Structural Designers Handbook w; m LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Class STRUCTURAL DESIGNERS' HANDBOOK GIVING DIAGRAMS AND TABLES FOR THE DESIGN OF BEAMS, GIRDERS AND COLUMNS WITH CALCU- LATIONS BASED ON THE NEW YORK CITY BUILDING CODE BY WILLIAM FRY SCOTT Structural Engineer, Member American Society for Testing Materials or THE UNIVERSITY NEW YORK THE ENGINEERING NEWS PUBLISHING CO. 1904 Copyright, 1904 Bt WILLIAM FKY SCOTT PREFACE* This handbook, essentially a diagrammatic treatise on the sub- ject of Structural Design, contains also a full tabulation of the properties of market shapes of materials. It is presented to the architectural and engineering professions with the thought that it may be the means of shortening and pos- sibly eliminating much of the computation and drudgery which are necessary accompaniments of structural designing. It is hoped that it may prove useful to the expert designer, since the diagrams presented are time-saving devices ; useful and suggestive to the non-expert and the student, since the diagrams illustrate graphically the relations of the various factors of propor- tion, span loading, etc., for the variable conditions of ordinary practice. Throughout the work the New York Building Code has been followed, because it is everywhere recognized as conservative and safe. W. F. S. New York, July, 1904. 894 CONTENTS. PART I. SYNOPSIS OF MECHANICS OF THE BEAM AND COLUMN. 'CHAPTER I. BEAMS. Page Span .................................................... 1 Cross Section ............................................ 1 Section Moment .......................................... 1 Unit Stress .............................................. 2 Manner of Support ....................................... 2 Deflection ............................................... 2 End Reactions ........................................... 3 Buckling of Compression Flange ........................... 4 Loads on Beams .................. ; ...................... 4 Conventional Methods of Treating Loads on Floor Girders. ... 5 Conventional Methods of Considering Loads on Grillage Beams 7 CHAPTER II. COLUMNS. Concentric Loads ............................ . ........... 8 Eccentric Loads .......................................... & PART II. BEAMWORK. CHAPTER III. FLOOR FRAMING. Utility of Diagrams ..................................... 11 Explanation of Diagrams 1 to 15 ....................... 12 Explanation of Tables 1 to 15 ............................. 13 Explanation of Diagrams 16 to 21 ......................... 14 Explanation of Diagram 22 .............................. 15 Explanation of Tables of Properties of Shapes ............. 1(J Tables 1 to 15. Giving Percentage of Allowable load, Spac- ing and End Reaction for I-Beams from 3-in. x 5.5 Ib. to 24-in. x 80-lb ....................................... 18-46 Diagrams 1 to 15. Giving Allowable Uniform Load, Spac- ing, Span, etc., for I-Beams from 3-in. 1 x 5.5-lb. to 24- in. x 80-lb ......................................... 18-46 Diagrams 16 to 21. Giving Allowable Uniform Load, Spac- ing, Span, etc., for Angles and Tees as Beams or Gir- ders ........................................... 48-51 Diagram 22. For Reducing the Value of a Concentrated Load to an Equivalent Value of Uniform Load per Unit Floor Area ................................... 52 CHAPTER IV. SPANDREL BEAMS. Explanation of Diagram 23 .............................. 53 Explanation of Diagrams 24, 25, 26 ....................... 54 Diagram 23. For Giving an Equivalent Value of Load Con- centrated in the Middle of a Span for any Value of a Concentrated Load at any Other Point ................ 56 vi CONTENTS, Diagram 24. For giving the Allowable Load on Standard and Special 3-in. to 15-in. I-Beams 57 Diagram 25. For giving the Allowable Load on Standard and Special 10-in. to 24-in. I-Beams 58 Diagram 26. For giving the Allowable Load on 3-in. to 15- in. Standard and Special Channels 59 CHAPTER V. GRILLAGE BEAMS. Footings 60 Design 60 Bending 60 Buckling of the Web 62 Explanation of Diagram 27 62 Diagram 27. For giving Size, Weight and Spacing of I- Beams necessary for each of the several tiers in a gril- lage footing 63 Example of Use of Diagram 63 CHAPTER VI. END REACTIONS. Explanation of Diagram 28 65 Design >and 'Sizes of Standard Connection Angles 66 Explanation of Table 16 67 Design of Bearing Plates 68 Explanation of Diagram 29 68 Table 16. For giving Maximum Allowable End Reaction on Standard and Special Connection Angles, also Relative Values of the Several Sizes of Rivets 69 Diagnam 28. For giving Values for Rivet Requirements in Connection Angles, also Areas 1 for Bearing Plates 70 Diagram 29. For giving Thickness of Beam Plates of Cast Iron, Wrought Iron or Steel 71 PART III. COLUMNS AND TRUSS MEMBERS. CHAPTER VII. STEEL COLUMNS. Ratio of Slenderness 73 Explanation of Diagrams 30 to 34 73-78 Diagram 30. For giving the Radius of Gyration of the most Common Forms of Column Sections of Wood, Cast Iron or Steel 79 Diagram 31. For giving the Radius of Gyration of the Most Common Forms of Built-up Column Sections 80 Diagram 32. For giving the Ratio of Slenderness of a Col- umn 81 Diagram 33. For giving the Safe Loads on Steel Columns as Called for by the New York Building Code for Ratios of Slenderness up to 120 and Web thickness Allowable load per square foot Allowable end reaction Web thickness * 3S |li * s? Allowable end reaction Web thickness Allowable load per square foot J1 Lbs. Ins. % W. Tons Tns. % w. Tons Ins. #W. Tons 9-75 0.21 IOO 4-7 0.21 IOO 4-7 0.21 IOO 47 12. O "7 A 114 7 6 12.25 0.36 113 8.1 0-34 113 7.6 13. 0.26 I ~" I c 8 14-75 0.50 127 II. 2 0.49 127 II. O 15.0 0.38 141 8.5 I 5 " CHAN NELS 6 o o 18 CJ. 4O 1 6-S 0.19 63 4-3 0.19 03 4-3 1 8 o o 70 64 6 7 9.0 0-33 73 7-4 0.32 73 7.2 0.25 81 56 IO.O O 71 86 7 o 0.48 88 10.8 o.47 88 10 6 12 O O 47 96 O 7 1 5 " ZEES n. 6 0.31 in 13-9 0-37 133 16.4 0.44 155 5 " BULB ANGLE I 10. 0.31 j 85 i 1 FLOOR FRAMING. Diagram No, 3 5-in. x 9.75-lb. I-Beams SPAN OF BEAMS OR GIRDERS IN FEET 5 G 7 8 9 \0 sr LU Q oc o QC o & e r e 9 \o & SPAN OF BEAMS OR GIRDERS IN FEET Safe loads given include weight of beam and maximum fiber stress, 16,000 Ibs. per sq. in. maximum deflection i-4Ooth of the span. STRUCTURAL DESIGNERS' HANDBOOK:. THE DIAGRAM ON OPPOSITE PAGE GIVES : (a) The allowable uniform load on 6=in. x 12.25 Ib. I=beams in Ibs. per sq. ft. of floor. (6) The allowable spacing C. to C. in ft. for any span and any uniform load, (c) The allowable span in ft. for any uniform load and any spacing. (a?) The weight of steel in Ibs. per sq. ft. of floor. \e} The percentage of load allowable for any unsupported length of top flange in feet. THE TABLE FOLLOWING GIVES : (/") The percentage of load allowable on special shapes other than the above standard. (g-) The same percentage factor to be used for spacing instead of load. (h) The allowable end reaction for safety of web without reenforcement for buckling. 6"! Beams Carnegie, Cambria, Jones & Lauerhlins, Phoenix Pencoyd Passaie tj"o co 4J o 03 III ll ^0 |^S ggo % 3 5 Z 5 <1 - ^1 3 2 Lbs. Ins. % W. Tons Ins. %W. T JES Ins. ox yT Tons 12 O O 22 OQ 5Q 12.25 0.23 IOO 6.2 0.23 IOO 6.2 y 14-75 0-35 no 9-4 0-34 III 9.2 I5.O 0.25 121 6 7 17.25 0.48 119 12.9 0.46 122 12.4 17. c O 3 *7 131 IO O 20. o 0.50 141 13 5 6 " CHAN NELS. 8 O.2O 59 5-3 O.2O 59 5.3 O.2O 58 5-3 Q 0.2? 62 6 7 IO o 30 66 8 i 105 0.32 6 9 8.6 0.27 75 7-3 12 0.28 85 7 c, 13 0.44 80 ii 9 O.4O 85 10.8 o-33 89 8.9 JC o 43 07 ii 6 0.56 8 9 I5-I 0.52 96 14.0 17 o 38 116 IO.2 18 O d3 I2O ii 6 20 o< 53 128 14.3 6 " ZEES 15.6 0-37 n 5 18.3 044 134 21.0 0.50 153 6' DECK BEAMS 14.1 0.28 84 17.2 0-43 99 6 BULB ANGLES 12.3 0.31 78 13.8 038 90 17.2 0.50 104 FLOOR FRAMING. 2$ Diagram No. 4 6-in. x J2.25-lb. I-Beams SPAN OF BEAMS OR GIRDERS IN FEET 9 \o 15 30 X 8 fc UJ u. z CO Q en O DC i UJ Q \ \ L V .. N POUNDS PER SQUARE FOOT OF FLOOR \ A ' 1 ^ A' \ \ \ \ \ \ V \ ^ \ > * \ ! N \ \ \, S \ V ^ ^ \ ^ \ \ \ \ V V \ \ \l\ \ \ \ - \ \ \ \ \ \ \ \ \l\ \ \ \ \ \ \ \ \ \ \ N ^ V \ \ I . \ 3 \ \ \ \ \ \ \ ' || \ \ V \ \ \ \ \ \ \ \ \ \ \ V \ V I\ v N \ i \ \ \ \ \ V \ \> \ \ \ \ ^ \ > A \ \ v I \ \\ \\ V , N ' iN \ \ \ \ \ \ \ \ \ \ s V \ \ \ \ \ \ \ \ x \ \ \ \ \ WE C?P fe 1C . c R. i a ^ if T- a o P M & g S \\ V v\ \ X \ \ N \-\ A \ d , \ J-L Ot *.e t-c f\ = = I J w 1 \\ s \\ :\ x \ \ N \ \ N N V ^ \ \ \ \ \ \ 1 JK 5 V A " \ \ \ \ k N \ \ \ \ \ N \ \ \ V \ \ \ \ c \V\\V \ \ 3 - \ \ \ * \ i "t* ft ' u_ O } s \ \ \ \ \ \ \ \ \ \ * \ ^ V\V \A 35 \ \ \ v \ K \ \ \ \ r- \ \ 1 \\\N \\ ! \ \ \\\ \ \ \ \ \ \ \ \\Aj ' \ V Sj s \ \ \ \\\\\ \ A \ ^ ir SPACING CENTEF .. 4 * 6 r rn \ ~~ ^ SB * s \ \\ \ k\ \ \ \ vv \ \ \ \ \ \ \\ Sw \ ^ \\ \v \ \\ \N \ V \\ A\ \ \ \ \ r \\ 533 \ ' L \ \ ] j \\ \ , \\\ \\ \ \ \ \, \ 2 4 ~ V \s \ ' \ I * \\\ k\\ \\\ \ \lv \ \ \ \\ \\v \\ N \ \\l A\UU \ \ \ \ \ \ i 2 -2 - - - \v \ ^ \ V \. V \ \ Vu \v \ \\i\ \ \\ ] \ \ \ \ - \ A \ V A N k \ \ \\ 55 \ \ \ SN \\\\\\ \\ \\ \ \ \ \ z ^ " -\ - S - S 3 X V - V -A r vlX^ J A \\^\\ \\ \-\ -\- ^-\ V- . ' . 1 .. _ ._ _ ., .-z. JF _. . \ \^ A 3 V \ \ \ \ \ \ \\ S\\\ ss \\\ \ \ \ \ (/ * - \ ft A \r ' ^ \ s ^> * \ \ ' '1 ^S ^\ v V^A \ T%M \Vs y A ** Le \ i/* r - UJ B 1 \ i A * \ \ A \ \ \* 1 \ \ ^ \\sja v\\ 8 sr r \ T e \% \' \ * IP h \ fe ^ \ \ A - -A \ \ \ m UTv M\W \\\ V \. \1-V \ _ V ... . 4 t i ' > 7 8> 9 10 15 2O 25 3O SPAN OF BEAMS OR GIRDERS IN FEET Safe loads given include weight of beam and maximum fiber stress, 16,000 Ibs. per sq. in. maximum deflection i-4OOth of the span. 26 STRUCTURAL DESIGNERS' HANDBOOK THE DIAGRAM ON OPPOSITE PAGE GIVES : (a) The allowable uniform load on 7=in. x 15 Ib. I=beams in Ibs. per sq. ft. of floor. () The allowable spacing C. to C. in ft. for any span and any uniform load. (c) The allowable span in ft. for any uniform load and any spacing. ( rf) The weight of steel in Ibs. per sq. ft. of floor. (e) The percentage of load allowable for any unsupported length of top flange in feet. THE TABLE FOLLOWING GIVES : CO The percentage of load allowable on special shapes other than the above standard. (^) The same percentage factor to be used for spacing instead of load. (Ji) The allowable end reaction for safety of web without reenforcement for buckling. 7"! Beams Carnegie, Cambria, Jones & Lautjhlins, Phoenix Pencoyd Passaic o> 03 9 10 15 20 UJ Q pc O cc O (D 1 2 LL O DC U z LU O O DC U \o \& 20 SPAN OF BEAMS OR GIRDERS IN FEET Safe loads given include weight of beam and maximum fiber stress, 16,000 Ibs. per sq. in. maximum deflection i-4OOth of the span. STRUCTURAL DESIGNERS' HANDBOOK. THE DIAGRAM ON OPPOSITE PAGE GIVES : (a) The allowable uniform load on !0=in. x 25 Ib. I=beams in Ibs. per sq. ft. of floor. () The allowable spacing C. to C. in ft. for any span and any uniform load. (/:) The allowable span in ft. for any uniform load and any spacing, (a?) The weight of steel in Ibs. per sq. ft. of floor. (*?) The percentage of load allowable for any unsupported length of top flange in feet. THE TABLE FOLLOWING GIVES : (_/) The percentage of load allowable on special shapes other than the above standard. (^) The same percentage factor to be used for spacing instead of load. (A) The allowable end reaction for safety of web without reenforcement for buckling. 10"! Beams Carnegia, Cambria, Jones & Laughlins, Phoenix Pencoyd Passaic -u-*^ 1 1 Web thickness Allowable load per square foot Allowable end reaction Web thickness Allowable load per square foot Allowable end reaction Web thickness Allowable Joad per square foot Allowable end reaction Lbs. Ins. #W. Tons Ins. %W. Tons Ins. %W. Tons 25 0.31 IOO 12. 0.31 100 12.0 0.31 IOO 12. 27 0.37 104 164 30 0.46 no 20.7 0.44 no 19.8 0.45 no 20. 2 33 o 77 1^2 16.4 35 0.60 I2O 27.0 0.44 J 34 19.8 0-43 J I 3 6 19.4 40 o.75 130 33-8 0-59 J 43 26.6 0.58 I 4 6 26.1 10 " CHANN ELS 15 0.24 55 6.0 0.24 55 6.0 0.25 54 6.8 17 0.29 58 IO.2 18 O.T.2 60 12.7 20 0.38 64 17.1 0.38 64 17.1 0.31 70 12.0 25 0-53 74 23-9 0-45 81 20. 2 o 46 83 20.7 30 0.68 84 30.6 0.60 92 27.0 O.6O 90 27.0 35 0.82 94 36.9 o-75 1 02 33-8 10 " DECK BEAMS 27-3 0.38 88 35-7 063 105 10 " BULB ANGLES 26.5 0.48 82 32.0 0.63 89 Diagram No. 8 FLOOR FRAMING. 33 JO-in. x 25-lb. I-Beams SPAN OF BEAMS OR GIRDERS IN FEET 7 S> 9 \0 \5> 20 25 -*>O U_ O Ld DC < O co -I cc LJ 51-J-l 0- co Q Z D O CQ V ... V CO ^S o LJ PS ^ 5 & 7 2> 9 \0 \& SPAN OF BEAMS OR GIRDERS IN FEET Safe loads given include weight of beam and maximum fiber stress, 16,000 Ibs. per sq. in. maximum deflection i-4.ooth of the span. 34 STRUCTURAL DESIGNERS' HANDBOOK. THE DIAGRAM ON OPPOSITE PAGE GIVES : (a) The allowable uniform loadon 12=in. x 31.5 Ib. I=beamsinlbs. per sq. ft. of floor. (6) The allowable spacing C. to C. in ft. for any span and any uniform load. (V) The allowable span in ft. for any uniform load and any spacing. ( 7 & \0 15 ZO 25 30 !D Q gc o tr O CO < UJ CQ Q UJ UJ v \ \\\\ \\ViWAteVs\Ji\ \ US'. \. \f fv Ajj-Xi -\ \ \\\OA\V\ :\\TX1\\\'\ \ \^vf\ \ ^ \\ \ \\ \\\\\\\\\\\\N\\ r\\\\ \\\\ \\\\ \\\\\\\ V \ -V-V \. \ \ \ \\\\ \\ \\\\\\\\\ \\\\\\\\\ \\v \ \ \-\ \\ \ \ \A \'\ \ \ \\\ v\ \ \ \\ \\\ A-X XX \V V \\ \\ ,p\ x\ s v \\ \\ \\\ \\ \v \ \\ \\\\\ \\ P lo i& 20 SPAN OF BEAMS OR GIRDERS IN FEET CQ Safe loads given include weight of beam and maximum fiber stress, 16,000 Ibs. per sq. in. maximum deflection i-4OOth of the span. 36 STRUCTURAL DESIGNERS' HANDBOOK. THE DIAGRAM ON OPPOSITE PAGE GIVES : (a) The allowable uniform load on 12=in. x 40 Ib. I=beams in Ibs. per sq. ft. of floor. () The allowable spacing C. to C. in ft. for any span and any uniform load. (c) The allowable span in ft. for any uniform load and any spacing. (of) The weight of steel in Ibs. per sq. ft. of floor. (ji) The percentage of load allowable for any unsupported length of top flange in feet. THE TABLE FOLLOWING GIVES : (f ) The percentage of load allowable on special shapes other than the above standard. (^) The same percentage factor to be used for spacing instead of load. (A) The allowable end reaction for safety of web without reenforcement for buckling. 12"! Beams Carnegie, Cambria, Jones & Laughlms, Phoenix Pencoyd Passaic 4J-g SI C SH ft Lbs. 40 gl 1 2 %3 Ins. Allowable load per square foot Allowable end reaction Web thickness Allowable load per square foot Allowable end reaction Web thickness Allowable load per square foot o y & 3 ^ *H Tons %W. Tons Ins. %W. Tons Ins. %W. 0.46 ICO 24.9 0.42 1 02 22.1 0-39 104 19-3 45 0.58 106 31-3 0-54 109 29.2 0.51 no 2 7 .6 50 0.70 "3 37-8 0-55 123 29.7 0.64 118 34-6 55 60 65 12" 20 20.5 23 25 27 30 33 35 0.82 119 44-3 0.56 0.68 0.80 137 143 150 30-3 36.8 43-2 0.63 o-75 0.88 0.28 o-35 0.40 0.38 0-45 0-53 0.58 133 139 146 46 50 53 60 64 68 70 34-0 40.5 47-5 8-5 15.6 20.3 18.4 24-3 28.6 31-3 CHAN NELS 0.28 48 8.5 0.28 48 8-5 0-39 54 19-3 0-39 54 19-3 0.51 60 27.6 0.51 60 27.6 0.64 67 34-6 0.50 77 27.0 40 0.76 73 41.1 0.62 83 33-5 FLOOR FRAMING. Diagram No* JO 37 J2-iru x 40-lb. I-Beams SPAN OF BEAMS OR GIRDERS IN FEET 9 \& \S> 20 -- cc ^ 10 IB 20 SPAN OF BEAMS OR GIRDERS IN FEET Safe loads given include weight of beam and maximum fiber stress, 16,000 Ibs. per sq. in. maximum deflection i-4OOth of the span. STRUCTURAL DESIGNERS^ HANDBOOK. THE DIAGRAM ON OPPOSITE PAGE GIVES : O) The allowable uniform load on 15=in. x 42 Ib. I=beams in Ibs. per sq. ft. of floor. (&) The allowable spacing C. to C. in ft. for any span and any uniform load. (V) The allowable span in ft. for any uniform load and any spacing. (d) The weight of steel in Ibs. per sq. ft. of floor. 