CONCRETE DESIGNERS' MANUAL 5K? Qraw-Ml Rook & 7m PUBLISHERS OF BOOKS Coal Age ^ Electric Railway Journal Electrical World * Engineering News-Record American Machinist v Ingenieria Internacional Engineering 8 Mining Journal ^ Power Chemical 6 Metallurgical Engineering Electrical Merchandising CONCRETE DESIGNERS' MANUAL TABLES AND DIAGRAMS FOR THE DESIGN OF REINFORCED CONCRETE STRUCTURES BY GEORGE A. HOOL, S.B. CONSULTING ENGINEER, PROFESSOR OF STRUCTURAL, ENGINEERING, THE UNIVERSITY OF WISCONSIN AND CHARLES S. WHITNEY, M.C.E. STRUCTURAL ENGINEER MT- r A UXEE r WI8. FIRST EDITION McGRAW-HILL BOOK COMPANY, INC. NEW YORK: 370 SEVENTH AVENUE LONDON: 6 & 8 BOUVERIE ST., E. C. 4 1921 H k7 COPYRIGHT, 1921, BY THE McGRAW-HiLL BOOK COMPANY, INC. THE MAPL>: I'KKHS YORK PA PREFACE The tables and diagrams presented in this manual make possible the rapid design- ing of reinforced concrete structures in accordance with the Joint Committee Recom- mendations, the American Concrete Institute Recommendations, the New York Building Code Requirements and the Chicago Building Code Requirements. Some of these tables and diagrams will also be found of such a general nature that they can be used when the designing requirements are different from any of those men- tioned. No tables are presented based on the flat slab recommendations of the Joint Committee as these recommendations are so conservative that they are not used to any extent. The authors have for some time been preparing and using in their practice various tables and diagrams in order to finally obtain complete data in the most convenient form and of the greatest value to the majority of designing engineers. The collection given in this book is the result. No attempt has been made to develop theory or to duplicate information not directly relating to concrete design which can conveniently be found hi other hand- books possessed by all designers. G. A. H. April, 1921. C. S. W. 47789 CONTENTS PAGE STANDARD NOTATION 1 FORMULAS ........ i. . 2 SECTION 1 SLABS . . . i ........ 5 SECTION 2 FLAT SLABS i ...... 31 SECTION 3 RECTANGULAR BEAMS 47 SECTION 4 DOUBLY REINFORCED BEAMS 63 SECTION 5 T-BEAMS 77 SECTION 6 SHEAR REINFORCEMENT . 83 SECTION 7 COLUMNS. 91 SECTION 8 BENDING AND DIRECT STRESS \. . . 199 SECTION 9 FOOTINGS 225 SECTION 10 MISCELLANEOUS . 237 APPENDIX RULINGS PERTAINING TO DESIGN AND WORKING STRESSES 243 Joint Committee Recommendations 243 American Concrete Institute Recommendations 255 New York Building Code Requirements 265 Chicago Building Code Requirements 270 VU CONCRETE DESIGNERS 1 MANUAL FLEXURE FORMULAS USED IN PREPARING TABLES AND DIAGRAMS The flexure formulas made standard by the Joint Committee relate to working stresses and safe loads, and are based on the straight-line theory of stress distribution. These formulas were used in preparing the tables and diagrams in this book. STANDARD NOTATION Rectangular Beams. f s = tensile unit stress in steel. f e = compressive unit stress in concrete. E = modulus of elasticity of steel. E e = modulus of elasticity of concrete. H. n = F c M moment of resistance, or bending moment in general. A s = steel area. b = breadth of beam. d = depth of beam to center of steel. k = ratio of depth of neutral axis to depth d. z = depth below top to resultant of the compressive stresses. j = ratio of lever arm of resisting couple to depth d. jd = d z = arm of resisting couple. ^ p = steel ratio = 7-3- T-Beams. b = width of flange. b' = width of stem. ? = thickness of flange. Beams Reinforced for Compression. A' = area of compressive steel. p' = steel ratio for compressive steel. // = compressive unit stress in steel. C = total compressive stress in concrete. C" = total compressive stress in steel. d' = depth to center of compressive steel. z = depth to resultant of C and C'. Shear, Bond and Web Reinforcement, r = total shear. V = total shear producing stress in reinforcement. v = shearing unit stress. fo 1 * TORMULAS u = bGiid^tres^pef >unii area of : bar. o = circumference or perimeter of bar. So = sum of the perimeters of all bars. T = total stress in single reinforcing member. s = Horizontal spacing of reinforcing members. A v = area of shear steel in section of beam considered (A. C. I. notation). f v tensile stress in web reinforcement (A. C. I. notation). a = spacing of shear steel measured perpendicular to its direction (A. C. I. notation). Columns. A = total net area. A s = area of longitudinal steel. Ac = area of concrete. P = total safe load. FORMULAS Rectangular Beams. k = V2pn + (pnT* -pn = - I = - or -, or jr.-ar.yCW, or w-^.- or f _ 2f s p f.k '~ n(l - k) T-Beams. With a T-beam it is necessary to distinguish two cases; namely, (1) the neutral axis in the flange, and (2) the neutral axis in the web. Case /. The Neutral Axis in the Flange. All formulas for "moment calculations" of rectangular beams apply to this case. It should be remembered, however, that b of the formulas denotes flange width, not web width, and p (the steel ratio) is A, x A, W not Vd Case II. The Neutral Axis in the Web. The amount of compression in the web is commonly small compared with that in the flange, and is generally neglected. The formulas to use, assuming a straight-line variation of stress and neglecting the com- pression in the web, are: 1 k = i+4 nf e 2ndA s + bt z 2nA a + 2bt = 3kd - 2t t_ 2kd - t'3 jd = d - 2 2 FORMULAS M M J A,jd pjbd* fe = n(l - fc) -V " ft , = f,Ajd Approximate formulas can also be obtained. The arm of the resisting couple is never as small as d %t, and the average unit compressive stress is never as small as K/c, except when the neutral axis is at the top of the web. Using these limiting values as approximations for the true ones, M c = V 2 f c bt(d - i#) M, = AJ.(d - HO, or A t = - The errors involved in these approximations are on the side of safety. Formulas which take into account the compression in the stem are recommended .where the flange is small compared to the stem. Such formulas may be found in the report of the Joint Committee, and are as follows : pnd \- A, + (6 - b')t* . fnA. + (b - b')i\ * nA, + (b - b')t [(kd - t(2kd - l)b + (kd - t)*b' jd = d - z f a =-**- . 2Mkd [(2kd - t)bt + (kd - t)*b']jd Rectangular Beams Reinforced for Compression. p' + n*(p + p'; 2 - n(p , M M Js Ajd pjbd* f f' k n(l - fc) >--*THi FORMULAS f e n(l - k) k M s = bd%pj Shear, Bond and Web Reinforcement. V Joint Committee (Recommended V = Vertical web reinforcement Tjd -- ' s / \ = -vj- (a) Bars bent up at angles between 20 and 45 deg. with the horizontal, and web members inclined at 45 deg. _ A s f g jd _ Tjd V^s ~ 0.75F' ~ 0.75F' 4 jd American Concrete Institute: A v f v jd _ V'a o, TTT or A v V Columns. Square Cored P = Afdl + (n - l)p] Round Cored Hooped P = Af e [l + (n - l)p] Joint Committee P = Af e [(l + 4np') + (n - l)p] Am. Cone. Inst. P = Af e [l + (n - l)p] + 2/ s p'A New York Code P = Af e (l + 2.5wp')[l + (n - Dp! Chicago Code (In the above formulas p f = percentage of spiral. /, in the New York formula is taken at 20,000 Ib. per sq. in.) SECTION 1 SLABS Diagrams 1 to 9 inclusive give the total safe loads on solid slabs of different depths for the various combinations of working stresses, bending moment coefficients and span lengths. Diagrams 10 and 11 give the bending moments for different values of the total load per square foot, the span length, and the bending moment coefficients. Diagrams 12 to 17 inclusive may be used to find the moments of resistance and area of steel required in solid slabs for various combinations of working stresses. Table 1 may be employed to find the size and spacing of round or square rods for a given sectional area of steel per foot of solid slab. Tables 2 to 7 inclusive give the total safe load for ribbed slabs for various combinations of working stresses. Example of Design of Solid Slab Given: Live load = 300 Ib. per sq. ft.; span length = 8 ft. 6 in.; M = ~; j c = 650; /. = 16,000; n = 15. Using Diagram 3, a slab of 8%-H. span, with a depth to steel of 4% in., is found to have sufficient strength to carry a total load of 405 Ib. per sq. ft. Assuming a 5>9-in. rough slab with 1 in. of finish on top (not placed monolithically) and plastered below, the loading will be as follows : 6^ in. of concrete =81 Plaster = 5 Live load =300 Total load =386 Ib. per sq. ft. Diagram 11 shows the bending moment for this load on an 8 3^ -ft. span, when rty/2 M = 12-, to be 27,900 in.-lb Entering Diagram 12 at the left with this bending moment, it is found that the area of steel required per foot width for a slab having a depth to steel of 4% in. is 0.42 sq. in., or K-in. round rods spaced 5^ in. on centers (see also Table 1). The use of the bending moment coefficient ^2 means that the slab is continuous over supports and that the area of steel over the supports must be the same as at the center of the span. From Diagram 25, page 57, it will be found that one-half of the rods can be bent up from the bottom at 22 in. from the support and these rods should be run to the quarter point of the adjacent span. Example of Design of Ribbed Slab Given: Live load = 100 Ib. per sq.ft.; hottow-tile floor; span of joists 19 ft; M = ~;f c = 650; /. = 16,000; n = 15. 5 SLABS Assuming a 2-in. topping and an 8-in. tile, Table 2 shows the total safe load to be 190 lb. per sq. ft., with a steel area per joist of 0.90 sq. in. The table also shows the dead weight of floor to be 73 lb. per sq. ft. which makes a total load to be carried of 173 lb. per sq. ft., or less than the maximum safe load. The floor is usually plastered below, which would make the total load 178 lb. per sq. ft. A 3)4- in. topping with 6-in. tile would also answer. When the size of tile and thickness of topping have been determined, it is necessary to design the joists with reference to shear, bond, and compression in the concrete at the haunch by treating them as individual beams. DIAGRAM 1 SOLID SLABS SAFE LOAD ON SOLID CONCRETE SLABS IT/ 2 M 8 f c =650 f s = 16,000 f s = 18,000 n=15 1900 1800 ^M \v^ Jl70O 1 n 00 IGOO 1500 \ \ \ \ v -\ \ \V 33 \\1 -v-v \ \\ V\ \ . \ . ~v ^ \ ~~- S \ -A- "V" t \ \ - 1600 - 1500 - ]400 1400 1300 Vv^ -Vv \ \ \ \ \ \ \ \ V v-V a \ V, -\ ^ . ~ V"' v - I I -\ \ v 1 v H - 1300 - |?OO 1ZOO -vAi \ \ ' \ \ Vv. , \ i \ .. \ ^ ^r x _v i i \ - iioo 1100 W^ S vV \ \ Y^ \ \ ^s 1 t \ \ \ ^ V \ \ \ , N \ \ \ ' 1000 1000 900 800 \ \ \ \ \ \ \ \ -V-N -V w rvS Sr^ y \- V \ \ V v \ \ V 1 \ V v 1 ^v \ ~-\ \ r \ ?- \ % ^ _x \ r : 800 - 700 u> It & -h q- cr 700 600 500 \ v v \ ^ v-v \ \ ^ v-v \ \ \ ^ v-v \ ' \ s v-V \ 1 \ -V V \ \ -v^ . \ \ CS v \ \ 5 s V r^ i v^ ^ ^ \ -v - >y~" \ -\ -\ \ S r ^ ! v^ H V V " \ v \ > \ B v ~v \ ^ 9 7* j ,v \ , i j [ \ ~N s s. ^ 5 S r -V- ( - 600 - 5OO O O^ ocT (J . ^ cUU- 0' ZOO x^ \ \ \ \ \\ \ \ \ \ - \ \ -*- \ \ V? t\ \ \ \ J>, \ \ ^ V s \ V ' " \ \ \ V re o \ \ V xA \ \ - \ \ 5 \> L\ S J \' \ \ - ^ T \ $. H \ \ \ o ' \ \ - \ \ - \ \\ V \ s \ \ \ 2 \ V^ \ \ \ \ \ \ 1 \ V S \ N ^ \ \ \ y f ^ \ V $ 5 - I \ \ \ \ \\ \ v t \ \ i V v \ \ \ *< \ \ \ \ \ \' S^ J s, \ S \ \ \ \? X \ \ \ \ s \ V \ 2 5 \ \ ! \ \ y \ \ \ \ \ \ ^ \ \ \ V \ \\ v \ \ ,\ v \ \ \ ^ \ \ \ \ \ | N \ \ \ V \ \ V \ \ \ V \ \ \ \ x \ \ i k\ ^ ^ S V~ IUU 100 \ \ \ \ \ \ . . \ . : \ 1 y - \ 1 ^. \ 5 \ 5 \ s \ \ ^ \ ^ 90 90 y \ \ \ i \ \ \ \ > \ ^ \ \ \ \ \ \ \ , \ , ^ , \ \ \ ' \ v \ \ - " 80 80 \ \ \ \ ^ \ ^ \ , 1 V V ;' \ \ \ ~ \ \ \ \ \ \ I \ \ \ ; ^ s > y 70 10 \ i \ \ x \ \ \ \ \ \^ 1 \ \ ; \ \ x \ \ . \ \ \ \ \ v -. \ s \ \ ! 60 60 Y \ 1 \ \ \ \ 1 \ ^ \ \ \ \ \ \ \ \ \ V cO Tf 10 VP t^ OO o un < < D \J m OJ c 3 P a n h n f se h SOLID SLABS DIAGRAM 2 f s =16,000 f s = 18,000 SAFE LOAD ON SOLID CONCRETE SLABS "5 1900 :W rVv i V- 1 V 1 V-\| V N v^ L A \ ,\ - 1800 noo 1600 -Vv v- \ \ 33; t~\-A S N -\- 3 A \ ^ "^~ -\ V S"" 1 A \ \ \-\ -\ V 4 \ \ \ \ -A -v J\ - 1700 - 1600 - I5QQ 1500 "V\ VAA Vv t J -A A' \ 3 k \ \ \ \ \ A \ 5 ^ V - !400 1400 12)00 ddi s s rV^ 1 V s \ v p -\ ^ V \r> -^ v - 1300 ieoo \ \ > \ \ \ \ \ v~ : __S S N ^ S \ s. \ V' \ ^ v X \ IcOO - 1100 1100 \ \ \ V v \. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v \ V \ \ V- \ \ r> \ ' \ > \ , \ x \ " , v \ \ ( ; 1000 1000 900 \ \ \ \ v \ \ \ \\ \ \ \ V \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 11 900 o 8 800 TOO ^ v~~^~i \ V- r\ y vS v y \ \A | < \ V \_ N ^ \ s - h =: - 800 - TOO O en" isT n & 600 -\ ' \ \ \ \ \ s \ \ \ ' V , \ \ \ \ \ \ -\- \ y \ o \ A 1 3 \ i \ V \ v N V \ g V ^ "\ r\: \ \ v~\ L v Vr \ o - >x \ \ \ ^ - ', \ \ \ \ \ - 600 - 500 it ^ 4- <*- 500 \ \ \ \ \ i \ \ \ \ \ \ \ V \ \ \ SA A ^ v v - 4- >^- \n i_ w _ JQ 400 vJ \ 5 \- \ y- Pi \ v k&'v, ~\ -V -A, ^ 1 H ^ x^ __-. ^ - :A \ .v.: ~ 1 = 400 i/) i- P_ ^C T5 300 \ \ B \ ^ _A \ \ \ V- \ ^ 5 i \ A M kc Jv f^ V-V g \ ~ 'A -A V \ \ K - V- - 300 5= 15 O \ \ \ \ -J^_ ^ \ -v- \ ^ x \ \ \ \ \ J ^s v \ \ \ \- ~ " O \ j o\ "X 313 h' ^ > r \ ! \ o o \ \ \^s \ \ j \ \ \~ \- \ ^ J , \ v \ \ 5 s \ \ x~ \ j \ V- s w 4- \ \ \;> C \ \ \ \ \ \ . \ , \ \ s \ \ \ V ^ 4- ft \ \ V ^ \ \ \ \ \ \ ; - \ I ^ . \ \ _ K \ \ \ Y\ i 5 s \ ^ \ \ \ \ \ \ \ \ In 00 \ \ \ > \- ^ \ \ \ ft V i \ r r \ "^~ dOO P \ Y r\- 5 \ \ \ s \ \ \ \ s \ \ \ v \ ^ o \ \ \ ,V\ \ \ \ \ \ \ \ \ \.\ \ \ \L V \, \ > ft H \ \ \ > S \ \ \ y \ \ ' \ N \ \ \\ \ \ \, ' \ \ \ \ \ L* \ \ \ \ \ \ \ \ \ \' \ \ \ \ \ ) , \ x \ \^ ^ \ ^ \ j \ x \ \^ \ \\ \ x \ \ \ ^ \\ \ \ \ \ \ \ \ \ N \ \ \ A \ 5 \ \ V \ \ \ \ \ \' \ \ v \ \ \ C A , \ > \ \\ \ \ j \ \\ \ \ \ \ \ \ x \ v \ x \ \ \ l\ \ A \ v \ ^ \ " \ \ \ \ \ \ \ \ \ \ \ v J V V A \ \ \ \ \ s ion -^ x \* \ ^ v 100 \ , \ \ \ \ X \ \ \ \^ \ \ \ \ \ i \ \ S s \ \ \ \ \ \, \ \ 1 - 90 90 \ \ \ \ \ \ x \ \ \ \ \ \, \ - \ \ \ \ \ \ x - 5 s x ^ \ \ \ '\ \ ^ - 80 80 \ \ \ \ \ \ 5 \ \ ', \ 1 \ - \ \ \ V \ 5 \ \ \ \ \ 11 \ \ \ A ,\ \ \ \ i - TO 70 \ \ \ \ \ \ \ " \ \ \ \ \ \ \ \ \ * y ^ > L s 1 s \ - 60 60 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \, \ CO 4 LO ^ r- CO o LO 4 O ~j ir rJ ^F 5C (n ') n f <2 ei- DIAGRAM 3 SOLID SLABS SAFE LOAD ON SOLID CONCRETE SLABS Jf-^ M ~ 12 f c =650 / = 16, 000 f g =18,000 = 15 SOLID SLABS " *.. w*- *' fc ON SOLID M = W 8 CONCRETE P ^E^^55 1J SLABS lAVjK./ LiVI 4 f c=700 f s =16,000 r e = 18,000 n=15 190Q rWt^s SAFE LOAD loOO 1700 1600 ^~V\ AA- I vV hd r^ i V" y- A A v _\ \A ^n E ^1 -V r V . 1500 O 1500 \ \ XV 1 1 -\ \ pA \ T \ N \ -v \\ v 1400 1400 I3>OO \ \ y \ 1300 \ \ \ \ V A s -V \ ' ^ -V ieoo \ \ A A \\ A \ \ \ \ Vn r * JIOO 1100 \ \ \ V ^ $ \ V \ y \ y \ y \ \ \ - JOOO 1000 y \ crrfc3 v\ \ \ 5 \ \ \ X\ A N ^ \ L \ \ \ \ \ \ \ \ \ i L_^ - 900 900 HOO 700 \ x 1 \A \ v \ V J \ ^. N -A ^ ^ A I -V \- V \ X A : - 800 TOO 4-' *r c/3 | 00 A - v\ -V' VA \ ' \ \ \ \ \ \ \ \ V -y \ \ N \ V \ \ \ \ 1 J i y \ 3 \ \< c A -\ A \ \ r \ ^ \ v ^\ ^S V GOO 500 00 II cr (n \ 2 ^A; \ \ \ \ ' \ \ \ \ ^ \ \ ( \ ^ \ x y \ ^ \ K A v \ \ 500 400 V \ \ \ \ \ \ \ \ \ \ V \ -f y \ ^ \ A y ^X" v -\ ^ .^ r ^ 400 A. \ IP \ A v- -v i i ! 3 | v-V -\- A, ~A- V \ \ 3 \ ' y \- -^r Jy 5 t y f-\ A L r \ c H 1 vv p-\ V A N - y S 1 n S in 300 V- VH f ._\ \ -V- . . \ \ \ \ \ x \ \ \ \- \ v \ \ v 3 \ \ V s " \ \ \ \ \ \ i s V \ Xi \ ^ \ \ \ s v\ \ \ \ \ ' \ \ \ \ \ \ \ \ y \ \ s A A v s \ V __y y v , \ V \ X \ \ 300 . o M- D vP | \ \ \ \ V \ \ \ L r\\ \ \ \ s y s. \ \ \ \ \ \ \ \ \ \ \ \ \ \ A \ \ \ \ ZOO ^ V^> l^ V * \ \ r \ r v \ \ \ y \ A' -^ r zoo 100 V \, \ ^ \ \ \ \ji\ \ \ \ \ \ \ \ > \ \ \^ \ \ y \ \ V \ s y A \ Ay' \ \ \ "X \ \ ^ \ \ \ \ \ \ y \ X \ \ \ \ y \ ^ \\ \ y \ N \ \ ^ \ \ ^ 1 -N ^ A \ V \ \ \, _ S" , \ \ \ \\ y \ \ y \ y \ \ ^ _ \ \ \ \ \ \ y \ \ \ s y \\ S7 y y v \ \ JOO n \ 1 ^ > y ^ V- r \ ^ N 3 V y \ \ \ y \ \\ y \ \ A A y \ \ \ ^ y v V \ \ \ ^ \ \ \ > 55 A \ A \ ^ k \ \ ^ \ 1 \ \ \ \ \ \ \ \ \ \ ^ \ S \ \ V y y s \ \ ^ ^ \ \ \ \ \A \ \\ \ N\ \ s A x ^ \ V \ \ \ \ \ ' \ \ \ \ \ \ A V A A v \ \ \ \ \ y ,\ \ \ \ \ y\ A \ \\ \ \ V \ ^~ \ \ y \ \ \ \ \ \ A V \ N A N \ \ K A N y \ \ \ ~ \ \ y \ v \ ' \ \ \ \ \ A \ X A \ N \ \ \ \ \ y \ 90 \ \ \ \ y \ \ X N \ y \ y \ y \ \ \ \ \ y \ \ y \ \ i \ \ \ c . \ ^ \ y V \ \ 80 89 \ V \ \ \ ^ v \ \ v \ y y" \ \ \ \ \ \ > \ \ , \ ^ \ \ \ \ \ \ \ \ N 70 70 \ \ \ \ \ \j \ X ^ \ \ s ' \ \ \ \ \ 11 \ \ y \ ^ \ \ \ \ \ S , \ \ \ \ \ \ y^ s y y \\ \ J9__ 60 A \ \ X \ - \ _^ \ s \ V x X y X \ \ \ V ^ \ \ x y \ \\ I: rO * * t- 00 o ID i < n o Span ir? feel" 10 DIAGRAM 5 SOLID SLABS SAFE LOAD ON SOLID CONCRETE SLABS M= Jo f e =700 f s =16,0 f s =18,0 71=15 fP A A- * 1 fc \ g 3 V \ -V -Vi V - I70Q - 1600 1500 1400 liOO \-V- X \ \-\ ft* \ X vv -\-\ X \~ Vv rV \ X V V s s s \\ \ \ ~^ A X . \ -V ip V L V > - 140O 12>00 \ \ b\ \ \ \ \ \X x \ v , V \ \ \ ^~"*"^ UOO 1100 \ X , ' \ ^ s \ \ ' \ \ i \ \ ^ \ ^ \ r \ \s \ ' \ \ s y V 4 V V . \ ^ \ \ \ \ \ \ , V \ ^ \, \ \ 'y n noo ' 1000 1000 900 ^\ <** VA 1 | \ ^ 1 -\ _-3 N ^ \~l \ 3 \ ^ \ ^ ^s O of II 800 700 \\ F? -^ V . X \ g \ \ s v- \ -\-4 \~ V V Vi o- v f i 1 rS V \ V ^ 5 i; E 5 k \ - GOO o CO ii 6- in 600 500 X X \ \ \ 1 \ \ \ V \ \ S > \ -V -v \ \ v s v 1 II v . v \ ! \ s v ^-v j v v \v i\ A \ \ i \ A- \ v i N \ 1 \ \ || - 500 4-' tr C- J3 400 V V 1 V c \ v -V J^ \- Y ^v ^ -^ vv vV TV -v V 3 V k N -\ g V- >_ ^ ^V- 0) _D \ V ^ 5 "V 1 . \ \ I \ i -v v _i ^ jr \ i \ \ -Vi \ \ V V N \ - v \ v \ \ \ ! t V ? !L. - r \ n 30 j: 5 o ^KL \ . -> V- ro <; \ x Vi \ k s \ \ 5 \ ' -\ , v V r r i \ o \ v ~\^^ \ \ V \ \ 5 \ x 5 \ \ 5 x \ X i .-0 o \ V ~\ - , V A \ N \ \ \ -v 1 \ \ " <+- \ V \ V A- \ \ \ \ \ \ \ \ \. ' ! o " o \ ^O \ \ X \ i 1 [ \ \ \ \ \ ^ \ 1 [ \ [ - \n L \ ' A \ s ^ \ V A \ \ \ S \ \ V \ \ \ \ - eoo * 200 X \ \" ^ v- - \ -X \ \ s vN \\ \ \ \N ^ ^ s \ P \ x x ^> \ \ \ \ \ \ \ \ \ ^ k, \ \ i \ ^ ^ \ s i ^ \ o \ \ ( \ ^ \ \ \ \ ^ \ \ \ \ \ \ \ v \ \^ \ \ ^ ^ \ H \ \ \ \ ^ \ \ \ 1 \ \ \ \ ^ \ V V \ i\ s \ V \ ' \ X s \ \ \ \ \ \ \ \ \ \\ r k ^ \ s \ v \ \ ,5 , \ \ V \ \ ^ V \ \ \ \ \ \ ^ \ \ \ \ \ \ N ^ \ \ \ \ \ \ \ \ s \ \ \ x \ \ " \ \ 2 A \ 1 \ ^ \ \ \ \ \ \ i \ 1 V \ \ s \ \ \ \ l\ y A \ \ , \ V \ \ \ \ \ \ ^ \ \ \ k \ \ x \ \ \ \ x \ x V V \ \ \ \ C A \ \ ^ ^\ X \ \ \ \ \ \ ion too x \ \ \ \ \ \ \ \ A \ \ \ \ \ A \ \ i \ \ \ \ \ \ \ \ \ S \ \ \ A \ \ \ \ 1 90 90 s 1 \ ^ \ v < \ \ \ \ s i \ \ \ \ \ \ \ ^ \ \ \ \ '> \ \ \ \ ^ \ \ \ \ L L 80 60 \ \ \ \ ^ \ \ \ \ ^ *i ' \ \ ( \ V \ \ \ \ \ \ \ \ \ \ \ \ \ \ ,, I 70 70 \ \ \ \ ^ \ \ \ \ \ A \ \ \ \ ^ \ \ \ \\ V \ \ \ \ \ \ \ \ \ \ \ \ \ , \ j \ \ \4 60 60 \ \ \ \ \ 1 \ \ ^ \ \ \ \ ^ \\ in - - 00 dl = - s c >p a n in ' re C h 11 SOLID SLABS DIAGRAM 6 f c =700 f s =16,000 f s = 18,000 71=15 SAFE LOAD ON SOLID CONCRETE SLABS M =" ~?ocr vV ^ ^5 ^ t: ^: t: leoo 1500 -V-N ST-V- _^._.\^_ ^ A; \ v-y- -\-\ V~\~ ^ V V ^ W 2? \\ ^ \\ A- \ *\ ! ^ ^ V L. \ V~ I v s L = - fsoo - 1500 - - |Arf> I40Q ^ tiC 3 S s s ^ \ S *r 1 ^ ) : - i^oo 1300 170D -tt Ys _V-i V-V V v v g V 5 S \\ ^ ~\ A A V V\ i \ . \ \ \ A V \ -^ r \ '. ' 1200 1100 v-\ 3 v S \\ \ I .\ 5 > 1 \- ' S V V \" \ \ v '(< * \ \ N"\ -- noo -" 1000 1000 900 \ v \~ \ -V \ \ =*F s A v s--\ ^ \ s \ \ V \ \ \ \ \ \ s. Y v \ \ \s S 2 ,\ -V \-\ V-^ 1 \ \ \ r\ S \. v\N ^^^ C : 900 uT ii , tf> 800 700 00 ^v- t^s v \ \ -\ . ^ \ \ V \ \ g V ^ v \ \ v^ \ V \ \ A \ -V \v'\ V'A \ \ 1 \ -A- V V I \ --Y \ 1 s \ \ A A y 1 V ~\ s \ V \ V 1 \ 3 \ ^ \^N \v v^ \v \\ 1 -v \ ^ A\ V v s ( 1 i -y -X- ^ \ ^ LP c \ n \ \ | y \ c ^v \ ^ \ s a -V t ^ \ S : 800 - : 700 - - GOO O ocT ii * ( +- 4-* \ \ \ ^Y \ \ \ \ \ \ \ \ \ \ \ V V \ \ \s i\_ v 4- \ \ \ v^. v \ \ \ V \ ; s \ ^ \ \- N \ \\ \ v v rt N" ^oo 4- 5

