .656 .688 .719 .750 .781 .813 .844 1.50 .938 .984 1.03 1.08 1.13 1.17 1.22 1.27 2.25 1 1.25 1.31 1.38 1.44 1.50 1.56 1.63 1.69 3.00 1.56 1.64 1.72 1.80 1.88 1.95 2.03 2.11 3.75 I 1.88 1.97 2.06 2.16 2.25 2.34 2.44 2.53 4.50 A 2.19 2.30 2.41 2.52 2.63 .73 2.84 2.95 5.25 2.50 2.63 2.75 2.88 3.00 3.13 3.25 3.38 6.00 JL 2.81 2.95 3.09 3.23 3.38 3.52 3.66 3.80 6.75 1* 3.13 3.28 3.44 3.59 3.75 3.91 4.06 4.22 7.50 H 3.44 3.61 3.78 3.95 4.13 4.30 4.47 4.64 8.25 i 3.75 3.94 4.13 4.31 4.50 4.69 4.88 5.06 9.00 is 4.06 4.27 4.47 4.67 4.88 5.08 5.28 5.48 9.75 ' 4.38 4.59 4.81 5.03 5.25 5:47 5.69 5.91 10.50 1 5 4.69 49?, 516 5.39 563 586 609 6.33 11.25 1 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 12.00 IJL 5.31 5.58 5.84 6.11 6.38 6.64 6.91 7.17 12.75 lj 5.63 5.91 6.19 6.47 6.75 7.03 7.31 7.59 13.50 5.94 6.23 6.53 6.83 7.13 7.42 7.72 8.02 14.25 H 6.25 6.58 6.88 7.19 7.50 ,7.81 8.13 8.44 15.00 1?8 6.56 6.89 7.22 7.55 7.88 8.20 8.53 8.86 15.75 If 6.88 7.22 7.56 7.91 8.25 8.59 8.94 9.28 16.50 iA 7.19 7.55 7.91 8.27 8.63 8.98 9.34 9.70 17.25 H 7.50 7.88 8.25 8.63 9.00 9.38 9.75 10.13 18.00 1 T 9 , 7.81 8.20 8.59 8.98 9.38 9.77 10.16 10.55 18.75 If 8.13 8.53 8.94 9.34 9.75 10.16 10.56 10.97 19.50 8.44 8.86 9.28 9.70 10.13 10.55 10.97 11.39 20.25 If 8.75 9.19 9.63 10.00 10.50 10.94 11.38 11.81 21.00 l-U. 9.06 9.52 9.97 10.42 10.88 11.33 11.78 ' 12.23 21.75 if 9.38 9.84 10.31 10.78 11.25 11.72 12.19 12.66 22.50 9.69 10.17 10.68 11.14 11.63 12.11 12.59 13.08 23.25 .& 10.00 10.50 11.00 11.50 12.00 12.50 13.00 13.59 24.00 r, .. , AREAS OP FLAT ROLLED IRON. (CONTINUED".) Thickness in Inches. 7// 7> 4 '" 1%" 7&" 8" aw 8K" \*X" 12" - A .438 .453 .469 .484 .500 .516 .531 .547 .750 i .875 .906 .938 .969 1.00 1.03 1.06 1.09 1.50 3 1.31 1.36 1.41 1.45 1.50 1.55 1.59 1.64 2.25 1.75 1.81 1.88 1.94 2.00 2.06 2.13 2.19 3.00 A 2.19 2.27 2.34 2.42 2.50 2.58 2.66 2.73 3.75 I 2.63 2.72 2.81 2.91 3.00 3.09 3.19 3.28 4.50 TS 3.06 3.17 3.28 3.39 3.50 3.61 3.72 3.83 5.25 i 3.50 3.63 3.75 3.88 4.00 4.13 4.25 4.38 6.00 A 3.94 4.08 4.22 4.36 4.50 4.64 4.78 4.92 6.75 B 8 4.38 4.53 4.69 4.84 5.00 5.16 5.31 5.47 7.50 4.81 4.98 5.16 5.33 5.50 5.67 5.84 6.02 8.25 3 i 5.25 5.44 5.63 5.81 6.00 6.19 6.38 6.6 9.00 H 5.69 5.89 6.09 6.30 6.50 6.70 6.91 7.11 9.75 6.13 6.34 6.56 6.78 7.00' 7.22 7.44 7.66 10.50 16 1 G 6.56 6.80 7.03 7.27 7.50 7.73 7.97 8.20 11.25 1 7.00 7.25 7.50 7.75 8.00 8.25 8.50 8.75 12.00 IrV 7.44 7.70 7.97 8.23 8.50 8.77 9.03 9.30 12.75 H 7.88 8.16 8.44. 8.72 9.00 9.28 9.56 9.84 13.50 IA 8.31 8.61. 8.91 9.20 9.50 9.80 10.09 10.39 14.25 11 8.75. 9.06 9.38 9.69 10.00 10.31 10.63 10.94 15.00 1& 9.19 9.52 9.84 10.17 10.50 10.83 11.16 11.48 15.75 U 9.63 9.97 10.31 10.66 11.00 11.34 11.69 12.03 16.50 i* 10.06 10.42 10.78 11.14 11.50 11.86 12.22 12.58 17.25 10.50 10.88 11.25 11.63 12.00 12.38 12.75 13.13 18.00 iA 10.94 11.33 11.72 12.11 12.50 12.89 13.28 13.67 18.75 if 11.38 11.78 12.19 12.59 13.00, 13.41 13.81 14.22 19.50 IH 11.81 12.23 12,66 13.08 13.50 13.92 14.34 14.77 20.25 if 12.25 12.69 13.13 13.56 14.00 14.44 14.88 15.31 21.00 HI 12.69 13.14 13.59 14.05 14.50 14.95 15.41 15.86 21.75 u 13.13 13.59 14.06 14.53 15.00 15.47 15.94 16.41 22.50 1M 13.56 14.05 14.53 15.02 15.50 15.98 16.47 18.95 23.25 2 i 14.00 14.50 15.00 15.50 16.00 16.50 17.00 17.50 24.00 AREAS OP FLAT ROLLED IRON. (CONTINUED.) Thickness in Inches. 9" w 9K 9%" 10" 1CH" 10i' 'iOf : 12" 1 1 rV .563 .578 .594 .609 .625 .641 .651 )' .672 75( i 1.13 1.16 1.19 1.22 1.25 1.28 1.31 1.34 1.50 j I 1.69 1.73 1.78 1.83 1.88 1.92 1.97 2.02 2.25 i 2.25 2.31 2.38 2.44 2.50 2.56 2.63 2.69 3.00 A 2.81 2.89 2.97 3.05 3.13 3.20 3.28 3.36 375 3.38 3.47 3.56 3.66 3.75 3.84 3.94 4.03 4.50 A- 3.94 4.05 4.16 4.27 4.38 4.48 4.59 4.70 5.25 4.50 4.63 4.75 4.88 5.00 5.13 5.25 5.38 6.00 * 5.06 5.20 5.34 5.48 5.63 5.77 5.91 ! 6.05 675 5.63 5.78 5.94 6.09 6.25 6.41 6.56 ' 6.72 7.50 A 6.19 6.36 6.53 6.70 6.88 7.05 7.22 7.39 8.25 i 6??5 6.94 7.13 7.31 7.50 7.69 7.88 1 8.06 9.00 it 7.31 7.52 7.72 7.92 8.13 8.33 8.53 ! 8.73 9.75 7.88 8.09 8.31 8.53 8.75 8.97 9.19 : 9.41 10.50 M 8.44 8.67 8.91 9.14 9.38 9.61 9.84 10.08 11.25 i " 9.00 9.25 9.50 9.75 10.00 10.25 10.50 10.75 12.00 H- 9.56 9.83 10.09 10.36 10.63 10.89 11.16 11.42 12.75 i 1 ! 10.13 10.41 10.69 10.97 11.25 11.53 11.81 12.09 13.50 IA 10.69 ! 10.98 11.28 11.58 11.88 12.17 12.47 '12.77 14.25 11.25 ; 11.56 11.88 12.19 12.50 12.81 13.13 ,13.44 15.00 I A 11.81 12.14 12.47 12.80 13.13 13.45 13.78 '14.11 15.75 if 12.38 12.72 13.06 13.41 1375 14.09 14.44 1478 16.50 12.94 13.30 13.66 : 14.02 14.38 ' 14.73 15.09 15.45 17.25 H 13.50 | 13.88 14.25 i 14.63 15.00 j 15.38 15.75 16.13 18.00 IA 14.08 14.45 14.84 i 15.23 15.63 ! 16.02 16.41 16.80 18.75 if 14.63 ! 15.03 15.44 15.84 16.25 ! 16.66 17.06 17.47 19.50 M* 15.19 15.61 16.03 16.45 16.88 17.30 17.72 18.14 20.25 it 15.75 16.19 16.63 i 17.06 17.50 17.94 . 18.38 18.81 21.00 HI 16.31 i 16.77 17.22 17.67 18.13 18.58 19.03 19.48 2175 1? 16.88 i 17.34 i 17.81 ! 18.28 18.75 : 19.22 ! 19.69 20.16 22.50 17.44 11 t7.92 ! 18.41 1S.89 19.38 19.86 i 20.34 20.83 23.25 2 16 13.00 8.50 19.00 19.50 20.00 20.50 21.00 21.50 24.00 ft | i 5 SQUARE AND ROUND BARS. (CONTINUED.) Thickness or Diameter in Inches. 2 A : Weight of ; Weight of [j Bar O Bar : One Foot long. : One Foot long. 13.33 10.47 14.18 11.14 15.05 11.82 15.95 12.53 Area of QBar in sq. inches. 4.0000 4.2539 4.5156 4.7852 Area of O Bar in sq. inches. Circumference of O Bar in inches. 6.2832 6.4795 6.6759 6,8722 3.1416 3.3410 3.5466 3.7583 A ,1 16.88 1 13.25 17.83 14.00 18.80 14.77 19.80 i 15.55 5.0625 5.3477 5.6406 5.9414 3.9761 4.2000 4.4301 4.6664 7.0686 7.2649 7.4613 7.6576 l 1 11 20.83 16.36 21.89 ! 17.19 22.97 1 18.04 24.08 ! 18.91 6.2500 6.5664 6.8906 7.2227 4.9087 5.1572 5.4119 5.6727 7.8540 8.0503 8.2467 8.4430 3 1 1 .! 25.21 19.80 26.37 20.71 27.55 : 21.64 28.76 22.59 7.5625 7.9102 8.2656 8.6289 5.9396 6.2126 6.4918 6.7771 8.6394 8.8357 9.0321 9.2284 3 A 30.00 23.56 31.26 24.55 32.55 25.57 33.87 26.60 9.0000 9.3789 9.7656 10.160 7.0686 7.3662 7.6699 7.9798 9.4248 9.6211 9.8175 10.014 T "3 35.21 27.65 36.58 28.73 37.97 29.82 39.39 I 30.94 10.563 10.973 11.391 11.816 8.2958 8.6179 8.9462 9.2806 10.210 10.407 10.603 10.799 1 I I 40.83 i 32.07 42.30 33.23 43.80 34.40 45.33 35.60 12.250 12.691 13.141 13.598 9.6211 9.9678 10.321 10.680 10.996 11.192 11.388 11.585 A w i 46.88 36.82 48.45 38.05 50.05 39.31 51.68 4O.59 14.063 14.535 15.016 15.504 11.045 11.416 11.793 12.177 11.781 11.977 12.174 12.370 TV fT SQUARE AND ROUND BARS. (CONTINUED.) Thickness or Diameter ill Inches. Weight of [jBar One Foot long. Weight of O Bar One Foot long. Area of QBar in sq. inches. Area of O Bar in sq. inches. Circumference of O Bar in inches. 4 i A 53.33 55.01 56.72 58.45 41.89 43.21 44.55 45.91 16.000 16.504 17.016 17.535 12.566 12.962 13.364 13.772 12.566 12.763 12.959 13.155 ! 60.21 61.99 63.80 65.64 47.29 48.69 50.11 51.55 18.063 18.598 19.141 19.691 14.186 14.607 15.O33 15.466 13.352 13.548 13.744 13.941 f H 67.50 69.39 71.30 73.24 53.01 54.50 56.00 57.52 20.250 20.816 21.391 21.973 15.904 16.349 16.800 17.257 14.137 14.334 14.530 14.726 I if 75.21 59.07 77.20 60.63 79.22 62.22 81.26 63.82 22.563 23.160 23.766 24.379 17.721 18.190 18.665 19.147 14.923 15.119 15.315 15.512 ! 83.33 85.43 87.55 89.70 65.45 67.10 68.76 70.45 25.000 25.629 26.266 26.910 19.635 20.129 20.629 21.135 15.708 15.904 16.101 16.297 | 91.88 94.08 96.30 98.55 72.16 73.89 75.64 77.40 27.563 28.223 28.891 29.566 21.648 22.166 22.691 23.221 16.493 16.690 16.886 17.082 | 100.8 103.1 105.5 107.8 79.19 81.00 82.83 84.69 30.250 30.941 31.641 32.348 23.758 24.301 24.85O 25.406 17.279 17.475 17.671 17.868 1 A 110.2 112.6 115.1 117.5 86.56 88.45 90.36 92.29 33.063 25.967 33.785 26.535 34.516 27.109 35.254 27.688 18.064 18.261 18.457 18.653 106 ^ *15 C SQUARE AND ROUND BARS. (CONTINUED.) Thickness Weight of Weight of Area of Area of Circumference ' or Diameter! Q Bar Q Bar [jBar O Bar of O Bar in Inches. ; One Foot long. One Foot long. in sq. inches. in sq. inches. in inches. 6 120.0 94.25 36.000 28.274 18.850 iV 122.5 96.22 36.754 28.866 19.046 Y 125.1 98.22 37.516 29.465 19.242 & 127.6 100.2 38.285 30.069 19.439 i 130.2 102.3 39.063 30.680 19.635 TV 132.8 104.3 39.848 31.296 19.831 f 135.5 106.4 40.641 31.919 20.028 7 T 138.1 108.5 41.441 32.548 20.224 1 140.8 110.6 42.250 33.183 20.420 A 143.6 112.7 43.066 33.824 20.617 f 146.3 114.9 43.891 34.472 20.813 li- 149.1 117.1 44.723 35.125 21.009 f 151.9 119.3 45.563 35.785 21.206 154.7 121.5 46.410 36.450 21.402 ? 157.6 123.7 47.266 37.122 21.598 160.4 126.0 48.129 37.800 21.795 7 163.3 128.3 49.000 38.485 21.991 T V 166.3 130.6 49.879 39.175 22.187 i 169.2 132.9 50.766 39.871 22.384 A 172 - 2 135.2 51.660 40.574 22.58O T% 175.2 178.2 137.6 140.0 52.563 53.473 41.282 41.997 22.777 22.973 3 f 181,3 142.4 54.391 42.718 23.169 TV 134.4 144.8 55.316 43.445 23.366 187.5 147.3 56.250 44.179 23.562 190.6 149.7 57.191 44.918 23.758 | 193.8 152.2 58.141 45.664 23.955 11 197.O 154.7 59.098 46.415 24.151 i 200.2 157.2 60.063 47.173 24.347 It 203.5 159.8 61.035 47.937 24.544 } 206.7 162.4 62.016 48.707 24.74O 11 210.0 T i 164.9 63.004 49.483 24.936 SQUARE AND ROUND BARS. (CONTINUED.) Thickness or Diameter in Inches. Weight of QBar One Foot long. Weight of O Bar One Foot long. Area of Area of [J Bar O Bar in sq. inches, in sq. inches. Circumference of O Bar in inches. 