USEFUL INFORMATION FOR Architects, Engineers, AND Workers in Wrought Iron, BY THE PHCENIX IRON COMPANY. OFFICE, 410 WALNUT STREET, PHILADELPHIA. WORKS, Phcenixville, Pa. REVISED EDITION, 1586. COPYRIGHT, 1885, BY PHCENIX IRON COMPANY. PRINTED BY J, B. LIPPINCOTT COMPANY, PHILADELPHIA. THE Ph(enix Iron Company 410 Walnut St., Philadelphia, MANUFACTURERS OF Wrought Iron Roof Trusses, EITHER CURVED, STRAIGHT, OR HIPPED. ALSO, Wrought Iron Purlins and Jack Rafters, ARRANGED TO SUIT SHEET IRON OR SLATE COVERING. LINKS, TO FORM BOTTOM CHORDS FOR BRIDGES, OF ANY SIZE OR LENGTH, MADE WITHOUT WELDING. Patent Wrought Iron Columns FOR TOP CHORDS OR POSTS OF BRIDGES OR PIERS, DEPOTS, FACTORIES, ETC. ALL PARTS OF Bridges or Fire Proof Floors and Roofs MADE AND FITTED TO SUIT DESIGNS OF ENGINEERS AND ARCHITECTS. BEAMS, ANGLES, T AND SHAPE IRON, REFINED BARS, ETC. OFFICERS. ^© DAVID REEVES, President, GEORGE GERRY WHITE, Secretary, JAMES O. PEASE, Treasurer, PHILADELPHIA. W. H. REEVES, General Superintendent, AMORY COFFIN, Chief Engineer, R. H. DAVIES, Master Mechanic, PHCENIXVILLE. Correspondents will please address PHCENIX IRON COMPANY, JflO Walnut Street, PHIZ, A DELPHI A, CONTENTS. PAGE Air, notes on . . 125 Angle brackets ........ 86 Angle iron, price-list 48 properties of 64 Arches of floors 90 Areas of circles 155 Avoirdupois weight .159 Bar iron, price-list 43 sizes of . . . . . . . .42 properties of 60 weight of 128 Beams, deck, price-list 45 I, as floor joists ....... 85 details of construction 90 elements of 75 girders 126 price-list 44 properties of 61 table for spacing 40 tables of strength and stiffness .... 78 Bearing values of rivets 59 Bending moments of pins 58 Boiler tubes, tables of ■' . 143 Bolts, tables of . . 141 Bracing of roofs 112 Brackets, angle ........ 86 Brass, weight of 136 Bricks, hollow 92 g2»4r' ' — —ws- I3 ? Channel iron// price-list ■ . 46 properties of 62 Circles, areas of . 155 circumferences of ...... 154 properties of . . 148 Cisterns, capacity of 145 Colors of iron caused by heat 124 Columns, cast and wrought 96 fire-proofing 95 Q THE PHCENIX IRON COMPANY, PAGE Columns, formulas for 98 price-list . 52 tables of sizes 100 Comparative strength of beams 72 columns . . . ... . . .98 Compound Girders 88 Copper, weight of 136 Corrugated iron 134 Cubic measure 158 Deck beams, price-list 45 Deflexion, formulae for 76 Diagram for I beams 40 Dies, list of 54 Diminution of tenacity of wrought iron . . . 122 Elasticity, modulus of 118 Elements of beams 75 Equivalents, trigonometrical 151 Eye bars, list of dies for 54 proportions of 104 Fire-proofing columns 95 Flagging 145 Floor glass 145 Floors 69 Formulae for columns 98 deflexion ......... 76 strength of beams 74 French measures . . 156 Galvanized iron 134 Gas-pipe 142 Gauges, wire ........ 135 Girders, beam 126 compound 88 Glass, sizes of . 144 Gravity, specific 147 Hollow Bricks ......... 92 Kirkaldy's conclusions 119 Lead, weight of 136 Linear expansion of metals 123 List of dies 54 Long measure 156 Machine-shop roofs 112 410 WALNUT ST., PHILADELPHIA. PAGE Mansard roofs 108 Melting point of metals 124 Miscellaneous shapes 51 Modulus of elasticity .... . . .118 Nails, sizes and weights 139 Natural sines, etc., table 152 Nuts, tables of sizes ....... 140 Phoenix columns, price-list 52 tables of sizes 100 tests of . . , 116 Pins, proportions of 104 Pipe, weight of cast-iron 133 Price-list, angles 48 bar iron ......... 42 beams, deck 45 beams, I 44 channels 46 miscellaneous shapes . . . . . . 51 Phcenix columns . 52 T bars 47 Properties of circles 148 iron 119 triangles 150 Purlins . . . . . . . . . 106 Railroad spikes and splices 135 Rails, weight per mile 135 Rivets, table of weights 138 shearing and bearing, values of 59 Roofs, bracing of . . . . „ . . . 112 general details 102 machine-shop 112 Mansard 108 Rules for weight of iron 132 Screw ends, upset, sizes of 55 Separators and bolts, tables of .... 86 Shearing values of rivets 59 Sines, table of natural ....... 153 Skew-backs 104 Slate, sizes of . . . . . . . 146 Spacing of beams 40 Specific gravity 147 1 1 THE PHCENIX IRON COMPANY. PAGE Specifications of quality 117 Splices and bolts 135 Square measure 157 Strength of beams 72 Surveying measure 156 Tables of beams. I. Elements of ... 75 II. Strength of 78 III. Spacing 40 Table of bolts 141 cast-iron pipe 133 glass 144 nails and tacks 139 nuts 140 rivets 138 round and square iron 130 sizes of columns 100 spacing of beams 40 strength of beams 78 strength of columns .98 washers 141 weight of bar iron 128 weight of wire . 137 T bars, price-list 47 properties of . . . . . . . . 68 Tension, notes on 117 Tests of beams . 114 columns 116 Triangles, properties of 150 Trigonometrical equivalents 151 Upset screw ends 55 Washers, table of 141 Weight of bar iron 128 brackets and fittings 86 brass, copper, and lead 136 round and square iron ...... 130 separators and bolts 86 various substances ....... 147 wire 137 Wight's fire-proofing for columns 95 Wire gauges 135 Wrought-iron columns 96 12 2 *3 THE PHCENIX IRON COMPANY, 410 WALNUT ST., PHILADELPHIA. THE PHCENIX IRON COMPANY, 1 6 No. 131 90 LBS No. 4 2 150 LBS .6 9 16 < 17 410 WALNUT ST., PHILADELPHIA. NEW BEAMS. 19 THE PHCENIX IRON COMPANY, IRON DECK BEAMS. MINIMUM SIZE. 20 THE PHCENIX IRON COMPANY, STEEL DECK BEAMS. MINIMUM SIZE. 23 THE PHCENIX IRON COMPANY, 24 4.10 WALNUT ST., PHILADELPHIA. 2 5 THE PHCENIX IRON COMPANY, 4 No. 110 50 TO 70 LBS 2-3- No. 53 70 TO 100 LBS 13 16 "2* — 1 No. 97 60 LBS ONLY r-t|cM o it 32^ No. 136 25 TO 34 LBS No. 137 35 TO 57 LBS VL r i> J 4' I f> J ?» J f» If, If, 2, 2f, 2f, 2f, 2j, 2f, 2f, 2f, 3, 3f> 3?> 3§» 3?> 3& 3f» 3h 4, 4l, 4i, 4|, 5> 5k 5}. 5f, 6, 6f, 6f, 6|, 7. ■ SQUARES. ■ 5 3. 7 1 9 5 1 1 3. 1 3 JL 1 3 T T 1 t1 t 3 If, If, If, if, If, If, 2, 2f, 2f, 2f, 2f, 2f, 2 i 3. 3h 3h 3h 4i 4^ 4f» 4|. 5- FLATS. "Width in Inches. Thickness in Inches. Width in Inches. Thickness in Inches. Min. Max. 4 f to f 4 to 3J i f to 4 4t \ to 3i 4* to 4 i to f »* f to i 5 \ to 4J *i if f to i to 1 1* 5t to 4J i* f to >i 6 to 5 if f to «i \ to 2 1 4 i to * to 1* 7 \ to 2j 'i 'i 7* 1 4 to 2 2 1 to if 8 1 tO 2$ at 1- to >t 4 a* 1 to it 9 \ to Ij 2| I to >t 10 i to if 3 -V to 2* 31 f to «f 1 1 1 4^ to if 3* 3i i to i to 3 3h 12 \ to If 42 410 WALNUT ST., PHILADELPHIA. J to 2 inches. I to 4 4i t0 6 ORDINARY SIZES. Round and Square Xfto in XI to I ( Flats 5 3 1 i and A I and li 4 to 2| 3 to 3J 3f to 4 EXTRA SIZES. ROUND AND SQUARE. 4j to 4} . . . r 3 oC. Wc. c. c. " c. To 2 TO • T(T EXTRA FLAT 4fto5 T %c. Si to i c. 5i to 6 i^c. 6\ to 6£ 2 c. 6| to 7 2 T %c. SIZES. IRON. 7 ¥ Xftof . . 4 r 7 X 2j to 3i ■ • Ac I XA • - 4 -C 7* X 3 8 to I . . • Ac I to 6 X i and T ¥ 2 r T0 C * 71 X Ii to 2 . . • Ac 2 to 4 X if to 2. 2 r 8 X 3 8 to I . . • Ac 2 to 4 X 2j to 3- 10^* 8 X to 6 c 4i to 6 X 4 to 2. To*"' 9 X 3 8 to I . . 6 r 4i to 6 X 2j to 3- 4 p T0 C * 9 X ii to 2 . . ? r • TIT 6^ X 1 to I . . 2 r IO X 1 to ii • TO*"' 6^ X ii to 2j . 4 r T0 C< 1 1 X 3 8 to ii • 9 r 7 X ftoi. . tV- 12 X 3 8 to ii • 9 r 7 X I* tO 2 . . tV- 6| to 12 wide X i thick, -fa extra over § thick. ADDITIONAL EXTRAS. CUTTING TO LENGTHS. ROUNDS AND SQUARES. Up to 4 inches, io to 20 feet long T 2 ^c. Over 4 " " " " , Under 10 and over 20 feet, subject to agreement. FLATS. 10 to 30 feet long ^c. Over 30, for every 10 feet or fraction thereof, -^c. extra. Under 10 feet, subject to agreement. 3 r To" 43 THE PHCENIX IRON COMPANY, I BEAMS. SHAPE. No. Depth. Width of Flange. Thickness of Web. Weight per Yard. Inches. Inches. Inch. Pounds. I I C J 8 M j 200 8q 1 c . so I mmm> n8 1 c 4# 4.2 12; 1 c c J J 12 J 2 I70 1 1 C7 j/ I 2 I2< J 1 I 12 4^ • 06 1 IIzL ioi C J . Co I ^8 J Ah •44 10c 1 I ^1 IO^ 4* 8 GO A V Q J 8 .60 I CO z J o y t 84. 6 Q Ol j 70 1 1 2 8 t2 • 81 CO 8 4 112 7 4 .38 69 7 7 3* •35 55 I 1 1 1 6 3i .31 50 8 6 z ± •25 40 106 5 3 •3° 36 105 5 2| •25 30 65 4 2f .25 30 100 4 2 .20 18 1 To fill special orders, the weight of any of the above can be increased about ten per cent. 44 410 WALNUT ST., PHILADELPHIA. DECK BEAMS. SHAPE. No. Depth. Width of Flange. Thickness of Web. Weight per Yard. Inches. Inches. Inch. Pounds. MM 104 »* 5 7 95 to 112 T 88 IO 5 A 85 to 105 I 60 9 5 1 1 69 to 80 1 61 8 4* 21 60 to 72 62 7 4* A 51 to 62 63 6 4i 9 "3~2 42 to 51 64 5 3 3 8 35 to 40 STEEL DECK BEAMS. 140 9 5 1 5 32 84 to 95 139 8 5 1 5 32" 73i to 84 137 6 4i A 54 to 63 62 7 4} 5 Tl> 51 to 62 63 6 4* 9 3? 42 to 51 64 5 3 f 35 to 40 The dimensions given correspond to the minimum weights. 45 THE PHCENIX IRON COMPANY, CHANNEL BARS. SHAPE. No. Width of Flange. Thickness of Web. Inches. Inches. Inch. 124 1 5 4 5 f 140 15 3i 52 12 3 1 141 12 3 1 6 97 I ol- Jo 1 24 J 1 130 io 2| 1 2~ 129 IO 2} R g 142 IO 2| 2 5 1 <» 53 9 2f J no 9 | 143 9 2l _5 1 B" 123 8 2f | 122 8 2 1 l 37 7 2} 5 T6" 136 7 2 3V 50 6 9} _7 1 6 51 6 2 T V 1 6 1 144 6 4 11 6 4" 121 5 2 5 1 6 120 5 A 4 3 T6 119 4 2 5 1 6 118 4 If 3 T6" 117 3 If 3 8 116 3 ij 1 4 Weight per Yard. Pounds. 1 50 to 200 115 to 150 88 to 1 50 60 to 88 60 only 75 to III 57 to 75 48 to 60 7o to 100 50 to 70 37 to 47 to 30 to 45 35 to 57 25 to 34 47 to 56 28 to 36 22 tO 28 27 to 30 17 to 24 to 15 to 18 tO 21 15 to 18 50 57 21 27 18 Any increase in thickness of web adds to the width of flanges and to the weight. No. 97 does not admit of any change in its dimensions. The dimensions given corre- spond to the minimum weights. 4<> 4IO WALNUT ST., PHILADELPHIA. T BARS. SHAPE. No. DIMENSIONS. Weight per Yard. Inches. Pounds. 23 5 X 2| v A i 35 2 5 5 X 4 v A i 29 132 4jT X 3 V A 5 25 T i 46 4 X -.3 04 A 3. 4 49 4 X 2 V A 5 T6 16J 101 3j X 3l v A § 28J 45 3 X 3i X A 32 24 3 X 3i X 2 30 102 3 X 3 X 1 3 3 2 21 T 98 ^2 X 2^ z 4 X 1 3 "3 2 18 84 2j X 2j X 3 8 16 103 2 X 2 X 9 3 2 9 47 2j X 'A X 3 T6 6i Note. — No change can be made in the above dimen- sions. 47 THE PHCENIX IRON COMPANY. EQUAL-SIDED ANGLES. SHAPE. Ko. DIMENSIONS. Weight per Yard. Inches. Pounds. 127 6 X° XA to ft 50-3 to 93.5 126 5 X 5 X it f 1 1 37.0 to 62.0 H 4 X4 X 1 28.1 to 51.6 r 15 3} X 3i X A to g 20.5 to 41.0 16 3 X3 Xi to J 15.0 to 28.1 37 2| X*!X i to i 13.4 to 25.8 17 X 2} X A fo I 10.5 to 23.6 38 X 2} X A to V 8.0 to 18.3 r 18 19 2 it X2 xA X *t X A to | to A 7/5 to 14.0 6.1 to 10.1 20 X ij X A to i 4.4 to 7.1 39 •ft X 1] X ft to A 2.8 to 4.3 40 X 1 X ft ^ A 2.4 to 3.6 Note. — The sides of Angles agree only with the mini- mum thickness in table; they increase in width as the thickness increases. Orders should specify either the thickness or the weight required, but never both. 48 4IO WALNUT ST., PHILADELPHIA. UNEQUAL-SIDED ANGLES. SHAPE. No. DIMENSIONS. Weight per Yard. 87 Inches. /NT 1 A 32 to 3 4 Pounds. 40.7 to 74.8 91 6 /NT" /\ H to 3 4 36.5 to 71.2 r i 92 6 y ^1 y § A J2 A 8 to 5 8 33.8 to 56.2 41 /\ T" /\ 8 to 5 8 31.9 to 53.1 93 e V *l V A- to 1 1 1 6 27-5 to 55.0 42 e j to L 8 23.6 to 47.1 43 /\ J /\ 8 to 9 16 26.5 to 39.7 94 4 X 32 X 1 to 9 26.5 to 39.7 44 4 X 3 Xn to r 9 1 5 X 2 5 X i 5 X 2 Diameter of Pin. 2ll Z l 6 ol 5 Z T6 3A 3A J16 4ft 4ft 5ft 3i 6 3T6 Ol6 4A 3 i 3t6" 3t6 2 1 5 4A 4A 4H Jl 6 3t 7 6 OT6 4.11 t-1 6 5X6 oil J16 4ft 4ft SIZE OF HEAD. Inches 4 X 44 X 5 X 54 X 44 X 54 X 6 X 6i X X X 74 X 71 X 84 X 8f X 7 X 74 X 8 X 84 X 74 X 7t X X 8| X 8| X 94 X 94 X io X 9 X 94 X io X ioJ X 94 X 2j io X I* io X 24 Thicker than Bar. 54 410 WALNUT ST., PHILADELPHIA. LIST OF DIE-FORGED EYES ON FLAT BARS. SIZE OF BAR. Diameter of Pin. SIZE OF HEAD. Head Thicker than Bar. DIE No. Inches. Inches. 5 X i 5 X 2 5 X if t y ii 5 X 2 5 X if 5 X if A 1 1 4T6 4H sA St* J 1 b 5U 6A °T¥ io| X 1} ">J X 2} 11 X ii II* X 2i IlJ X *i 12 X 2j 12* X 2j i 1 2 1 1 1 ? i i 164 163 91 166 165 93 7i 6 X if 6X2 6 X 2f 6 X i| 6 X If 4i 6 4?4 t-1 6 4l 6 °T<7 11 X 2| 12 X 2| 12 X 3 13 X 2| 14 X 2j 5 8 § 8 5 8 f "8" 178 173 174 68 179 Dies for flat bars may be used for bars that are thicker or thinner than sizes specified. The thickness of a bar should never be less than one- fourth of its width nor more than one-half. UPSET SCREW ENDS ON ROUND BARS. Diameter Diameter Length Threads Diameter Diameter Length Threads of of of per of of of per Bars. Upsets. Upsets. Inch. I Bars. Upsets. Upsets. Inch. Inches. Inches. Inches. Inches. Inches. Inches. f 3 4 2} IO H ^4 7 4 1 I 2| 8 2 2f 7i 4 7 8 Ii 3 7 2i 2} 8 I Ii 3* 7 2i 2^- 8 : ii If 4 6 2f 2 3 2 4 B* 3* ^ *i 4} 6 2i ^8 9 3} if if 5 5 2f 3 9 3* 1} if Si 4 2| 3«- 9* 1 1 J2 3i if 2 6 4i 7 2 8" 3f 9i if 2i 6} 4i 3 3i 10 3i 55 THE PHOENIX IRON COMPANY, GENERAL FORMULAE EXPLANATORY OF THE FOLLOWING TABLES AND THEIR APPLICATION. Let A represent the area of cross section in square inches. Let I represent the moment of inertia of A about an axis passing through its centre of gravity. Let d represent the distance, in inches, of the most re- mote fibre from the axis for I. Let r = (^) ^ represent the radius of gyration of the section A. All the preceding quantities are given in the following tables for the various sections of beams, channels, angles, etc. Let M represent the greatest bending moment, in inch- pounds, for any loading or span. Let / represent the span in feet. With the load W pounds at the centre of the span I : — M = 3 W / for ends of beam simply supported, r X5L W /I M=|_ 8 9 ^-^|for one end simply supported and the other fixed. M = | I W / j ^ or k° tn ends of beam fixed. With the uniform load of w pounds per lineal foot of span : — M = \w I 2 for ends of beam simply supported. M = | 3 |^^ 2 lfor one end simply supported and the other fixed. {— w I 2 ) 2 ,„ > for both ends of beam fixed. - w I 2 j The preceding negative values belong to points of support. Let K. represent the greatest stress in pounds per square inch, — i.e., the stress in the most remote fibre. 