^ \ \ \ ,x\ \ \ \ \ s \ \ v \ \ \ . V \ ^ A \ \ 5 V \ V - 5\ \ \ \ \ \ \ v \ \ > \ \ A \ \ ^ \ 5S P -+- r\ S \ V f \ \ \ \ s \ V \ v \ \ \ \ N \ \ \ 53i s .0 F \ \ \ \ \ V \ \ \ s: , ^ \ \ \ \ A ,\ \ \ \v\ H v \ \ \ \ \ \ \ \ \ \ \ } \ \ \ \ \ \ S 0^ ^ \ \ v \ \ \ \ y \ V \ \ \ \ s^ \ \ ^ v j \ \ V0i\ \ V \ \ \ \ \ \ \ \ \ \ \ \ \ \ > ^ V \ \u\ v ~ \ \ \ \ i \ \ k y \ ,\ A \ \ \ \ \ \ \ \\v ^ V \ \ \ \ \ \ \ \ \ \ \ \ y \ \ \ \ \ v y y N \\\ ^> L |OO 100 \ I \ V \ \ \ \ \ \ \ ^ \ \ \ \ \ N\\ ^ : 90 \ *r. \ \ \ V \ \ S k \ \ \ \ \ \ V V ^_ b)U \ \ s \ \ \ \ \ \ ^ \ \ \ \ s^ \ \ n A " \ \ \ \ \ \ s. \ \ \ SJ 80 go \ \ \ \ \ \ \ \ \ \ \ \ \ \ s \ \ >^"^ k - \ \ \ \ \ \ \ \ \ \ 5 \ \ \^\ ? : TO 70 \ \ \ \ ^ \ \! \ \ \ \ V V \ ^: V \ \ x \ \ \ \ \ \ \ \ \ \ > i _^_\ \ : 60 GO \ \ \ ^ \ \ \ \ \ \ \ V \ \ N fO irmrr- f < e< D a1 i m %j i c n \i .~&~m 12 DIAGRAM 7 SOLID SLABS SAFE LOAD ON SOLID CONCRETE SLABS wl 2 M 8 f s =18, n=15 I90O jgoo \ \ ^V ^ ^ E -S \ _\^_, ^ y - - 700 TOO GOO 1500 \ \ \-vs s. \ \ \ \ ^\ ^ V- 2 y 5 \ , 1 A y - GOO - 1500 - J4QQ V-M y \\ VV \ \ \ , \, '-, -X. V 1300 1300 \ \ \ \ \ \, ' \ aA \ i \ v ; \ j j -J S5 " IZOO IZOO \ S \ \ V ST S ^ A k ^ A^ \'" r^ s , ', , ', \ noo At 00 \ \ \ \ \ \ \ \ \ \ \ , \ \ -T- \ \ 'N, s \ A \ j ; \ \ \ v \ \ \ \ k \ i \ lUvJO 1000 QOo \ \ -VA \ \ \ \ d^ \ \ rV \ ^v ^ \ 3 -, \ ~\ \ \ \ I \ \ \ ^ \ \ \ \ : 900 800 ^v 3=5 V ~S v ^ 3 s V | [ ;X 1 \, : 800 700 \ \ \ ' \ , \ VN 5 \_ \ !_, J,-4 y^ ^ 3 \ ^ y^ s jy V - 700 Q o -X ^ =^ \ \ V V c \ i i \ 1 ^ ^ \ Vi V j \ [ S \ -V - GOO O \H \-A \ -v- \ ^ -\ t ^V rY \- \ \~ . _2_:i. o b JU \ \ , \ \ J _x \ j ly j j . \ \ & v i - 4- to it \ \ \ \ \ Y^ \ \ \ \ ' \ . N . \ x \ v \ -, c \ v 1 i \ J y j [ \ \- - 500 n t i t 500 400 -V- ~s \ \ \ \ > \ \ \ v A \ v\ \ \ \ v^ -v A \ \ V \ \ s \ \ i s \5 ', L \ \ \"\~^ ^r-V HP \ \ \A "V \ v -A \ V \ s -\ \" i ^ , 1 3 ^ p r i 2 ^r - 40O & .s- S" S- -ti ^c c 6 300 Ar-J \ \ A ipj a-V vV \ ' \ v ^ \ \ \ j i \ j V V \ \0 V i \ u \ ! 5 \ V s -s \ \ \ 1 v- \ H \ \ Vr 1 \ ^ rV S -\ Sp -V \ V J -v p V H V HN ^ \ r V ^ \ \ ' \ V \ t s v 1 T ^v cE \ ^300 C- _c c 7J Q \ V rt \ V i \ V i \ s \ s \ -V^ \ \ \ \ \ \ \ o 3- \ \ \ , v \ \ ! \ \ \ - T\ v ', ; ' v ^ ^ \ \ _ \ \ \ ^ \ \ \^ . i \ \ '. V \ ., j \ \ \ \ \ \ s s - 3 f\ft o to V V \ i \ >. N \ > s y \ \ , i\J(J ^oo A \ : \ \ \ - : \ \ ' V k \ \ \ \ ', v s o \ \ \ l f , \ L 5 \ \ M \ \ X \ , 1 ^ ' v \ \ \ L i \ -t- \ \ \v ^ \ , \ \ "\ S \ ^ \ \ S L \ \ \ 75 \ \ \ ^ * \ \ \ \ - \ , \ ' \ , i S 5 3 \ i s^ \ sp 1 \ \ \ V . \ \ . \ \ \ ^ \ \ y ,\ s 1 \ \ s L\ p. -, ' , I \ v ' \ \ * s \ v s \ j s y \ \ \ \ \ \ \ \ \ . ! \ T \ \ \ \ , \ A V \ \ \ \ \ \ ' 5 \N A \ s 2 \ s \ \ \ \ \ \ \ ' \ \ \ V A \ . \ -,\ \ v ~ \ \ \ \ V \ \ \\ A \ L \ , \ V s \ \ t \ J \ \ ^ s \ , \ \ V \ \ k \ > \ IUU 100 90 HO \ j \ \ \ \ > \ \ s i ^ i Sj \ V \ i - 70 70 60 rt 1 \" *- \- \ -\ tO \ ~^ & . \ r- E o , L JL \ v^_ \ v \ ul S"^ . * P V y D 'V/ -S \ N , \ If) f\J - 60 c f on T ir 1 fc EG A SOLID SLABS DIAGRAM 8 to = 7 50 f s =16,000 f s =18,000 n=15 SAFE LOAD ON SOLID CONCRETE SLABS **% OOO 1800 \ \ \ \ r~VA Vv ^\ \ \\ vv Ar 5 Aj- v -\) ^T * M -\ -\ -\[ noo noo 1600 1500 1400 vv \ \ , \ -v\ \ \ \ rVN \ \ v^ t x_ \ N Vv y V Sj \ ^ \ V A y~ V Y V^ ^ _v r 7. 1GOO - 1500 - 1400 1300 1300 \ - \ \ *. \ \ \ L \ v-V \\ \ \ \\ \ \ 5 \ \ ^ \ -A \ \ g 'J : izoo ieoo -\-A \\ A_l _4- A- s \ \ \ \ S s \ \ \ \ \ - 1100 noo \- \ \ rV \ \ V \ \ ^ \ \\ S \ \ \ \ -V 1 \ , \ \ \ i - 1000 1000 \ \ \ J \ \ \ |g \ \ *v~S \ \ \ v 2 \ \ \ \ \ \ \ \ \ \ \ \^ ~ -~ 900 yuu $00 -V- 4 r V~ V -y-^ \A ^r VA -V -V c | jr rV v\ \^ -^ r^J V rV V~ V-N A-j A- ^-S v- ^\ 5 ^ F v~ -\ A -\ \ f\ 3n 700 o o o o TOO V V V \ \ AJJ s -V \ \ V 3 \ S s H y \ I \ 1 \ 1 V \ -\ -V \ \ \ [ \-v- fs - 600 2 If ,rT 600 \ \ \ \ -^y \ ^ \ ^ \ I \ \ \ r^ \ y ^ \ [ \\- \ ^, *"~ \\ \ \ \ V \ V \ s \ \ u \ \ V \ \ \ X k- \ ~ it v \ \ \ \ ] \ \ \ \ \ \ \ ffi ^N A V \ V \ \A : - 500 q- ^ --* k - 300 .E "6 5 o ^ \ \ V V * LA. \ \ \ \ \ \ \ \ \ \-\ V \ 1 3 v \ v\- \ . O \ \ $ \ ., s. \ \ 5 vP s \ \ \ \ \ \ \ \ \ \ \ , \ \ \ \ \ n s v \ \ \ \ \ k_ r \ ^^ \ \ \ n S \ \ ^ V \ \ N , \ \ \ v \ \\ ; k \ N _ w \ \ \ V s \ \ \ ^ \ \ \ , \ \ \ \ \ V \ \ \ 5 - ^ r\f\ in ^f- \ \ \ V \ \ \ \ \ \ \ \ \ , \ \ \ \ S. J\ \ ^oo \ \ *s \ "V - \ \ \ \ \ \ \ \ \ , \ ^ \ \\ \ > r \ $ (0 \ \ \x k \ j \ ^ [ \ \ \ \ \ \ *\ \ \ ^ \ 3 \ \ i \ \ 4- \ \ \ \ \ \ \ \ \ *\ s \ \ \ \ \ IN I \ \ \ !i \ > P \ \ \ ^ A N \ i \ \ V \ \ \s \ \ s \ \ r V \ \\ .0 \ \ \ \ \ v \ \ \ k \ \ \ \ t \ \ . \ \ N, ' ^ V \ 1 \ \ \ \ \ r V \ \ N \ \ \ V \ \ N \ \ \ \ \\ V \ \ \ \ V \ \ \ ^ \ \ \ ^ \ \ \ V \ ^ V \ ^L L_ ^ \ \ \ \ \ V \ s \ \ \ \ \ N ^ \ \ ^ \ \ " \ \ \ \ \ \ \ . V \ \ \ s \ \ \ \ \ \ \ A \N\. 'T - \ I \ \ \ \ \ \ \ i \ A \ ,\ \ \ \ \ C \ \ S5 t i n r> 100 \ \ \ \ \ \. \ \ \ \ \ \ \ \ s s \ \ \ \\\ \ . \ \ \ ^ \ \ \ \ \ \ \ 5 V i V 90 90 \ \ \ \ \ \ $ \ \ \ \ , 1 \ A ^ SI \J \ \ ^ \ \ \ \ \ \ \ \ \ \ \ \ \ \\\ 5 80 80 i s , L L L V \ \ \ \ \ \ \ \ \ \ \ \ A \ \ ^ r-V-*r 5 70 70 \ \ . \ \ \ \ \ , ^ \ \ \ S\\ \ . \ \ \ ^ \ \ \ \ \ \ \ s\\ y - GO GO \ \ \ \ \ \ \ \ \ \ \ \ \ ,l\ V \ (5 M- \ \ \ \ \ \ \ \ \ \ , \ \ \ ^ \ \ ^ \\\ cD \ \ \ \ \ \ \ \ \ \ \ \ v \ \ Sy \ J \\\s F \ \ \ v \ \ \ \ \ \ \ \ \ \ \ \ \\\\ i " | V \ \ \ \ \ \ \ \ \ \ \ ^ ' S \ \\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\\K - 100 SO 80 \ 1 V \ i \ \ \ \ \ \ \ \ -- S \ \ \ \ \ \ \\NN 100 ^ - 80 70 60 rO ~v m ^ 1 v h- -\- N^ ^ y v t: k j\- in k~ i AT y L J _I 1 i - - 70 ^- 60 o u S P< >r 1 in i r e e h SOLID SLABS DIAGRAM 10 SLABS CO j j II r 40 30 10 XZSffSXSZZ'SSSSl'SSXSSSi'SK^SSSZS'SSSSi'StXZ LULL ~fh I U- &. t 8? 00 \r\ Span in feel* 10 DIAGRAM 11 SOLID SLABS BENDING MCMENt- 'FOR SLABS :; ' : SOLID SLABS DIAGRAM 12 f c =650 MOMEOT * OP kfcSlSTAWCE AttD STEEL REQUIRED f s =16,000 FOR n=15 SOLID CONCRETE SLABS Area of steel in sq. in. per ft width DIAGRAM 13 SOLID SLABS MOMENT OF RESIST AN CE> AiNLX ST-EET^ -RfcQtf HED f c =650 'FOR' f 8 = 18,000 SOLID CONCRETE SLABS n = 15 Area of steel in sq. m. per ft width or s ab SOLID SLABS DIAGRAM 14 f c =700 f a =16,000 n=15 AND STEEL REQUIRED ' 1 SOLID CONCRETE SLABS Area of steel in sain, per ft width of felab DIAGRAM 15 SOLID SLABS MOMENT OF RESISTANCE AND 3TELT,. REQUEUED "" SOLID CONCRETE SLABS f s =18,000 n = 15 Area of steel in sq. in. per ft width of slab SOLID SLABS DIAGRAM 16 f c = 750 f s =16,0 n=15 Or RESISTANCE AND STEEL REQUIRED "-FOR SOLID CONCRETE SLABS Area of steel in sq.in.perft.widthof slab 22 DIAGRAM 17 SOLID SLABS MOMENT OF RESISTANCE* AWD : 8TEE ''REQUIRED f e =750 FOR f. = 18,C SOLID CONCRETE SLABS n = 15 Area of steel in sa in, oer ft. width o SOLID SLABS TABLE 1 SPACING OF RODS IN SLABS ROUND RODS Diam- eter (inches) Sectional area of steel per foot of slab when spaced as follows: 2 in. 2Y 2 in. 3 in. 3^ in. 4 in. 4^ in. 5 in. 5H in. 6 in. 7 in. Sin. 9 in. 10 in. 12 in. K Ke H Ke H Me *A 1 X< % l *A* H We 1 1 H i H i i M 0.29 0.46 0.66 0.90 0.23 0.36 0.53 0.72 0.94 0.20 0.31 0.44 0.60 0.78 0.99 0.17 0.26 0.38 0.51 0.67 0.85 0.15 0.23 0.33 0.45 0.59 0.75 0.92 0.13 0.20 0.29 0.40 0.52 0.66 0.82 0.99 0.12 0.18 0.26 0.36 0.47 0.60 0.74 0.89 0.17 0.24 0.33 0.43 0.54 0.67 0.81 0.96 0.15 0.22 0.30 0.39 0.50 0.61 0.74 0.88 0.13 0.19 0.26 0.34 0.43 0.53 0.64 0.76 0.89 0.17 0.23 0.29 0.37 0.46 0.56 0.66 0.78 0.90 0.15 0.20 0.26 0.33 0.41 0.49 0.59 0.69 0.80 0.92 0.13 0.18 0.24 0.30 0.37 0.45 0.53 0.62 0.72 0.83 0.94 0.15 0.20 0.25 0.31 0.37 0.44 0.52 0.60 0.69 0.78 0.99 1.23 1.48 ,.77 1.18 1.49 1.84 1.19 1.47 1.78 1.23 1.48 1.77 1.05 1.27 1.51 1.78 2.23! 2.65 3.11 3.61 1.11 1.32 1.56 1.80 2.12 2.48 2.88 3.31 3.77 1.18 1.38 1.60 1.84 1.06 1.24 1.44 1.66 1.88 2.07 2.40 2.76 3.14 3.98 1.13 1.31 1.51 1.71 .04 .20 .38 .57 .99 2.06 2.37 2.69 3.41 1.03 1.18 1.35 1.70 4.14 4.71 2.07 2.36 2.98 3.68 1.03" 1.18 1.49 1.84 2.23 2.65 2.09 2.65 3.27 3.96 1.05 1.33 1.64 1.98 4.77 2.39 2.95 3.56 2.17 2.68 3.24 3.86 1.19 1.47 1.78 4.91 4.21 2.45 2.97 3.53 2.10 2:55 3.03 5.09 4.45 5.30 4.71 4.24 2.36 2.12 SQUARE RODS Di- men- sion (inches) Sectional area of steel per foot of slab when spaced as follows: 2 in. 2M in. 3 in. 3H in. 4 in. 4M in. 5 in. 5H in. 6 in. 7 in. 8 in. 9 in. 10 in. 12 in. K -6 ^ Me K Ke ^ *Ha % l 6 % % 1 i H i K 1 ^8 1 H 0.37 0.59 0.84 Iti6 1.50 1.90 0.30 0.47 0.67 0.92 0.25 0.39 0.56 0.77 0.21 0.33 0.48 0.66 0.86 0.19 0.29 0.42 0.57 0.75 0.95 0.17 0.26 0.37 0.51 0.67 0.84 0.15 0.23 0.34 0.46 0.60 0.76 0.13 0.21 0.31 0.42 0.55 0.69 0.12 0.19 0.28 0.38 0.50 0.63 0.17 0.24 0.33 0.43 0.54 0.15 0.21 0.29 0.37 0.47 0.13 0.19 0.25 0.33 0.42 0.17 0.23 0.30 0.38 0.14 0.19 0.25 0.32 1.20 1.52 1.00 1.27 1.08 2.34 2.84 3.37 3.96 1.87 1.56 1.99 1.34 1.62 1.93 1.17 '1.42 1.69 1.98 1.04 1.33 1.50 1.76 0.94 0.85 0.78 0.94 0.67 0.81 0.96 0.59 0.71 0.84 0.99 0.52 0.66 0.75 0.88 0.47 0.57 0.67 0.79 0.92 0.39 0.47 0.56 0.66 0.77 0.88 2.27 2.70 3.17 3.67 1.13 1.35 1.58 1.84 1.03 1.23 1.44 .1.67 1.92 2.25 2.64 3.06 3.52 1.12 1.32 1.53 1.76 2.26 2.62 3.01 3.43 4.34 5.36 6.48 1.13 1.31 1.51 1.71 4.59 5.27 6.00 2.30 2.64 3.00 3.80 2.04 2.34 2.67 3.37 1.15 1.32 1.50 1.89 l.t)2 1.17 1.33 1.69 4.22 4.80 6.08 2.11 2.40 3.04 3.75 1.05 1.20 1.52 1.87 4.00 5.06 6.25 2.18 2.76 3.41 2.00 2.53 3.12 3.78 1.00 1.27 1.56 1.89 2.17 2.68 3.24 3.86 4.69 5.67 6.75 4.17 5.04 6.00 2.34 2.84 3.37 2.08 2.52 3.00 .... .... 4.54 5.40 4.12 4.91 2.27 2.70 4.50 2.25 TABLE 2 RIBBED SLABS SAFE LOAD OH RIBBED SLASS : : c = 650 f s =16,000 n=15 urn 'Si; ~ N-i CCXXCCM-CNO cc 05 OS C <-( XXOSCO iCN OS O O rH i-> 01 CO O01X XCOCOCSC O CO * OJ OS 1C 01 X^CSO-HOO COOlXCOCt*l^ i-I^O t-XOSOO OSOtHOlOlCOrf OSi-iOl-*CCOCO OCNCOCCOI^X iCCOO) ^-^- ^-^-C>C COlOl^HCSXt^ OS <-i <-i X C O CO t^XCS^Ol -(CO>Ct^XOOI f X ~ n '* Gl ~ < OS <-i <-i X C O CO C Ol OS t^ O ^ t^ OSi-H O5 CO CO O Tf N. O 01CO 1-1 01 01 CO CO CO * OIOICO OIOICOCO'* OlOlCOCO'TtO CO O OS CO OS XOrHCO-^Ol>. rHCOOXOlMCO ^t^OCOOXrH "2 8 iCXrH O C >C i-H O5 O T}H rHXCOOCOt^OS OOC^O5rHOS XOSrH O5i-HCO>COXO COiCXi-HCOCl> OOCOOO5CO>C 1 SXO-N S^gSg.^ SS^^gc?^ SSSS^SS ^ tj 3 ONOCOrH Ot^COOOCOX XiCOCl>O5O OrHOCOOrnX xorHco>c eocxocoici> t^i-ncxrHTfx XO-^rHO CI> 1C X I-H * t^ O CO I-H 1C OS Tf t^ rH 1C ONXCOXCOX 3 ttj'C I-S 1 2 o OS C^TfOOSrH XCVJOO5COOO iCi-nOi-HiCO 1 ^ C^IOS^C^X^O rH I-H I-H I-H (N i-H (N (N IM CO CO ^* C >C O t^ -V '13 fella o OS COO t>CO>CCOi-H X rH (M O5 X T}< rj* rji CO OS 1C O X 1> O >C rH O O t O XO COOXi-H-^l O'OOSiMOO'^ X-^O3COiCO O CO r-H X >C I-H X rH rHrHi-<(MOl (N C >C O t l> ^ a I 03 | ^ ^ - X COOOS i-HXrtrf(MOO li c~ o 1 03 5 rJH Tfl >C rHCONOi-H O -^l O I-H OS 1C rt< U7iO5XO(NOX O * OS C (N XOM lOCOOO OrHOrHlCOiC >C(NC5t^COO5iC kCrfCO^i-H rt^H rHC rH O 1-H t^ (N OXOTfrHXlC O rH Ol IM I-H rH !-HCOt^X O t, fe^ -2l||S 1C X CO I-H OS rH N. (M O COCOOXOSXi-H OOOirHrH Xt^OS OCOO rHOOS-^X COOt-iMX-^i-H iCiCCOCOi-H t>.O:rH . . . I s O Si ^ rH <*COIC (NO*-H(NCO (NOJOSOOCOO CONTtC O 1C O N. X tX a ^ (MXO XC(NiCX O X N O 11 ^ .X 1 s - OS -0 a, 0)^3 2 oJ 3 "^ >< >,> JO 03 .2 ft! ^ ; : ~ S . ^>C>COO iCiCOOt^OOX "COOt>.XXOS OOt^XXOSO 03 fl 1 e ll j.c ^H- OS-^Xt-OS XOrHOOSOlM i-HOOCOi-HOOS XXt>-(MCO'!J ^t^OSOrHCO-* OXr-iCOiCOt^- OOSC^JiCt^OSrH O V W 0) N c OQ = 3 -.- .3 If 1 1 11 !"|I' ? . . . rHTfOXO XrHiCXrHiCX * C5 -^ O3 CO X (M i- 1 1- -COO5*C COOSiCNXr^O CO OS "O (M X rJH O CO C3 O l^X l^t^XOSOiOrH XXOSOOr-lN OSOSOrHrHlMCO ll >~ US' d 3 n jfc|c ~ COOt" OOiCrHO OS CO t- 1>- O CO i-H b Tf O 1C t- l>- O OiOC-5cO C OOSCOOO3IMIC OiCOSCOt^-rHiC rHrHl-H l-H i-H rH rH (N (M (N rH rH (N (N (N CO CO IM (N (N CO CO -* Tf* ;s.o *o II ^ ^ 02 X. CW M tH % & - NNCO NNCOCO^ NNCOCO^^^ NNCOCO^^U, NNCOCO^iC ^5 "o o Q - " s * CO X O Ol rH pt.fe * H- 26 TABLE 4 SAFE LOAD ON f e 3 gl 5MCX~Tji b- CO O CO t^ t^ 00 2lil eoicx coco osb->c -^^ ^NCJdCO S SSSfggT rH rH rH CM(N(MCCCO (N "3 O ifl O O N CO CO CO O O Tf b- t 1C T}* rH X >C rH 00 rjt CO^lTti C OOb- O >C 1C rH CO CO 1C X O T}< C<> C5 O CO COTjfiCOOb-X * O5 O 00 C) CO COc t~ J OOCO CO OC >C CO OS CO i 'OO^Ot** i-l I-H CM COCOTjC CS t^ CO 00 b-OOO rJ.Tj<(NO5t^ CM <*< O TjfCMCSt^ Nt^CO Tj O.Ct*i-iO t>- O CO C 1-- CS i-( 00 I-H Tj< b OS CM ^< O C (N t- rfi C^iCOOOCO OCCr^-^HiCOOCN ^rt rt cN-COQOCOt^ CCi-HXCi-it^T)' (Meow*-* 1C "3 CO -* ^ it} CO CO b- CS COe -b. ^H C rHX^CiOXCO XiCMb-O^CO C-^rHb-CSCNCO ! TtCCO XO(NCOC CO O X O CO C 00 b-r-irjoO. O OJ T* *O OO rH i < O 00 ^ Ci "*t* O5 *O ^ *O *> Ci> 00 OOOrHCOCO^ OCO^iCb-000 CO 1C 00 CO T}I g 5 CO * O 1C 00 CO 1C O CO OS rH CO OS b" CO GO OS b- 1C rH CO GO OS 00 O rH CO Tt< 1C b- rH CO CO 00 OS rH CO T}< b- O CO CO 00 O ,0 S Tf< 1C 00 OO CD ^ OS 1C O b- 1C >H t> rH rH CO rH CO CO O CO CO rH b- OOO3O OS <-< CO ^ CO 00 OS CO CO OO rH CO 1C b- b-O-^b-OCOiC 1 5 * -S * CO r^CO ^^ s5 8 j s _, ., CO OOCOb-COrH b- CO b- 00 O CO 1C 00 * rH * CO rH 00 O OS CO rH CO CO 03 XOrHCOiC CO CO 00 O CO 1C b- OO CO CO OS CO 1C b- Tf< OO CO 00 CO CO OS rQ,O 33 !i 1 S COCOCOrHCO CO b- CO CO 00 1C CO OO CO CO CO O 1C 00 rHOCDrHrHOCO OCO-^COCO CO OS CO 1C b- O CO CO b- rH 1C OS CO 1C OSiCOcOrHCOO >> TJ^a Sslla ss 0) OS rH 00 b* b- 00 CO CO 00 rH OS 00 00 OS CO rH O 1C CO rH b CO 00 O rH CO O O5 rHCOlCb-O 00 rH 1C b- O CO CO lCOlCO5COb-O CO OO 1C rH CO CO CO - 03 c3 fg ii 8 * M a 00 1C rHCOCOOSCO Tf* CO O rH CO CO rH CO CO O O CO 1C CO O5 CO CO O rH rH 1C ^ -HrHrnScO CO CO CO CO CO CO ^ CO CO CO ^ * 1C 1C CO * 1C 1C CD CO b- 2 2.2 Si i 1 b- COCO t^rHb-COCO O CO ^ O5 CO CO rH CO J> 00 CO rH O5 1C CO 1C CO O5 00 1C CO GOO ^ b- OS CO 1C CO b rH ^ 00 CO CO rH b- CO OS ^ 00 CO O 00 "^ CO O t^ CO rH rH rH rH CO CO CO CO CO CO CO * Tf CO CO Tt* CO 1C 1C CO *# Tj< 1C CD b- b- 00 "0*0 5 " "s-a 1 . ih CO OOOO COCOCOCOCO OS 00 Tj< CO ^ CO O CO 1C -^ CO O * 1C TftCDiCOCS^i OOOCO COOSCOiCOO 1C O 1C OS CO b- CO 1C CO OS 1C rH CO rH IC-^COCOOSb- rH rHrHCOCOCO CO CO CO CO * M* 1C CO Tt< Tj< 1C CO CO b- * 1C CO b- b- 00 _fe S3 *t 2 S M ii 1C CO rH CD OSOCOCOiC ^ O CO b- 1C rH CO CO CO rH Tt< 1C 1C rt< COCOCOO OJrHCO OOCOiCOOCO OS 1C O * OS T}H OS O 00 CO CO OS 1C rH rH CO CO CO rHrH rH CO CO CO CO CO CO Tj< * TJH 1C 1C * Tt< 1C CD CO b- 00 1C CO b- 00 S cS g 1 si SI * - rH iCb-CO b-COOOOCO 00 CO CO <* 00 CO O CDiCiCOOOOb- rt*iCO O CO 1C rHiCOSCOb- CO O CO rH CO CO 00 CO 1C Tt< CO OS CO OSrHCO .... rHrHrH COCOCOCOCO CO ^ Tt* 1C 1C CO CO ** 1C CO b- b- 00 iCb-00 -22 ft fp 11 a 1 CO COOOrH rHCOb-rHCO CO CO CO CD OS CO OS O <* 00 Tj* OSO3 PH S r^ rHrHrH CO CO CO CO Tj( CO * 1C 1C CO b- b- lCCOb-00 OOO CP CJ 8 CO rHrHCO CO CO CO Tj< 1C Tj< 1C CO b- b- 00 CDb-00 .... 00 O a> a ,_, OCDCO rHOOOCO-* OOrHOSCO--- J* OJ ' M $ rH^CO CO^^icS ^CDb^OO t2oO rS' S o 'TJ-C ^S tn K" 1 2 J a' S ^ a 1 COOCOCOOO OCDCOOSiCrHb. COCOOOiCrHb-CO COOO^Ob-COOS . TjHiCiCcOCO 1C 1C CO CO t^ 00 00 1C CO CD b- GO 00 OJ CO CO b 00 00 OS OS >> >> ^^ s S S 3 3 C3 i _L a; co as Sfejj , . . . OOb-iCCOO CO CO Tj< CO O b. 1C CO CO * 00 O5 00 1C * b- b- CO rH Tj) CO OSOrHCOCO rH CO * 1C CO CO b- CO r}H CD t>. GO OS O CO 1C t^ OS rH CO CO 'o'o G U "* ^ JSJS CO J, II 11| rHOOCOiCiC OS O b- CO b- CO OS 00 rH CO CO CO OS O OS CO rH CO O b. Oi OrHCOlCb- 1- 5 OS rH Tj< CD OS rH rH CD O * b- O *< b- CO OS * OS CO b- .S S S S IS* 33 || Or fls* I SCOCO ObCOOSiC CO OS 1C CO 00 * O CO OS 1C CO 00 "* O CO OS CO CO 00 * rH u; CO COCOb-b-00 b- b- 00 OS OS O rH GO 00 OS O O rH CO OS OS O rH rH CO CO II >. >> 3^ FH *Q) s ^!s r- CDrHCO ICrHCOrHb. b- 00 CO rH b- CO b- "* b- OS OS CO CO b- OS 1C 00 O rH OS CO tiCiC CDbb-OOOO t^OOOSOOrHrH OO O3 O rH CO CO CO OO O rH CO Tj< rf< 1C 3 3 e s 1-1 02 c a ft .- ".9 OOO OOOOO OOOl-lrHrHrH O O rH rH rH rH rH O rH rH rH rH rH rH II I Is ({I 1 COOOi OOOSrHCOb. CO CO 1C rH 00 1C CO CO -* CO 00 O CO CO CO * 1C b- 00 CO CO-*"* COb-OSOrH O CO Tt< CO b- OS rH rf< b- CO 10 b- OS 00 CO CD OS CO 1C 00 rHrH rHrHrHrHrHrHCO rHrHCOCOCOCOCO rHC>lCOCOCOCOCO ;s;s "0*0 M M S " |M -3 COCOCO COCOCOCOM* COCOCOCO^TftiC COCOCOCO^rtiC COCOCOCO^'*1C ft ft tn CQ II O O H 3 * ? 00 O CO II H 28 TABLE 6 RIBBED SLABS SAFE LOAD ON *IBBEJ> SLABS f c =700 f, = 18,000 oad. Total safe load in pounds per square foot including weight of floor (dead and live) on M - ~~ For M - ~. add 20% to ! g rH TO C O 10 -*t> CS CM * t^ rHW* CO rH 00 Tf O "5 rH t- CO t* rH CM * CM QOOSO OS i-l CM <* O t OS CM O t> O N ^ 5O ^H rH i-l ^H ^H ^i i-> i-l ^ i-l CM CM CM CM O>t^"5CM-i OObOTO^T}t tt^O TJICOOOOCM * r^ O TO 00 O 00 CM t^ ^ >O CO t* 00 OS CM "3 *> OS ^H TO O Tj<00-HCM O TO ifl OS t^ I-H ^ OS OS D ^H O -H iO 00 O * IO CM OS CC CM X Tt* TO * * 1C CO CO t- CO USOl^'tTO OXi-iOSCOTOi^ O -*t>.OSCMO CMW^TfXCMCO rH ,-H i-H T-I CM CM CM CM M TO TO T}< * SOXOCOi-n t^CMXTOCi TO Tf Tf it} it} O'O^'CTO'tf' OS t* C CM OS CO TO rfi iO CO CO t^ CMOO-HTO TO-HXCMTO-^t* COOSCMOX O O Tj< OS TO t^ 1-1 >^>-lCMCMCM CM TO TO TO Tf ^ O CO IO O "3 i O CO CC t* t* CM <-> O CO TOTOCMCt^O & IO CO 1-- t^ X TOIOOS r-ICMCM 1-1 os CM c os t XTOU3 OSOOOX CO CO rf< t* OC Oi CM OCMX i-H^t* TOXCMt^^H t & 1-1 1^ TO OS CO ^<-COOSiO OSCCMX-*O TO OS C CM X * O TO OS CO CM X * .-i CCO cOOt-t^X t^ t* X OS OS 1-1 XXOSOO iCM OS OS O "H rH CM TO 000 00000 00-1,-lrHrHrH Q rH rH rH rH rH rH O rH rH rH rH rH rH tXOrHTO rHTOCOX >CMCMCMX Ol < i-i CM CM CM TO : I O N. T} CJ CO O )TtC 16. 24. ter of joists and divid ter of joists and divid ce center to ce center to the d the d mns mns col er spacing of joists multiply the values in these er spacing of joists multiply the values in these oth For For 29 RIBBED SLABS TABLE 7 LPADPJJF RIBBED SLABS ' fc = 750 ' 24." ' co OrH 00 CO CO OS Tt* OS IO O iO OS CN CO iO O COCOCOcOHHCOO OSO OOOCNCOIOCOOO CNHHCOOSrHCOiO lOOOrHrfb-OCO . oo OOOCOlO rH CN rH OS b- * CN OOb-^OiOOCO lO rf 00 CO "0 GO OS b-OSOrH O CN HH IO b- OS rH CO CO OS CN Tfl b- OS b rH Tjl 00 rH HH b- 1 CD CN sj S -g ! s OS CO CO O b GO CD CN t> rH Tf OS 00 b- H^ OS CO b* 00 OS rH b IO OS HH IO COOCN^tiiO COCOO5rHTtO CD CO TfH rH O O CN rH 00 CN O CO rH HH OS >O * CO CO OOO HHCDOSCNIO cNCDOH^COcNCO OCDcNb-COOOCO OOCOCOrHCOiOCN rH THrHrHCNCN CM CN CO CO CO Ttl Ttl CO CO HH H/ O IO CO CO Tt< >O CD CO b- 00 f S II 8 fe "S J a ^ OS CO CO OOOSOOOSO iO O rH CO CO OS CO Tf CO OS CN CN CN 00 rJH b- O O IN rH b-OSrH lOOOrHTtlOO Tf OS HH CO CN CO rH CO O CD CO O5 IO O CN rH O 00 CO Tf< rH rHrHCNCNCN CNCNCOCOHHHHIO COTf*TjO HHH^cOb-H^rHr)< COOCOOOlO H " rHrH rHCNCNCNCO O COHHlO'OCCb-b- HHlOCOb-OO 1'S t ^i 02 ; co 8CN OS OOSCOiOHi O CO OCO ,-lrHTH CN CN CN CO CO COCOHlTtiiO'OCD H^iOiOCDb-CO lOCDb-OO rHrHrH CN CN CO CO TjH CO ^ ** IO CO CO b- Tf >O CD b- GO CO b- CO "3 fl II SH a'l * t s rHQSiO CNCNOrHCN lOOO^oOOOiOOO CNCOOO CN>O---- COIOOS COrHCOrHCD OOOCOCOOb-^ -*COb-OO O'O rHrHrH O OS rH 2 COCNrH CNCNCDiOCO * CNCOCO lOCDb-COCS b- 2 8,1 1 a-; V : . COOCOCNGO O CO CN OS iO rH b- CDCNOOiOrHb-CO CNOO^Ob-COOS . . . HHiOiOCOCO iOOCOCOb-OOCO >OCOCOb-OOOOO3 CO CD b- 00 00 OS Oi rj S 'o c ^ ! J 'all? OiOHHrffCO OS OS b- rH CN rH rH O >O 00 00 CO GO O OS GO CO CO CO rfi rH CNCO-tiiOCD CO>Ol--OSOrHCN lOb-Oli-iCO^CD "OCOrHCOiOb-OS c ^- .rt CNCNCN CNCNCNCN CN CN CN CN CN O i co -L .2M 3 8.S "> OH . . H/IGOOCOb- .HOsCOOCOiOOS OSH^TiOOb-O OCNb-CNCNCOCN CN'tt^.CSrH OCNCDOfOCOOS IO rH O rH CD O IO COOCOCOOJlOrH oU 1 1! j "~ OCDCO Ob-COOSiO COCSiOCNOO-^O COOsiOCNGOTjO CO b- O CN * >O b- GO OS ^ W C * M 1-5 rt"* III rHOrH CNCOCOOSiO b-COb-OOJCOO COOSCOCOb-COb- OOOrH0'OO>O TjHiOCO OOOSrHcN't' CN'Ob-OcN'fCO b- O rt< b- O CO CO CNCDrHiOOSCOb- .-HrHrH rH rH rH CN CN CN CN rH CN CN CN CO CO CO CN CN CO CO CO Tt< "* H fl " ~I CN CN CO CN CTsTcO CO T>< CN CN CO CO*-* - :jo ' *>! ^ !a \ I J- T\ w; LM- a *:0> ^f i *|^0 ;0^ I t ab. ^jv] j-. iQ .^J > + i i^n -J. \ l^;|i ;gfi i^^ tii -j (Vj Aj -s\j a: JSP ? IS S)i * 231 SI /" ' lltll ! Drop Construction j ' Cap Construction h Section A-A Bending Moment Coefficients Moment coefficients shown on diagram are to be multiplied by WL. W = wL\ w = total dead and live load in pounds per square foot. L = span center to center of columns for square panels. Values shown above moment coefficients are percentages of numerical sum of moments in one direction across panel. Numerical sum of moments in one direction across panel = 0.0648 WL. Minimum size of drop =0.3L. Minimum diameter of capital = 0.225L. ,,. . [ 0.02L\/w + 1 (t in inches, L in feet) Minimum t = t = total thickness of slab. 32 TABLE 8 FLAT SLAB FLOORS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS INTERIOR SQUARE PANELS DROP CONSTRUCTION f c = 650 for positive moment f c = 750 for negative moment f, n=15 FLAT SLABS Superimposed load = 100 Ib. per sq. ft. Panel size (feet) Capital ttiam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq.ft. Direct Across direct Diagonal 16X16 3' 6" 4' 10" X 4' 10" 6 2K 0.52 14-%" 8-% H-% 1.95 17X17 3' 9" 5' 2*X5' 2" 6j- 2J4 0.56 16-%" 9-% 13-% 2.14 18X18 4' 0" 5' 6"X5' 6" 6^i ovz 0.58 18 %" 10-% 15 % 2.25 19X19 20X20 4' 3" 4' 6" 5' 8"X5' 8" 6' 0"X6' 0" ?i iM 0.62 0.65 21-%" 17-Ke" 11-% 16-% 15 K * 2.38 2.53 21 X21 4' 9" 6' 4"X6' 4" 8 25^ 0.69 20-Ke* 10 -K 16-K * 2.70 22X22 5' 0" 6' 8"X6' 8" O I/ 0.71 21 -He* 12-H 16-K * 2.81 23X23 24X24 5' 3" 5' 6" 7' 0"X7' 0" 7' 4"X7' 4" 9^ 3M 0.76 0.78 23-Ke" 26-K6* 13-K 14- K 18-K * 21-K * 3.06 3 . 30 25X25 5' 9" 7' 6"X7' 6" 9K 3J 0.82 29-K6* 16-K 23 K * 3.44 26X26 6'0" 7' 10" X 7' 10" 9% 3^ 0.84 31-Ke* 17-K 25-K * 3.55 Superimposed load = 150 Ib. per sq. ft. Panel size (feet) Capital diam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6" 4' 10" X 4' 10" 6 2% 0.52 18-%" 10-%" 15-% 2.54 17X17 3' 9" 5' 2"X5' 2" 6J^ 2 3 4 0.56 20-%" 16-% 2.56 18X 18 4' 0" 5' 6"X5' 6" gax 3K 0.59 23-%" 14-%" 19 % 2.90 19X19 4' 3" 5' 8"X5' 8" 7H 0.63 26-%" 14-%" 20-% 3.00 20X20 21X21 4' 6" 4' 9" 6' 0"X6' 0" 6' 4*X6' 4" J* 3H 3M 0.65 0.69 22-Ke" 12-He* 24-Ke" 13-He* 17-K 20 K 3.27 3.52 22X22 5' 0" 6' 8*X6' 8" 8J<4 4 0.72 26-K6* 14-Ke" 22 K 3.62 23X23 5' 3" 7' 0"X7' 0" 8^i 4 0.76 29 -He* 16-He* 23-K 3.78 24X24 5' 6" 7' 4"X7' 4" & 0.78 31-Ke' 18-He* 26-K 3.98 25X25 5' 9" 7' 6"X7' 6" 9M 4j| 0.83 35 Ke" 29- K 4.27 26X26 6'0" 7' 10" X 7' 10" 9*i 4% 0.85 39-Ke* 21-He* 31-K 4.45 Superimposed load = 200 Ib. per sq. ft. Round steel rods in each band Panel size (feet) Capital diam- eter. Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 17X17 3' 6" 3' 9* 4' 10" X 4' 10" 5' 2"X5' 2" i 3 0.58 0.59 20-% 24-% 11-%" 13-%" 17-%" 19-%" 2.83 3.07 18X18 4' 0* 5' 6"X5' 6" 7J4 3?i 0.63 26-% 15-%" 22-%" 3.45 19 X 19 4' 3" 5' 8"X5' 8" 7H 4 0.66 30-% 16-%" 25-%" 3.50 20X20 4' 6" 6' 0"X6' 0" 8 4 0.70 25- K * 13-Ke* 20-Ke* 3.70 21X21 22X22 4' 9" 5'0" 6' 4"X6' 4" 6' 8"X6' 8" m A 1 ^ 0.72 0.76 27- K * 30 -H * 16-Ke* 22-Ke" 25-K 6* 3.87 4.15 23X23 5' 3" V 0"X7' 0" 9 J4 4- ^> 0.81 33- K * 18-He* 26-K.6" 4.26 24X24 5' 6" V 4"X7' 4" 9M 5 0.83 36-K * 20-K6* 30-Ke" 4.45 25X25 26X26 5' 9" . 