0) The percentage of load allowable for any unsupported length of top flange in feet. THE TABLE FOLLOWING GIVES : (/") The percentage of load allowable on special shapes other than the above standard. (,-) The same percentage factor to be used for spacing instead of load. (7z) The allowable end reaction for safety of web without reenforcement for buckling. 15"! Beams Carnegie, Cambria, Jones & Laughlins, Phoenix Pencoyd Passaic .11 15 20 25 30 -4o SPAN OF BEAMS OR GIRDERS IN FEET LU UJ 50 Safe loads gfiven include weig-ht of beam and maximum fiber stress, 16,000 Ibs. per sq. in. maximum deflection i-4OOth of the span. 40 STRUCTURAL DESIGNERS' HANDBOOK. THE DIAGRAM ON OPPOSITE PAGE GIVES : (a) The allowable uniform load on 15=in. x 60 Ib. I=beams in Ibs. per sq. ft. of floor. () The allowable spacing C. to C. in ft. for any span and any uniform load. (c) The allowable span in ft. for any uniform load and any spacing. () The percentage of load allowable for any unsupported length of top flange in feet. THE TABLE FOLLOWING GIVES : (/) The percentage of load allowable on special shapes other than the above standard. (>) The same percentage factor to be used for spacing instead of load. (A) The allowable end reaction for safety of web without reenforcement for buckling. 15"! Beams Carnegia, Cambria, Jones & Laughlins, Phoenix Pencoyd Passaic f! Web thickness ||| ^1 Allowable end reaction Web thickness \ Allowable load per j^ square foot Allowable end reaction Web thickness \ Allowable 5 load per ) The percentage of load allowable for any unsupported length of top flange in feet. THE TABLE FOLLOWING GIVES : (_/") The percentage of load allowable on special shapes other than the above standard. ( g) The same percentage factor to be used for spacing instead of load. (A) The allowable end reaction for safety of web without reenforcement for buckling. 20"! Beams Carnegie, Cambria, Jones & Laughlins, Phoenix Pencoyd Passaic 2 n Web thickness Allowable load per square foot Allowable end reaction Web thickness Allowable load per square foot 1-1 Web thickness g S<2 gft ^1 Allowable end reaction Lbs. Ins. *W. Tons Ins. *W. Tons Ins. %W. Tons 65 0.50 IOO 25.0 0.50 IOO 25.0 0.50 99 25.0 70 0-57 104 38.5 0.56 105 38.5 0-57 102 38.5 75 0.65 109 50-5 0.64 109 48.6 0.66 1 06 51-7 80 0.60 125 41.8 0.63 120 46.6 0.69 115 56.6 85 0.66 129 51-7 0.70 124 54-5 0.76 II 9 66.9 90 0.74 133 64.0 0.78 128 57-8 0.78 I2 9 70.2 95 0.81 137 72.9 0.74 137 68.5 IOO 0.88 142 79.2 0.81 141 76.5 i FLOOR FRAMING. 45 Diagram No* J4 20-in. x 65-lb. I-Beams SPAN OF BEAMS OR GIRDERS IN FEET 15 20 25 Z>0 AO CO DC LU Q. 05 Q z => o so SPAN OF BEAMS OR GIRDERS IN FEET Safe loads given include weight of beam and maximum fiber stress, 16,000 Ibs. per sq. in. maximum deflection i-4OOth of the span. 46 STRUCTURAL DESIGNERS' HANDBOOK. THE DIAGRAM ON OPPOSITE PAGE GIVES : (a) The allowable uniform load on 24=in. x 80 Ib. I=beams in Ibs. per sq. ft. of floor. () The allowable spacing C. to C. in ft. for any span and any uniform load. (<:) The allowable span in ft. for any uniform load and any spacing. ( t-i & Web thickness Allowable load per square foot Allowable end reaction Web thickness Allowable load per square foot Allowable end reaction Web thickness Allowable load per square foot 1 \ \ ,3 H s SN \\\ \ \ \ \ V s\\ \\ \ \ \ Ins Ins # tn X X 3bs. 0.6 0.8 0.8 1.2 i-5 0.87 1.23 % W. \A ' S\\ s N \ VJk \ Angles Tees % I i 55 77 1:0 142 i So 97 1 60 \\\ V \\ N 1 *\ \ \ \, \\\\ \\ ^\ N N 1 \ \ \ S \\ ^ \V A \ \ \ \ V 1 V w.pj>> A \ yX \ x J \ A V \ \ 1" 2' y -4* SPAN IN FEET & \0' V Diagfram No* M Angles Tees 2 Ins IX iX iX IK 2^ ? Ins # *# iX i# i# i# i# 4 Ins | /* 5 i,; ^ T 3 G /4- T 5 , H 5 Lbs. I.O i-5 1.9 2.4 1.2 1.8 2.4 2.9 3-4 'S3 3-6 2.9 1.84 2.4 6 %W. 70 IOO 130 156 IOO 150 190 230 270 IOO 214 129 157 2CO OvV ?v \ \ \ \ \ \ \r4 SPACING IN FEET r 2' & \\\ A-\ \ \ A \- ;< \\\ s \ is \ x \ \ \ v' \ \ \\ \ \ \ c fi \\ \\ v \ ^ \ \ '\ \ S \ * V NN \ \\\ \v \\ Cj \ \ \ \ * \ V \\ 2 y \ \ > t\ \ \ \ \ S \\ ^ s \ \ ^ \ \ s ^ X \ ^ V S \ ^ \ \ \tt $ kS N x\ \ \\ \ \ \ V \ \_ \ r Z* $ A' SPAN IN FEET &' 10* FLOOR FRAMING. 49 SPACING IN FEET Diagram No* J8 I 2 Ins 3 Ins 4 Ins 5 6 Angles Tees Lbs. % W. '^ \ \ \ ^ A\\ \ \ \ \ A \ \ j i i \ 1 4 2 2 4 2 2 2 I H V H 2.1 2.8 3-4 4.0 2-5 3-2 4.0 4.7 3-7 4-3 6.6 7-9 56 76 92 104 76 IOO 120 140 7 6 IOO 133 136 160 A \ \ \\\\ \ \ \ ^ \ \ \ > ^ \ \ \v \ E \\s \ \ \ \ Q ^\ r > \ L \ *i "rf\ \\ \ \ \ s \\\ SQ3 -AV ^ \ \ \ \ ss \ ,\\\ A A \ v 0\ \ \ \ V A \ \ \\\ \ \ t \ \\\ 00 \ A -\> J L L LA 3> \ \ \\\ E \ v \\ \ \ \ k J J * i V^ \ \ \ >i \\ ,\\ \ s . SS^ V rS5^ \ s \\ \ ^ \ s \\ \ AwS BS^ [^ ,\V\ t \ \ \v \\ Is 8$ 55 \ \ \ V s \^t KS A^vV ^\\\ \ \ \ \ W.F i. s \\ \\ v |JSs^ H s \ \ y r 2* SPAN 3* 4 IN FEET >+ u JO* Diagram No* 19 I 2 3 4 5 6 Angles Tees Ins 2 3 3K 3 4 Ins 2X Ins V 1 Lbs. ICO 130 160 190 103 138 196 138 170 200 228 255 140 170 200 2JO 260 1 10 H5 170 200 1 80 200 190 210 190 22O 2OO 25O 2.8 3-7 4-5 5-3 4.1 5-9 4-5 1:1 7 .6 4.9 7.2 8.3 9.4 4.1 4-9 5-5 6.4 6.1 7.2 7-3 8.6 8.0 9.3 5-8 6-7 j> \ \ \ g \v fi \\ ^ t-^ A\ \ \ \ \ \v \\ \ v \ S ; \ A ^ ^ ^ t \ J \\\ \ *> N ^ \\^ \\ A \\\ \ \ ' ^ ^ A. IS ^ !CC 3 \ \ \\ \ \ \\s \\ \ \ \ i c \\\ \ \ \ v \\ A x\V V' \ \ K vX. i V V \\\ \ \ y \ \ V V \ Si \ A 0^ K V \ r \\\ \\ \ \ \\ \\ A, A\^\ \^ N ^S v ^ C>l Q \\ \\^1 \ ^\ V \\ \ \ v \L\ \ \ \ \ \ ^ \ \\\ y \ \ \^ 2 SSsi i L^ X i \\\ ,\\ r> \ v x\ s t ^ sJiJ 3^v \ ? s \\ A }, T ' s -^H\ \ \ \ \ \\ 1 \ \\ >m \\ \ \ vw. :. 1 ^ s ^ !\ V \ V ^1! | sNOVO \\ ^ \ 1 2 3 -4. J5 6 7 3 9 SPAN IN FEET 10 15 STRUCTURAL DESIGNERS' HANDBOOK. I 2 3 4 5 6 Ins Ins Ins Lbs. *W. Angles 2^ 3 K 4-5 ICO T B (! 5-5 123 3 /8 6.6 145 7.6 1 66 # 8.5 185 3 3 ^ 4.9 103 5 Te 6.1 127 Diagram No. 20 T 7 ' 7-2 8-3 148 170 lit "^ T-V \. ' n \1 - ^ T ---fin *=( ^ 9-3 190 t s V^ 6^3 S \ ^ v C ::: - 3>2 3 F 6.6 7.8 129 152 gft X V \ \ \ \ ^ \ ^ s > V ^ Tfi 9.1 10.2 196 V \ \ \ \ \ \ t^ V" \ v \ \ \ V \ \ ^ x \\\^ ^ ^ fj JL _ i. \ \ \\ \ \ \ \ V N \ V k A \ \ \\ \\ \ |!a \ ! k \ \-- \ 4 3 S 8.5 132 155 \ A' ,\ \ \ \ \ \ \ \ \\ s \ \ \ \ ^ \ ^ C 5|jv V \ \ \\ \ \ \ T?- Q.8 177 fc \ \v \ A V ' ^ \ \ 1 ,\ \ \ \\\ \ \ \ Yz II. I 200 \\ V \ ^ ^ x A ; :\ \ s V t j \^\ \ 5 3 ft # 8.2 9.8 134 1 6O V f.p. * \ t \ \ \^ ffl ' V \ \\ \ I 2 3 4 5673 910 15 n TI -3 12.8 2O6 SPAN IN FEET Tees 2>^ 3 6.1 136 7-2 I 5^ 6.6 132 -. . 7.8 153 9.1 1 80 IO.O 196 7.8 128 -5 i57 10.9 200 9-3 i57 is 145 IO.O 1 68 13.6 210 FLOOR FRAMING. OO OO OsOO O M >-> IH *3- - lOVO t^OO VO t^OO CA \/-i co' O"> O t-i M CO ON !> O\( O O O O 00 t^ N C\CX) ir>l>.O\M iOMC\C)O\ Example. A beam supports a load of 1,000 pounds (10 C. or i M.) i ft. from the end of a 12-ft. span. What equivalent value of load concen- trated in the middle would require a beam of the same strength? Answer: 305 pounds (3.05 C. or 0.305 M.). SPANDREL BEAMS. 57 Diagram No. 24* For giving the allowable load on standard and special I-beams. SPAN IN FEET SPAN IN FEET The deflection curves are shown by full lines for loading concen- trated in the middle and dotted lines for uniformly distributed; thus a 6-in. x i2 1 /4-lb. beam with a span of 15 ft. will carry 1.15 tons concentrated in the middle or 1.85 tons uniformly distributed. STRUCTURAL DESIGNERS' HANDBOOK. Diagram No. 25 For giving the allowable load on standard and special I-beams. SPAN IN FEET UrtlFORfl C" 10 20 30 =33= 5a N\ \\ \\ \ \ 12 ^ \\ N\ \ \ \\ S\"\ X^k _ \\ !O \ \ \\ KS 10 20 30 SPAN IN FEET Example. A 2O-in. x 6s-lb. beam 42-ft. span will carry 7.35 tons con- centrated in the middle of the span or 12.35 tons uniformly distributed. SPANDREL BEAMS. Diagram No. 26 59 For giving the allowable load on standard and special channels. SPAN IN FEET a CO o * SPAN IN FEET Example. A 12-in. x 2O.5-lb. beam 24-ft. span will carry 2.35 tons con- centrated in the middle of the span or 4.2 tons uniformly distributed. 60 STRUCTURAL DESIGNERS' 1 HANDBOOK. CHAPTER V. GRILLAGE BEAMS. FOOTINGS. The use of steel beams in footings is a problem of frequent occurrence with the structural designer. This chapter deals with the design of the steel beams for grillage footings and presupposes a general acquaintance with the subject of founda- tions* on the part of the reader. Grillage footings are in general either footings of walls or foot- ings of columns. The former are somewhat the simpler in design, but their treatment is precisely the same as that for column foot- ings. They will therefore not be especially referred to in the fol- lowing. When two or more columns occur on a single footing the problem, on the other hand, becomes so complex that only those familiar with the mechanics of engineering should presume to deal with it. The properties of beams as given in Chapter VIII may be used for this latter case. The known quantities in the design of a footing are the load on the column and the allowable pressure per unit area on the soil (or other material) which supports the grillage. The area of the surface of a footing which comes in contact with the soil is found by dividing the load on the footing by the allowable pressure on the soil. The accompanying drawing, Fig. 2, shows a design of a grill- age footing for a single column having two tiers of grillage. From this drawing the elements of the design of the different tiers of beams may readily be understood. The load on the column is transferred to the grillage by a "base," of cast iron or of steel, and the size of this base must be known or assumed before the grillage beams can be designed. DESIGN OF GRILLAGE BEAMS. BENDING. As explained in the short treatment on the "Con- ventional Methods of Considering Loads on Grillage Beams" in Chapter I there are two methods of designing these beams. The most common method is to consider only the projecting length of these beams beyond the edge of the tier or base imme- *For this aspect of the subject such books as Baker's Treatise on Masonry Construction; Kidder's Building Construction and Superin- tendence, Part I; and Patton's Practical Treatise on Foundations, and the back files of the Engineering News and Engineering Record should be consulted. GRILLAGE BEAMS. 61 diately above them. Within certain limits this method will give satisfactory results. It will always give safe results if b / 2a does not exceed 0.3, where b equals the breadth of the base or tier above, and a equals the projection of the beams beyond the edge of this base (2a + b) equals the entire length of the grillage beam under consideration. The second method is more conservative although the follow- ing is a modification of it by 30% limit allowance for the value 1 ] \ 1 rf s/ 1 1 \ 7 M 1 I j ._ . _.i [ 5 c I 5 fr " -b- Fig. i > *---- - <4 x Vl 6 x 4 X 7 A. Anonymous 3^ x ?/* x H 3^x 3 y 2 x 6 A. END REACTIONS. 6? The lengths of standard angles for the several sizes of beams are usually as follows : For 24" I s i' 6" 1 g. For . .10" to 7" Is and [ s o' 5" 1 g_ " 20" and 18" i' 3" " .. 6" o' 3" 15" Is and [s o' 10" " .. 5" o' 2]/ 2 " " " 12" I s and [ s o' 7y 2 " " " .. 4" and 3" o' 2" The numbers of shop and field rivets in the above standards do not vary very much, although Pencoyd and the American Bridge Co. put in one extra shop rivet in the I5~in. and in the lo-in. to 7-in. standards over what is called for in the same standards in the fol- lowing table. The strength of a pair of connection angles (sometimes called knees) not only depends upon the number and strength of the rivets in them, but also upon the strength of the metal upon which the rivets bear. These values for both standard and special connection angles are given in the following table. TABLE GIVING MAXIMUM ALLOWABLE END REACTION ON STANDARD AND SPECIAL CONNECTION ANGLES: This table (No. 16) gives the maximum load that can be safely carried by different standard and special connection angles in terms of the strength of the shop and field rivets in shear or bearing. Evidently, the end reaction on the beam must not be greater than these values for shear or for bearing. The tabular values are for safe shearing capacity (single shear) and safe bear- ing capacity (for bearing on 1 / 10 -in. metal in web). The construc- tion of the table needs no further explanation. Whenever there is reason to suspect that a standard connection will not be sufficient for conditions indicated by Diagram No. 28, the capacity of this standard should be found from the table. The use of this table is best illustrated by an example. Example: A 12-in. 31.5 Ib. I-beam has lo-in. beams i6 l / 2 ft. long framing into it from both sides. The web of the 12-in. girder is 0.35 in. thick, thus giving a bearing value of o.i75-in. for each field connection. Suppose, wrought iron rivets are used in the field, the permissible end reaction would then be 0.175 x 2.26, or 3.95 tons. According to Diagram No. 28 this is the safe limit for uniformly loading the lo-in. beams. In designing special connection angles their length is limited by the clear distance between the fillets of the beam. This dis- tance is given for all I-beams and channels in the tables given in Chapter VIII. On general principles it is advisable to use as large connection 68 STRUCTURAL DESIGNERS' HANDBOOK. angles as practicable, because they add stiffness to the framing. This is especially of value in high buildings. DESIGN OF BEARING PLATES. The elements in the design of a bearing plate or template are its bearing area and its thickness. The bearing area depends upon the load to be carried (the end reaction) and upon the permissible unit load on the material sup- porting the template. This latter is specified in the "Code" (N. Y. C.) as follows : On Brickwork: 8 tons per sq. ft. when lime mortar is used; 15 tons per sq. ft. when cement mortar is used; 18 tons per sq. ft. when Portland cement (i to 3) is used. For Rubble Masonry: 5 tons per sq. ft. when lime mortar is used. These values will be found to be the column headings for tem- plates in Diagram No. 28 ; then, by the use of this diagram the area of bearing required is at once obtained, and a convenient size of template selected. The thickness of the bearing plate depends upon the material of the plate, the amount of projection of the plate beyond the flange of the beam or beams supported,* and the unit pressure on the bottom of the plate. The material may be cast iron, wrought iron or steel ; the unit pressure on the bottom of the plate is that used in finding the area of the plate (i. e., 5, 8, 15, or 18 tons per sq. ft., as above). DIAGRAM NO. 29 enables the required thickness to be readily obtained. The abscissas are amount of projection in inches. The ordinates are thickness of plate, there being three different ordinate scales, for cast iron, wrought iron and steel, respectively. Differ- ent diagonal lines represent the different allowable unit pressures on the supporting material. To use the diagram, take an abscissa equal to the projection of the plate, in inches, and follow up to the diagonal. The hori- zontal at the intersection gives, when followed to the right, the thickness of the plate. *The clear distance between the inside flanges of a pair of beams must not exceed 2.45 times the projection of the plate beyond the outside flanges. END REACTIONS. Table Giving Maximum Allowable E,nd Reaction on Standard and Special Connection Angles TABLE 16 All Klvets % Diam. Number of Holes in Shop or Field End of Connection Angles. SHEARING Values Given for Single Shear BEARING Values Given for T Vinch Bearing of Rivets Steel Wrought Iron Steel Wrought Iron Shop Field Shop Rivet Field Shop Rivet Field Shop T'ns i-5 Field Shop Field Rivet Bolt Rivet Bolt a 2 2 Tons Tons Tons Tons Tons Tons Tons Tons Tons 4-4 3-5 3- 1 3-3 2.6 2-4 i-5 I-I3 i- J 3 "3 4 6.6 7.0 6.2 5-o 5-2 4.8 2.2 3- 1.70 2.26 C S 6 II. 10.5 9-3 8-3 7-8 7.2 3'7 4-5 2.82 3-39 "5 8 II. O 14.0 12.4 8-3 10.4 9.6 3-7 6.0 2.82 4.52 "5 10 II. 17-5 15-5 8-3 13.0 12.0 3-7 7-5 2.82 5-65 f 6 12 13.2 21. 