56 410 WALNUT ST., PHILADELPHIA. K I Then M = —j- (i): Ud Or, K== T - (2). If r is known, as it sometimes may be, Md A =K7* (3). Let D represent the greatest deflection in inches. Let E represent the coefficient of elasticity in pounds per square inch. Then W at span centre. Uniform load. W /3 w /4 D = 36 ^ j- 22.5 ~j?~Y f° r supported ends. W /3 W I* D = 1 7. 1 1 j 9.366 g j for one supported and one fixed end. W /3 W /4 D = 9 g j 4,5 j for both ends fixed. ttR4 For a circular section I = — — — and d = R (the radius). Hence, M =0.7854 K R3 (4). Eqs. (1), (2), (3), and (4) are of great practical value. The values in table on page 58 are computed from Eq. (4), with K equal to 15,000, 18,000, and 20,000. RIVET BEARING AND SHEARING. Let S represent the shearing resistance in pounds per square inch. Let p represent the bearing pressure in pounds per square inch. Let (2R) represent the rivet diameter in inches. Let / represent the thickness of plate in inches. Then, Shearing resistance of rivet = tt R 2 S . (5). Bearing resistance of rivet =2R// . (6). The values of Eqs. (5) and (6) for S =7500, and p = 12,000 and 15,000 are given for various values of (2R) and / on page 59. 5* 57 THE PHCENIX IRON COMPANY, MAXIMUM BENDING MOMENTS TO BE ALLOWED ON PINS FOR FIBRE STRAINS OF 15,000, 18,000, AND 20,000 POUNDS. Diam. of Pin. Inches. BENDING MOMENTS. Diam. of Pin. Inches. BENDING MOMENTS. S=15,000 S=18,000 S=20,000 S=15,000 S-18,000 S=20,000 1 I* I& Ij Ift If ift 4 i ft if i» if f ?» 2* 2ft 2ft 2f 2ft 2j 2ft 2| 2}i 2| 24-4 2i ■H 3 3ft 3* 3ts 3i 3ttt 3l 3t\ 3i 1,470 1,770 2,100 2,470 2,880 3.330 3.830 4,370 4.970 5,620 6,320 7,080 7,890 8,770 9710 10,710 11,780 12,920 14.13° 1541° 16,770 18,210 19,720 21,320 23,000 24,780 26,620 28.580 30,630 32,760 34.980 37,330 39.750 42,290 44,940 47,690 1 50,550 53.520 56,600 59,810 63,130 1,770 2,120 2,520 2,960 3.45o 4,000 4,59° 5.250 5 960 6,740 7.58o 8,490 9-470 10,520 11,650 12,850 14,140 15,500 16,960 18,500 20,130 21,850 23.670 25,59° 27,600 29,730 31,95° 34,30° 36,75° 39 3 IQ 41,980 44,800 47,700 5o,75° 53.93° 57,230 60,660 64.230 67.930 71,780 75,76o 1,960 2,35o 2,800 3-290 3,830 4.440 5,ioo 5830 6,630 7,49° 8- 420 9- 43° 10.520 11 690 12,940 14,280 i5,7io 17,220 18,840 20,550 22,360 24,280 26,300 28,43c 30,670 33.040 35.5oo 38,110 40,830 43 680 46,650 49,770 53.ooo 56,39° 59.920 63.59° 67,400 71,370 7547° 79-750 84 180 si 3» 3* 3« al m 4 4tV 4* 4i% 44 4& 4* ' 4A 4i 4t 9 h invO VO O oo m c t^o cm vo N co cm^ on t^vo cm cm oo VO OiNO> NOW o oo" m" o* on m -- m h vo^ m q^oo__ incM o vo mo o\ m n o h co cn m rf m -tf-vo" Tfvo" m m cCvo" rCvo"oo~vo"oo" O000O0000000OO0O0O00O0<_ cm on in o oo m <- cm m n tj- oMn m \o m t^oo oo o on co vO no On h cm mvo^ on On ro in Mn h on m cm on in co on c^ cm cm co cm trntrotmintin -^no ^no mvo m m c-CvcT 0000000000000000000000000 r~- w mvo co h w on cm r^vo cm -<*• o. cm cm ooooo covo oo tt 0\co cm h m moo oo o cm co mvo on On cm cmvo in on n co o vo co I CM CM CO CM CO CM CO C - m - ONOO OO C-n t>* in 1>nO vO rj- H O O H W O M O" O" W O" O O O* 6 O* 6 O 6 O' O O RADIUS OP Neutral Axis Perpendicular to Axis of Web. N H N rj- tOOO CO ON lO^rOCOiOTf-fOCOfOi-CO OnvO 0000 t>> t>. cnj q cm 10 vq 10 « n 00 00 t ro q q tototoTfTf4-^^^cococococNooi cm" cm* cm" cm* cm! h m P INERTIA. Neutral Axis Coincident with Axis of Web. CO CM vO 00 00 O CM CO COO 00 CM On 00 (M K ON to w COM onvo cm o onvo t^qvqiH N^^^t^^l" ^ CO CO O' "i- (Ni t^vd ON C~n COO CO 4" to CO CNl h m H M 6 CM m m 0) M H CM MOMENT Neutral Axis Perpendicular to Axis of Web. rj- ON w MD lO ONO OO C^COtv.'rfTj-rJ-CM iOO\H CM CO M \jT) m *-OvO *-0 CO^O O ^i" i-O t^* 0) vO *0 ^^vO ^* vO* vO* vO* H CM m" O uSoo OnO vO* "4*00 iO 4 On h tJ- CM* t> ^ ko moooo o ^ t-> tooo m oo oo vo to rj- cm cm m h VOIO"^COCMCMCMMHHM Width of Flange. Inches. oo to co to oooo to to to co i>.vq lONioqiococoqioioq q *o m i>« q t>. q lOTfrfiorfTtlO^Tt-iOrfcO^^^COCOCM* CO CM* CM* CM* Thickness of Web. Inches. ir) in to to to CM On On t>> K h NOO NiOH U) to to VO trj rj- lo rj- CO to rt" COVO rfcOCOCOCOCOCOCM CO (M CM CM OOOOOOOOOOOOOOOOOOOOOO Area of Section. Sq. In. q q to q iovo to to q q ^ q h to on to q q vq q q oq 6 to CM K CM ON CO O' ON to 00* N CX3 vO vO if) 4 OT CO CO H CM M M M H WM M Weight Per Yard. Lbs. O to tovO m to o o n- O m to On to O OvO O O 00 O LOCM CM ON CO O On to 00 NCOvO vO to to ^t" CO CO CO M (Nj i_i M I— i H H H H Sz= o EH -=H CD . g . g &; f . . s U CU tuO CO ^ r-^vo On looo hh CM N <^LO CO "+ 4 M' N N h N RADIUS OF GYRATION. Neutral Axis Coincident with Web Axis. r^oc oo nnio o o c o o o o Neutral Axis Parallel to Flange. i-i CM O co i>> On CI N N 0~\ lO h N 4 4 N CM CM « MOMENT OF INERTIA. Neutral Axis Coincident with Web Axis. vO iO iT) 0\ m mOOOO COOO in io ^ f o n m Neutral Axis Parallel to Flange. iO fO On t^OO On uovo co <-ovo cs 00 1 co O M On h Width of Flange. Inches. O O Thickness of Web. Inches. 00 00 ^j-oo rOH u-> CO CO 0) i- oo ^ CO CO CO CM CO d o d d d d ci Area, Sq. In. to lO ON O CM UO ON00 v O vO lo ro Weight Per Yard. Lbs, u-> io On O '-i CM lo ONOO VO VO ir> tJ- ro DESIGNATION. fcUO^G ^ JZ ^ 'r\ OJO OJO OJO OA CJO OJO ^ h133 Jh33 *S V V < < V V HWV V V V V V "i O ONOO r^vO 1— 1 1— 1 1x0. 01 Shape. ^00 O h M f^rt 00 "O vO vo ON O *0 ONOO tJ-00 CO l>» CO CO CM CM CM O O O O O O ONOO ioO^) H M CO CO CM CM CM "tf- ^f- LO CO CM w w H CO 0*00 uo uS rj- rf 00 00 00 00 lo co co co co r^. ^- ^" co d d d d d CM CM CO CO oo j>» »o rj- J ^ ^ ^ ^3 > ^ OJO OJO OJO g OX 3 3 3 W 3 V V V V V V V V V V ONOO t>»vO O ONOO JT^-O co co co co THE PHCENIX IRON COMPANY, Distance of Centre of Gravity from Outside of Web. oo O CO O ONNvOvOvOvOvOvO C0\0 O O 00 OO CO \D OO 00 VO LO LO lo LO l>> hhOOOOOOOOOOOOOO GYRATION. Neutral Axis Parallel to Web through Centre ot Gravity. OO h n lovO On h On OnvO CO CO O N n O m On ON t>. 0\0 tNvO vO vO vO iO lO ts N hhOOOOOOOOOOOOOO RADIUS OF Neutral Axis Perpendicular to Web Axis at Centre. N N covO hvO ^ O h tJ- coco tN oo CM CO LO ON CO (N LO -j-vO lovO tJ- lo O 01 ioioioioco444corncocomcococci -si Eh pa Neutral Axis Parallel to Web through Centre of Gravity. M tr^ONM t)- N C\ H VO H Onh ONt^"^"ON vq cm coo o m q cj lo lo m ^ on cm vo co oo cm d oo" lo 4 co lo co cm" cm cn'hloco 01 H Hi H MOMENT 0: Neutral Axis Perpendicular to Web Axis at Centre. Hi KvO CO CO O hvO ONNNNO LO Hi 00 LO t>> t>» ^t" LOVO CO O NO Hi HI CN 0) 4 Omi h lo CO On CO 00 K rj- COOO CO "i" lo lo t)~ CM lo COO lo 01 01 On t^vO CO NON LO ^ ^3" CO CM H Hi HI M Thickness of Web. Inches. LO CO CO LO 00 CO LO LO CO CM LO VO H N COH IONH OvO MO lo lo COOO LOrfcOLOCOOO lo h d o 6 M d d d d d d d 6 o 6 d Width of Flange. Inches. 00 LO LO CO CO CO LO vO LO co q lo lo q cm q q vq vq lo rt- cm o t>. ^^cococococococooi oi oi cm' cm co cm' Area of Section. Sq. In. q q q lo o co oo q m lo q oo io n q o O LO LO Hi LO 00 00 vO H tNvO* 4- IN LO o" 0) H H H H HI HI Weight Per Yard. O O lo O oo oo h lo O oo lon O lo lo m loco 00 vO hi C^vO tMOO N CM HI Hi H H M H | EH «4 5Z5 HH 1 Qj 0J3> in t>» to o tv to ^- tovq t>*vq oo oo n q n h n n t*-oo tooo to ^totocoto^^cotocococN torfcocN cm' oi co oi on H cn oi H H H >"+^ ^-M* *j ^.^j _j >>^. t^^. "on "on "on "on 00 00 00 00 *tx*bs*K*Kvb Co Co vb vb vb ^^^V)\^-%t%t-%j-*co*co O O CO CO CO CO CN 01 t^^O vOOOHHrJ-rhHMOOON On 00 00 t^vO H M "^-rJ-CN CN CN CN COCOCOCOtOtOtOXO^T^CN CN CN CM H m h H M h 63 THE PHOENIX IRON COMPANY, N vO 00 M HI O o PC M w o as W Q M (0 < a w rj- vO On i-i m « on o M m O m d vo oo oo oo vo 6 ro vO ON O 00 .2^ I 2*1*" "5 b£C3 SS 13 ^ 2 ° °* £-5 2^ vd vo 0> O ro ro N o g d ro 00 00 vO hh ro 00 O OO vO ^t- ro ro vO O ro *-n xo ro vO hh ro O N -> oo Q\ iO VO ro lo 04 KH 00 h* ro lo r^ d oo Heavy. Light. Heavy. Light. Heavy. V V V vb vb X X X X X V vb V vO N VO vO tJ- lO U-> VO 64 410 WALNUT ST., PHILADELPHIA. 6 6 6 6 6 6 6 6 d 6 6 6 6 6 6 6 6 6 6 6 6 6 6 On o M CO 6 6 cji-ic^io^t->.OWC^r^vDrrcsc^i-i»-( vO^-LocqroHHC^i-HCHOOOOOOO 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 NvOOO N (N O O On 00 00 iO 00 CO 00 VO 00 iO 00 CO 00 00 hh 00 iO iO 00 woo N vr> N loM Tj-t-H CO hh dodo 6 6 00 vO CO iO O CO 00 00 CO 00 . 4 4 CO V «M «h< H|(N r-l|iM r4tf r-l!^l V V M|<^ C0\-# H w> i/-> i-O oooooooo 00 4 V V V V V V V V V V V V rH|£M iH|N V V xxxxxxxx i: — I — i— i ^_ 0^ C^l i i 00 00 o\ o> ^- 66 410 WALNUT ST., PHILADELPHIA. CO coOvOONCOMvONNOO ON ON O 6 d « ON ON VO ON 00 oc o o o o o o o CO ON 00 co vo rj- co ro O O O Tj- N On 00 vO 00 ir>i-H ro N N t^vO ON O OO 00 vO vO vO vO N Is vO vO ^ io vo Tt" tJ- CO Tf" 6666666666666666 6 6 vO o vo vO N iO tJ- N N O W M M M O o o o o o o 00 ro »-« vo vO ON O 00 00 00 00 d m d 6 6 6 fO m O ON N O O 00 00 00 m m d d d O N m vO M M Q\ N N iO m ^ 6 6 6 6 6 6 6 M rj- m i>.ONroON»-ivOvO vo vO >-h\0 On vo tJ- ioON'-i ON 00 - 00 ON N VO N CO M fj M 4 00 ro N 00 O r(- N vO 00 vO CO On N O in vO cowvoco^< i-h eirii-iciMHioooob 00 covococovocovococococo oo m >-vor^vor^vo >-.^d _ vO ro vO covocovocovocovocovo 00 VO 1 00 N 0} i-i oooooooooooooooo vo on vo ON vO vO O w ^ 00 00 t On in ro N voW N COW COM COM CO ON 6 6 lO N UN VO ON vo i- t>» 00 00 in n n ro On vd On "O no* O 4 o\ in ro N iOMTj-fNCOMrOMcOMCO>-iMhH»-H hi 3 b/3 M 4 W bjO 3 3 w OJO t-H OJO GS ojo W 3 CO CO co co M xxxxxxxxxxxxxxxxxx lO vo vo vo CO CO CO M M rO ro N M roro^rJ-'t^miniOvO On ON vO vO ONON'txJ-rj-'tONON^'tONONOOOO O O ON ON 67 THE PHCENIX IRON COMPANY, CO PC < W w H X SBi e 53 'J D ° w 03 m au o PC a. Distance of Centre of Gravity from Top. r^vo vo t^OO 00 tJ- f^vO NN iOm On 00 CO ooo^o^ooo GYRATION. Neutral Axis Coincident with Web. N t^OO 00 00 CO vr> M hH OnOO O "TO^h hh* m 6 d w d d d d RADIUS OF Neutral Axis Parallel to Flange. On On 00 iO O N 'sf-vD r^O CO m \0 w O 00 ro d 6 6 m d hh' ~ d d F INERTIA. Neutral Axis Coincident with Web. Tj- On t^OO 00 hh O w> Oi On CO "tf-NO O O ^ *-* irirofl fOH m m c5 O MOMENT Neutral Axis Parallel to Flange. h 0\t}-0 O N TfvO vO N roa tOVQ i-j m -< d 6 6 6 6 6 6 6 6 Thickess of Web. Inches. co co i-O t"-» I—* 00 On i>» \Q ^ N OnOO <0 »-0 On d d 6 d d d d d d Area. ! Sq. In. iO On ir> OnvO N 0000 ro » On CO m d d CO ►J ' w CO Tt- ^J- LO CO CO C4 d d d d rt CO CO N d d d d 00 vO On c4 m* <-h* d xxxx hh N CO O O 00 O 68 410 WALNUT ST., PHILADELPHIA. DETAILS OF CONSTRUCTION IN Wrought-Iron Work. OR the convenience of Architects, Engineers, and i- Builders, some of the details of construction em- ployed in wrought-iron work are given in the following pages, and the adaptations of the various shapes to struct- ural uses will be illustrated and explained under the several heads into which the work is classified. In the building of Floors and Roofs, it is customary to make use of Beams, Channels, Columns, and other shapes of rolled iron. In planning a floor, the first point to be determined is the load that will probably be placed upon it. The weight of the materials composing the floor is usually termed the dead load, and the weight of the per- sons or stores of any kind that may be placed upon the floor is called the live load. The dead load of a fire-proof floor, made of rolled beams and four-inch brick arches, filled in above with concrete, may be taken at 70 pounds per square foot, and the live load for dwellings or offices may be assumed at 70 pounds additional, and on these assumptions the table on page 85 has been calculated. But FLOORS. 6* 69 J THE PHCENIX IRON COMPANY, in public buildings or churches, where large crowds of per- sons in motion may congregate, or in warehouses where heavy goods may be stored, it is evident that the loads will have to be determined by the circumstances, and will exceed the amounts above specified. For ordinary conditions the following total loads per square foot may be assumed as giving a safe approximation in practice : Dwellings or Orifice Buildings . . 140 pounds. Public Halls or Churches . ... 