8 ! 213.3 167.6 216.7 170.2 220.1 172.8 223.5 175.5 64.000 65.004 66.016 67.035 50.265 51.054 51.849 52.649 25.133 25.329 25.525 25.722 i 226.9 230.3 233.8 237.3 178.2 180.9 183.6 186.4 68.063 69.098 70.141 71.191 53.456 54.269 55.088 55.914 25.918 26.114 26.311 26.507 I 240.8 244.4 248.0 251.6 189.2 191.9 194.8 197.6 72.250 73.316 74.391 75.473 56.745 57.583 58.426 59.276 26.704 26.900 27.096 27.293 it it 255.2 258.9 262.6 266.3 200.4 203.3 206.2 209.1 76.563 60.132 77.660 6O.994 78.766 61.862 79.879 62.737 27.489 27.685 27.882 28.078 9 t 270.0 273.8 277.6 281.4 212.1 215.0 218.0 221.0 81.000 63.617 82.129 64.504 83.266 65.397 84.410 66.296 28.274 28.471 28.667 28.863 A 285.2 289.1 293.0 296.9 224.0 227.0 230.1 233.2 85.563 86.723 87.891 89.066 67.201 68.112 69.029 69.953 29.060 29.256 29.452 29.649 I 300.8 304.8 308.8 312.8 236.3 239.4 242.5 245.7 90.250 91.441 92.641 93.848 70.882 71.818 72.760 73.708 29.845 30.041 30.238 30.434 it , * 316.9 321.0 325.1 329.2 1 248.9 252.1 255.3 258.5 95.063 96.285 97.516 98.754 74.662 75.622 76.589 77.561 30.631 30.827 31.023 31.220 SQTJAKE AND ROUN^&ff&ST (CONTTOTED.) HUKIVBRS! Thickness Weight of Weight of Area of ^^Dj m$$ or Diameter [~] Bar O Bar Q Bar O^ StEJac^ in Inches. One Foot long, i One Foot long. in sq. inches. \ in sq. inches. in inches. 10 333.3 261.8 100.00 78.540 31.416 TtT 337.5 265.1 101.25 79.525 31.612 341.7 268.4 102.52 80.516 31.809 I 346.0 271.7 103.79 81.513 32.005 l 350.2 275.1 105.06 82.516 32.201 A 354.5 278.4 106.35 83.525 32.398 358.8 281.8 107.64 84.541 32.594 rV 363.1 285.2 108.94 85.562 32.790 } 367.5 288.6 110.25 86.590 32.987 T 9 T 371.9 i 292.1 111.57 87.624 33.183 I 376.3 295.5 112.89 88.664 33.379 a 380.7 299.0 114.22 | 89.710 33.576 | 385.2 302.5 115.56 90.763 33.772 if 389.7 306.1 116.91 91.821 33.968 i 394.2 309.6 118.27 92.886 34.165 ft 398.8 313.2 119.63 93.956 34.361 11 403.3 316.8 121.00 95.033 34.558 407.9 320.4 122.38 96.116 34.754 412.6 324.0 123.77 97.205 34.95Q 417.2 327.7 125.16 98.301 35.147 i ~r 421.9 331.3 126.56 99.402 35.343 A 426.6 335.0 127.97 100.51 35.539 1 431.3 338.7 129.39 101.62 35.736 TV 436.1 342.5 130.82 102.74 35.932 440.8 346.2 132.25 103.87 36.128 445.6 350.0 133.69 105.00 36.325 f 450.5 353.8 135.14 106.14 36.521 tt 455.3 357.6 136.60 107.28 36.717 i I 460.2 361.4 138.06 108.43 36.914 if 465.1 365.3 139.54 | 109.59 37.110 1 470.1 369.2 141.02 110.75 37.306 it 475.0 373.1 142.50 111.92 37.503 WEIGHT OF SHEETS OF WROUGHT IRON, STEEL, COPPER AND BRASS. (From Haswell.) Weights per Square Foot. Thickness by Birmingham Gauge. 2SE ^on. | Steel. Copper. Brass. 0000 i .454 18.22 18.46 20.57 19.43 000 .425 17.05 17.28 19.25 18.19 00 .38 15.25 15.45 17.21 16.26 .34 13.64 13.82 15.40 14.55 1 .3 12.04 12.20 13.59 12.84 2 .284 11.40 11.55 12.87 12.16 3 .259 10.39 10.53 11.73 11.09 4 .238 9.55 9.68 10.78 10.19 5 .22 8.83 8.95 9.97 9.42 6 .203 8.15 8.25 9.20 8.69 7 .18 7.22 7.32 8.15 7.70 8 .165 6.62 6.71 7.47 7.06 9 .148 5.94 6.02 6.7O 6.33 10 .134 5.38 5.45 6.07 5.74 11 .12 4.82 4.88 5.44 5.14 12 .109 4.37 4.43 4.94 4.67 13 .095 3.81 3.86 4.30 4.07 14 .083 3.33 3.37 3.76 3.55 15 .072 2.89 2.93 3.26 3.08 16 .065 2.61 2.64 2.94 2.78 17 .058 2.33 2.36 2.63 i 2.48 18 .049 1.97 1.99 2.22 2.10 19 .042 1.69 1.71 1.90 1.80 20 .035 1.40 1.42 1.59 1.50 21 .032 1.28 1.30 1.45 1.37 22 .028 1.12 1.14 1.27 1.20 23 .025 1.00 1.02 1.13 1.07 24 .022 .883 .895 1.00 .942 25 .02 .803 .813 .906 .856 26 .018 .722 .732 .815 1 .770 27 .016 .642 .651 .725 .685 28 .014 .562 .569 .634 .599 29 .013 .522 .529 .589 .556 30 .012 .482 .488 .544 .514 31 .01 .401 .407 .453 .428 32 .009 .361 .366 .408 .385 33 .008 .321 .325 .362 .342 34 .007 .281 .285 .317 .300 35 .005 .201 .203 .227 .214 Specific Gravity, 7.704 7.806 8.698 8.218 Weight Cubic Foot, 481.25 487.75 543.6 513.6 . " " Inch, .2787 .2823 .3146! .2972 WEIGHT OF SHEETS OF WROUGHT IRON, STEEL, COPPER AND BRASS. (From Haswell.) "Weights per Sq. Foot. Thickness by American (Browne & Sharpe's) Gauge. No. of Thickness Gauge. in inches. Iron. Steel. Copper. Brass. OOOO .46 18.46 18.70 20.84 19.69 000 .4096 16.44 16.66 18.56 17.53 00 .3648 14.64 14.83 16.53 15.61 .3249 13.04 13.21 14.72 13.90 1 .2893 11.61 11.76 13.11 12.38 2 .2576 10.34 10.48 11.67 11.03 3 .2294 9.21 9.33 10.39 9.82 4 .2043 8.20 8.31 9.26 8.74 5 .1819 7.30 7.40 8.24 7.79 6 .1620 6.50 6.59 7.34 6.93 7 .1443 5.79 5.87 6.54 6.18 8 .1285 5.16 5.22 5.82 5.50 9 .1144 4.59 4.65 5.18 4.90 10 .1019 4.09 4.14 4.62 4.36 11 .0907 3.64 3.69 4.11 3.88 12 .0808 3.24 3.29 3.66 3.46 13 .0720 2.89 2.93 3.26 3.08 14 .0641 2.57 2.61 2.90 2.74 15 .0571 2.29 2.32 2.59 2.44 16 .0508 2.04 2.07 2.30 2.18 17 .0453 1.82 1.84 2.05 1.94 18 .0403 1.62 1.64 1.83 1.73 19 .0359 1.44 1.46 1.63 1.54 20 .0320 1.28 1.30 1.45 1.37 21 .0285 1.14 1.16 1.29 1.22 22 .0253 1.02 1.03 1.15 1.08 23 .0226 .906 .918 1.02 .966 24 .0201 .807 .817 .911 .860 25 .0179 .718 .728 .811 i .766 26 .0159 .640 .648 .722 .682 27 .0142 .570 .577 .643 .608 28 .0126 .507 .514 .573 .541 29 .0113 .452 .458 .510 .482 30 .0100 .402 .408 .454 .429 31 .0089 .358 .363 .404 .382 32 .0080 .319 .323 .360 .340 33 .0071 .284 .288 .321 .303 34 .O063 .253 .256 .286 .270 35 .0056 .225 .228 .254 .240 As there sre many gauges in use differing from each other, and even the thicknesses of a certain specified gauge, ss the Birmingham, are not assumed the same by all manufacturers, orders for sheets ana wire should always state the weight per square foot, or the thickness ^ in thousandths of an inch. AREAS and CIRCUMFERENCES OF CIRCLES. For Diameters from -fe to 100, advancing by Tenths. Diam. Area. Circum. Diam. Area. Circum. 0.0 4.0 12.5664 12.5664 .1 .007854 .31416 .1 13.2025 12.8805 .2 .031416 .62832 .2 13.8544 13.1947 .3 .070686 .94248 .3 14.5220 13.5088 .4 .12566 1.2566 .4 15.2053 13.8230 .5 .19635 1.5708 .5 15.9043 14.1372 .6 .28274 1.8850 .6 16.6190 14.4513 .7 .38485 2.1991 .7 17.3494 147655 .8 .50266 2.5133 .8 18.0956 15.0796 .9 .63617 2.8274 .9 18.8574 15.3938 1.0 .7854 3.1416 5.0 19.6350 15.7080 .1 .9503 3.4558 .1 20.4282 16.0221 .2 1.1310 3.7699 .2 21.2372 16.3363 .3 1.3273 4.0841 .3 22.0618 16.6504 j 1.5394 4.3982 .4 22.9022 16.9646 .5 1.7671 4.7124 .5 23.7583 17.2788 .6 2.0106 5.0265 .6 24.6301 17.5929 .7 2.2698 5.3407 .7 25.5176 17.9071 .8 2.5447 5.6549 .8 26.4208 18.2212 .9 2.8353 5.9690 .9 27.3397 18.5354 2.0 3.1416 6.2832 6.0 28.2743 18.8496 .1 3.4636 6.5973 .1' 29.2247 19.1637 .2 3.8013 6.9115 .2 30.1907 19.4779 .3 4.1548 7.2257 .3 31.1725 19.7920 .4 4.5239 7.5398 .4 32.1699 i 20.1062 .5 4.9087 7.8540 .5 33.1831 20.4204 .6 5.3093 8.1681 .6 34.2119 20.7345 .7 5.7256 8.4823 .7 35.2565 21.0487. .8 6.1575 8.7965 .8 36.3168 21.3628 .9 6.6052 1 9.1106 .9 37.3928 | 21.6770 3.0 7.0686 9.4248 7.0 38.4845 21.9911 .1 7.5477 9.7389 .1 39.5919 I 22.3053 . .2 8.0425 10.0531 .2 40.7150 22.6195 .3 8.5530 10.3673 .3 41.8539 ! 22.9336 .4 9.0792 10.6814 43.0084 ! 23.2478 .5 3.6211 10.9956 .5 44.1786 1 23.5619 .6 10.1788 11.3097 .6 45.3646 23.8761 .7 10.7521 11.6239 .7 46.5663 : 24.1903 .8 11.3411 11.9381 .8 47.7836 24.5044 r - 9 11.9459 12.2522 .9 49.0167 > 24.8186 . s 1 12 JLJ ""- a AKEAS and CIRCUMFERENCES OF CIRCLES. (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 8.0 50.2655 25.1327 12.0 113.0973 37.6991 .1 51.5300 25.4469 .1 114.9901 38.0133 .2 52.8102 25.7611 .2 116.8987 38.3274 .3 54.1061 26.0752 .3 118.8229 38.6416 .4 55.4177 26.3894 .4 120.7628 38.9557 .5 56.7450 26.7035 .5 122.7185 39.2699 .6 58.0880 27.0177 .6 124.6898 39.5841 .7 59.4468 27.3319 .7 126.6769 39.8982 .8 60.8212 27.6460 .8 128.6796 40.2124 .9 62.2114 27.9602 .9 130.6981 40.5265 9.0 63.6173 28.2743 13.0 132.7323 40.8407 .1 65.0388 28.5885 .1 134.7822 41.1549 .2 66.4761 28.9027 .2 136.8478 41.4690 .3 67.9291 29f2168 .3 138.9291 41.7832 .4 69.3978 29.5310 .4 141.0261 42.0973 .5 70.8822 29.8451 .5 143.1388 42.4115 .6 72.3823 30.1593 .6 145.2672 42.7257 .7 73.8981 30.4734 .7 147.4114 43.0398 .8 75.4296 30.7876 .8 149.5712 43.3540 9, 76.9769 31.1018 .9 151.7468 43.6681 10.0 78.5398 31.4159 14.0 153.9380 43.9823 .1 80.1185 31.7301 .1 156.1450 44.2965 .2 81.7128 32.0442 .2 158.3677 44.6106 .3 83.3229 32.3584 .3 160.6061 44.9248 .4 84.9487 32.6726 .4 162.8602 45.2389 .5 86.5901 32.9867 .5 165.1300 45.5531 .6 88.2473 33.3009 .6 167.4155 45.8673 .7 89.9202 33.6150 .7 169.7167 46.1814 .8 91.6088 33.9292 .8 172.0336 46.4956 .9 93.3132 34.2434 .9 174.3662 46.8097 11.0 95.0332 34.5575 15.0 176.7146 47.1239 .1 96.7689 34.8717 .1 179.0786 47.4380 .2 98.5203 35.1858 .2 181.4584 47.7522 .3 100.2875 35.5000 .3 183.8539 48.0664 .4 102.0703 35.8142 .4 186.2650 48.3805 .5 103.8689 36.1283 .5 188.6919 48.6947 .6 105.6832 36.4425 .6 191.1345 49.0088 .7 107.5132 36.7566 .7 193.5928 49.3230 .8 109.3588 37.0708 .8 196.0668 49.6372 .9 111.2202 i 37.3850 .9 198.5565 49.9513 c 1 3 ^ 8 AREAS and CIRCUMFERENCES OP CIRCLES. (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 16.0 201.0619 50.2655 20.0 314.1593 62.8319 .1 203.5831 50.5796 .1 317.3087 63.1460 .2 206.1199 50.8938 .2 320.4739 63.4602 .3 , 208.6724 51.2080 .3 323.6547 63.7743 .4 ! 211.2407 51.5221 .4 326.8513 64.0885 .5 213.8246 51.8363 .5 330'.0636 64.4026 .6 216.4243 52.1504 .6 333.2916 64.7168 .7 219.0397 52.4646 .7 336.5353 65.0310 .8 221.6708 52.7788 .8 339.7947 65.3451 .9 224.3176 53.0929 .9 343.0698 65.6593 17.0 226.9801 53.4071 21.0 346.3606 65.9734 .1 ; 229.6583 53.7212 .1 349.6671 66.2876 .2 232.3522 54.0354 .2 352.9894 66.6018 .3 i 235.0618 54.3496 .3 356.3273 66 9159 .4 ! 