6' 0" 7' 6"X7' 6* 7' 10" X 7' 10" 10 5 0.87 0.92 39 -He" 43-K6* 22-Ke* 23-Ke* 31-He* 4.59 4.92 33 FLAT SLABS TABLE 8 FLAT SLAB FLOORS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS INTERIOR SQUARE PANELS DROP CONSTRUCTION f c = 50 for positive moment f c = 750 for negative moment f s = 16,000 n=15 Superimposed load = 250 Ib. per sq. ft. Round steel rods in each band Panel size (feet) Capital diam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6" 4' 10" X 4' 10" 7 3K 0.61 22-%" 12-%" 18-% 3.05 17X17 3' 9" 5' 2"X5' 2" 7M 3^ 0.65 25-%" 14-%" 20 % 3.32 18X18 4'0" 5' 6"X5' 6" 4 0.68 28-%" 17-%" 23 % 3.55 19X19 4' 3" 5' 8"X5' 8" SjJ-i" 0.72 23- KG" 20- K 3.77 20X20 4' 6" 6' 0"X6' 0" 8H 4H 0.74 27- fi 6 " 14-Kc" 22-K 4.00 21X21 22X22 4' 9" 5'0* 6' 4"X6' 4" 6' 8"X6' 8" 9 4% 0.79 0.83 30-K 6 " 33-Me" 16-Ko" 18-Kc" 23- K 26-K 4.15 4.42 23X23 5' S" 7' 0"X7' 0" 10 5 0.87 35-Kc" 20-Kc" 29 K 4.60 24X24 5' 6" 7' 4"X7' 4" 5 0.91 39-Kc" 22-Kc" 31-K 4.81 25X25 5' 9" 7' 6"X7' 6" 11 5/4 0.96 43-Kc" 23-Kc" 36-K 5.21 26X26 6'0" 7' 10" X 7' 10" UK 5% 0.98 47-Kc" 26-K 6 " 38-K 5.39 Superimposed load = 300 Ib. per sq. ft. Panel size (feet) Capital diam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6" 4' 10" X 4' 10" 7K 3% 0.66 25-%" 14-%" 19-%" 3.35 17X17 3' 9" 5' 2"X5' 2" 7% 4 1/ 0.68 29-%" 16-%" 23-%" 3.70 18X18 4' 0" 5' 6" X 5' 6" 4% 0.72 31-%" 18-%" 25-%" 3.83 19X19 4' 3" 5' 8"X5' 8" 8% 434 0.77 14-Kc" 21-Kc 4.07 20X20 4' 6" 6' 0"X6' 0" 9M 4% 0.81 29 ^KG" 16 KG" 23- KG 4.30 21X21 4' 9" 6' 4"X6' 4" 9% 5 0.85 3 1 - K G " 26- KG 4.47 22X22 5' 0" 6' 8"X6' 8" 10 0.88 35-Kc" 20-Kc" 29- K e 4.82 23X23 5' 3" 7' 0"X7 / 0" 10H 5% 0.92 3 6- KG 21-Kc" 30- KG 4.77 24X24 5' 6" 7' 4"X7' 4" 11 6M 0.96 18- M" 26- Yz" 5.25 25X25 5' 9" 7' 6"X7' 6" i iM 6M 1.01 35-^ " 20 Yv " 29 -K" 5.52 26X26 6'0" 7' 10" X 7' 10" 12 7 1.05 39- W* 22-M" 5.77 Superimposed load = 350 Ib. per sq. ft. Panel size (feet) Capital diam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6" 4' 10" X 4' 10" 7% 4% 0.68 27-%" 14-%" 23 %" 3.79 17X17 3' 9" 5' 2"X5' 2" 8 z4 5 0.73 30 %" 16-%" 25-%" 3.91 18X18 4' 0" 5' 6"X5' 6" 8% 5M 0.77 26-Kc 20-Kc" 4.10 19X19 4' 3" 5' 8"X5' 8" 5% 0.82 27- KG 14-Kc" 22-Ke* 4.27 20X20 4' 6" 6' 0"X6' 0" 9% 6 0.86 17-K 6 " 25 KG" 4.55 21X21 4' 9" 6' 4"X6' 4" 10J4 6J4 0.90 34- KG 18-Kc" 4.81 22X22 5' 0" 6' 8"X6' 8" 10% 6% 0.95 36-K 6 30-K 6 " 4.96 23X23 5' 3" 7' 0"X7' 0" \\YL 0.99 40- KG 23 KG" 33-K K " 5.26 24X24 5' 6" 7' 4"X7' 4" 11% 7% 1.04 34- M" 19-M" 28-^" 5.54 25X25 5' 9" 7' 6"X7' 6" 1.09 37 M" 2\-Yz" 30- K" 5.76 26X26 6'0" 7' 10" X r 10" 12% 8H 1.13 41-K" 33-M" 6.07 34 TABLE 9 FLAT SLAB FLOORS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS INTERIOR SQUARE PANELS CAP CONSTRUCTION f c = 650 for positive moment f e = 750 for negative moment f s = 16,000 n=15 FLAT SLABS Superimposed load = 100 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l Across Diagonal each way 16X16 3' 6* 6M 0.542 17-%* 4-%* Q a/ it 13-%* 2.54 17X17 3' 9* Q^A, . 563 20-%* 4-%* n-%" 15-%* 2.66 18X18 4' 0* 7 0.584 23 %* e 3 / tt 12-%* 2.84 19X19 4' 3* 7^4 0.625 25-%* 5-%* 13- %* 19-%* 3.04 20X20 21X21 4' 6* 4' 9* 8 0.667 0.688 24-Ke" 4 Ke*. 11-Ke" 16-Ke" 18-Ke" 3.24 3.45 22X22 5'0* 8% 0.730 26-Ke" 5 Ke* 14-Ke" 19-Ke" 3.62 23X23 24X24 5' 3* 5' 6* 9 0.750 0.792 29 7^e* 32-Ke" 4-Ke* 15-7^6* 17-Ke* 23-Ke* 3.78 3.96 25X25 5' 9* 9?i 0.813 35-Ke" 5 Ke* 18-Ke" 26-Ke" 4.17 26X26 6'0* 10 0.833 39-Ke* 5 Ke 21-Ke* 29-Ke" 4.36 Superimposed load = 150 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l Across Diagonal each way 16X16 3' 6 7 0.583 20-%* 4-%* n-%* 14-%* 2.83 17X17 3' 9 0.605 23-%* 4-%* 12 %* 17_i^ 2.98 18X18 4' 7% 0.646 26-%* 4%* 14-%* 19 %* 3.14 19X19 4' 3 8M 0.688 21 Ke 4-Ke" 12-Ke" 15-Ke* 3.27 20X20 21X21 22X22 4' 6 4' 9 5' I/ 9 Ql/ 0.709 0.750 0.792 mi 29- K e 4-Ke" 6-Ke" 5-Ke" 13-Ke" 15-Ke" 16-Ke" 18-Ke" 20-Ke" 21-Ke* 3.48 3.78 3.91 23X23 24X24 25X25 26X26 5' 3 5' 6 5' 9 6'0* Q3X IOH 11 0.813 . 854 0.875 0.917 32- K e 35-Ke 39-Ke 42-Ke 5-Ke" 6-Ke" 5 Ke" 6 Ke" 18 Ke* 19-Ke* 21-Ke" 24-Ke" 24 -Ke" 26-Ke* 28-Ke" 31-Ke* 4.16 4.34 4.51 4.76 Superimposed load = 200 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l each way Across direct Diagonal 16X16 17X17 3' 6* 3' 9* JM 0.625 0.667 22-%* 1 5-%* 25 %* 5-%* 12 %* 14-%* 19-%* 3.12 3.29 18X18 4' 0* 8^ 0.708 29-%* 5-%* 16-%* 21-%* 3.49 19X19 4' 3* 9 0.750 23 Ke 5-Ke" 13-Kfi* 17-Ke" 3.66 20X20 21X21 4' 6* 4' 9* 10 2 0.791 26 Ke 0.833 29-Ke 4-Ke" 5-Ke* 14-Ke" 16-Ke" 19-Ke" 21-Ke" 3.88 4.04 22X22 5'0* 10^ 0.875 ! 32-Ke 4-Ke" 17-Ke" 23-Ke* 4.20 23X23 5' 3* \\y\ 0.938 34-Ke 5-Ke* 19 Ke" 25-Ke" 4.37 24X24 5' 6* 12 1.000 j SS-Tie 4-Ke" 21-Ke" 28-7^6* 4.64 25X25 5' 9* 12% 1.063 41-Ke 4~Ke* 23-Ke* 4.78 26X26 6'0* 13J4 1.142 47~Ke i 5-Ke" 26 Ke" 34 -Ke" 5.23 35 FLAT SLABS TABLE 9 FLAT SLAB FLOORS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS INTERIOR SQUARE PANELS CAP CONSTRUCTION f c =650 for positive moment f c =750 for negative moment f s = 16,000 n = 15 Superimposed load = 250 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l each way Across direct Diagonal 16X16 3' 6" 8% 0.730 21-% 6-%" n-%" 16-%" 3.00 17X17 3' 9" 0.771 26-% 4-%" 14 %" 19%" 3 30 18X18 4/0" 10 0.833 29-% 4-%" 16-%" 23-%" 3.61 19X19 20X20 4' 3" 4' 6" }?| 0.896 0.959 23- H " 26 -H " 4-He" 4-He" 13-Ke" 15-He" 17- He" 19 He" 3.64 3.91 21X21 22X22 23X23 24X24 25X25 26X26 4 / 9 // 5' 0" 5' 3" 5' 6" 5' 9" 6' 0" 12 13 15 g 4 .000 .083 .146 .188 .250 .313 28-He" 31-He" 34-He" 38-He" 41 -He" 45-Ke* 2-Ke" 4-He" 5-He" 4-He^ 4-He" 15- He" 17-He" 19-He" 21 He" 23-He" 25-He" 20-He" 23 He" 25-He" 28-He" 30-He" 33-He" 3.84 4.16 4.37 4.65 4.81 5.03 Superimposed load = 300 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct over Direct column, add'l each way Across direct Diagonal ! 16X16 3' 6" 10 0.833 23-%" 3-%" 13-%" 17-%" 3.17 17X17 3' 9" 10% 0.896 26-%" 2-%" 14-%" 19-%" 3.27 18X18 4' 0" 11 J^ 0.958 29-%" 3-%" 16-%" 21 %" 3 45 19X19 4' 3" 12M .042 32-%" 2-%" 23-%" 3.58 20X20 21X21 4 / 6 " 4' 9'^ 13 14 .083 .174 27 He" 29 He" 3-He" 3 He" 15-He" 16-He" 19- He" 21-He" 3.88 4.02 . 22X22 23X23 5'0" 5' 3" 15 16 .250 .333 32- He" 34 He" 2-He" 4-He" IB-He" 19 He" 23- He" 25-He" 4.20 4.33 24X24 25X25 26X26 5' 6" 5' 9" 6'Q" 17 2 18 .375 .417 .500 38-He" 42-He" 46-He" 3 He" 21-He" 24 -He" 25-He" 28-He" 31-He" 30-He" 4.64 4.76 4.84 Superimposed load = 350 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l each way Across direct Diagonal 16X16 3' 6" HM 0.958 23-%" 2-%" 13-%" 17 %" 3.16 17X17 ! 3' 9" 12K 1.021 26-%" 2-%" 14-%" 19-%" 3.23 18X18 4' 0" 13 1.083 29 %" 3 %" 16-%" 21-%" 3.45 19X19 4' 3" 13% 1.146 33 %" 3-%" 18-%" 24-%" 3.74 20X20 21X21 22X22 23X23 24X24 4' 6" 4' 9" 5' 0" 5' 3" 5' 6" - 14% 15% 16% 17% 18% 1.230 1.313 1.396 1.480 1.563 27-He" 29-He" 32-He" 35-He" 37-He" 2-He" 3-He" - 3-He HK 3- He 14^He" 18~8 f6 " 20-He" 21-He" 19-He" 21- He" 23-He" 26-He" 27-He" 3.85 4.02 4.22 4.48 4.50 25X25 5' 9" 19% 1.646 41-He" 30-He" 4.79 26X26 6'0" 20% 1.730 45-He" 3-Ke" 25-He" 33-Ke" 5.00 36 FLAT SLAB FLOORS NEW YORK CITY BUILDING CODE INTERIOR SQUARE PANELS f c =650 for positive moment f c =750 for negative moment f t = 16,000 FLAT SLABS Bending Moment Coefficients Moment coefficients shown on diagram are to be multiplied by WL. W = wL* w = total dead and live load in pounds per square foot. L = span center to center of columns for square panels, or average span for rectangular panels where long dimension is not more than 1.1 times short dimension. Values shown above coefficients are percentages of numerical sum of moments in one direction across panel. Numerical sum of moments in one direction across panel = 0.0587TFL. Minimum size of drop = 0.33L. Minimum diameter of capital = 0.225L. '6 0.02L\/wJ_+ 1 with drop 0.024L\/w + IK without drop L/32 t = total thickness of slab. Minimum t = (t in inches, L in feet) 37 FLAT SLABS TABLE 10 FLAT SLAB FLOORS NEW YORK CITY BUILDING CODE INTERIOR SQUARE PANELS DROP CONSTRUCTION f c = 650 for positive moment f c =750 for negative moment ft =16, 000 n=15 Superimposed load = 100 Ib. per sq. ft. Panel size (feet) Capital diameter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. 1 Round steel rods in each band Steel in Ib. per sq. ft. Direct Across' direct Diagonal i 16X16 3' 6" 5' 4" 6 3 0.528 13-% 9-% 9-%" 1.76 17X17 3' 9" 5' 8" 3 0.570 15-% 10-%" 1.89 18X18 4' 0" 6' 0" 6% 334 0.593 17-% 12-% 12-%" 2.04 19X19 4' 3'" 6' 4" 734 33^2 0.636 19-% 14-% 13-%" 2.14 20X20 4' 6" 6' 8" 7^| 3% 0.660 21-% 16-% 15-%" 2.30 21X21 4' 9" 7'0" 8 4 0.704 23 -% 17-%" 17-%" 2.40 22X22 5' 0'' 7' 4" 4 0.725 26-% 19 %" 19-%" 2.57 23X23 24X24 5' 3" 5' 6" 7' 8" 8'0" 8% *H ' 0.770 0.794 22-Ke" 24-Ke" 16-Ke" 16-Ke" 17-Ke" 2.85 2.95 25X25 5' 9" 8' 4" 9^<2 *H 0.835 26-Ke" 19-Ke* 3.10 26X26 6'0" 8' 8" 9% 5 . 858 29-Ke" 21-Ke" 21-Ke" 3.30 Superimposed load = 150 Ib. per sq. ft. Panel size (feet) Capital diameter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6" 5' 4" 6 3 0.528 16-% 12-% 12-%" 2.24 17X17 3' 9" 5' 8" 63-4 334 0.571 18-% 13-% 13-%" 2.32 18X18 4' 0" 6' 0" 6% . 595 20-% 15-% 15-%" 2.48 19X19 4' 3" 6' 4" 734 4 0.641 22-% 17-% 16-%" 2.54 20X20 4' 6" 6' 8" 7^| 4 0.662 25-% 19-% 19-%" 2.62 21X21 4' 9" 7' 0" 8 434 0.706 27-% 20 % 20 %" 2.82 22X22 5'0" 7' 4" SM 0.727 23 Ke" 17-Ke" 3.15 23X23 5' 3" 7' 8" 4% 0.774 25 Ke" 19 Ke" 18-Ke" 3.24 24X24 5' 6" 8' 0" 934 5 0.817 27 Ke" 20-Ke" 20-Ke" 3.36 25 X 25 26X26 5' 9" 6' 0" 8' 4" 8' 8" 10 0.841 0.887 30-Ke'' 32-Ke" 22-K 6 " 24-Ke" 22-Ke" 24-Ke" 3.58 3.72 Superimposed load = 200 Ib. per sq. ft. j ~ Round steel rods in each band Panel size (feet) Capital diameter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6" 5' 4" 6H 334 0.571 18-%" 13-%" 13-%" 2.46 17X17 3' 9" 5' 8" 7 0.618 20 %" 15 %" 14-%" 2.54 18X18 4' 0" 6' 0" 734 434 0.643 22-%" 17-%" 16-%" 2.67 19X19 4' 3" 6' 4" 434 0.685 24-%" 18-%" 18-%" 2.80 20X20 21X21 4' 6" 4' 9" 6' 8" 7' 0" gg JM 0.729 0.775 20-Ke" 15-Ke" 15 Ke" 16-Ke" 3.04 3.14 22X22 5' 0" 7' 4" 9 O '4. 0.799 25-Ke" ig_7^ 6 " 18-Ke" 3.38 23X23 5' 3' 7' 8" 93^ 5H 0.841 27-Ke" 21-Ke" 20-Ke" 3.54 24X24 25X25 5' 6" 5' 9" 8' 0" 8' 4" 10 $ 0.887 0.954 31- Ke" 22-Ke" 24-Ke" 23-Ke" 3 . 66 3.77 26X26 6'0" 8' 8" 1 1 34 GH 1.002 34-Ke" 26-Ke" 25-Ke" 3 . 94 : 38 TABLE 10 FLAT SLAB FLOORS NEW YORK CITY BUILDING CODE INTERIOR SQUARE PANELS DROP CONSTRUCTION f e =650 for positive moment f e =750 for negative moment fs=16,000 FLAT SLABS Superimposed load = 250 Ib. per sq. ft. Panel size (feet) Capital diameter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6 5' 4* 7M 4 0.662 17-%; 13-%* 13-%* 2.39 17X17 3' 9 5' 8* 8 4% 0.706 15-%* 15-%' 2.62 18X18 i 4' 19X19 4' 3 6' 0' 6' 4* 8* 4% 0.752 0.797 22-%* 25-%* 17-%* 19 %\ 17%* 18-%* 2.76 2.87 20 X 20 4' 6 6' 8* 9% 5 0.859 21-^6" 15-Ke*. 3.11 21X21 4' 9 7' 0* 10% 0.906 23-He" 17 Ke". 3.29 22X22 5'0* 7' 4* 10% 6 0.953 25-Ke" 18 M 3.38 23X23 5' 3* 7' 8* HM 6 1.014 27-He" 20-^g* 20-He 3.51 24X24 5' 6* 8' 0* 12 6H 1.060 30-He* 22 He". 22-^6 3.71 25X25 26X26 5' 9* 6'0* 8' 4* 8' 8* 12% 7% 13% m 1.129 1.215 32-^6* 27-M" 19-^* 3.80 3.98 Superimposed load = 300 Ib. per sq. ft. Panel size (feet) Capital diameter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 17X17 3' 6* 3' 9* 5' 4* 5' 8* 8j* J* 0.749 0.796 20-%* i3-% : 13-%* 15-%* 2.46 2.62 18X18 4' 0* 6' 0* 9% 5 0.858 22-%* 17-%* 16-%* 2.67 19X19 4' 3" 6' 4* 5% 0.928 25-%* 19-%\ 1 ?-^" / , 2.87 20X20 4' 6* 6' 8* lit! 6% 0.996 20-Ke" 3.04 21X21 4' 9* 7' 0* n% 6% 1.043 22-Ke* 17-K6" 16 -He* 3.14 22X22 5' 0* 7' 4* 12 J^ 6% 1.104 25-He" 18 T^R* 18-Ke" 3.36 23X23 24X24 5' 3* 5' 6* 7' 8* 8' 0* 13% 13% 7% 7 V*> 1.169 1.215 27-Ke* 30-He* 20-^6* 22-He* 20-K6*. 3.51 3.71 25X25 5' 9* 8' 4* 14^ 8 1.283 32-Ke* 24-K6* 23 J^ * 3.80 26X26 6'0* 8' 8* iS 9 1.375 19-8* 19-M* 3.90 Superimposed load = 350 Ib. per sq. ft. Panel size (feet) Capital diameter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic' feet per sq.ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Across direct Diagonal i | 16X16 3' 6* 5' 4* 9^ 5 0.827 18-%* 13-%* 13-%* ! 2.46 17X17 3' 9* 5' 8* 10 5% 0.882 21-%* 15-%* 15-%* 2.68 18X18 4' 0* 6' 0* 10% 6 0.951 23-%' 17 %; 16-%* 2.74 19X19 4' 3* 6' 4* 11 4 6% .017 26-%* 18-%*^ i 2.90 20X20 4' 6* 6' 8* .101 21-He*. 1 5- K 6 * 21X21 4' 9* 7' 0* i 13% 7% .169 17 "^i e* 16-Ke* 3^21 22X22 5' 0* 7' 4* 14 7% .239 25-lil" 19-Ke* IS-Mo" 3.38 23X23 5' 3* 7' 8* 15 8 .324 28-K 6 * 20 Ke* 24X24 5' 6* 8' 0* 15% 8% .393 22- He* 21 7A*," 3.64 25X25 5' 9* 8' 4* 16% 9% .483 32-T<" 24-Ke* 23 TY* 3.80 26X26 6' 0* 8' 8* 17% 9% .569 27-H* 20-M* 19-M" 3.98 39 FLAT SLABS FLAT SLAB FLOORS NEW YORK CITY BUILDING CODE INTERIOR SQUARE PANELS CAP CONSTRUCTION f c =650 for positive moment f c =750 for negative moment f, =16,000 n = 15 Superimposed load = 100 Ib. per sq. ft. Round steel rods in each band Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Steel in Ib. per sq. ft. Direct Direct over column, add'l each way Across direct Diagonal 16X16 3' 6" W 0.562 14-% 8-% 8-%" 8-%" 1.91 17X17 18X18 4'0" ^ 0.605 0.645 18-% 10-% n-% 10-%" 9 %" 10-%" 2.04 2.14 19X19 4' 3" 8 0.667 21-% n-% 12-%" 12-%" 2.34 20X20 4' 6" 8K 0.708 23-% 13-% 13-%" 13-%" 2.44 21X21 22X22 23X23 4' 9" 5' 0" 5' 3" 9 9K 10 0.750 0.791 0.833 19-K 21-K 24-K IO-K 12-K 11-Ke" 12-K e " 13-Ke" 11-Ke" 12-Ke" 13-Ke" 2.66 2.78 2.95 24X24 5' 6" IOK 0.875 26-K 15-Ke" 14-K e" 3.08 25X25 5' 9" 11 0.917 29-K 15-K 16-Ke" 15-K e" 3.22 26X26 0.937 32-K 16-K 18-Ke" 18-Ke" 3.56 Superimposed load =150 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab, (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l each way Across direct Diagonal 16X16 3' 6* 7% 0.645 16-%" 8-%" 9-% 9-%" 2.12 17X17 3' 9" S^A 0.687 18-%" 10 %" 10-% 10-%" 2.25 18X18 4'0" O 1 * 0.708 21-%" n-%" 12-% 12-%" 2.48 19X19 4' 3" 9 0.750 24-%" 13-%" 13 % 13-%" 2.62 20X20 4' 6" 9K 0.792 20-Ke" 10-Ke" 11-K " 11-Ke" 2.85 21X21 4' 9" 10 0.833 22-Ke" 12 K e" 12-K " 12-K e" 2.99 22X22 23X23 5' 0" 5' 3" 11 0.875 0.917 25-Ke" 27-Ke" 15-Ke" 14-K " 15-K " 13 K 6 " 14-K e " 3.20 3.30 24X24 5' 6" UK 0.958 23-K" 13 K 3.60 25X25 5' 9" 12 1.000 26-K" 12-K" 14-K" 3.78 26X26 6'0" 12K 1.042 14-K" 15-K 15-K" 3.93 Superimposed load = 200 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l Across Diagonal each way 16X16 3' 6" 8^ 0.687 18-%" 10-% 10-%" 10-%" 2.39 17X17 3' 9" 8% 0.729 21-%" 11-% 12 %" 11-%" 2.55 18X18 19X19 4'0" 4' 3" IH 0.771 0.812 18-Ke" 19-K e" 10-K " ii-K " IO-K e" ll-K e" 9-Ke" 11-K e" 2.72 2.96 20X20 4' 6" IOK 0.855 22-Ke" 12-K " 12-Ke" 12-K e " 3.27 21X21 22X22 4' 9" 5'0" 10 UK 0.896 0.958 25-Ke" 21-K" 13-K " \&' 13-Ke" 11 K" 3.34 3.52 23X23 5' 3" 12 1.000 23-K" 12-K 13_^ 12-K" 3.61 24X24 5' 6" 12K 1.042 25 K" 13-K 14-K" 3.90 25X25 26X26 5' 9" 6' 0" 13 1.083 1.145 QO I/ ' * 30-K" 16-K 15-K" 17-K" 15-K" 16-K" 4.09 4.25 40 TABLE 11 FLAT SLAB FLOORS NEW YORK CITY BUILDING CODE INTERIOR SQUARE PANELS CAP CONSTRUCTION f c =650 for positive moment f e =750 for negative moment f,=16, n=15 FLAT SLABS Superimposed load = 250 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l Across direct Diagonal * 1 each way 16X16 i 3' 6" 9 0.750 19-%" 10-%" 11-H" n-%" 2.53 17X17 i 3' 9* 9^ 0.791 17^6* 9 ^" 9~J^e" 9 'T i R " 2.75 18X18 4' 0* 10 0.833 19 M 6* 10-Ke* 11-K" 10-J^e" 3.01 19X19 1 4' 3* 0.875 21-Jl 6* 12-Ke* i2-Kfr 3.21 20X20 4' 6" 11% 0.937 23 Ms* 12 1A e" 13-K" 3.32 21X21 4' 9* 11% 0.979 20-}^" 11-^" 11-^|" ii-%" 3.57 22X22 5'0" 12M .042 oo \& 12 J^" 12^6" 12 J^" 3.74 23X23 5' 3* 13% .104 24-y 2 13 V^" ! 13 J^" 13-^" 3.87 24X24 5' 6* 14 .167 13-^" I 15-J^" 1 5-J4 " 4.08 25X25 5' 9* 14% .229 29-^ 14 M" 16 J-* 16-H* 4.27 26X26 15% .292 14-K" 17-K' 4.36 Superimposed load = 300 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l each way direct j 16X16 3' 6" 10% 0.854 19-%* 10-%" 11-%* 11-%* 2.53 17X17 3' 9* 11 0.917 17-He* 8 J^ " 9 J*f e* 9 M e* 2.81 18X18 4'0* 0.958 Q-T^g" 10-J^ 6 * 10-Ke* 2.95 19X19 4' 3* 12% .021 21 J^ e* H~J^6* 12-Ke* 3.12 20X20 4' 6* 13 .083 23 %K" H-Ke* 13 J^e" 3.29 21X21 4' 9" 13% . 146 20-^ 11 Jl 11-M" 3.55 22X22 5' 0* 14^ .208 22 % 11 " 12 J^ 12 i^ 3.69 23X23 5' 3* 15% .271 24 i^ 12 W" 14 J^ 13 J-^ 3.87 24X24 5' 6* 16 .333 27~M 13-^" 15-M 14~M 4;07 25X25 5' 9* 17 .417 29-H lg_i,^ Igi^, 4.22 26X26 6'0" 18 .500 its- 17-M" 17-H 4.36 Superimposed load = 350 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Direct over column, add'l each way Across direct Diagonal 16X16 17X17 3' 6* 3' 9" 12% 0.958 1.021 83f- 9~/8 n : ?|;. 11-%" 2.58 9-Jie* 2.81 18X18 4'0" 13 1.083 19- JH* 9-He" 10-Jie" 10-H" 2.95 19X19 4' 3* 13% 1.146 10 Ji e* 12 J^e* 12 Ke" 3.18 20X20 4' 6* 14% 1.229 23 IA R" 11 Me* 13 J^is" 13-Ke" 3.29 21X21 4' 9* 15^ 1T292 20-M* 9 .H n-H 11-M* 3.52 22X22 5' 0* 16^ 1.375 22-K* 10 V 12 J^ 12->i" 3.69 23X23 5' 3* 17% 1.437 11 i^ 14_i^ 13-M" 3.84 24X24 5' 6* 18% 1.521 27-M" 12-M 15 J-^ 4.11 25 X 25 5' 9* 1.604 29-M" 16 H 16-1^" 4.22 26X26 6'0" 20 1.667 32-M* 14->r 17-K 17-M" 4.41 41 FLAT SLABS FLAT SLAB FLOORS CHICAGO BUILDING CODE INTERIOR SQUARE PANELS f c = 700 for positive moment f c =805 for negative moment f s =18,000 .--4- &m l^p -+ i ^dT\ i #;vo 5 i ^ ^4. wj Drop Conatuction X -J D! Section on C-C ^-^ Bending Moment Coefficients Moment coefficients shown on diagram are to be multiplied by WL. W = wL* w = total dead and live load in pounds per square foot. L = span center to center of columns for square panels, or average span for rectangular panels where long dimension is not more than 1.05 times short dimension. Values shown above moment coefficients are percentages of numerical sum of moments in one direction across panel. Numerical sum of moments in one direction across panel: for drop construction O.OS25TFL for cap construction 0.0679 WL Minimum size of drop = \%L Minimum diameter of capital = 0.225L (6 Minimum t = j VW/44 lL/32 t = total thickness of slab. t is in inches, L is in feet. 42 TABLE 12 FLAT SLAB FLOORS CHICAGO BUILDING CODE INTERIOR SQUARE PANELS DROP CONSTRUCTION f e = 700 for positive moment f e =805 for negative moment f s =18,000 n = 15 FLAT SLABS Superimposed load = 100 Ib. per sq. ft. Panel size (feet) Capital diam- eter Sise of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq.ft. Direct Across direct Diagonal 16X16 3' 6* 5' 4*X5'4* 6 3M 0.54 13-%* Q a/ 10-% 1.83 17X17 3' 9* 5'8*X5'8* 3$i 0.58 15 %* 10% 11 % 1.94 18X18 4'0* 6' 0* X 6' 0* 6?4 411 0.60 H-% 12 % 2.04 19X19 4' 3* 6' 4*X6' 4* 7J4 4 \s 0.65 19-%* 13-% 14% 2.19 20X20 21X21 4' 6* 4' 9* 6' 8* X 6' 8* 7'0*X7'0* 8 * 4X. 0.67 0.72 22-%* 24-%* 14-% 16-% 16-% ! 2.35 17 % ! 2.45 22X22 5' 0* 7' 4*X7' 4* 5 0.74 27-%* 18-% 19-% 2.63 23X23 5' 3* 7' 8*X7'8* 8^i 51-4 0.78 22-Ke* 14 Ke" 16-K * 2.81 24X24 5' 6* 8' 0*X8' 0* 9 / 5H 0.81 25- K 6* 16-K e* 17-K " 2.99 25X25 26X26 5' 9* 6'0* 8'4*X8'4* 8' 8*X8'8* 6 6 0.85 0.87 27-Ke* 30-Ke* %-%l"' 18-K * 21-Ke" 3.04 3.33 Superimposed load 150 Ib. per sq. ft. Panel size (feet) Capital diam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6* 5'4*X5'4* 6 *y* 0.54 17-% n-% 12-% 2.31 17X17 3' 9* 5'8*X5'8* 6K 3% 0.58 19-% 13 % 14-% 2.46 18X18 4'0* 6' 0* X 6' 0* 4 0.61 21-% 15-% 16-% 2.63 19X19 4' 3* 6' 4*X6' 4* 7j^ 0.65 25-% 17-% 18 % 2.84 20X20 4' 6* 6' 8* X 6' 8* 71,4 4% 0.67 27-% 18-% 20-% 2.95 21X21 4' 9* 7'0*X7'0* 8 5 0.72 30-% 20-% 22-% 3.09 22X22 5' 0* 7'4*X7'4* 0.74 25-Ke* 16 y\ 17-K 6 3.23 23X23 5' 3* 7' 8*X7'8* 8^| 5$i 0.79 17-K 18-Ke 3.33 24X24 5' 6* 8' 0*X8' 0* 9 5% 0.81 30-Ke* 20-K 21-Ke 3.56 25X25 5' 9* 8'4*X8'4* 9K 6 0.85 34-Ke* 22 -K 23-Ke 3.83 26X26 6'0* 8'8*X8'8* 10 6 0.89 36-Ke* 24-K 25-K. 3.94 Superimposed load = 200 Ib. per sq. ft. Panel size (feet) Capital diam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. 1 direct Diagonal 16X16 3' 6 5'4*X5' 4* 6J4 3H 0.56 j 21-% 13-%* 14-%* 2.74 17X17 3' 9 5' 8*X5'8* 6^ o *x . 