175 " Warehouses 150 to 300 " In order to support these loads with entire safety, J beams of various dimensions are offered in the accompanying tables. For floors of small span the lighter beams can be economically used, but for greater spans larger beams are necessary. That a beam should be strong enough to support a given load for a given span is not all that is requisite — it is equally important that it should be stiff enough. Rigidity prevents vibration, and the avoidance of this is of great importance, since repeated movements in the floor would injure and possibly destroy the masonry in the brick-work. It is, therefore, advisable, where circumstances permit, to consider whether deep beams placed further apart might not prove to be more economical than light beams near to each other. For the proper spacing of beams under various loads, reference may be had to the diagram given on page 40. Under no circumstances, however, should beams be strained beyond the limits of their elasticity; or, in other words, so strained that on the removal of the load they will not return to their original condition without set or per- manent deflexion. If a beam is required to sustain a load concentrated at the centre of the span, it must be noted that only one-half as much weight can be borne when so concentrated as could be supported if the load were uniformly distributed over the whole beam. 70 410 WALNUT ST., PHILADELPHIA. The figures given in the tables for the load-bearing capacity of any beam must then be divided by 2 to ascertain the safe load concentrated at the middle of the span, and this concentrated load will cause the beam to deflect t 8 q as much as would the distributed load named. If the load is to be concentrated at any other point than the centre, then the following statement of proportion will determine the case: The weight that the beam can carry at the centre is to the weight that it can carry at any other point as the rectangle of the segments of the span at the given point is to the square of half the span. For example, supposing a 12-inch 125-pound beam to support with safety a central load of five tons for a span of 20 feet, what load will it carry concentrated at a point 5 feet from one wall? Here, 5 tons : X tons : : 5 X x 5 : 10 X IO > or 6f tons. This rule is of service in such cases as when it is required to provide proper beams in floors under heavy local loads, such as safes or vaults. Having determined the load per square foot to be sus- tained, the proper beams to use may be ascertained by reference to Table II. The coefficient of safety is placed above each beam in this table, and this divided by the clear span in feet will show the strength of the beam at this span for a distributed load in net tons of 2000 pounds. The deflexion of the beam corresponding to this load will be found in the next line, and the weight of the beam should be deducted from the safe load. For any less load uniformly distributed the deflexion will be directly pro- portionate to that given in the table. To determine the strength of beams many experiments have been made, and the generally accepted theory with regard to the effect of applied loads is that which assumes a neutral axis at the centre of gravity of the cross-section of the beam, and supposes the material above this axis to be compressed while that below the axis is extended, the re- sistance of any element to the strains of compression or ex- tension being directly as its distance from the neutral axis. 7i THE PHCENIX IRON COMPANY, Certain general principles have been fully confirmed by experiment, such, for instance, as that in beams of equal length and breadth the strength varies directly as the square of the depth, and in beams of equal length and depth di- rectly as the breadth. Hence the strength of any beam may be represented by the following expression : breadth X .square of dept h length ^ The value of the constant being dependent upon the material of the beam. This may also be written, •^y area X depth X constant a X d X c length L Representing the various conditions of loading, it has further been determined by experiment that the following proportions obtain for all beams Fixed at one end and loaded at the other, \V — a X dXc . Fixed at one end and uniformly loaded, Supported at both ends and centrally loaded, w,. 4 r x ; !Xc ) ; Supported at both ends and uniformly loaded, W=8 ( a - X 4^). To apply these formulae to any given beam, it is necessary to obtain by experiment the value of the constant c, taking the average of a number of tests. One-sixth, one-fourth, or even one-third of this value may be taken as the working load, according to the conditions of service for which the beam may be designed. For wrought-iron rolled beams, c may be taken as 48,000 pounds, and the safe load per square inch of effective section at 12,000 pounds, or six net tons, and with this as a constant the tables showing the strength of Phoenix beams have been computed. 72 410 WALNUT ST., PHILADELPHIA. By " effective section" is meant that portion of the total section which is effective in resisting the strains of tension or compression, and it is ordinarily computed by adding one-sixth of the area of the stem or web to the entire area of one flange ; thus, a -f- ^ . In this estimate of the effective section two-thirds of the area of the web have been omitted from the calculation, because of the assumption that this portion of the web lies too near to the neutral axis to assist in offering any resist- ance to the strains caused by a load. The " effective depth" of a beam is the distance between the centres of gravity of its two flanges, and in Table I this effective depth has been expressed, both in feet, D, and in inches, d; the former being required in the formula for strength, while the latter is required in the formula for deflexion. For rolled beams, under the equally distributed loads of floors, the effective section of the lower flange is in tension and the upper flange in compression, so that if the safe load of six tons per square inch is assumed, the general formula will be w=8 /axdxc) = 8 D ( a + -e) 6 - L L Now, in this formula, it is only necessary to insert the proper values for "effective depth" and " effective section" given in the table for each particular beam, in order to de- termine its strength for any given span. The load-factor for each beam is thus dependent upon its depth and the quantity of metal in its flanges. This load-factor, when divided by the number expressing the clear span in feet, will give as a quotient a number indicating the weight in tons that the beam will carry with safety. For the several beams, the tables show what the proper loads are that may be placed upon them for each foot of clear span. Stiffness is a different quality from strength. A beam that may be quite strong enough to carry a given load may deflect under this load more than is desirable. 73 THE PHCENIX IRON COMPANY, About one-thirtieth of an inch per foot of clear span is the usual maximum of deflexion that is permissible. Under ordinary loads this is attained when the clear span is about twenty-six times the depth of the beam, and the heavy lines in the tables show for each beam where this limit may be found. Like the load-factor, the bending moment is dependent upon the effective depth and the effective section of the beam to which it is to be applied; the general formula for the deflexion of any beam under an equally distributed load .004 W. L3 By inserting the values proper to each beam, the results given in the following tables have been obtained. For the process of deriving this formula, see page 76 following. A close approximation to the actual deflexion at the centre, under the maximum safe load, may be obtained by dividing the square of the length of the span in feet by 62 times the depth of the beam in inches. DEFINITION OF TERMS USED IN FORMULA. W === Equally distributed load on any beam in net tons. L == Length of clear span, expressed in feet. a = Area of top, or bottom, flange, in square inches. a 7 = Area of stem of beam, in square inches. D == Effective depth of beam, expressed in feet. d — Effective depth of beam, expressed in inches. S ss= Strain per square inch of effective section ^a -f- ^) in tons of 2000 pounds. d = Deflexion in inches at middle for a central load. 6 / = Deflexion in inches at middle for a uniformly dis- tributed load. General formula for any I beam \ ^ 8 D (a -|- |) S under an equally distributed load, j L 74 410 WALNUT ST., PHILADELPHIA. TABLE I. ELEMENTS OF PH(ENIX BEAMS. Si T O CO [S l-O T M CO CO CO 01 H M H M i + 1 Tt-CO o" ON a o^oo Bo N NMD V)\o» 75 THE PHCENIX IRON COMPANY, The general formulae for deflexions given below are taken from Pro- fessor Moseley's " Mechanics of Engineering," edited by Professor Mahan, in 1856, changing the letters which he has employed to agree with those used in this work. Let / = The clear span, in inches. E = Modulus of elasticity — 24,000,000 pounds = 12,000 tons. I = Moment of inertia for the several forms. 5 = Deflexion at middle, in inches. W= Load, in tons, producing deflexion, a = Area, and d = depth of beam, in inches. Then, for a beam fixed at one end and loaded at the other, For a beam fixed at one end and uniformly loaded, W /3 6 ~ SET For a beam supported at both ends and loaded at the centre, W/3 ° 48 EI For a beam supported at both ends and uniformly loaded, For the several sections of beams the value of I will be as follows : b d 3 , l _ b dM>' d' 3 5. 'v^pi I = % jbd3+b'd'3-(b'-b)d"3 j a r2 pppr r b d 3 -b' d'3 I=. 7 8 54 r4 -= 6. I = By substituting, in formula 6, the effective areas of flange and stem, d2 I = (6 a + a') 12 Then, for shape 6, supported at both ends and loaded at the centre, W/3 48 X i2,oooX~— (6 a + a') Substituting 1728 L 3 for / 3 , to express the length of span in feet instead of inches, we have : W L 3 .036 W L 3 .006 W L 3 <5 = = , a/\ 27.78 (6 a + a') d2 (6 a + a') d2 (^a + -) d2 And for shape 6, supported at both ends and uniformly loaded, .004 W L 3 , In this form the formula for deflexion will be found in the table of beams, Table I. 76 1 410 WALNUT ST., PHILADELPHIA. i TABLES OF BEAMS, SHOWING THE PROPER SIZES FOR Varying Conditions of Mini and Spacing WITH THE CORRESPONDING DEFLEXIONS UNDER THE SAFE LOADS. 7 77 THE PHCENIX IRON COMPANY, TABLE II. Comparative Strength and Stiffness OF THE DIFFERENT SECTIONS OF WR0U6HT-IR0N BEAMS, MADE BY THE PHCENIX IRON COMPANY, FOR Sustaining, with entire safety, a Uniformly Distributed Load. i 89 138 15 15 15 200 Lbs. 150 Lbs. 125 Lbs. L L L d j= d 1 M <§ .5 a % eg .2 s§ bo a" s§ ta | be n at tf CO «$ ►3 \ PQ 1 "g PQ 1 ! (-=1 t2 CO 1 CO O IO 4I.O // .116 667 30.2 — f — .114 500 24.8 .112 417 1 1 37-2 .140 733 27.4 .138 550 22.5 .135 458 12 34-2 .167 800 25.2 •154 600 20.7 .162 500 *3 31.6 .I96 867 23.2 .182 650 I9.0 .189 542 H 293 .227 933 21.6 .212 700 17.7 .219 583 15 27.4 .26l 1000 20.0 • 2 54 750 l6.6 .253 625 16 25.6 .296 1067 18.9 .289 800 i5-5 .287 667 17 24.1 •334 1 133 17.8 .327 850 14.6 •3 2 4 708 18 22.8 .376 1200 16.8 •3 6 7 900 13.8 •3 6 4 75° 19 21.6 .419 1267 15.9 .410 950 13.0 .403 792 20 20.5 .463 1333 15.1 •455 1000 12.4 •449 833 21 195 .510 1400 14.4 .502 1050 11.8 •494 875 22 18.6 .560 1467 137 •55i I IOC 1 1.2 •539 917 2 3 17.8 .612 1533 131 .602 1 150 10.7 .589 958 24 17. 1 .667 1600 12.6 .656 1200 10.3 .644 1000 25 16.4 .725 1667 12. 1 .712 I25O 9.9 .699 1042 26 158 .785 1733 11. 6 .769 I3OO 9-5 •755 1083 27 15.2 .846 1800 I 1.2 .828 I350 9.2 .819 1 125 28 14.6 .906 1867 IO.8 .889 I4OO 8.9 .884 .966 1 167 29 14.1 •972 1933 10.4 .942 I450 8.6 1208 30 137 1.040,2000 10.0 1.017 I5OO 8-3 1.014 1250 78 410 WALNUT ST., PHILADELPHIA. TABLE II. Comparative Strength and Stiffness OF THE DIFFERENT SECTIONS OF WROUGHT-IRON BEAMS, MADE BY THE PHCENIX IRON COMPANY, FOR Sustaining, with entire safety, a Uniformly Distributed Load. 55 57 139 12' 12 12 170 Lbs. 125 Lbs. 96 Lbs. T J- 6, j CO a •| CO 3 "h CO -3 o E-< .2 E-i .2 far) a" a" OS ?==; « fac 1 ai "a a "g PQ 03 "0 I ►S « 1 *© i-q i 4 OO 1 O s | "el C/3 CJ> ¥ 29.2 .147 567 20.8 .144 417 15-6 .140 320 IO 20. .177 023 ,00 I0.5 .174 458 14.2 .170 352 I I 243 .210 680 17.3 .207 500 I3.0 .202 384 12 22.4 .246 737 l6.0 .243 542 I2.0 .237 416 n 20.9 .286 793 I4.9 .282 583 I I.I .252 448 14 19.4 .328 850 13.8 •325 625 IO.4 .316 480 15 I8.3 .374 907 I3.0 .360 667 9-7 .351 512 16 17.2 .423 9 6 3 12.2 .408 708 9.2 .407 544 17 l6.2 .475 1020 « 5 •459 750 8.7 .457 576 18 15-4 .530 1077 10.9 •513 792 8.2 •537 608 19 14.6 .587 1133 10.4 .578 833 7-8 .562 640 20 13-9 .648 1 190 9.9 .636 875 7-4 .617 672 21 13-3 .711 1247 9.4 .698 917 71 .685 704 22 12.7 .777 1303 9.0 .763 958 6.8 •744 736 23 12.2 .846 1360 8.7 .832 IOOO 6.5 .809 768 24 11. 7 .918 1417 8.3 .903 1042 6.2 .872 800 25 11. 2 .992 1473 8.0 .997 1083 6.0 .950 832 26 10.8 1.068 1530 7.7 1.053 1 125 5-7 1. 010 864 27 10.4 1. 147 1587 7-4 1.131 1 167 5-5 1.087 896 28 10. 1.230 1643 71 1.2 1 1 1208 5-3 1. 