237.7871 54.6637 .4 359.6809 67.2301 .5 240.5282 54.9779 .5 363.0503 67.5442 .6 243.2849 55.2920 366.4354 67.8584 .7 246.0574 55.6062 369.8361 68.1726 .8 248.8456 55.9203 !s 373.2526 68.4867 .9 251.6494 56.2345 .9 376.6848 68.8009 18.0 254.4690 56.5486 22.0 380.1327 69.1150 .1 257.3043 56.8628 .1 383.5963 69.4292 .2 260.1553 57.1770 .2 387.0756 69.7434 .3 263.0220 57.4911 .3 390.5707 70.0575 .4 265.9044 57.8053 .4 394.0814 70.3717 .5 268.8025 58.1195 .5 397.6078 70.6858 .6 271.7164 58.4836 .6 401.1500 71.0000 .7 274.6459 58.7478 .7 404.7078 71.3142 .8 277.5911 59.0619 .8 408.2814 71.6283 .9 280.5521 59.3761 411.8707 71.9425 19.0 283.5287 59.6903 23.0 415.4756 72.2566 .1 286.5211 60.0044 .1 419.0963 72.5708 .2 289.5292 60.3186 .2 422.7327 72.8849 .3 292.5530 60.6327 .3 426.3848 73.1991 .4 295.5925 60.9469 A 430.0526 73.5133 .5 298.6477 61.2611 .5 433.7361 73.8274 .6 301.7186 61.5752 .6 437.4354 74.1416 .7 304.8052 61.8894 .7 441.1503 74.4557 .8 ! 307.9075 62.2035 .8 444.8809 74.7699 .9 311.0255 62.5177 .9 448.6273 75.0841 . 11 '>L ? " AREAS and CIRCUMFERENCES OF CIRCLES. (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 24.0 452.3893 75.3982 28.0 615.7522 87.9646 .1 456.1671 75.7124 .1 620.1582 88.2788 .2 459.9606 76.0265 .2 624.5800 88.5929 .3 463.7698 76.3407 .3 629.0175 88.9071 .4 467.5947 76.6549 .4 633.4707 89.2212 .5 471.4352 76.9690 .5 637.9397 89.5354 .6 475.2916 77.2832 .6 642.4243 89.8495 ry 479.1636 77.5973 .7 646.9246 90.1637 is 483.0513 77.9115 .8 651.4407 90.4779 .9 486.9547 78.2257 9 655.9724 90.7920 25.0 490.8739 ' 78.5398 29.0 660.5199 91.1062 .1 494.8087 78.8540 .1 665.0830 91.4203 a 498.7592 79.1681 .2 669.6619 91.7345 Is 502.7255 79.4823 .3 674.2565 92.0487 - .4 506.7075 79.7965 .4 678.8668 92.3628 .5 510.7052 80.1106 .5 683.4928 92.6770 .6 514.7185 80.4248 .6 688.1345 92.9911 .7 518.7476 80.7389 .7 692.7919 93.3053 .8 522.7924 81.0531 .8 697.4650 93.6195 .9 526.8529 81.3672 .9 702.1538 93.9336 26.0 530.9292 81.6814 30.0 706.8583 94.2478 .1 535.0211 81.9956 .1 711.5786 94.5619 .2 539.1287 82.3097 .2 716.3145 94.8761 .3 543.2521 82.6239 .3 721.0662 95.1903 .4 547.3911 82.9380 .4 725.8336 95.5044 .5 551.5459 83.2522 .5 730.6167 95.8186 .6 555.7163 83.5664 .6 735.4154 96.1327 .7 559.9025 83.8805 .7 740.2299 96.4469 .8 564.1044 84.1947 .8 745.0601 96.7611 .9 568.3220 84.5088 .9 749.9060 97.0752 27.0 572.5553 ! 84.8230 31.0 754.7676 97.3894 .1 576.8043 85.1372 .1 759.6450 97.7035 .2 581.0690 85.4513 .2 764.5380 98.0177 .3 585.3494 85.7655 .3 769.4467 98.3319 .4 589.6455 ; 86.0796 .4 774.3712 98.6460 .5 593.9574 86.3938 .5 779.3113 98.9602 .6 598.2849 86.7080 .6 784.2672 99.2743 .7 602.6282 87.0221 .7 789.2388 99.5885 .8 606.9871 87.3363 .8 794.2260 99.9026 9 -9 611.3618 87.6504 .9 799.2290 100.2168 , ! I AREAS and CIRCUMFERENCES OF CIRCLES. (CONTINUED.) Diam. Area. Oircum. Diam. Area. Oircum. 32.0 804.2477 100.5310 36.0 1017.8760 . 113.0973 .1 809.2821 100.8451 .1 1088.6887 113.4115 .2 814.3322 101.1593 .2 1029.2172 113.7257 .3 819.3980 101.4734 .3 1034.9113 114.0398 .4 824.4796 101.7876 .4 1040.6212 114.3540 .5 829.5768 102.1018 .5 1046.3467 114.6681 .6 834.6898 102.4159 .6 1052.0880 114.9823 .7 839.8185 102.7301 .7 1057.8449 115.2965 .8 844.9628 103.0442 .8 1063.6176 115.6106 .9 850.1229 103.3584 .9 1069.4060 115.9248 33.0 855.2986 103.6726 37.0 1075.2101 116.2389 .1 860.4902 103.9867 .1 1081.0299 116.5531 .2 865.6973 104.3009 .2 1086.8654 116.8672 .3 870.9202 104.6150 .3 1092.7166 117.1814 .4 876.1588 104.9292 .4 1098.5835 117.4956 .5 881.4131 105.2434 1104.4662 117.8097 .6 886.6831 105.5575 .6 1110.3645 118.1239 .7 891.9688 105.8717 .7 1116.2786 118.4380 .8 897.2703 106.1858 1122.2083 118.7522 .9 902.5874 106.5000 .9 1128.1538 119.0664 34.0 907.9203 106.8142 38.0 1134.1149 119.3805 .1 913.2688 107.1283 .1 1140.0918 ' 119.6947 .2 918.6331 107.4425 .2 1146.0844 120.0088 .3 924.0131 107.7566 .3 1152.0927 120.3230 .4 929.4088 108.0708 .4 1158.1167 120.6372 .5 934.8202 108.3849 .5 1164.1564 120.9513 .6 940.2473 108.6991 .6 1170.2118 121.2655 .7 945.6901 109.0133 .7 1176.2830 121.5796 .8 951.1486 109.3274 .8 1182.3698 121.8938 .9 956.6228 109.6416 .9 1188.4724 122.2080 35.0 962.1128 - 109.9557 39.0 1194.5906 122.5221 .1 967.6184 110.2699 .1 1200.7246 122.8363 .2 973.1397 110.5841 .2 1206.8742 123.1504 .3 978.6768 110.8982 .3 1213.0396 123.4646 .4 984.2296 111.2124 .4 1219.2207 123.7788 .5 989.7980 111.5265 .5 1225.4175 124.0929 .6 995.3822 111.8407 .6 1231.6300 ' 124.4071 .7 1000.9821 112.1549 .7 1237.8582 124.7212 .8 1006.5977 112.4690 .8 1244.1021 125.0354 .9 1012.2290 112.7832 .9 1250.3617 ! 125.3495 AREAS and CIRCUMFERENCES OF CIRCLES. i (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 40.0 1256.6371 125.6637 44.0 1520.5308 138.2301 .1 1262.9281 125.9779 .1 1527.4502 138.5442 .2 1269.2348 126.2920 .2 1534.3853 138.8584 .3 I 1275.5573 126.6062 .3 1541.3360 139.1726 .4 1281.8955 126.9203 .4 1548.3025 ; 139.4867 .5 1288.2493 127.2345 .5 1555.2847 139.8009 .6 1 1294.6189 127.5487 .6 1562.2826 140.1153 .7 1301.0042 127.8628 .7 1569.2962 140.4292 .8 1307.4052 128.1770 .8 1576.3255 140.7434 .9 1313.8219 128.4911 .9 1583.3706 141.0575 41.0 1320.2543 128.8053 45.0 1590.4313 141.3717 .1 1326.7024 129.1195 .1 1597.5077 | 141.6858 JB 1333.1663 129.4336 .2 1604.5999 142.0000 .3 1339.6458 129.7478 .3 1611.7077 142.3142 4 1346.1410 130.0619 .4 1618.8313 142.6283 .5 1352.6520 130.3761 .5 1625.9705 142.9425 .6 1359.1786 130.6903 .6 1633.1255 143.2566 .7 1365.7210 131.0044 .7 1640.2962 143.5708 .8 1372.2791 131.3186 .8 1647.4826 143.8849 .9 1378.8529 131.6327 .9 1654.6847 144.1991 42.0 1385.4424 131.9469 46.0 1661.9025 144.5133 i 1392.0476 132.2611 .1 1669.1360 144.8274 J8 1398.6685 132.5752 .2 1676.3853 145.1416 .3 1405.3051 132.8894 .3 1683.6502 145.4557 .4 1411.9574 . 133.2035 .4 1690.9308 145.7699 .5 1418.6254 133.5177 .5 1698.2272 146.0841 .6 1425.3092 133.8318 .6 1705.5392 146.3982 .7 1432.0086 134.1460 .7 1712.8670 146.7124 .8 1438.7838 134.4602 .8 1720.2105 147.0265 .9 1445.4546 134.7743 .9 1727.5697 147.3407 43.0 1452.2012 135.0885 47.0 1734.9445 147.6550 .1 1458.9635 135.4026 .1 1742.3351 147.9690 .2 1465.7415 135.7168 .2 1749.7414 148.2832 .3 1472.5352 136.0310 .3 1757.1635 148.5973 .4 1479.3446 136,3451 .4 1764.6012 148.9115 .5 1486.1697 136.6593 .5 1772.0546 149.2257 .6 1493.0105 136.9734 .6 1779.5237 149.5398 .7 1499.8670 137.2876 .7 1787.0086 149.8540 .8 1506.7393 137.6018 .8 1794.5091 150.1681 .9 ! 1513.6272 137.9159 .9 1802.0254 150.4823 . v l, AREAS and CIRCUMFERENCES OP CIRCLES. (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 48.0 1809.5574 150.7964 52.0 2123.7166 163.3628 .1 1817.1050 151.1106 .1 2131.8926 i 163.6770 .2 1824.6684 151.4248 .2 2140.0843 : 163.9911 .3 1832.2475 151.7389 .3 2148.2917 164.3053 .4 1839.8423 152.0531 .4 2156.5149 164.6195 .5 1847.4528 152.3672 .5 2164.7537 164.9336 .6 1855.0790 152.6814 .6 2173.0082 i 165.2479 .7 1862.7210 152.9956 .7 2181.2785 i 165.5619 .8 1870.3786 153.3097 .8 2189.5644 165.8761 .9 1878.0519 153.6239 .9 2197.8661 166.1903 49.0 1885.74C9 163.9380 53.0 2206.1834 : 166.5044 .1 1893.4457 154.2522 .1 2214.5165 : 166.8186 .2 1901.1662 154.5664 G) 2222.8653 j 167.1327 .3 1908.9024 154.8805 ]3 2231.2298 167.4469 .4 1916.6543 155.1947 .4 2239.6100 167.7610 .5 1924.4218 155.5088 .5 2248.0059 i 168.0752 .6 1932.2051 155.8230 .6 2256.4175 168.3894 .7 1940.0042 156.1372 .7 2264.8448 168.7035 .8 ! 1947.8189 1 156.4513 .8 2273.2879 : 169.0177 .9 1955.6493 156.7655 .9 2281.7466 169.3318 50.0 1963.4954 157.0796 54.0 2290.2210 169.6460 .1 1971.3572 157.3938 .1 2298.7112 169.9602 .2 1979.2348 157.7080 .2 2307.2171 170.2743 .3 1987.1280 158.0221 .3 2315.7386 170.5885 A 1995.0370 158.3363 .4 2324.2759 170.9026 .5 2002.9617 158.6504 .5 2332.8289 171.2168 .6 2010.9020 158.9646 .6 2341.3976 171.5310 .7 2018.8581 ! 159.2787 .7 2349.9820 171.8451 .8 2026.8299 159.5929 .8 2358.5821 172.1593 .9 2034.8174 159.9071 .9 2367.1979 172.4735 51.0 2042.8206 i 160.2212 55.0 2375.8294 ! 172.7876 .1 2050.8395 \ 160.5354 .1 2384.4767 173.1017 .2 2058.8742 160.8495 .2 2393.1396 173.4159 .3 2066.9245 161.1637 .3 2401.8183 173.7301 .4 2074.9905 161.4779 .4 2410.5126 , 174.0442 2083.0723 161.7920 .5 2419.2227 ! 174.3584 .6 i 2091.1697 162.1062 .6 2427.9485 174.6726 .7 I 2099.2829 162.4203 .7 2436.6899 174.9867 .8 i 2107.4118 162.7345 .8 2445.4471 \ 175.3009 .9 ! 2115.5563 163.0487 .9 2454.2200 ' 175.6150 , < AREAS and CIRCUMFERENCES OF CIRCLES. (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 56.0 2463.0086 175.9292 60.0 ; 2827.4334 188.4956 .1 2471.8130 176.2433 .1 2836.8660 188.8097 .2 2480.6330 176.5575 .2 2846.3144 189.1239 .3 2489.4687 176.8717 .3 2855.7784 ; 189.4380 .4 2498.3201 177.1858 .4 2865.2582 189.7522 .5 2507.1873 177.5000 .5 2874.7536 | 190.0664 .6 2516.0701 177.8141 .6 2884.2648 190.3805 .7 2524.9687 178.1283 .7 2893.7917 190.6947 .8 2533.8830 178.4425 .8 2903.3343 191.0088 .9 2542.8129 178.7566 .9 2912.8926 191.3230 57.0 2551.7586 179.0708 61.0 2922.4686 191.6372 .1 2560.7200 179.3849 .1 2932.0563 191.9513 .2 2569.6971 179.6991 .2 2941.6617 192.2655 .3 2578.6899 180.0133 .3 2951.2828 192.5796 .4 2587.6985 180.3274 .4 2960.9197 192.8938 .5 2596.7227 180.6416 .5 2970.5722 193.2079 .6 2605.7626 180.9557 .6 2980.2405 193.5221 .7 2614.8183 181.2699 .7 2989.9244 193.8363 .8 2623.8896 181.5841 .8 2999.6241 194.1504 .9 2632.9767 181.8982 .9 3009.3395 194.4646 58.0 2642.0794 182.2124 62.0 3019.0705 194.7787 .1 2651.1979 182.5265 .1 3028.8173 195.0929 .2 2660.3321 182.8407 2 3038.5798 195.4071 .3 2669.4820 ! 