58 24-% 16-%* 17-%* 3.01 18X18 4' 6' 0* X 6' 0* 7 4^i 0.62 27-% 18-%* 20-%* 3.25 19X19 4' 3 6'4*X6'4* 7J4 4L 0.67 31-% 21-%* 22-%* 3.47 20X20 4' 6 6' 8* X 6' 8* 8 4i 0.72 24-K 17-Ke 18-Ke* 3.52 21X21 4' 9 7' 0* X 7' 0* 8J^ 5J4 0.76 26-K 18-Ke" 3.54 22X22 5'0 7'4*X7'4* 9 5^| 0.80 28-K 18-Ke 20-K e" 3.66 23X23 5' 3 7' 8*X7'8* 9J^ 6 0.85 30-K 20-K 6 21-Ke* 3.71 24X24 5' 6 8'0'XS'O* 10 0.89 34-K 22-Ke 24-K e* 4.03 25X25 26X26 5' 9* 6' 0* 8'4*X8'4* 8' 8*X8' 8* 11 i 0.94 0.98 37-K 39- K 24-K 6 28-K 25-Ke* 29-Ke* 4.13 4.39 43 FLAT SLABS TABLE 12 FLAT SLAB FLOORS CHICAGO BUILDING CODE INTERIOR SQUARE PANELS DROP CONSTRUCTION f e =700 for positive moment f e =805 for negative moment f s =18,000 n=15 Superimposed load = 250 Ib. per sq. ft. Round steel rods in each band Panel size (feet) Capital diam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6" 5' 4"X5' 4" 6% 4K 0.60 23-%" 14-%" 16-%" 3.03 17X17 3' 9" 5' 8" X 5' 8" 7 1/: 4/4 0.65 24-%" 17-%" 18-%" 3.12- 18X 18 4' 0" 6' 0" X 6' 0" 7 3 i 4 3 1 0.69 27-%" 18-%" 19-%" 3.21 19X19 4' 3" 6' 4" X 6' 4" 8J4 5M 0.74 30-%" 20-%" 21-%" 3.33 20X20 21X21 22X22 23X23 24X24 4' 6" 4' 9" 5' 0" 5' 3" 5' 6" 6 8" X 6' 8" 7' 0" X 7' 0" 7' 4" X 7' 4" 7' 8" X 7' 8" 8' 0" X 8' 0" 8M 10>| 5/"4 5* 88' 0.78 0.82 0.87 0.92 0.96 Al 8$j 37-Ke* 18 -He" 20-Ke" 22-Ke" 24-Ke" 18-Ke* 20-Ke" 24l# 3.63 3.77 3.91 4.16 4.31 25X25 26X26 5' 9" 6'0" 8' 4"X8' 4" 8' 8"X8' 8" 12 7*4 7M 1.03 1.08 39-He" 42-Ke* 25-Ke" 28-Ke" 30-Ke" 4.41 4.63 Superimposed load = 300 Ib. per sq. ft. Round steel rods in each band Panel size (feet) Capital diam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6" 5' 4"X5' 4" 7X 4M 0.65 24-%" 16-%" 17-%" 3.20 17X17 3' 9" 5' 8" X 5' 8" 8 4% 0.72 27-%" 17-%" 18-%" 3.28 18X18 4' 0" 6' 0" X 6' 0" si* 0.77 21-Ke" 14-Ke" 3.49 19X19 4' 3" 6' 4"X6'4" 9 5/-^ 0.81 24-Ke" 16-Ke" 17 H e" 3.66 20X20 4' 6" 6' 8" X 6' 8" 9M 6 0.85 27-He" 19_7^ 6 * 3.85 21X21 4' 9" 7' 0" X 7' 0" 10 6/4 0.89 20 -He" 21-Ke" 4.09 22X22 5' 0" 7' 4" X 7' 4" 6*4 0.94 33-Ke" 4.20 23X23 5' 3" 7' 8" X 7' 8" 1 1 7 0.99 35 He" 23-He" 25 He" 4.40 24X24 5' 6" 8' 0"X8' 0" 11% 7K 1.05 39-Ke" 25-Ke" 26-He" 4.55 25X25 5' 9" 8' 4"X8' 4" I2H 7 3 ' 1.10 33-M" 23-^" 4.78 26X26 6' 0" 8'8"X8' 8" 8 1.15 35-^" 25-K" 26-K" 5.15 Superimposed load = 350 Ib. per sq. ft. Round steel rods in each band Panel size (feet) Capital diam- eter Size of drop panel Depth of slab (inches) Depth of drop (inches) Concrete in cubic feet per sq. ft. Steel in Ib. per sq. ft. Direct Across direct Diagonal 16X16 3' 6" 5'4"X5' 4" 8 4H 0.71 24-%" 16-%" 17-%" 3.20 17X17 3' 9" 5' 8"X5' 8" 8/^ 5% 0.76 27-%" 18-%" 19-%" 3.36 18X18 4' 0" 6' 0" X 6' 0" 9 5/-^ 0.80 23-He" 16-Ke" 3.64 19X19 20X20 4' 3" 4' 6" 6' 4" X 6' 4" 6' 8" X 6' 8" 10 2 6 0.84 0.89 25 He" 27-H'e" 17-Ke" 19-Ke" 18-Ke" 20- 1{ 6 " 3.82 4.00 21X21 22X22 23 X 23 24X24 4' 9" 5' 0" 5' 3" 5' 6" 7'0"X7'0" 7' 4"X7' 4" 7' 8"X7'8" 8' 0"X8' 0" 12 * p 0.95 .00 .07 .12 31-Ke" Ijirk 20-Ke" 22-Ke" 25-Ke" 22-He" 24-He" ttfy" 4.24 4.42 4.63 4.76 25X25 5' 9" 8' 4"X8' 4" 13 8 .16 34- \/ " 23i^" 5.00 26X26 6' 0* 8' 8"X8' 8" 13?i .22 38-M" 25-H" 26-M" 5.29 44 TABLE 13 FLAT SLAB FLOORS CHICAGO BUILDING CODE INTERIOR SQUARE PANELS FLAT SLABS CAP CONSTRUCTION f c = 700 for positive moment f c =805 for negative moment f s =18,000 n=15 Superimposed load = 100 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Add'l in each band over each column Across direct Diagonal 16X16 3' 6* 6% 0.562 13-% o S/ 9-% 9-% 2.17 17X17 3' 9* 0.604 14% 10^ 10-% 10-% 2.34 18X18 4'0* 7% 0.646 16-% H-% H-% H-% 2.46 19X19 4' 3* 8 0.667 12-% 13-% 13-% 2.69 20X20 4' 6" 8K 0.708 21% 14-% 14-% 14-% 2.85 21X21 4' 9" 9 0.750 17-Ke* 12-K 3.04 22X22 5'0* 0.792 19-Ke" 13-K 13_j^ 6 * 3.23 23X23 5' 3* 9% 0.812 21-Ke" 15-K 14 K 6* 14-K 3.40 24X24 5' 6* 10% 0.854 24-K6* 16-K 16-K 6* 16-K 3.65 25X25 5' 9* 10% 0.896 26-K6" 17-K 18 ~K K" 18-K 3.85 26X26 6'0* UX 0.937 19-K 19-He' 19-K * 3.97 Superimposed load = 150 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. . Round steel rods in each band Steel in Ib. per sq. ft. Direct Add'l in each band over Across Diagonal each column 16X16 3' 6" 7K 0.625 15-% 10-%* 10-% 10-% 2.50 17X17 3' 9" 8 0.667 17-% 11-%* H-% 11-% 2.65 18X18 4'0* 0.708 19-% 12-%* 13-% 13-% 2.83 19X19 4' 3* 9 0.750 21-% 14-%* 14-% 14-% 2.96 20X20 4' 6" 0.771 24-% 16-%* 17-% 17-% 3.32 21X21 4' 9" 10 0.833 20-K" 13-Ke" 13 K 13 K 3.46 22X22 0.875 22-Ke* 15 K 15 K 3.67 23X23 5' 3" 11 0.917 24-Ke" lg_7^ K " 16-K 3.83 24X24 5' 6* 0.958 26-K* 17-K" 18-K 18-K 3.96 25X25 5' 9* 12 1.000 29-Ke" 19 KB* 20-K 20-K 6 4.26 26X26 i 6' 0* 1.042 16-H" 4.54 Superimposed load = 200 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Add'l in each band over each column Across direct Diagonal 16X16 3' 6* 8^ 0.687 16-%* n-%" H-% n-% 2.76 17X17 3' 9" 8% 0.729 18-%* 13-% 13-% 2.95 18X18 4'0* 0.771 15-K 6 10 Ks* ll-K 3.21 19X19 4' 3* o &/ 0.813 17-K 12-K 6* 12 K 12-K 3.42 20X20 4' 6" 10^4 0.854 20-K 6 13-K 13-K 3.60 21X21 4' 9" 10% 0.896 22-Kc 14-K e" 15-K 15-K 3.82 22X22 5' 0" 11 \^L 0.937 24-Ke 16 K 16-K 4.00 23X23 5' 3* 12 1.000 13 1 ^" 14 14 4.21 24X24 5' 6" 12M 1.042 23->i* 14 * 15~M 15~M 4.46 25X25 5' 9* 13 1.083 25-M* 1 Q1,4 " 17 M 17_i^ 4.76 26X26 6'0* 13H 1-125 27->i* i8-y z " i*4j 18-H 4.94 45 FLAT SLABS TABLE IS FLAT SLAB FLOORS CHICAGO BUILDING CODE INTERIOR SQUARE PANELS CAP CONSTRUCTION / c =700 for positive moment f c =805 for negative moment f s =18,000 n=15 Superimposed load = 250 Ib. per sq. ft. Panel size (feet) Capital diameter 1 Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ibs. per sq. ft. Direct Add'l in each band over each column Across direct Diagonal 16X16 3' 6" 9 0.750 17-%" n-%" 12-%" 12-%" 2.92 17X17 3' 9" 0.792 13_s^/> 13-%" 13-%" 3.12 18X18 19X19 20X20 4' 0" 4' 3" 4' 6" 10 1 1 \A 0.833 0.896 0.937 19-Me" 21-He" jjjjjj: 13-Ke" 13-Ke" 14-J-le" 3.42 3.67 3.86 21X21 4' 9" 11% 0.979 15 7.Y" 1 6- 7-<" c " 16-Ke" 4.05 22X22 5' 0" 1.042 20-3-i" 13-3-2" 13-3-2" 13->2 4.29 23X23 5' 3" 133-1 1.104 21 \4t" 14-jJ* 153-2" 15_L 4.51 24X24 5' 6" 14 1.167 24-3-2 " Jg-l^l' 16-3-2 4.71 25X25 5' 9" 143-2 1.208 26-3-2" 16 !," 173-2 " 173-2 4.91 26X26 6' 0" 15^ 1.271 28-3-2" 18-X 2 " 19-H" 19->2 5.13 Superimposed load = 300 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct A4d'l in each band over each column Across direct Diagonal I 16X16 3' 6" 103-4 0.854 18-%" H-%" 12-%" 12-^" 3.01 17X17 3' 9" 11 0.917 10-Kc 3.20 18X18 4' 0" 113-2 0.958 17-Me" 11 M 1 1-J.fg ii-Ko 3.42 19X19 4' 3" 1224 1.021 19-Ke" 12-K 13 J-Y 3.67 20X20 4' 6" 13 1.083 13-H 14-Ke 14-Ke 3.80 21X21 4' 9" 133-2 1.125 23 J-f e" 15-H 4.05 22X22 5' 0" 1434 1.187 20^2" 13 3-2 13 3-2" 4.27 23X23 5' 3" 15 1.250 22-3V' 14-3*2 14-3-2 14-3-2" 4.47 24X24 5' 6" 16 1.333 24-3-2" 15 l-o' Igi^ jgi,^" 4.71 25X25 5' 9" 17 1.417 16-3-2 17-3-2 17-3-2" 4.84 26X26 6'0" 17% 1.479 28-3-2" 18-J-2 19-H 19->2" 5.13 Superimposed load = 350 Ib. per sq. ft. Panel size (feet) Capital diameter Depth of slab (inches) Concrete in cubic feet per sq. ft. Round steel rods in each band Steel in Ib. per sq. ft. Direct Add'l in each band over each column Across direct Diagonal 16X16 3' 6" 17X17 3' 9" 18X18 4' 0" 19X19 4' 3" !$ 13 0.958 1.021 1.083 1.146 18-%" 15-Ke" 17-Ke" 19-Ke" io-K* 12-He" 11 ~? i C H-Ke" 13-He" 3.01 3.28 3.42 3.67 20X20 4' 6" 14> 2 1.208 14 J-f e" 14-Me" 3.86 21X21 4' 9" 15J4 1.271 23 J--f " 15 M e" 16 M e" 4.05 22X22 5' 0" 163^ 1.354 20 V2 " 133^" 133-2" 133-2" 4.29 23X23 5' 3" 17K 1.437 22-^" 14-3-2" 14-3-2" 14-3-2" 4.47 24X24 5' 6" 1.521 23-3-2" 15-3-2" lg_ i^" jg_i^^ 4.64 25X25 5' 9" 19 1.583 17-3-2" 17_i<" 173-2 " 4.91 26X26 6' 0* 20 1.667 28-M" 19-3-2" 19-M" 5.13 46 SECTION 3 RECTANGULAR BEAMS Table 14 and Diagram 18 may be used in the design of rectangular beams. Dia- gram 18 may also be employed to determine the safe resisting moment of a given beam and the greatest unit stresses due to a given bending moment. Example of Design of Rectangular Beam Design a simply supported rectangular beam to carry a total load, of 3000 Ib. per ft. on a span of 20ft.;f e = 650; /. = 16,000; n = 15. Reading from the intersection of lines representing f c = 650 and /, = 16,000 in Diagram 18, it is found that ^ = 107.5 and j = 0.875 (Table 14 gives values of 107.7 and 0.874 respectively). a - f = (300 s )(20); (12) - 1,800,000 in.*. o o - 16 ' 75 Assuming b = 14 in. d = 34.5 in. M ' _ 1,800,000 o 7 "A/a " (16,000) (0.875) (34.5) " or A s = (0.0077) (14) (34.5) = 3.72 sq. in. From Table 15 which gives areas and perimeters of combinations of four rods, we find that the area of three 1^-in. and one 1-in. round rods is 3.77 sq. in. To make a complete design, the bond stress and shearing stress should also be investigated. Reviewing Design of Rectangular Beam Given a beam 12 in. wide, 30 in. deep to steel, reinforced with four l-in. round rods and subjected to a bending moment of 1,500,000 in.-lb. Find the unit stresses in the steel and concrete, n = 15. M_ 1,500,000 _ bd* (12) (30) 2 '- KF - - - 87 From Diagram 18 f e = 805 and /. = 18,200 Using Diagrams for Rectangular Beams One Inch Wide Design a rectangular beam to resist a moment of 1,000,000 in.-lb., assuming f c = 750 andf, = 18,000. Taking b = 12 in., the bending moment per inch of width is ^00 = 83,333 in,lb. Then from Diagram 24 d = 26 in. and A, = (12) (0.204) = 2.448 sq. UL, 47 RECTANGULAR BEAMS Finding Points to Bend Horizontal Steel Diagram 25 is for use in determining the points at which horizontal steel in beams or slabs can be bent so that the steel remaining will not be less than that required to take the bending moment. The curves in the lower left hand corner are maximum bending moment curves for the center and supports of beams for different conditions of loading and restraint. They give the proportion of the steel required at different points along the beam from support to center. How far from the support of a simple beam of 2Q-ft. span, uniformly loaded, can four tenths (0.4) of the steel be bent up? Using the scale which reads up from the bottom, enter at 0.4 and follow hori- zontally to the curve marked "uniform load, simple span, bottom steel." The bend point is shown to be 0.183 of the span length from the support. Following up to the line for a 20-ft. span and then horizontally to the right hand scale, this distance is found to be 44 in. from the support. 48 TABLE 14 RECTANGULAR BEAMS VALUES OF Ar, /, p AND K nf c K = n = 12 / fc k 3 P K /. fc k 3 P K 500 0.300 0.900 0.0054 67.5 . 500 0.261 0.913 0.0038 59.6 550 0.320 0.893 0.0063 78.7 550 0.280 0.907 0.0045 69.4 600 0.340 0.887 0.0073 90.5 600 0.298 0.901 0.0053 80.5 650 0.358 0.881 0.0083 102.5 650 0.315 0.895 0.0060 91.6 14,000 17,000 700 0.375 0.875 0.0094 114.8 700 0.331 0.890 0.0068 103.1 750 0.391 0.870 0.0105 127.6 750 0.346 0.885 0.0076 114.7 800 0.407 0.864 0.0116 140.6 800 0.361 0.880 0.0085 127.1 850 0.421 0.860 0.0128 154.0 850 0.375 0.875 0.0094 139.5 900 0.435 0.855 0.0140 167.4 900 0.389 0.870 0.0103 152.2 500 0.286 0.905 0.0048 64.7 500 0.250 0.917 0.0035 57.2 550 0.306 0.898 0.0056 75.5 550 0.268 0.911 0.0041 67.2 600 0.324 0.892 0.0065 86.7 600 0.286 0.905 0.0048 77.6 650 0.342 0.887 0.0074 98.6 650 ' 0.302 0.899 0.0055 88.4 15,000 18,000 700 0.359 0.880 0.0084 110.4 700 0.318 0.894 0.0062 99.6 750 0.375 0.875 0.0094 123.4 750 0.333 0.889 0.0069 111.1 800 0.390 0.870 0.0104 135.7 800 0.348 0.884 0.0077 123.0 850 0.405 0.865 0.0115 149.2 850 0.362 0.879 0.0085 135.2 I 900 0.418 0.861 0.0125 162.0 900 0.375 0.875 0.0094 147.7 500 0.273 0.909 0.0043 62.0 500 0.231 0.923 0.0029 53.3 550 0.292 0.903 . 0050 72.5 550 0.248 0.917 0.0034 62.6 600 0.310 0.897 0.0058 83.5 600 0.265 0.912 0.0040 72.6 650 0.328 0.891 0.0067 94.9 650 0.281 0.906 0.0046 82.7 16,000 20,000 700 0.344 0.885 0.0075 106.7 700 0.296 0.901 0.0052 93.3 750 0.360 0.880 0.0084 118.8 750 0.310 0.897 0.0058 104.3 800 0.375 0.875. 0.0094 131.3 800 0.324 0.892 0.0065 115.6 850 0.389 0.870 0.0103 144.0 850 0.338 0.887 0.0072 127.4 900 0.403 0.866 0.0113 157.0 900 0.351 0.883 0.0079 139.4 n = 15 /. fc k i P K f. fc k 3 P K 500 0.349 0.884 0.0062 77.1 500 0.306 0.898 0.0045 68.7 550 0.371 0.876 0.0073 89.4 550 0.327 0.891 0.0053 80.1 600 0.391 0.870 0.0084 102.1 600 0.346 0.885 0.0061 91.8 650 0.411 0.863 0.0095 115.2 650 0.365 0.878 0.0070 104.2 14,000 17,000 700 0.429 0.857 0.0107 128.6 700 0.382 0.873 0.0079 116.7 750 0.446 0.851 0.0120 142.2 750 0.398 0.866 0.0088 129.2 800 0.462 0.846 0.0132 156.3 800 0.414 0.862 0.0097 142.7 850 0.477 " 0.841 0.0145 170.4 850 0.429 0.857 0.0107 155.9 900 0.491 0.836 0.0158 184.8 900 0.443 0.853 0.0117 169.7 500 0.333 0.889 0.0056 74.1 500 0.294 0.902 0.0041 66.3 550 0.355 0.882 0.0065 86.4 550 0.314 0.895 0.0048 77.4 600 0.375- 0.875 0.0075 98.4 600 0.333 0.889 0.0056 88.9 650 0.394 0.869 0.0085 111.3 650 0.351 0.883 0.0063 100.8 15,000 18,000 700 0.412 0.863 0.0096 124.4 700 0.368 0.877 0.0072 113.1 750 0.428 0.857 0.0107 137.6 750 0.385 0.872 0.0080 125.7 800 0.444 0.852 - 0.0118 151.2 800 0.400 0.867 0.0089 138.7 850 0.460 0.847 0.0130 165.1 850 0.415 0.862 0.0098 151.9 900 0.474 0.842 0.0142 179.5 900 0.429 0.857 0.0107 165.3 500 0.319 0.894 0.0050 71.3 500 0.273 0.909 0.0034 62.0 550 0.339 0.887 0.0058 82.9 550 0.292 0.903 0.0040 72.5 600' 0.360 0.880 0.0068 95.0 600 0.310 . 897 0.0047 83.5 650 0.379 0.874 0.0077 107.7 650 0.328 0.891 0.0053 94.9 16,000 20,000 700 0.396 0.868 0.0087 120.4 700 0.344 0.885 0.0060 106.6 750 0.413 0.862 0.0097 133.5 750 0.360 0.880 0.0068 118.8 800 0.429 ,0.857 0.0107 146.9 800 0.375 0.875 0.0075 131.2 850 0.443 0.852 0.0118 160.6 i' 850 0.389 0.870 0.0083 144.0 900 0.458 0.847 0.0129 174.5 900 0.403 0.866 0.0091 157.0 49 RECTANGULAR BEAMS DIAGRAM 18 VALUES OF k, j, p AND K 71=75 rercentaqe of steel DIAGRAM 19 \ RECTANGULAR BEAMS MOMENT OF RESISTANCE AND AREA OF STEEL FOR BEAMS ONE INCH WIDE f e =650 f s =16,0 = 15 Area or steel in so. in. RECTANGULAR BEAMS DIAGRAM 20 f c =650 f s =18,0 n=15 MOMENT OF RESISTANCE AND AREA OF STEEL FOR BEAMS ONE INCH WIDE DIAGRAM 21 RECTANGULAR BEAMS MOMENT OF RESISTANCE AND AREA OF STEEL FOR BEAMS ONE INCH WIDE f e =700 f,=16, Area of stee in sg. in. RECTANGULAR BEAMS DIAGRAM 22 f c =700 f s =18,0 n=15 MOMENT OF RESISTANCE AND AREA OF STEEL FOR BEAMS ONE INCH WIDE Area or steel m sa. in RECTANGULAR BEAMS MOMENT OF RESISTANCE AND AREA OF STEEL FOR BEAMS ONE INCH WIDE f e = 750 f, = 16,000 Area or steel in sq. in. RECTANGULAR BEAMS DIAGRAM 24 / =750 MOMENT OF RESISTANCE AND AREA OF STEEL f t =18,000 FOR n=15 BEAMS ONE INCH WIDE Area of stee m sa. in. DIAGRAM 25 RECTANGULAR BEAMS DIAGRAM FOR LOCATING POINTS TO BEND HORIZONTAL STEEL RECTANGULAR BEAMS AREAS AND PERIMETERS OF COMBINATIONS OF FOUR RODS Square rods Number and size Round rods II Area (sq. in.) Perimeter (in.) M H H y* 1 1H IK Area (sq. in.) Perimeter (in.) 1 00 80 4 1 79 6 28 l!l4 8 . 5 3 l 0.89 6^68 1.28 9.0 2 2 1.01 7.07 1 31 90 i 3 1 1 03 7 07 l'42 9.5 1 3 1.12 7^46 1.52 9.5 3 i 1.19 7.46 1.56 10.0 4 1.23 7.85 1.63 10.0 2' 2 1.28 7 85 1.73 10.5 3 1 1.36 8.25 1.91 11.0 2 2 1.50 8.64 1.94 11.0 3 i 1.52 8.64 1.94 11.0 l" 3 1.52 8 64 2.03 11.0 2 2 ;; \ '.'. 1.60 8.64 2.08 11.5 i 3 1.63 9.03 2.17 11.5 3 i 1.71 9.03 2.25 12.0 4 1.77 9.43 2.31 ' 12.0 2 2 1.82 9.43 2.45 12.5 3 1 1.93 9.82 2.55 12.5 'l 3 2.00 9 82 2.66 13.0 2 2 2.09 10.21 2.69 13.0 1 3 2.11 10.21 2.69 13.0 3 i .... 2.11 10.21 2.78 13.0 2 2 ! .- ; - 2.18 10 21 2.86 13.5 1 3 2.24 10.60 2.95 13.5 3 " " 1 2.32 10 . 60 3.06 14.0 - 4 2.41 11.00 3.13 14.0 2 2 . . 2.45 11 .00 3.30 14.5 3 1 . . 2.59 11 39 3.39 14.5 "l 3 2.66 11.39 3.53 15.0 2 2 2.77 11.78 3.56 15.0 1 3 2.80 11.78 3.56 15.0 3 .. 1 2.80 11.78 3.66 15.0 2 . . i . . i 2 2.87 11.78 3.77 15.5 1 3 I .. 2.96 12. 17 3.86 15.5 . . . . 3 .... 'l 3.03 12.17 4.00 16.0 _ .. 1 .. 4 3.14 12.56 4.06 16.0 I 2 . ; 2 3.19 12,56 4.27 16.5 _ 31 3.35 12.96 4.36 16.5 1 . . | . . 3 3.42 12.96 4.53 17.0 2 2 3.56 13.35 4.56 17.0 3 ; 1 3.58 13.35 4.56 17.0 i 3 3.58 13.35 4.66 17.0 2 2 3.66 13.35 4.80 17.5 V 3 3.77 13.74 5.06 18.0 4 3.98 14.14 5.13 18.0 2 2 4.02 14.14 5.36 18.5 3 1 4.21 14.53 5.45 18.5 1 3 4.28 14.53 5.66 19.0 2 2 4.44 14.92 5.69 19.0 1 3 4.47 14.92 5.95 19.5 1 3 4.67 15.32 6.25 20.0 4 4.91 15.71 58 TABLE 16 RECTANGULAR BEAMS AREAS AND PERIMETERS OF COMBINATIONS OF SIX RODS 1 | Square rods Number and size Round rods Square rods Number and size Round rods Area Perim- Area Perim- Area Perim- Area Perim- (sq. 1 eter N ^ % 1 IK IK (sq. eter (sq. eter N ;! i H 1 IK IK (sq. eter in.) (in.) in.) (in.) in.) (in.) in.) (in.) 2.34 15.0 ft 1.84 11.78 5.39 22.5 * " 5 1 4.23 17.67 2.52 15.5 5 I \' m \\ 1.98 12.17 5.48 22.5 3 3 4.31 17.67 2.69 16.0 4 9 2.11 12.57 5.53 23.0 2 4 4.34 18.07 2.72 16.0 5.. 1 2.14 12.57 5.56 23.0 1 5 4.37 18.07 2.86 16.5 3 3 2.25 12.96 5.59 23.0 4 2 4.39 18.07 2.95 16.5 5 1 2.32 12.96 5.77 23.5 1 5 4.53 18.46 3.03 17.0 2 4 2.38 13.35 6.00 24.0 6 4.71 18.85 3.09 17.0 4 . t 2 2.43 13.35 6.09 24.0 3 3 4.79 18.85 3.20 17.5 1 5 2.52 13.74 6.19 24.0 2 4 4.86 18.85 3.38 18.0 6 2.65 14.14 6.19 24.0 4 2 4.86 18.85 3.47 18.0 3 3 2.72 14.14 6.27 24.5 .. .. .. 5 1 4.92 19.24 3.56 18.0 4 2 2.80 14.14 6.53 25.0 4 2 5.13 19.64 3.58 18.5 5 1 '] 2.81 14.53 6.56 25.0 5 1 5.15 19.64 3.78 19.0 4 2 2.97 14.92 6.59 25.0 2 4 5.18 19 64 3.81 19.0 6 1 2.99 14.92 6.80 25.5 3 3 5.34 20.03 3.84 19.0 2 4 .. 3.02 14.92 6.89 25.5 1 5 . .5.41 20.03 3.98 19.5 . 3 3 . 3.13 15.32 6.98 25.5 3 . 3 5.48 20.03 4.08 19.5 5 1 . . 3.20 15.32 7.06 26.0 2 4 5.55 20.42 4.17 19.5 3 3 3.28 15.32 7.09 26.0 1 5 5.57 20.42 4.19 20.0 2 4 3.29 15.71 7.13 26.0 - 4 2 5.60 20.42 4.22 20.0 1 5 3.31 15.71 7.33 26.5 1 5 5.76 20.81 4.25 20.0 4 2 3.34 15.71 7.59 27.0 6 5.96 21.20 4.39 20.5 . 1 5 3.45 16.10 7.69 27.0 3 3 6.04 21.20 4.59 21.0 6 3.61 16.49 7.78 27.0 2 4 6.11 21.20 4.69 21.0 3 3 3.68 16.49 7.89 27.5 5 1 6.19 21.60 4.78 21.0 2 4 3.76 16.49 8.19 28.0 4 2 6.43 21.99 4.78 21.0 4 2 3.76 16.49 8.25 28.0 2 4 6.48 21.99 4.83 21.5 5 1 ; . 3.79 16.89 8.48 28.5 3 3 6.66 22.38 5.06 22.0 . . 4 2 3.98 17.28 8.58 28.5 1 5 6.74 22.38 5.09 22.0 5 1 4.00 17.28 8.78 29.0 2 4 6.90 22.78 5.13 22.0 3 4 4.03 17.28 8.81 29.0 1 5 6.92 22.78 5.30 22.5 3 3 ! 4.16 17.67 9.08 29.5 1 5 7.13 23.17 5.39 22.5 1 5 4.23 17.fi7 9.38 30.0 6 7.36 23.56 59 RECTANGULAR BEAMS TABLE 17 AREAS AND PERIMETERS OF COMBINATIONS OF EIGHT RODS Square rods Number and size Round rods Square rods Number and size I ; Round rods Area Perim- Area Perim- Area Perim- Area Perim- (sq. eter H 7 A 1 IK iH (sq- eter (sq. eter 3 A y* 1 1M 1J-4 (sq. eter in.) (in.) in.) (in.) in.) (in.) in.) (in.) 4.50 24.0 8 3.53 18.85 8.12 32.0 4 4 6.38 25.14 4.70 24.5 7 l 3.69 19.24 8.27 32.5 7 1 6.49 25.53 4.91 25.0 6 2 3.85 19.64 8.52 32.5 5 3 6.69 25.53 4.94 25.0 7 1 3.88 19.64 8.53 33.0 6 2 6.70 25.92 5.11 25.5 5 3 4.01 20.03 8.56 33.0 7 1 6.72 25.92 5.20 25.5 7 1 4.09 20.03 8.62 33.0 3 5 .. 6.77 25.92 5.31 26.0 4 4 4.17 20.40 8.72 33.0 2 6 6.85 25.92 5.38 26.0 6 2 4.22 20.40 8.80 33.5 5 3 6.91 26.31 5.52 26.5 3 5 4.33 20.81 9.06 34.0 4 4 7.12 26.70 5.72 27.0 2 6 4.49 21.20 9-12 34.0 2 6 7.17 26.70 5.81 27.0 5 3 4.57 21.20 9.13 34.0 6 2 7.17 26.70 5.91 27.0 6 2 4.64 21.20 9.31 34.0 4 4 7.31 26.70 5.92 27.5 1 7 . 4.65 21.60 9.33 34.5 3 5 7.33 27.10 6. 12 28.0 8 . 4.81 21.99 9.42 34.5 1 7 7.40 27.10 6.25 28.0 4 4 4.91 21.99 9.59 35.0 2 6 7.53 27.49 6.36 28.5 7 1 4.99 22.38 9.62 35.0 1 7 7.56 27.49 6.59 29.0 6 2 5. 18 22.78 9.69 35.0 5 3 7.61 27.49 6.61 28.5 5 3 5. 19 22.38 9.86 35.5 1 7 7.74 27.88 6.62 29.0 7 1 5.20 22.78 10.11 35.5 3 5 7.94 27.88 6.69 29.0 3 5 5.25 22.78 10.12 36.0 8 7.95 28.28 6.83 29.5 5 3 5.36 23.17 10.25 36.0 4 4 8.05 28.28 6 92 29.5 7 1 5.44 23.17 10.42 36.5 7 1 8.19 28.67 7.06 30.0 4 4 5.55 23.56 10.72 37.0 , , 6 2 8.42 29.06 7.12 30.0 6 2 5.60 23.56 10.81 37.0 3 5 8.49 29.06 7.13 30.0 2 6 5.60 23.56 10.91 37.0 2 6 8.56 29.06 7.30 30.5 3 5 .. 5.73 23.96 11.02 37.5 .. 5 3 8.65 29.45 7.31 30.0 4 4 5.74 23.56 11.31 38.0 . . 4 4 8.88 29.85 7.53 31.0 2 6 5.91 24.35 11.38 38.0 . 2 6 8.93 29.85 7.56 31.0 1 7 5.94 24.35 11.61 38.5 3 5 9.12 30.24 7.63 31.0 5 3 5.9 24.35 11.70 38.5 1 7 9.19 30.24 7.72 31.0 6 2 6.06 24.35 11.91 39.0 2 6 9.35 30.63 7.77 31.5 1 7 6.10 24. 74 111 1.94 39.0 1 7 9.37 30.63 8.00 32.0 8 6.28 25. 14 12.20 39.5 1 7 I 9.58 31.02 8.02 31.5 3 5 6.30 24.74 12.50 1 40.0 8 ' 9.82' 31.42 60 TABLE 18 RECTANGULAR BEAMS AREAS AND PERIMETERS OF GROUPS OF RODS OF UNIFORM SIZE Number Size of rods H H M M H H 1 1M IK 1H 1H 1 1 1 1 1 . 0625 1.0 0.1406 0.2500 0.3906 0.5625 0.7656 3.5 1.000 4.0 1.266 1.563 1.891 2.250 2 . 1250 2.0 0.2812 3.0 0.5000 4.0 0.7812 5.0 1.125 6.0 1.531 7.0 2.000 8.0 2.531 9.0 3.125 10 3.781 11.0 4.500 12.0 3 0.1875 3.0 0.4218 4.5 0.7500 6.0 1.172 7.5 1.688 9.0 2.297 10.5 3.000 12.0 3.797 13.5 4.688 15.0 5.672 16.5 6.750 18 4 0.2500 4.0 . 5624 6.0 1.000 8.0 1.563 10.0 2.250 12.0 3.062 14.0 4.000 16.0 5.062 18.0 6.250 20.0 7.562 22.0 9.000 24.0 5 0.3125 5.0 0.7030 7.5 1.250 10.0 1.953 12.5 2.813 15.0 3.828 17.5 5.000 20.0 6.328 22.5 7.813 25.0 9.453 27.5 11.25 30 6 . 3750 60 0.8436 9.0 1.500 12.0 2.344 16.0 3.375 18.0 4.594 21.0 6.000 24.0 7.594 27.0 9.375 30.0 11.34 33.0 13.50 36.0 7 0.4375 7.0 0.9842 10.5 1.750 14.0 2.734 17.5 3.938 21.0 5.359 24.5 7.000 28 8.859 31.5 10.94 35.0 13.23 38.5 15.75 42.0 8 0.5000 80 1.125 12.0 2.000 16.0 3.125 20.0 4.500 24.0 6.125 28.0 8.000 32.0 10.12 36.0 12.50 40.0 15.12 44.0 18.00 48 9 . 5625 90 1.265 13 5 2.250 18.0 3.516 22.5 5.063 27.0 6.890 31.5 9.000 36.0 11.39 40.5 14.06 45.0 17.02 49.5 20.25 54.0 10 0.6250 10.0 1.406 15.0 2.500 20 3.906 25.0 5.625 30 7.656 35.0 10.00 40.0 12.66 45 15.63 118.91 50.0 55.0 22.50 60.0 1 0.0491 0.785 0.1105 1 18 0.1964 1.571 0.3068 1 96 0.4418 2 35 0.6013 2 75 0.7854 3.14 9940 3 53 1.227 1.485 3 93 4 32 1.767 4.71 2 0.0982 1.57 . 2209 2 36 0.392*7 3.14 0.6136 3 93 0.8836 4 71 1.203 5.50 1.571 6.28 1.988 7.07 2.454 7 85 2.970 8 64 3.534 9.42 3 0.1473 2.36 0.3313 3 53 0.5890 4.71 . 9204 5 89 1.325 7.07 1.804 8 25 2.356 9 43 2.982 10.6 3.681 11.8 4.455 13.0 5.301 14.1 4 1964 3.14 0.4418 4.71 . 7854 6.28 1.227 7.85 1.767 9 42 2.405 11.0 3.142 12.6 3.976 14.1 4.908 15.7 5.940 17.3 7.068 18.8 5 . 2455 3.93 . 5522 5.89 0.9817 7.85 1.534 9 82 2.209 11.8 3.006 13.7 3.927 15.7 4.970 17.7 6.135 19.6 7.425 21.6 8.835 23 6 6 0.2946 4.71 0.6627 7.07 1.178 9 43 1.841 11 8 2.651 14.1 3.608 16.5 4.712 18 9 5.964 21.2 7.362 23 6 8.910 25.9 10.60 28.3 7 0.3437 5.50 0.7731 8.25 1.374 11.0 2.148 13.7 3.093 16.5 4.209 19.2 5.498 22.0 6.958 8.589 24.7 27.5 10.39 30.2 12.37 33.0 8 0.3928 6.28 0.8836 9 42 1.571 12 6 2.454 15 7 3.534 18.8 4.810 22 6.283 25.1 7.952 | 9.816 28.3 ! 31.4 11.88 34 6 14.14 37.7 9 0.4419 7 07 0.9940 10.6 1.767 14 1 2.761 17.7 3.976 21.2 5.412 24.7 7.069 28 3 8.946 31.8 11.04 35 3 13.37 38 9 15.90 42 4 10 0.4910 7.85 1.105 11.8 1.964 15.7 3.068 19.6 4.418 ! 6.013 23 . 6 27 . 5 7.854 1 9.940 31.4 ! 35.3 I 12.27 39 3 14.85 43.2 17.67 47.1 61 RECTANGULAR BEAMS TABLE 19 AREAS, PERIMETERS AND WEIGHTS OF RODS Round rods Square rods Size (inches) Area (square inches) Perimeter (inches) Weight per foot (pounds) Area (square inches) Perimeter (inches) Weight per foot (pounds) H 0.0491 0.785 0.167 0.0625 1.00 0.212 KG 0.0767 0.982 0.261 0.0977 1.25 0.333 H 0.1104 1.178 0.375 0.1406 1.50 0.478 KG 0.1503 1.374 0.511 0.1914 1.75 0.651 y 2 0.1963 1.571 0.667 0.2500 2.00 0.850 MG 0.2485 1.767 0.845 0.3164 2.25 1.076 % 0.3068 1.964 1.043 0.3906 2.50 1.328 % 0.3712 2.160 1.262 0.4727 2.75 1 . 608 H 0.4418 2.356 1.502 0.5625 3.00 1.913 13 Ae 0.5185 2.553 1.763 0.6602 3.25 2.245 7 /8 0.6013 2.749 2.044 . 7656 3.50 2.603 ^6 0.6903 2.945 2.347 . 8789 3.75 2 . 989 1 O.V854 3.142 2.670 1.0000 4.00 3.400 1M 0.9940 3.534 3.379 1 . 2656 4.50 4.303 \y 1.2272 3.927 4.173 1.5625 5.00 5.312 l 3 /8 1.4849 4.320 5.049 1 . 8906 5.50 6 . 428 IX 1.7671 4.712 6.008 2.2500 6.00 7.650 1% 2.0739 5.105 7.051 2.6406 6.50 8.978 1% 2.4053 5.498 8.178 3.0625 7.00 10.41 1% 2.7612 5.891 9.388 3.5156 7.50 11.95 2 3.1416 6.283 10.68 4.0000 8.00 13.60 2M 3.9761 7.069 13.52 5.0625 ' 9.00 17.22 2H 4.9087 7.854 16.69 6.2500 10.00 21.25 2% 5 . 