18.6 9.9 15.6 14-4 4-5 9.0 3-39 6.78 7 H 154 24-5 21.7 "5 18.2 16.8 5-2 10.5 3-96 7.91 8 16 17.6 28.0 24.8 13.2 20.8 19.2 6.0 12. 4.52 9.04 9 18 19.8 31-5 27.9 14.6 23-4 21.6 6-7 13-5 5.08 10.17 10 20 22. 35-o 31.0 16.5 26.0 24.0 7-5 15.0 5-65 11.30 Relative Values of the Several Sizes of Rivets Sizes of Kivets Eatio in Shear Bearing Ratio 3/ rivet is to ^" as I is to 4 or as 3 is to 6 y 2 " " "3^ "4 " " 9 " " 4 " " 6 ft " " " X " ii " " 16 " " 5 " "6 7/ & " " tf "4 " " 3 " " 7 " " 6 i " " "3^ "9 " " 5 " " 8 " " 6 i}6 " " "3^ "9 " " 4 " " 9 " " 6 is for standard connections for 3 '' to 6 " I 3 and 7 to 10 12 15 18 and 20 24 Diagram No. 28 For giving values for rivet requirements in connection angles, also areas for bearing plates. (70) EAD REACTIONS. Diagram No* 29* For giving thickness of bearing plates of cast iron, wrought iron or steel. PROJECTION OF PLATES 4' 5" 6" 7" C.I. W.I. m f */ S */& Yz / *&_ 7" 8 PROJECTION OF PLATES , Note. When the clear distance between the inside flanges of a pair of beams supported by a single plate exceeds 2.45 times the projection of the plate beyond the outside flanges, the thickness of the plate is to be obtained by the following modification of abscissa value for projection (not the real projection). Multiply the clear inside distance between flanges by 0.41 and use this value on the abscissa scale. Part ffl. Columns and Truss Members. CHAPTER VIL STEEL COLUMNS. The usual methods of designing built steel columns are either quite complex or else they apply to specific forms of section, as for instance, to the so-called zee-bar, channel or plate and angle columns. In the following system of diagrams and tables, how- ever, the form and make up of the section is treated as a subject for secondary rather than primary consideration. The radius of gyration is an important factor in the design of columns. Numerically the radius of gyration is the square root of the quotient obtained by dividing the moment of inertia of a cross section by the area of the section. This mathematical com- putation is quite laborious in the case of a built up section, mainly because it has to be repeated for every variation in area and dis- tribution of the material in the cross section. It is believed, how- ever, that such computations as these are unnecessary. Diagrams Nos. 30 and 31 give the radii of gyration for the different forms of rolled sections and for the most common forms of built sections (see explanations later). A little study of these diagrams will con- vince the designer that the radius obtained by this graphical means will give results as accurate as the most conservative could wish to use in his computations. This radius of gyration, r, is one of two variables that deter- mine the ratio of slenderness* of a column. The other is the un- supported length, 1, of the column. This ratio of slenderness is 1 expressed by the quotient of , which is the factor that determines r the allowable unit compressive stress to be obtained from the aforementioned column formulas (see Chapter II). However, in the treatment of the subject of columns herewith, the allowable unit stress does not come directly into question, because it has been taken into account in the construction of the diagrams for safe loads. *See Chapter II. STEEL COLUMNS. 73 THREE STEPS ARE TAKEN IN THE DESIGN OF A COLUMN : First, determination of the ratio of slenderness ; second, the area of the cross section is found ; third, the make up of the section is decided. These steps will be considered in this order, the third step being taken up in Chapter VIII. ; RATIO OF SLENDERNESS. Three diagrams are 'given, two of which Nos. 30 and 31 are used for obtaining the radius of gyration for standard sec- tions and for built up sections respectively, and the third Diagram No. 32 is used for obtaining the ratio of the length of the col- umn to the radius of gyration or the so-called ratio of slenderness of the column. DIAGRAM NO. 30: Here abscissas represent thickness of metal expressed as a percentage of the depth or diameter of the section. Ordinates represent the radius of gyration in inches. The curves represent the different arrangements of material as in- dicated in the left hand margin. Thus the lowest line is for an H section with neutral axis coincident with the web, or for a star shaped section (it will be observed that the for- mer has a depth greater than the width of the flanges, thus corresponding to the average I-beam properties); the next line is for a square H section with neutral axis as before; the next is for a solid circular cross section, etc. The uppermost curve in the diagram (that represented by a full black line) gives the theoretical values for a section of two plates at a fixed dis- tance back to back and gradually reduced in thickness. In practice this section is very nearly represented by two channels or two I-beams latticed when the diameter is taken as the distance apart of their centers of gravity. Theoretically, this distribution of material gives the highest possible radius, but practically, it is impossible to make use of it because the latticing does not transmit the stresses due to eccentric loading satisfactorily. Beside the diagram proper, supplementary abscissa scales and ordinate scales are given. Since the abscissas represent the thickness of metal in the section expressed as a percentage of the diameter or depth of the section, different scales may be used to give the thickness directly in inches for different diameters. Such a series of scales is given in tabular form above the diagram, cov- ering diameters from 3 ins. to 28 ins. The principal ordinate scale on the right hand edge of the dia- gram proper gives the radius of gyration. A series of supplemen- tary scales to the right of this give the radius directly in inches for 74 STRUCTURAL DESIGNERS' HANDBOOK. any diameter of section. Seven scales are given, covering diam- eters from 6 ins. to 18 ins. inclusive. The abscissa scales (those in tabular form above the diagram) show a dotted irregular line which divides the scales into two parts. This line in- dicates the thickness of metal which the "Code" (N. Y. C.) specifies as the minimum for the different diameters of cast iron columns: Steel column sections are as a general rule found to the left of the line; at any rate they should for the sake of economy fall to the left of the line, since otherwise the metal is needlessly thick and may be better utilized by making the sec- tion larger and using thinner metal. The values in this diagram are entirely independent of the material of the column, and the sections shown cover the common forms of cast iron and wooden columns as well as the built-up sec- tions of steel columns. It should be remembered that for all ma- terials a similar distribution gives similar values for the radius of gyration. To use Diagram No. 30, after the general style of the section of the column has been decided upon, take an abscissa representing the thickness of metal (either as a percentage of the diameter on the lower scale, or in inches on the proper scale above the diagram) and follow the vertical up to the curve which represents the style of section selected. The horizontal at the intersection gives the radius of gyration on one of the ordinate scales at the right of the diagram. DIAGRAM NO. 31 is for the same purpose as the preceding except that the sections are for the most common built-up steel columns. Its construction is similar to that of, the preceding dia- gram: Curves are drawn for different sections, and the ordinates to these curves give the radius, of gyration in inches ; a series of or- dinate scales is provided at the right for different values of the diam- eter (depth) of the section, and the radius of gyration is read off on the appropriate scale. The left hand end of the curves denotes the minimum thickness of metal ordinarily used in practice for any one of the sections represented by a curve, while the right hand end corresponds to the usual maximum thickness employed for that type of section. The curves then show the variation of the radius of gyration as the thickness of metal used increases from the least to the greatest thickness ordinarily used. t NOTE: Attention is drawn to the fact that in the outline sketches for the different sections represented by curves on this diagram, dimension ar- rows are shown which indicate the particular dimension taken to be the STEEL COLUMNS. 75 "diameter." Thus, in the case of the Z-bar column, the width of the web plate is the diameter for the neutral axis perpendicular to the web. The use of Diagram No. 31 will be quite clear from the pre- ceding. It presupposes a selection of the type of section to be used in the particular case, and further the ability to judge approx- imately what relative thickness of metal will be required with that section to carry the load. DIAGRAM NO. 32: The ratio of slenderness of a column is graphically represented on this diagram. Abscissas represent length in feet and ordinates represent the ratio of slenderness. Curves drawn on the diagram represent various values of the ra- dius of gyration in inches. It is to be noted that while for convenience the abscissa scale shows length in feet and the radius of gyration in inches the ratio of slenderness or quotient of the two is given as if both were in inches. To use the diagram for any particular problem, take an ab- scissa equal to the length of the column in feet and follow the ver- tical up to the curve representing the radius of gyration of the column section selected. The horizontal at the intersection shows on the ordinate scale the desired quotient, i. e., the ratio of the length to the radius of gyration. SECTION AREAS. As previously stated the second set of diagrams give the areas of cross sections of columns for known loads and known values for the ratio of slenderness. These areas may conveniently be divided into three classes ; area necessary for concentric load when ends of columns are "flat" ; area or areas necessary for eccentric load when ends are flat and securely braced laterally in the direction or directions of the eccentricity ; and, area necessary when pin ends are used. Values for these three classes of loading are given on Diagrams Nos. 33 and 34 Diagram No. 33 which gives the area required for concentric loading on a column with flat ends facing the principal diagram of this group, because the two latter values are given in per cent, of the first. This is more fully ex- plained below under the separate heads. SECTION AREAS FOR CONCENTRIC 10 ADING : Diagram No. 33 gives the safe load on medium steel columns for any ratio of slenderness and any area of cross section. In this diagram, 76 STRUCTURAL DESIGNERS' HANDBOOK. abscissas represent values for any ratio of slenderness from 10 t> 200 ; ordinates represent the area of cross section in square inches ; curves on the diagram represent different values for the safe load capacity of the column. Several supplementary scales appear on the diagram. At the bottom, just above the main abscissa scale, is a scale showing "Rate of increase of area" for any given load and length of column with varying ratio of slenderness. This scale will be found valuable in indicating the effect of changes in dimensions of cross sections upon the amount of metal required in a col- umn. Thus it shows the importance of keeping the ratio of slenderness down as low as possible. For instance, a ratio of 170 calls for three times as much material as a ratio of 10. At the extreme right of the diagram is a scale of weights ; it shows the weight of the column per lineal foot for any area of cross section in square inches. A further supplementary abscissa scale on the lower part of the diagram gives the area for pin end columns in the form of percent- age factors, based on the section area required for an equivalent load on a column with flat ends i. e. as found on the main part of the diagram. SECTION AREAS FOR CONCENTRICALLY LOADED COL- UMNS WITH PIN ENDS: When the ends of a column are hinged or have pin bearings it is less rigid than when the ends are flat. For this reason lower unit stresses are allowed for pin end columns. The "Code" (N. Y. C.) makes an equivalent provision by saying "the working stress in struts of pin connected trusses shall not ex- ceed 75% of the working stresses for flat ends." This gives a flat increase of 33V 3 % in tne area of tne section for all column ratios. The percentages given by the aforementioned supplementary scale show values increasing as the column ratio increases. Thus,, for a column ration of 100 the percentage is 120, i. e., the pin end column should be given one-fifth more section area than a flat-end column with the same ratio of slenderness and with the same load ;. for a column ratio of 150 the percentage is nearly 155. SECTION AREAS FOR TENSION MEMBERS: The scale on Diagram No. 33 to the left of the scale of weights, on the right hand edge of the diagram, gives values for loads in tension for dif- ferent areas of section (or weights per lineal foot), based on a ten- sile strength of 16,000 Ibs. per sq. in. of net section. STEEL COLUMNS. 