183.1549 .3 3048.3580 195.7212 .4 2678.6476 183.4690 .4 3058.1520 196.0354 .5 2687.8289 183.7832 .5 3087.9616 196.3495 .6 2697.0259 184.0973 .6 3077.7869 196.6637 .7 2708.2386 184.4115 .7 3087.6279 196.9779 .8 2715.4670 184.7256 .8 3097.4847 197.2920 .9 2724.7112 185.0398 .9 3107.3571 i 197.6062 59.0 2733.9710 185.3540 63.0 3117.2453 197.9203 .1 2743.2466 185.6681 .1 : 3127.1492 198.2345 .2 2752.5378 i 185.9823 .2 3137.0688 I 198.5487 .3 2761.8448 186.2964 .3 3147.0040 ! 198.8628 .4 2771.1675 186.6106 .4 3156.9550 199.1770 .5 2780.5058 186.9248 .5 3166.9217 199.4911 .6 2789.8599 , 187.2389 .6 3176.9043 l , 199.8053 .7 1 2799.2297 , 187.5531 .7 3186.9023 200.1195 .8 2808.6152 ; 187.8672 .8 3196.9161 200.4336 .9 2818.0165 188.1814 .9 3206.9456 200.7478 , 119 *- AREAS and CIRCUMFERENCES OP CIRCLES. (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 64.0 3216.9909 201.0620 68.0 3631.6811 j 213.6283 .1 3227.0518 201.3761 .1 3642.3704 , 213.9425 .2 3237.1285 201.6902 .2 3653.0754 214.2566 .3 3247.2222 202.0044 .3 3663.7960 214.5708 .4 3257.3289 202.3186 .4 3674.5324 214.8849 .5 3267.4527 202.6327 .5 3685.2845 215.1991 .6 3277.5922 202.9469 .6 3696.0523 215.5133 .7 3287.7474 203.2610 .7 3706.8359 215.8274 .8 3297.9183 203.5752 .8 3717.6351 216.1416 .9 3308.1049 203.8894 .9 3728.4500 216.4556 65.0 3318.3072 204.2035 69.0 3739.2807 216.7699 .1 3328.5253 204.5176 .1 3750.1270 217.0841 .2 3338.7590 204.8318 .2 3760.9891 217.3982 .3 3349.0085 205.1460 .3 3771.8668 217.7124 .4 3359.2736 205.4602 .4 3782.7603 218.0265 .5 3369.5545 205.7743 .5 3793.6695 218.3407 .6 3379.8510 206.0885 .6 3804.5944 218.6548 .7 3390.1633 206.4026 .7 3815.5350 218.9690 .8 3400.4913 206.7168 .8 3826.4913 219.2832 .9 3410.8350 207.0310 .9 3837.4633 219.5973 66.0 3421.1944 207.3451 70.0 3848.4510 219.9115 .1 3431.5695 207.6593 .1 3859.4544 220.2256 .2 3441.9603 207.9734 .2 3870.4736 220.5398 .3 3452.3669 208.2876 .3 3881.5084 220.8540 .4 3462.7891 208.6017 .4 3892.5590 221.1681 .5 3473.2270 208.9159 .5 3903.6252 221.4823 .6 3483.6807 209.2301 .6 3914.7072 221.7964 .7 3494.1500 209.5442 .7 3925.8049 222.1106 .8 3504.6351 209.8584 .8 3936.9182 222.4248 .9 3515.1359 210.1725 .9 3948.0473 222.7389 67,0 3525.6524 210.4867 71.0 3959.1921 223.0531 .1 3536.1845 210.8009 .1 3970.3526 223.3672 .2 3546.7324 211.1150 .2 3981.5289 223.6814 t .3 3557.2960 211.4292 .3 3992.7208 223.9956 .4 3567.8754 211.7433 .4 4003.9284 224.3097 .5 3578.4704 212.0575 .5 4015.1518 224.6239 .6 3589.0811 212.3717 .6 4026.3908 224.9380 .7 3599.7075 212.6858 .7 4037.6456 225.2522 .8 3610.3497 213.0000 .8 4048.9160 225.5664 . .9 3621.0075 21&3141 .9 4060.2022 225.8805 , AREAS and CIRCUMFERENCES OP CIRCLES. (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 72.0 4071.5041 226.1947 76.0 4536.4598 238.7610 .1 4082.8217 226.5088 .1 4548.4057 239.0752 .2 4094.1550 226.8230 .2 4560.3673 239.3894 4105.5040 227.1371 .3 4572.3446 239.7035 '.4 4116.8687 227.4513 .4 4584.3377 240.0177 .5 4128.2491 227.7655 .5 4596.3464 240.3318 .6 4139.6452 228.0796 .6 4608.3708 240.6460 .7 4151.0571 228.3938 .7 4620.4110 240.9602 .8 4162.4846 228.7079 .8 4632.4669 241.2743 .9 4173.9279 . 229.0221 .9 4644.5384 241.5885 73.0 4185.3868 229.3363 77.0 4656.6257 241.9026 .1 4196.8615 229.6504 .1 4668.7287 242.2168 .2 4208.3519 229.9646 .2 4680.8474 242.5310 .3 4219.8579 230.2787 .3 4692.9818 242.8451 .4 4231.3797 230.5929 .4 4705.1319 243.1592 .5 4242.9172 230.9071 .5 4717.2977 243.4734 .6 4254.4704 231.2212 .6 4729.4792 243.7876 .7 4266.0394 231.5354 "7 4741.6765 244.1017 .8 4277.6240 231.8495- 4753.8894 244.4159 .9 4289.2243 232.1637 .9 4766.1181 244.7301 74.0 4300.8403 232.4779 78.0 4778.3624 245.0442 A 4312.4721 232.7920 .1 4790.6225 245.3584 9 & 4324.1195 233.1062 .2 4802.8983 245.6725 .3 4335.7827 233.4203 .3 4815.1897 245.9867 .4 .4347.4616 233.7345 .4 4827.4969 246.3009 .5 4359.1562 234.0487 .5 4839.8198 246.6150 .6 4370.8664 234.3628 .6 4852.1584 246.9292 .7 4382.5924 234.6770 .7 4864.5128 247.2433 .8 4394.3341 234.9911 .8 4876.8828 247.5575 .9 4406.0916 235.3053 .9 4889.2685 1 247.8717 75.0 4417.8647 235.6194 79.0 4901.6699 248.1858 .1 ' 4429.6535 235.9336 .1 i 4914.0871 ! 248.5000 .2 4441.4580 236.2478 .2 ! 4926.5199 248.8141 .3 4453.2783 . 236.5619 .3 4938.9685 249.1283 .4 4465.1142 236.8761 .4 i 4951.4328 249.4425 .5 4476.9659 237.1902 .5 4963.9127 249.7566 .6 4488.8332 237.5044 .6 4976.4084 , 250.0708 .7 4500.7163 237.8186 .7 4988.9198 250.3850 .8 4512.6151 238.1327 .8 5001.4469 250.6991 .9 4524.5296 238.4469 .9 5013.9897 251.0133 J E AREAS and CIRCUMFERENCES OF CIRCLES. (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 80.0 5026.5482 251.3274 84.0 5541.7694 263.8938 .1 5039.1225 251.6416 .1 5554.9720 264.2079 .2 5051.7124 251.9557 .2 5568.1902 264.5221 .3 5064.3180 252.2699 .3 5581.4242 264.8363 .4 5076.9394 252.5840 .4 5594.6739 285.1514 .5 5089.5764 252.8982 .5 5607.9392 265.4646 .6 5102.2292 253.2124 .6 5821.2203 265.7787 .7 5114.8977 253.5265 .7 5634.5171 266.0929 .8 5127.5819 .253.8407 .8 5647.8296 266.4071 .9 5140.2818 254.1548 .9 5661.1578 266.7212 81.0 5152.9973 254.4690 85.0 5874.5017 267.0354 .1 5165.7287 254.7832 .1 5687.8614 267.3495 .2 5178.4757 255.0973 .2 5701.2367 267.6637 .3 | 5191.2384 255.4115 .3 5714.6277 267.9779 .4 5204.0168 255.7256 .4 5728.0345 268.2920 .5 ! 5216.8110 256.0398 .5 5741.4569 268.6062 .6 5229.6208 256.3540 .6 5754.8951 268.9203 .7 5242.4463 256.6681 .7 5768.3490 269.2345 .8 5255.2876 256.9823 .8 5781.8185 269.5486 .9 5268.1446 257.2966 .9 5795.3038 269.8628 82.0 5281.0173 257.6106 86.0 5808.8048 270.1770 .1 5293.9056 257.9247 .1 5822.3215 270.4911 .2 5308.8097 258.2389 .2 5835.8539 270.8053 .3 5319.7295 258.5531 .3 5849.4020 j 271.1194 .4 5332.6650 258.8672 .4 5862.9659 : 271.4336 .5 5345.6162 259.1814 .5 5876.5454 ! 271.7478 .6 5358.5832 259.4956 .6 5890.1407 : 272.0619 .7 5371.5658 259.8097 .7 5903.7516 1 272.3761 .8 5384.5641 280.1239 .8 5917.3783 1 272.6902 .9 5397.5782 260.4380 .9 5931.0208 i 273.0044 83.0 5410.6079 260.7522 87.0 i 5944.6787 ' 273.3186 .1 5423.6534 261.0663 .1 ' 5958.3525 i 273.6327 .2 5436.7146 261.3805 .2 5972.0420 ! 273.9469 .3 5449.7915 261.6947 .3 5985.7472 ; 274.2610 .4 5462.8840 262.0088 .4 5999.4681 274.5752 .5 5475.9923 262.3230 .5 6013.2047 274.8894 .6 5489.1163 262.6371 .6 6026.9570 275.2035 .7 5502.2561 262.9513 .7 i 6040.7250 ! 275.5177 .8 5515.4115 263.2655 .8 i 6054.5088 ! 275.8318 .9 5528.5826 263.5796 .9 6088.3082 : 276.1460 . AREAS and CIRCUMFERENCES OF CIRCLES, (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 88.0 6082.1234 276.4602 92.0 6647.6101 289.0265 .1 6095.9542 276.7743 .1 6662.0692 289.3407 .2 6109.8008 277.0885 .2 6676.5441 289.6548 .3 6123.6631 277.4026 .3 6691.0347 289.9690 .4 6137.5411 277.7168 .4 6705.5410 290.2832 .5 6151.4348 278.0309 .5 6720.0630 290.5973 .6 6165.3442 278.3451 .6 6734.6008 290.9115 .7 6179.2693 278.6593 .7 6749.1542 291.2256 .8 6193.2101 278.9740 .8 6763.7233 291.5398 .9 6207.1666 279.2876 .9 6778.3082 ! 291.8540 89.0 6221.1389 279.6017 93.0 6792.9087 I 292.1681 .1 6235.1268 279.9159 .1 6807.5250 292.4823 .2 6249.1304 280.2301 .2 6822.1569 292.7964 .3 6263.1498 280.5442 .3 6836.8046 293.1106 .4 6277.1849 280.8584 .4 6851.4680 293.4248 .5 6291.2356 281.1725 .5 6866.1471 293.7389 .6 6305.3021 281.4867 .6 6880.8419 294.0531 .7 6319.3843 281.8009 .7 6895.5524 294.3672 .8 6333.4822 282.1150 .8 6910.2786 294.6814 .9 6347.5958 282.4292 .9 6925.0205 294.9956 90.0 6361.7251 282.7433 94.0 6939.7782 295.3097 .1 6375.8701 283.0575 .1 6954.5515 295.6239 .2 6390.0309 283.3717 .2 6969.3106 295.9380 .3 6404.2073 283.6858 .3 6984.1453 i 296.2522 .4 6418.3995 284.0000 .4 6998.9658 296.5663 .5 6432.6073 284.3141 .5 7013.8019 296.8805 .6 6446.8309 284.6283 .6 7028.6538 297.1947 .7 6461.0701 284.9425 .7 7043.5214 297.5088 .8 6475.3251 285.2566 .8 7058.4047 297.8230 .9 6489.5958 285.5708 .9 7073.3033 298.1371 91.0 6503.8822 285.8849 95.0 7088.2184 298.4513 .1 6518.1843 ' 286.1991 .1 7103.1488 298.7655 .2 6532.5021 286.5183 .2 7118.1950 299.0796 .3 6546.8356 286.8274 .3 7133.0568 299.3938 .4 6561.1848 287.1416 .4 7148.0343 299.7079 .5 6575.5498 287.4557 .5 7163.0276 300.0221 .6 6589.9304 287.7699 .6 .7178.0366 300.3363 .7 6604.3268 288.0840 .7 7193.0612 300.6504 .8 6618.7388 288.3982 .8 7208.1016 300.9646 n - ' 9 6633.1666 288.7124 .9 7223.1577 301.2787 . AREAS and CIRCUMFERENCES OF CIRCLES. (CONTINUED.) Diam. Area. Circum. Diam. Area. Circum. 96.0 7238.2295 301.5929 98.0 7542.9640 1 307.8761 .1 7253.3170 301.9071 .1 7558.3656 , 308.1902 .2 7268.4202 302.2212 .2 7573.7830 ! 