9396 8.639 20.20 7.5625 11.00 25.71 3 7.0686 9.425 24.03 9.0000 12. CO 30.60 62 SECTION 4 DOUBLY REINFORCED BEAMS Diagrams 26 to 30 inclusive are particularly useful in checking the supports of con- tinuous T-beams when the value of -j- is approximately 3^i o- The results are on the safe side when -r is less than %Q. For different values of j-^ they give directly the amounts of compressive and tensile steel required. When the value of -j- does not approximate Ho? the formulas given below may be used. These are based on the fundamental fact that for any given values of f e and /,, k has exactly the same value regardless of the shape or type of beam. It follows from this that if steel is added to the section without changing the extreme fiber stresses, this added tensile and compressive steel must form a balanced couple whose stresses conform to the stresses already in the section. Let pi = steel ratio for the beam, without compressive steel. p-2 = steel ratio for the added tensile steel. Pf = Pi + P* p' = steel ratio for compressive steel. Mi = moment of the beam without compressive steel. M z = moment of the added steel couple. M = Mi + M 2 Then I J- Pl ^ 2f* ^=/*i(i-gw 3/o = M - Mi P2 = 1 - A P Diagram 31 is of general use. By means of this diagram and Table 20 it is possible to readily determine the stresses in the concrete and steel of a doubly reinforced rectangular beam for a given bending moment. Diagram 32 is used to determine the length of embedment necessary to develop the actual compressive stress in the rods in the bottom of a continuous T-beam at the 63 DOUBLY REINFORCED BEAMS supports. The upper part of the diagram is general, and may be used to find length of embedment to provide for bond when the stress is the steel is either tension or compression. Finding Percentages of Tensile and Compressive Steel M ~_ What percentages of tensile and compressive steel will be required when f ,., = 200, t oa~ d' iff c is not to exceed 750 and / is not to exceed 18,000? j- = 0.10. n = 15. From Diagram 28 we find that for f c = 750, / = 18,000, and ^ = 200 p = 0.0127 and p' - 0.010 If p should be increased to 0.0143, /, will be lowered to 16,000 and p' to 0.0086. Given: b = 12 in., d = 18 in., j = 0.15, M = 750,000 in.-lb., f c = 750 and / = 16,000, n = 15. Determine the required percentages of tensile aud compressive steel. From Table 14, k = 0.413 pi = 0.0097, and K = 133.5 M[ = (133.5) (12) (18) 2 = 519,000 in.-lb. M 2 = 750,000 - 519,000 = 231,000 in.-lb. 231,000 * (16,000) (0.85) (12) (18) 2 P = Pi + p 2 = 0.0141 ' = (0.0044) _ = 0.0097 Finding Length of Embedment of Compressive Steel Given a continuous beam reinforced with 1-in. rods (either square or round) in com- pression so that f c = 750; / = 16,000; -7- = 0.10; n = 15; u = 80. Find required length of embedment of compressive steel. From the lower part of Diagram 32, the compressive stress// is found to be 8540 Ib. per sq. in. The upper diagram shows the length of embedment for 1-in. plain rods, with u = 80, to be 26>2 in. Finding Stresses in Concrete and Steel A continuous T-beam, uniformly loaded, has a bending moment at the center of each span of 356,300 in.-lb. Negative bending moment at the supports and the positive bending wl 2 moment at the center of span are figured by the formula, M = ^r. The tensile steel at the center of span consists of four %-in. round bars, b' = 10 in. d 15 in. Design the supports. At the supports the flange of the T-beam, being in tension, is negligible and the T-beam changes into a rectangular beam with steel in top and bottom. Two of the tension bars on each side of the supports will be bent up and made to lap over the top of the supports, while the other two bars on each side will be continued straight and lapped over supports at the bottom of beam. 64 DOUBLY REINFORCED BEAMS The ratios of steel in tension and compression are the same, and are respectively : a 118 (1.77 in above equation taken from Table 18.) d ' - 2 - o m T U From Diagram 31, knowing p' = p, we obtain d' k = 0.361 For - 0.10.... d' k = 0.377 For = 0.15... Thus, k =0 ' 372 = 0.873 (It is usually well within the precision of the actual work, and on the safe side, to use the curves for the value of -r next larger than the actual value. Thus in this problem the values of k and j for -j =0.15 could be used with sufficient accuracy.) Then M 356,300 (1.77X0.873X15) and, using Table 20, f c = n(l k _ fc) /, = (0.0394) (15,400) = 607 Ib. per sq. in. The stresses in the concrete and steel are within the allowable and no haunch or additional steel is necessary. The moment of resistance at the supports may be found as follows: f e n(l - k} 650 fc- = 0^394 = 16,500 Ib. per sq.m. Thus the moment of resistance depends on the steel and Ms = bd%pj = (10) (15) 2 (16,000) (0.0118) (0.873) = 371,000 in.-lb. 65 DIAGRAM 26 DOUBLY REINFORCED BEAMS DOUBLY REINFORCED RECTANGULAR BEAMS VALUES OF ^p, p, ANDp' *' JL d, 10 f c =650 f ,=16,000 f s = 18,000 n=15 Percentage of -tensile steel, p DOUBLY REINFORCED BEAMS DIAGRAM 27 f t =7 00 f,=16, f.= 18,000 n=15 DOUBLY REINFORCED RECTANGULAR BEAMS VALUES OF ~t, p, ANDp' Percentage of tensile steel, p DIAGRAM 28 DOUBLY REINFORCED BEAMS DOUBLY REINFORCED RECTANGULAR BEAMS VALUES OF ~, p, AN Dp' f e =750 f s =16,000 f s =18,000 = 15 Percentage of tensile steel , p DOUBLY REINFORCED BEAMS DIAGRAM 29 f c =800 f s =16,000 f s = 18,000 15 DOUBLY REINFORCED RECTANGULAR BEAMS VALUES OF , p, ANDp' Percentage of tensi le steel , p DIAGRAM 30 DOUBLY REINFORCED BEAMS DOUBLY REINFORCED RECTANGULAR BEAMS VALUES OF ^ p, ANDp' <*L=L d~ 10 , f e =850 f,=16,000 f, = 18,000 71 = 15 DOUBLY REINFORCED BEAMS DIAGRAM 31 DOUBLY REINFORCED RECTANGULAR BEAMS VALUES OF k AND j DIAGRAM 31 DOUBLY REINFORCED BEAMS DOUBLY REINFORCED RECTANGULAR BEAMS VALUES OF k AND j DOUBLY REINFORCED BEAMS VALUES OF IN FORMULA f c TABLE 20 J* 48 s > o " ^S. ^"^X. ^ * -1 X- ^ S ^x_* n * 5 o.is .35! >JjIS ZS ' nS^ "X. X^ ^ . 1 y X^?/") "* s "^x ^ix^i- ^h*? 1 Xv xj X ^'Tp^p ^t s. VN x /e~ n^O ^X B^^ s k 0.10 ^?P N > " v v x ^^xT ^ s^ ^xl ^ ^ T* ^ x "*< & _ _ . . f~ Lii"" s" '^~ "^ ; r"&: n = ID o.is ISIIIS !.!uj ^ ; ^ X, ' v ^ rTrPf ** I ' ^v S X^ S ** V ^ > ' S "^l ' TrS s. X. ^^S^^ l^i ^ ^X_ ^s 9.10 sPM x X s^ ^ i ^s ""^ ^ ^^V 'V^ V V ^^ s X X. s v^ s s^ **,. *S S > ^v s ^ X, ^s s 005 I s ** i J__L ^. s > s i ik O O O S? \T) *O r ~ ., find the section of stem required. Consider the stem width to be 12 in., and the width of flange as found from the Joint Committee recommendations to be 56 in. M t To obtain the value of r^> it is necessary to know the value of -v Since this is unknown it must be assumed. For -, = 0.2, Diagram 33 shows rnr; = 87.6. and d oa 2 3^000,000 , t 5.5 = 24 - 8 m - and = = - Taking = 0.23, = 94, and d = J'M^OW 23.9 or 24 in. and'. - 222 0.229 a The required depth therefore is 24 in. Entering the right hand side of Diagram 33 with -i = 0.229 and K = 93, it is found that j = 0.902, and M - 3,000,000 " JITd ~ (16,000) (0.902) (24) ~ Diagram 35 may also be used in making this design. The value of -5 is assumed as before. Entering at the lower right hand scale with / = 16,000, follow vertically to f e = 650 and then to the left to ^ = 0.23. The percentage of steel is 0.0065. Now follow vertically along -\ = 0.23 to p = 0.0065 in the upper left hand part of the dia- gram. From there follow to the right to/ = 16,000 and then vertically to obtain the value of f-T^ = 94. oa 2 A. * From Vol. I of "Bridge Engineering," by Waddell. 77 T-BEAMS Usually the section of the stem of a T-beam is controlled by the shearing stresses. The procedure in ordinary building design is to design the stem to take the shear at the support and then determine the concrete stress in the flange at the center of span, using the value of -j already determined. Reviewing T-Beams M t In reviewing a beam already designed, the values of r-> 3> and p are known. From these the value of f s is found from the upper half of Diagram 35. Then using the values of -v p and/ s , the value of f c is found from the lower half of this diagram. 78 DIAGRAM 33 T-BEAMS DESIGN OF T-BEAMS VALUES OF L, f c , p, ANDj f a =16,000 71=15 79 T-BEAMS DIAGRAM 34 f s =18,000 n=15 DESIGN OF T-BEAMS VALUES OF **, , f c , p, ANDj 80 DIAGRAM 35 T-BEAMS DESIGN OR REVIEW OF T-BEAMS* 15 * From Vol. 1 of "Bridge Engineering,' by Waddell. 81 SECTION 6 SHEAR REINFORCEMENT Diagram 36 may be used to find unit shear or bond stress for any beam. Uniformly Loaded Beams Diagram 37 gives the total number of stirrups in each end of a uniformly loaded beam, assuming the concrete to take one-third of the total shear, as recommended by the Joint Committee. The total number -of stirrups at each end of beam is found by entering the diagram with the unit shear at the support and the clear span in feet, and following the directions of the arrows to the upper left hand part of the diagram. Note that Diagram 37 is made for U-stirrups only with the exception of the K-in. W-stirrup which has a total cross-sectional area equal to the %6-in. square U-stirrup. The number of W-stirrups required in any given case will be one-half the number of U-stirrups of the same size. Diagram 38 gives the distance (I') from the face of support to the point where v = 40 Ib. per sq. in., beyond which no stirrups are required. Diagram 39 is used for locating the stirrups in the beam. It is so constructed that if any one of the horizontal light lines is assumed to pass through the face of the sup- port and the top line marked "center of span" is assumed to pass through the center of span, the intermediate light lines will divide the triangular shear diagram into equal areas and the heavy lines will pass through the centers of gravity of these areas. The heavy lines therefore represent the location of the stirrups. A convenient scale is placed with the zero on the fine line marked with a number corresponding to N s . The scale is then rotated until it reads (in inches) at the top z line (center of span line). The distances from the face of support to the heavy lines are then read directly from the scale, stopping when I' is reached. One side of a triangular engineers' scale may be used for all ordinary cases. Required to space %-4n. round U-stirrups in a beam 10 in. wide and of IS-ft. clear span, having a shear at the support of 118 Ib. per sq. in. From Diagram 37 Ns = 12 From Diagram 38 I' = 71 in. Placing scale on Diagram 39 to read zero at N g = 12 and 108 on line marked "center of span," the distances in inches from the face of support to the points where stirrups should be placed are: 2^, 7, 12, 17, 2% 28^, 35, 42, 50, 59, and 70. This theoretical spacing will usually be modified by practical considerations, such as the maximum spacing allowable for the depth of beam. The spacing of stirrups should not be greater than about one-half the beam depth. Beams with Concentrated Loads Diagrams 40 and 41 may be used to find the theoretical spacing of stirrups for beams with concentrated loads, the concrete assumed to take one-third of the total shear. Diagram 40 is based on unit shear and Diagram 41 on total shear. The spacing of stirrups will ordinarily be made uniform between load concentrations. 83 SHEAR REINFORCEMENT DIAGRAM 36 UNIT SHEAR AND BOND STRESS j = 0.875 -. \L n, V bid u ZQJZ ?& ^? #^^ DIAGRAM 37 SHEAR REINFORCEMENT STIRRUPS FOR UNIFORMLY LOADED BEAM f a =16,000 Unit shear at support AT, = Total Number of Stirrups in Each End of Uniformly Loaded Beam From Support to Center Concrete Taking One-third of Total Shear. vbl 6AJ, f a = 16,000 Ih. per sq. in. 85 SHEAR REINFORCEMENT DIAGRAM 38 UNIFORMLY LOADED BEAMS LENGTH OF BEAM REQUIRING SHEAR REINFORCEMENT Clear span in feet. . 86 DIAGRAM 39 SHEAR REINFORCEMENT DIAGRAM FOR LOCATING STIRRUPS IN UNIFORMLY LOADED BEAMS ^-Center of span ^ I <5 I v v 2 3 4- T 5 ^ r 6 1 7 T Q 1 9 i 10 II 1 j f \ \z \ I / 13 N = 1 14 87 SHEAR REINFORCEMENT DIAGRAM 40 SPACING OF U-STIRRUPS CONCRETE TAKING ONE-THIRD OF TOTAL SHEAR f s = 16,000 DIAGRAM 41 SHEAR REINFORCEMENT SPACING OF STIRRUPS CONCRETE TAKING ONE-THIRD OF TOTAL SHEAR f s = 16,000 89 SECTION 7 COLUMNS The following tables of safe loads on columns are based on the requirements of the respective codes in regard to maximum and minimum percentages of vertical steel and spiral, and also on such practical considerations as the minimum spacing of vertical steel. The number of rods in the square cored columns is limited to eight because every rod should be tied back into the column by the binders and it is ordinarily better practice to iise a spiraled column if more than eight rods are found necessary. The tables for round cored hooped columns are so complete that it should be possible to select a satisfactory design for any condition of concentric loading without additional computation. The values of safe loads given in Tables 35 to 42 inclusive are based on the percentages of spiral listed and, if desired, another spiral of equal volume may be substituted from Table 46. Diagrams 42 and 43 will be found valuable for determining building column loads for preliminary work. For the design of columns which are eccentrically loaded, see Section 8. Diagrams for the design of round columns subjected to bending and direct stress have been constructed and are published here for the first time. What size of square cored column and what amount of longitudinal steel will be re- quired to support a centratty applied load of 200,000 lb., assuming the recommendations of the Joint Committee to govern? Ratio of unsupported length of .column to column side is less than 15. Tables 21, 22 and 23 show the following possible designs: 2000-to. concrete. ( 6-134 in- square 22-m. column So,,/. I 8-1 Y% in. square ( 6-1 in. square 23-in. column \ - . , I 8-1 in. round 2500-&. concrete. - n. square 20-in. column < ,* . 181>B in. square f 6-1 in. square 21-m. columns _ ., . I 8-1 in. round 3000-&. concrete. 19-in. column { 8-1 ^ in. round - n. square 20-m. column < ' . ( 6-1 in. round Lateral ties must be used of not less than 34 in. in diameter and spaced not over 12 in. apart. For %-in. rods the spacing should never be more than 10 in. What size of round column and what amount of longitudinal steel will be required by the Joint Committee Recommendations to support a load of 1,100,000 lb.? A 3000-lb. concrete is to be used with 1 % of spiral reinforcement. Unsupported length of column is less ttian 10 diameters. 91 COLUMNS From Table 34, page 114, it is found that a 37-in. round column with 33-in. core, and with fourteen l^-in. square longitudinal rods will safely support a load of 1,105,000 Ib. Table 47 shows that a spiral of 7/0 gage and 2%-m. pitch will give 1 % of reinforce- ment; or that a %-in. spiral may be used with 2%-in. pitch. Table 46, page 188, gives other satisfactory sizes and pitch of spirals to obtain the required 1% of spiral re- inforcement. This table also gives the weight in pounds per foot of column for each spiral. Table 45 gives the volume and weight of columns per foot and Table 44 gives the weights of column rods per foot. What would be the design of the column of the preceding problem assuming the American Concrete Institute recommendations to govern? A number of satisfactory designs may be taken from Table 37. One possible design is to- use a 37-in. column with 33-in. core and a spiral of 7/0 gage, 2^-in. pitch, sixteen IJ^-in. round longitudinal rods. Reduction Formula for Long Columns. Where long columns must be used, the reduction which follows, taken from the Los Angeles Building Code, may be employed in the design of columns whose unsupported length (1} is between 15 and 30 times the least dimension of effective section (d). Let r represent the quantity by which the working stress for columns with -i less than 15 should be multiplied to give a working stress which may be used for long columns. Then r-l.6-H.fi 92 TABLE 21 COLUMNS ^ .Gi'umn size J SQUARE CORED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS Max. /unsupported length\ side 15 2000- Ib. concrete 1:6 mixture n = 15 f t =450 "of* column (.inches) Size of core (inches) Number of rods Square rods Round rods X H H 1 1H IK K H H i IK IK 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 8 9 10 . 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 4 4 4 6 8 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 6 8 4 6 8 6 8 38.6 46.3 i 54.8 i 59.7 ; 64.7 64.3 69.2 1 74.1 74.6 79.5 84.5 '90^8 i 95.7 102.9 107.9 iie.6 120.9 134.9 i49.7 43.0 50.6 59.2 66.3 36.5 44^2 52.7 56.6 60.4 62.2 66.0 69.9 "76 A 80.2 87.6 91.5 103.6 40.0 47.6 56.2 61.7 67.2 65.6 71.1 76.7 76.0 81.5 87.0 87.2 92.7 98.3 i04.9 110.4 44.0 51.6 60.2 67.7 69.6 77.2 84.8 80.0 87.5 95.1 91.2 98.8 106.4 103.4 110.9 118.5 116.4 124.0 131.6 56.2 64.8 74.2 84.1 84.6 94.5 95.8 105.7 115.6 108.0 117.9 127.8 121.0 130.9 140.8 135.0 144.9 154.8 149.8 159.7 169.6 70.1 79.5 89.9 101.1 113.6 113.3 125.7 126.3 138.8 151.3 140.3 152.8 165.3 155.1 167.6 180.1 170.9 183.3 195.9 187.5 200.0 212.5 205.1 217.5 230.1 95.7 107.0 119.1 134.6 132.2 147.6 146.1 161.6 177.1 161.0 176.4 191.9 176.7 192.2 207.7 193.4 208.8 224.3 210.9 226.4 241.9 229.4 244.8 260.3 248.7 264.2 279.7 284.4 299,9 305.6 321.1 327.6 343.1 350.6 366.0 55.7 64.3 70.2 68.6 75.7 82.8 79.0 86.1 93.2 90.2 97.3 104.4 102.4 109.5 116.6 115.4 122.5 129.6 i36.5 143.6 ioi.3 158.4 73.7 83.4 79.7 84.1 93.7 95.3 105.0 114.6 107.5 117.1 126.8 120.5 130.2 139.8 134.5 144.1 153.8 149.3 159.0 168.6 90.0 96.1 101.3 113.9 113.4 126.0 107.9 115.4 i 120.1 127.6 136.0 126.5 139.1 151.7 140.4 153.0 165.6 155.3 167.9 180.5 171.0 183.6 196.2 187.7 200.3 212.9 205.2 217.8 230.4 133.1 149.1 147.1 163.0 179.0 161.9 177.9 193.8 177.7 193.6 209.6 194.3 210.3 226.2 211.9 227.8 243.8 230 3 140.6 117.9 123.5 154.6 174.3 116.7 131.9 137.4 137.9 145.5 i52'.8 160.4 169.4 189.1 185.2 204.9 224.6 201.8 221.5 241.2 219.4 239.1 258.8 237 8 i52.3 ::::: 167.1 174.2 174.7 184.4 168.5175.5 176.1 185.4 168.0 191.4 201.0 185.2 192.1 192.8202.0 190.8 . . 208.9 208.4218.6 209.7 219.6 210.3 227.4 237.0 236.3 248.9 246.3 262.2 249.7 265.6 281.6 285 '.9 301.8 257.5 277.2 257.2 276.9 296.6 277.4 297.1 316.8 298.6 318.3 338.0 320.6 340.6 360.0 363.3 383.0 228.1 238.0 236.0 248.5 226.8 228.8 255.6 268.2 275 '.9 288.5 255.3 267.9 275.6 288.1 296.7 309.3 33i'.3 354.3 256.4 257.4 277 ".6 i" 276 '.6 i . . . . 297.0 309.6 307.0 323.0 297.8 ::; ;;;;; 298.8 320 '.8 33i'.7 329.1 345.0 352.0 368.0 354.6 93 COLUMNS TABLE 22 SQUARE CORED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS 2500-lb. concrete 1:4% mixture n = 12 f c =565 Max. /unsupported length^ side 15 Size of column (inches) Size of core (inches) Number of rods Square rods Round rods H H y* 1 IK IK H H V* 1 IK IK 12 13 14 15 16 17 18 19 20 21 22 23 24 25 20 27 28 29 30 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 4 4 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 : i 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 6 8 45.9 55.5 ! 66.2 71.1 75.9 1 78.1 ! 82.9 87.8 91.1 95.9 ;100.8 50.1 59.8 70.5 77.5 82.4 89.3 96.3 95.3 102.3 129.3 109.5 116.5 123.5 124.7 131.7 138.7 141.1 148.1 155.1 ies'.e 172.6 184 3 64.8 75.5 ! 43.8 53.4 64.1 67.9 71.8 76.0 79.8 83.6 '92 '.8 96.6 ioe>'.9 110.7 47.1 56.8 67.5 73.0 78.5 79.4 84.8 90.3 92.3 97.8 103.3 106.5 112.0 117.5 i27! 2 132.7 51.1 60.7 71.5 78.9 83.3 90.8 98.3 96.3 103.8 111.3 110.4 117.9 125.4 125.7 133.2 140.6 142.1 149.6 157.0 i<37\i 174.5 185' 7 65.3 76.0 87.9 97.7 100.9 110.7 115.0 124.8 134.5 130.3 140.0 149.8 146.7 156.4 166.2 164.2 173.9 183.7 182.8 192 6 81.2 93.1 106.1 120.2 132.6 135.5 147.8 151.8 164.2 176.6 169.4 181.7 194.1 188.0 200 4 111.9 126.0 141.3 156.5 157.6 172.9 175.2 190.4 205 . 7 193.8 209 1 81.4 87.4 96.9 93.2 100.4 109.9 106.2 112.8 114.5 124.0 133.6 129.8 139.3 148.8 146.2 155.7 165.2 163 . 7 173.2 182.7 182.3 191 8 120.4 132.8 135.6 148.0 127.0 142.2 157 9 134.3 149.6 J110.1 1114.9 i25.3 130.2 i4i'.7 146.6 iei'.i 126.0 152.0 164.4 176.9 169.5 181.9 194.4 188.2 200 6 158.6 174.3 176.1 191.8 207.6 194.8 210.5 166.0 183.5 202.9 202.1 221 6 l42'.4 143.6 149.1 iei '. i 166.6 182.7 191.3 204 '.6 211.0 201.4 2ii'.6 22}. 1 213.0 207.9 220.4 232.8 228.8 241.3 253.7 250 9 226.2 214.5 230.3 246.0 235.4 251.2 266.9 257 5 185.3 193.2 202.3 212.7 207.8 220.1 232.5 228.7 241.0 253.4 250.7 263.1 275.4 224.3 213.6 228.8 244.1 234.5 249.7 265.0 256.5 271.8 287.0 279.7 294.9 310.2 304.0 319.2 334.5 344.7 359.9 371.2 386.5 398.9 414.1 427.7 443.0 221.9 241.3 260.8 242.8 262.2 281.7 264 8 '.'.'.'.'. 205 '.6 205.5 213.0 226 '.4 233.9 212.4 222.1 233.3 243.0 1 231 '.9 232.5 242.0 254.6 264.1 277 '.7 287.2 263.3 275.7 286 '.5 298.9 273.2 288.9 280.6 296.4 312.1 304.9 320.7 336.4 284.3 303.7 288.0 307.4 326.9 312.3 331.7 351.2 337.7 357.2 376.6 364.3 383.7 403.1 392.0 411.4 430.8 440.2 459.6 255.9 255.3 265.1 1 254.0 277'.! \ 279 . i 278.5 288.2 286.2 298.6 310.5 322.9 336.0 348.3 362.5 374.9 402 '.6 43i.4 3ii.5 310.8 323.2 312.5 336.2 348.6 362 '.7 375.2 346.1 361.8 372 '.6 388.4 400 '.3 416.1 429 .1 444.9 337.6 363 . 5 337.9 364 '.5 392 '.2 1 402 '.9 43i'.7 94 TABLE 23 COLUMNS , Cotumnsizf SQUARE CORED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS /unsupported length\ Max. [ - T3 I = 15 V side / 3000- Ib. concrete 1:3 mixture n = 10 f c =675 Size of column (inches) Size of core (inches) Number of rods Square rods Round rods K H H 1 IX IK % y* H 1 IK IK 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 4 4 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 6 8 52.7 64.2 78.0 81.7 86.5 91.2 95.9 100.7 '106.7 111.4 116.2 'i28'.3 133.1 i46.5 1151.3 iee'.i 170.9 igi'.s 2i4'.i 56.9 68.3 81.2 86.0 50.7 62.1 75.0 78.7 82.4 89.1 92.9 96.6 i08.4 112.1 i25'. 