77 NOTE: This latter scale has absolutely no bearing on the use of this .diagram for the design of columns. It is intended for use in the design of trusses where both compression and tension members occur together and will be very useful for such work. The tables of properties of shapes in Chapter VIII, are convenient for use with this scale as well as for use with the diagram proper. THE USE OF DIAGRAM NO. 33 will be evident from the pre- ceding. Taking an abscissa equal to the ratio of slenderness of the column, the intersection of the vertical with the curve represent- ing the load gives the required area of section on the ordinate scale to the left, or, the required weight per lineal foot on the ordinate scale to the extreme right. If the column has pin ends this area (or weight) must be multiplied by the percentage factor found on the scale above the column ratio. The other scales are used in ac- cordance with the foregoing descriptions. It is generally not advisable to employ columns with a higher ratio of slenderness than 120. The "Code" (N. Y. C.) limits important columns to this ratio as a maximum, and the allowed stresses for columns are given only for ratios of 120 and less. As it was considered advisable to extend the use of Diagram No. 33 beyond this point so as to include ratios up to 200 the following method was used to supply safe values for allowable unit stress in case of ratios between 120 and 200. Different well established column formulas were plotted and the curve representing the unit stresses allowed by the "Code" was extended parallel to the direction of the mean of the other curves. The resulting curve was used to get safe allowable unit stresses for ratios beyond 120. SECTION AREAS FOR ECCENTRIC LOADING: It will be re- membered that Chapter II contains discussions on the strength of columns under concentric and eccentric loading. The term z y there defined as the coefficient of eccentricity when divided by the square of the radius of gyration about the axis for which the load is eccentric gives a percentage factor for the area necessary to take care of the bending moment due to this eccentricity. NOTE: A little care in the arrangement of beams and girders will of- ten eliminate the eccentricity of loading on columns. There are, however, many cases where it cannot be avoided. For such cases the "Code" (N. Y. C.) provides that: Any column eccentrically loaded shall have the stresses caused by such eccentricity computed, and the combined stresses resulting from such eccen- tricity at any part of the column, added to all other stresses at that part shall in no case exceed the working stresses stated in the "Code." The ec- centric load of a column shall be considered to be distributed equally over the entire area of that column at the next point below at which the column is securely braced laterally in the direction of the eccentricity. ? STRUCTURAL DESIGNERS' HANDBOOK. It will be apparent that these provisions have been adhered to in the treatment of eccentric loads herewith presented. DIAGRAM NO. 34 gives the aforementioned percentage of area necessary to take care of eccentricity of loading. In this dia- gram abscissas represent the radius of gyration, while ordinates represent coefficient of eccentricity. Curves on the diagram rep- resent the percentage of area to be added to a cross section for the eccentricity of the loading on the column. An example will best il- lustrate the use of Diagrams Nos. 33 and 34. Example: A column 10 ft. long has a load of 140 tons, 15 tons of which is located 5 ins. from each neutral axis. The column section is built up with plates and angles in the form of an H. The assumed dimension back to back of angles is 10 ins., and 8 ins. is the dimension the other way. Solution: The center of gravity of the combined concentric and ec- centric load is located 0.535 in. from both principal axis. The coefficient of eccentricity in the direction parallel to the web is 0.535 times 5 or 2.68; in the direction perpendicular to the web it is 0.535 times 4 or 2.14. For the direction parallel to the web in which case the radius is 4 ins., the diagram No. 33 gives the area of metal required for this eccentricity as 17% of what would be required for the same load concentrically located. For the direc- tion perpendicular to the web in which case the radius is 2 ins., it is 53% of that same area. The sum of these three areas which go to make up the material of the cross section can be found in two ways from these diagrams. First: The area required for a concentric load of 140 tons may be found on Diagram No. 33 and the foregoing 70% (17 + 53) can then be added to it, giving the total area of cross section. Second: The load may be increased to what would be an equivalent concentric load 170% of 140 or 238 tons. Evidently the area may then be found directly on Diagram No. 33. This same diagram also gives the equiv- alent weight per lineal foot of the section. For a concentric load of 140 tons and a ratio of slenderness of 60 this weight is 81.5 Ibs. and for a load of 238 tons, the weight of the cross section is about 139 Ibs. According to this diagram 139 Ibs. per lin. ft. represents 41 sq. ins. of cross section. This would require approximately 1^4 in. thickness of metal for the assumed dimensions of the section, thus, it would be advisable to in- crease the dimensions until the thickness is much reduced. The areas and weights, of structural shapes used for column sections, are given in the next chapter. STEEL COLUMNS. 79 Example. The radius of gyration of a round column about %- metal is 3.25 for 10 ins. diameter. inch So STRUCTURAL DESIGNERS' HANDBOOK. Diagram No. 3J For giving the radius of gyration of the most common forms of built-up column sections. DIAMETER OF SECTION IN INCHES 6 7 8 9 10 11 12 13 14 15 STEEL COLUMNS. 81 Diagram No. 32 For giving the ratio of slenderness of a column. UNSUPPORTED LENGTH IN FEET co UJ cc. UJ Q UJ _J co u_ O O i UNSUPPORTED LENGTH IN FEET Example. A column 12 ft. long with a radius of gyration of 2.6 ratio of slenderness of 55. has a Diagram No. 33 For giving the safe loads on steel columns as called for by the New York Building Code for ratios of slenderness up to 120, and as recommended by the author for ratios between 120 and 200. RATIO OF SLENDERNESS Example. A column having a ratio of slenderness of 70 and a load of 54 tons requires 9.8 sq. ins. in its cross-section (or 33.3 Ibs. per lin. foot). (82) STEEL COLUMNS. 83 Diagram No* 34 For Eccentric Loading on Columns. This diagram gives the percentage of material necessary to add to the cross-section of a column for any eccentricity of the centre of gravity of its load with reference to the axial planes through its neutral axis. RADIUS OF GYRATION IN INCHES RADIUS OF GYRATION IN INCHES Note. The material in a column-section with two principal axes of sym- metryas in Figs. 3 to 23 may be said to perform three functions when the load on the column is eccentric: Part cares for the load as purely concentric, another part cares for the load as eccentric on the axis where the radius of gyration is a minimum, and the remainder on the axis where the radius is a maximum. STRUCTURAL DESIGNERS' HANDBOOK. CHAPTER VIII. TABLES. PROPERTIES OF SINGLE AND BUILT-UP STEEL SHAPES OF I-BEAMS, CHANNELS, ANGLES, TEES, ZEES, AND FLATS FOR USE IN COLUMNS, BEAMS AND TRUSSES. EXPLANATIONS: The tables of properties in this chapter while intended to cover the whole range of needs in structural de- sign, are grouped with the treatment of column design for two reasons; first, the subject of beam design is so thoroughly covered t>y independent diagram treatment, that only occasional use will be made of beam properties; second, the subject of column design, being impossible of independent diagram treatment because of the complex forms of built sections, makes necessary a combination of diagrams and tables. In the first case the use of independent dia- grams was made possible by the simplicity of form of the standard section, the I-beam (occasional use of channels, angles and tees excepted), being used almost exclusively. On the other hand, col- umns have only to a very small extent become standardized as re- gards section ; practically all steel columns are built sections, i e. are built up of elementary structural shapes, and their proportions and sizes vary widely. This is one of the conditions that compli- cates column design and makes it impossible of independent dia- gram treatment. The properties of the standard sections given in the tables are for the single shapes, for a pair of shapes, and also, in the case of angles and zees, for four shapes combined. In the latter case as well as in the cases of pairs of I-beams or pairs of channels these combined shapes are supposed to be latticed* together. The aforementioned standard sections,f adopted by the Amer- ican Association of Steel Manufacturers, as represented by Car- negie, Cambria, Jones and Laughlins and Phoenix are given in these tables; also distinctive and well marked differences in the Passaic and Pencoyd standards have been taken into account. ' *When plates are used instead of lattice bars, the radius of gyration should be taken from the diagrams in the preceding chapter and not from these tables, except when special tables are appended with these values which is the case for channel and zee-bar columns. These give correct values for radius of gyration about both axes for cover and web plates respectively. fSee note in Chapter III. TABLES. 85 NOTE: The first mentioned group of rolling mills do not in every case roll the full list given in the tables, but differences of this kind have not been noted. DIMENSIONS AND WEIGHTS: The dimensions and weights per lineal foot given for all the sections in the tables are fully ex- plained under their respective heads. However, it should be men- tioned that the ''Practical Detailing Dimensions" given in most of these Tables are not to be considered as arbitrary values they represent mean values. The gage given for the I-beam is the dis- tance between the two lines of rivets on the flanges. Thus, the dis- tance from the center line of the web to the rivet line in the flange on either side is equal to one-half of the gage given in the table. The gage for channels is given from their back. Gages for a sin- gle and double line of rivets on the legs of angles are given in the table of angles with even legs. The first dimension in each case is given for the gage of a single line of rivets and directly below it is given the gages for a double line of rivets for the same leg. As stated in the foregoing the range of application of these tables includes : beams and columns used in buildings ; tension and compression members used in trusses ; and flanges used in plate girders. These several uses will now be considered under their separate heads. BEAMS. The more generally used beam property is the section-mo- ment. It is given in all of the following tables for the two principle axes of each section in foot-pounds for angles and tees and foot- tons for all other shapes. This is the safe resisting property of a beam which opposes the bending moment of the external forces acting upon it ; and the Formulas Nos. I to 14, given in Chapter I arc for the purpose of illustrating the application of this section- moment in the design of beams or girders. The allowable values for the web of I-beams in compression and for the end reactions on beams have been fully described in Chapters I and V and the use of these values will be readily un- derstood without further explanations. WHEN IT is DESIRED TO USE PLATES ON THE TOP AND BOTTOM FLANGES OF AN I-BEAM or a pair of I-beams, or on the top and bottom flanges of a pair of channels, the following method may be employed to determine the area of the plates : From the external bending moment deduct 75% of the section-moment 86 STRUCTURAL DESIGNERS' HANDBOOK, of the beam or beams (given in the tables) and divide this by the product of the depth (c. to c. of plates in feet) and 7.2. (Formula 22) This quotient gives the net area of the plates on each flange. Diagram No. 33 may be used to find an equivalent weight per lineal foot for such an area of metal and Table No. 25 will give the several possible dimensions for the width and thickness of these plates. TRUSSES AND PLATE GIRDERS. The theory and practice of the design of trusses and plate girders (including the subject of rivet spacing) is beyond the scope of the present book and in the following a general knowledge of the subject, on the part of the reader, is assumed. IN THE DESIGN OF TRUSSES, pure compression and pure tension usually prevail in both the web and chord members. How- ever, when loads occur on the top and bottom chords, flexure stresses are thereby added to these direct stresses. For the design of members in pure tension and pure compression, no further ex- planations will be required than have already been given ; while for cases of combined stresses of flexure and tension or flexure and compression the diagram for eccentric loading may be utilized in a very simple manner : For instance, the eccentric load P (see Fig. i) considered in the subject of column design now becomes a transverse instead of an axial load on the truss member, and this transverse load produces a similar bending moment on the member. This bending moment due to transverse loading is found by introducing a new value for s, which is obtained as follows : Suppose, a and b are the respective distances of the load from the two ends of the member, then, z ab equals for any position of the load on the truss member. a + b Therefore, the percentage of area of the cross section necessary to take care of the flexure stress (either tension or compression) can be found by the use of Diagram No. 34, after having determined upon the value of the radius of gyration of the proposed section, either from the following tables or from Diagram Nos. 30 or 31. ab The coefficient of eccentricity being y instead of z y as in a + b TABLES. 87 the case of columns where y is the distance from the neutral axis p to the extreme fiber, as before. Thus A = (23). When the load P is in the middle of the beam and both ends are fixed, the area will be one-half that given by the above formula. The use of the diagrams and tables for tension and compres- sion members has already been described in the preceding chapter on steel column design. NOTE: Deductions for rivet holes in tension 'members may be made as follows: The area of metal required for a fy-in. rivet is 0.88 sq. ins. for every inch thickness of metal this is equivalent to a reduction. of 3 Ibs, pec lin. ft. in the weight of the section. Thus, if the metal is ^2 in. thick, iV? Ibs. per lin. ft. should be added to the net section. Accurate values for various thicknesses of metal from l /\, in. to 2 ins. are given in Table No. 25 for l / 2 in. and ^ in- rivets. PLATE GIRDERS: A general discussion of the subject of plate girder design is beyond the scope of this book. The tables given herewith, however, lend themselves readily to the design of an important element of plate girders the flanges. The area of the flange is found by the use of the following formula when the value of the section-moment in the web is neglected : Mb Fa = 0.143 (24a) * . ' h where Fa = the net area of the tension flange in square inches, Mb = the external bending moment in foot-tons, and h = the distance, in feet, between centers of gravity of flanges. Now, as the weight per lineal foot of pairs of angles is given in the tables in preference to the area of the sections, this formula becomes Mb Fw - 0.485 , (24) h where Fw = the weight in pounds per lineal foot of the tension flange, and the other values same as foregoing. It is customary to make the compression flange of a plate girder the same as the tension flange. 88 STRUCTURAL DESIGNERS' HANDBOOK. COLUMNS MADE OF BUILT STEEL SHAPES. In Figs. 3 to 18 herewith, are exhibited a number of built steel column sections. They do not represent every possible variation in arrangement of material ; as a matter of fact it is not desirable to more than indicate the general methods of distributing the mate- rial in a cross section, because the system presented in this book Pig. 3. Fig. 4. HH Fig. e. Fig. 6. for the design of columns admits of any arrangement or distribu- tion of the material that the ingenuity of the designer may dictate. This fact will be better understood from a description of the various types of column sections* : COMBINATIONS WITH I-BEAMS : Figs. 3 to 6 refer to the use of an I-beam to combine channels, I-beams or plates, etc. For a single I-beam, and a pair of latticed I-beams, the tables given in this chapter are complete. When an I-beam is used to connect a pair of I-beams or a pair of channels, as in Figs. 5 and 6, special tables may be easily made by the designer. The only values re- quired in these special tables being the sum of the weights of the combined sections, and the dimensions with which to determine the radii of gyration from Diagrams Nos. 30 and 31. CHANNEL COLUMNS : This type of column, Figs. 7, 8, and 9, aaax...... Mb ^j Fig. 7. Fig. 8. Fig. 0. is the most popular of the closed sections. For this reason a special table has been appended to the general table of properties of channels. The properties of a pair of latticed channels are given in the general table. When plates are added to the webs of the channels as in Fig. 9 special tables may be made. *No attempt is made to enter into a discussion of the relative merits of column sections. This aspect of the subject is taken up in books like Frie- tag's "Architectural Engineering" and books by Birkmire. TABLES. 