308.5044 .3 7283.5391 - 302.5354 .3 7589.2161 308.8186 .4 7298.6737 302.8405 .4 7604.6648 309.1327 .5 7313.8240 303.1637 .5 7620.1293 309.4469 .6 7328.9901 303.4779 .6 7635.6095 309.7610 .7 7344.1718 303.7920 .7 7651.1054 310.0752 .8 7369.3693 304.1062 .8 7666.6170 310.3894 .9 7374.5824 304.4203 .9 7682.1444 i 310.7035 97.0 7389.8113 304.7345 99.0 7697.6893 311.0177 .1 7405.0559 305.0486 .1 7713.2461 1 311.3318 .2 7420.3162 305.3628 .2 7728.8206 311.6460 .3 7435.5922 305.6770 .3 7744.4107 311.9602 .4 7450.8839 305.9911 .4 7760.0166 312.2743 .5 7466.1913 306.3053 .5 7775.6382 312.5885 .6 7481.5144 306.6194 .6 7791.2754 312.9026 ty 7496.8532 306.9336 .7 7806.9284 313.2168 .'s 7512.2078 307.2478 .8 7822.5971 313.5309 .9 7527.5780 307.5619 .9 7838.2815 313.8451 100.0 7853.9816 314.1593 To compute the area or circumference of a diameter greater than 100 and less than 1001 : ^Takeout the area or circumference from table as though the m^H&erliacl one decimal, and move the decimal point two places to the right for the area, and one place for the circumference. EXAMPLE Wanted the area and circumference of 567. The tabular area for 56.7 is 2524.9687; and circumference 178.1283. Therefore area of 567 = 252496.87 and circumference = 1781.283. To compute the area or circumference of a diameter greater than 1000: Divide by a factor, as 2, 3, 4, 5, etc., if practicable, that will leave a quotient to be found in table, then multiply the tabular area of the quotient by the sqtiare of the factor, or the tabular circumference by the factor. EXAMPLE Wanted the area and circumferenee of 2109. Dividing by 3, the quotient is 703, for which the area is 388150.84 and the circumference 2208.54. Therefore area of 2109 = 388150.84 X 9 = 3493357.56 and circumference = 2208.54 X 3 = 6625.62. 124 WEIGHT OF RIVETS, and ROUND HEADED BOLTS WITHOUT NUTS, PER 100. Length from under head. One cubic foot weighing 480 Ibs. Length. yi, 1 A" V %" W '' 1" l}" 1^" Inches. Dia. Dia. Dia. Dia. Dia. Dia. Dia. Dia. Ijf 5.4 12.6 21.5 28.7 43.1 65.3 91.5 123. 1/12 ; 6.2 13.9 23.7 31.8 47.3 70.7 98.4 133. IX 6.9 15.3 25.8 34.9 51.4 76.2 105. 142. 2 7.7 16.6 27.9 37.9 55.6 81.6 112. 150. 2^ ^ 8.5 18.0 30.0 41.0 59.8 87.1 119. 159. 2^1 9.2 19.4 32.2 44.1 63.0 92.5 126. 167. 10.0 20.7 34.3 47.1 68.1' 98.0 133. 176. 3 4 10.8 i 22.1 36.4 j 50.2 72.3 103. 140. .184. 3J4 11.5 23.5 38.6 53.3 76.5 109. 147. 193. 3X 12.3 24.8 40.7 56.4 80.7 114. 154. I 201. 3% 13.1 i 26.2 42.8 59.4 84.8 120. 161. i 210. 4 13.8 27.5 ; 45.0 62.5 \ 89.0 , 125. 167. ! 218. 4^ 14.6 i 28.9 ' 47.1 65.6 ! 93.2 131. 174. 227. 41^ 15.4 30.3 i 49.2 68.6 ! 97.4 136. 181. ; 236. 4% 16.2 31.6 51.4 71.7 102. 142. 188. 244. 5 16.9 33.0 53.5 74.8 106. 147. 195. 253. 5M 17.7 34.4 55.6 77.8 110. 153. 202. 261. 5)-^ 18.4 35.7 57.7 80.9 114. 158. ! 209. 270. 5% 19.2 37.1 59.9 84.0 118. 163. 216. 278. 6 20.0 38.5 62.0 87.0 122. 169. 223. 287. 6j 21.5 41.2 66.3 93.2 131. 180. 236. 304. 7 " 23.0 43.9 70.5 99.3 139. 191. 250. 321. 7/12 24.6 46.6 74.8 106. 147. 202. 264. 338. 8 26.1 49.4 79.0 112. 156. 213. 278. 355. S 1 ^ 27.6 52.1 83.3 118. 164. 223. 292. 372. 9" 29.2 54.8 87.6 124. 173. 234. 306. 389. 9}<2 30.7 57.6 91.8 130. 181. 245. 319. 406. 10 32.2 60.3 96.1 136. 189. 256. 333. 423. 1()1 33.8 63.0 101. 142. 198. 267. 347. 440. 11 35.3 65.7 105. 148. 206. 278. 361. 457. ll/^ 36.8 68.5 109. 155. 214. 289. 375. 474. 12 38.4 71.2 113. 161. 223. 300. 388. 491. Heads. 1.8 5.7 10.9 13.4' 22.2 38.0 57.0 82.0 v I "Yj UPSET SCREW ENDS FOR ROUND AND SQUARE BARS. Standard Proportions of the Keystone Bridge Company. Dia. of Round or Side of Square Bar. Inches. ROUND BARS. SQUARE BARS. Dia. of Upset Screw End. Inches. Dia. of Screw at Root of Thread. Inches. Threads per Inch. No. Excess of Effective Area of Screw End over Bar. Per Cent. Dia. of Upset Screw End. Inches. Dia. of Screw at Root of Thread. Inches. Excess of Threads i ^J 0< t over Bar. j Per Cent. A X .620 i 10 X -620 10 54 21 I .620 .731 10 21 9 33 If % .731 9 37 1 .837 8 48 i i .837 8 41 .837 8 17 it 1 .837 8 1M .940 i 7 25 34 W .940 7 1.065 7 23 35 i! IK ! 1.065 7 W ! 1.065 7 48 29 1 1.160 6 1.160- 6 38 20 i IA IK 1-160 6 1% 1-160 6 35 19 ! 1.284 6 1.389 5^ 29 34 j 1)1 1.284 1.284 6 6 30 17 IS 1.389 5^ 1.490 5 20 24 IA }| 1.389 1.490 5 2 23 29 11 1.615 1.615 5 5 31 19 }g i 1.490 1.615 5 5 18 26 2 1.712 1.837 *& 22 28 IA 2 2 1.712 1.712 $ 36 20 1! 1.837 1.962 *& 18 24 iff % 1.837 1.837 $ 28 18 If 2.087 2.087 4K 80 20 Iff. 3$ 1.962 1.962 *% 26 17 9 1/ 673 2.175 2.300 4 4 21 26 i S* 2,087 2.175 4 2 24 26 i 2.300 2.425 4 4 18 23 2 If 2.175 i 4 2.300 4 18 24 2% 2.550 2.550 4 4 28 20 1 2.300 2.425 j 4 17 23 fc. 2.629 2.754 1 20 24 ^TJ UPSET SCREW ENDS. (CONTINUED.) Dia. of ROUND BARS. SQUARE BARS. Round or Side of Square Bar. Inches. Dia. of Dia. of Upset Screw at Screw Root of End. ; Thread. Inches. Inches. Threads per Inch. No. Excess of Effective Area of Screw End over Bar. Per Cent. Dia. of Upset Screw End. Inches. Dia. of Screw at Root of Thread. Inches. Threads per Inch. No. Excess of Effective Area of Screw End over Bar. Per Cent. ~2K~ 2 7 2.550 4 28 m 2.754 3K 18 2fV 2% 2.550 4 22 3% 2.879 3/1 22 gS/ 3 2.629 3^ 23 3% 3.004 3K 26 gJL 3)8 2.754 3>2 28 3.004 3jl> 19 l% 3^5 2.754 21 3M 3.100 3^ I 21 3}^ 2.879 3J 26 3^ 3.225 3K 24 2% 3i/ 2.879 3> 20 3% 3.225 314 19 3K 3.004 3K 25 8g 3.317 3 20 2% 3/8 3.004 3/ 19 3K 3.442 3 , 23 3> 3.100 3^ 22 % 3.442 3 18 2% 3% 3.225 3^f 26 4 3.567 3 21 3.225 3K 21 413 3.692 3 24 3 32/ 3.317 3 22 4 3 8 ' 3.692 3 19 3% 3.442 3 21 3.923 2% 24 3L/ ! 4 3.567 3 20 4% 4.028 2% 21 3M 4>8 3.692 3- 20 4%$ 4.153 19 3^ 414 '3.798 2% 18 3% 4/i> 4.028 23 3K w 4.153 2% 23 3% . K 4.255 m 21 EEMARKS. As upsetting reduces the strength of iron, bars having the same diameter at root of thread as that of the bar, in- variably break in the screw end, when tested to destruction, without developing the full strength of the bar. It is therefore necessary to make up for this loss in strength by an excess of metal in the upset screw ends over that in the b ar. The above table ii ! the ree tilt of numerous tests on finished bars made at the Keystone Bridge Company's Works in Pittsburgh, and gives proportions that will cause the bar to break in the body in preference to the upset end. The screw threads in above table are the Franklin Institute standard. To make one upset end for 5" length of thread allow 6" length of rod additional. 197 4 STANDARD SCREW THREADS, NUTS AND BOLT HEADS. Recommended by the Franklin Institute. SCREW THREADS. Nuts and Bolt Heads A?/ ^ ^ ,m are determined by the fol- /^ll^a .0 /^ll^ o j //|l||k. lowing rules, which apply to " ^ /^HlK. Square and Hexagon Nuts both : ^^^^^^J^^^^^^^^^^^^^^^^^^^^ Short diameter of rough nut Angle of Thread 60. Flat at Top and Bottom^ % of pitch. = IJ^ x dia, of bolt - y 3 in. Dia. of Dia. at Root Threads Short diameterof finished nut Screw. of Thread. per Inch. = V :< dia. of bolt + 1-18 in. Inches. Inches. No. Thickness of rough nut i/ .185 20 = diameter of bolt. 5 .240 18 Thickness of finished nut % .294 16 = diameter of bolt 1-16 in. T^ff .344 14 Short diameter of rough head y .400 13 = 1^ X dia. of bolt -f %in. ^ .454 12 Short dia. of finished head %, .507 11 =1% x dia. of bolt - 1-16 in. % .620 10 Thickness of rough head % .731 9 = y 2 short dia. of head. I .837 8 Thickness of finished head .940 7 = dia. of bolt 1-16 in. 1% 1.065 7 The long diameter of a 1% 1.160 6 hexagon nut may be obtained \y 1.284 6 by multiplying the short \y 1.389 diameter by 1.155, and the 1 3/ 1.490 5 long diameter of a square 10 1.615 5 nut by multiplying the short 2 1.712 diameter by 1.414. 1.962 4 1/ The above standards for 23^ 2.175 4 /2 screw threads, nuts and bolt fc>/2 2.425 4 heads, were recommended by /4 the Franklin Institute in 3 2.629 aorrrk 3K Dec. 1864. The standard for 3/^ .879 31 r\/\ 3/2 screw threads has been very i| .100 3.317 3 4 generally adopted in the United States, but the pro- 4 3.567 3 portions recommended for 4M 3.798 2 nuts and bolt heads have not 4f^ 4.028 found general acceptance be- 4% 4.255 *& cause of the odd sizes of bar 5 4.480 2> not usually rolled by the 5^ 4.730 2M mills which they would re- 5K 5.053 m quire from which to make 5% 5.203 the nut. . 6 ! 5.423 2M X WHITWORTH'S STANDARD ANGULAR SCREW THREADS. Angle of Thread 55. Depth of Thread = pitch of screw. Y & of depth is rounded off at to and bottom. p Number of threads to the inch in square threads = ^ the "number in angular threads. Dia, of ; Threads Screw, to the Inch. In. No. Dia. of Screw. In. Threads to the Inch. No. Dia. of Screw. In. Threads to the Inch. No. Dia. of Screw. In. Threads to the Inch. No. 1-4 20 1 8 2 4 1-2 4 3 5-16 i 18 1 1-8 7 2 1-4 4 4 1-4 2 7-8 3-8 16 1 1-4 7 2 1-2 4 4 1-2 2 7-8 7-16 : 14 1 3-8 6 23-4 3 1-2 4 3-4 2 3-4 | 1-2 i 12 11-2 6 3 3 1-2 5 2 3-4 5-8 11 1 5-8 5 3 1-4 3 1-4 5 1-4 2 5-8 3-4 10 1 3-4 5 3 1-2 3 1-4 5 1-2 2 5-8 7-8 9 1 7-8 4 1-2 3 3-4 3 5 3-4 2 1-2 6 2 1-2 WOOD SCREWS. Diameter = number X 0.01325 -f 0.056. No. Dia. No. Dia. No. Dia. No. Dia. No. Dia. 1 2 3 4 5 .056 .069 .082 .096 .109 .122 6 7 8 9 10 11 .135 .149 .162 .175 .188 .201 12 13 11 16 17 .215 .228 .241 .255 .268 .281 18 19 20 21 22 23 .293 .308 .321 .334 .347 .361 24 25 26 27 28 29 30 .374 .387 .401 414 .427 .440 .453 TACKS. Title. fe Length. In. No., per Ib. Title. Oz. Length. In. No. perlb. Title. Oz. Length. In. No. perlb. Title. Oz. Length. In. No. perlb. i 1 1-2 2 21-2 1-8 3-16 1-4 5-16 16000 10666 8000 6400 3 4 6 8 3-8 7-16 9-16 5-8 5333 4000 2666 2000 10 12 14 16 11-16 3-4 13-16 7-8 1600 1333 1143 1000 18 20 22 24 15-16 1 - 1 1-16 1 1-8 888 800 727 666 WROUGHT SPIKES. Number to a keg of 150 Ibs. In. / in. No. 3 2250 3 1-2 1890 4 i 1650 4 1-2 1464 5 1380 6 1292 n. o. 1135 1064 742 570 Length. In. v- 1161 in. 635 573 455 424 391 445 384 270 249 256 240 322 129 ? r. SIZES AND WEIGHTS OF HOT PRESSED SQUARE NUTS. As manufactured by Charles & McMurtry, Pittsburgh, Pa. The sizes are the usual manufacturers', not the Franklin Institute Standard. Both weights and sizes are for the unfinished Nut. Size of 1 Weight of Rough Thickness Side of n: i 1 No. of Nuts in Bolt. 1 One Nut. Hole. of Nut. Square. 