3 129.0 53.9 65.4 78.2 83.6 89.0 92.4 97.8 103.2 107.9 113.3 118.7 124.8 130.2 135.6 57.8 69.3 82.1 89.4 96.3 103.6 110.9 111.8 119.1 126.4 128.7 136.0 143.3 146.9 154.2 161.5 166.5 173.8 181.1 73.8 86.6 100.8 110.3 116.3 125.8 133.2 142.7 152.3 151.4 160.9 170.5 171.0 180.5 190.1 191.9 201.4 211.0 214.6 223.7 233.3 91.7 105.7 121.4 138.2 150.3 156.5 168.5 180.6 176.0 188.1 200.2 197.0 209.0 221.1 219.2 231.3 243.4 242.9 254.9 267.0 267.8 279.9 292.0 294.2 306.2 318.3 127.0 143.9 162.1 177.0 181.7 196.6 202.6 217.5 232.4 224.9 239.8 254.7 248.5 263.4 278.3 273.5 288.4 303.3 299.8 314.7 329.6 327.5 73.3 86.1 91.8 95.3 102.2 109.0 110.9 117.7 124.5 127.7 134.6 141.4 146.0 152.8 159.6 165.5 172.4 179.2 i93.3 200.1 2is'.6 222.4 100.3 109.6 106.0 115.8 125.1 121.5 128.0 132.7 142.0 151.3 150.9 160.2 169.5 170.5 179.8 189.1 191.4 200.7 210.0 213.7 223.0 232.3 138.4 150.5 144.8 152.0 156.6 168.8 163.1 178.4 170.3 148.4 153.8 ies'.o 173.4 147.2 iee'.s 176.2 188.3 200.5 197.1 209.3 221.4 219.4 231.5 243.7 243.0 255.2 267.3 268.0 280 1 182.6 198.0 203.6 218.9 234 3 189.8 210.8 229.8 188.9 194.3 194.7 202.0 225.8 241.2 256.6 249.5 264.8 280.2 274.4 289 8 233.0 252.0 256.7 275.7 294.6 281.6 300 6 217.0 224.3 216.6 ::::: 239.2 246.0 246.6 255.9 27i 6 240.2 240.6 247.9 247.3 256.9 i 265.6 272.9 299 '.2 272.3 281.9 298 '.6 308.2 :;!"!! 271.0 297 '.3 280.9 297.9 307.2 325 '.6 334.9 363 '.9 292.3 294,3 306.5 318.6 334. i 346.3 363 '.2 375.3 305.2 300.8 316.1 331.5 328.4 343.8 359.2 357.5 372.8 388.2 319.6 308.0 327.0 345.9 335.5 354.6 373.6 364.7 383.7 402.6 395.0 414.0 433.0 426.8 445.8 464.7 459.8 478.8 497.8 513.3 532.2 326.3 335.9 364 '.9 395.3 333.9 346.0 362 '.9 375.0 393.3 405.4 425.0 437.1 470 '.2 504 '.6 342.3 357.3 356.5 371.4 386.3 401.8 416.7 433.5 448.4 466.3 481.5 501.0 515.9 325.0 326.9 ::::: | 394 '.3 393.5 405.7 403.2 418.6 434 '.9 450.3 ::::.: 426.6 425.3 437.4 i 427.0 460. i '.'.'.'.'. 470 '.5 504.9 468.0 483.4 502.4 517.8 95 COLUMNS TABLE 24 SQUARE CORED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS AND NEW YORK CITY BUILDING CODE REQUIRE- MENTS 2000 -Ib. concrete P =Af c [l + (n-l)p] 1:6 mixture ,_ (unsupported length\ n = 15 Max.(- -J =15 f c =500 ( Column cize j? sksSs^ ip.^ iCV.-.-.--o-.-.-:i J ^liftl x ConrSize > Size of column (inches) Size of core (inches) Number of rods Square rods Round rods H 'H y* 1 1H IK % H 14 i 1H iy* 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 4 4 4 e 8 4 6 8 4 6 8 4 6 .8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 42.9 51.4 60.9 66.4 71.9 71.4 76.9 82.4 82.9 88.4 93.9 95.4 '100.9 106.4 108 9 1 14 . 4 119.9 123.4 128.9 134.4 138.9 144.4 149.9 155.4 160.9 166.4 178.4 183.9 igeig 202.4 2ie'.4 221.9 236 '.9 242.4 47.8 56.3 65.8 73.6 40.6 49.1 58.6 62.9 67.2 69.1 73.4 77.7 80.6 84.9 89.2 93.1 97.4 101.7 106.6 110.9 115.2 121.1 125.4 129.7 146 '.9 145.2 i57.4 161.7 174 '.9 179.2 i93.'4 197.7 44.4 52.9 62.4 68.6 74.7 72.9 79.1 85.2 84.4 90.6 96.7 96.9 103.1 109.2 110.4 116.6 122.7 124.9 131.1 137.2 140.4 146.6 154.7 156.9 163.1 169.2 174.4 180.6 186.7 199. 'i 205.2 48.8 57.3 66.8 75.3 77.3 85.8 94.2 88.8 97.3 105.7 101.3 109.8 118.2 114.8 123.3 131 . 7 129.3 137.8 146.2 144.8 153.3 161.7 161.3 169.8 178.2 178.8 187.3 195.7 197.3 205.8 214.2 216.8 225.3 233.7 237.3 245.8! 254.2 267.3 275.7 289 '.8 298.2 sis. 3 321.7 62.5 72.0 82.5 93.5 94.0 105.0 106.5 117.5 128.5 120.0 131.0 142.0 134.5 145.5 156.5 150.0 161.0 172.0 166.5 177.5 188.5 184.0 195.0 206.0 202.5 213.5 224.5 222.0 233.0 244.0 242.5 253 . 5 264.5 264.0 275.0 286. ; 286.5* 297.5 308.5 310.0 321.0 332.0 334.5 345.5 356.5 77.8 88.3 99.8 112.3 126.3 125.8 139.8 140.3 154.3 168.2 155.8 169.8 183.7 172.3 186.3 200.2 189.8 203.8 217.7 208.3 222.3 236.2 227.8 241.8 255.7 248.3 262.3 276.2 269.8 283.8 297.7 292. 3 1 306.3 320.2 315.8 329.8; 343.7 340.3 354.3 368.2 365.8 379.8 393.7' 106.4 118 .9 132.4 149.5 146.9 164.0 162.4 179.5 196.7 178.9 196.0 213.2 196.4 213.5 230.7 214.9 232.0 249.2 234.4 251.5 268.7 254.9 272.0 289.2 276.4 293.5 310.7 298.9 316.0 333.2 322.4 339.5 356.7 346.9 364.0 381.2 372.4 3S9.5 106.7 61.9 71.4 78.0 ! 76.3 84.1 92.0 87.8 95.6 103.5 100.3 108.1 116.0 113.8 121.6 129.5 128.3 136.1 144.0 143.8 151.6 159.5 160.3 168.1 176.0 177.8 185.6 193.5 196.3 204.1 212.0 215.8 223.6 231.5 236.3 244.1 252.0 81.9 92.7 88.5 93.4 104.2 100.0 105.4 105.9 116.7 127.4 119.4 130.2 140.9 133.9 144.7 155.4 149.4 160.2 170.9 165.9 176.7 187.4 183.4 194.2 204.9 201.9 212.7 223.4 221.4 232.2 242.9 241.9 252.7 263.4 263.4 274.2 284.9 285.9 296.7 307.4 309.4 320.2 330.9 344 . 7 355.4 112.5 126.5 126.0 ITO.O 119.9 128.3 133.4 151.2 141.8 140.5 154.5 168.5 156.0 170.0 184.0 172.5 186.5 200.5 190.0 204.0 218.0 208.5 222.5 236.5 228.0 242.0 256.0 248.5 262.5 276.5 270.0 284.0 298.0 292.5 306.5 320.5 316.0 330.0 344.0 340.5 354.5 368.5 366 147.9 165.7 156.3 163.4 181.2 198.9 179.9 197.7 215.4 197.4 215.2 232.9 215.9 233.7 251.4 235.4 253.2 270.9 255.9 273.7 291.4 277.4 295.2 312.9 299.9 317.7 335.4 323.4 341.2 358.9 347.9 365.7 383.4 373 4 171.8 193.6 188.3 210.1 205.8 227.6 249.5 224.3 246.1 268.0 243.8 265.6 287.5 264.3 286.1 308.0 285.8 307.6 329.5 308.3 330.1 352.0 331.8 353.6 375.5 356.3 378.1 400.0 381 8 2i7'.2 237 '.7 259.2 28i .-7 218.6 224.7 239. i 245.2 260 . 6 266.7 283 '.i 289.2 263 '.9 286 '.4 309.9 334 '.4 265.6 273.5 288 '.1 296.0 3ii.6 319.5 336! 1 344.0 :::: 3i2'.7 .... 337 '.2 337.8 346.2 36i.6 369.5 376.2386.6|391.2403.6 380.9394.0,408.9 425.5 363.3 371.7 371.0 382.0 362.7 96 TABLE 25 L Colur^n sira J COLUMNS SQUARE CORED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS Max. /unsupported length^ side 15 2500 -Ib. concrete 1:4% mixture n=12 f c = 625 Size of column (inches) Size of core (inches) Number of rods Square rods 1 I IK I IK Round rods K 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 50. 7j 61.4 73.2 78.6 84.0: 86. 4J 91.1 91.7 98.8 55.5 66.1 78.0 85.7 71.7 83.6 107.2 97.5 103.1 97.1 loee .... 100.7105.51111.1 106.1 113.2121.6 111.5 120 9 117.5124.8 . 116 121 127 | 133 ; 138 I 144 151 156 162 170, 176, 181. 191. 196. 202. 218 224 241 247 4 121 7 128 1 136 2!l38 6; 145 0153 4' 156 7 163 1171 7|175. 11183. 5190. 4J196. 7203. 211. 218. 6225. 0233. 241. .7248. 256. 48.4 59.1 70.9 75.2 79.4 84.1 88.3 92.5, 52.2 62. 8 ! 74.7J 56.5 67.2 79.0 80.71 87.3 86.8J 87. 8i 92.2 93.9 100.4 99.9 108.7 1 IK IK 72.2 84. l' 89.8 97.2103.0 108.0 98.4 102.2 106.5 111.6117.3 102.7108.2 114.8122.4 106.9 114.3 123.1 .l'l26.7 132 .8137.2146 .6J147.7 . .. .0!l43.6il50.o'l57.3 i 165.5 130.9 .7154.1163.8174.7 135.2 41164.6 | 139.4 1 161.7 8172.2 6182.7 181.1 2 191 202 201 8:212 6 J 222 1 140.4 148.6 114.1 117 9 i 118.3 123 .| i ! 122.5129 134 140 146 8 122.2J127.2 9 130.4 138.0 9 ! 138.7148.8 123.8 133.0 139.4 146.6 168. 181. 195. 187. l'l75.4183 9 192.8 ... 6'.. . 6 5 194.8203 6201.3212.2224 0^29.6, 266.1 271.5 291.7 297.1 352.1 38i' 7234 4244 l!246, 8257. 6267 215. 7 2|221 7J235.6250.2 61230 1 243 6257 1215. 4^223. 9232.8J245. 265.5271 273.2281 280.9:292 291.1296 298.8307 306.6317 .J323 325.7,334 324.0333.4344 7,243 2 ! 266 .71280, .1277, .6291, . 1 305 , .7303. .2316. .7,330. .6330. .1 343. .6357. 0237.3245.5 8:254.7267.0 5272.1 288.4 l'260.4268.6 9277.8290.1 6295.2311.6 .351.7358 353.8362.2371 361.6372.7385 .'381 383 2391.6401 5390.9402 .1 413.8422 421.6432 445 7 454 453.4464 415 418 2431 .7445 450 463 6|477 5284 3302 OJ319 11310 9327. 6345. 0337. 8354. 5372. 1365. 9382. 6,400. 5! 394 . 3*412. OJ429. T425. 9442. 6460. 0457. 8474. 5:492. .8293.0 .2314.5 .6335.9 .4318.6 .8340.1 .2.361.6 s'345.5 7'367.0 1 388.4 4373.6 8 395 . 1 2j 416.6 8403.0 21424 5 6J445.9! 4433.6' 8455.1 2476.6 3465.5 7487.0 1 508.4 7 139 7147 8155 149.1 152.8157 9 165 9 173 . 153.3 158 157.5164 172 172.7 178 176.9 184 192 193.3 198 197.5204 2 176. 2184. 3193. 8197. 9 205. 9213. 0144 3 ! 154 6 165 2162 4 173 7 183 5181 8192 1 203 2202 4J213 7223 1149 9 163 7 | 2 168 0181 8 195 6187 4 201 2.214 2' 208 0221 8235 .8156.3 .5173.1 .0 174.4 .6191.3 .31193.8 .OJ210.6 .7227.5 ,0!214.4 .6231.3 .3 248.1 214.7219.0224.1 229.8 ! 236.3 215.2220.7|227.3234.9:243.5253.1 219. 41226.8235.6245.71257.2 270.0 242. 2247. 2^53. 0*259. 4 238.3243.9250.4258.0266.6276 3 242.5249.9 258. 7 268. 8280. 3J293.1 266.5271.6277.3283.8 268.2,274.8282.4 291.0300.6 266.9 274 .3|283 . l!293 .2 304 .7*317 .5 !292.2297.2 ! 303.0309.4 293.9300.4308.0316.6:326.3 292 .5 299 .9j308 .7 318 .8|330 .3 343 . 1 324.r329.s'336.3 334.91343.5353.1 319.4326.8335.6345.71357.2370.0 320.7327.3 347 . 348 5354 3S4 414 446 9355 I) 303 . 384 .3393 . 415 .9423 . 447 8455 . 352 . .4 363. .7J373. .381. .8392. .1408. . ! 412. 4423. 7433. 3454. 6 465 . 2358 0371 8J385 6387. 4401. 2414. 2,418. 0|431. 8445. . 449'. 9463. 7477. .0364.4 .6381.3 .3398.1 .3(393.8 .0410.6 .7427.5 .0424.4 .6441.3 .3458.1 8456.3 5473.1 2490.0 97 COLUMNS TABLE 26 SQUARE CORED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMJttKK I 3000-lb. concrete 1:3 mixture - 7i 12 Max. f 750 JAJN UUJNUK..&J..& 1HS11J RECOMMENDATIONS P = Af c [l + (n l)p] /unsupported length\ U1H, 15 Cofumn size &*$$]* siny ! j N, \ side ) Size of column (inches) Size of core (inches) Number of rods Square rods Round rods H K % 1 IK IK H K Vs i IK IK 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 8 9 10 11 12 13 14 15 10 17 18 19 20 21 22 23 24 25 26 4 4 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8. 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 60.9 73.6 87.9 94.3 100.8 103.6 110.1 116.5 120.9 127.3 133.8 139.6 146.1 152.5 159.9 166.3 172.8 181.6 188.1 194.5 204.9 211.3 217.8 229.6 236.1 242.5 262.3 268.8 290.1 296.5 3i9'.3 325.8 350 '.i 356.5 66.6 79.3 93.6 102.8 86.0 100.3 58.1 70.9 85.1 90.2 95.3 100.9 105.9 111.0 118.1 123.2 128.3 136.9 141.9 147.0 157.1 162.2 167.3 178.9 183.9 189.0 207.2 212.3 23i'.9 237.0 258 '.2 263.3 285.9 291.0 320.3 62.6 75.3 89.6 96.9 104.2 105.3 112.6 119.9 122.6 129.9 137.2 141.3 148.6 155.9 161.6 168.9 176.2 183.3 190.6 197.9 206.6 213.9 221.2 231.3 238.6 245.9 257.6 264.9 272.2 292 '.6 299.9 32i'.9 329.2 67.8 80.6 94.8 104.8 110.6 120.4 130.4 127.8 137.8 147.7 146.6 156.5 166.4 166.8 176.8 186.7 188.6 198.4 208.4 211.8 221.8 231.7 236.6 246.5 256.4 262.8 272.8 282.7 290.6 300.5 310.4 319.8 329.8 339.7 350.6 360.5 370.4 392 '.8 402.7 86.7 100.9 116.7 129.6 133.9 146.9 152.7 165.6 177.6 172.9 185.9 198.8 194.7 207.6 220.6 217.9 230.9 243.8 242.7 255.6 268.6 268.9 281.9 294.8 296.7 309.6 322.6 325.9 338.9 351.8 356.7 369.6 382.6 388.9 401.9 414.8 422.7 435.6 448.6 457.9 470.9 483.8 494.7 507.6 520.6 107.8 123.6 140.8 159.6 176.0 179.8 196.1 201.6 218.0 234.4 224.8 241.2 257.7 249.6 266.0 282.4 275.8 292.2 308.7 303.6 320.0 336.4 332.8 349.2 365.7 363.6 380.0 396.4 395.8 412.2 428.7 429.6 446.0 462.4 464.8 481.2 497.7 501.6 518.0 534.4 539.8 556.2 572.7, 148.5 167.3 187.5 207.7 209.3 129.5 232.5 252 . 8 273.0 257.3 277.5 297.8 283.5 303.8 324.0 311.3 331.5 351.8 340.5 360.8 381.0 371.3 391.5 411.8 403 . 5 423.8 444.0 437.3 457.5 477.8 472.5 492.8 513.0 509.3 529.5 549.8 547.5 567.8 588.0 108.0 109.3 118.6 127.9 126.6 135.8 145.1 145.3 154.6 163.9 165.6 174.8 184.1 187.3 196.6 205.9 210.6 219.8 229.1 235.3 244.6 253.9 261.6 270.8 280.1 289.3 298.6 307.9 318.6 327.8 337.1 349.3 358.6 367.9 116.0 128.7 123.8 133.3 145.9 141.0 149.8 152.0 164.7 177.3 172.3 184.9 197.5 194.0 206.7 219.3 217.3 229.9 242.5 242.0 254.7 267.3 268.3 280.9 293.5 296.0 308.7 321.3 325.3 337.9 350.5 356.0 368.7 381 -.3 388.3 400.9 413.5 422.0 434.7 447.3 457.3 469.9 482.5 506 '.7 518.3 544.9 557.5 159.8 176.3 168.5 178.3 180.0 196.5 188.8 209.7 198.6 201.8 218.3 234.8 225.0 241.5 258.0 249.8 266.3 282.8 276.0 292.5 309.0 303.8 320.3 336.8 333.0 349.5 366.0 363.8 380.3 396.8 396.0 412.5 429.0 429.8 446.3 462.8 465.0 481.5 498.0 501.8 518.3 534.8 540.0 556.5 573.0 210.5 231.4 220.3 233.8 244.7 275.5 258.5 279.4 300.3 284.8 305.7 326.5 312.5 333.4 354.3 341.8 362.7 383.5 372.5 393.4 414.3 404.8 425.7 446.5 438.5 459.4 480.3 473.8 494.7 515.5 510.5 531.4 552.3 548.8 569.7 590.5 243.6 269.3 268.3 294.1 294.6 320.3 346.1 322.3 348.1 373.9 351.6 377.3 403.1 382.3 408.1 433.9 414.6 440.3 466.1 448.3 474.1 499.9 483.6 509.3 535.1 520.3 546.1 571.9 558.6 584.3 610.1 351.0 383 '.3 4i7.6 352.6 359.9 384 '.9 392.2 388 '.8 422.5 390.8 400.1 424 '.6 433.9 418.6 425.9 426.5 436.4 457 '.8 494 . 5 459.8 469.1 496 '.6 505.9 534.8 544.1 : : ; ; ; 46i.2 46i.8 471.7 497.9 498.5 508.4 536 '.2 536.8545.9 546.7^58.8 98 TABLE 27 COLUMNS Column size SQUARE CORED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS mixture = 12 Size of column (inches) Size of core (inches) Number of rods Square rods Round rods H H \ X \ H 1H 12 13 14 15 16 17 18 19 20 21 22 23 24 25 20 27 28 29 30 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25. 20 I 48. 7| 53.3 j! 58.91 63.5 68.8 i 70. 3 ! 54. 9 ! 80.2 ! 75.5! 82.3 .. 82.9 87.5! 92.8 94.9 102 9 93.2 102. 3| 96.7 101.3106.6 '101.9 108.7,116.7 |107. 0116.1 111. 7 116.3121.6 86.4 99 112.8 127 116.9 123.7|131.7 141 122.0 131.1141.8 .. - 8134 0. .. 127.9 133.1 138.2 142.7 132.5 137. 8' 144 139.9'l47.9 157 147.3,158.0 .... ! 151 2 167 145.3149.9 155.2161 150.5 157.3 165.3 174 155.6164.71175.4^87 163. 9! 168.5; 173. 8 180 169.1 175.9 183.9 193 ,184.21183. 3 194. 0206 .0158. .7 .... 183.7 188 188.91195 194. 0| 203 '209 209.9'216 215.0J224 .....231 232.1 238 237.2246 3193 7203 1,213 3214 7224 1 234 5*236 9246 3257 .6199 .7213 .8226 .6 ! 220 .7234 .8,247 . 8*243 .9 256 .0269 254.9260.21266 255.5262.3270.3:279 260.6269.7280.41292 279.5284 !280.1J286.9294 285.2294.3305 . . . 310 312.7320 311.0320.1 330 ,337 339.71347 338.0347.1357 365 367.9375 366.2375.3386 .8291 .930-4 .0317 .6316 .7330 .8343 .6343 .7357 .8370 .8372 . . 401 168 6 185 o'l87 2203 4220 8 ( 206 0223 2240 8227 0244 2261 01250 2266 4J283 4273 6290 8306 0298 2314 4 331 s'323 0340 8350 0367 2384 0379 2395 4412 4408 .4176. .1 ____ .o'l94. .7215. .8214. .5235. .2255. .8235 .5256 .2276 .o'257 .7278 .4299 .4381 .1 301 .8322 o'sos .7326 ,4|347 .s'331 5352 .2372 .8358 .4379 .2399 .0386 .7407 .4428 46.5 56.7 68.1 72.2 76.2 80.7 84.7 88.8 94.5 98.6 102.6 109.5 113.6 117.6 50.1 60.3 71.7 77.5 83.3 84.3 90.1 95.9 104 98.1 103.9 109. 125.7129 129.8 135 133.8,140 143.1 146 147.2152 151.2 158 54.3 64.5 75.9 83.8 69.3 80.7 .5 93.3 .4 103.7 . 4| 102.3 107.1 110.2 117.5 7118.2 117.3 122.1 113 118.9 125.2 132.5140.8! 124.7133.2,142.9 86.2 98.8 112.6 118.8 127.6133.8 ..,,133. 5 138. 3 143. 8 150.0 .1 141.4 148. 7J157.0 166.2 .9 149.4 159.1 .7 !3|166.8 176.5ll87.5i 150.9,155.7161.2167.4 158.8 I 166.1!174.4 183.6 .3 185 189 206 210 !165.3'l69.5 174.3 179.8 186.0 .8 171. l|l77. 4 184.7 193.0202.2 .8 176.9 185.4,195.1:206.1 218.4 6190 6196 .206 6212 6227 189. 197. 1 210. 0|218. 7226. 3193 2204 7205.2214 3215 2225 2235 228 232 8234. 8239. 256 2SO 232 . 240. 248. 5 237 4247 4258 1 199 5212 9 225 l' 220 5233 9,246 3 '242 7256 i;269 .6205.8 .81222.0 .9238.2 .6226.8 .8243.0 .9,259.2 .9^249.0 .0265.2 .1281.4 ? ::: 397.3405.3414 395.6404.7415.4 427 432 427.9435.9J445 435.3446.0458 6425 ,8 ( 441 0439 ,2455 4472 1436 ,8457, 01447 7J467, 4488. .. 255.9260.7266.2272.4 . . 257.5 263 .8 271 . 1 279 .4 288.6 .2263.3271.8^81.5292.5304.8 ..':.... 280. 5285. 3i290. 8297.0 . . 282. H288. 4 295. 7^304.0313. 2 .8 287. 9 296. 4 306.1 347. 1 ( 329. 4 . .'311.l'316.6322.8 . . 307.9314.2321.5329.8339.0 .6 313.7 322.2 331 .9 342.9 355.2 333 . 334 6340 361 9341 7349 .9,377 I 8368 '. 398.3406 ! 428 . 429 ,9437 . 338 .2348 .2358 .1366 ,4376 .4387. .395 8406 8416. 4436 4447 1343 5356. 9369. 3371. 7385. 1 ( 398. 7401. 1414. 5427. .6349.8 .8366.0 .5372.2 .8378.0 .0394.2 .1410.4 2407.4 4 423 . 6 5439.8 . 431.8438.0 7445.0454.2 1 458.1 470.4 99 COLUMNS TABLE 28 SQUARE CORED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS 2000-lb. concrete 1: 6 mixture 71=15 f c =400 Ma X .( lenff * h }=12 \ side I Size of column (inches) Size of core (inches) Number of rods Square rods Round rods M H 14 1 IK IK H H K 1 IK IK 12 g 4 41 .2 45 39.3 42 3 45.9 13 10 4 48.8 52.6 46.9 49.9 53.5 14 4 57.2 61 65.6 55 3 57.3 61.9 66.0 6 6l'5 67^3 58^7 63.2 68.6 g 65.9 62.2 68.2 15 12 4 66.4 70.2 74.8 80.0 64.5 67.5 71.1 75.2 79.9 70 7 76.5 67 9 72 4 77.8 8 75 .'l 71 !4 77 'A 16 13 4 76.4 80.2 84.8 90.0 96.0 74.5 77.5 81.1 85.2 89.9 95.1 6 80 7 86.5 93.3 77.9 82.4 87.8 94.0 8 1 HS ' 1 92^8 81 .4 87.4 94 .5 17 14 4 87.2 91.0 95.6 100.8106.8 85.3 88.3 91.9 96.0 100.7 105.9 6 ! 91.5 97.3 104.1 88.7 93.2 98.6 104.8 8 ! 95.9 103.6 92.2 98.2 105.3 18 15 4 99.8 102.6 107.2 112.4118.4 125.0 96.9 99.9 103.5 107.6 112.3 117.5 6 103.1'108.9 115.7 123.6| 100.3104.8110.2116.4 123.4 8 107.5 115.2 124.3 i 103.8109.8116.9 125.2 19 16 4 111.2 115.0 119.6 124.8 130.8 137.4 .. 112.3 115.9 120.0 124.7 129.9 6 115^5 121.3 128.1 136.0 144.9 112.7117.2 122. 6! 128. 8 135.8 143.6 8 1119.9127.6 136.7 116.2 122.2 329.3 137.6 20 17 4 124.4128.2 132.8 138.0144.0150.6 . . 125.5 129.1 133.2 137. 9 : 143.1 6 , 128.7 134.5 141.3 149.2158.1 ; 125. 9130. 4135. 8142.0 149.0156.8 i 8 133.1 140.8 149.9 160.4 129.4135.4 142.5 150.8 160.1 1 21 18 4 ' 142.2 146.8 152.0 158.0 164,61 139.5 143.1 149.2 151.9 157.1 6 142.7148.5 8 147. 1 154.8 155.3 163.2 163 9 174 4 172.1 182.1 1139. 9|144. 4 J143 4 14Q 4. 149.8 156.5 156.0163.0170.8 1fU S 174 1 22 19 4 157.0 161.6 166.8172.8 . . J.40.4 179. 4 1 . 157.9 162.0 166.7 171.9 6 157.5163.3 8 161.9169.6 170.1 178.7 178.0 186.9 196.9 154.7 159.2 164.6:170.8 177.8 185.6 189.2201.1 (158.2164.2171.3179.6188.9199.4 23 20 4 172.6177.2182.4188.4 195.0 173.5 177.6 182.3 187.5 6 173.1178.9185.7193.6202.5212.5 ..174.8180.2186.4 193.4201.2 8 177 5 185 2 194 3 9n4 s 21 fi 7 17 ^ fi 17Q 8 1Rfi Q 10.1 9 9fU A 91.1 H 24 21 4 |l 189.0 193.6 198.8204.8 211.4' . . . 189.9 194.0198.7203.9 6 189.5 195.3 202.1 210.0218.9 228.9 191 .2196 .6 202 .8 209.8217.6 1 8 193.9 201.6210.7 221.2233.1246.4 190.2196.2203.3211.6 220.9 231.4 25 22 4 210.8 216.0222.0228.6 . . 211.2215.91221.1 6- '. '. 212.5 219.3 I 227.2 236.1 246.1 208.4,213.8220.0 227.0234.8 1 8 211.1218.8227.9238.4 250.3263.6 207.4 213.4,220.5228.8238.1 248.6 26 23 4 . . 228 . 8 234.0 240.0246.6 229.2 233.9 239.1 6 '.'.'.'.'. 230.5237.3245.2 254.1 264.1 226.4231.8238.0 245.0i 252. 8 8 229.1 236.8245.9 256.4 268.3 281.6 231.4238.5246.8 256.1 266.6 27 24 4 1 247.6 252.8 258. 8 265. 4 ! l248.0 ! 252.7 257.9 6 !| 249.3 256.1 264.0 272.9282.9 250.6256.8263.8 271.6 8 247.9255.6,264.7 275.2 287.1 300.4 '.'. '.'. '. 250.2257.3265.6274.9 285.4 28 25 4 272.4 278.4 285.0 267.6272.3 277.5 6 268 '.9 275. 7 283.6 292.5302.5 . . 270.2276.4 283.4 291.2 8 267.5 275.2284.3 294.8 306.7320.0 269.8276.9285.2,294.5 305.0 29 26 4 292.8 298.8305.4 292.7 297.9 6 8 289.3296.1 304.0 295.6304.7315.2 312.9 327.1 322.9 340.4 '.'. '.'. ^290.2 290^6296.8303.8 297.3305.6,314.9 311.6 325.4 30 27 4 292.8 298.8 305.4 292.7 297.9 6 296 '.i 304.0 312.9 322.9 296.8 303.8'311.6 ! 8 '..... 295.6304.7 315.2 327.1 340.4 '.'.'.'.'. 297.3 305.6 | 314.9|325.4 100 TABLE 29 K J COLUMNS SQUARE SAFE LOAD IN CHICAGO BUILD Ma. V "* CORED COLUMNS THOUSANDS OF POUNDS ING CODE REQUIREMENTS Af[l + (n l)p] 2400-lb. concrete /length\ 19 1:4 % mixture ic; ' * *> J ? * -lilt *'\ side ) /* JL6 f c =480 Size Size of of column core (inches) (inches) Number of rods Square rods Round rods H % K 1 i 1,4 IK i! *A 1 1 IK IK 12 9 13 10 14 11 15 12 16 13 17 14 18 15 19 16 20 17 21 18 22 19 23 20 24 21 25 22 26 23 27 24 28 25 29 26 30 27 4 4 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 I I 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 A 6 8 4 6 8 4 6 8 47.1 56.3 66.3 70.5 74.6 77.4 81.5 85.6 89.4 93.5 97.6 102.3 108.5 110.6 116.3 120.4 124.5 131.1 135.3 139.4 147.0 151.1 155.2 50.8 59.9 69.0 75.9 74.3 45.4 54.5 64.6 67.8 71.0 75.6 78.8 82.1 87.6 90.8 94.1 100.6 103.8 107.0 114.5 117.7 121.0 132.6 135.8 l48'.4 151.7 48.2 57.3 67.4 72.1 76.7 78.5 83.1 87.8 90.5 95.1 99.8 103.4 108.1 112.7 117.3 122.0 126.7 132.2 136.9 141.5 148.1 152.7 157.4 164.9 51.1 60.7 70.8 77.1 81.8 88.2 93.8 100.2 106 5 106.8 113.-1 119.5 120.7 127.1 133.4 135.6 141.9 148.3 151.4 157.8 164.1 168.2 74.7 85.7 97.7 106.0 110.7 119.0 124.6 132.9 141.2 139.5 147.8 156.1 155.3 163.6 171.9 172.1 90.1 102.1 115.1 129.0 139.5 143.9 154.4 159.7 170.2 180.7 176.5 107.0 120.0 133.9 148.8 161.8 164.6 177.6 181.4 81.0 86.9 85.3 90.2 93.0 98.9 104.9 106.0 111.9 117.8 119.9 125.8 131.8 134.8 140.7 146.6 150.6 156.5 162.5 167.4 97.3 105.4 102.2 107.9 110.3 118.3 115.2 120.8 124.2 129.1 132.3139.7 140.3! 139.1 144.0 147.1 154.6 155.2 154.9159.8 163.0170.4 171.1 181.0 171.7176.6 134.7 141.0 149.6 163.0 165.5 178.8 182.3 155.9 171.7 188.5 167.9 172.0 173.3 179.8 187.2 179.3 187.9197.8 185 2 189 5 194 4 195.6 200.0 205.0 206.3 165.2 168.5 169.5 174.2 174.6 180.9 186.0 192.3 198.7 204.7 211.1 217.4 224.4 180.4 188.7 189.9 198.2 206.5 208.6 216.9 225.2 228.3 236.6 244.9 248.9 257.2 265.5 270.5 278.8 287.1 283.1 301.4 309.7 316.6 324.9 333.2 349.4 357.7 187.0|194.4 197.5 194.3 199.2 204.8212.2 215.3225.1 213.0217.9 223.5230.9 234.0243.8 232.7237.6 243.21250.6 253.7263.5 253.3258.2 263.81271.2 274.3284.2 274.9278.8 285.4292.8 295.9305.8 297.5302.4 308.0315.4 318.5328.3 321.0325.9 331.5338.9 342.0351.8 345.5350.4 356.0363.4 366.5^76.3 370.9375.8 381.4388.8 391.9401.8 185.7 189.8 204 '.4 208.5 191.1 197.5205.0 197.0205.6215.5 203.9208.2'213.1 209.8:216.3223.7 215.8224.3234.2 223.6227.9'232.8 213.4 226.7 218.7 232.1 245.5 238.4 222.8 225.0 241.5 244.7 183.0 186.2 205 '.6 187.3 191.9 206 '.6 210.7 224.1 228.2 248 '.8 229.5 235.4 250 '.i 256.1 235.9 244.0 248.5 256.6 264.7 270.1 278.2 286.3 292.7 300.7 308.8 324 '.3 332.3 348 '.7 356.8 243.4 253.9 253.4 264.0 274.6 275.0 285.6 296.2 297.6 308.2 318.7 321.1 331.7 342.2 345.6 356.2 366.7 371.0 381.6 392.2 251.8 265.1 259.1 272.4 285.8 280.7 294.0 307.4 303.2 316.6 329.9 326.7 340.1 353.5 351.2 364.6 377.9 376.7 390.0 403.4 261.2 277.7 265.3 281.8 298.3 286.9 303.4 319.9 309.5 326.0 342.5 333.0 349.5 366.0 357.5 374.0 390.5 382.9 399.4 415.9 224 . 