89 PLATE AND ANGLE COLUMNS: Figs. 10 to 16 illustrate in a small way the various combinations that may be made by the use of angles and plates. The type of column indicated by Figs. 10 and ii is most popular with advocates of open sections. For this reason a special table is also appended to the tables of properties ixwn Fig. 10. Fig. 11. Fig. 12. Fig. 13. Fig. 14. Fig. 15. Fig. 16. of angles. Evidently other special tables can be made to cover an endless variety of combinations of these two sections. ZEE-BAR COLUMNS: Figs. 17 and 18 illustrate two of the more common forms of this type of column. Table No. 24 though small gives quite a variety of information on these column sections. For instance : Two methods of design are considered, one giving weight of section for varying widths of web and the other for a constant width of web. This latter is a favorite idea with some designers, giving as it does, one important constant dimension for H Fig. 17. Fig. 18. the column. Other special tables can also be made for any other desired arrangement of material. MISCELLANEOUS SECTIONS: The several tables on I-beams, channels, tees, and angles may evidently be used for the application of any single shape to strut design. STEEL I=BEAMS For Beams, Girders, Columns, or Truss Members TABLE 17 2 3 4 5 6 7 8 I Weight Per Foot Dimensions 1 1 " Neutral Axis Perpendicular to Web i i I "o 3 a 42 i.i 2-5 11.9 19.8 X to 43 0.8 1.8 23 i 43-5 24/ 44 I.O 2.8 20.7 38.0 45 0.8 2.O 6-4 29.6 58.0 7A STEEL I=BEAMS For Beams, Girders, Columns, or Truss Members TABLE 17 I 2 3 4 5 6 7 8 i I Plr^ot Dimensions I d Neutral Axis .2 B Perpendicular to is Web *& * * ^ 0= i_ "d B - |l o| ,0d 11 11 11 a t> c. PQ r flB P^t^ 3 ^j O c3 ^ g^^Tj ! ' 1 W H BO ccS Inches Lbs. Lbs. Inches Inches Square Inches Inches i Tons 46 d IO 25 50 4-66 o 31 7.35 4.1 16.3 47 b 27 54 4-81 0.37 7.93 4.0 17-0 48 d 30 60 4.81 0.46 8.82 3.9 17.9 49 b 33 66 5.00 0.37 9.70 4.1 21.5 50 d 35 7 4-95 0-60 10.29 i 3-8 19-5 51 d 40 80 5.10 0.75 ii 75 3.7 21.2 52 d 12 3L5 63 5.00 0.35 9-26 4.8 24.0 53 d 54 d 35 70 5-9 0.44 10.29 j 4-7 25.4 40 80 5.25 0.46 11.75 4.8 29.9 55 d 45 90 5-37: 0.58 13.22 4.6 31.7 56 d 5 loo 5.49 0.70 14.69 4-5 33-7 57 d 55 no 5.61 0.82 16.16 4-4 35 7 58 59 be be 60 65 120 6 12 130 6.25 0^88 17-63 19.10 4.6 4-5 41.7 43-7 60 d 15 42 84 5.50 0.41 12.34 6.0 39-3 61 d 45 9 5 55 0.46 13 22 5-9 405 62 d 50 loo 5 65 o 56 14.69 5-7 43 o i 63 64 d & no 5-75 120 6.00 066 0.59 16.16 17.63 5-6 5-9 454 54-1 65 d 65 130 6.10 0.69 19.10 \ 5.8 56.5 66 d 70 140 | 6.19 j o 78 I 20.57 5.7 59 67 d 75 150 629 0.88 22.04 5.6 61.4 68 d 80 lOo 6.40 0.81 23.51 5-8 70.7 69 Came gie 85 170 6.48 0.89 24.98 5.7 72 7 70 11 90 180 658 099 2645 5.6 75 i ',' 95 190 6 68 1.09 27 92 56 77.6 72 " IOO 200 6.78 1.19 29.39 5.5 800 73 d 18 55 no 6.00 0.46 .6.10 7.1 58.9 74 d 60 I2O 6.10 o 56 17.63 6*9 62 4 75 d 65 130 6 18 0.64 19.10 6.8 653 76 d 70 140 6.26 0.72 2057 6.7 68.2 77 be 75 15 6.16 0.66 22.O4 70 808 78 be 80 160 6.38 o 69 23 5 1 6.9 83 8 79 c 85 170 7.00 0.74 2498 6.8 852 80 c 90 180 7.08 0.82 2645 6-7 88.0 81 d 20 65 130 6.25 0.50 19.10 7-8 78.0 82 d 70 140 6-33 0.58 20.57 7-7 813 83 d 75 150 6 40 o 65 22.04 76 84.6 84 d 80 IOO 7.00 0.60 23.51 7-9 97-8 85 d 85 170 706 0.66 2498 7.8 100. 6 86 d 90 1 80 7.14 o 74 26.45 7-7 103.9 87 ac 95 190 7.21 0.81 27.92 7.6 107.1 88 ac IOO 200 7.28 0.88 29-39 7-5 110.4 89 ac 24 80 160 7.OO 0.50 23.51 9-5 116.0 90 ac 85 170 7.07 0-57 24.98 9-3 120.5 ac 9 180 7-13 0.63 26.45 9-2 124.4 92 ac 95 190 7.19 0.69 27.92 9.1 128.3 93 ac IOO 200 7-25 0-75 29-39 9.0 132.2 a denotes beams rolled by Carnegie, Cambria, Jones & L., and Phrenix; Pencoyd ; d by all mills (includes a, b, c). 6 by Passaic; c by STEEL I=BE.AMS Continued For Beams, Girders, Columns, or Truss Members TABLE 17 9 10 II 12 13 14 15 16 Neutral Axis Co- i incident with Web clSl Is IJ Practical Detailing ^'3:3 o 1 W ff A Dimensions 3ra fl A " <->" ~r 03 . , ,# Flange a a -S -SSs o^ .2^ - 1 1 11 11*1 ?| -2| "SgdS agj Gage of ?S 11 5s 2* #% \ $%$* *.s2 Rivet | {Jo ocS s^ao ^ ! e*Ki i g pt s 1 Inches ?oot- ons Inches j Tons Tons Inches Inches Inches 46 I.O 2.O 7.9 12. l8.6 ' 47 I.O 2.1 16.4 24.6 48 0.9 2.1 20.7 32.4 2 /^ 49 i.i 3- 1 16.4 24.6 X to 50 0.9 2.3 27.0 45.2 3 5' 0.9 2-5 7-i 33-8 58-8 7/2 52 i.o 2.5 9.5 15.6 20.0 53 I - 2.8 23.8 28.5 54 i-i 3.5 9.3 | 24.9 30.0 55 i.i 3-7 3i-3 4i.o X 234 56 i 3.9 | 37.8 52.0 to to 57 .0 4.1 8.7 44.3 63.0 8-^ K 3^ 58 2 5-6 40.5 56.5 59 .2 6.1 47-5 68.5 60 ., 3-5 11.7 19.1 22.3 \ 61 .1 3.6 i 25.5 26.6 | 3 62 .0 3-8 37-2 36.0 to 63 64 .0 .2 4.0 ! ii. i 44.6 45.0 5.8 11.5 39.9 38.8 i\% \ 3/2 65 .2 6.0 46.6 47.9 X 3/4 66 .2 6.2 52.7 56.2 to to 67 .2 6.5 n.o | 59.4 65.5 7/z 4 68 .3 8.7 11.3 54.7 59 o 69 .3 9.0 60. i 66.0 70 .3 9-3 66.9 75.0 I to 7 1 -3 9-6 73-6 84.5 1 4 72 -3 10.0 10.8 79.7 93.2 io3^ 73 .2 4.7 14-0 22.4 23.4 74 -I 4-9 ! 3 6 - 2 33- 75 .1 5.1 49-4 40-0 76 .1 5.2 13.2 58.3 47.6 14% ^ ' 3/4 77 -3 8.1 46.2 46.0 to i to 78 79 3 3 8.2 8.4 56.7 53-2 59-9 48.5 7/8 1 4 80 .3 8-7 66.4 56.0 81 .2 5.9 15.5 25-0 25.0 1 82 .2 6.1 39-9 32.5 83 .2 84 .4 6-3 8.7 15-0 50-5 38.7 15-5 41 8 34-2 3/2 85 -4 8.9 51-7 39-5 H to 86 .4 i 9.1 64.0 ! 47.3 4^( 87 -3 9-4 72.9 53-5 88 .3 9.6 14.8 79.2 60.0 i 16 89 .4 8.2 l8.7 20.4 19.2 90 .3 8.3 30.9 26.O H 3^ 9i -3 8.5 42.3 32.0 to to 92 .3 8.7 54-5 37-5 I 4^2 93 -3 8.9 17.8 66.3 43.2 20^/2 STEEL CHANNELS For Beams. Girders, Columns, or Truss Members TABLE 18 I 2 3 4 5 6 7 8 Weight per foot Dimensions "3 & a Neutral axis Perpendicular to Web a -=> en C- < 1 a 03 9 a is! CO 1 t A 1 .0 M ^ 1* ff) g a rl 1 1 1 fl* o 9 cd ^ & QQ o c ^ t. o> g 6 6 P EH co J^oo^ & M o cJ ^ c3 .H s P I EH 1 f 5 i 1 i Inches Lbs. Lbs. Inches Inches Square Inches Inches Foot- Tons I ac 3 4 8 .41 0.17 17 1.2 0.7 2 ac 5 10 50 26 47 I.I 0.8 3 ac 6 12 .60 36 76 I.I 0.9 4 b 4 5 IO 59 0.17 47 1.6 1.2 5 ac 5-25 10.5 .58 0.18 54 1.6 i-3 6 b 6 12 .66 0.24 .76 i. 5 7 ac 6.25 12-5 65 0.25 84 1.5 1.4 8 ac 7-25 H-5 73 -33 2.13 I.e z -5 9 b 8 16 .86 0.27 2-35 1.5 1.8 10 b 10 20 .01 0.42 2-94 J -5 2.1 ii b 5 6 12 .66 0.18 1.76 1.9 i-7 12 ac 6.5 13 .75 0.19 1.91 1.9 2.0 13 b 8 16 .78 0.30 2-35 1.8 2.1 14 d 9 18 .89 0-33 2.64 1.8 2-3 15 b 10 20 97 0.31 2.94 1-9 2-7 16 ac "5 23 2.04 048 3.38 2.8 17 b 12 24 2.09 o,43 3-5 2 1.8 3-i 18 d 6 8 16 1.92 0.20 2.35 2.3 2.8 19 1. 9 18 1-99 0.25 2.64 2-3 3 20 b 10 20 2 04 o 30 2 94 2.2 32 21 i'C 10.5 21 2.04 0.32 308 2.2 3-3 22 b 12 24 2.19 0.28 3-52 2-3 23 d 13 26 2.16 0.44 3-82 2.1 3-9 24 b 15 30 2-34 0-43 4.41 2.2 4-7 25 ac 15.5 31 2.28 0.56 4-5 6 2.1 4-3 26 b 17 34 2.41 0.38 5.00 2-3 5-6 27 b 18 36 2.46 0-43 5-29 2-3 5-8 28 b 20 40 2.56 0-53 5.88 2.2 6.2 29 b 7 9 18 2.00 O.2O 2.64 2-7 3-6 30 ac 9-75 19-5 2.09 0.21 2.86 2.7 4.0 3 1 b 10 20 2.04 O.24 2-94 2.6 3.8 22 b 12 24 2.13 -33 3-5 2 2.6 4.3 33 ac 12.25 24-5 2.20 0.32 3-6o 2.6 4-6 34 b 13 26 2.22 0.28 3.82 2-7 5-2 35 ac 14-75 29.5 2.30 0.42 4-34 2-5 5-2 36 b 15 2.30 0.36 4.41 2.6 5-6 37 b 17 34 2-39 0.45 5.00 2.5 6.1 38 ac 17.25 34-5 2.41 0-53 5.07 2.4 5-7 39 ac 19-75 39-5 2.51 0.63 5.80 2.4 6-3 a denotes beams rolled by Carnegie, Cambria, Jones & L., and Phoenix; Pencoyd ; d by all mills (includes a, b, c). by Passaic; c by STEEL CHANNELS Continued For Beams, Girders, Columns, or Truss Members TABLE 18 9 10 II 12 13 14 15 16 i? Neutral Axis Parallel with Web Practical Detailing Dimensions d Flange Lattice Bars | adius of Gyration Section-Moment 8 tons per D " Max. fibre stress istance of Centre of Gravity from Back o Channel Distance B. to B. required to make Radii of Gyration equal lear Distance Betwee Fillets on Web [aximum Diam- eter of Rivet age of Rivet Lines T3 i *0 SoSId flip Mil!* Itlilla CO Flanges Out Flanges In ft M fi ! O m [nches Foot- Inches Inches Inches [nches Inches Inches Ft. and Ins. W. Tons l 0.41 0.14 0.44 1-3 2 0.41 0.16 0.44 y% Y& 3 0.42 0.18 0.46 i.i 1% 4 o.45 0.17 0.46 2.0 % 5 0.45 0.19 0.46 6 0.46 0.45 Y% 7 0.45 0.21 0.46 to 8 0.46 0.2 3 0.46 y* 9 0-55 0.36 0-59 10 0-55 0.42 0.60 1.8 2% J>8 TI 0.47 O.2I 0.45 2.8 4-6 H 12 0.50 0.25 0.49 '3 0.46 0.44 y* H 0.49 0.30 0.48 15 0.56 0-57 16 0.49 0.36 0.51 17 0.56 0-49 0.58 2.3 4-6 3'/s IT* 18 0.54 0.33 0.52 3.5 5.6 y z ! \y z " x #" 19 0-55 051 C. toC: 20 0-54 0.50 Mx.o' ii)4" 21 o-53 0.38 0.50 Mn.o'-6^" 22 0.63 O.6O 0.65 23 0-53 0-43 0.52 24 0.63 0.65 25 0-53 0.49 0-55 4^8 26 0.70 0.98 0.78 y* 27 0.71 0-79 to 28 0.72 I. II 0.80 2.6 5-8 # *H 2 9 0.56 0-37 0.51 4.3 6-3 ^ i l A i^" x X" ' 3 0.59 0.42 o.55 C. toC: o-55 0.50 i MX. I -iW 32 0.54 0.49 Mn. 0-7^" 33 0.58 0.47 0-53 34 0.63 0.63 0.62 35 0-57 0-53 0-54 36 0.63 0.62 37 0.63 0.74 0.62 H 38 0.56 0.58 0.56 tO l l / 2 39 0.56 0.64 0.58 3-5 6.0 5# * STEEL CHANNELS For Beams. Girders, Columns, or Truss Members TABLE 18 , 3 4 5 6 7 8 Weight Dime nsions a a Neutral axis Perpendicular to Web ; o 1 d- 8 1 "5 +3 S ! -'- i J9 J d Q *H o * * A 9 31 ^ ^ X ^ o a 3 T3 M O O 1 rr ^ 1 B *o I A O 1 1 03 "o | II" 1-3 a 1 *S a oJ o *e3 | w H K ^ < tf M I Inches Lbs. Lbs. Inches Inches Square Inches Inches Foot- Tons 40 b 8 IO 20 2.08 0.20 2-94 3-i 4-7 b ii 22 2.12 0.24 3-23 3.0 4.9 42 ac 11.25 22.5 2.26 0.22 3-30 3.1 i 5-4 43 b 12 24 2-15 0.27 3-52 3- 5-3 44 b 13 26 2.22 0.25 3.82 5-9 45 ac 13-75 27-5 2-35 0.31 4.04 3-o 6.0 46 b 15 30 2.29 0.32 4.41 3- 6.4 47 ac 16.25 32.5 2-44 0.40 4-77 2-9 6-7 48 b 17 34 . 2-37 0.40 5.00 2.9 7.0 49 ac 18-75 37-5 2-53 0.49 5-51 2.8 7-3 50 ac 21.25 42.5 2.62 058 6.24 2.8 7-9 5I b 9 13 26 2.36 0.23 3.82 3-5 6-7 52 ac 13.25 26.5 2.43 0.23 3.89 3-5 7.0 53 b 14 28 2-39 0.26 4. 1 1 3-4 7.0 54 d 15 3 2.49 0.29 4-41 3-4 7-5 55 b 16 3 2 2.56 o. 28 4. 76 3-5 8.4 56 b 18 36 2.63 o-35 5-29 3-4 9.0 57 ac 20 40 2.65 0-45 5.88 3-2 9.0 58 b 21 42 2-73 0.45 6.17 3-3 9.9 59 ac 25 50 2.82 0.62 7-35 34 10.5 60 d IO 15 30 2.60 0.24 4.4" 3.9 8.9 61 b 17 34 2.64 0.29 5.00 3.8 9-5 62 b 18 36 2.67 0.32 5-29 3-7 9.8 63 d 20 40 2-74 0.38 5-88 3.7 10.5 64 d 25 5 2.89 -53 7-35 3-5 12. 1 65 d 30 60 3.04 0.68 8.81 3.4 13-7 66 ac 35 70 3-i8 0.82 10.29 3-4 15-4 67 68 b ac 12 20 20.5 40 2.88 2.94 0.28 0.28 5.88 6. 02 4.6 4.6 13-8 14-3 69 b 23 46 2-95 0.35 6.76 4-5 15.0 70 d 25 50 3-05 0-39 7-35 4-4 16.0 71 b 27 54 3-13 0.38 7-93 4-5 17.8 72 d 30 60 0.51 8.81 4-3 17.9 73 b 33 66 3^8 0-53 9-7P 4-3 20.2 74 d 35 7o 3-30 0.64 10.29 4-2 19.9 75 ac 40 80 3.42 0.76 11.75 4-1 21.9 1 76 d 15 33 66 3.40 0.40 9.70 i 5.6 2 7 .8 77 d 35 70 3-43 0.43 10.29 5-6 28.5 78 d 40 80 3-52 0.52 11-75 5-4 3.9 79 d 45 90 3-62 0.62 13.22 5.3 33-3 80 81 d ac 50 55 IOO no 3-72 3-82 0.72 0.82 14.69 16.16 5-2 5-2 35-8 38.3 a denotes beams rolled by Carnegie, Cambria, Jones & L., an*t Phoenix; & by Passaic; c by Pencoyd; d by all mills (includes a, b, c). STEEL CHANNELS Continued For Beams. Girders, Columns, or Truss Members TABLE 18 9 10 ii 12 13 14 15 16 i? Neutral Axis Parallel with Web Practical Detailing Dimensions 75 0.75 .64 0.72 6.6 9.9 9i\ % 76 0.91 2. II 0.79 9-5 12.7 * 1 A 2 /4" X "5/g" 77 0.91 2 - I 5 0-79 C. to C': 78 0.89 2.29 0.78 IT MX. 2'-2}4" 79 0.88 2.42 0.79 to Mn. i'-3X" 80 0.87 2-57 0.80 H 2)4 81 0.87 2.72 0.82 8-5 11.7 ii^ PLATE, AND CHANNEL COLUMNS (Supplement to Table 18) TABLE 19 2 3 4 5 6 I 2 3 4 5 6" CHANNELS 7" CHANNELS 8" Plates 9" Plates 9" Plates 11" Plates Weight of each Channel Thickness of Plates 1 Least Badius of Gyration Weight of Column Kadius of Gyration equal on both Axes Weight of each Channel Thickness of Plates Weight of Column Least Badius of Gyration il Badius of Gyration equal on both Axes Lbs. per ft. Inches Lbs. per ft. [nche: Lbs. per ft. Inches Lbs. per ft. Inches Lbs. per ft Inches Lbs. per ft. Inches 3 * 29.6 2-3 2-7 9-75 X 34-8 2.6 38.2 3-2 rV 33- 35-1 38.6 42.9 y* 36.4 39-0 y* 42.5 47-6 yV 39-8 42.8 yV 46.3 52.2 ^ 43-2 46.6 1/ 2 50.1 56.9 A 46.6 50-4 & 53-9 615 # 50.0 2-3 54-3 2.7 57-8 2.6 66.3 3-3 10.5 34 6 2-3 36.3 2-7 12.25 K 39-8 2-5 43-2 3-i 38.0 40.1 A 43-6 47-9 y$> 41.4 44.0 y?> 47-5 52.6 7 44.8 47-8 A 57-2 K 48.2 51.6 % 55-i 61.9 51.6 55-4 & 58.9 66.5 s 55- 2-3 59-3 2.6 4 62.8 2.6 71-3 3-3 13 X 39-6 2.2 41-3 2-5 14-75 # 44-8 2-5 48.2 3.0 yV 43- TZ 48.6 52.9 y& 46.4 49.0 y& 52.5 57-6 yV 49-8 52.8 A 56.3 62.2 ^ S3- 2 56.6 H 60. i 66.9 y 9 F 56.6 60.4 y 9 g" 63-9 71-5 > 60.0 2.2 64.4 2.6 H 67.8 2-5 76.3 3-3 15.5 X 44-6 2. I 46.3 2.5 17.25 tf 49.8 2.4 53-2 2.9 TS 48.0 50.1 A 53-6 57-9 y% 5^4 54-0 ^8 57-5 62.6 7 TTT 54*8 57-8 A 61.3 67.2 58.2 61.6 65.1 71.9 y 9 F 61.6 65-4 68.9 76-5 # 65.0 2.2 69-3 2.6 H 72.8 2-5 8i-3 3-2 19.75 ^ 54-8 2.4 58.2 2.9 5 58.6 62.9 y?> 62.5 67.6 T 7 (T 66.3 72.2 i^ 70.1 76.9 T 9 tT 73-9 8i.5 N 77-8 2.4 86.3 3-2 PLATE- AND CHANNEL COLUMNS (Continued) (Supplement to Table 18) TABLE 19 I 2 3 4 5 6 I 2 3 4 5 6 8" CHANNELS 9" CHANNELS 10" Plates 12" Plates 11" Plates 13" Plates Weight of each Channel Thickness of Plates 11 Ss Least Badius of Gyration Weight of Column ill Weight of each Channel ll i o fl |1 Least Badius of Gyration "o a S| |||l Lbs. per ft. Inches Lbs. per ft. Inche; Lbs. per ft. Inches Lbs. per ft. [nchee Lbs. per ft Inches Lbs. per ft. Inches 11.25 * 39.5 3-0 42.9 3.6 13.25 ,/ 45-2 3.3 48.6 4-1 TK 43-7 48.0 A 49-9 54.i y* 48.0 53.1 3/8 54-6 59.7 T^B 52.3 58.2 A 59-2 65.2 X 56.5 63.3 63.9 70.7 TS 60.8 68.4 9 68.5 76.2 H 65.0 2.9 73-5 3-7 H 73-3 3-3 81.7 4.0 13.75 If 44-5 2.9 47-9 3-5 15 # " 48.7 3-3 52-1 4.0 TS 48.7 53-o 53-4 57-6 |4 53-0 58.1 r 58.1 63.2 & 57-3 61.5 63.2 68.3 $ 62.7 67.4 68.7 74-2 T 9 1 65.8 73-4 T 9 ft 72.0 79-7 H 70.0 2-9 78.5 3-6 H 76.8 3-3 85.2 4.0 16.25 3S/ 49-5 3-0 52.9 3-4 20 x 58.7 3-2 62.1 3-8 T*V 53-7 58.0 T% 63-4 67.6 y% 58.0 63.1 y& 68.1 73-2 T 7 ir 62.3 68.2 A 72.7 78.7 K 66.5 73-3 y z 77-4 84.2 T 9 ff 70.8 78.4 T 9 ? 82.0 89.7 > 75- 3. 83.5 3-6 H 86.8 3-2 95.2 3-9 18.75 # 54-5 2.8 57-9 3.3 25 X 68.7 3-i 72.1 3-6 T*V 58.7 63.0 j-V 73-4 77.6 H 63.0 68.1 N 78.1 83-2 T 7 1T 67.3 73-2 TT 82.7 88.7 8 71-5 78.3 87.4 94-2 T 9 ff 75-8 83-4 y 9 T 92.0 99-7 H 80.0 2.8 88.5 3.6 M' 96.8 3-i 105.2 3-9 21.25 tf 59-5 2.7 62.9 3-3 T 5 F 63-7 68.0 fi 68.0 73- I A 72.3 78.2 y z 76.5 83-3 T 9 ?r 80.8 88.4 j 85.0 2.8 93-5 3-6 PLATE. AND CHANNEL COLUMNS (Continued) (Supplement to Table 18) TABLE 19 I 2 3 4 5 I 6 i 2 3 4 5 6 10" CHANNELS 12" CHANNELS 12" Plates 15" Plates 14" Plates 16" Plates Weight of each Channel Thickness of Plates Od ga 1 P Least Badius of Gyration "Sd 11 P itadius ul Gyration equal on both Axes 43 '-'3 III "^$2 og Thickness of Plates "oc II p Least Badius of Gyration Ofl 11 P 3fld$ 33-2 OX fill $$, Lbs. per ft. [nches Lbs. per ft. Inches Lbs. per ft. Inches Lbs. per ft. Inches Lbs. per ft Inches Lbs. per ft. Inches 15 X 5-4 3-6 55-5 45 20.5 X 64.8 4-4 68.2 5- 2 A 55-5 61.9 & 70.8 75-0 #' 60.6 68 T> y* 76.7 81.8 65.7 74-6 A 82.7 88.6 K 708 81.0 ^ 88.6 95-4 A 75-9 87.4 & 94.6 102.2 & 81.0 3-5 938 4.6 H 100.5 4-3 lOQ.O 5- 20 X 60.4 3-5 65-5 4-3 25 % 738 4-4 77-2 5- 1 A 65.5 71.9 & 798 840 3 A 70.6 783 H 85-7 90.8 7 Iff 75-7 846 TV 91.7 97.6 % 80.8 91.0 % 97.6 104.4 T 9 * 85-9 974 T 9 103.6 III. 2 rf 90.1 3-5 103.8 4.6 H 109.5 4-3 118.0 5-o 25 X 70.4 3-4 75-5 4-' 30 X 83.8 4-3 87.2 4-9 T\ 75-5 81.9 5 T7T 89.8 90.4 3 /8 80.6 88.3 H 95-7 100.8 A 85-7 94-6 i TH 101.7 107.6 K 90.8 IOI.O % 107.6 114.4 A 95-9 107.4 & 113.6 121. 2 N IOI.O 3-4 113.8 4.6 H "9-5 4-2 128.0 5- 30 % 80.4 3-3 85-5 4.0 35 X 938 4.2 97.2 4-8 T 6 ff 85.5 91.9 A 99-8 104.0 3 /8 90.6 98.3 X 105-7 1 10. 8 A 95-7 104.6 TW in. 7 117.6 3 100.8 III.O ^ 117.6 124.4 A 105.9 117.4 T 9 .T 123.6 131.2 H III.O 3-4 123.8 4-5 H 129.5 4.1 138.0 4-9 35 X 90.4 3-3 95-5 3-9 40 X 103.8 4.1 107.2 4-7 T 5 * 95-5 101.9 T B 109.8 114.0 x 100.6 108.3 3/8 "5-7 120.8 TV 105-7 114.6 TV 121.7 127.6 % 1 10. 8 121. K 127.6 134.4 & "5-9 127.4 A 133-6 141.2 % 121. 