186 928 29 9-7 1.314 1700 6.9 1.294 1250 5.2 1.265 960 30 79 THE PHCENIX IRON COMPANY, TABLE II. Comparative Strength and Stiffness OF THE DIFFERENT SECTIONS OF WROUGHT-IRON BEAMS, MADE BY THE PHCENIX IRON COMPANY, FOR Sustaining, with entire safety, a Uniformly Distributed Load, 114 58 131 135 Lbs. 105 Lbs. 90 Lbs. 5 L L L • d .2 c/i d •2 CO d _© & «§ .2 1 a .5 S3~ a" § « i 0) Pi "a « "el « pq 1 O § g .1 <2 & $. CO | IO 17.8 .149 450 15.5 11 .164 350 133 II .162 300 1 1 l6.2 .180 495 14.0 .197 385 12. 1 .197 330 12 14.8 .214 54o 12.9 .236 420 I I .O .232 360 x 3 137 .251 585 11. 8 .278 455 I0.2 .274 390 14 12.7 .291 630 I I.I .322 490 9 5 .318 420 15 1 1 .8 •333 675 10.2 •3 6 4 525 8.8 •363 450 16 1 1.1 .380 720 9-7 .414 560 8-3 .415 480 17 10.5 •43i 765 9.1 .470 595 7.8 .468 5IO 18 99 .481 810 8.6 .528 630 7-4 .527 540 19 9-3 •533 855 81 .589 665 7.0 .587 570 20 8.9 •595 900 7-7 .652 700 6.6 .645 600 21 8.5 .658 945 7-3 .719 735 6-3 •713 630 22 8.1 .721 990 7.0 .788 770 6.0 .781 660 23 7-7 .784 io35 6.7 .862 805 5-7 .848 69O 24 7-4 .856 1080 6-5 .941 840 5-5 .930 720 25 7-1 .928 1125 6.2 1.025 875 5-3 I.OI3 750 26 6.8 1. 00 1 1 70 5-9 1. 105 910 5-i I.O96 780 27 6.6 1.08 1215 5-7 1 187 945 4-9 I. 179 8lO 28 6-3 1. 16 1260 5-5 1.27 1 980 4-7 1.262 84O 29 6.1 1.24 1305 5-3 1.360 1015 4.6 1.372 870 30 5-9 i-33 i35o 5.1 1-455 1050 4-4 1-453 9OO 80 410 WALNUT ST., PHILADELPHIA. TABLE II. Comparative Strength and Stiffness OF THE DIFFERENT SECTIONS OF WROUGHT-IRON BEAMS, MADE BY THE PHCENIX. IRON COMPANY, FOR Sustaining, with entire safety, a Uniformly Distributed Load. 4 5 6 3 S 9 150 Lbs. 84 Lbs. 70 Lbs. w = - 108 - — L L L ■4 g — CO d 1 E-< ►-^ .S E-i ff -s « a" bo p) i s "a e as 0- l-p cS 'o & i O & eg 1 a . 00 s CO CO co 10 197 .203 500 10.8 .192 280 9.2 .190 233 j 1 17.8 .243 C CO 9.8 .231 308 8.4 .231 256 1 2 16.4 .296 600 9.0 •276|336 7-7 •275 280 r 3 15.2 •347 050 8.3 •324S364 7.0 .318 303 14 I4.I .402 700 7-7 •376 392 6-7 .380 326 T c 1 J 13-2 •459 7 CO 7.2 .432 420 6.2 •432 350 16 12.3 .530 800 6.7 488448 5-7 .448 373 17 11. 6 .585 85O 6-3 •55O476 5-4 .548 396 18 10.9 •654 9OO 6.0 .622 504 5i •615 420 *9 10.3 •737 950 5-7 •695I532 4-8 .690 443 20 9.8 .807 IOOO 5-4 .768 56O 4.6 .761 466 21 9-3 .891 I050 5-i .839 588 4-4 .842 490 22 8.9 .980 I IOO 4.9 •927 6l6 4.2 •925 5i3 23 8-5 1.07 I I50 4-7 I. OI 644 4.0 I.OI 536 24 8.2 1. 17 I200 4-5 I. IO 672 3-8 I.08 560 25 7-9 1.27 I25O 4-3 I. I 9 700 3-6 1. 16 583 26 7.6 1,38 I3OO 4-i 1.27 728 3-5 1.27 606 27 7-3 148 !35° 3-9 I.36 756 3-4 1.38 630 28 7-o;i.59 1400 3-8 I.48 784 3-3 1.49 653 29 6.8 1.70 145° 3-7 I.6O 8l2 3-2 I.60 676 30 6.6 1.83 1500 3-6 i-73 84O 3-i i-73 700 7* 81 THE PHOENIX IRON COMPANY, TABLE XX. Comparative Strength and Stiffness OF THE DIFFERENT SECTIONS OF WROUGHT-IRON BEAMS, MADE BY THE PHCENIX IRON COMPANY, FOR Sustaining, with entire safety, a Uniformly Distributed Load, 113 8 81 Lbs. 9-4 8.5 7.8 7.2 6.7 6.2 5-9 5-5 5-2 5-o 47 4-5 4.2 4-i 3-9 3-7 3-6 3-5 3-3 3-2 3-1 .215 .258 297 .308 324 .361 .420 378 .478 405 .546 432 270 35i .617 459 .693 486 .783 513 .859 540 .952 567 1.02 1. 14 1.23 1.32 1.44 i-57 1.65 1.78 1.91 594 621 648 675 702 729 756 783 810 59 8 7-4 6.8 6.2 5-7 5-3 4.9 4.6 4-3 4-i 3-9 3-7 3-5 3-4 3-2 3-1 2.9 2.8 2.7 2.6 2-5 2.4 •215 .312 •365 216 264 238 260 282 .424 3°3 •475 325 •549 347 .6i6 ! 368 .697i39° .780 412 .863 433 .946 455 1.05 477 1 13 1.25 1.32 i-43 1-55 1.66 1 77 1.88 498 520 542 563 585 607 628 650 112 *7" 69 Lbs. w=4 2 - 7.2 6.5 6.0 5-5 5-i 4.8 4.5 4.2 4.0 3.8 3.6 3-4 3-2 .252 230 .303 253 •3635276 .424,299 .491 322 .568 345 .645 368 .724 391 .818414 •9 1 4 437 1 .01 1. 10 1. 19 31 r "32 3-o !-45 2-9! I -59 2.8 1.72 2.7 1.86 2.6 2.00 2.5 2.14 2.4 I2.27 460 483 506 529 552 575 598 621 644 667 690 82 410 WALNUT ST., PHILADELPHIA. TABLE II. Comparative Strength and Stiffness OF THE DIFFERENT SECTIONS OF WROUGHT-IRON BEAMS, n MADE BY THE PHCENIX IRON COMPANY, FOR Sustaining, with entire safety, a Uniformly Distributed Load. io II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 SO 7 *7" 55 Lbs. 5-4 4.8 4-5 4.2 3-9 3.6 3-4 3-2 3-o 2.8 2.7 2.5 2.4 2.3 2.2 2.1 2. 1 2.0 1.9 1.8 1.8 .248 •293 •357 .423 .491 .651 .992 .06 .17 .28 •39 5o .69 80 90 01 23 183 201 220 238 256 558 275 293 .722 311 .803 330 .882 348 366 385 403 421 440 458 476 495 513 53i 55o ill 6 50 Lbs. 4.5 4.1 3-7 3-4 3-2 3-o 2.8 2.6 2-5 2.4 2.2 2.1 2.0 1.9 1.8 1.8 i-7 1.6 i.6 i-5 1.5 .290 •352 .412 167 183 200 . " 217 .566 233 •653 250 267 .740 .824 283 .940 300 1.06 125 1-37 1.49 1.60 1.81 1.92 2.02 2.26 2.36 2.61 3i7 333 350 367 383 400 417 433 45o 467 483 500 W d c/5 s « bo a s3 ►3 &" PQ c£ CO C 3.5 - // .286 133 3.2 .348 I46 2.9 .410 l6o 2.7 .486 173 2-5 .562 186 2.3 .636 200 2.2 .738 213 2.0 .805 226 .907 24O 1.8 I.OI 253 i-7 1. 11 266 1.6 1. 21 28o 1.6 i-39 293 io 1.49 306 l i 1.58 320 1.4 1.79 333 1.87 346 1.3 2.09 360 1.2 2.15 373 1.2 2.39 386 1.1 1 2.43 400 S3 THE PHGENIX IRON COMPANY, TABLE XT. Comparative Strength and Stiffness OF THE DIFFERENT SECTIONS OF WROUGHT-IRON BEAMS, MADE BY THE PHOENIX IRON COMPANY, FOR Sustaining, with entire safety, a Uniformly Distributed Load. 106 105 65 S" 5" 4 36 Lbs. 30 Lbs. 30 Lbs. - L L L i | . £ "1 1 .5 & « 1 « bo bC cj ei o 3 of pq cj O ~a |< PQ ? CO 42 1 i J 00 CO 2.5 .337 120 2.1 •336 IOO I.8O .448 IOO 10 2.3 •413 132 1.9 .405 no I.63 •545 no II 2.0 .466 144 i-7 .471 I.50 .643 1 20 1 2 1.9 .563 1^6 1.6 •563 I 30 1.38 •752 1 ^0 I 7 1.8 .667 168 i-5 .660 I40 1.28 .872 140 14 i-7 .774 180 i-4 •757 I50 I.20 1. 00 150 15 1.6 .885 192 1-3 .854 l6o 1. 12 113 160 16 15 •995 204 1.2 •945 I70 I.06 1.29 170 17 i-4 1. 10 216 1.2 1. 12 l8o I. OO 1.44 180 18 1-3 1.20 228 1.1 1. 21 I90 •95 1.62 190 19 1.2 1.29 240 1.0 1.28 200 .90 1.79 200 20 1.2 1.50 252 1.0 i-45 2IO .85 1.95 210 21 II 1.58 264 •95 1.62 220 .81 2.14 220 22 I.I 1.80 276 90 i.75 230 •782.35 230 23 I.O 1.86 288 .85 1.88 24O •75 2-57 240 24 1.0 2. 11 300 .82 2.05 250 .72 2.79 250 25 •95 2.25 312 .80 2.25 260 .693.01 260 26 .92 2.44 324 •77 2-43 270 .66 3.26 270 27 .90 2.66 336 •75 2.64 28o •64 3-5I 280 28 .86 2.83 348 .72 2.81 29O .62 3-77 290 29 .83 j3-20 360 .7013.03 300 .60 4.02 300 30 84 410 WALNUT ST., PHILADELPHIA. PHCENIX BEAMS. THEIR ADAPTATION AND DUTY AS FLOORING JOISTS. Clear Span. 3' apart 3 l A' apart 4' apart apart 5' apart apart 6' apart 10 feet. Load lbs. I 30 □ ' 4,200 35 □' 4,900 6 40 5,600 45 6,300 50 □' 7,000 55 7,700 7 or 8" 6j n' 8,400 12 feet. Load lbs. I 36 □' 5,040 6 42 5,88o r 7" 48 6,720 54 7,56o 7" 60 8,400 66 9,240 8 7 2 10,080 ff 14 feet. Load lbs. I 42 5,88o 7 49 6,860 r 8" 56 7,840 63 8,820 3 or 9" 70 70 9,800 77 10,780 9" 84 11,760 70 16 feet. Load lbs. I 48 □ ' 6,720 8 56 7,840 64 8,960 9" 70 72 10,080 9" 80 11,200 84 88 12,320 IO / / 2 96 13,440 " 105 18 feet. Load lbs. I 54 7,56o 8 or 9" 1 6 g* 8f 6*" 9i 91 Sf ys Hi m hi 9J 7A 9f 7A 9H ONE COLUMN. Area of Weight Least SIZE OF Cross per Foot Radius of RIVETS. Section. in Gyration. Sq. Inches. Pounds. Inches. 3-8 12.6 1-45 IX ii 4.8 16.O I.50 I* 5.8 19-3 i-55 If 6.8 22.6 1-59 1* 6.4 21.3 1.92 i X if 7.8 26.O 1.96 if 9.2 3O.6 2.02 if 10.6 35 3 2.07 i* 12.0 40.0 2.1 1 "1 *3-4 44.6 2.16 2 14.8 49-3 2.20 7-4 24.6 2.34 !*x if 9.0 30.0 2-39 *4 10.6 35-3 2-43 i If 12.2 40.6 2.48 If 13.8 46.0 2.52 If 15-4 5i-3 2.57 2 17.0 56.6 2.61 2f IOO 410 WALNUT ST., PHILADELPHIA. GO GO DIAMETERS IN INS. ONE COLUMN. SIZE OF M D Over Area of Weight Least -si M J Q Out- side. Cross per Foot Radius of RIVETS. W Inside. Section. in Gyration. E-> Flanges Sq. Inches. Pounds. Inches. 1 4 7 1 6 7 i l 7 1 6 TT 9 IO O 33 3 2.8o f X H 7 1 3 /T6 I2.0 2 8c z *°j H 8 8 f I / 1 6 1 1 1 6 I4.0 46.6 2.90 2 7 T6 8- 1 - 10 II# 1 14 1 6.0 jj" j 2 Qd. H ] 2 (I 1 1 1 3 10 18.O 60.0 2.98 9 T 5oo 5.602 Beam yields slowly at this load. 114 410 WALNUT ST., PHILADELPHIA. 9-inch Beam. 150 Lbs. per Yard. Area, 15 Sq. Inches. Clear Span, 14 Feet. Centre Deflex- In- Centre Centre Deflex- In- Load, ion, crease, Remarks. Load, Load, ion, crease, Inches. in Lbs. Inches. Tons. ______ 5,6o8 .102 6,720 3 .048 6,720 .126 .024 8,960 4 .060 .012 7 840 .148 .022 11,200 5 •073 .013 8,960 .170 .022 13,440 6 .090 .017 10,080 .192 .022 15,680 7 .105 .015 11,200 .214 .022 17,920 8 .120 .015 12,320 •239 .025 20,160 9 •134 .014 i3,44o .261 .022 22,400 10 .148 .014 14,560 .287 .026 24,640 11 .161 •°I3 15,680 .310 .023 26,880 12 .178 .017 16,800 •336 .026 29,120 11 .191 .013 17,920 •359 .023 3^360 .206 ■015 19,040 .382 .023 33,609 15 .222 .016 20,160 .409 .027 35,840 16 •234 .012 21,280 •435 .026 38,080 17 .246 .012 22,400 .458 .023 40,329 18 .258 .012 23,520 .487 .029 42,660 J 9 .271 .015 24,640 .516 .029 44,800 20 .287 .016 25,760 •543 .027 47,040 21 •305 .018 26,880 • 572 .029 28,000 .600 .038 29,120 .633 load left Weight removed. Permanent set, .016. •033 J stand After lapse of one hour the load of It 29,120 .682 .049 1 % hour. Wt.rem. tons was replaced, and caused a total ,082 deflexion of .222 inches as before. Perm, set 15-inch Beam. 200 Lbs. per Yard. Area, 20 Sq. Inches. Clear Span, 14 Feet. 12-inch Beam. 125 Lbs. per Yard. Area, 12]4 Sq. Inches. Clear Span, 27 Feet. Centre Load, Deflexion, Increase, in Lbs. Inches. Inches. 6,720 7,840 .691 .821 .130 8,960 .948 .127 10,080 1. 061 •"3 11,200 1. 186 .125 12,320 1.328 .142 *3,34o 1.466 .138 14,560 1 630 .164 15,680 1.800 .170 i6,8co 1.976 .176 17,920 2.228 .252 19,040 2-455 .227 20,160 2.742 .287 20,720 2.900 .158 20,720 2.965 .065 Last load left on 15 minutes. Deflexion increasing to 2.965. 15-inch Beam. 155 Lbs. per Yard. Area, 15}^ Sq. Inches. Clear Span, 27 Feet. I I Centre Load, i Deflexion, Increase, in Lbs. ! Inches. I Inches. 6,720 7,840 8,960 10,080 11,200 12,320 13,440 i 4j56o 15,680 16,800 17,920 19,040 20,160 22,400 24,640 25,760 342 .402 .462 •523 .580 •639 .707 .778 •845 ■9*3 •992 1.063 1. 149 1.309 1-505 1.603 .060 .060 .061 •057 •059 .068 .071 .067 .068 •079 .071 .086 .160 .196 Load removed. Deflexion decreased to .261 permanent set after lapse of x / 2 hour. "5 THE PHCENIX IRON COMPANY, RECORD OF TESTS OF PHCENIX COLUMNS Made with Hydraulic Press, 260 □ " Piston Area. SIZE. Length. S May B B 1 A A A A B B C c 3, 1873. 1.46 1.46 0.92 0.92 1.01 1.01 53-5 53.6 35-9 35.o 8" 8" 4// 4" 4// 4// 23.8' 24/ 23-3" 22.8 / July 19, 1873. C I 23.2 / '34.5 C I 23.2 I34.5 June 2, 1875. C | 27' '39.9 € I 27 I39.9 Aug. 5, 1875. C i 28 / 140.7 c ! 28 40.7 4 6.97 6.97 5.62 5.62 2.92 2.92 5.84 5-95 io.53 8.50 13.31 12.85 1370 13.89 13.58 13.58 © -T3 2 § 3 422 421 37o 37o 166 162 176 97 383 325 5°o 200 500 500 400 5°o 800 ■^3 Pi 50016 500 36 000 38 573 387 867 867 889 555 274 387 436 800 455 000 422 400 302 400 472 584 497 028 32 742 35 408 31 000 21 700 34 800 36 600 -3 ^ -2 o 35 974 35 974 35 99o 35 990 36 000 36 000 18 430 7 457 Flat. 419 25 235 25 182 562 Round. Flat. 25 774 25 774 23 415 11 420 Round. 23 165 23 165 Flat. The breaking-load of a bar of wrought iron one inch square I2 7/ c. to c. of points of support is just 2240 pounds. 116 410 WALNUT ST., PHILADELPHIA. NOTES CONCERNING SPECIFICATIONS OF QUALITY FOR IRON. The tensile strength of iron is properly determined by- ascertaining the load under which permanent set takes place, and the amount of stretch under the proof load, rather than from the ultimate load that causes the fracture of the bar. In other words, the elastic limit rather than the breaking strain should be regarded as the measure of quality in a bar, and working loads should be proportioned with reference to the elastic limit instead of to the so-called ultimate strength. Tough, sinewy iron is what is required in a tension bar, and although a hard, unyielding iron may show greater ultimate strength under a gradually applied strain, yet it is not suitable for use under tension for the reason that a sudden shock may cause it to snap under a weight that it ought to carry with entire safety. Good bar iron should be of uniform character and pos- sess a limit of elasticity of not less than 25,000 pounds per square inch. The ultimate resistance of prepared test- bars having a sectional area of about one square inch for a length of 10 inches should be not less than 50,000 pounds per square inch when the test-bars have been prepared from full-sized bars having not more than 4 square inches of sectional area. For- each additional square inch of full- sized bar area above 4 square inches a reduction of 500 pounds per square inch may be allowed down to a mini- mum ultimate resistance of 46,000 pounds. The amount of stretch under the breaking load should be not less than 15 per cent, in 10 inches of the test-bar. 117 THE PHCENIX IRON COMPANY, Bars that are to be used in tension should stand, without cracking, a cold bending test to 90 degrees to a curvature the radius of which is about the thickness of the bar under test, and at least one third of the lot should stand bending to 180 degrees under the same conditions. A round bar, one inch in diameter, should bend double, cold, without signs of fracture. A square bar of the same quality may show cracks on the edges under such a test. Under a breaking pull