6 245 '.3 225.7 230.3 246 '.3 251.0 230.7 237.1 25i'.4 257.7 271.7 277.7 267.9 272.6 273.0 279.3 270.4 293.6 3ie>'.5 294.3 300.2 3i7'.8 323.8 342 '.3 348.2 295.5 301.9 sig'.i 325.4 343.5 349.9 295.1 sis '.7 ..... 343.1 374.2 '373.7382.3 374.8 375.3 ( 383.1 101 COLUMNS TABLE 30 U V H 1 J SQUARE LOAD IN JO BUILD Ma CORED COL1 THOUSANDS ING CODE RI Af c [l + (n-l)p /length} JMNS OF POUNDS SQUIREMENTS ] 2 - Column $fr e > SAFE CHICAC 2900- Ib. concrete 1:3 mixture n 1 ft 1 1 71 J.U f c = 580 *' V side ) ~ JJ3SSS Size of column (inches) Size of core (inches) Number of rods Square rods Round rods X| % 1 m IK H X H i . | . 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 4 4 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 55.1 66.2 78.3 82.4 86.5 91.7 95.7 99.8 106.2 110.2 114.3 121.8 125.9 130.0 138.7 142.7 146.8 156.6 !l60.7 164.8 175.8 179.8 183.9 266 '.i 204.2 22i.6 225 7 58.7 69.8 81.9 87.8 53.4 64.4 76.6 79.8 83.0 89.9 93.1 96.3 104.4 107.6 110.8 120.1 123.3 126.5 136.9 140.1 143.3 iss'.i 161.3 177 '.2 180.4 i97.5 200.7 219 .0 222 2 56.2 67.2 79.4 84.0 88.6 92.8 97.4 102.0 107.3 111.9 116.5 122.9 127.5 132.1 139.7 144.3 149.0 157.7 162.3 166.9 176.9 181.5 186.1 197.2 201.8 206.4 223 '.2 227 8 59.5 70.6 82.7 89.0 96.1 102.4 110.6 116.9 123.1 126.2 132.5 138.8 143.1 149.3 155.6 161.0 167.3 173.6 180.2 186.5 192.7 200.5 206.8 213.0 221.9 228.2 234 5 86.6 99.9 114.4 122.6 130.1 138.3 146.9 155.1 163.3 164.9 173.1 181.3 184.0 192.2 200.4 204.3 212.5 220.7 225.8 234.0 242.2 104.3 118.8 134.4 151.3 161.6 169.2 179.6 188.4 198.8 209.2 208.7 219.1 229.5 230.1 240.5 251.0 123.6 139.3 156 . 1 174.1 186.9 193.2 206.1 213.5 226.4 235.0 247.8 260 . fi 86.2 95.3 101.1 109.8 115.6 121.5 125.4 131.3 137 2 99.5 104.4 114.0 122.0 118.9 124.5 129.7 137.7 134.6 140.1 142.3 148.1 154.0 160.2 166.1 172.0 179.4 185.2 191.1 199.7 205.5 211.4 221.1 227.0 232.9 146'5 154.5 162 5 151.4 161.8 156.9 163.1 164.5 172.5 180.5 183.6 191.6 199.6 203.9 211.9 219.9 225.4 233.4 241.4 169.4 179.8 188.5 198.9 209.4 208.8 219.2 229.7 230.3 240.7 251.1 174.9 188.1 181.1 194.1 207.3 214.4 227.6 235.8 249.0 262.2 200.3 220.6 236.9 242.0 258.3 243.8 249.6 255.5 267.5 273.4 279.3 248.0 256.0 264.0 271.8 279.8 287.8 296.7 304.7 312.7 322.8 330.8 337.9 350.1 358.1 366.1 252.9 263.3 273.8 276.7 287.1 297.5 301.6 312.0 322.5 327.7 338.1 348.6 355.0 365.4 375.8 383.4 393.8 404.3 413.0 423.4 433.8 443.7 454.1 464.6 258.4 271.6 284.9 282.2 295.4 308.6 307.2 320.4 333.6 333.3 346.5 359.7 360.5 373.7 386.9 388.9 402.1 415.4 418.5 431.7 444.9 449.3 462.5 475.7 264.6 280.9 288.4 304.7; 321.0| 313.4 329.7 346.0! 339.5 355.9 372.1 366.7 383.0! 399.3 395.1 411.4 427.8, 424.71 441.0 457.3; 455.5 471.8 488.1 245 '.8 250.5 244.6 250.8 257.1 268.3 274.6 280.9 248.4 256.6 264.8 272.2 280.4 288.6 297.1 305 . 3 313.5 323.2 331.4 339.6 350.5 358.7 366.9 378.9 387.1 395.3 4i6'.7 424.9 252.8 ! 257.6 263.1 270.4 273.6,283.3 276.5281.4 286.9294.2 297.4307.0 301.5 306.3 311.9319.2 322.3 332.0 327.6332.4 338.0345.3 348.4358.1 354.8359.7 365.2372.5 375.7385.3 383.3388.1 393.6400.9 404.1 413.8 412.8417.7 423 . 2 430 . 5 433.7|443.3 443.8448.4 454.0461.3 464.4474.1 244.2 248.3 268 ! 6 272.1 244.8 268 '.6 293 . 5 269.6 274.2 298.3 304.2 294.6 299.2 299.6 305.8 325 '.7 831.9 352 '.9 359.2 38i'.3 387.6 4i6.9 417.2 297.0 323 '.i 324.4 330.3 320.7 325.3 351.7 357.6 350.4 352.5 378 '.8 380.1 386.0 409 '.7 415.6 386.5 393.5 iie'.i 424.1 38i.6 iiois 446 '.3 446.8 454.8 447.4 455.6 447.9 102 TABLE 31 ( Column sire J SQUARE CORED COLUMNS COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS .OS ANGELES BUILDING CODE REQUIREMENTS 1:6 mixture P = Af c (l + (n-l)p} n =15 f c =550 j: e' '.'. -a- " BVJ <:$* mm - i^-SliXs. 3M Jj'l l J Size of column (inches) Size of core (inches) Number of rods Square rods Round rods H X H 1 1H IK H H K 1 1M IK 12 13 14 15 16 * 17 18 19 20 21 22 23 24 25 26 27 28 29 30 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 4 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 4 6 8 6 8 6 8 56.6 67.0 73.0 79.0 78.6 84.5 90.6 91.2 97.2 103.2 111.0 117.0 125.8 131.8 141.8 147.8 61.9 72.3 81.0 89.7 83.9 92.6 101.2 96.5 105.2 113.9 110.3 119.0 127.6 125.1 133.8 142.5 141.1 149.8 158.4 iee'.s 175.5 iss'.o 193.6 204 '.2 212.9 233.2 254 '.7 68.1 78.6 75.4 85.8 54.0 64'. 5 69.2 73.9 76.0 80.7 85.4 93.4 98.1 107.1 111.8 58.2 68.6 75.4 82.2 80.2 87.0 93.7 92.8 99.6 106.4 106.6 113.4 120.1 63.1 73.5 82.8 I 92.0 85.1 94.3 103.6 97.8 107.0 116.2 111.5 120.7 130.0 126.4 135.6 144.8 142.3 151.5 160.8 68.7 79.2 | 75.2 85.6 92.8 J 90.3 J 91.3 90.7 102.8 103.4 116.5 97.2 104.4 90.1 101.9 97.4 105.5 112.8 112.4 109.8 117.0 102.8 114.5 Il26.3 116.5 128.3 140.1 131.4 143.1 154.9 147.3 159.1 170.9 164.4 176.1 187.9 182.5 194.3 206.1 2i3'.5 225.3 233.9 245.7 255.3 267.1 110.0 118.2 127.3 J125.4 125.1 130.8 J149.6 145.6 164.5 1127.6 117.1 129.2 141.3 132.0 144.1 156.2 147.9 160.0 172.1 165.0 177.1 189.2 183.1 195.2 207.3 2i4'.5 226.6 234 '.8 246.9 256 '.3 268.4 123.6 138.8 J154.2 138.4 153.7 123.8 139.2 |154.6 138.6 154.0 131.9 141.1 151.4 146.8 166.2 155.9 180.0 126.7 128.2 135.0 169.4 154.6 170.0 185.4 171.6 187.0 202.4 189.8 205.2 220.6 209.0 224.4 239.8 229.4 244.8 260.2 250.8 266.2 281.6 |169.0 183.4 154.4161.6 169.6180.4 185.0|199.4 171.4 178.6 186.7197.5 202.0216.4 189.6196.8 204.8215.6 220.2234.6 208.8 ! 216.0 224.1 234.8 239.4253.8 229.2'236.4 244.4255.2 259.8274.2 250.6257.8 265.9276.7 281.2295.6 . .280.4 162.7 182.2 201.7 179.8 199.2 218.7 197.9 217.4 236.9 217.2 236.6 256.1 237.5 257.0 276.5 259.0 278.5 297.9 281.5 301.0 320.5 305 2 171.9 196.0 142.6 144.2 150.9 188.9 213.0 237.1 207.1 231.2 255.2 226.3 250.4 274.5 246.7 270.8 294.8 268.1 292.2 316.3 290.7 314.8 338.8 314 3 161.2 168.0 168.6 177.8 i86'.7 196.0 206.6 215.2 226 '.3 235.6 257 '.6 164.8 iss'.o 186.1 205 '.4 ::::: ' 277 '.2 277.9 289.7 288.8 304.2 279 '.6 278.8 290.9 288.4 303.8 299.2 318.2 304.0 322.9 341.8 347.6 366.5 373.4 392.4 400.4 419.4 428.5 447.4 457.6 476.6 312.4 327.8 324 . 6 344.1 338.4 362.5 339.1 363.2 387.2 364.9 389.0 413.1 391.9 416.0 440.0 444.0 4fi8 1 312.1 327.4 336.8 352.2 362.7 378.0 405.0 313.3 3i4.6 337.2 352.6 349.4 368.9 338.1 :.... 339.3 365 '.2 392.1 .'.'.'.'. 363 '.9 363.0 378.4 375.2 394.7 402.2 421.7 430.2 449 7 ..... ..... 405.4 433 4 433.0 459.4473.2 478.9,497.2 462.6 462. 2j Below and to right of zig-zag lines, reinforcement is more than 4 per cent. 103 COLUMNS TABLE 32 ROUND CORED HOOPED COLUMNS Column size 2000 -Ib. 1:6 mixti nje JOINT C01V concrete Volume of Max. 1MITTEE RECOMMENI P = Af c (l + (n-l}p] Hooping = 1% of Volume /unsupported length\ )ATIONS of Core 10 1 f 7nn \ core diameter / t^&r Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods H H 14 1 1H 1>4 H H 7 A l 1H 1M 12 13 14 15 16 17 18 19 20 21 . 22 23 24 25 8 9 10 11 12 13 14 15 16 17 18 19 20 21 6 6 8 6 8 6 8 10 6 8 10 6 8 10 6 8 10 12 ' 6 8 10 12 8 10 12 14 8 10 12 14 8 10 12 14 8 10 12 14 16 8 10 12 14 16 10 12 14 16 53.2 62.5 68.6 73.0 79.1 84.5 90.6 96.6 97.2 103.3 109.3 110.9 116.9 123.0 125.7 131.8 137.8 143.8 141.7 147.8 153.8 159 .8 164.9 170.9 176.9 182.9 183.0 189.0 195.0 201.0 208 '.3 214.3 220.3 81.0 92.5 101.1 105.2 113.8 122.5 118.9 127.5 136.2 133.7 142.3 151.0 159.7 149.7 158.3 167.0 175.7 175.4 184.1 192.8 201.4 193.5 202.2 210.9 219.5 212.8 221.5 230.2 238.8 233.1 241.8 250.5 259 . 1 267.8 254.5 263.2 271.9 280.5 289.2 285.8 294.5 303.1 311.8 101.9 114.6 128.3 140.0 143.1 154.8 166.6 159.1 170.8 182.6 187.9 199.7 211.5 206.0 217.8 229.6 241.4 225.3 237.1 248.9 260:7 245.6 257.4 269.2 281.0 292.8 267.0 278.8 290.6 302.4 314.2 301.4 313.2 325.0 336.8 139.1 153.9 169.9 185.3 202.4 217.8 220.5 235.9 239.8 255.2 270.6 260.1 275.5 290.9 306.3 281.5 296.9 312.3 327.7 343.1 319.5 334.9 350 . 3 365.7 166.1 182.1 218.7 236.8 256.1 275.6 276.4 295.9 297.8 317.3 336.8 339.9 359.4 . 274.4 294.7 316.1 340 . 1 362.7 67.5 78.0 85.6 89.5 97.1 102.2 109.8 117.5 115.9 123.5 131.2 130,7 138.3 146.0 153.6 146.7 154.3 162.0 169.6 171.4 179.1 186.7 19r?4 189.5 197.2 204.8 212.5 208.8 216.5 224.1 231.8 229.1 236.8 244.4 252 . 1 259.8 250.5 258.2 265.8 273.5 281.2 280.8 288.4 296.1 303.8 99.6 112.3 123.3 126.0 137.0 137.9 140.8 151.8 162.8 156.8 167,8 178.8 189.9 184.9 195.9 206.9 2ig":o 203.0 214.0 225.0 236 1 152.7 167.7 166.5 168.7 183.7 182.5 . . f> : 200.8 215.8 219.2 218.9 2 3L- 9 237.3 222.3 233.3 244.4 255.4 - 242.6 253.6 264.7 275.7 286.7 264.0 275.0 286.1 297.1 308.1 297.6 308.7 319.7 330.7 238.2 253.2 268.2 256.6 276.2 277.4 258.5 273.5 288.5 303.5 m 309.9 32T.9 339.9 317.5 332.5 347.5 362.5 276.9 296.5 298.3 317.9 337.5 340.5 360 . 1 297 7 319.1 342.4 343.9 ... 366 . 5 j 228.6 234.6 240.6 246.6 256 '.6 262.0 268.0 278 '.6 284.6 290.6 104 TA^LE 32 Column Size ^ ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS Volume of Hooping = 1% of Volume of Core ,_ /unsupported length\ Max. I j-. I = 10 \ core diameter / COLUMNS 2000- Ib. concrete 1:6 mixture 71=15 f c =700 Size I Diameter of of column i core (inches) I (inches) Number of rods Square rods Round rods ?s L>7 28 29 SO lio 27 20 10 12 14 16 18 10 12 14 16 18 10 12 14 16 18 10 12 14 16 18 20 12 14 16 18 20 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 24 304.4 .321.21341.1 364.1 390.1 312.0332 3!356 1 383.7414.9 319.7 343. 31 371.1 403? 327.4354.3 335.0365.3 346.0 357.1 368.1 379.1 390.1 365.9388.9414 380.91408.5439 395.9J428.1 410.9447.7 425.9 1309.4325.0343 J318.1 336.8 308.2 326.7 348.6 314.2335.4360.4 320.2 344.0 372.2 444.0 469.8 371.8391.7414.7440.7 382. 9 406. 7 434. 31465. 5 393.9 421.7 453.9:490.3 404. 91436.71473. 5; 315. 9!451. 7J493.1 .. 398.7:418.6441.6476.6496.7! 409.8 433.6 461 .2 ! 492.4 ! 527. 4 420.8 1 448.6480.8517.2 431.8463.6500.4 442.8478.6520.0 453.9493.7 437.8461.6489.2520.4 448.8 476.6508.81545.2 459.8491.6528.4 570.0 470.8 506.6548.0 481.9521.7:567.6 467.0490 478.01505. 489.0520 500.0 535 511.1 550 522 . 1 565 .6 615.2 8518.4549.6584 8538.0574.4 8557.6599.2 8]577.2 624.1 9596.8 9616.4 | . 497.3521 . 508.3536 , 519.3551 . 530.3566 . 541.4581 . 552.4596.2646.7 .. 555.4 1548.7579.9614.9 1 568.3 604.7645.5 1 587.9:629.5 ...... 1 607.5654.4 2627.1 , 528.6552.4580.0611.2646.2 .539.6567.4599.6636.0676.8 . 550.6582.4619.2660.8707.4 . 561 .6 597.4 638.8 685. 7J |, 572. 7 612.5|658. 4'710. 5i j, 583.7627.5678.0'.. ... 584.8:612.4:643.6678.6 572.0 599.81632.0 668.4 709.2 583.0614.8651.6|693.2 739.8 594. 0629. 8^671. 2718.1 770 .4 605.1 644.9690.8742.9 616.1 659.9710.4 767.7 627.1 674.9730.0,... 349.8367.9388.3411.1 8435.2 334.2 342.9 361 351.5373. 360.2 385.2 414 368.8397.0429.4 375.6 .7387.4 393.7414 409.1 3399.2424.5 0439.9 .2 368 377. 386.0411 394.6422 402.5420.6 6414.3436.0 .11363.5386.3 358.5 383.01410.4 373.9402.5 389.3 404.6 383.3 398.7 407. 427.3 446.8 8455. 395. 404.2426.1 412.9 437.9466 421.5449 430.2461.5497 423.6442.3464 432.2454 440.9465.9494 449.5477 458.2489.5525 .0 479.4 .8 510.1 .5 471.5493.2517.754 483.3 495.1 461.4 470.1 478.7506.9539 487.4518 496.1 .7 530.4 508.6 524.0 556 .3 554.7595 570.1 501 491.7513 500.4 525 509.0537 517.7549 526.4560 544 531.7556 540.3568 549.0580 557.7592 '564.1 .8523, .6538, .4'554 .2569 .0585 .7600 .1;554, .9570. .7585. .5J600, .3'616. .0631. 433. 453.1 472.6 492.0 436.9 6461.0 485.0 441.0463 460 . 5 487 451.4 480.0 499.5 536 518.9 488. 508.0539 527.5 546.9 566.4 537.2 .7 576.1 .6 615.1 5548. 9|567. 3587. 6606. 0625. 4645. 8579. 2,598. 61618. 9,637. 3 657. 7676. .s .9 511.9 .0 5 51; .9 564.0 5.1 569.1 593.2 617.2 0575.4 5599.4 623 . 5 4647.5 9671.6 4 1 3 606.7 8 630'. 7 3 654.8 7678.8 2 702.9 7 565.51587.2 611.7 639.1 577.3602.6631.2663.1 589.1 618.0650.7687.2 1572.7600.9633.3670.1 711.2 581 .4 612.7 648.7 689.6 735.3 590.1 624.4 664.1 709.1 759.3 598.7636.2 ! 679.5;728.6 105 COLUMNS TABLE 32 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS Column size ._.> 2000 -lb. concrete 1:6 mixture n = 15 f c =700 l}p] Volume of Hooping =1% of Volume of Core Max unsu PP rted core diameter / Size of column (inches) 3f> 36 37 38 Diameter of core (inches) 10 31 32 33 34 35 3(1 37 38 Number of rods Hi 18 20 22 24 26 28 Hi 18 20 22 21 26 28 Hi 18 20 22 21 26 28 30 Square rods 1605.6 633. 4,665. 6i702.0 742.8 616.6 648.4)685.2 726.8 773.4 .627.6663.4 704. 8 751. 71804.0 638 7678.5 724.4 776.5 .649.7693.5744.0801.3 .660.7708.5763.6' 667.9700, 682.9719, 697.9 739, 713.0758 728.01778, 743.01798, 703.7i735. 718.7755. 733.7 775. 748.8794. 763.8 ! 814. 778.8 : 833. >793.8'853. 740.5772. i 755.5| 792. 770.5811. 1785.61831. '800.6:851. 815.6870. 830.6890. 778.5810. 793.5J830. 808.5849. 823.6 ; 869. . '838.6'889. 853.6908. . I868.6J928. ,832.5869, '847. 5(888, 862.6;908 i877.6i928 I892.6J947 ;907. 61967 922.61986 1 736 7 761 3786 9811 5835 1 860 9772 5,797 11822 7!846 3 871 9 896 5 921 5777.3 3807.9 2838.5 0869.2 3813.1 1 843 . 7 0874.3 8905.0 7 809.11849.9 3833.9880.5 9i858. 8)911.1 51883.6)941.8 1:908.4)972.4 71933.2 ..... 3 958.0). 7847.1887.9 3 871.9918.5 9 896.8,949.1 5 921.6979.8 1 946.4 7971.2 3 996.0 3 910.91957.5 ,9 935.8)988.1 1010 1041 5 960.6 1 985.4 71 1010 3) 1035 9 1060 872.6909.4 951.0997.6 887.6929.0975.9 902.7 948.6 '917.7'968.2 ^932.7987.8 1947.7 1007 ! 962.7 1027 1001 1025 1050 1075 1100 1019 1049 1080 1111 913.9950.7992.3 928. 9970. 3' 10171 1944.0 989.9) 1042) 959.0) 1009 1067 974.0 1029 1092 989.0 1004 1019 1049 1116 1068 1088 1141 1166 1028 1059 1089 1120 1151 1039 1069 1100 1131 1161 1192 1223 Round rods 606. 615. 623. 632. 610.9636.2 664.8696.7 622.7651.6684.3 720.8 3 634.5 666.9 703.7|744.8 0646.3682.3723.21768.9 7658.0697.7742.7792.9 3669.8713.1 762.2 817.0 645. 657.2 686 680.8 692. 704 4670.7699.3 731.2 718.8755.3 0701.4 738.2 779.3 716.8757.7J803.4 5732.2 777.2827.4 .3747.6796.7851.5 753.4 765.1 693.0 704.8737.2 716.6752 728.3 740.1 751.9 706.5735.1 767.0 721.9 754.6791.1 774.0815.1 .6 793.5)839.2 768.0:813.0863.2 783.4 832.5:887.3 798.8,852.0911.3 743.3j771.9803.8 729.8758.7 791. 4 ; 827. 9 741.6774.0)810.8:851.9 789.4l830.3 1 876.0 804.81849.8)900.0 776. 9 820. 2'869. 31924.1 788.7835.6 ! 888.8948.1 781.3 809.9 841.8 767.8)796.7i829.4865.9 779.6812.0848.8i889.9 791.4)827.4,868.3 914.0 803.1 842.8:887.8938.0 814.9)858.2 907.3 962.1 826.7873.6926.8,986.1 835.7868.4 ; 904.9 818.6851.0.887.8928.9 830.4866.4 907.3953.0 842.1(881.8926.8977.0 853.9 897.2 946.3 865.7912.6965.8 877.51928.0985.3 1001 1025 1049 875.8908.5945.0 858.71891.1 927.9969.0 870.5906.5947.4993.1 882.2921.9966.9 " 894.0937.3986.4 905.8952.2 917.6968.1 1006 1025 1017 1041 1065 1089 ...1917.1949.8986.3 ...1932.4969.2 1010 911.8 I 947.8988.7 923.5963.2 935.3978.6 947.11994.0 958.9 1009 970.7 1025 1008 1028 1047 1067 1086 1034 1058 1083 1107 1131 1155 100 TABLE 32 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS Volume of Hooping Max. 1% of Volume of Core **ngth\ ==w \ core diameter I 2000 -Ib. concrete 1:6 mixture n=15 f c =700 Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods H H T4 : l i IX U4 X H H 1 IX IK 43 44 45 46 47 48 49 50 39 40 41 42 43 44 45 46 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 20 22 24 26 28 30 956.2 971.2 986.3 1001 1016 1031 1046 1061 993.0 1012 1032 1052 1071 1091 1111 1130 1036 1056 1076 1095 1115 1134 1154 1174 1101 1120 1140 1159 1179 1199 1218 1146 1166 1186 1205 1225 1244 1264 1193 1213 1232 1252 1271 1291 1311 1241 1260 1280 1300 1319 1339 1358 1290 1309 1329 1349 1368 1388 1407 1359 1379 1399 1418 1438 1457 1035 , 1060 1084 1109 1134 1159 1184 1208 1078 1103 1128 1153 1178 1202 1227 1252 1148 1172 1197 1222 1247 1272 1296 1193 1218 1243 1268 1292 1317 1342 1240 1265 1289 1314 1339 1364 1389 1288 1313 1337 1362 1387 1412 1437 1337 1361 1386 1411 1436 1461 1485 1411 1436 1461 1486 1511 1535 1081 1112 1143 1173 1204 1234 1265 1296 1125 1155 1186 1217 1247 1278 1308 1339 1200 1231 1261 1292 1322 1353 1384 1245 1276 1307 1337 1368 1399 1429 1292 1323 1353 1384 1415 ii 1340 1371 1401 1432 1463 1493 1524 1389 1420 1450 1481 1511 1542 1573 1470 1500 1531 1561 1592 1623 959.4 974.7 990.1 1005 1021 1036 1052 1067 1003 1018 1034 1049 1064 1080 1095 1110 1063 1078 1094 1109 1124 1140 1155 1108 1124 1139 1155 1170 1185 1200 992.1 1012 1031 1051 i 1070 1090 1109 ; 1128 1036 1055 1074 1094 1 1113 1133 1152 1172 1100 1119 1139 1158 1178 1197 1216 1145 1165 1184 1204 1223 1243 1262 1192 1211 1231 1250 1270 1289 1309 1240 1259 1279 1298 1318 1337 1357 1289 1308 1328 1347 1367 1386 1406 1358 1378 1397 1417 1436 1456 1029 1053 1077 1101 i 1125 1149 1173 1197 1072 1096 1120 1144 1168 1192 1216 1240 1141 1165 1189 1213 1237 1261 1285 1186 1210 1234 1258 1282 1307 1331 1233 1257 1281 1305 1329 1353 1377 1281 1305 1329 1353 1377 1401 1425 1330 1354 1378 1402 1426 1450 1474 1404 1428 1452 1476 1500 1524 i 954.1 965.8 977.6 989.4 1001 1013 ioog 1021 1033 1045 1056 1654 1066 1077 1089 1101 iiii 1123 1135 1147 1 P 1015 1030 1045 1060 1075 1090 1105 1059 1074 1089 1104 1119 1134 1149 1 1 : : : : . - - 1120 1135 1150 1165 1180 1195 iiee 1181 1196 1211 1226 1441 i2i4 1229 1244 1259 1274 1289 i 1170 1186 1201 1217 1232 1247 1170 1182 1193 ::::: '1218 1229 1241 1218 1234 1249 1265 1280 1295 1278 1293 1308 1323 1338 i328 1343 1358 1373 1388 1283 1298 1313 1329 1344 '1278 1290 1333 1348 1363 1379 1394 1328 1340 107 COLUMNS TABLE 33 2500 -Ib. concrete 1:4% mixture n=12 f c =870 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS P=Af e [l+(n-l)p] Volume of Hooping 1% of Volume of Core Max ( unsu PP rted length\ = w ' \ core diameter I fc Column size >i Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods H K 1 1H IK 1 % K K 1 IK l l A 12 13 14 15 16 17 18 19 20 21 22 23 24 ^ 25 8 9 10 11 12 13 14 15 16 17 18 19 20 21 6 6 8 6 8 6 8 10 6 8 10 6 8 10 6 8 10 12 6 8 10 12 8 10 12 14 iS 12 14 X 8 10 12 14 ii 12 14 16 8 10 12 14 16 10 12 14 16 1 61 73 79 86 92 100 106 112 116 122 128 133 139 145 152 157 163 169 171 177 183 189 198 204 210 216 221 227 233 239 ; - 2&i 257 263 "276 282 288 294 "309 314 320 337 342 348 94 108 116 124 132 141 141 149 158 159 168 176 185 179 188 196 204 209 217 226 234 231 240 248 257 255 264 272 281 280 289 297 306 314 307 316 324 333 341 344 352 361 369 117 133 150 161 168 180 191 188 200 211 221 233 244 244 255 267 278 267 279 290 302 293 304 316 327 339 319 331 342 354 365 359 370 382 393 161 179 199 214 235 250 258 273 282 297 312 307 322 337 352 333 349 364 379 394 377 392 407 422 191 211 251 274 298 317 323 342 349 368 388 396 416 3ir, 341 367 391 419 78 91 98 105 113 115 121 128 136 138 145 153 156 164 171 179 176 184 191 199 205 212 220 227 ! 227 1 235 1 242 i 250 251 259 266 274 ; 277 i 284 292 299 306 303 311 318 326 333 339 346 354 361 131 141 148 158 166 177 189 186 197 208 218 218 229 240 250 241 251 262 273 264 275 286 297 290 300 311 322 333 316 327 238 349 359 355 366 377 388 :::: .... 159 178 193 198 212 234 248 191 211 252 256 271 280 295 309 305 320 335 349 332 347 361 376 391 375 389 404 419 274 298 317 323 342 350 369 388 ;::: 397 416 318 344 .... 370 394 422 108 TABLE 33 ^ Columr> sift? tt ROUND SAFE LOAI JOINT CO1V Volume of Max. CORED HOOPED COLl ) IN THOUSANDS OF ] IMITTEE RECOMMENI P=Af e (l + (n-l)p] Hooping =1% of Volume /unsupported length\ IMNS >OUN )ATIC of a 10 COLUMNS DS )NS 9re 2500 -lb. concrete 1:4]^ mixture n = 12 f c =870 H \ core diameter / Tt*J&r Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods H % H 1 IK \Vi H H 7 A 1 IH IH 26 27 28 29 30 31 32 33 34 22 23^ 24 25 26 27 28 29 30 10 12 14 16 18 10 12 14 16 18 10 12 14 16 18 10 12 14 16 18 20 12 14 16 18 20 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 24 368 376 383 391 398 385 395 406 417 428 415 426 437 448 458 447 458 469 480 490 481 492 502 513 524 535 526 537 548 559 570 563 574 584 595 606 617 600 611 622 633 643 654 639 650 661 672 682 693 404 419 433 448 463 435 449 464 479 493 467 482 496 511 525 500 515 530 544 559 574 550 564 579 594 608 586 601 615 630 645 659 624 638 653 668 682 697 663 677 692 707 721 736 703 718 732 747 762 776 791 426 452 373 381 390 398 407 404 412 421 429 438 '444 453 461 470 '478 486 495 503 512 513 521 530 538 546 '557 566 574 583 594 '595 603 612 620 629 'e>4i 651 659 668 683 691 700 708 716 388 400 411 423 434 419 431 442 454 465 451 463 474 486 497 485 496 508 519 531 542 531 542 554 565 577 567 579 590 602 613 625 605 616 628 639 651 662 644 655 667 678 690 701 684 696 707 719 730 743 753 406 421 436 451 466 437 452 467 482 497 469 484 499 514 529 502 517 532 547 562 577 552 567 582 597 612 588 603 618 633 648 664 626 641 656 671 686 701 665 680 695 710 725 740 705 720 735 750 765 780 795 426 445 464 457 476 495 514 489 508 527 546 565 522 541 560 579 598 517 576 595 614 633 650 612 631 650 669 688 707 650 669 688 707 726 745 689 708 727 746 765 784 729 748 767 786 805 824 843 448 472 479 502 511 535 558 545 568 592 615 603 626 647 639 663 686 710 677 700 724 747 771 716 739 763 786 810 756 779 803 826 850 873 446 476 372 378 384 457 476 495 515 483 507 511 489 508 528 547 566 523 542 561 580 599 515 539 563 543 .... 