100 Ibs. . K -014 .7 H K .71 6900 A H .029 .048 ft Ps 1 .88 1.06 3450 2080 A .078 H _7_ K 1.24 1280 P .088 & y* 1.24 1140 .116 T V % 1 1.41 860 1 _9 .161 % i IK 1.59 620 y% .172 9 % 1/8 1.59 580 H .22 ft % ik 1.77 460 %. .31 H % IX 1.94 320 % .38 f 1 H 2.12 260 i/ .56 If IM 2.30 180 % .63 If H IX 2.47 160 1 .69 % i IK 2.47 144 l .91 Js i 2 2.83 110 IK 1.00 It l/'S 2 2.83 100 1.43 it 1)1 2^ 3.18 70 1& 1.54 lyV IK 2^ 3.18 65 lx^ 1.79 ly 1 ^ IK 2/^ 3.54 56 1>8 2.4 I* 2^ . 3.89 42 IK 3.1 1ft 'i 1 ^ 3 4.24 32 4.0 ift i|S 31^ 4.60 25 i| 5.0 5.9 iii L P ii 4.95 5.30 20 17 2 7.1, iff 2 4 5.66 14. 7.4 1% 4 5.66 13.5 2^ 8.1 2 2^ 4^ 6.01 12.3 2% 8.3 2K 2% 41^ 6.01 12.0 2y z 10.9 2/2 2/^ 4^ 6.36 9.14 2% 13.2 2 T V 2^ 4^ 6.72 7.55 3 14.9 aj| 3 5 7.07 6.72 3^ ! 17.5 31^ 5j^ 7.78 5.70 : SK-. 121.1 3/8 3K 6 8.49 4.75. iS ' SIZES AND WEIGHTS OP HOT PRESSED HEXAGON NUTS. As manufactured by Charles & McMurtry, Pittsburgh, Pa. The sizes are the visual manufacturers', net the Franklin Institute Standard. Both weights and sizes are for the unfinished Nut. M Size of * Belt. Weight of One Nut. Rough Thickness Hole. of Nut. Short Diameter. Long Diameter. No. of Nuts in 100 Ibs. ~77 .013 ,', H I./ .58 8000 A .026 "K A ^ .72 3840 3> .042 M K .87 2400 A .071 P TV % 1.01 1400 I/ .069 & 1 / Js 1.01 1440 k .100 M 1 1.15 1000 A .161 }l A iNf 1.30 620 M .147 9 ^ 1?8 ' 1.30 680 /N} .200 T 9 G M 1'4 1.44 500 5/ ts& li y lx^ 1.44 53 7 '23 % .26 f? 3 4 1^8 1.59 380 3/ .33 % 11^ 1.73 300 7X .45 J5/ 1.88 220 % .53 25 3 2 i , 1M 1.88 190 1 .59 J i IK 2.02 170 1 .63 ]_?8 2.02 160 1 L 3 .95 it 1M 2 /4 2.31 105 l 1 ^ 1.43 IT a 1^8 2^ 2.60 70 13/ 1.64 JJL l 1 ^ 2^ 2.89 61 1& 2.4 1& 1M 2% 3.18 42 1 5 8 3.0 i'A IK 3 3.46 33 1/4 3,7 1A 1/8 3M 3.75 27 U-8 4.8 IT! 2 4.04 21 2 4.5 Iff 2 31 / 4.04^ 22 5.1 1% 3/1 4.33* 19.5 2>4 5.4 2 2K 3% 4.33 18.4 2 3 6.3 2^ 2% 4 4.62 15.84 2'4 7.6 2K' 4 1 4 4.91 13.11 2% , 9.3 2^ 2^, 4)^ 5.20 10.80 3 11.8 2|-i 3 4% 5.48 8.46 3*4 15.9 2tf 31^ 5 5.77 6.30 3! CC OO T IT IT-" GvJCOlOCOJN- '^is.aS, .looc^-co =^^'a?"-;iOo " C ,g \ "** ^ ,3o^> r -- -^f lO T-< CO I s - IN- CO ^ 10 co oq os cooqo"? Anstver : Bending moment = 20000 Ibs. x 2> == 50000 inch Ibs., therefore %% pin required for 15000 Ibs. fiber strain, since the allowed moment for 3>(" = 50600, as per table. Required the thickness of metal in the top chord or in a post of a bridge, that will give sufficient bearing area to a 3^ ;/ pin, having to transmit a stress of 63300 Ibs., the allowed pressure per square inch on bearing being 12500 Ibs. maximum. The bearing value of a 3^ /x pin for \" thickness of plate = 42200 Ibs., therefore the thickness of metal required l/^'j r each of the two plates in the chord or post will have to be " thick. 134 o ; -3 ooo t>CO CO-^ IOI> (M (MOO lOi-H 10 (M 10 (MOO lOi-H C^CO CD (MOO COCO l>00 0005 OO rHiH 135 MAXIMUM BENDING MOMENTS TO BE AL- LOWED ON PINS TOR MAXIMUM FIBER STRAINS OF 15000, 20000 AND 22500 LBS. PER SQUARE INCH. Diam. of Pin. Inches. Moment for 8 = 15000. Lbs. in. Moment for S = 20000. Lbs. in. Moment for S = 22500. Lbs. in. Diam. of Pin. Inches. Moment 1 Moment Moment for for for S = 15000. S = 20000. S = 22500. Lbs. in. j Lbs. in. Lbs. in. 1 1470 1960 2210 4 94200 125700 14140O 1 2100 2800 3140 4M 103400 137800 155000 1# 2880 3830 4310 4 1 4 H13000 150700 169600 IK 3830 5100 5740 4% 123300 164400 18500O IX 4970 663O 7460 4* 134200 178900 201300 1% 6320 8430 9480 4* 14570O 194300 21850O i% 7890 10500 11800 4% 157800 21O400 23670O i% 9710 12900 14600 4^ 170600 227500 255900 2 11800 15700 17700 5 184100 245400 276100 2# 14100 18800 21200 5M 198200 264300 29730O 2^ 16800 2240O 25200 5# 213100 284100 319600 2% 19700 26300 29600 5% 228700 304900 34300O 2# 23000 30700 34500 &x 245000 326700 367500 2% 26600 35500 40000 5% 262100 349500 39310O 2M 30600 40800 45900 5% 280000 373300 419900 2% 35000 46700 52500 5% 2986OO 398200 44790O 3 39800 53000 59600 6 318100 424100 477100 3^ 44900 59900 67400 8M 338400 451200 507600 3^ 50600 67400 75800 8 3595OO 479400 53930O 3% 56600 75500 84900 6% 381500 5087OO 572300 33^ 63100 84200 94700 Q 1 A 404400 539200 606600 3% 70100 93500 105200 6% 428200 57090O 64230O 3M 77700 103500 116500 6M 452900 603900 679400 3% 85700114200128500 m 478500 638000 71780O REMARKS The following is the formula for flexure applied to pins: M= moment of forces for any section of the pin. % S = strain per sq. in. in extreme fibers of pin at that section. A=area of section. d= diameter. 7T=3.14159. The forces are assumed to act in a plane passing through the axis of the pin. The above table gives the values of M for different diameters of pin, and for three values of S. If M max. is known, an inspection of the table will therefore show what diameter of pin must be used, in order that 12500 Ibs. 15000 Ibs. square In'ches. per square inch. ; per square inch. Lbs. Lbs. .785 .994 1.227 1.485 1.767 12500 14100 15600 17200 18800 15000 16900 18800 20600 22500 ! 5 /8 i 2 2.074 2.405 2.761 3.142 | 20300 21900 23400 25000 24400 26300 28100 30000 2# 2M 2& 2# 3.547 3.976 4.430 4.909 26600 28100 29700 31300 31900 33800 35600 37500 2^ 2% 2% 3 5.412 5.940 6.492 7.069 32800 34400 35900 37500 39400 41300 43100 45000 3' 8 ' 3% 3% 3J 8 X 7.670 8.946 10.32 11.79 39100 42200 45300 48400 46900 50600 54400 58100 4 1 8 m m 4 7 8 x 13.36 15.03 16.80 18.67 51600 54700 57800 60900 61900 65600 69400 7310O 5M m 5H SH 20.63 22.69 24.85 27.11 64100 67200 70300 73400 78900 80600 84400 88100 8? B X 6M 6% 6. 7 ' 8 29.46 31.92 34.47 37.12 76600 91900 79700 95600 82800 99400 85900 103100 WOODEN BEAMS. Safe Load, Uniformly Distributed, for Rectangular White or Yellow Pine Beams one inch thick, allowing 1200 Ibs. per square inch fiber strain. To obtain the safe load for any thickness, multiply the safe load given in table, by the thickness of beam. To obtain the required thickness for any load, divide by the safe load for 1 inch, given in table. a "* -^s DEPTH OF BEAM. 6" 7// 8" 9" 10" 11" 12" 13" 14// 15" 16" Feet. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. 5 960 1310 1710 2160 2670 3230 3840 4510 5230 6000 6830 6 800 1090 1420 1800 2220 2690 3200 3760 4360 5000 5690 7 690 930 1220 1540 1900 2300 2740 '3220 3730 4290 4880 8 600 820 1070 1350 1670 2020 2400 2820 3270 3750 4270 9 530 730 950 1200 1480 1790 2130 2500 2900 3330 3790 10 480 650 850 1080 1330 1610 1920 2250 2610 3000 3410 11 440 590 780 980 1210 1470 j 1750 2050 2380 2730 3100 12 400 540 710 900 1110 1340 1600 1880 2180 2500 2840 13 370 500 660 830 1030 1240 1480 1730 2010 2310 2630 14 340 470 610 770 950 1150 1370 1610 1870 2140 2440 15 320 440 570 720 890 1080 1280 1500 1740 2000 2280 16 300 410 530 680 830 1010 1200 1410 1630 1880 2130 17 280 380 500 640 780 950 1130 1330 1540 1760 2010 18 270 360 470 600 740 900 1070 1250 1450 1670 1900 19 250 340 450 570 700 850 1010 1190 1 1380 1580 1800 20 240 330 430 540 670 810 960 1130 1310 1500 1710 21 230 310 410 510 630 770 910 1070 1240 1430 1630 22 220 300 390 490 610 730 870 1020 1190 1360 1550 23 210 280 370 470 580 700 830 980 1140 1300 1480 24 200 270 360 ; 450 560 670 800 940 1090 1250 1420 25' 190 260 340 430 530 650 770 900 1050 1200 1370 26 180 250 330 420 510 620 740 870 1010 1150 1310 27 180' 240 320 400 500 600 710 830 970 1110 1260 28 170! 230 300 390 480 580 690 800 930 1070 1220 29 1701 230 390 370 460 560 660 780 900 1030 1180 '4 Si EXPLANATION OF TABLES ON MAXIMUM STRESSES IN PRATT AND WHIPPLE TRUSSES. Pages 141 to 143, inclusive. These tables give the stress in each member of a Pratt (single quadrangular) or Whipple (double quadrangular) truss, for any number of panels not exceeding twelve in the former, and twenty in the latter case, on the assumption that the load is uniform per foot, and the panels are all of the same length. The stresses are given in terms of the truss-panel dead and moving loads, repre- sented respectively by W and L. These are obtained by multi- plying the dead load per foot of bridge, in the case of W, and the moving or live load per foot of bridge, in the case of L, by half the panel length. The letters W and L are placed at the top of column, in tables, and not next to the figures to which they belong, for want of space. The stress in aB, for example, in a twelve panel Pratt truss, = 5.5 W X 5.5 L, and in Be = 4.5 W X f | L, both multi- plied by the quotient specified in the last column. The system of lettering employed is shown by Figs. 7 and 8, on page 26 of the lithographs, and, it is believed, is the best in use. By making a sketch of the truss under consideration and lettering the vertices in the manner shown, the truss members to which reference is had in the tables, can be readily identified. In the following tables, "the dead load is assumed as concen- trated at the lower vertices of the trusses, for through bridges, and at the upper vertices, for deck bridges. For through bridges of very large span, the stresses thus obtained for the posts must be increased by the truss-panel weight