the reduction of area should be not less than 25 per cent, of the original section. The shape of a bar has much influence in determining the breaking-strain. The ultimate strength of round bars is, for this reason, considerably greater than that of flat bars, but in either case the elastic limit will be found to occur at about the same point for equally good qualities of iron. Within the elastic limit the extension of iron may, for all practical purposes, be stated as follows : Wrought iron, of its length per ton per square inch. Cast iron, -^Vo" of its length per ton per square inch. The compression of wrought iron within the limits of elasticity follows the same law, and the amount of shorten- ing under pressure will be in direct proportion to the weight applied. But with cast iron the amount of compression does not follow a constant ratio, the compression per ton becoming greater with the increase of the weight. Thus, a cast iron bar, one square inch in section was compressed Wot °^ l en gth by a load of one ton ; but under a load of 17 tons, instead of being compressed -^Jq, it was com- pressed The Modulus of Elasticity is a term used to des- ignate such a weight as would extend a bar through a space equal to its original length, supposing the elasticity of the bar to be perfect. Or, the modulus of elasticity of any given material in feet is the height in feet of a column of this material, the weight of which would extend a bar of any determinate length through a space equal to this length. Thus, if one ton extends an inch bar of wrought iron one ten-thousandth of its length, it is evident that, upon the 118 410 WALNUT ST., PHILADELPHIA. supposition that the bar is perfectly elastic, 10,000 tons would extend it to twice its original length. Hence, on this assumption, 10,000 tons, or 22,400,000 pounds, will be the modulus of elasticity of the wrought iron stated in weight. But an inch bar of wrought iron to weigh 22,400,000 pounds, at 2t}i pounds per foot, would be 6,720,000 feet long, and this would express the modulus of elasticity in feet. The modulus of elasticity will, of course, vary according to the character of the material tested, being much higher in the better than it is in the lower grades of iron, but it forms a very useful and convenient standard of comparison in determining quality. KIRKALDY'S CONCLUSIONS. Mr. Kirkaldy sums up the results of his experimental in- quiry in the following concluding observations, which the student should study carefully : 1. The breaking-strain does not indicate the quality, as hitherto assumed. 2. A high breaking-strain may be due to the iron being of superior quality, dense, fine, and moderately soft, or simply to its being very hard and unyielding. 3. A low breaking-strain may be due to looseness and coarseness in the texture, or to extreme softness, although very close and fine in quality. 4. The contraction of area at fracture, previously over- looked, forms an essential element in estimating the quality of specimens. 5. The respective merits of various specimens can be cor- rectly ascertained by comparing the breaking-strain jointly with the contraction of area. 6. Inferior qualities show a much greater variation in the breaking-strain than superior. 7. Greater differences exist between small and large bars in coarse than in fine varieties. 119 THE PHCENIX IRON COMPANY, 8. The prevailing opinion of a rough bar being stronger than a turned one is erroneous. 9. Rolled bars are slightly hardened by being forged down. 10. The breaking-strain and contraction of area of iron plates are greater in the direction in which they are rolled than in a transverse direction. 22. Iron is less liable to snap the more it is worked and rolled. 33. The ratio of ultimate elongation may be greater in short than in long bars in some descriptions of iron, whilst in others the ratio is not affected by difference in the length. 44. Iron, like steel, is softened, and the breaking-strain reduced, by being heated and allowed to cool slowly. 54. A great variation exists in the strength of iron bars which have been cut and welded ; whilst some bear almost as much as the uncut bar, the strength of others is reduced fully a third. 55. The welding of steel bars, owing to their being so easily burned by slightly overheating, is a difficult and un- certain operation. 56. Iron is injured by being brought to a white or weld- ing heat, if not at the same time hammered or rolled. 57. The breaking-strain is considerably less when the strain is applied suddenly instead of gradually, though some have imagined that the reverse is the case. 61. The specific gravity is found generally to indicate pretty correctly the quality of specimens. 62. The density of iron is decreased by the process of wire-drawing, and by the similar process of cold rolling,* instead of increased, as previously imagined. 64. The density of iron is decreased by being drawn out under a tensile strain, instead of increased, as believed by some. * Note. — The conclusion of Mr Kirkaldy in respect to cold rolling is undoubtedly true when the rolling amounts to wire-drawing; but when the compression of the surface by rolling diminishes the sectional area in greater proportion than it extends the bar, the result, according to the experience of the Pittsburgh manufacturers, is a slight increase in the density of the iron. I20 410 WALNUT ST., PHILADELPHIA. 200. It must be abundantly evident from the facts which have been produced that the breaking-strain when taken alone gives a false impression of, instead of indicating, the real quality of the iron, as the experiments which have been instituted reveal the somewhat startling fact that frequently the inferior kinds of iron actually yield a higher result than the superior. The reason of this difference was shown to be due to the fact, that whilst the one quality retained its original area only very slightly decreased by the strain, the other was reduced to less than one-half. Now surely this variation, hitherto unaccountably completely overlooked is of importance as indicating the relative hardness or softness of the material, and thus, it is submitted, forms an essential element in considering the safe load that can be practically applied in various structures. It mtist be borne in mind that although the softness of the material has the effect of lessen- ing the amount of the breaking-strain, it has the very oppo- site effect as regards the 7uorking-strain. This holds good for two reasons : first, the softer the iron the less liable it is to snap; and second, fine or soft iron, being more uniform in quality, can be more depended upon in practice. Hence the load which this description of iron can suspend with safety may approach much more nearly the limit of its break- ing-strain than can be attempted with the harder or coarser sorts, where a greater margin must necessarily be left. 202. As a necessary corollary to what we have just en- deavored to establish, the writer now submits, in addition, that the working- strain should be in proportion to the break- ing-strain per square inch of fractured area, and not to the breaking-strain per square inch of original area as hereto- fore. Some kinds of iron experimented on by the writer will sustain with safety more than double the load that others can suspend, especially in circumstances where the load is unsteady, and the structure exposed to concussions^ as in a ship or railway bridge. KIRKALDY'S RULE FOR COMPARING THE QUALITIES OF IRON: The breaking-weight per square inch of the frac- tured area, instead of the breaking-weight or strain per square inch of the original area. 121 THE PHCENIX IRON COMPANY, DIMINUTION OF TENACITY OF WROUGHT IRON At High Temperatures. EXPERIMENTS FRANKLIN INSTITUTE, 1839. WALTER JOHNSON AND BENJAMIN REEVES, COM. c. Fahr. 1 Diminution per cent, of Max. Tenacity. C. Fahr. Diminution per cent, of Max. Tenacity. 271° 520 O.0738 500° 932° 0.33 2 4 299 O.0869 508 o-3593 313 O.0899 554 0.4478 316 O.0964 599 o.55H 332 630 0.1047 624 "54 0.6000 350 0.1I5S 626 0.601 1 378 O.1436 642 0.6352 389 732 O.1491 669 0.6622 390 O.I535 674 1245 0.6715 408 O.1589 708 1306 0.7001 410 O.1627 440 0.20IO The contraction of a wrought-iron rod in cooling is about equivalent to yoiroo" OI " l en g tn from a decrease of 15 Fahr., and the strain thus induced is about one ton for e very- square inch of sectional area in the bar. For a rod of the lengths given below the contraction will be as follows : Length of rod, in feet, 10 30 40 50 75 Contraction, in inches, for 15° .012 .024 .036 .048 .060 .090 .120 .180 100° -080 .160 .240 .320 .400 .600 .800 1.200 150° .120 .240 .360 .480 .600 .900 1.200 1.800 Contraction and expansion being equal, the pressure per square inch induced by heating or cooling is as follows : For temperatures varying by 15 Fahr. : Variation, 15 30 45 60 75 105 120 150 degrees. Pressure, 123457 8 10 tons. Stoney gives 8° C. =c 14.4 Fahr. as equivalent to a press- ure of one ton per square inch for wrought iron, and 15 C. = 27 Fahr. for cast iron. 122 410 WALNUT ST., PHILADELPHIA. LINEAR EXPANSION OF METALS. Between o° and ioo° C. For i° C. For i° Fahi*. Zinc .... 0.00294 Lead .... 0.00284 Tin .... 0.00222 Copper, Yellow . 0.00188 Copper, Red . . 0.00171 Forged Iron* . 0.00122 .0000122 .00000677 Steelf .... 0.001 14 .0000114 .00000633 Cast Iron* . . o.ooiii .0000111 .00000616 For a change of ioo° Fahr., a bar of iron 1475' long will extend 1 foot. Similarly, a bar 100 feet long will extend .0678 foot, or .8136 inch. According to the experiments of Du Long and Petit, we have the mean expansion of iron, copper, and platinum, between o° and ioo° C, and o° and 300 C, as below : From o° to ioo° C. o° to 300 C. Iron 0.00180 0.00146 Copper 0.001 7 1 0.00188 Platinum 0.00884 0.00918 The law for the expansion of iron, steel, and cast iron at very high temperatures, according to Rinman, is as follows : From 25 to 525 C. Red Heat=5oo° C. For i° C. i° Fahr. Iron 00714 .0000143 = .0000080 Steel 01071 .0000214= .0000119 Cast Iron . . .01250 .0000250 — .0000139 From 25 to 1300 . Nascent White=i275° C. Iron 01250 .00000981 = .00000545 Steel 01787 .00001400 = .00000777 Cast Iron . . .02144 .00001680 = .00000933 From c;oo to 1500 . . Dull Red to White Heat=iooo° C. Difference. Iron °°535 -0°ooo535 = .0000030 Steel 00714 .00000714 — .0000040 Cast Iron . . .00893 .00000893 = .0000050 Ratio of Expansion in Hundred Parts, assuming Forge Iron to Expand between o° and ioo° C. =.00122. From o° to ioo°. 25 to 525 . 25 to 1300°. 500 to 1500 . Iron. .100 per ct. 117 per ct. 8operct. 44 per ct. Steel . 93 " 175 " 114 " 58 " Cast Iron 91 " 205 " 137 " 73 " * Laplace and Lavoisier. f Ramsden. I23 THE PHCENIX IRON COMPANY, DIFFERENT COLORS OF IRON CAUSED BY HEAT. POUILLkT. C. Fahk. Color. 2io° . . . 410 . . . Pale Yellow. 221 . . . 430 . . . Dull Yellow. 256 . . . 493 . . . Crimson. 261 ' * ' 502 }. . . Violet, Purple, and Dull Blue; be- 370 . . . 680 J tween 261 C. to 370 C. it passes to Bright Blue, to Sea Green, and then disappears. 500 . . . 932 . . . Commences to be covered with a light coatingof oxide; losesagood deal of its hardness, becomes much more impressible to the hammer, and can be twisted with ease. 525 • c . 977 . Becomes Nascent Red. 700 . . . 1292 . . . Sombre Red. 800 . . . 1472 . . . Nascent Cherry. 900 . . . 1657 . . . Cherry. IOOO . . . 1832 . . . Bright Cherry. I IOO . . . 2012 . . . Dull Orange. 1200 . . . 2192 . . . Bright Orange. 1300 . • • 2372 . . . White. 1400 . • • 2552 . . . Brilliant White— Welding Heat. 1500 . • • 2732 \ . Dazzling White. 1600 . . . 2912 I MELTING POINT OF METALS. Name. Fahr. Fahr. Authority. Platina ...... 4593° Antimony .... 955 ... 842 ... J. Lowthian Bell. Bismuth 487 ... 507 .. . Tin (average) . . 475 Lead " . . 622 . . . 620 ... " Zinc 772 ... 782 .. . ^ t f I022..2OI2 . .White.) -n :il . CastIro11 20IO {20l2..2i 9 2 . .Gray. } PoUlllet Wrought Iron . . 2910 . . 2733 . . . Welding Heat. " Steel 2370 . . 2550 Copper (average). 2174 124 410 WALNUT ST., PHILADELPHIA. NOTES ON THE WEIGHT AND COMPOSITION OF AIR, l cubic foot of air at 32 Fahr., under a pressure of 14.7 lbs. per square inch, weighs .080728 lb. Therefore, 1000 cubic feet = 80.728 lbs. I cubic foot = 1.292 oz. . 1 cubic foot of air contains I cubic foot of air contains 53.85 cubic feet of air contain f 23 per 1 1 77 per ' 23 per cent. Oxygen. cent. Nitrogen. .29716 oz. Oxygen. .99484 oz. Nitrogen. 1.29200 total weight. .0185725 lb. Oxygen. 555 lb. Nitrogen. .080728 lb. r 1. 000 lbs. Oxygen. , 3-347 lbs. Nitrogen. 4.347 lbs. J. 0185 ( .0621 Carbonic acid = C 2 == 22. :6. Ot=\ 2 = 16. 6 -f- 16 — 22. For combustion to carbonic acid I lb. of coal requires 2§ lbs. of oxygen, or 143.6 cubic feet of air, supposing all of the oxygen to combine with the coal. 280 to 300 cubic feet of air pet pound of coal is the usual allowance for imperfect combustion. 