3-3 133-8 4-4 % 139-5 4-1 148.0 4-9 tl) J O 3 O^ & sexy uo I OQ 1 I . ri-vo oo O N ^- 1^ M ,CO co * LO 10 VO CO * rh too O t-. uo UO jo sni jo snippy; jo ^q jo 1C tvo-ri-t M (S CO 'Jj- 1O *VO OO O C7NO COW O M rl- 1C (101) STEE.L ANGLES (E,ven Legs) For Beams, Girders, Columns, or Truss Members TABLE 20 I 2 3 4 5 6 7 8 9 IO II 12 13 14 1 Weight per Foot "o NeutralAxis on Line 45 to Legs Neutral Axis Perpendicular to Leg o Gages # O 03 A ] TD - fcD OQ^ %i! Sw O CD tf-u 111 Radius of Gyration go is i O bo QQ QQ O a M a o o (J 31 h M O a if c . Iv rt .go 3it ^ Tl 53 III 1 a 1 I c $$ s M o3<3 |t 53 I 1 all Inches Ins. Lbs. Lbs. Lbs. Square Inches Ins. Ins. Ins. Ins. Ins. Foot- Lbs. In. Inches I XI y % 0.8 1.6 3-2 0.24 O.2O 0.42 0.30 0.31 0.62 4i 3/8 A A 1.2 2-3 4.7 0.34 58 X i-5 6.0 0.44 0.19 0.48 0-34 0.29 0.66 74 iX*iX 1 A 1.0 2.O 4-i 0.30 0.25 0.50 0-35 0.38 0.72 65 X X A i-5 3-o 5-9 0.43 94 X 1.9 3.8 7.6 0.56 121 A 2.4 4.7 9-3 0.68 0.23 0.60 0.42 0.36 0.77 145 I^XI^ # 1.2 2.5 4-9 o 36 0.30 o 60 0.42 0.46 0.83 93 # ft T 8 3 1.8 3.6 7-2. 0-53 138 X 2.4 4-7 94 0.69 178 2.9 5-7 11.4 0.84 216 H 3-4 6.7 13-4 099 0.29 0.72 0.51 0.44 0.88 253 iX XI X A 2.1 4-2 8.4 0.62 035 0.72 O5i 0.54 0-93 186 % i X 2.8 5-5 II. 0.81 253 A 3-4 6.8 13-6 1. 00 306 ?4 4.0 8.0 I5.9 1.1,7 346 x 4.6 9-2 18.3 1.30 0-33 0.83 0.59 0.51 0.98 400 2 X2 A 2-5 5 o 10.0 0.72 0.40 0.80 0-57 0.62 1.03 253 y& i# X 3-2 64 12.8 0.94 333 6 4.0 80 16.0 15 400 M 4-7 9-4 18.8 36 467 A 53 10.6 21.2 .56 0-39 0-93 0.66 0-59 i. 08 533 2X*2X A 2.8 5.6 II. 2 0.81 0.44 0.89 0.63 0.70 1. 12 320 X J X Special X 3-7 7-4 14.8 .06 426 4-5 9.0 18.0 .31 520 3/6 5-3 10.6 21.2 55 600 A 6.1 12.2 24.4 78 693 6.8 13.6 27.2 2.OO o.43 1.05 0.74 0.66 I.I9 773 2^X2^ A 3-i 6.2 12.4 0.90 0.49 0.98 0.69 0.78 1.22 400 X H X 4-i 8.2 16.4 I.I9 533 5 o 10.0 2O. O 1.47 640 3^ 5-9 n.8 23.6 i-73 760 A 6.8 13.6 27.2 2.OO 866 7-7 154 30.8 2.25 0.47 I-I5 0.81 0.74 1.29 973 23^x2 3^ X 4-5 9-o 18.0 I-3I 0-55 1. 10 0.78 0.85 1-34 640 X m Special 5-5 II. 22. 1.62 786 3/8 6.6 13.2 26.4 1.92 920 A 7-6 15 2 30.4 2.22 1050 8-5 17.0 34-0 2.50 0.52 1.23 0.87 0.82 i-39 1180 3 *3 X 4-9 9 .8 19.6 1.44 0-59 1.19 0.84 0-93 1-43 773 ft iX A 6 i 12.2 24-4 1.78 946 H 7-2 14-4 28.8 2. II IIOO A 8-3 166 33-2 2-43 1260 9-4 18.8 376 2-75 1420 A 10.4 20.8 41.6 3.06 1580 N ii. 4 22.8 45- 6 3-36 o-57 1.41 I.OO 0.88 I-5I 1730 Above angles are rolled by nearly all mills. STEE,L ANGLES (E,ven Legs) Continued. For Beams, Girders, Columns, or Truss Members TABLE 20 I 2 3 4 5 6 7 8 9 10 II 12 13 14 13 Weight per Foot 3 Neutral Axis on Line 45 to Legs Neutral Axis Perpendicular to Leg. 1 Gages 02 Thickness of M One Anglo 03 & To (3 o H Four Angles Area of Sectior One Angle Perpendicular Distance from C. G. to Back Eadius of Gyration Section-Moment (Single Angle) Max. Size of E Single and Double Lines of lUvets in Leg Basins of Gyration Distance from C. G. to Apex If fi a 02 0> if ill H Erl PR fl |S c 35 H % |i 5^ * ^ 0? Inches Ins. Lbs. Lbs. Lbs. Sq. Ins. Ins. Ins. Ins. Ins. Foot- Lbs. Ins. Ins. Ins. Foot- Lbs. I;H?Xl % I.O 2.O 4.0 0.28 O.22 0.44 0.44 80 0.26 0.29 40 Special X 1.8 3-6 7-2 o-53 0.48 I2O 0.29 66 2 XI;H$ A 2.1 4-2 8.4 0.60 031 0.66 0.63 240 0-35 0.40 120 Special X 2.7 5-4 10.8 0.78 0.69 3 06 0-37 1 60 2^X1^ * 2-3 4-6 92 0.67 O.4O 0-75 0.72 3 06 0-37 0-43 146 Special 3-0 6.0 12.0 0.88 4OO 186 A 3-7 7-4 I 4 8 .07 480 226 H 4-3 8.6 17.2 .27 5 60 266 10.0 2O.O 45 640 307 >l 5-5 II. 22.0 63 0-39 0.86 0.71 786 0.48 0.40 346 2^X2 A 2.8 5-6 II. 2 0.81 0.43 0.76 0.79 1.29 386 0.51 0.60 0.97 266 X 3-7 7-4 148 .06 5 06 333 A 4-5 90 18.0 .31 626 5-3 10.6 21.2 55 733 480 A 6.1 12.2 24.4 .78 826 546 6.8 13.6 27.2 2.OO 0.42 0.88 0-75 1-35 933 0.63 0.56 1.04 613 3 x2 X 4.0 8.0 16.0 I.I9 0.43 0-99 0-95 1.56 720 0.49 0-57 0-93 333 Special A 5 o IO.O 20 o 1.47 780 426 N 5-9 ii. 8 23.6 1-73 1040 493 _7_ 6.8 13.6 27.2 2.00 1180 560 )l 7-7 15-4 30.8 2.25 0.43 i. 08 0.92 1.61 1330 0.58 0-55 0.98 626 3 y^-Yz X 4-5 9.0 18.0 L3I 0-53 0.91 0-95 1.50 746 0.66 o.75 1.18 533 ft 5-5 II. O 22. 1.62 920 653 3* 66 13.2 26.4 1.92 1080 773 7-6 15.2 30.4 2.22 1240 880 ^ 8.5 17.0 34-0 2.50 1380 986 A 9-5 19.0 38.0 2. 7 8 0.52 1.02 0.91 1.56 1530 0.77 0.72 1-25 1090 3Xx2 X 4-3 8.6 17.2 1-25 0.45 1.0 9 1.04 1.70 840 0.48 o.57 0.92 346 Special A 5-3 10.6 21.2 i-54 I02O 426 H 6.2 12.4 24.8 1.83 1210 493 7-2 144 288 2. II 1400 573 /2 8.1 16.2 32.4 2.38 1560 640 A 9.0 18.0 36.0 2.64 0.44 1. 21 I.OO i.77 1730 0-59 0-53 0.99 706 3^x2^ X 4-9 9.8 19.6 1.44 0-54 I. II 1. 12 1.76 IOCO 0.61 0.74 I.I3 546 5 6.1 12.2 24.4 1.78 1240 666 H 7.2 14.4 28.8 2. II 1450 786 8-3 16.6 33-2 2-43 1680 906 X 9-4 18.8 37-6 2.75 1880 IOIO JL 10.4 20.8 41.6 3.06 2080 1 120 ff$ 11.4 22.8 45-6 3.36 2280 I22O H 12.4 24.8 49-6 3.65 o-53 1.27 1. 06 1.86 2460 0.77 0.67 1.23 1320 Above angles are rolled by nearly all mills. STEEL ANGLES (Uneven Legs) Continued For Beams. Girders, Columns, or Truss Members TABLE 21 i 2 3 4 5 6 7 8 9 10 ii 12 13 M 15 1 Weight per Foot r ,2 Long Leg Perpendicular Short Leg Perpendicular ** to Neutral Axis to Neutral Axis i ! s 0? : ^ "tie TJ> 1 ~2 II if ||| Radius of Gyration |l |g| Radius of Gyration 1 CD vm C3 | "-" ^ *>^ ^5 PQ *< 3 | O fl I "fl 11 II ll| o'si gfl-2 %&>. || ||l i! H ^ ? J.2 oc H < '$'& |o 00 % $' Inches Ins. Lbs. Lbs. Lbs. Sa. Ins. Ins. Ins. Ins. Ins - LbsV lns - Ins. Ins. Foot- Lbs. 3^x3 T 5 15-7 31-4 62 8 4.61 473 1850 \\ 17.1 342 68.4 5-03 2010 x 18.5 37-0 74.0 5-44 555 2170 it 19.9 39-8 79.6 5-84 0.64 , 1.86 i-55 2.62 5940 0.86 0.80 1.37 2320 Above angles are rolled by nearly all mills. STEEL ANGLES (Uneven Legs)-Continued For Beams, Girders, Columns, or Truss Members TABLE 21 2 3 4 5 6 7 8 9 IO II 12 13 14 15 1 Weight per Foot "o h Long Leg Perpendicular to Neutral Axis Short Leg Perpendicular to Neutral Axis i 00 "8 3 M 1 CC Q) 11" ?3 3]? IN Pi 73 o o Badius of Gyration Moment Angle) pj Badius of Gyration 11 -g 03 13 1 o g So &K 03 6 y 23.0 46.0 92.O 6.76 i-34 2.47 2. 5 6 3-74 10710 i-47 1.79 2.48 6410 Pencoyd only 1 25.8 28.7 51.6 57-4 103.2 II4.8 7-59 8.44 11946 13180 7142 7875 tt 3 1 7 63-4 126.8 9-32 14420 8607 33-8 67.6 135-2 9-94 15655 9340 if 36.6 73-2 146.4 10.76 16890 10070 !/% 39-5 79 158.0 11.62 18127 10805 if 42.5 85.0 I7O.O 12.50 19363 H537 i 45-6 91.2 182.4 i-37 2.72 2-53 3.00 20600 1.72 1.77 2.65 12270 Above angles are rolled by all mills except as noted. PLATE AND ANGLE COLUMNS. (Supplement to Table 21.) TABLE 22 WITH COVER PLATES Weight per Lineal Foot of Cross Section Including | Angles, Web and Cover Plates 5?5* *M *"* H s 9 tn 5 1 irb T I 45 KJ 1 s <* M ONVO <$ M ONVO TJ- >-i OO M roVO* ON N* ^ Is* O rO vo oo ON o M ro <* "> t^oo M M M N N NNNMtt 02 5 ^ _b S ^5 3 1 J8 CO ro Tj- Ti- no *OVO VO t-s Is. rOVO' t~s. OO" ON O i-" N vo t^oo o o M N Th LOVO _ M M M * ^2 Pi 1 CO iH 2 1 3' to xovo vo r^ oo oo Cs Os o ro rf 10 VO t>- OO O\ O ** ro N ro * iOVO t^OO O "- 1 N b^kild JBAOQ JO ssaujioiitx peuiquioQ >t X^^t X^^: MMMM NNNNfO WITHOUT COVER PLATES Weight per Lineal Foot of Cross Section Including Angles and Web Plate X" Web Plato s I s' ^(t iH s a r-l d n4 1 3 N N 00 * O N -*fVO OO fOMOOO Tfi-iOO ION OOC^^OMNMCO^- VOOOOOVO ^OCCOM 1 * OOONOOON Tj-VO ci cf\ 10 M vo N vo to i-I oo' >o c\ r^> ^ ci cf\ t-- ^- M od VO O r^OO 00 O\ t^OO C\ ON O t^OO ON O O -" N ro ro M M M M !-(- co 1-. t^ ^ fO fO^t^^M is. t^ ro 0\tn t^ ONM ro 00 rt- O VO N OO N OSVO rOM ThNOt>.iONOMs.^- 10VO t^ t^sOO OO t^ t^-00 ON O t^OO ON O^ O <-> <-* N ro M M 1 Pi ft * ? ^ H Lbs. per L. ft. \oooovovo voooow-^- OOVONOOON -*vo VOfOONiOQ^ O^ONON fOMOOVOfOMOOiON lOVO VO fs.00 00 t^t^OO ON ON r^OO 00 ON O M HH N ro 5 ci H N VO VO V> N M N -^-VO 00 O VO VO N 00 Tj-VO 00 O N f^O\Oi-it^fO t^rJ-MOOVO ONt^iONOt^-^J-NON lOtoVO t^ fsOO VO t^OO 00 O-. VO t^OO ON O O n N N s b H OONNNOOOO OOON -^-VO O\vo" N OO" CO ON fO M OO' O N ^ iovo vo t^ i^ vo t~ t>OO ON M ^ si I s ls^Hsx!s^ ^-SXHs^ ^*x!5:$>*:^ 03 O rorj-rt-io w->VO ^ ^ 10 ^OVO VO 5 00 NNVOVON OOVOO -^-00 VO "d-VO O 00 N VO N VO ^O -^-vO OONVOO^" ONrj-O\rot^ VOinVOt-iOO OO'sJ-ONT^-ONTj- Ncoro-rl-^ NcorOTh-^- fOTf-Tl-xo iovo ro rf * to iovo 5 6 (S.IS.M M Is, 10 ON TJ-OO M N M CO CO * ii XHS^HSX X ro rh STEEL TEES For Beams, Girders, Columns, or Truss Members TABLE 23 I 2 3 4 5 6 7 8 9 Dimensions and Weights Axis Parallel with Flange Axis Coincident with Stem ngo c fl 45 be 5 ^o 1 oiji 1 1 1 ^^ g E* s *S*>: e o 2 1 O i i 1 ^3 1 | 1 1 1 a 9 1 .lol 1 1 OQ ^ -j fl PH 02 PH CQ Ins. Ins. Lbs. SQ. Ins. Ins. Ins. Foot-lbs. Ins. Foot-lbs. i I 0.87 0.26 0.29 0.29 40 0.21 26 i 1.23 0.36 0.32 0.29 66 0.21 53 *tf *# J -53 045 0.38 o-37 93 O.26 66 !# 2.04 0.60 0.40 0.36 J 33 0.27 93 *H 1/4 1.84 0-54 0.44 c>-45 146 0. 3 I 93 !^ 2.4 075 0.42 0.49 1 86 034 133 13 X J X 3-6 1.05 0.91 0-33 200 o 41 293 i# 0.90 0-54 0.51 253 0.37 186 2 !^ 3-i 0.90 0.42 0.42 200 o-45 240 2 3-7 i. 08 0-59 0.60 330 0.42 240 2 4-3 1.26 0.63 0.60 440 0-43 306 2 X 2^ 4.1 1.20 066 0.67 426 0.47 293 2^ 4-9 1.44 0.69 0.68 5 60 0.48 400 2% 1^ 2.9 0.84 0.29 0.31 120 0.58 306 2^ 5-5 1.62 0.74 0.74 666 052 466 2^ 64 1.89 0.76 0.74 786 -53 560 2^1 5 8 I-7I 0.83 083 800 05 1 466 6 7 087 084 972 0.58 706 3 6.1 1. 80 o 92 0.94 IOIO 0.51 466 3 7-2 2.IO 0.97 0.92 1160 0.51 573 2% 2 7.4 2.16 o-53 0.71 looo 0.54 600 3 2# 6.1 1. 80 0.68 0-73 693 0.65 666 2^ 7-2 2.10 o 71 o 72 800 0.66 800 3" 6.6 i-95 0.86 0.90 985 0.62 666 3 7-8 2.28 0.88 o 90 1140 0.63 800 3 9.1 2.67 0.92 o 90 1340 0.64 960 3 IO.O 2.94 093 0.88 1460 0.64 1070 85 2.49 .09 .09 1610 0.61 826 3% 9.8 2.88 .11 .08 1825 0.68 1170 3% 10.9 3.21 | .12 .06 1980 0.62 1070 4 9-3 2-73 .29 .26 2090 0-59 826 4 10.6 3.12 32 25 2370 0.60 960 4 ii. 8 3.48 32 23 2580 o-59 1080 As there is no uniform standard for Tees, the Carnegie rolls are given as representative for variety of size and weight. (108) STEEL TEES Continued For Beams, Girders, Columns, or Truss Members TABLE 23 I 2 3 < 5 6 7 8 9 Dimensions and Weights Axis Parallel with Flange Axis Coincident with Stem - JJf 53 "fl < 1 1 1 ~.t5 1 g I 1 I fil 1 a o 1 i 1 i C/Q * 1 |o 1 1 i 1 Ins. Ins. Lbs. Sq. Ins. Ins. Ins. Foot-lbs. Ins. Foot-lbs. 3^ 3 7-8 2.28 0.78 0.89 960 0.76 906 3 8.5 2-49 0.83 0.88 1170 0-75 1080 3 10.9 3.21 0.88 0.87 1500 o.77 H40 3 l /4 9.2 2.70 1. 01 1.05 1590 0-73 1080 3)4 ii-7 3-45 i. 06 1.04 2025 0.74 1440 4 9-9 2.91 1.19 1.22 2060 0.70 jo8o 4 12.8 3-75 1-25 1. 21 2640 0.72 1440 4 2 6.6 1-95 0.51 0.51 454 0.95 1170 2 7-"9 2.31 0.48 0.52 534 0.96 1400 2)4 7-3 2.16 0.60 O.7O 733 0.91 1170 2)4 8.6 2.52 0.63 0.69 826 0.92 1400 3 9-3 2-73 0.78 0.86 1170 0.88 1400 4 10.9 3-21 .15 .23 2180 0.84 1454 4 13-7 4.02 .18 .20 2690 0.84 1870 4/4 ii. 4 3.36 .31 38 2640 0.80 1410 4/4 14.6 4.29 37 37 3400 0.81 1880 5 12. 3-54 51 56 3740 0.78 1410 5 15-6 4-56 56 54 4140 0.79 1880 4K 2^ 9-3 2.79 0.60 0.68 866 i. 08. 1840 2)4 8.0 2.40 0.58 0.69 746 1.07 1546 3 IO.O 3.00 0-75 0.86 1250 1.04 1840 3 8-5 2-55 0-73 0.87 1080 1.03 1546 3^ 15.8 4-65 i. ii 1.04 2840 0.90 2200 5 2# II. 3-24 0.65 0.71 1140 1.16 2260 3 13-6 3-99 0-75 0.82 1570 1.19 2960 X- 4 15-3 4-54 i. 08 1.17 2810 1.09 2880 * 3> 17.0 4-95 i. 06 1.03 2890 1.05 2920 * 6 5^ 39-0 11.58 1-75 1-57 10920 1.27 8330 * 4 15.6 4.61 0.97 1. 12 2560 i-33 3HO *Pencoyd only. (109) STE.EL ZE,E=BARS For Beams, Girders, Columns, or Truss Members TABLE 24 2 3 4 5 6 7 8 9 10 II 12 13 M 15 Dimensions B S Beams Zee-Bar Columns Practical Detailing Dimensions 1 tt CO "O S . O tfl a .2 lickness of Metal p If 44 'Ction-Momer.t s Perpendicular to Web dth of Web Plate -^^3 Radius ol Gyration *"" en 'S, X dius of Gyration is Perpendicular j 8" Web Plate Web Flango s Coincident i Web Plate s Perpendic- ar to Web 5 "o a o i o O EH ^ o5 H f *5 31 5 V as a S In. Tn. ; Tn. Lbs. Foot- Tn Lbs. Tn Tn Lbs. Ins. Tn Tn Tn In 3 X Tons 4.0 2 1.1 6-7 1.28 6 3i-9 1.9 3.0 33-6 1# 3 4 15/8 3A 2% A 8.4 1-58 40.0 42.1 3 2H 3/ ; 9-7 1.72 46.5 49.0 3ft * ii. 4 1.98 54-5 57-5 3 2 H */ t ; 12-5 2.04 60.2 63.6 3A 2^ A 14.2 2.28 68.3 1-9 2-9 72.1 3-8 4 3A i/ 8.2 2.09 6^ 38.3 2-5 3-3 39-6 4.0 2 7 A 2 u 4A 3/8 T 5 tf 10.3 2.60 48.1 49-7 4X 3A 3/8 12.4 3-n 57-9 59-8 4 3A A 13-8 3-22 64.9 67-1 4A 3/8 ^ 3-67 74-2 76.8 A 17.9 4.12 84.0 86.9 4 3A 5^ 18.9 4.03 89.4 92.6 4A 3/8 H 20.9 4-43 98.8 102.3 3A 22.9 4.84 108.2 2.6 3-i 112. 3-8 5 zX T 6 * ii. 6 3-56 7 53-8 31 3-S 54-9 4.0 2 y 2 H 2*A H 3 T 5 ^ 13-9 4.26 64-5 65.8 S/s 3/8 7 16.4 4.96 76.0 77-5 5 3* ^ * 17-8 5- 12 83-1 84.8 sA A 20. 2 5-75 94.2 96.1 3/8 22.6 6.38 i5-3 107.4 5 1% n 23-7 6.32 III. 2 "3-5 sA 3 ITS 26.O 6.89 I2I.9 124-4 5/8 3/8 H 28.3 7-47 132.5 3.2 3-3 135-3 3-8 6 3* N 15.6 5-63 7^ 72.0 3-7 3-7 72.6 4.0 3 7/z 2% y* ^A 7 18.3 6-55 84.4 85,1 6/s 3^ # 21.0 7-48 96.8 97.6 6 3^2 A 22.7 7.70 IO5.I 106.1 ^A 3r 9 6 N 25-4 8-55 II7-5 118.6 6^ 3/8 28.0 9.40 129-5 130.7 6 3^ / 29-3 9-36 136.3 137.6 ^A 3A 8 32.0 10.15 148.7 150-1 jj 3/8 34-6 10.93 160.7 3-8 3-5 162.2 3-7 Section for 1 Rivet Holes Lbs. per L. ft. Diameter of Rivets OO O 04 Tj-VO ONMCOLO t^ONM*^- VOOOO04 ^i-VO OO M CO to !* ON M CO LOOO o" MMMM M oi oi oi oi 04 oo co co co *^ 'xf TJ-TJ-TJ-Lo LOLOLOLO vo'vo'vo'vo p LO VO OO ON O 04 CO Tf to t^OO ON O 04 CO TJ-VO t^OO ON M O4 CO ^-VO t-^OO ON i-i fe^ej\[ jo | 02 SSOU^OItfJ, *: >**- &*$& 3$SZ -ttSHSX HSfrtf* P*3* T N WEIGHTS OF FLAT KOLLED STE,EL TABLE 25 Pounds Per Lineal Foot 3 s *0 00 H O 04 VO ON O ^ LOOO 04 04 VO OO O 04 LOOO O CO LO O O CO LOOO O CO LOOO O CO M ON t^VO 'd- 04 O ON l 1 ^ LO CO 04 OoOVOLO CO M O OO VO^-04M ONt^LOrh LO ON oi vo' O* -^-od 04* LO ON co t~" M LOOO oi vo" o" ^fod M to ON co *" O* TJ-OO* 04 M M 04 04 CO CO CO Tt" 'xi- Tj- to LOVO VOVOt^t> OOOOOOON ONONOO MMM04 f- H T^- VOOOOOON 040404VO VOOOO O Tf- H-VQ VOOOOOO M CO Tj- 10 VO OO ON Q T^- OO M LOOO 04 VO O^ CO VO O ^d" *** M LOOO 04 LO ON COVO O CO t"^ M ^OO M LO M M 04 04 04 CO CO CO ^" ^d" LO LO LO VO VO VO t*-* t** t^OO OO ON ON ON O O O M M O OOOO OOOO OOOO OOOO OOOO OOOO OQOO VO O xJ-00 04 VO O -^-00 04 VO O T- 00 04 VO O rJ-OO O4 VO O ^00 04 VO O Tj-00 CO *^ O CO I s -" O ^- t~~ O "$ t^~ M Tj- r-- M rJ-OO M Tj-OO M LOOO LO OO OJ LOOO M M040404 OO CO CO x}- ^ ^i- LO LO LOVO VO VO t" l* t^OO OOOOONON ONOOO MMM IO TH LO Tj-rl-O4O OOOVOVO CO04O4Q O ^VC VO to 04 04 M ONQO VO LO ^ CO M Q t-o ON M CO LO t~>.OO O 04 "^VO OOO 04COLOt^ ONMCOLO VOOOO04 rJ-VO OO 04 to ON 04 to 00 M LOOO MrJ-t^M Tf-t^OcO VOO COVO ON OJ VO ON 04 lOOO O4 M MM0404 04COCOCO ThTj-Tj-Lo to LOVO VO VO *- ** ** t-^OO 00 00 ON ON ON O TH O OOVO04O OOTJ-04M r-~LOCOO l^.LOO4O t^iO04O OOLOrOO OOLOCOO M T^t^OcO VOON04LO OOMTj-t^ O COVO ON 04 LOOO M rJ-t^OcO VOON04LO M M M 04 04 04 04 CO co co ^d" ^* ^t to LO LO LO VO VO VO t^ f^ t"^OO OO OO OO ON ON CO VO MOO^-O VO04ONVO MCXDrJ-O VO04OOLO 04f^rJ-O VOcoO>LO MOO^-O O OOLOCOM OOVOcOM ONVO ^i-04 ONt-^Tj-04 Ot^tocO OOQtocO MOOVOrJ- M COVO ON 04* rf t~. O" CO LOOO M TJ- VO O^ oj to OO o' COVO* O\ M rf r4 o' 04 LOOO M MMM04 0404COCO cocorh'd- ^-TJ-LOLO LOVO VOVO VOt^t^t^ OOOOOOOO H O toOLoO LOQLOO LoOtoO toOtoQ toOioO LoOtoO LO O to o 04 t> cooo rh ONLOOVO Mt^oiOO coON^O LOMVO04 t^ COOO ^t ON to O vO O 04 LO t^ O 04 LOOO O CO LOOO O CO LOOO M COVO 00 M COVO 00 M COVO ON M M MMM04 N0404CO COCOCOrJ- ^J-ri-'^'LO LOLO LOVO VO VO VO t^ *" t** t^OO iH Tj- 00 COVO O 040OOLO O04VOO H-00 04VO 0004VOO O400OtO OO4VOO co voOoot*- Ocot^O ^t^O^h t^O^J-*^ O^f^-M T^-i^MTj- OOMT^-OO oS M rj-vd od M co LOOO' o" N" LO rA. o\ 04" rf vd ds M covo* oo* o" co to t-" o" 04" TJ- MMMM 04040404 COCOCOCO CO^^^ TfiOLOLO LOVO VO VO - OMT^-LO OOONMCO ?J-VOOOO oo o* 04' TJ-VO oo o" 04" ^j- vo* oo o' oi rf vd od o* 04" TJ-VO' oo o* 04* TJ-VO oo" O* oi M- MMMM M040404 0404COCO COCOCO^t" V ^* V ^* LOLOLOLO toVO VO VO 0> to VO 00 O O 04 CO -3-VO VO 00 ON O 04 CO -*VO VO 00 O O O4 "O --J-VO VO OO ON O VO to^rj-co 04MQON 00 t^VO VO LOrtcON MQOON 00 f^VO LO rj- CO 04 04 t^. O"N M' CO to t^. ON M' 04 rj-vd 00 O* 04* Tt-VO 00 O N rt- to t-". O*N M co LO r-" ON M* MMM MM0404 0<04C4rO rOfOCOOO 'T^J-J^l M^LOLO totO LOVO 00 04 cOTj-Tj-rh VOVOVOOO OO^OO O04M04 COrf-^-LO VOVOVOOO OOOQO 04 OOOVOrJ- 04OOOVO TJ-COMON t^LOCOi-* ONI^LOCO MONt^iO CONOOO t^ ONO04TJ- VOOOONM COtot^OO O 04 rt-VO t> ON M CO LOVO OO O O4 T*-VO t^ M M 04 040404C4 rOfOfOCO COrO*Jn n^J'TLrj LriLriLOLn 00 O OOOO OOOO OOOO OOOO OOOO OOOO OQOO 00 to 04 ONVO ooOr^Th MOOL004 ONVO COO t^ "d- M 00 to 04 ONVO CO O *^ * VO OO O* M CO to t^OO O* 04*COLOI>. OOO'oirj- LOt>oNo" oiTJ-LOl^ O\M04*^j- l> VO t- I^VO to T*-T-COCO 0404MQ OOOOOOO OOVOVOVO ^Tj-COCO 0404MO CO ONtOMt^ COONLOM t^cOONtO MVO0400 rJ-QVOOJ OO^-OVO 0400rJ-O VO t>- O\ M 04' Tj- to t-*. O\ O' 04' CO to r^-00 O* M CO LOVO* 00 O*NMro-. MVOMVO MVOMVO to t^OO O M co ^1-vo *> ON O 04 co LOVO OO ON M 04 rt- to t-^OO O M co rJ-VO 4 s * C4 04 04 04 04 04 04 CO CO CO CO CO CO 'T "T ^ -J xl 3 1 CO OONt^tO COMOOO to^OlO OOI^.rh04 MONt^to COMCOO tor^04O to ON 04 VO O ^-OO 04 to ON CO t^- M ^-OO 04VO OcOt^M LOON COVO O ^OO 04 to VO 00 ON M 04* co LOVO' t-". ON O" oi co -^-vo" l>. ON O" M co rj- to t^-OO* O* M 04* '4- CO O OOLOCOO OOLOCOO OOtOCOO OQLOCOO OQtocoO OOLOCOO OQtoooO M COVO ON 04 <* t^ O CO toOO MTj- VOON04LO r^O COVO OO M xl- t> O\ 04 LOOO to vo r>-oo' O* M oi ^- LO vo* i> o\ O* M IN TJ- LO vo oo ON o* M co rj- to vo* oo ON o' ifl r^ -X1-0400LO 04ONLOCO ONVO COO t^rfMOO rfMOOLO 04OMOCO ONVO CO O VO 00 O M CO LOVO OOO MCOLOt^ OOO04CO LO t>00 O 04COLOI>. 