of the upper portion of the truss, including the lateral bracing; but in small spans, the increase of stress on this account is so inconsiderable that it is usually neglected. Note : In order to calculate the stresses in a Whipple or double quadrangular truss by statical methods, it is necessary to consider the truss as the combination of two Pratt trusses or single systems of bracing, and assume that each of these two systems is strained in the same manner as if one were independent of the other. If the number of panels is odd, each of the two systems is unsym- metrical, which has the effect of making the stress in the middle panel of the lower chord slightly smaller than the stress in the corresponding panel of the top chord. To avoid this peculiarity and obtain equal stresses in these members, a division into sym- metrical systems is sometimes assumed for the dead load stresses and for the full load, by considering the counter ties canceled. For the live load stresses obtained by partial loading, however, it is again necessary to divide into unsymmetrical systems, so that, while there appears to be no good reason in favor of this method, it has the objection of inconsistency. The difference in the resulting stresses obtained by the two methods is so small as not to be of practical consequence. Each of the two systems is assumed to carry one-half of the panel load at the top of the inclined end posts. ILLUSTRATION OF APPLICATION OF TABLES, ALSO OF THE USE OF TABLE OF NATURAL SINES, TANGENTS AND SECANTS. A Pratt truss of 135' span and 18' depth, is divided into nine panels of 15' each. Required the stress in first main tie Be, and in middle panel DE of top chord, for a dead load of 1200 Ibs. and a moving load of 3000 Ibs. per lineal foot of bridge. 1900 W = ~- x .15 = 9000 Ibs. -^i x 15 = 22500 Ibs. Q / /> -IO DE=(10W + 10 L)-j|- The factor -^r- , or panel length divided by depth of truss, is lo the tangent of the angle, for which the length Be, divided by depth of truss, is the secant. By table of natural sines, tangents and secants, for tangent = - = 0.833, the secant = 1.302; lo therefore Be == 97000 X 1.30 = 126100 Ibs. DE = 315000 X -j|~ = 262500 Ibs. 140 :5 MAXIMUM STRESSES UNDER DEAD AND MOVING LOADS IN PRATT OR SINGLE QUADRANGULAR TRUSSES With inclined end posts and equal panel 3, for Through and Deck Bridges. W = deac 1 load and L = moving load per truss and per panel. Member. 12 Panel 11 Panel Truss. Truss. 10 Panel Truss. 9 Panel 8 Panel Truss. , Truss. Multi- ply by: W+L W+L W+L W+L W+L aB 5.5+5.5 5+5 4.5+4.5 4_1_4 3.5+3.5 1 Be 4.5+f! 4+ff 3.5+3.6 8+Vi 2.5+ V Cd 3.5+fl 3+ff 2.5+2.8 2+V; 1.5+ V 6* De 2.5+f| ! 2+ff- 1.5+2.1 1+V 5 | 0.5+ V 'a s Ef 1.5+|4 1 H -ff 0.5+1.5 O+io -0.5+f Pg 0.5+f| I 0+H -0.5+1.0 -1+ f -1.5+ f Gh -0.5-1 -15, ! _1_| ~TT -1.5+0.6 -2+ 1 -& Hi -1.5- -[H -2H -TT I abc 5.5+ 5.5 5+ 5 4.5-| - 4.5 4H - 4 3.5H -3.5 o BO, cd 10.0+10.0 9+ 9 ' 8.0- - 8.0 7- - 7 6.0- -6.0 |f . CD, de 13.5+13.5 12+12 10.5- -10.5 9- - 9 7.5- -7.5 DE, ef 16.0+16.0; 14+14 12.0- -12.0 10- -10 8.0H -8.0 1^"^ EF, fg 17.5+17.5 15+15 12.5- -12.5 <:i FG 18.0+18.0 Thro'. Deck. Cc 4.5-| -ff 44 -f 3.5- h3.6 3H r 2.5+ V Cc, Dd 3.5- 4 2.5- -2.8 -V 1.5+ V Dd, Ee 2.5- _3.i 2-1 4 1.5- -2.1 1- rV 0.5+ V > Be, Ff 1.5- rl! 1+1 0.5- -1.5 o+v -0.5+ | ti Ff; Gg 0.5- 4i o+l- -0.5- -1.0 -0.5+M Member. 7 Panel Truss. 6 Panel Truss. I 5 Panel Truss. 4 Panel Truss. 3 Panel Truss. Multi- ply by: W+L W+L W+L W+L W+L aB 3+3 2.5-1 -2.5 2+2.0 1.5+1.51 1+1 Jui Be 24 -v 1.5- rV 1+1.2 0.5+ | i s^^ Cd 1_| -V 0.5- -1.0 0+0.6 -0.5+ J 1 o-3' s De 0- _ 6. -0.5- -0.5 -1+0.2 tf Ef -1- -f g * abc 3+3 2.5+2.5 2+2 1.5+1.5 1+1 f-^i BC, cd 5+5 4.0+4.0 3+3 2.0+2.0 1+1 3 "2? CDE,de 6+6 4.5+4.5 Thro'. De&k. Cc 2H - 1.5+ V 1+1.2 0.5+f Cc, Dd 1- -V 0.5+1.0 0+0.6 -0.5+ i jj r, Dd 2+| -0.5+0.5 '3 MAXIMUM STRESSES UNDER DEAD AND MOVING LOADS IN WHIPPLE OR DOUBLE QUADRANGULAR TRUSSES With inclined end posts and equal pane .s, for Through and Deck Bridges. W = dead load and L = moving ioad per truss and per panel. TUT 1. 20 Panel 19 Panel 18 Panel ! 17 Panel 16 Panel a^ Member. Truss. Truss. Truss. Truss. Truss. ^a W+L W+L W+L W+L W+L aB 9.5+9.5 9+9 8.5-1 -8.5 8+8 7.5+7.5 Be 4.5- - 9^5 - .0 _j_8^5 -W ff+W 3.5+ T G ,f ^ Bd 4.0- "JKi t+W 3.5- -w 5.6. +5^ 3-0+ *i "S Ce 3.5- f- e r 3.0- -W 16. -j-' 1 ^"' 2.5H hW f Df 3.0- ~^t' ' <; - _565 2.5- - 4 ft 5 H+W 2.0- -W ^ | Eg 2.5- -w r- - -W 2.0- -y -g- j y y | 3 Ty- 1.5- _3_05 J^ Fh 2.0- _4J^5 1.- 1.5- _ 35.5 1 2. _j_ 3^0 fr 5 1.0- -W S S _ca Gi 1.5- -W -f- -w 1.0- - 3 r 1.2 _[_ 2 4^5 0.5H -20.5 II Hk 1.0- -w i+j T 0.5- -t 5 fV ~l~ 2 f*" 0.0+ W 11 0.5- -S 0.0- -w-^v+w -0.5+ W Km 0.0- \ + ? T ir -0.5- -W-if+W -1.0+ -J-f 3 Ln -0.5+ ^ 41 4- W -1.0- -Wrff+4'f Mo -1.0+ i}t 5 -ft+ l r abc 9.5+ 9.5 9+9 8.5+ 8.5 8-f -8 7.5+7.5 cd 14+14 WH ~w 12.5+12.5 WH -W 11+11 ^> BC, de 22- -22 \ -3_9^5 19.5+19.5 3 T V- -w 17+17 -a CD, ef 29- -29 5 TV^ - 5 T y 25.5+25.5 W- 22- -22 | | DE, fg 35- -35 6 T ^-4 - 6 T 30.5+30.5 W- -w 26- -26 ^C^ EF, gh 40- -40 w- -W 34.5+34.5 5 T 3 7 9 - _5_39 29- -29 ^^ FG, hi 44- -44 w- -W 37.5+37.5 W+W 31- -31 J & GH, ik HI, kl 47- 49- -47 -49 W J w- "S* 39.5+39.5 6 T y+TV* 40.5+40.5 W+ 6 T y 32- HI= -32 =GH r IKL 50- -50 VM ,1 IK=HI ^k Thro'. Deck. ii T+W W+7 7 Cc 4.5H hW - .0 _j_ 8^5 4.0+ W ff - ~6ft 5 3.5H - 5 -r Dd 4.0- -W f + ^V 5 3.5+fift 5 if ~ ~ ft 5 3.0- -w Cc, Be 3.5- -w i+W 3.0+ 5f ^ ff ~ -'ft 5 2.5- Dd, Ff 3.0- -8fjS 1 _j_ 5^ 2.5-f f 7 ~ '-ft 5 2.0- " S T ^ Ee, Gg 2.5- _5j>^5 t+ 4 T ~7 - _3_5.5 1.5- _30.5 '"a Ff| Hh 2.0- ~~M f+W 1.5-| _3^?5 T7~ - 3 ft 5 1.0+ 4 3 Gg, li 1.5- I+W i.o+ 3 f? T7~ -w 0.5+ W Hh, Kk 1.0- -4v il+W ^ +2^ 0.0+ i t li, LI 0.5- -w T\+ 3 T o!o+w -^-[-IfyS -0.5+ W Kk 0.0- -W-iV+W -1^^5 .LI -0.5+ S ; MAXIMUM STRESSES UNDER DEAD AND MOVING LOADS IN WHIPPLE OR DOUBLE QUADRANGULAR TRUSSES With inclined end posts and equal panels, for Through and Deck Bridges. W = dead load and L = moving load per truss and per panel. Member. 15 Panel Truss. W+L 14 Panel Truss. W+L W+L 6.5+6.5 2.0+^! 1.5+2 1.0+ 0.5+1 0.0+ J 7+7 W+W W+W W+W ; V+^ 3 6.5+ 6.5 6+6 9.5+ 9.5; W+W 14.5+14.5 n * 18.5+18.5 21.5+21.5 23.5+23.5, , 24.5+24.5! W+ 2 T V ~ - ~~=FG 4.24.5 It5 i 15.0+16.0 W+ 17.0+17.0! " 18.0+18.0' W+ FG=EF 2.5-[_30 y5 2.0+ wi W+W 2^5 1.0+1 __^s 0.5+1 --W o.o- -r 4 T+4-f -0.5+-' 143 +-W 1 NATURAL SINES , TANGENTS AND SECANTS , Advancing by 1O min. Beg. Min. 00 10 20 Sine. Tangent. Secant. Deg. Min. Sine. Tangent. ! Secant. ! 4 .0000 .0000 .0029 .0029 .0058 .0058 1.0000 1.0000 1.0000 5 00 .0872 10 .0901 20 .0929 .0875 .0904 .0934 1.0038 1.0041 1.0043 30 4fc 50 .0087 .0087 .0116 .0116 .0145 .0145 1.0000 1.0001 1.0001 30 40 50 ;0958 .0987 .1016 .0963 .0992 .1022 1.0046 1.0049 1.0052 1 00 10 20 .0175 .0175 .0204 .0204 .0233 .0233 1.0002 1.0002 1.0003 6 00 10 20 .1045 .1074 .1103 .1051 .1080 .1110 1.0055 1.0058 1.0061 30 40 50 .0262 .0262 .0291 .0291 .0320 .0320 1.0003 1.0004 1.0005 30 40 50 .1132 .1161 .1190 .1139 .1169 .1198 1.0065 1.0068 1.0072 2 00 10 20 .0349 .0349 .0378 i .0378 .0407 | .0407 1.0006 1.0007 1.0008 7 00 10 20 .1219 .1248 .1276 .1228 .1257 .1287 1.0075 1.0079 1.0082 30 40 50 .0436 .0437 .0465 .0466 .0494 .0495 1.0010 1.0011- 1.0012 30 40 50 .1305 .1334 .1363 .1317 .1346 .1376 1.0086 1.0090 1.0094 3 00 10 20 .0523 .0524 .0552 .0553 .0581 .0582 1.0014 1.0015 1.0017 8 00 10 20 .1392 .1421 .1449 .1405 .1435 .1465 1.0098 1.0102 1.0107 30 40 50 .0610 .0612 .0640 .0641 .0669 .0670 1.0019 1.0021 1.0022 30 40 50 .1478 .1507 .1536 .1495 .1524 .1554 1.0111 1.0116 1.0120 4 : 00 ' .0698 .0699 ; 10 ; .0727 .0729 | 20 .0756 .0758 1.0024 1.0027 1.0029 9 00 10 20 .1564 .1593 .1622 .1584 .1614 .1644 1.0125 1.0129 1.0134 30 .0785 .0787 40 i .0814 .0816 | 50 i .0843 .0846 ft. -1 ' 1.0031 1.0033 1.0036 30 1 40 50 .1650 I .1673 1 1.0139 .1679 i .1703 1.0144 .1708 i .1733 1.0149 > NATURAL SINES, TANGENTS AND SECANTS. Min. Sine. (CONTINUED.) Deg. 10 Tangent. Secant. Deg. Min. Sine. Tangent. Secant. 00 .1736 10 .1765 20 .1794 .1763 1.0154 .1793 1.0160 .1823 1.0165 15 00 10 20 .2588 .2679 1.0353 .2616 .2711 1.0361 .2644 .2742 1.0369 i 30 .1822 ! 40 .1851 ; 50 .1880 .1853 1.0170 .1883 1.0176 .1914 1.0181 30 40 50 .2672 ! .2773 1.0377 .2700 .2805 1.0386 .2728 .2836 1.0394 11 00 .1908 10 .1937 20 .1965 .1944 1.0187 .1974 1.0193 .2004 1.0199 16 00 10 20 .2756 .2784 .2812 .2867 1.0403 .2899 : 1.0412 .2931 1.0421 * 30 .1994 40 .2022 50 .2051 .2035 1.0205 .2065 1.0211 .2095 1.0217 30 40 50 .2840 .2868 .2896 .2962 .2994 .3026 1.0429 1.0439 1.0448 12 00 .2079 10 .2108 20 .2136 .2126 1.0223 .2156 1.0230 .2186 1.0236 17 00 10 20 .2924 .2952 .2979 .3057 .3089 .3121 1.0457 1.0466 1.0476 30 .2164 40 .2193 50 .2221 .2217 1.0243 -.2247 .1.0249 .2278 1.0256 30 40 50 .3007 .3035 .3062 .3153 .3185 .3217 1.0485 1.0495 1.0505 13 00 .2250 10 .2278 20 .2306 .2309 1.0263 .2339 1.0270 .2370 1.0277 18 00 10 20 .3090 .3118 .3145 .3249 .3281 .3314 1.0515 1.0525 1.0535 30 .2834 40 .2363 50 .2391 .2401 1.0284 .2432 1.0291 .2462 1.0299 30 40 50 .3173 .3201 .3228 .3346 .3378 .3411 1.0545 1.0555 1.0566 14 00 .2419 10 .2447 20 .2476 30 .2504 40 i .2532 50 : .2560 i .2493 1.0306 .2524 1.0314 .2555 1.0321 .2586 1.0329 .2617 1.0337 .2648 1.0345 19 00 10 20 30 40 50 .3256 .3283 .3311 .3338 .3365 .8393 .3443 '.3476 .3508 .3541 .3574 .3607 1.0576 1.0587 1.0598 1.0608 1.0619 1.0631 c 14 & '* NATURAL SINES, TANGENTS AND SECANTS. (CONTINUED.) Deg. Min. Sine. .3420 .3448 .3475 Tangent. Secant. I Deg. Min. 00 10 20 Sine. Tangent. Secant. 