11.59 lbs. of air for perfect combustion. 24 lbs. of air for imperfect combustion. 125 THE PHCENIX IRON COMPANY, THE above cut illustrates a girder composed of two beams supporting a wall. During the construction a tem- porary prop should be placed beneath the girder after several courses of brick have been laid, and the prop should not be removed until the masonry is dry. This will prevent undue deflexion of the girder. The girder should be of sufficient strength to sustain the entire weight of the wall between perpendicular lines above the span to a height corresponding to the apex of the dotted lines. Assuming the weight of a cubic foot of brick wall to be 112 pounds, a superficial square foot of 9 inch wall will weigh 84 pounds, of 13 inch wall 121 pounds, and of 18 inch wall 168 pounds, and the following table specifies suitable beams for use as girders over the several spans named. PROPER SIZES OF BEAMS TO USE AS GIRDERS FOR SUPPORTING WALLS. SPAN. 13 r/ Wall. SPAN. 13" Wall. Feet. Feet. 8 to IO 2- —6" 40 lbs. l8 to 20 2— -\o\" 90 lbs. IO to 12 2- —7" 55 lbs. 20 to 22 2 — -12" 96 lbs. 12 to 14 2- -8" 65 lbs. 22 to 24 2— -I2 // 125 lbs. 14 to 16 2- — 9 // 70 lbs. 24 to 26 2— 15" 150 lbs. 1 6 to 18 2- -9" 84 lbs. 26 to 28 2 — 15" 200 lbs. 126 410 WALNUT ST., PHILADELPHIA. TABLES ■— W« O F«W- — lit, 127 THE PHCENIX IRON COMPANY, WEIGHT OF FLAT BAR IRON. PER FOOT. CO THICKNESS, IN INCHES. 1 16 1 8 3 16 1 4 5 16 3 g 7 16 1 2 5 8 3 4 7 8 1 lbs. lbs. lbs. lbs. COS . lbs. lbs. lOS. lbs. lbs. lbs. lbs. i .21 .42 .63 .84 1 .05 1 .26 1.47 47 1.68 2. II 2.53 2.95 3-37 •24 •47 •7 1 •95 1.18 1.42 1.66 1 .90 2 -37 2.84 3-32 3-79 *X .26 •53 •79 1.05 1.32 1.58 1.84 2. 11 2.63 3.16 3.68 4.21 .29 .58 .87 M 6 1.45 1 . 74 2.03 2.32 2.89 3-47 4-05 4-63 •3 2 .63 •95 1.26 ».58 1.90 2.21 2. S3 53 3.16 3-79 .4-42 5-05 •34 .68 1.03 1.37 1 . 71 2. 30 39 2.74 3-4 2 4. 11 4-79 5-47 •37 •74 1. 11 i-47 1.84 2.58 2.0 = 3.68 4.42 5.i6 5.89 .40 •79 1. 18 1.58 I 07 97 2 -37 6 2. 70 3.16 3-95 4-74 5-53 6.32 2 .42 .84 1.26 1.68 2.1 1 2.53 2.Qs 9 3.37 4.21 5-05 5.89 6.74 •45 .90 1 34 1.79 2.24 2.68 3.13 3.58 4-47 5-37 6.26 7.16 2l X •47 •95 1.42 1.90 2.37 2.84 3.32 3.79 4-74 5-68 6.83 .7.58 2% .50 1. 00 1.50 2.00 2.50 3.00 3.50 4.OO 5.00 6.00 7.00 8.00 2/ •53 1.05 i.58 2. 11 2.63 3.16 3.68 4.21 5.26 6.32 7-37 8.42 2^8 •55 1. 11 1.66 2.21 2.76 3.32 3.87 4.42 5-53 6.63 7-74 8.84 2^ .58 1. 16 1.74 2.32 2.89 3*47 4.05 4.63 5-79 6-95 8.10 9.26 2% .61 1. 21 1.82 2 42 3-°3 3-^3 4.24 4.84 6.05 7.26 8.47 9 .63 3 .63 1.26 1.90 2-53 3.16 3.79 4.42 5.05 6.32 7.58 8.84 10.10 3/ .68 1-37 2.05 2.74 3*4 2 4. 11 4. 70 < .4.7 6.84 8.21 9.58 10.95 3% •74 1-47 2.21 2-95 3.68 5.16 ^.8q 7-37 8.84 10.32 11.79 3% •79 1.58 2 -37 3.16 3-95 4-74 5-53 6.32 7.89 9-47 11.05 12.63 4 .84 1.68 2-53 3-37 4.21 5-o5 5.89 6.74 8.42 10.10 11.79 13-47 4/ .90 1 . 7Q 2.68 3-58 4-47 5-37 6.26 7.l6 8-95 10.74 I2 -53 I4-3 1 4/2 •95 I.90 2.84 3-79 4-74 5-68 6.63 7-58 9-47 n.38 13.26 15.16 4^ 1. 00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 10.00 12.00 14.00 16.00 5 1.05 2. II 3.16 4.21 5.26 6.32 7-37 8.42 10.53 12.63 14-74 16.84 sH «... 2.21 3-3 2 4.42 5-53 6.63 7-74 8.84 11.05 13.26 15-47 17.68 5% 1. 16 2.32 3-47 4-63 5-79 6.95 8.10 9.26 n.58 13.89 16.21 18.52 128 4-10 WALNUT ST., PHILADELPHIA. WEIGHT OF FLAT BAR IRON. PER FOOT. THICKNESS, IN INCHES. 1 1 3 1 5 3 7 1 5 3 7 16 8 16 4 16 8 16 2 8 4 8 1 lbs. lbs. ids. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. sYa 1.21 2.42 3.63 4.84 6.05 7.26 8.47 9.68 12.10 14.53 16.95 I 9-37 6 1.26 2-53 3-79 5-05 6.32 7-58 8.84 10.10 12.63 15.16 17.68 20.21 2.63 3-95 5-27 6.58 7.90 9.21 J o-53 13.16 15-79 2- .05 ey 2 1.36 2-73 4.10 5-47 6.84 8.21 9-58 10.94 13-68 16.42 19. 16 21.88 6% 1.42 2.84 4.26 5-69 7.10 S-53 9-95 11.36 14.21 17.05^9.90 22.73 7 2-94 4.42 5-9° 7-36 8.84 10.32 11 79 14.74 17.68 2O.64 23-58 7 l A i-53 3-°5 4-58 6.11 7- 6 3 9.16 10.68 12.21 15.26 18.32 2137 24.42 7 l A 1.58 3.16 4-74 6.32 7.90 9.48 n.c6 12.64 15.78 18.94 22. I I 25.28 7% 1.63 3.26 4.90 6-53 8.16 9-79 11.42 13.06 16.31 19-57 22.84 26.12 8 1.68 3-36 5-05 6.74 8.42 10.10 11.78 13.48 16.84 20.20 23.58 26.94 ** 1.74 3-47 5.21 6-95 8.68 10.42 12.16 13.89 17.37 2O.84 M* 27.79 3% .0, 3 58 5.36 7.16 8.94 10.74 12.52 14-3 2 17.90 2I.48 25.06 28.63 1.84 3-68 5-53 7-37 9.21 11.05 12.89 M.74 18.42 22.IO 25.79,29-47 9 1.90 3-79 5-68 7.58 9.48 11.36 13.26 15-16 18.95 22 75 , 1 20 52 30 32 1 9 T X -95 3-9° 5-84 7-79 9-74 11.68 13-63 I5-58 19 47 23.38 27.26 31 . 16 9% 2.00 4.00 6.00 8.00 10.00 12.00 14. oc 16.00 20.00 24.OO 28.OO 32.00 9K 2.05 4. 11 6.16 8.21 10.26 12.32 14-37 16.42,20.53 24.63 28.74 32.84 IO 2. 10 4.21 6.32 8.42|io.52 12.64 14-74 16.84 21.05 25.26 29.48 33-68 2.16 4-3 2 6.48 8.63 10.79 12.95 15. 11 17.26,21.58 25.89 30.2I 34-52 ™y 2 2.21 4.41 6.64 8.84 11.05 13.26 15.48 17.68 22.10 26.52 30-95 35-36 xoyi 2.26 4.53 6. 79 9-°5 II.32 13.58 15.84 18.10 22.63 27.16 31.68 36.21 ii 2.32 4.64 6-95 9.26 II.58 I3.90 1 16.21 18.52 23.16 27.78 1 32.42 37.04 2 -37 4-74 7.11 9.47 11.85 14.21 16.58 18.94 23.68 1 28.42 33.15 37.89 2.42 4.84 7.26 9.68 12.10 1 14-52 16.94 19.36 24.20 29.06 33-9° 38.74 ii% 2.47 4.94 7.42 9.89 12-37 14.84 i7-3i 19.78 24.73,29.69 34.63 39.56 12 2.52 5-05 7-58 10.10 12.64 15.16 17.68 20.20 25.26 3°-3 2 35.36 40.40 129 THE PHCENIX IRON COMPANY, WEIGHT OF WROUGHT IRON. Thickness or Diam.in Dec'ls, Inches. of a Foot. Wt. of a Sq. Foot, Lbs. Wt. per Foot Sq. Bar, Lbs. A 3 2 .0026 _ 1 .2D3 •°°33 JL_ .0052 2 . 5 26 .0132 Jif .OO78 3 7 5 9 .0296 f .OIO4 A .OI3O 3 l 5 A .OI56 7o7 5 T T Qa . L 1 04 3 2 .0182 8.841 1 6 1 2 1 4 .0208 10 10 A .O234 JI -37 .2665 _5_ 1 6 .0260 1 2 . 63 .329O 1 1 f .0287 15 l6 •473^ 1 3 3 2 .0339 1 6.42 rrrR •555° 1 6 •°3§5 I7.68 •6446 1 5 3 2 .0391 15-95 .7400 .0417 20. 2 1 _9_ l r 6 .0469 22.73 I .Out) .0521 25 26 1. 316 11 .0573 27.79 A 09 z 4 .0625 3° 3 1 T 8n- 1 3 !_ G .0677 -2 9 8/1 32.04 2.223 % .0729 35-37 2 -579 1 5 1 6 .0781 37 89 2.960 I • o8 33 40.42 3-3°° It? .0885 42.94 • 3-^03 1 8~ .0018 45 47 3 1 6 .OQQO 40. 00 4-75° 1 .IO42 5°-5 2 5- 2 ^3 5 .IO94 53 -°5 you/ » 8 .1 I46 55 57 6 -268 JL 1 6 .II98 58. 10 6 960 1 .1250 OU.Uj 7 C7# 7 -57° 5. 8 .1 ^4 05.05 5.093 3. .1458 7°-73 IO.3I 7 8" 1 1 .04 2 .1667 80 83 T "5 /I 7 A 3-4/ * .1771 15.21 I .1875 90 94 17.05 8 8 .1979 95-99 19.00 .2083 101.0 21.05 6 1 .2188 106. 1 23.21 3 4" .2292 in. 2 25-47 7 8 .2396 1 16.2 27.84 .2500 121.3 30-3I ! Wt. per Foot Round Bar, Lbs. .0026 .OIO4 .0233 .O4I4 .0646 .O93O .1266 •1653 .2093 •2583 .3126 .3720 •4365 .5063 •5813 .66I3 .837O IO33 I.25O I.488 I.746 2.025 2.325 2.645 2.986 3.348 3- 73° 4.133 4- 557 5.001 5.466 5- 952 6.985 8.101 9.300 10.58 11 95 13-39 14.92 16.53 18.23 20.01 21.87 23.81 130 410 WALNUT ST., PHILADELPHIA. WEIGHT OF WROUGHT IRON. Thickness or Diam. in Dec'ls, ! Wt. of a So. Wt. per Foot Wt. per Foot Inches. of a Foot. Foot, Lbs. bq. Bar, Lbs. Round Bar, Lbs. 3l .2604 I26.3 32.89 25.83 i 4 .2708 I3M 35-57 27.94 3 | .2813 i3 5 8 4583 222.3 101.9 80.02 .4688 227.3 106.6 83.70 3 4 •479 2 232.4 1 1 1.4 87.46 7 8" .4896 237.5 1 16.3 91.31 6 .5000 242.5 121.3 95.23 | .5208 252.6 131.6 103.3 1 •5417 262.7 142.3 in. 8 3 4 •5625 272.8 153-5 120.5 7 •5833 282.9 165.0 129.6 i 4 .6042 293.0 177.0 139.0 1 2 .6250 303-1 189.5 148.8 3 4 .6458 3I3-2 202.3 158.9 8 .6667 3 2 3.3 215.6 169.3 i 4 .6875 333-4 229.3 1 80. 1 1 2 .7083 343-5 243-4 191. 1 3 4 .7292 353-6 247.9 202.5 9 .7500 363.8 272.8 214.3 i 4 .7708 373-9 288.2 226.3 1 2 .7917 384.0 304.0 238.7 .8125 394-1 320.2 251.5 IO •8333 404.2 336.8 264.5 1 .8750 424.4 371.3 291.6 11 .9167 444.8 407.5 320.1 .9583 464.6 445-4 349-8 12 1 Foot. 485. 485. 380.9 131 THE PHCENIX IRON COMPANY, GENERAL RULES FOR DETERMINING THE WEIGHT OF ANY PIECE OF WROUGHT IRON. One cubic foot of wrought iron . One square foot, one inch thick . One square inch, one foot long . One square inch, one yard long . . ... = 480 lbs. . . = = 40 lbs. • • = « = 3i lbs. • =3iX3= 10 ^s. Hence it appears that the weight of any piece of wrought iron in pounds per yard is equal to 10 times its area in square inches. Example. — The area of a bar 3" X l " = 3 square inches, and its weight is 30 lbs. per yard. For round iron the weight per foot may be found by taking the diameter in quarter inches, squaring it, and dividing by 6. Example. — What is the weight of 2 r/ round iron ? 2 /7 =ss 8 quarter inches. 8 2 = 64. = io§ lbs. per foot of 2 // round. Example. — What is the weight of \ ff round iron ? | y/ == 3 quarter inches. 3 2 = 9. % = \\ lbs. per foot of \ ff round.. The above rules are highly convenient, and enable mental calculations of weight to be quickly obtained with accuracy. 132 410 WALNUT ST., PHILADELPHIA. CAST-IRON PIPE. WEIGHT OF A LINEAL FOOT. THICKNESS OP METAL, IN INCHES. Bore, Inche 1 4 3 1 2 5 8 3 4 7 8 JL J-8 -u % lbs. lbs. lbs. lbs. 2 5-5 R T °-7 12.3 16 I 20.3 24.7 29.5 34-5 39-9 6 8 J 4-7 I 9 2 24.0 29.0 34-4 46.0 3 7-9 12,4 17.2 22.2 27.6 3 2 -3 39-3 A f A M 9.2 x 4-3 19.6 2 5-3 3i-3 37-6 44.2 51.0 cR 4 10.4 16 1 28 4 35-° 41.9 49.1 50. D D4.4 11. 7 18.0 2 4 5 3!-5 3 8 ;7 40.2 54-° 70.6 5 12.9 19.8 27.0 34-5 4 2 -3 5°-5 59-9 67.7 76.7 sA 14. 1 21.6 2 9-5 37-o 460 54-° 63 8 73- 2 82.9 6 x 5-3 2 3 5 3*-9 40.7 49 7 59- 1 68 7 78.7 Ir 7 t n R 27.2 3^-9 46 8 57- 1 67.7 7°o 89 8 8 20.3 30.8 41.7 5 2 -9 04 4 70.2 88 4 1 14. 9 22.7 34-5 46 6 59- 1 71.8 84 8 98.2 IO 25.2 38.2 5 r -5 Oj.2 79 2 93-4 IOo. 123. ttR 13a. 1 1 27.6 41.9 565 7*3 R£ - 00. j Il8 *34- 150. 12 30.I A - (s 61 4 77-5 93-9 in. 128. I 45- It)3. 13 3 2 -5 49.2 00.3 03.O 119. T ->R ISO. x 75- I 4 35-° 5 2 -9 71.2 »9.7 109. f28 . 147. 107. , _ 107. 1 5 37-4 56 6 95-9 116 I3t>. l 57- 17b. 199. 16 39 - 1 00.3 81 123. 145. IO7. 189 18 44.8 67.7 90.9 114. 138. l62. I87. 211. 236. 20 49-7 75-2 101 . 127. 153- 179. 206. 2 33- 261. 22 54-6 82.6 in. 139- 168. 197. 226. 2 55- 285. 24 59-6 89.9 120. 1 Si- 182. 214. 2 45- 278. 310. 26 64-5 97-3 131. 164. 198. 231. 266. 300. 335- 28 69.4 105. 140. 176. 212. 249. 286. 3 2 3- 360. 30 74.2 112. 150. 188. 227. 266. 3°5- 345- 384. Note. — For each joint, add a foot to length of pipe, 133 I THE PHCENIX IRON COMPANY, GALVANIZED AND BLACK IRON. Weight in Pounds per Square Foot of Galvanized Sheet Iron, both Flat and Corrugated. The numbers and thicknesses are those of the iron before it is galvanized. When a flat sheet (the ordinary size of which is from 2 to 2 J feet in width, by 6 to 8 feet in length) is converted into a corrugated* one, with corrugations 5 inches wide from centre to centre, and about an inch deep (the common sizes), its width is thereby reduced about y^th part, or from 30 to 27 inches ; and consequently the weight per square foot of area covered is increased about ith part. When the corrugated sheets are laid upon a roof, the over- lapping of about 2J inches along their sides and of 4 inches along their ends diminishes the covered area about -£th part more; making their weight per square foot of roof about Jth part greater than before. Or the weight of cor- rugated iron per square foot in place on a roof is about J greater than that of the flat sheets of above sizes of which it is made.