00004^- TJ- to r-".oo" o\ o" M 04" rf LOVO' t^od O"N M oi co ^ LOVO' oo ON O* M oi co LOVO t^" 0404O4 0404O404 04COCOCO CO^OCOCO i, LO MOO^-O t~.COONLO Mt^^-Q VOCOONLO OlOO^t-O t^COONLO Mt^Tj-Q 04 CO CO xt' LO toVO VOt^* OOOOONQ OMM04 COCO^to LOVO VO l* OO OO ON O TJ- LOVO l>od ONO*M04* cOT*-tot-* OOONO*M oicorj-to VO t-"OO ON O* M oi rj- J&J& co fl 1 1 X -^^-|S^ :>t "'H^"M HS^HSX H^-^^ "M^ 35^:$ MMM MM 04 112 STRUCTURAL DESIGNERS' HANDBOOK. CHAPTER IX. CAST IRON COLUMNS. Cast iron columns are rarely used for very high skeleton con- struction. They should never be so used when there is great eccentricity in the loading.* They are widely used for buildings of medium height, where outer bearing walls are provided or where a sufficient distribution of substantial inclosure and curtain walls exists to brace the building adequately against lateral forces. Cast iron columns do not lend themselves readily to the at- tachment of wind bracing, and because of the loose connections of the beams they should seldom be used where wind bracing is neces- sary. Different forms of cross section are used for cast iron columns. The square section is used a great deal where the column is to be built into a wall ; the round section is generally used for columns standing free in a room ; and the other form of section the H shape is very popular for either wall or free columns the latter only when it is to be encased in brick or plaster work. This section has the advantage of being open for inspection and it is easy to core. A special section of the same class designed by the author is shown in Fig. 20. It is suitable for large size columns, in fact, it is simply a practical extension of the use of the H section beyond the limits of the simple form. For small posts or struts such as stair posts and the like, the star section (Fig. 23) is some- times used. IN THE. DESIGN OF A CAST IRON COLUMN three steps are taken: first, the ratio of slenderness is fixed within certain limits; second, the area of the section is found; and third the section is designed. The first step has already been described in Chapter VII and the Diagrams Nos. 30 and 32 (as well as Diagram No. 34) found in that chapter will be used in conjunction with the diagrams in this chapter. The second and third steps will be fully explained in the de- scriptions of Diagrams Nos. 35 and 36. Diagram No. 35 is based on the provisions for allowable stresses contained in the "Code" (N. Y. C). Diagram No. 36 *Small eccentricities of loading are sometimes allowed by increasing the area of the section enough to take care of the bending stress due to the ec- centricity. CAST IRON COLUMNS. 113 embodies what the author considers to be more conservative values* for use in general practice. For a column ratio of 10 the allowed stress is just the same as for the preceding diagram, but the reduction of stress with increasing 1 ratio of slenderness is much greater than that provided by the "Code." DIAGRAMS NOS. 35 AND 36: The construction of these dia- grams is similar to that of No. 33 for steel columns. Abscissas represent column ratios, ordinates represent areas and the loads are represented by the curves on the diagram. A supplementary ordinate scale at the right of these diagrams also gives the weight per lineal foot for any area of cross section. This value is given in the tables following these diagrams in preference to the area of the section because of its double value for both design and esti- mates. An example will best illustrate the application of diagrams to the design of cast iron columns loaded with concentric and eccen- tric loads. Example: A column 10 ft. long has a load of 75 tons, 8 tons of which is located 6 in. from the neutral axis perpendicular to the web. The column section is the H as shown in Fig. 19 and is assumed to be 10 ins. square. Solution: The center of gravity of the combined concentric and ec- centric load is 0.64 in. from the neutral axis perpendicular to the web. The coefficient of eccentricity is 5 times 0.64 or 3.2. The radius of gyration is 4 ins. about the axis perpendicular to the web, in which case the area re- quired for this eccentricity is 20% of what would be required for the same load concentrically located, thus for the above load eccentrically located an equivalent concentric load is 120% of 75 or 90 tons. On Diagram No. 36 the area required for a load of 9.0 tons on a column with a ratio of slenderness of 50 is 3.15 sq. ins., therefore, for a column load of 90 tons the area would be 31.5 sq. ins. This same diagram gives the weight per lineal foot of column section for the above load as 98.5 pounds. According to Table No. 26 a 10 x 10 column ij in. metal is the nearest to this requirement. The reader is referred to a valuable discussion on the strength of cast iron columns in "Kent's Mechanical Engineer's Pocket Book," pp. 250-252. 114 STRUCTURAL DESIGNERS' HANDBOOK: Diagram No. 35 For giving the safe loads on cast-iron columns as specified by the New York Building Code. \> u 5 20 .10 -40 70 RATIO OF SLENDERNESS Diagram No. 36 For giving the safe loads on cast-iron columns as recommended by the author. RATIO OF SLENDERNESS U15) n6 STRUCTURAL DESIGNERS' HANDBOOK. CAST IRON COLUMN SECTIONS H Fig. 19 WEIGHT IN POUNDS PER FOOT Size Thickness of Metal Table No. 26 X 1 1* IX IK 2 5* 5* 6x6 6x 8 7x 7 7x 9 8x 8 8 x 10 9x9 9 x 10 10 X 10 10 X 12 12 X 12 21.8 26.5 g! 43-4 45-5 40.6 499 56.2 59-3 65.6 68.6 75-o 78.0 81.2 8 7-5 93-6 106.0 48.6 60.5 64.8 72.0 80.2 84.0 91.6 95-5 96.4 108.0 115 o 130.0 84.2 895 98.2 107.8 112. II7.0 126.0 136.0 155-0 155-8 177-8 175-0 200. o 52.7 59-8 * Second dimension is in direction of web. Fig. 20 WEIGHT IN POUNDS PEE FOOT Size Thickness of Metal Table No. 27 1 IK IK 1% 2 2X 2K 2K 3 12 X 16* 20 24 16 x 16 20 24 20 X 20 24 28 24X24 28 24 x 28 1 60 172 185 197 2IO 222 199 214 2 3 2 J5 261 276 237 256 275 293 312 33i 369 388 407 443 462 490 275 297 319 34i 363 385 428 450 472 515 537 575 3 J 3 338 363 388 4i3 438 487 5i2 III 613 663 434 462 490 547 575 603 660 688 753 606 637 669 725 762 840 734 802 836 93i 798 873 910 1023 * Second dimension is in direction of web. O CAST IRON COLUMNS. CAST IRON COLUMN SECTIONS 117 Fig. 21 WEIGHT IN POUNDS PER FOOT Outside Diameter Thickness of Metal Table 28 X 1 IK 1* IX 2 2* 2X 2M 3 I 8 9 10 ii 12 13 H n 18 20 31.2 38.6 45-9 53-3 60.6 39-i 490 58.8 68.6 78.4 88 2 98.0 107.8 58.2 70.5 82.7 95-o 107.2 II9-5 I3I-7 1440 156.2 168.5 100.3 125.0 139-7 154-4 169.0 189.0 198.5 213-3 243.0 I4L5 158.7 175-8 193.0 210.0 227.5 2445 279.0 3I3-0 196.0 215-5 235-5 255-0 275-0 314.0 253-0 281.5 303-0 348.0 392.0 331-0 380.0 429.0 411.0 465.0 441-0 500.0 D rig. 22 WEIGHT IN POUNDS PEE FOOT Size Thickness of Metal Table 29 X 1 2& IX IX 2 2# 2K 2% 3 6x 6 49 63 74 8 59 75 90 10 68 88 105 12 77 100 121 16 96 125 152 8x8 68 88 105 10 77 IOO 121 12 87 112 137 16 105 137 1 68 IO X IO 87 112 137 159 12 96 125 152 178 16 H5 !5 183 215 12 X 12 1^7 1 68 J 97 224 250 l6 162 199 234 268 300 16 x 16 187 230 272 311 35 386 20 261 TOO 7CC 400 442 24 ^46 7QQ 4"?o 499 546 20 x 20 ^46 7 OQ 4 C JO 499 ^46 24 384 442 499 ccc 609 24 x 24 421 486 549 611 671 730 787 STRUCTURAL DESIGNERS' HANDBOOK. CAST IRON COLUMN SECTIONS WEIGHT IN POUNDS Fig. 23 PER FOOT Thickness of Metal Size Table 30 % * % K X 1 3"x 3 " 6.6 8.6 10.5 12.4 4x4 9.0 11.7 14.4 17.0 5 *5 14.9 18.3 21.7 25.0 28.1 6x6 18.0 22.3 26.4 3- 4 34-4 CAST IRON GAS PIPE, WEIGHT IN POUNDS PER FOOT Size Thickness of Metal Table 31 % K T 7 B y 1 A 39.36 & 54-o 2"

mOO 5 0wwew4^weinwmtno to to to 10 ^ o 4H . M. Hi ci co covd vb d\ t^ M M vood N o\ rj- M torot^ri r^xod CD THB9JI JO 1 ^ to ^ ^o to VO MO NtoQi-'>-"VotoOtOMU-)OO vot--C>rot^-rO'-i (^CNr^M ior>-'^-M roco J>.OO G\ M M ^t-VO l^. O\ M' rj-VO M t^. ^t M O\ N OOOVO Tj- N M C\t^-torJ-M O\ t>> t--o6 CO C\ C^i ds O O M" M M' M' ro ** <* -o vl31) -uoj^oeg 1 1 o O 'sJ-NVOVO M M t> M OQ ON fOOO ro *O ON M OO N VQ 00 OO COM N d\ r^-vo 06 o\ ci >-ood M ri M" M* oo oo oo oo' <* ^ M d O o\vd rj-vo o ^ MMMMfOMMMiHNrjNMrO'd-rO'd-Tt-rOLOTj-vooo en CO CO * * "^VO CO T- u-> LOVO "->O t^ !>. tnt?9g jo VOCX5 VOOO O->O OOO M M LOW M'VO O co ] - I * '. vr>VO 1>-CO ON O I>- Oi ON CO t^.00 00 O\ M 1-1 M LO tII139fI JO M 9 ' I ^^2 jo vo VO ON M (135) 136 STRUCTURAL DESIGNERS' HANDBOOK. CHAPTER XIV. FLEXURAL EFFICIENCY OF I-BEAMS AND CHANNELS. An interesting matter in connection with the design of beams and girders is the relative "efficiency" of the different standard sec- tions. An 8-in. 18 Ibs. I-beam has a certain section moment. If this beam be taken as a standard of comparison, then the value of its section-moment divided by 18 may be taken as a unit of effi- ciency, i. e., 1 00%. Thus a 2O-in. 65 Ib. I-beam, for instance, shows a much greater bending strength per pound of metal contained in a lineal foot of the beam , DIAGRAM NO. 41 herewith gives curves representing the rel- ative efficiency of all the standard and special section of I-beams and channels. In this diagram abscissas represent efficiencies, based on the above standard. Ordinates represent weights per lineal foot. Different lines drawn on the diagram represent the various sections of beams. The full heavy lines represent the I-beams of the American Association of Steel Manufacturers. The light full lines represent Pencoyd I-beams (only shown where they differ considerably from* the Association standards). The dotted lines represent standard and special channels. As a matter of comparison some foreign sections of I-beams are also represented on this diagram. The solid dots represent some of the oddest of the Belgian I-beams. The depth of the beam is in each case noted next the dot in figures representing inches. In like manner, a number of representative German sec- tions of I-beams are shown by circles with black centers. The sizes they represent are given as for the Belgian shapes. FLEX URAL EFFICIENCY OF I-BEAMS AND CHANNELS. 137 Diagram No* 4f For giving the relative flexure efficiency of I-beams and chan- nels per pound of steel. PERCENTAGE OF EFFICIENCY 50 60 70 80 90 100 % UJ o CO 10 50 150 ? i tt \, 200 250 I- ift O rt o a z 8c LU Q. CO Q lO Z O Q. LJ 8 i o cc o i / 100 150 PERCENTAGE OF EFFICIENCY 200 250 138 STRUCTURAL DESIGNERS' HANDBOOK. CHAPTER XV. BASES AND LINTELS OF CAST IRON. CAST IKON BASES OR SHOES FOR COLUMNS: These usu- ally bear upon concrete, dimension stone, brickwork or upon grill- age footings. They are usually set in place upon small blocks and grouted with Portland cement paste from one-half to three-fourths of an inch in thickness. A better practice is to ram the Portland cement mortar in from the side of the shoe, to do which requires not less than an inch and a half to two inches of clear space under the shoe when temporarily supported by the blocks. The area of the bottom side of this shoe is determined by the allowable unit pressure on the supporting material. The height and thickness of metal depend upon a variety of certain and uncer- tain conditions. Only a few of the more important of these con- ditions will be considered because they arise in specific cases rather than in general practice. A slight unevenness in the grouting of a cast iron shoe is not an unusual occurrence, and this is sure to set up irregular and indeterminate stresses in the metal. When grillage beams are used in footings the slightest deflection of the beams will cause the load on the shoe to be carried on its two edges at right angles to the beams. The distance of the webs or ribs apart should never exceed the limits fixed by the strength of the bottom plate between these webs. A "rule of thumb" method of designing cast-iron shoes is to let h == iM a (25) where h = height of shoe, a = projection of shoe beyond the edge of the column. The thickness of metal is made the same as that of the column sup- ported. The purely theoretical methods for computing the flexure strength of shoes are laborious and tedious. The following sim- ple empirical formulas give results within a very small percentage of absolute accuracy. Two cases are considered : (1) When a uniform unit pressure is assured on the bottom of the shoe for instance, a bearing on a granite block. (2) When the load is likely to be carried on two edges "of the s h oe a condition existing when grillage footings are used. BASES AND LINTELS OF CAST IRON. 139 FIRST CASE: a 2 W A (26) (2 a + b) h where a = projection in inches. b = diameter of column in inches, h = height of shoe in inches. W = total load in tons. A = area* of cross section (in square inches). SECOND CASE: A - W (27) h where the values are same as above. When the thickness of metal in the various parts of a cast iron shoe is not uniform, or nearly so, flaws are apt to develop in the process of the cooling off of the casting. For this reason the de- sign of an economical shoe requires skill in choosing the height and distance apart of the webs so that the metal in the several parts shall be one thickness. The thickness of metal directly under the column section must always be sufficient for the load on the column. The safe limits for the distance between the webs or ribs of cast iron shoes are given on DIAGRAM NO. 42 herewith. It gives the safe distance in inches for various unit loads on the bottom of the shoe and for various thicknesses of metal in the bottom plate. EXAMPLE: For a unit pressure, on the bottom of a shoe of n l /2 tons per sq. ft., the brackets should not be more than 10 ins. apart for i^-in. metal in the bottom plate, while for 18 tons the metal should be 2 ins. for the same spacing of brackets. CAST IRON LINTELS: When the height of the stem of a cast iron lintel is not less than about 4 / 10 ths of the width of the lintel per stem, the formulas following can safely be used. Two stems should be used for widths greater than 16 ins. B L 3 Wab A = - + - , (28) 115 h 83 L h where A area of cross section of lintel at the centre in square inches. B = thickness of brick wall in inches. L = span of lintel in feet. h height of cross section at centre of lintel in inches. W = concentrated load (at distance a and b from each end) in Ibs. (Note: If more than one concentrated load occurs W a b = W a' b' + W" a" b" + etc. *This area includes only the area of the ribs at a distance "a" from the dge of the shoe plus the area of the base plate. 