20 00 10 20 .3640 .3673 .3706 1.0642 1.0653 1.0665 25 .4226 .4663 .4253 .4699 .4279 .4734 1.1034 1.1049 1.1064 30 40 50 .3502 .3529 .3557 .3739 .3772 .3805 1.0676 1.0688 1.0700 30 40 50 .4305 .4331 .4358 .4770 .4806 .4841 1.1079 1.1095 1.1110 21 00 10 20 .3584 .3611 .3638 .3839 .3872 .3906 1.0711 .1.0723 1.0736 26 00 10 20 .4384 .4410 .4436 .4877 .4913 .4950 1.1126 1.1142 1.1158 30 40 50 .3665 .3692 .3719 .3939 .3973 .4006 1.0748 1.0760 1.0773 30 40 50 .4462 .4488 .4514 .4986 .5022 .5059 1.1174 1.1190 1.1207 22 00 10 20 .3746 .3773 .3800 .4040 .4074 .4108 1.0785 1.0798 1.0811 27 00 10 20 .4540 .4566 .4592 .5095 .5132 .5169 1.1223 1.1240 1.1257 30 40 50 .3827 .3854 ,3881 .4142 .4176 .4210 1.0824 1.0837 1.0850 30 40 50 .4617 .4643 .4669 .5206 .5243 .5280 1.1274 1.1291 1.1308 23 00 10 20 .3907 .3934 .3961 .4245 .4279 .4314 1.0864 1.0877 1.0891 28 00 10 20 .4695 .4720 .4746 .5317 .5354 .5392 1.1326 1.1343 1.1361 30 40 50 .3987 .4014 .4041 .4348 .4383 .4417 1.0904 1.0918 1.0932 30 40 50 .4772 .4797 .4823 .5430 .5467 .5505 1.1379 1.1397 1.1415 24 00 10 20 .4067 .4094 .4120 .4452 .4487 .4522 1.0946 1.0961 1.0975 29 00 10 20 .4848 .4874 .4899 .5543 .5581 .5619 1.1434 1.1462 1.1471 30 40 50 .4147 .4173 .4200 .4557 .4592 .4628 1.0989 1.1004 1.1019 30 40 50 .4924 .4950 .4975 .5658 .5696 .5735 1.1490 1.1509 1.1528 c y NATURAL SINES , TANGENTS AND SECANTS. (CONTINUED.) Deg. Min. Sine. Tangent. Secant. Deg. Min. Sine. .5736 .5760 .5783 Tangent. Secant. 30 00 10 20 .5000 .5025 .5050 .5774 .5812 .5851 1.1547 1.1566 1.1586 35 00 10 20 .7002 .7046 .7089 1.2208 1.2233 1.2258 30 40 50 .5075 .5100 .5125 .5890 .5930 .5969 1.1606 1.1626 1.1646 30 .5807 40 .5831 50 .5854 .7133 .7177 .7221 1.2283 1.2309' 1.2335 31 00 10 ! 20 .5150 .5175 .5200 .6009 .6048 .6088 1.1666 1.1687 1.1707 36 00 .5878 10 .5901 20 .5925 .7265 .7310 .7355 1.2361 1.2387 1.2413 30 40 J50 .5225 .5250 .5275 .6128 .6168 .6208 1.1728 1.1749 1.1770 30 40 60 .5948 .5972 .5995 .7400 .7445 .7490 1.2440 1.2467 1.2494 32 00 10 20 .5299 ,5324 .5348 .6249 .6289 .6330 1.1792 1.1813 1.1835 37 00 ! .6018 10 .6041 20 .6065 .7536 .7581 .7627 1.2521 1.2549 1.2577 30 40 50 .5373 .5398 .5422 .6371 - .6412 .6453" 1.1857 1.1879 1.1901 30 40 50 .6088 .6111 .6134 .7673 .7720 .7766 1.2605 1.2633 1.2661 33 00 ' .5446 10 .5471 20 .5495, .6494 .6536 .6577 1.1924 1.1946 1.1969 38 00 10 20 .6157 .6180 .6202 .7813 .7860 .7907 1.2690 1.2719 1.2748 30 .5519 40 .5544 50 .5568 .6619 .6661 .6703 1.1992 1.2015 1.2039 30 40 50 .6225 .7954 .6248 ; .8002 .6271 i .8050 1.2778 1.2808 1.2837 34 00 .5592 10 .5616 20 .5640 .6745 .6787 .6830 1.2062 1.2086 ' 1.2110 39 00 10 20 .6293 j .8098 .6316 .8146 .6338 .8195 1.2868 1.2898 1.2929 30 40 50 < - .5664 .5688 .5712 .6873 .6916 .6959 1.2134 1.2158 1.2183 30 40 50 .6361 .6383 .6406 .8243 .8292 .8342 i 1.2960 1.2991 1.3022 i NATURAL SINES, TANGENTS AND SECANTS. (CONTINUED.) Deg. Min. Sine. Tangent. Secant. Deg. Min. Sine. Tangent. Secant. 40 00 .6428 10 .6450 20 .6472 .8391 1.3054 .8441 1.3086 .8491 1.3118 45 00 10 20 .7071 1.0000 .7092 1.0058 .7112 1.0117 1.4142 1.4183 1.4225 30 .6494 40 .6517 50 .6539 41 00 .6561 10 .6583 20 .6604 .8541 1.3151 .8591 1.3184 .8642 1.3217 .8693 1.3250 .8744 I 1.3284 .8796 1.3318 30 40 50 46 00 10 20 .7133 ; 1.0176 .7153 i 1.0235 .7173 1.0295 .7193 l 1.0355 .7214 1.0416 .7234 1.0477 1.4267 1.4310 1.4352 1.4396 1.4439 1.4483 30 .6626 40 .6648 50 .6670 .8847 1.3352 .8899 1.3386 .8952 1.3421 30 40 50 .7254 1.0538 .7274 1.0599 .7294 1.0661 1.4527 1.4572 1.4617 42 00 .6691 10 .6713. 20 .6734 .9004 1.3456 .9057 1.3492 .9110 1.3527 47 , 00 : 10 20 .7314 1.0724 .7333 1.0786 .7353 1.0850 1.4663 1.4709 1.4755 30 .6756 40 .6777 50 .6799 .9163 1.3563 .9217 1.3600 .9271 1.3636 30 40 50 .7373 1.0913 .7392 1.0977 .7412 1.1041 1.4802 1.4849 1.4897 43 00 .6820 10 .6841 20 I .6862 .9325 1.3673 .9380 1.3711 .9435 1.3748 48 00 10 20 .7431 1.1106 .7451 1.1171 .7470 : 1.1237 1.4945 1.4993 1.5042 30 .6884 40 ! .6905 50 .6926 .9490 1.3786 .9545 1.3824 .9601 '1:3863 30 i 40 50 .7490 1.1303 .7509 1.1369 .7528 1.1436 1.5092 1.5141 1.5192 44 00 .6947 10 .6967 20 .6988 .9657 1.3902 .9713 1.3941 .9770 1.3980 49 00 10 20 .7547 1.1504 .7566 1.1571 .7585 1.1640 1.5243 1.5294 1.5345 30 ! .7009 40 .7030 50 .7050 '4 .9827 1.4020 .9884 1.4061 .9942 1.4101 30 40 50 .7604 1.1708 .7623 1.1778 .7642 1.1847 1.5398 1.5450 1 1.5504 NATURAL SINES , TANGENTS AND SECANTS. Tangent. (CONTI Secant. VUED.) Deg. Min. Deg. :Min. Sine. Sine. Tangent. Secant. 50 00 .7660 ' 10 .7679 : 20 .7698' 1.1918 1.1988 1.2059 1.5557 1.5611 1.5666 55 00 10 20 .8192 .8208 .8225 1.4281 1.4370 1.4460 1.7434 1.7507 1.7581 30 ' .7716 40 .7735 i.50 .7753 1.2131 1.2203 1.2276 1.5721 1.5777 1.5833 30 40 50 .8241 .8258 .8274 1.4550 1.4641 1.4733 1.7655 1.7730 1.7806 51 00 .7771 ; 10 .7790 20 .7808 1.2349 1.2423 1.2497 1.5890 1.5948 1.6005 56 00 10 20 .8290 .8307 .8323 1.4826 1.4919 1.5013 1.7883 1.7960 1.8039 30 .7826 i 40 .7844 ; 50 .7862 1.2572 1.2647 1.2723 1.6064 1.6123 1.6183 30 40 50 .8339 .8355 .8371 1.5108 1.5204 1.5301 1.8118 1.8198 1.8279 52 00 .7880 i 10 .7898 20 .7916 1.2799 1.2876 1.2954 1.6243 1.6303 1.6365 57 00 10 20 .8387 .8403 .8418 1.5399 1.5497 1.5597 1.8361 1.8443 1.8527 30 .7934 , 40 .7951 50 .7969 1.3032 .1.3111 1.3190' 1.6427 1.6489 1.6553 30 40 50 .8434 .8450 .8465 1.5697 1.5798 1.5900 1.8612 1.8699 1.8783 53 00 ' .7986 ! 10 ' .8004 20 .8021 1.3270 1.3351 1.3432 1.6616 1.6681 i 1.6746 58 00 10 20 .8480 .8496 .8511 1.6003 1.6107 1.6213 1.8871 1.8959 1.9048 ' 30 .8039 40 .8056 50 : .8073 54 i 00 .8090 10 .8107 20 .8124 1.3514 1.3597 1.3680 1.3764 ' 1.3848 1.3934 1.6812 i 1.6878 1.6945 I : 1.7013 i 1.7081 1 1.7151 50 30 40 50 00 10 20 .8526 .8542 .8557. .8572 .8587 .8601 1.6319 1.6426 1.6534 1.6643 1.6753 1.6864 1.9139 , 1.9230 1.9323 i 1.9416 1.9511 1.9606 30 .8141 40 .8158 50 .8175 2u 1.4019 ! 1.4106 ' 1.4193 1.7221 1.7291 1.7362 30 40 50 .8616 .8631 .8646 1.6977 1.7090 1.7205 i 1.9703 1.9801 1.9900 '4 NATURAL SINES, TANGENTS AND SECANTS. (CONTINUED.) Deg. Min. 00 10 20 Sine. Tangent. Secant. Deg. Min. 65 00 10 20 Sine. Tangent. 2.1445 2.1609 2.1775 Secant. 60 .8660 1.7321 2.0000 .8675 1.7437 2.0101 .8689 1.7556 2.0204 .9063 .9075 .9088 2.3662 2.3811 2.3961 30 40 50 .8704 1.7675 , 2.0308 .8718 1.7796 2.0413 .8732 1.7917 2.0519 30 .9100 40 .9112 50 .9124 2.1943 2.2113 2.2286 2.4114 2.4269 2.4426 61 00 10 20 .8746 .8760 .8774 1.8040 2.0627 1.8165 2.0736 1.8291 2.0846 66 00 10 20 .9135 .9147 .9159 2.2460 2.2637 2.2817 2.4586 2.4748 2.4912 30 40 50 .8788 .8802 .8816 1.8418 ! 2.0957 1.8546 2.1070 1.8676 2.1185 30 40 50 .9171 .9182 .9194 2.2998 2.3183 2.3369 2.5078 2.5247 2.5419 62 00 10 20 .8829 1.8807 .8843 1.8940 .8857 1.9074 2.1301 2.1418 2.1537 67 00 10 20 .9205 .9216 .9228 2.3559 2.3750 2.3945 2.5593 2.5770 2.5949 30 40 50 .8870 .8884 .8897 1.9210 1.9347 1.9486 2.1657 2.1786 2.1902 30 40 50 .9239 .9250 .9261 2.4141 2.4342 2.4545 2.6131 2.6316 2.6504 63 00 10 20 .8910 .8923 .8936 1.9626 1.9768 1.9912 2.2027 2.2153 2.2282 68 00 10 20 .9272 .9283 .9293 2.4751 2.4960 2.5172 2.6695 2.6888 2.7085 30 40 50 .8949 .8962 .8975 2.0057 2.0204 2.0353 2.2412 2.2543 2.2677 30 40 50 .9304 .9315 .9325 i 2.5386 2.5605 ; 2.5826 2.7285 2.7488 2.7695 64 00 10 20 30 40 50 .8988 .9001 .9013 .9026 .9038 .9051 2.0503 2.0655 2.0809 2.0965 2.1123 2.1283 2.2812 2.2949 2.3088 2.3228 2.3371 2.3515 69 00 10 20 30 40 50 .9336 .9346 .9356 .9367 .9377 .9387 2.6051 2.6279 2.6511 2.6746 ! 2.6985 2.7228 2.7904 2.8117 2.8334 2.8555 2.8779 2.9006 NATURAL SINES r , TANGENTS AND SECANTS. Deg. Min. Sine. Tangent. 2.7475 2.7725 2.7980 (CONTl Secant. NUED.) Deg. Min . Sine. Tangent. Secant. 70 00 ! 10 20 .9397 .9407 .9417 2.9238 2.9474 2.9713 75 00 10 20 .9659 .9667 .9674 3.7321 3.7760 3.8208 3.8637 3.9061 3.9495 30 40 50 .9426 .9436 .9446 2.8239 2.8502 2.8770 2.9957 3.0206 3.0458 30 40 50 .9681 .9689 .9696 3.8667 3.9136 3.9617 3.9939 4.0394 4.0859 71 00 10 i 20 .9455 .9465 .9474 2.9042 2.9319 2.9600 3.0716 3.0977 3.1244 76 00 10 20 .9703 .9710 .9717 4.0108 4.0611 4.1126 4.1336 4.1824 4.2324 30 40 50 .9483 .9492 .9502 2.9887 , 3.0178 3.0475 ! 3.1515 3.1792 3.2074 30 40 50 .9724 .9730 i .9737 4.1653 4.2193 4.2747 4.2837 4.3362 4.3901 72 00 10 |20 i 30 40 50 .9511 .9520 .9528 .9537 .9546 .9555 3.0777 3.1084 i 3.1397 3.1716 3;2041 3.2371 3.2361 3.2653 3.2951 3.3255 3.3565 3.3881 77 00 10 20 30 40 50 1 .9744 .9750 .9757 .9763 .9769 .9775 4.3315 4.3897 4.4494 4.5107 4.5736 4.6382 4.4454 4.5022 4.5604 4.6202 4.6817 4.7448 73 00 10 '20 .9563 .9572 .9580 3.2709 3.3052 3.3402 3.4203 3.4532 3.4867 78 00 10 20 .9781 .9787 .9793 4.7046 4.7729 4.8430 4.8097 4.8765 4.9452 30 40 50 .9588 .9596 .9605 3.3759 3.4124 3.4495 3.5209 3.5559 3.5915 30 40 50 .9799 .9805 .9811 4.9152 4.9894 5.0658 5.0159 5.0886 5.1636 74 00 10 20 .9613 .9621 .9628 3.4874 3.5261 3.5656 3.6280 3.6652 3.7032 79 00 10 20 : .9816 .9822 .9827 5.1446 5.2257 5.3093 5.2408 5.3205 5.4026 30 40 ,50 .9636 .9644 .9652 3.6059 3.6470 3.6891 3.7420 3.7817 3.8222 30 40 50 .9833 .9838 .9843 5.3955 5.4845 5.5764 5.4874 5.5749 5.6653 i5 1 NATURAL SINES, TANGENTS AND SECANTS. (COiNTINUED.) Deg. Min. Sine. Tangent. 1 Secant. Deg. txfX.,^ 'J-^*-S 11 j D D * o i i D n > r> Z - JD 3D fi O Uji ) c - \ \ ) ) 5 o : i n ^ D )f _ ^^^^^^^^_