. m in m n h o\m h ro ro ts in H w ro m iln m ts < OQ Q W UJ S3 GO GO GO PQ Q PC w Ph Oh o GJ w Q W o PC Gu O GD >— c GJ ►OOOOOOHMMNcoirit^CTiM covo 00 m rj-oo ^ ^ ! > co ts o ts "h in co in co ts ro m oo m cm qwo rn o. cm "O o ^ o\ co t> O w cm 4- invd co on 6 covo On m •<*■ ts o\ f HMWHCMCMCMCMC ro oi in n tj-vo on w> moo m in O h n t n O Tfoo on cm ts m m co no 0\h ion cm cm cm o oo m - ^ on ON O co ts co on tsvo m' m* m" cm" cm cm co co -4*vo" tsco d hi co m . in on Tt-co h i-NO m oo _^ „ ^ „ ^ c, O H Is CM NrOHOO O\lO'+N'ftONN0 i 256 6 2 204 8 ■* 102 10 3 80 12 3t 65 20 3i 46 CORE. // 6 d 2 H3 8 68 10 *J 60 12 3i 42 20 31 25 30 4} 18 40 4| H W H *i 69 WHL 72 SLATE. 3 d 'A 288 4 1 ft 244 5 A 4 187 6 2 146 TACKS. Size. 4 Number to Pound. Size. Length. Number to Pound. Size. Length. Number to Pound. I oz. ij 2 a} 3 3 T¥ 1 4 5 ¥ 6 1 60CO IO066 80OO 6400 5333 4 oz. 6 8 10 12 ft 9 1 1 1 ¥ 4 4000 2666 2000 1600 1333 14 oz. 16 18 20 22 1 3 ¥ 8" 1 5 1 6 I ift I H3 lOOO 888 800 727 139 THE PHCENIX IRON COMPANY, UNITED STATES STANDARD SIZES SQUARE AND HEXAGON NUTS. Number of each size in lOO Lbs. BLANK NUTS-NOT TAPPED, SIZE OF NUT. SQUARE. Size 01 Bolt. Width. Thick- No. in Weight ness. 100 Lbs. each in Lbs. l 4 i 2 - 1 4 74.00 .OI ^ 5 TS 1 9 3 2 5 1 6 4OOO 02 £ 3 8 1 1 1 6 3 8 27^0 .036 7 TF 25 3 2 7 1 6 170O .058 1 1 ¥ 1 I l6o .086 g T¥ 52 9 IF 9OO .III 5 f I- 1 - 1 1 6 8 6<3 j j .1 3 4 4 3 4 386 .259 ¥ 7 8 260 .184 O r I 1 8 I I70 .588 T i T 13 A 16 T 1 122 .819 2 90 I. II I If o 3 2 TF •I 69 1.44 If 2^ Z 8 54 1.85 If 2 T6 it 43 2.32 If 2^- 1 4 35 2.85 I| T 7 29 3 44 2 3J 2 24 4.16 a* 3tf 4 20 5.00 32" *i 17 5.88 -1 1 1 14 7-H 08 12 8-33 2f 4l 23- ^4 10 10.00 3 4| 3 8 12.50 HEXAGON. No. in Weight 100 Lbs. each in Lbs. 8880 .OI I 4800 .020 3276 .030 2040 .050 1392 .071 1080 .092 784 .127 4 6 3 .215 3 12 .320 204 .490 14.6 .684 108 .925 83 I.20 65 1.53 52 I.92 42 2.38 35 2.85 30 3-33 26 3-84 22 4-54 19 5.26 16 6.25 13 7.69 10 10.00 140 410 WALNUT ST., PHILADELPHIA. BOLTS. WITH SQUARE HEADS AND NUTS. Weight of lOO of the Enumerated Sizes. 4.16 4.22 4- 75 5- 34 5-97 6.50 TO. 62 11.72 12.38 12 90 14.69 l6.47 1787 18.94 20 59 21.69 23.62 25 8l 26 87 14 in. 23.87 39 3 1 25.06 41.38 26.44 4569 73.62 28 62 49-5o 76. 29.50 5 1 - 2 5 79-75 31 16 53- 83. 32-44 56. 85.38 39 -7b 63 12 93-44 42.50 74.87 108. 12 44.37 79.62 113 12 48.81 83. 122. 51.38 87.88 128.62 53-31 92.38 13I-75 56.87 96 88 I39-56 59- 12 99 8 7 I45.50 61.87 105 75 150.88 64 44 109.50 157.12 70.50 118.12 169.62 77- 128 13 184. 82.88 136.19 I95-I3 86.37 144.87 209.75 92. i55-5o 219-37 97-75 163 58 237.50 103.25 17075 249.06 1 in. ij/glTl. 127.25 140.56 1 4°-37 228. 296 158.76 239- 3IO. 167.25 250. 324. 174.88 261. 338. 204.25 272. 352. 214.69 283. 366. 228.44 294. 370. 235 3 1 3°5- 384: 239.88 3'6. 398. 258.12 338. 426. 276.18 360. 454- 295.69 382. 482. 3H-94 404 510. 335 81 426. 538. 351.88 448. 566. 39*-75 47o. 594- STANDARD SIZES OF WASHERS. Number in lOO Pounds. Diamater. Size of Hole. Thickness Wire Gauge. Size of Bolt. Kumber in 100 Lbs. Inch. Inch. Ao. Inch. I 3 4 t 16 16 i 16" 29300 18000 I 7 T5" 3 8 7600 H 9 ft 1 1 1 I I i 3300 2180 1 1 16 1 3 1 6 II II t f 2350 1680 2 2* ill 4 2 IO 8 8 I 1 140 580 3 3 ii •I 1* 8 7 6 i* ii if 470 360 360 12* THE PHCENIX IRON COMPANY, w < o 3 3 b ft o © 3 3 >> >> © o <*5 w CO o CO w W Q _J W £ O PS 1 H o o cr cr «0 (0 ^ 5% p ft ft 1) © § ft 0) JD & C3 c c CC OS © © •h i>0 O Pi Ej o e*H HT4 ©.So 00 Tf m M m hiCOOCOOCOCOOOOOOOCOOOOO . ro (N M lOVO O OO i-N'ON to CO 04 rj- N O 00 HI «o ^ 04 NO 04 in o\vo t-^ •<*■ in 01 On NO vO m t}- ►Ci 01 + lOOO m NO N vO \0 MO N-tintvtrOOO ^ " ' " ' m h n M ro ic ts On O (N 4- 00 rood o' HI M HI M 04 04 0O ^* 10 m no m onnO hi ro OO 04 00 NO O ^ 10 tj- o\n^o mm tmmo N o\ »>o0 04 00 ^> 6 IO M 04' O NO NO 6 04 o' On m ON 4" CO 04* 04 M •J 1 O CO m N t^vo 0, N Tf rr. m M M » S hi ro 04 -1-nO On C4 loot* moo ro <1 MMHfirOtlONO •~i • n m CO ro N 2 - ?Nri-H-trOM\OcOiri rooo On On On rooo r; <*> MX to O On O ro\C On ro moo 0O 00 ro ro ONOO ro ro ro ro 5 s-< O hi 1- ro toco ro i>. rooo t» on Onoo no 00 rf"* 1 S* m n ro^Nooi 10 onoo 00 rood ■ — • | • — , m m 11 04 ro tnvo Length of Pipe per □ Foot, Outside Surface ^ l/lSCM SrOH HCOHiOCMOaMOi-'tm s, -t MT) ro O hi m 04 0\m-. O -4- Cn m O "O invC On ro O NO ro OnOO t^.NO in in -.o4 ^1 hi m no m no no f> rooo in 04 Onoo t~^vo m t t o, 04NO hi 04 Oi 10 h 04NOVO f^oO to ro -<4-nO ro 04 «y i>-On04 m o\ ro m '£) \o ro on NO ro o " to on ro »^04NOHiNO04HI04ON'^-0ONinHlt^ rtCO ON O t> 00 -' r '^-0'*--^-tn--vo r^t^- NO04040400 1O ^ tnvo 00 O rovo On rooo in to invo no no no t>« h m tnNO t^co on O J, "*oo hi r^co r^co no co in in ro cj m o ■Z t^VO On N 04 tJ-00 hi nO no NO 04 ^"NO 04 CO m ^ 04 ro Tf NO 00 rONO O m m 0_ O ON O O ' ' h m' hi ci oi ff) ro 4 4 to no' On ^^^^ - to NO tr^CO ON I 142 410 WALNUT ST., PHILADELPHIA. LAP WELDED AMERICAN CHARCOAL IRON BOILER TUBES. Tables of Standard Sizes. Diameter. Diameter. rnal ference. rnal ference. ipe per □ e Surface. gth Pipe per □ Outside Surface. Area. Area. per Foot. ;rnal irnal 1 Exte rcum Inte rcum t£ jrnal ernal bp % '& g - ^ £ r* m tar In. In. In. In. In. _ rt. Fi. In. In. jLos. 0.856 0.072 3-M2 2.689 4.460 3.819 o.575 0.785 0.708 1. 106 0.072 3-927 3 474 3-455 3 056 0.960 1.227 0.9 i-334 0.083 4.712 4.191 2.863 2-547 1.396 1.767 1.250 1.560 0.095 5-498 4.901 2.448 2.183 1. 911 2.405 T.665 2 1.804 6.283 5.667 2. 118 1.909 2.556 3- x 42 1 981 2.054 098 7.069 6.484 1.850 1.698 3-3M 3-976 2.238 * X A 2.283 0.109 7-854 7.172 1-673 1.528 4.094 4.909 2-755 2% 2-533 0. 109 8.639 7-957 1.508 1.390 5-o39 5-94o 3-045 3 2.783 0.109 9-425 8-743 1-373 i- 2 73 6.083 7.069 3-333 3.012 0.119 10.210 9.462 1.268 1. 175 7-i 2 5 8.296 3-058 3% 3.262 0.1 19 10.995 10.248 1. 171 1. 09 1 8-357 9.621 4.272 3% 3 5*2 0.119 ii. 781 n.033 1.088 1. 018 9.687 11.045 4 59o 4 3-741 0.130 12.566 n-753 1.023 o.955 10.992 12.566 5-320 SA 4.241 0.130 M.137 13-323 0.901 0.849 14.126 15-904 6.010 5 4.72 0.140 15.708 14.818 0.809 0.764 17-497 I9-635 7.226 6 5-699 0.151 18.849 17.904 670 0.637 25-509 28.274 9-346 7 6.657 0. 172 21.991 20.914 o.574 o.545 34-805 38.484 50.265 12 435 8 7.636 0. 182 25.132 23.989 0.500 0.478 45-795 15.109 9 8.615 0.193 28.274 27-055 0.444 0.424 58.291 63.617 18.002 IO 9-573 0.214 31.416 130.074 o.399 0.382 71-975 78.540 22 19 WROUGHT-IRON WELDED TUBES. Extra Strong. llominal Diameter. Actual Outside Diameter. Thickness, Extra Strong Thickness, Double Extra Strong. Actual Inside Diameter, Extra Strong. Actual Inside Diameter, Double Extra Strong. •405 .100 .205 I •54 .123 •294 .675 .127 .421 •84 .149 .298 •542 .244 1.05 •157 •3 J 4 •736 .422 1 i-3i5 .182 •364 -951 .587 % 1.66 .194 .388 .406 1.272 .884 1.9 .203 1.494 1.088 2 2-375 .221 .442 J-933 1. 491 2.875 .280 .560 2.315 i-755 3-5 •304 .608 2.892 2.284 h 4- .321 .642 3-358 2.716 4 4-5 .34i .682 3.818 3-i3^ 143 THE PHOENIX IRON COMPANY, WINDOW GLASS. Number of Lights per Box of SO Feet. Inches. No. Inches. No. Inches. No. Inches. No. .... 6 V 8 ox. O I 5° 1 I2X J & 33 t6 V 44 1U /\ 44 nf\ \( ">o ^ u y\ 5 Z 9 7X9 20 3° ,Q Von 18 ^ 20 20 34 x 8 V io 90 27 22 18 •36 8 82 24 25 24 17 1 1 7 40 7 12 75 26 23 26 1 5 42 7 J 3 70 28 08 28 44 5 °4 3° 20 30 4° 5 1 5 60 32 18 32 \\ 5° t) 16 55 34 T 7 34 12 54 5 n V T T 9 X 11 72 J 3 X x 4 40 3° 11 5° 5 12 16 35 3° 08 V m 20 X 3° 9 *3 62 18 3 1 40 10 3 2 B M 0/ 20 28 44 9 8 : 5 53 22 25 2 °X 22 16 3° 7 16 5° 24 23 2 4 J 5 ^8 3° 7 *7 47 26 21 26 J 4 40 6 18 44 28 J 9 28 *3 44 6 \s 2 ° 3° 18 3° 12 46 6 IO X 12 60 V t6 i 4 y\ 1U 32 3 2 5° J 3 55 18 34 5 J 4 5 2 20 26 3° 10 J 5 40 2 23 ^8 3° 9 3° X 30 7 16 45 24 40 9 40 6 r 7 42 26 44 8 42 • 6 18 40 28 18 40 3 44 5 3° 3° l 7 ^8 40 8 4 U 5 22 33 32 16 5° 7 48 5 2 4 3° 34 1 5 60 6 5° *? 26 28 3° J 4 22 X 2 4 x 4 54 28 26 40 *3 J 3 5 U 3° 24 44 28 60 4 3 2 i<; V 18 1 A o y\ 10 27 3° 11 02Y42 O /\ 4^ 5 34 21 20 24 32 44 5 1 1 V 1 1 1 1 X 1 3 5° 34 10 4 U **4 47 24 3° 9 ^8 45 5 15 44 26 Io 38 9 5° 4 16 4i 28 17 40 ! 8 54 4 i 7 39 3° i6 44 8 56 4 18 36 32 15 46 7 60 4 20 33 16X18 25 5o 7 34X4o 22 30 20 23 24X28 11 44 24 27 22 20 30 10 46 1 26 25 24 32 9 5o 28 23 26 17 36 8 5 2 4 30 21 28 16 40 8 56 4 32 20 30 15 44 36X44 5 34 19 32 14 46 7 50 4 12X14 43 34 13 48 6 56 4 15 40 36 12 50 6 60 3 16 38 38 12 54 5 64 17 35 40 11 56 5 40X60 3 144 4-10 WALNUT ST., PHILADELPHIA. SKYLIGHT AND FLOOR GLASS. Weight per Cubic Foot, 156 Pounds. WEIGHT PER SQUARE FOOT. Thickness . i 3 i 3 1 1 8 2 t 2. 4 I inch. Weight . . 1.62 2.43 3.25 4.88 6.5O 8.13 975 13 lbs. FLAGGING. Weight per Cubic Foot, 168 Pounds. WEIGHT PER SQUARE FOOT. Thickness . 1 2 3 4 5 6 I 7 8 inch. Weight . . 14 28 42 56 70 84 98 112 lbs. CAPACITY OF CISTERN. In Gallons, for each Foot in Depth. Diameter, in Feet. Gallons. Diameter, in Feet. Gallons. 2. 23-5 9- 475.87 2-5 36.7 9-5 553-67 3. 52.9 10. 5875 3-5 71.96 11. 710.9 4- 94.02 12. 846.4 4-5 119. 13- 992.9 5- 146.8 14. 1151-5 5-5 177.7 15. 1321.9 * 6. 211. 6 20. 2350.0 6.5 248.22 25- 3570.7 7- 287.84 30. 52877 7.5 33048 35- 7189. 8. 376. 40. 9367.2 8.5 424.44 45. 1 1893.2 The American standard gallon contains 231 cubic inches, or 8J pounds of pure water. A cubic foot contains 62.3 pounds of water, or 7.48 gallons. Pressure per square inch is equal to the depth or head in feet multiplied by .433. Each 27.72 inches of depth gives a pressure of one pound to the square inch. 145 THE PHCENIX IRON COMPANY, ROOFING SLATE. General Rule for the Computation of Slate. From the length of the slate take three inches, or as many as the third covers the first ; divide the remainder by 2, and multiply the quotient by the width of the slate, and the product will be the number of square inches in a single slate. Divide the number of square inches thus procured by 144, the number of square inches in a square foot, and the quotient will be the number of feet and inches required. A square of slate is what will cover 100 square feet, when laid upon the roof. Weight per Cubic Foot, 174 Pounds. WEIGHT PER SQUARE FOOT. Thickness . i 3 T6 1 4 3 8 i t 3 4 i inch. Weight . . 1.81 2.71 3.62 5-43 7.25 9.06 IO.87 14.5 lbs. TABLE OF SIZES AND NUMBER OF SLATE In One Square. Size No. of Slate Size, No. of Slate Size, No. of Slate in Inches. in Square. in Inches. in Square. in Inches. in Square. 6X 12 533 8 X 16 277 12 X 20 141 7 12 457 9 16 246 H 20 121 8 12 400 10 16 221 I I 22 137 9 12 355 12 16 184 12 22 126 10 12 320 9 18 213 14 22 I08 12 12 266 10 18 192 12 24 114 7 H 374 11 18 174 14 24 98 8 14 327 12 18 l6o 16 24 86 9 H 291 18 137 14 26 89 10 14 261 10 20 169 16 26 78 12 218 11 20 154 146 J 410 WALNUT ST., PHILADELPHIA. SPECIFIC GRAVITY AND WEIGHTS OF VARIOUS SUBSTANCES. Name of Substance. Per Cubic Foot. WEIGHTS. Per □ Foot, 1 In. Thick. Per Cubic Inch. Specific Gravity. Water, Pure . 62.3 5- J 9 .036 I. OOO Water, Sea 6 4-3 5-3 6 •°37 I.028 Wrought Iron 480 40.00 .277 7.70 Cast Iron .... 45° 37-5° .260 7.20 490 40.84 .283 7.84 T A 7 10 59.16 .410 11.36 Copper, Rolled. . 54 8 45.00 •3*7 0.0O .brass, Rolled 5 2 4 43.66 .302 8.40 98 8.23 .057 1-57 1 20 10.00 .009 I.92 Brickwork, Common 1 20 10.00 .069 I.92 " Close Joints 140 T T 66 1 1 .00 .001 2.24 Limestone T 6Q loo 18.00 .124 2.68 13.00 .090 2.49 Pine, White . . . 30 2.50 .017 .48 Pine, Yellow . . . 35 2.91 .019 .56 Hemlock .... 25 2.08 .015 .40 Maple 49 4.08 .028 7 8 Oak, White . . . 5o 4.16 .030 .80 Walnut .... 4i 3-41 .023 .65 147 THE PHCENIX IRON COMPANY, PROPERTIES OF CIRCLES. B D— h — R (i— cos. a) Sin. a = - (i.) Given, chord ADC and vers, sine or rise B D, to find radius, ADC ^ A D 2 + B D 2 = A D or D C .-. ±— = BE 2 2 B D c 2 + 4 h 2 R — 8 h (2.) Given, chord ADC and radius B E, to find rise B D, BE — v/BE 2 -AD 2 = B D h = R— R2- (3.) Given, the radius and rise, to find the chord ADC, AD = v/B E 2 — (B E-BDf Chord ADC = 2AD = 2 \/ BE 2 — ( B E — B D) 2 c = 2 \/ 2 h R — h 2 148 410 WALNUT ST., PHILADELPHIA. (4.) Given, the chord of an arc and the chord of half the arc, to find the length of the arc, 8 A B — ADC f -d / , x — — arc ABC (very nearly). (5.) To find the number of degrees in the arc of a circle, when the diameter, or radius, and the length of the arc are given, Arc ABC 7r X diameter X 360°= degrees in arc ABC (6.) Length of an arc of one degree = R X .01 74533 Length of an arc of one minute =R X .0002909 Length of an arc of one second = R X .0000048 Example. — Let radius =100 feet, and the angle of the arc be 90 . What is the length of the arc ? 100 X - OI 74533 X 90°= 157.08 feet. MENSURATION OF SURFACES. Area of circle = Diameter 2 X -7^54 Area of ellipse = Transv. axis X con j u g- ax i s X -7^54 Area of sector of circle — Arc X 2 radius Area of parabola = Base X I height Surface of sphere = Diameter 2 X 3- I 4 J 6 MENSURATION OF SOLIDS. Cylinder == Area of one end X length Sphere = Diameter 3 X .5236 Cone, or pyramid == Area of base X 3 height Any prismoid = Sum of areas of the two parallel sur- faces -f- 4 times the area of a mid- way section X length, and the total product divided by 6. 13 149 THE PHCENIX IRON COMPANY, PROPERTIES OF TRIANGLES. In right-angled triangles hypoth. 2 rrr base 2 -J- perpend. 2 base 2 p= (hyp. + perp.) X (hyp.— perp.) perp. 2 = (hyp. + base) X (hyp.— base) VALUE OF ANY SIDE A. B sin. a C sin. a A : Sin. b ~ Sin. c A = \/"B a + C2^2B^~cos77 B A = cos. c -\- sin. r cot. a A= ^ cos. b -f- sin. £ cot. a A = B cos. c -f- B sin. <- Radius-- > Complement of an angle == its difference from 90 . Supplement . . . . = its difference from 180 . TRIGONOMETRICAL EQUIVALENTS. v/ (i_Sin 2 ) = Cosin. v/ (1— Cosin 2 ) : — Sine. Sin ~ Tan — Cosin. Cosin : — Cotan = Sine. Sin X Cotan = Cosin. - Cotan = Tangent. Sine -i- Cos — Tangent. - Sin — Cosecant. Cos -r- Sine == Cotang. - Cosin = Secant. Sin 2 + Cos 2 == Rad 2 . - Cosecant = Sine. Rad 2 -f Tan 2 == Secant 2 . - Secant = Cosin. 1 h- Tan = Cotang. Rad — Cosin — Versin. Rad — Sin = Coversin. 151 THE PHCENIX IRON COMPANY, USE OF TABLE OF NATURAL SINES, Eic. Example I. To find the angle a, when A D and W D are given, from table of natural sines and tangents, p. 153. A D = 20. 10. W D A D being radius, W D = tan a. L' Vb'D= Then 10 AD ~~ 20 : .50000. Referring to table we find for 26 , the natural tangent to be .48773 27 , the natural tangent to be .50952 Difference 02179 The angle, therefore, is more than 26 and less than 27 degrees. If greater accuracy is required, take the difference between natural tangent of 26 and 27 as above, viz., .02179, and divide by 60, which will give .00036 for one minute. Now subtract from .50000 the natural tangent for 26 , viz., .48773, leaving .01227, and divide the difference by .00036; the quotient will be 34 minutes. The angle, therefore, is 26 34'. Example 2. If A D — 20, and B D : the angle subtended by B D ? • 20, what will be B D A~D : 20 ' 20 The natural tangent of 45 is I. 152 410 WALNUT ST., PHILADELPHIA. NATURAL SINES, ETC. Deg. Sine. Cover. Cosecant Tangent Cotang. Secant. Yersine. Cosine. Deg. o .00 1. 