140 STRUCTURAL DESIGNERS' HANDBOOK. Diagram No* 42 For giving the minimum thickness for bottom plate of cast- iron shoes. CLEAR DISTANCE BETWEEN BRACKETS 10" 15" 20" 3 .X u Jfc 2" / <-y / 10" 15" 20" CLEAR DISTANCE BETWEEN BRACKETS 3ASES AND LINTELS OF CAST IRON. 141 The width required for a lintel is always known and in the case of brick walls is usually 8, 12, 16, 20, 24 or 28 ins., according to the thickness of the wall above it ; with the above formula, by assuming a height for the lintel, say 6, 8, 10 or 12 ins., and deciding upon the use of one or two sterns, the area of the cross section is found from the first factor of the above formula if no concentrated load occurs; and from the summation of the factors when one or more concentrated loads occur along with the brick wall load. 142 STRUCTURAL DESIGNERS HANDBOOK. CHAPTER XVI. WOODEN BEAMS AND POSTS. For structural purposes wood is almost exclusively employed in rectangular form. This uniformity of section makes the appli- cation of wood to framing a comparatively simple problem; and lends itself peculiarly to independent diagram treatment for the solution of such problems. This will be evident from the descrip- tion of the diagrams presented in this chapter without further dis- cussion on the mechanics of the subject, the treatment of which has been fully covered in Part I. SAFE LOADS ON WOODEN JOISTS. Two sets of diagrams are given, one set (Diagrams Nos. 43 and 44) for the strength of white pine, spruce or chestnut joists, for various depths from 3 to 16 ins. ; the other set (Diagrams Nos. 45 and 46) for yellow pine and locust. DIAGRAMS FOR WOODEN JOISTS: In each diagram ab- scissas represent span of joist in feet; the ordinates represent spac- ing of joists in inches ; curves on the diagrams show safe load* in pounds per square foot of floor. The spans represented vary from 3 to 30 ft., and the spacings from 12 to 24 ins., and the load per square foot from I to 1,000 Ibs. The load lines show a bend which indicates where deflection enters as a factor. For spans to the right of the bend the beams are designed for a limiting deflection of one four-hundredth of the span. NOTE: If oak joists are to be used, work out the problem by each of the preceding sets of diagrams, and take a mean of the two results. It will be evident that floor planking 3 ins. or over in thickness can also be figured by these diagrams. SAFE LOADS ON WOODEN GIRDERS. Two sets of diagrams (including Nos. 47 to 50) are also given for these as in the preceding. DIAGRAMS FOR WOODEN GIRDERS : These diagrams are constructed the same as those for joists. The depths of girders represented by the diagrams run from 6 to 16 ins. ; spans from 3 *It is to be remembered that the diagrams are for beams I in. wide; for a beam 2 ins. wide double the load obtained from the diagram; for a beam 3 ins. wide, triple the load. etc. WOODEN BEAMS AND POSTS. 143 to 25 ft. are shown, and loads from I to 100 Ibs. per sq. ft. The spacing of girders represented by the ordinates is given in feet and runs from 7 to 18 ft. The limiting deflection is same as in the preceding diagrams. The diagrams are also for girders I in. wide. SAFE LOADS ON V'OODEN POSTS. The strength of wooden posts is represented on Diagram No. 51. The general arrangement of this diagram is similar to those for steel and cast iron columns. It is constructed on the basis of the stresses provided by the "Code" (N. Y. C.) and is a combina- tion of three distinct diagrams representing, respectively, white : -.1 pine, white oak, and yellow pine. In all three diagrams abscissas represent column ratios, ordinates represent area of section, and the curves represent concentric loads. It will be noted that the upper scale of abscissas differs from the scale at the bottom of the diagram. The former represents the ratio of slenderness of the posts as hitherto defined the quotient of the length divided by the radius of gyration of the cross section and is given so that Diagrams Nos. 30, 32 and 34 can be com- bined with it for the purpose of designing wooden posts for eccentric loads. The latter, the scale at the bottom, represents , , another ratio much used for wooden posts : the length divided by the least width of the section. This latter ratio is the one com- monly used. Two supplementary ordinate scales are given at the right of the diagram. The first of these shows the usual sizes of posts, at proper vertical intervals to represent the areas given on the ordi- nate scale on the extreme left. One column is given for square posts, another for round posts. The other supplementary scales show the weight per lineal foot for any cross section area of post. One column is given for white pine and another for yellow pine and white oak which woods are approximately twice as heavy as white pine. EXAMPLE: Posts of white pine, white oak or yellow pine 10" x 10" will carry concentric loads of 32 to 18 tons, 36 to 20 tons, or 40 to 23 tons, respectively, for unsupported lengths of 25 ft. to 8 ft. 4 ins. 144 STRUCTURAL DESIGNERS' HANDBOOK. Diagram No* 43 For giving the safe load on white pine, spruce or chestnut joists for each inch in breadth. PERTH OF JO\5J5 3" \ 9 10 15 20 , PERTH Or JOISTS 4 o d - PERTH OF j0is>Tb 6" ^ 2 " \\\\\\\ V\\ \ \ \X\W\ N \\\W \\ \ N\\\ \ \ ^ \ N 8 9 JO SPAN OF JOISTS IN FEET 3O WOODEN BEAMS AND POSTS. 145 Diagram No* 44 For giving the safe load on white pine, spruce or chestnut joists for each inch in breadth. PERTH Of JO\5Tf> 10 vo . \\ \ \\\ \\ 1 \ fc a & 9 10 PERTH I2 1 \ 3 _ \ ~ 15 20 DEPTH OF JO5T 16 \\ \\\ \\\\ \ \\\ ^1 \\ 6 7 & 9 10 SPAN OF JOISTS IN FEET 20 25 30 146 STRUCTURAL DESIGNERS' HANDBOOK. Diagram No* 45 For giving the safe load on long leaf yellow pine or locust joists for each inch in breadth. DEPTH OP J01575 4" 15 20 D&PTH OP JT OP JOI5T5 O V0 Nk\\ \\\ \\ \\ \\ \\ \\ \\\\ \\\> 7 & 9 \O .15 SPAN OF JOISTS IN FEET 20 3O WOODEN BEAMS Diagram No* 46 For giving the safe load on long leaf yellow pine or locust joists for each inch in breadth. DEPTH OF 15 ZO 3O PERTH OF JOISTS = 14" 7 8 9 IO 15 SPAN OF JOISTS IN FEET 20 25 30 148 STRUCTURAL DESIGNERS 1 HANDBOOK. Diagram No. 47 For giving the safe load on white pine, spruce or chestnut girders for each inch in breadth. PERTH Of WRITER 6" \\\\\\\\ \\ \ \ \ \v xw XXXxNXX \A\\ \ \ \ \ \ \ \ \ \k x \$ \5 CO If a s 10 PePTh OF GIRPER 8" \\\\\\\\ \\ \v\\v\\ \\ \\\ \ 7 & 9 \0 \5 SPAN OF GIRDER IN FEET 20 7.5 WOODEN BEAMS AND POSTS. 149 Diagram No* 48 For giving the safe load on white pine, spruce or chestnut girders for each inch in breadth. PEPTH OP GIRPE-R 12" ~ VvV \\V\\\\\VA\VA 10 15 20 in PfPTH OP GIRPrrR 14 \\\V\\\ v\\\\\\\\\A\\\\\\\\U\\ v\> \ \ \ \ \ \\\\v x\\v\ \\ \A\ \\ \\\\ 678 10 15 20 PEPTH OP GIRPER 16' \\\\ .\\\ \ ss \\ \\\v \\ \\ \\\\ ^ \\\ VN \c\ \\\ \\\ SSSwSss^SSSSvS^sv \ \ \ \\vv ^\\ \\ v\\ sis:: \ O c? e 7 8 9 \Q 15 SPAN OF GIRDER IN FEET 2O 25 ^ 30 ISO STRUCTURAL DESIGNERS' HANDBOOK. Diagram No. 49 For giving the safe load on long leaf yellow pine or locust girders for each inch in breadth. PERTH OF (TlffPER 6" Ift \\\ WOs SSSS \\\ \\ \\\ \\\\ \\ \ ss \\ \\ \ S^SMSS^ \\\\\\ v IM irm \\ \A \N^ A? \k u UJ UJ ** v N^ \\\ \ \\ S \\ \\ \\ \' V \ 5S i^^^^N\s\\\ -7 a SPAN OF 3 10 15 GIRDER IN FEET \\ 20 25 30 152 STRUCTURAL DESIGNERS 1 HANDBOOK. Diagram No. 5J For giving the safe load on wooden posts. AREA OF SECTION IN SQUARE INCHES INDEX. Page American Assoc. of Steel Mfrs. : Standard shapes 14 Angles : Radius of gyration 102106 Section area .102106 Section moment 102, 106 Steel: Table for beams, girders, columns, or truss members having even and uneven legs 102 106 Thickness of metal 102106 (See also Connection Angles.) Angles and Tees: Explanation of diagrams for 14 Base 63 Bases, cast iron: For columns 138, 140 Beams: Angles, diagrams described 14 Belgian I 133135 Buckling of compression flange 4 Cross section 1 Definition of 11 Deflection 2 Diagram, concentrated load converted to uniform load.. 52 Diagram, concentrated load at any point reduced to con- centrated load at middle 56 Diagram for I-beams, 3-in. to 24-in 19 47 Diagrams for angles and tees, spacing and span for given loading 4851 Diagram for grillage beams 63 Diagram, deflection various loadings on 3-in. to 15-in. I-beams 57 Diagram, deflection various loadings' on 10-in. to 24-in. I-beams 58 Diagram for converting concentrated load to equivalent uniform load 15 Diagram, safe loads on 3-in. to 15-in. channels 59 1 Diagram, spandrel beams 56 Diagrams, utility of 11 English I 133135 End reactions $ Explanation of diagrams 12 Explanation of diagrams for I-beams and channels .... 54 Explanation of tables 13, 14 Flexural efficiency, I-Beams 136, 137 German I 133 135 154 INDEX. Page Grillage. (See Grillage Beams.) Loads % 4 Manner of support 2 Maximum end reaction 13 Maximum per cent, of bending load 13 Mechanics of 1 Method of using diagram for I-beams 12 Properties of 85 Properties of Foreign 134, 135 Resistance 1 'Section moment 1 Span 1 Spandrel 53, 54 Steel, I Tables for beams, girders, columns or truss mem- bers 90-93 Tables for 3-in. I-beams, channels and zees IS , 4-in. I-beams, channels and zees -0 5-in. I-beams, channels, zees and bulb angles '22 6-in. I-beams, channels', zees and deck beams 24 7-in. I-beams, channels, zees and bulb angles 26 8-in. I-beams, channels, deck beams and angles. ... 28 9-in. I-beams, channels, deck beams and angles. ... 30 10-in. I-beams, channels, deck beams and angles. ... 32 12-in. I-beams, channels and deck beams 34 12-in. I-beams and channels 3(1 15-in. I-beams and channels 38, 3!) 18-in. I-beams 42 20-in. I-beams 44 24-in. I-beams 46 Tees, explanation of diagrams 14 Unit stress 2 Beam work H Bearing capacity of soil 128 Bearing plates: Design of 67 Tables of 7O-71 Brick walls. (See Walls, Brick.) Brickwork, safe load on . 68 Buckling of compression flange 4 Buckling of web 62, 64 Cast iron bases and lintels 138 Channels 'Beams. (See Beams.) Channels: Flexural efficiency 136, 137 Height of 94, 96 Section area 9496 Tables for beams, girders, columns, truss' members. ...94 97 Web thickness 9496 Weight per foot 94101 Channel columns. (See Columns, Plate and Channel.) Columns: Base, cast iron or steel 60 Built steel shapes , 88 INDEX. 155 Page Columns. Continued. Cast Iron, Design of 112 Diagrams giving safe loads' as recommended by the author 115 Diagrams giving safe loads as specified by New York Building Code 114 Diagram giving weight in pounds per foot, thickness of metal and outside diameter 116 118 Channel 88 Concentric loads 8 Cross section of 9 Diagram for eccentric loading 83 Diagram giving radius of gyration of the most common forms of built-up sections 80 Diagram giving radius of gyration of the most common forms of wood, cast iron or steel sections 79 - Diagram giving ratio of slenderness 81 Diagram giving safe loads, New York Building Code, for ratios of slenderness up to 120 and as recommended by the author for ratios 120 and 200 82 Eccentric loads 8 Footings 60 Mechanics of 1 Plate and angle 89 Radius of gyration 72 Ratios' of slenderness 73 Designing built columns 72 Table for plate and angle 107 Tables for plate and channel 98101 Weights of 98101 Zee-bar 89 Columns and truss members 72 Connection angles: Bearing values 69 Design of 60 End reaction 67, 69 Holes in shop or field end 69 Rivets 70 Shearing values 69 Diagram, explanation of equivalent load on spandrel beams.. 53 Diagrams. (See Beams, Diagrams; Columns, Diagrams, etc.) Dimensions and weights 85 Dimensions for practical detailing 91 110 End reaction, allowable. (See Beam Tables.) End reactions 3, 13, 14, 65, 67, 69, 70, 91, 93 Beams: Connection angles 67, 69 Explanation of diagram 65 Floor: Explanation of diagram for converting concentrated load to equivalent uniform load 15 Diagram for converting concentrated load to uniform load. 52 156 INDEX. Page Floor arches: Weight of 123 Floor beams, wooden: Weight of 123 Floor framing 11 Diagram giving weight of steel where loads are a mini- mum 120 Diagram giving weight of steel where. loads are a maxi- mum 121 Floor framing, steel: Weight of 119 Floor Girders: Conventional method of treating load on 5 Flooring material: Weight of 123 Footings 60 Diagram for grillage beams 63 Live load on 1^5 Foundation walls 131 Girders. (See Beams, Definition of; Plate Girders.) Grillage beams 60 Conventional methods of considering loads on 7 Explanation of diagram 62 Diagram, safe pressure in tons per sq. ft 63 Illustration of footing 61 Load on 5 I-Beams. (See Beams.) Joists, weight per sq. ft. of floor 122 (See also Beams'.) Lattice bars \ 84, 95, 97 Lintels, cast-iron 139 Load, allowable per sq. ft. (See Beam Tables.) Loads, dead: Carried by columns 119 Carried by floor girder 119 Loads: Diagram for eccentric column loading 83 Explanation of diagram for reducing concentrated load to equivalent uniform load 16 Explanation of equivalent load diagram 53 Loads, live, New York Building Code 124, 125 On beams 4, 57, 58 On columns 8 On floor girders 5 On footing 125 On grillage beams 5, 7 On wooden girders 143, 148151 On wooden joists 142, 144147 On wooden posts . . . . 148, 152 Web in compression 91 93 INDEX. 157 Page Partitions ; Weight of 124 Plate and angle columns. (See Columns, Plate and Angle.) Plate girders: Design of 87 Properties of 86 Plates, 'bearing. (See Bearing Plates.) Plates, thickness of 98101" Pressure, wind 125 Properties of Foreign I-beams 134, 135 Radius of gyration 72, 79, 80, 83, 91, 98, 102106, 108110 Diagram common forms', wood, cast-iron or steel sections. 79 Diagram built up sections 80 Rafters. (See Beams.) Reactions. (See End Reactions.) Retaining walls, thickness of 131 Rivets: Diameter of 9197 Gage of lines 9197 Relative values various sizes 69 Size of 102103 Size and gage for zee-bars j. 110 Rubble, safe load on 68 Section areas: For concentric loading 75 For concentrically loaded columns with pin ends 76 For eccentric loading 77 For tension members 76 Section moment 1, 9197, 101106, 108, 109 Shapes. (See Structural Shapes.) Soil, bearing capacity 128 Spacing c. to c. (See Beam Tables.) Span, allowable. (See Beam Tables'.) Spandrel beams, explanation of diagrams 53 Standard shapes 14 Steel, flat rolled, weight of Ill Steel angles. (See Angles Steel.) Steel columns. (See Columns.) Strength of web 9193 Stresses, unit: Safe load on masonry work 126 Strength of columns 126 Working stresses: Compression (direct) 127 Safe extreme fiber stress (bending) 128 Shear 128 Tension (direct) 128 Structural shapes, properties of 16, 84 Table's. (See Beams, Columns, Connection Angles, etc.) 158 INDEX. Page Tees: Beam diagrams described 14 Dimension and weights' 108, 101) Radius of gyration 108, 109 Section moment 108, 109 Tables for beams, girders, columns or truss members. 108, 109 Template, size of 70 Timber. (See Wood.) Trusses: Design of , 86 Properties of 86 Unit stresses. (See Stresses, Unit.) Walls: Footing 60 Foundation 131 Retaining, thickness of 131 Thickness and weight 129, 132 Walls, brick: Weight of 124 For dwelling houses 129 For inclosing skeleton structures 129, 131 For warehouses 129 Web: Buckling of 62, 64 Compression allowable load 9193 Strength of - 9193 Thickness 94, 96 (See also Beam Table.) Weight, floor framing. (See Floor Framing.) Weight, per foot. (See Beam Tables.) Weight, flat rolled steel Ill Weights and dimensions per lineal foot 85 Wind pressure 125 Wooden girders, safe loads 143, 148150 Wooden joists, safe loads 142, 144147 Wooden posts, safe loads 143, 152 Zee-bars 89, 110 Flange width 110 For beams, girders, columns or truss members 110 Radius of gyration 1 10 Size and gage of rivets 110 Thickness of metal 110 Web height 110 Weight per foot 110 Width of web plate . 110 V i O I