00000 Infinite- .0 Infinite. 1 .00000 .0 1. 00000 90 89 i .01745 •9 82 54 57.2986 •01745 57.2899 1. 0001 5 .0001 •99984 2 .03489 .96510 28.6537 .03492 28.6362 1.00060 .0006 •99939 88 3 .05233 .94766 19-1073 .05240 19.081 1 1. 00137 .0013 .99862 87 4 .06975 .93024 J 4-3355 .06992 14.3006 1.0^244 .0024 •99756 86 5 .08715 .91284 11.4737 .08748 11.4300 1. 00381 .0038 .99619 85 6 .10452 .89547 9.5667 .10510 9-5H3 1.00550 .0054 .99452 84 7 .12186 •87813 8.2055 .12278 8.1443 1.00750 .0074 •99254 83 8 •I39 1 ? .86082 7.1852 .14054 7- II 53 1.00982 .0097 .99026 82 9 •15643 .84356 6.3924 .15838 0.3137 1. 01246 .0123 .98768 81 IO • 1 7364 .82635 5-7587 .17632 5.6712 1. 01542 .0151 .98480 80 ii . 19080 .80919 5.2408 .19438 5-1445 1.01871 .0183 .98162 79 12 .20791 .79208 4.8097 .21255 4 7046 1.02234 .0218 .97814 78 13 .22495 .77504 4-4454 .23086 4-33M 1.02630 .0256 •97437 77 14 .24192 •75807 4- I 335 .24932 4.0107 1. 03061 .0297 .97029 76 15 .25881 .74118 3-8637 .26794 3-7320 1.03527 .0340 .96592 75 16 •27563 .72436 3.6279 .28674 3-4874 1.04029 .0387 .96126 74 i7 .29237 .70762 3 4203 •30573 3.2708 1.04569 .0436 •95630 73 18 .30901 .69098 3.2360 •3249 1 3.0776 1. 05146 .0489 •95105 72 *9 •32556 .67443 3-0715 •34432 2.9042 1 .05762 •0544 •94551 7 1 20 .34202 •65797 2.9238 .36397 2-7474 1. 06417 .0603 .93969 70 21 .35836 .64163 2 7904 .38386 2.6050 1.07114 .0664 •93358 69 22 •3746o .62539 2.6694 .40402 2.4750 1-07853 .0728 .92718 68 23 •39073 .60926 2-5593 .42447 2.3558 1.08636 .0794 92050 67 24 •40673 •59326 2.4585 .44522 2.2460 1.09463 .0864 •9 X 354 66 25 .42261 •57738 2.3662 .46630 2.1445 1. 10337 .0936 .90630 65 26 •43837 .56162 2.2811 •48773 2.0503 1. 1 1 260 .1012 .89879 64 27 •45399 .54600 2.2026 .50952 1.9626 1. 12232 .1089 .&9100 63 28 •46947 .53052 2.1300 •53*70 1.8807 I-I3257 .1170 .88294 .87461 62 29 .48480 •51519 2.0626 •5543o 1 . 8040 I-I4335 •1253 61 30 . 50000 . 50000 2.0000 •57735 1 . 7320 1-1547° ■*339 .86602 60 3 1 •5 1 503 .48496 .60086 1 .6642 1 .16663 .1428 .85716 59 32 5299 1 .47008 ^8870 .62486 .64940 1.6003 1.17917 •1519 .84804 58 33 •54463 •45536 1.8360 I-539 8 1. 19236 .1613 •83867 34 •559 x 9 .44080 1.7882 •67450 1.4825 1 .20621 .1709 .82903 56 35 •57357 .42642 1-7434 . 70020 1. 4281 1.22077 .1808 .81915 55 36 .58778 .41221 1. 7013 •7 2 654 I-3763 1.23606 .1909 .80901 54 37 .39818 1 .6616 •75355 1 .3270 1. 25213 .2013 •79863 53 38 .'61566 •38433 1.6242 .78128 1.2799 1 .26901 .2119 .78801 52 39 .62932 -37067 1.5890 .80978 1.2348 1.28675 .2228 •777*4 5i 40 .64278 •357 21 1-5557 .83909 1.1917 1-30540 •2339 . 76604 50 41 .65605 •34394 1.5242 .86928 1-1503 1. 32501 •2452 •7547o A l 42 .66913 .33086 1.4944 .90040 1.1106 I-34563 .2568 •74314 48 43 .68199 . 3 1 800 1.4662 •93 2 5i 1.0723 1.36732 .2680 •73 I 35 47 44 .69465 •30534 1-4395 .96568 1-0355 1. 39016 .2806 •71933 46 45 .70710 .29289 1. 4142 1. 00000 1. 0000 1. 41421 .2928 .70710 45 Cosine. Versine. Secant. Cotang. Tangent Cosecant. Cover. Sine. 13* •53 THE PHCENIX IRON COMPANY, CIRCUMFERENCES OF CIRCLES. Advancing by Eighths. CIRCUMFERENCES. I Diam. .O •J \ a • 8 % •f •1 * 8 o .0 •3927 •7 8 54 1 . 1 78 T -57° 1.963 2.356 2.748 3- I 4 I 3-534 3-9 2 7 4-3 x 9 4.712 5- io 5 5-497 5.890 2 6 283 °.°7d 10 21 J 7.461 7-854 8 246 R non 0-639 9.032 2 9.424 r> R 1 n 9.517 10.99 12.17 4 12.56 I2.95 13-35 J.3-74 M-i3 J 4-52 14.92 i5-3 r 5 15-70 l6.IO 16.49 16.88 17.27 17.67 I8.06 18.45 6 18.84 I9.24 19.63 20.02 20.42 20.81 21 .20 21.59 7 21.99 22.38 22 77 23. 16 23.56 23-95 24-34 24.74 8 25-13 25-52 25-9 1 26 31 26.70 27.09 27.48 27.88 9 28.27 28.66 29.05 29-45 29.84 30-23 30-63 31.02 IO 3M* 3I.80 32.20 32.59 32.98 33-37 33-77 34-i6 1 1 34-55 34-95 35-34 35-73 36-12 36-5 2 36.91 37-3° 12 37-69 38.09 38.48 38.87 39- 2 7 39.66 40.05 40.44 13 4 I - 2 3 42.41 43- J 9 43-58 M 43-98 44-37 44.76 45-i6 45-55 45-94 46.33 46.73 15 47.12 47-51 47.90 48.30 48.69 49.08 49.48 49.87 16 50.20 50-65 5 I -°5 5 J -44 5 r -83 52.22 52.02 53- 01 17 53-4o 53-79 54- I 9 54-58 54 97 55-37 55-76 56.15 18 56.54 56.94 57-33 57-7 2 cR T T 5O.II rR CT 58.90 59 - 2 9 19 59-69 60.08 60.47 6o.86 6l.26 61.65 62.04 62.43 20 62.83 63.22 63.61 64.01 64.4O 64.79 65.18 65.58 21 65-97 00.30 66.7 3 67- T 5 67-54 67-93 £R -10 OO.32 AR -to OO. 72 2 2 69.11 69.50 69.9O 70.29 70.68 71.07 7 T -47 71 86 23 72.25 72.64 73 °4 73-43 73-82 74.22 74.61 75.00 24 75-39 75-79 76.18 76.57 76.96 77-36 77-75 78 14 25 78.54 78.93 79 -32 79.71 8O.IO 80.50 80.89 81.28 26 81.68 82 82 46 02.05 R^ 9C Ro f,A 03.04 04.03 R/i A -> °4-43 27 84.82 85 21 85.60 86 00 Rn on OO.39 86.78 07.17 R-7 C7 28 87.96 88.35 88.75 89.14 8 9-53 90.32 90.71 29 91.10 91.49 91.89 92.28 92.67 93.06 93-46 93-85 30 94.24 94.64 95-o3 95-42 95.81 96.21 96.60 96.99 31 97-39 97.78 98.17 9 b o7 c 98.96 99-35 99-75 100.14 32 IOO.53 100.92 101.32 101.71 102.10 102 . 8q 103.29 33 103.67 104.07 104 46 104.05 105.24 105 64 106.03 34 106.81 107.21 107.60 107.99 108.39 108 78 109 17 109*56 35 109.96 no.35 110.74 in. 13 "i. 53 in. 92 112.31 112. 71 36 113. 10 H3-49 113.88 114.28 114.67 115.06 "5-45 ^15-85 37 116.24 116.63 117.02 117.42 117. 81 118.20 118.60 118.99 38 119.38 119.77 120.17 120.56 120.95 121.34 121.74 122.13 39 122.52 122.92 123.31 123.70 124.09 124.49 124.88 125.27 40 125 66 126.06 126.45 126.84 127.24 127 63 128.02 128.41 ♦« 128.81 129.20 127.59 129.98 130.38 130.77 131.16 131-55 42 i3i-95 13234 132.73 I33-I3 133-52 I33-9 1 I34-30 134-70 437 35-09 I35-48 135 87 136.27 136.66 I37-05 137-45 | 13784 44 138.23 138.62 139.02 I39-4I 139 80 140.19 140.59 140.98 45ii4i-37 141.76 142.16 142.55 142.94 143-34 143-73 1 144.12 154 I 410 WALNUT ST., PHILADELPHIA. AREAS OF CIRCLES. Advancing by Eighths. AREAS. I Diam. 1 •O 1 •s 1 •4 8 •# 1 •2 1 •8 a •4 7 't o .1963 3068 .4417 "~6oi3 i '7854 .9940 I.227 I.484 1.767 2.073 2.405 2. 761 2 3.1416 3.546 3 976 4.430 4.908 5-4H 5-939 6.491 3 7.068 7.669 8.295 8.946 9.621 10.32 11.04 11 79 4 12.56 14.18 I5-03 15-9° 16.80 17.72 18.66 5 19.63 20.62 21.64 22.69 23-75 24 85 25.96 27.10 6 28.27 29.46 30.67 3I-9 1 33 18 34-47 35-78 37.12 7 38 48 39-87 41.28 42.71 44 1 7 45.66 47 I 7 48.70 8 50.26 51-84 53-45 55.o8 56.74 58.42 60 13 61.86 9 63.61 65.39 67.20 69.02 70.88 72 -75 74.66 76.58 TO 78.54 80.51 82.51 84-54 86.59 88 66 90 76 92.88 II 95-03 97.20 99.40 101.6 103.8 jo6.i 108.4 no. 7 12 113.0 "5-4 117. 8 120.2 122.7 125. 1 127.6 1 30. 1 *3 J 32.7 J 35-2 137-8 140.5 I43-I 145.8 148.4 151. 2 1 4 153-9 156.6 159-4 162.2 165. 1 167.9 170.8 173-7 15 176.7 179.6 182.6 185.6 188.6 191. '7 194.8 197.9 16 201.0 204.2 207.3 210.5 213.8 217.0 220.3 223.6 1 7 226.9 230-3 2 33 7 2 37- 1 240 5 2 43-9 247.4 250 9 18 2 54-4 258.0 261.5 265.1 268.8 272.4 276.1 279.8 i9 283.5 287.2 291.0 294.8 298.6 302.4 3063 310.2 20 314-1 318.1 322.0 326.0 33°-o 334-1 338 1 342.2 21 346.3 35o.4 354 6 358.8 363-0 367.2 371-5 375-8 22 380.1 384-4 388.8 393-2 397-6 402.0 406.4 410.9 23 4I5-4 420.0 424-5 429.1 433-7 438.3 443-o 447.6 24 452.3 457- 1 461.8 466.6 471.4 476.2 481. 1 485-9 25 490.8 495-7 500.7 505-7 510.7 5I5.7 520.7 525 8 26 530-9 536.o 54i-i 546.3 551-5 556.7 562.0 567.2 27 572.5 577-8 583-2 588.5 593. y 5y9-3 604.8 610.2 28 615-7 621.2 626.7 632.3 637 9 643 5 649.1 654-8 29 660.5 666.2 671.9 677.7 683.4 689 2 695.1 700.9 3° 706.8 712.7 718.6 724.6 73o.6 736.6 742.6 748.6 3. 754-8 760.9 767.0 773-1 779-3 785.5 791.7 798.0 848.8 32 804.3 810.6 816.9 823 2 829.6 836.0 842.4 33 855-3 861.8 868.3 874.9 881.4 888.0 894.6 901.3 34 907.9 9M-7 921.3 928.1 934-8 941.6 948.4 955-3 35 962.1 969.0 975-9 982.8 989.8 996.8 1003.8 1010.8 36 1017.9 1025.0 1032. 1 1039.2 1046.3 1053 5 1060.7 1068.0 37 1075.2 1082.5 1089.8 1097. 1 1 104. 5 mi. 8 1119.2 1126.7 381134-1 1141.6 1149.1 1156.6 1164.2 1171 7 "79-3 1186.9 39 1194.6 1202.3 1210.0 1217.7 1225.4 1233.2 1241.0 1248.8 40 1256.6 1264.5 1272.4 1280.3 1288.2 1296.2 1304.2 1312.2 1320.3 1328.3 1336.4 1344-5 1352.7 1360 8 1369.0 I377- 2 42 1385-4 1393-7 1402.0 1410.3 1418 6 1427.0 M35-4 1443-8 43]M52.2 1460.7 1469. 1 1477.6 1486.2 M94-7 1503.3 1511-9 44;i52o.5 1529.2 I 537-9 1546.6 J555-3 1564.0 1572.8 1581.6 45 i59o.4 1599-3 1608.2 1617 1626 1634.9 1643-9 1652.9 155 J THE PHCENIX IRON COMPANY, SURVEYING MEASURE. (LINEAL.) Inches. Feet. Yards. Chains. Mile. I. = .0833 = .0278 = .OOI26 = .OOOOI58 12. I. •333 .OI515 .OOO189 36. 3. I. .04545 .OOO568 792. 66. 22. I. .OI25 63360. 5280. I760. 80. I. One knot or geographical mile = 6086.07 ^ eet = 1855.II metres = 1. 1526 statute mile. One admiralty knot = 1 . 15 1 5 statute miles = 6080 feet. LONG MEASURE. Inches I. 12. 36. I98. 7920. 63360. Feet. .083: Yards. Poles. .02778 = .005 : Furl. Mile. OOOI26 == .OOCOI58 I- -333 3- *• i6j£. $%. 660. 220. 5280. 1760. A palm = 3 inches. A span = 9 inches. 0015 1 00454 025 .0606 .182 1. 40. 320. A hand = 4 inches. A cable's length =120 fathoms. 0001894 000568 00J125 125 FRENCH LONG MEASURE. Millimetre..... Centimetre Decimetre Metre Decametre .... Hectometre... Kilometre Myriametre... Inches. •03937 .39368 3.9368 39.368 393.68 Feet. .0033 .0328 .3280 3.2807 32.807 328.07 3280.7 32807. Yards. .IO936 I-Q9357 10 9357 109.357 1093.57 I0935-7 Miles. .062134 .621346 6.213466 156 410 WALNUT ST., PHILADELPHIA. Inches. I. I44. 1296. 39204. 627264O. SQUARE MEASURE. Feet. Yards. Perches. z= .00694 == .0007 7 2=1.000025 5: 1. .111 .00367 9. 1. .0331 272X- 3°X- I- 43560. 4840. 160. 100 square feet 10 square chains I chain wide 1 hectare Acre. =.000000159 .000023 .0002066 00625 1 square mile 1 = Acres I square. I acre. 8 acres per mile. 2.471 143 acres. 27,878,400 square feet. 3,097,600 square yards. 640 acres, square miles, square miles, square yards, acres. X .0015625 Square yard X .000000323 Acres X 4^4° Square yards X .0002066 A section of land is I mile square, and contains 640 acres. A square acre is 208.71 ft. at each side ; or, 220 X ft- A square x / 2 acre is 147.58 ft. at each side; or, no X l 9& ft- A square acre is 104.355 ft. at each side ; or, 55 X l 9% ft- A circular acre is 235.504 ft. in diameter. A circular acre is 166.527 ft. in diameter. A circular % acre is 117.752 ft. in diameter. FRENCH SQUARE MEASURE. Square. Square Inches. Square Feet. Square Yards. .00154 .0000107 .000001 Centimetre.... .15498 .0010763 .000119 15.498 .1076305 .011958 Metre or Cen. 1549.8 10.76305 1.19589 Decametre.... 154988. 1076.305 119.589 107630.58 II9S8 95 .38607 □ mis 10763058. II95895. Myriametre... 38.607 J57 THE PHCENIX IRON COMPANY, CUBIC MEASURE. Inches. Feet. Yard. Cubic Metres. I. = .OOO5788 == .OOOOO2144 === .OOOO16386 1728. I. .03704 .028315 46656. 27. I. -764513 A CUBIC FOOl 1728 cubic inches. .037037 cubic yard. .803564 U. S. struck bushel of 2150.42 cub. in. 3.21426 U. S. pecks. 7.48052 U. S. liquid gallons of 231 cubic in. 6.4285 1 U. S. dry gallons of 268.8025 cubic in. IS EQUAL TO 29.92208 U. S. liquid quarts. 25.71405 U. S. dry quarts. 59.84416 U. S. liquid pints. 51.42809 U. S. dry pints. 2 39-37662 U. S. gills. .26667 fl°ur barrel of 3 struck bushels. .23748 U. S. liquid barrel of 31% gallons. A cubic inch of water at 62 Fahr. weighs 252.458 grains. A cubic foot of water at 62 Fahr. weighs 1002.7 ounces. A cubic yard of water at 62 Fahr. weighs 1692. pounds. FRENCH CUBIC OR SOLID MEASURE. Centilitre | Decilitre -j Litre j Decalitre | Hectolitre -| Kilolitre or f Cubic Metre... \ Myriolitre -j Dry... Liquid Dry... Liquid Dry... Liquid Dry... Liquid Dry... Liquid Dry... Liquid Dry... Liquid Pint, j Quart. .0181 .021 1! .1816I .0908 .21131 .1056 1 . 8 1 6 1 .908 2. 113! 1.056 9.08 10.56 90.8 105.6 Bush. 21.13 211. 3 IO56.5 IO565. .2837 2837 28.37 283.7 Cubic Inch. Cu. Ft. j .61016 j 6.IOI6 j 61.016 .0353 j 610.16 .3531 j6lOI.63.53i |6ioi6. 35.31 } 353-1 158 410 WALNUT ST., PHILADELPHIA. AVOIRDUPOIS WEIGHT. The standard avoirdupois pound is the weight of 27.7015 cubic inches of distilled water, weighed in the air, at 39.83 degrees Fahr., barometer at thirty inches. Ounces. Pounds. Quarters. Cwts. Ton. I. — .0625 = .OO223 = .OOO558 = .OOOO28 16. I. .0357 .00893 .OOO447 448. 28. I. .25 .OI25 1792. 112. 4. I. .05 35840. 2240. 80. 20. I. A drachm = 27.343 grains. A stone =14 pounds. A quintal = 100 kilogrammes. 7000 grains = 1 avoir, pound = 1. 21528 troy pounds. 5760 grains = I troy pound = .82285 avoir, pound. Kilos p. sq. centim. X 1 4- 22 = Pounds p. sq. inch. Pounds p. sq. inch X -°7°3 = Kilos p. sq. centim. FRENCH WEIGHTS. EQUIVALENT TO AVOIRDUPOIS. Grains. Ounces. Pounds. Decagramme Hectogramme Millier or Tonne, .OI5433 .154331 1.54331 I5433I I 54-33 I I543.3I 1 5433- 1 .000352 .003527 .035275 •352758 3-52758 35.2758 352.758 3527.58 35275.8 .000022 .000220 .002204 .022047 .220473 2.20473 22.0473 220.473 2204.73 159 I THE PHCENIX IRON COMPANY, 1 60 s $8o