548 572 597 577 607 577 596 615 634 653 613 632 651 670 689 709 651 670 689 708 727 746 689 709 728 748 766 785 730 749 768 787 806 826 845 607 631 656 641 644 668 692 716 678 708 681 705 730 754 715 745 .... 720 744 768 793 817 760 785 809 833 857 881 754 784 814 794 824 854 884 .'' 690 701 712 723 733 744 109 COLUMNS TABLE 33 2500- Ib. concrete I'AV^ mixture n = 12 f c =870 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS P=Af e [l+(n-iyp] Volume of Hooping =1% of Volume of Core (unsupported length\ _ Max. [ j-. ] =10 \ core diameter I Column sire , Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods H H H 1 IX 1H H H H 1 IH IK " 35 36 37 38 39 40 41 42 31 32 33 34 35 36 37 38 14 16 18 20 22 24 14 16 18 20 22 24 14 16 18 20 22 24 26 14 16 18 20 22 24 26 14 16 18 20 22 24 26 16 18 20 22 24 26 28 16 18 20 22 24 26 28 16 18 20 22 24 26 28 30 732 743 754 765 775 786 760 774 789 804 819 833 802 817 832 846 861 876 847 861 876 891 905 920 935 892 907 922 936 951 966 980 940 954 969 984 998 1013 1028 1003 1017 1032 1047 1061 1076 1091 1053 1067 1082 1097 1111 1126 1141 1104 1119 1133 1148 1163 1177 1192 1206 791 810 829 848 868 887 834 853 872 891 910 929 878 897 916 936 955 974 993 924 943 962 981 1000 1020 1039 971 990 1009 1028 1048 1067 1086 1039 1058 1077 1096 1115 1134 1154 1089 1108 1127 1146 1165 1184 1203 1140 1159 1178 1197 1216 1235 1255 1274 827 851 875 899 924 866 896 926 '733 742 750 759 738 749 761 772 784 795 780 792 803 815 826 838 '836 848 860 871 882 894 '881 893 905 916 928 939 '929 941 952 964 975 987 '989 1001 1012 1024 1035 1047 i039 1051 1062 1074 1085 1097 iio2 1113 1125 1136 1148 1159 762 777 792* 807 822 837 805 820 835 850 865 880 849 864 879 894 909 925 940 895 910 925 940 955 970 985 942 957 972 987 1002 1017 1032 1006 1021 1036 1051 1066 1081 1096 1056 1071 1086 1101 1116 1131 1146 1107 1122 1137 1152 1167 1182 1197 1212 790 809 828 847 866 885 833 852 871 890 909 928 877 896 915 934 953 972 991 923 942 961 980 999 1018 1037 970 989 1008 1027 1046 1065 1084 1038 1057 1076 1095 1114 1133 1152 1088 1107 1126 1145 1164 1183 1202 1139 1158 1177 1196 1215 1234 1253 1272 821 845 868 892 915 939 864 888 911 935 958 982 909 932 956 979 1002 1026 1049 954 978 1001 1025 1048 1072 1095 1001 1025 1048 1072 1095 1119 1142 1073 1097 1120 1144 1167 1191 1214 1123 1147 1170 1194 1217 1241 1264 1175 1198 1222 1245 1269 1292 1316 1339 869 893 918 942 966 990 914 938 962 986 1011 1035 1060 959 984 1008 1032 1056 1081 1105 1007 1031 1055 1079 1103 1128 1152 1079 1104 1128 1152 1176 1200 1225 1129 1154 1178 1202 1226 1250 1275 1180 1205 1229 1253 1277 1302 1326 1350 909 939 969 999 953 983 1013 1043 999 1029 1059 1089 1119 1046 1076 1106 1136 1166 1196 1125 1155 1185 1215 1244 1274 ' .... 1175 1205 1234 1264 1294 1324 1226 1256 1286 1316 1346 1375 1405 110 TABLE 33 Column size COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS Volume of Hooping /unsupported length\ Max. [ \ 1% of Volume of Core 10 j-. core diameter I 2500 -Ib. concrete 1:4% mixture n=12 f c =870 Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods H H y* 1 1H IK H H y* 1 1H IK 43 44 45 46 47 48 49 50 39 40 41 42 43 44 45 46 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 20 22 24 26 28 30 1157 1171 1186 1200 1215 1230 1244 1259 1192 1212 1231 1250 1269 1288 1307 1326 1246 1266 1285 1304 1323 1342 1361 1380 1321 1340 1359 1378 1397 1417 1436 1378 1397 1416 1435 1454 1473 1492 1436 1455 1474 1493 1512 1531 1551 1495 1514 1533 1553 1572 1591 1610 1556 1575 1594 1613 1632 1652 1671 1637 1656 1676 1695 1714 1733 1233 1257 1282 1306 1330 1354 1378 1403 1287 1311 1335 1360 1384 1408 1432 1457 1367 1391 1415 1439 1464 1488 1512 1423 1448 1472 1496 1520 1544 1569 1481 1506 1530 1554 1578 1603 1627 1541 1565 1589 1614 1638 1662 1686 1602 1626 1650 1674 1699 1723 1747 1688 1712 1736 1761 1785 1809 1279 1308 1338 1368 1398 1428 1458 1488 1332 1362 1392 1422 1452 1482 1512 1542 1418 1448 1478 1508 1537 1567 1597 1474 1504 1534 1564 1594 1624 1654 1533 1562 1592 1622 1652 1682 1712 1592 1622 1652 1682 1712 1742 1771 1653 1683 1713 1743 1772 1802 1832 1745 1775 1805 1835 1865 1894 1160 1175 1190 1205 1220 1235 1250 1265 1214 1229 1244 1259 1274 1289 1304 1319 1284 1299 1314 1329 1344 1359 1374 1341 1356 1371 1386 1401 1416 1431 1192 1211 1230 1249 1268 1287 1306 1325 1245 1264 1283 1303 1322 1341 1360 1379 1320 1339 1358 1377 1396 1415 1434 1377 1396 1415 1434 1453 1472 1491 1435 1454 1473 1492 1511 1530 1549 1494 1513 1532 1551 1570 1589 1608 1555 1574 1593 1612 1631 1650 1669 1636 1655 1674 1693 1712 1731 1227 1251 1274 1298 1321 1345 1368 1392 1281 1305 1328 1352 1375 1399 1422 1446 1360 1384 1407 1431 1454 1478 1501 1417 1440 1464 1487 1511 1534 1558 1475 1498 1522 1545 1569 1592 1616 1534 1558 1581 1605 1628 1652 1675 1595 1619 1642 1666 1689 1712 1736 1681 1704 1728 1751 1775 1798 1154 1166 1177 1189 1200 1212 :::: 1225 1240 1254 1269 1284 1298 1313 1281 1295 1310 1325 1339 1354 1368 i352 1366 1381 1396 1410 1425 iiio 1425 1438 1454 1469 1483 1469 1484 1499 1513 1528 1543 i220 1231 1243 1254 1266 1275 1287 1298 1310 1321 .... '.'.:: 1343 1355 1366 1378 .... 1413 1425 1436 1414 1429 1444 1459 1474 1489 '.'.'.'. i472 1484 1495 1473 1488 1503 1518 1533 1548 1545 1560 1574 1589 1603 1549 1564 1579 1594 1609 1545 1556 .... 1607 1622 1636 1651 1666 .... 1611 1626 1641 1656 1671 ieo7 1618 111 COLUMNS TABLE 34 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS 3000- Ib. concrete 1:3 mixture n = 10 -p Volume of Hooping =1% of Volume of Core Max /unsupported length\ \ core diameter ) Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods H H % 1 IK U4 H H H 1 1H 1>4 12 13 14 15 16 17 18 19 20 21 22 23 24 25 8 9 10 11 12 13 14 15 16 17 18 19 20 21 6 6 8 6 8 6 8 10 6 8 10 6 8 10 6 8 10 12 6 8 10 12 8 10 12 14 8 10 12 - 14 8 10 12 14 8 10 12 14 16 8 10 12 14 16 10 12 14 16 70 84 90 100 105 117 123 129 136 142 148 157 163 168 179 185 191 196 203 209 215 220 234 240 246 252 262 267 273 279 107 125 133 144 152 161 164 173 181 187 195 203 212 211 219 227 236 245 253 . 261 271 272 280 289 298 301 309 317 327 331 339 348 357 364 363 372 380 389 397 405 414 423 431 134 153 173 185 196 207 218 219 231 242 257 268 279 284 295 307 318 313 324 335 347 343 355 366 377 389 375 387 398 409 421 421 432 443 455 184 206 230 245 271 285 298 313 327 341 356 357 372 387 402 389 404 419 434 449 438 453' 468 482 218 242 286 314 342 361 373 392 405 424 443 458 476 360 390 423 446 480 89 105 112 122 129 132 141 148 156 161 169 176 184 191 199 206 208 215 222 230 241 248 255 263 268 275 283 290 297 304 312 319 327 335 342 349 357 359 367 374 382 389 401 408 415 423 151 161 171 182 193 204 215 217 228 239 249 243 254 264 275 281 292 302 313 310 320 331 342 340 351 361 372 383 372 383 394 404 415 417 428 438 449 183 205 219 218 229 243 242 269 284 287 296 311 314 .... 325 340 354 356 370 384 399 343 362 373 392 363 393 296 302 308 '327 332 338 344 '365 371 376 '399 404 410 388 402 417 431 446 436 451 465 479 406 424 443 426 450 448 458 477 483 112 TABLE 34 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS Volume of Hooping =1% of Volume of Core )p] Vol Max. /unsupported length\ \ core diameter ) 10 3000 -Ib. concrete 1:3 mixture n = 10 f c =1050 Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods K H 1 IK IK H H H 1 1H IK 2(3 27 28 29 30 31 32 3.3 34 22 23 24 25 26 27 28 29 30 10 12 14 16 18 10 12 14 16 18 10 12 14 16 18 10 12 14 16 18 20 12 14 16 18 20 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 24 436 443 451 458 466 452 463 474 484 495 489 500 511 521 532 528 539 549 560 571 569 579 590 601 611 622 621 632 643 653 664 665 676 686 697 708 718 710 721 732 742 753 764 757 768 779 789 800 810 '817 827 838 849 859 870 471 486 500 515 529 509 523 538 552 567 547 562 576 591 605 588 602 617 631 646 660 644 659 673 688 702 688 703 717 731 746 760 733 748 762 777 791 806 780 795 809 824 838 853 829 844 858 872 887 901 916 494 513 531 519 543 441 449 458 466 474 478 487 496 503 511 "525 534 542 550 456 467 479 490 501 493 504 516 527 539 532 543 555 566 577 572 584 595 606 618 629 626 637 648 660 671 669 681 692 704 715 726 715 726 738 749 760 772 762 773 784 796 807 819 810 822 833 845 856 867 879 473 488 503 518 533 511 525 540 555 570 549 564 579 594 609 590 605 619 634 649 664 647 661 67Q 691 706 690 705 720 735 750 765 736 751 765 780 795 810 783 797 812 827 842 857 831 846 861 876 891 906 920 493 512 531 530 549 568 587 569 588 607 625 644 609 628 647 666 685 670 689 708 727 745 714 733 752 770 789 808 759 778 797 816 834 853 806 825 844 863 881 900 855 874 893 911 930 949 968 515 538 552 575 591 614 637 631 655 678 701 697 720 743 740 764 787 810 786 809 832 855 879 833 856 879 902 925 881 905 928 951 974 997 440 445 451 531 550 569 587 556 580 584 570 588 607 626 645 610 629 648 667 686 595 619 642 635 659 683 623 663 693 ! 566 575 582 591 599 608 617 624 633 641 671 690 709 728 746 715 734 752 771 790 809 760 779 798 817 836 854 807 826 845 864 883 901 856 875 893 912 931 950 969 701 725 749 745 769 793 817 790 814 838 862 837 861 885 909 933 886 910 934 958 981 1005 735 .... 778 808 .... 661 668 676 685 693 '706 713 722 730 738 760 769 777 785 824 853 871 900 930 919 949 979 1008 '.'.'.'. 809 817 826 834 842 .... 113 COLUMNS TABLE 34 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS .^Column sire ^ 3000 -lb. concrete 1:3 mixture n = 10 f c =1050 Volume of Hooping =1% of Volume of Core M I unsupported length\ =lg \ core diameter I Size of Diameter of Number Squar e rods Roun< irods column (.inches) core (inches) of rods H H K 1 IK IK ^ H K 1 1H IK 35 31 14 867 894 925 960 999 872 896 924 955 16 878 908 944 984 1029 883 911 943 978 18 888 923 963 1008 1058 '868 895 926 962 1001 20 899 937 982 1032 877 906 941 980 1024 22 909 952 1000 1056 884 918 956 999 1048 24 920 966 1019 893 929 971 1018 1071 36 32 14 946 977 1012 1051 924 948 976 1007 16 960 996 1036 1081 935 963 995 1030 18 975 1015 1060 1110 947 978 1014 1053 20 989 1033 1084 1140 958 993 1032 1076 22 1004 1052 1108 969 1008 1051 1100 24 1018 1071 1131 981 1023 1070 1123 37 33 14 999 1030 1066 1105 1002 1030 1060 16 1014 1049 1089 1135 '989 1017 1048 1084 18 1028 1068 1113 1164 1000 1032 1067 1107 20 1043 1087 1137 1193 1012 1047 1086 1130 22 1057 1106 1161 1023 1061 1105 1153 24 1072 1125 1185 1034 1076 1124 1176 26 1086 1144 1209 1046 1091 1142 1200 38 34 14 1055 1086 1121 1160 1057 1085 1116 16 1069 1105 1145 1190 1044 1072 1104 1139 18 1084 1123 1169 1219 1056 1087 1122 1162 20 1098 1142 1192 1249 1067 1102 1141 1185 22 1112 1161 1216 1278 1078 1117 1160 1208 24 1127 1180 1240 1090 1131 1179 1232 26 1141 1199 1264 1101 1146 1198 1255 39 35 14 1111 1143 1178 1217 1114 1142 1173 16 1126 1161 1202 1246 iioi 1129 1161 1196 18 1140 1180 1225 1276 1112 1144 1179 1219 20 1155 1199 1249 1306 1124 1159 1198 1242 22 1169 1218 1273 1335 1135 1173 1217 1265 24 1184 1237 1297 1365 1147 1188 1236 1289 26 1198 1256 1321 1158 1203 1254 1312 40 36 16 1185 1220 1260 1305 1188 1219 1254 18 1199 1239 1284 1335 ii7i 1202 1238 1278 20 1213 1258 1308 1364 1182 1217 1257 1301 22 1228 1277 1332 1394 1194 1232 1275 1324 24 1242 1296 1356 1423 1205 1247 1294 1347 26 1257 1315 1380 1453 1217 1262 1313 1370 28 1271 1333 1404 1228 1277 1332 1394 41 37 16 1245 1280 1320 1365 1248 1279 1315 18 1259 1299 1344 1395 i23i 1263 1298 1338 20 1274 1318 1368 1424 1243 1277 1317 1361 22 1288 1337 1392 1454 1254 1292 1336 1384 24 1303 1356 1416 1483 1265 1307 1354 1407 26 1317 1375 1464 1513 1277 1322 1373 1430 28 1332 1394 1488 1288 1337 1392 1454 42 38 16 1307 1342 1382 1427 1310 1341 1376 18 1321 1361 1406 1457 1324 1360 1400 20 1336 1380 1430 1486 1304 1339 1379 1423 22 1350 1399 1454 1516 1316 1354 1397 1446 24 1364 1418 1478 1545 1327 1369 1416 1469 26 1379 1437 1502 1575 1339 1 384 1435 1492 28 1393 1455 1526 1605 1350 1398 1454 1516 30 1408 1474 1550 1361 1413 1473 1539 114 TABLE 34 ^Column si COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS p Volume of Hooping =1% of Volume of Core ._ / ' \ unsupported length\ _ core diameter ) 3000-lb. concrete 1:3 mixture /i = 10 f c =1050 Size of column (inches) Diameter of core (inches) Number of rods Square rods- Round rods *A H H 1 i 1W IK M H H 1 IK i IK 43 44 45 46 47 48 49 50 39 40 41 42 43 44 45 46 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 20 22 24 26 28 30 1370 1385 1399 1414 1428 1442 1457 1471 1450 1464 1479 1493 1508 1522 1536 1517 1531 1545 1560 1574 1589 1603 1599 1614 1628 1643 1657 1672 ie7o 1684 1698 1713 1727 1742 l74i 1756 1770 1785 1799 1814 i829 1844 1858 1873 1887 1904 1919 1933 1948 1962 1406 1424 1443 1462 1481 1500 1519 1538 1471 1490 1508 1527 1546 1565 1584 1603 1556 1575 1594 1613 1632 1651 1670 1625 1644 1663 1681 1700 1719 1738 1695 1714 1733 1752 1771 1789 1808 1767 1786 1804 1823 1842 1861 1880 1840 1859 1878 1897 1916 1935 1953 1934 1953 1972 1991 2010 2029 1446 1470 1494 1517 1541 1565 1589 1613 1511 1535 1559 1583 1606 1630 16.54 1678 1602 1626 1649 1673 1697 1721 1745 1670 1694 1718 1742 1766 1790 1813 1740 1764 1788 1812 1836 1860 1884 1812 1836 1860 1884 1907 1931 1955 1885 1909 1933 1957 1981 2005 2029 1984 2008 2032 2056 2080 2104 1491 1520i 1550 1579 1609 1638 1668 1697 1556 1585 1615 1644 1674 1703 1733 1762 1652 1682 1711 1741 1770 1800 1829 1720 1750 1780 1809 1839 1868 1898 1791 1820 1850 1879 1909 1938 1968 1862 1892 1921 1951 1980 2010 2039 1936 1965 1995 2024 2054 2083 2113 2040 2070 2099 2129 2159 2188 i368 1379 1391 1402 1413 1425 1373 1388 1403 1418 1432 1447 1462 1477 1438 1453 1468 1483 1498 1512 1527 1542 1520 1535 1550 1564 1579 1594 1609 1588 1603 1618 1633 1648 1662 1677 1(373 1688 1703 1718 1733 1747 i745 1760 1775 1790 1804 1819 1405 1423 1442 1461 1480 1499 1517 1536 1470 1489 1507 1526 1545 1564 1582 1601 1555 1574 1593 1612 1631 1649 1668 1624 1643 1661 1680 1699 1718 1736 1694 1713 1731 1750 1769 1788 1807 1766 1784 1803 1822 1841 1860 1879 1839 1858 1877 1895 1914 1933 1952 1933 1952 1970 1989 2008 2027 1440 1463 1486 1509 1533 1556 1579 1602 1505 1528 1551 1575 1598 1621 1644 1667 1595 1618 1641 1665 1688 1711 1734 1663 1687 1710 1733 1756 1779 1803 1734 1757 1780 1803 1826 1850 1873 1805 1828 1852 1875 1898 1921 1944 1879 1902 1925 1948 1971 1995 2118 1977 2000 2023 2047 2070 2093 '.'.'.'. - i444 1456 1467 1479 1490 . .*. . isii 1523 1534 1545 1557 ::: is9i 1602 1614 1625 .... 1673 1684 1695 i744 1756 1767 '.'.'.'. :::: 1833 1848 1863 1878 1893 i908 1923 1938 1953 1968 1829 1840 | :::: i904 1915 115 COLUMNS TABLE 35 2000- Ib. concrete 1:6 mixture n = 15 f c =500 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS = Af c [(l+4np'}+(n-l}p] /unsupported length\ \ diameter / . Column Size Size of column inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core H K M 1 1H IK 12 8 6 1M 1 6 53 13 9 5 1M 1 6 8 64 68 14 10 4 IH 1 6 76 8 80 81 15 11 3 1*8 1 6 8 - 10 89 93 97 95 101 101 16 12 2 3/0 ^K l$i 1 2 6 8 10 6 8 10 103 108 112 'i42 146 109 115 121 143 149 155 116 150 17 13 1 4/0 IK 1% 1 2 6 8 10 6 8 10 119 123 128 'l67 125 131 137 165 171 177 131 140 171 180 139 179 18 14 1 4/0 IK IK 1 2 6 8 10 12 6 8 ' 10 12 136 140 145 149 142 148 154 160 148 157 165 195 203 211 156 202 'i6i 195 194 200 206 19 15 5/0 1% 1% 1 2 6 8 10 12 6 8 10 12 154 159 163 167 '220 160 166 172 178 '2ig 225 231 166 175 183 220 228 236 174 185 227 238 183 236 20 16 2/0 6/0 2H 2 1 2 Q 10 12 14 8 10 12 14 178 182 187 191 '251 186 192 198 204 '252 258 265 195 203 211 255 263 272 205 216 265 276 217 277 116 TABLE 35 COLUMNS Column size > ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS P = Af e [(l+4np') + (n- ._ /unsupported length\ ,_ Max. [ -- I =15 \ diameter / 2000 -Ib. concrete 1:6 mixture n = 15 f c =500 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core H H H 1 1H 1H 2 1 17 2/0 6/0 2 I 1 2 8 10 12 14 8 10 12 14 199 203 207 212 206 213 219 225 215 224 232 241 283 292 300 309 226 237 294 305 237 305 .... '287 293 22 18 3/0 7/0 2H 2 1 2 8 10 12 14 8 10 12 14 8 10 12 14 16 8 10 12 14 16 '225 229 234 228 235 241 247 '317 323 237 246 254 263 '322 330 339 248 259 270 324 335 346 259 273 336 350 272 349 23 19 3/0 7/0 2K 1 1 2 '248 253 257 261 252 258 264 270 276 '355 361 260 269 277 286 294 '354 362 370 379 271 282 293 304 356 367 378 389 282 296 368 381 296 381 24 20 3/0 7/0 2 m 1 2 8 10 12 14 16 8 10 12 14 16 277 281 286 276 282 288 295 301 '395 285 293 302 310 319 396 405 413 295 306 317 328 339 390 401 412 423 434 307 321 335 401 415 429 320 337 414 432 25 21 4/0 7/0 2X IH 1 2 10 12 14 16 10 12 14 16 '303 307 311 308 314 320 327 319 328 336 344 '432 440 448 332 343 354 365 436 447 458 469 347 361 451 465 363 467 430 117 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS L. Column size > 2000 -Ib. concrete 1:6 mixture n=15 f c =500 /unsupported length\ v I - ^ ~ - ~ I V diameter / Spirals Size of vertical round rods Size of Diam- eter Number ~r column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) UI Per cent rods of core [I H H H 1 1H IK 26 22 4/0 2H 1 10 335 346 359 374 390 12 .... 341 355 370 387 407 14 334 347 363 381 401 16 338 354 371 392 18 343 360 380 403 7/0 \Y % 2 10 473 488 504 12 484 502 521 14 '477 495 516 16 485 506 18 i 474 494 517 27 23 4/0 2K 1 10 363 374 387 402 418 12 .... 370 383 398 416 435 14 362 376 391 409 430 16 367 382 400 420 444 18 371 388 408 431 7/0 1H 2 10 i 527 543 * 12 523 540 560 14 '516 534 554 16 524 545 568 18 .... 533 556 28 24 4/0 2 1 10 404 417 431 448 12 j : 399 412 428 445 465 14 405 421 439 459 482 16 '396 411 429 450 473 18 401 418 438 461 487 7/0 \y, 2 10 567 584 12 .... '564 581 601 14 575 595 618 16 565 586 609 18 573 597 623 j 29 25 5/0 2M 1 10 435 448 462 479 12 I '436 443 459 476 496 14 436 452 470 490 513 16 427 442 460 481 504 530 18 431 448 468 492 20 436 455 477 504 7/0 1H 2 10 609 626 12 623 643 14 'eii? 637 660 16 .... 628 651 677 18 616 639 665 20 624 650 30 26 5/0 2H 1 12 462 475 491 508 528 14 468 484 502 522 545 16 474 492 513 536 562 18 '463 480 500 524 550 20 468 487 509 535 564 7/0 1H 1.93 12 656 676 14 '650 670 693 16 661 684 710 18 '649 672 698 20 657 683 712 118 TABLE 35 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS P=Af c ((l+4np' (unsupported length\ MaX '( -- diameter - ) =15 2000-lb. concrete 1:6 mixture n = 15 f c =500 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (.inches) Per cent of core y* H 1 IK | IK 31 27 5/0 7/0 2H IK 1 1.86 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 501 505 5oi 508 514 520 526 509 517 525 534 542 550 524 535 546 557 568 579 "683 694 705 716 727 542 555 569 583 597 611 689 703 717 731 745 759 561 578 595 613 709 726 743 760 "682 690 698 32 28 5/0 7/0 2 IX 1 1.80 543 552 560 568 577 585 559 570 581 592 603 614 576 590 604 618 632 646 723 737 751 765 779 793 596 613 630 647 664 743 760 777 795 812 829 . . . . 'MO 536 542 548 554 561 .... 717 728 739 750 761 724 733 33 29 6/0 7/0 2K 1H 1 1.73 12 14 16 18 20 22 12 14 16 18 20 22 '576 '578 584 590 596 579 587 596 604 613 621 594 605 616 627 638 649 612 626 640 654 668 681 756 770 784 798 812 826 631 649 666 683 700 776 793 810 828 845 .... .... '757 765 761 772 783 794 34 30 6/0 7/0 9X iy* 1 1.67 12 14 16 18 20 22 24 12 14 16 18 20 22 24 'ei7 '615 621 627 634 640 616 624 633 641 650 658 667 631 642 653 664 675 686 697 649 663 677 691 705 719 733 791 805 819 833 847 861 875 669 686 703 720 737 755 811 828 845 862 879 897 792 800 809 796 807 818 829 840 119 COLUMNS TABLE 35 2000 -lb. concrete 1:6 mixture n = 15 f c =500 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS P=Af c ((l+4np')+(n-l)p] __ /unsupported lengtn\ ,_ Max. I -=-. 1 =.Zo \ diameter / Spirals Size of vertical round rods Size of Diam- eter Number _r 1 column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core or rods H H H 1 1H 1H 35 31 6/0 2M 1 14 662 680 701 724 16 671 691 715 741 18 '659 679 702 729 758 20 665 687 713 742 774 22 671 696 724 756 792 24 678 704 735 770 710 7/0 IK 1.62 14 842 864 16 '832 856 882 18 843 869 899 20 854 883 916 22 '837 865 897 933 24 845 876 971 950 36 32 6/0 '2 1 14 702 720 741 764 16 711 731 755 781 18 719 742 769 798 20 '705 728 753 783 815 22 711 736 764 796 832 24 718 744 775 810 850 7/0 IK 1.57 14 878 901 16 '869 892 918 18 880 906 935 20 891 920 953 22 '873 902 934 970 24 881 913 948 987 37 33 7/0 2H 1 14 761 782 805 16 '752 772 796 822 18 760 783 809 839 20 '746 768 794 823 856 22 752 777 805 837 873 24 758 785 816 851 890 26 765 794 827 865 908 7/0 IK 1.52 14 915 938 16 929 955 18 '9i7 943 972 20 928 957 989 22 'gib 939 971 1007 24 919 950 985 1024 26 927 961 999 1041 38 34 7/0 2H 1 14 803 824 847 16 '794 814 838 864 18 802 825 852 881 20 810 836 865 898 22 '794 819 847 879 915 24 801 827 858 893 932 26 807 836 869 907 950 7/0 IK 1.48 14 954 977 16 968 994 18 '956 982 1012 20 967 996 1029 22 978 1010 1046 24 '958 989 1024 1063 26 966 1000 1038 1080 120 TABLE 35 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS = Af c [(l+4np' (unsupported length\ ( diarnettr ) 2000-lb. concrete 1:6 mixture n = 15 f c =500 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core ^ K % 1 IX IK 39 35 7/0 7/0 IK i 1 1.43 14 16 18 20 26 14 16 18 20 22 24 26 .... '.'.'.'. '845 854 862 871 879 847 858 869 880 891 902 913 867 881. 895 909 923 937 951 991 1005 1019 1033 1047 1061 1075 890 907 924 941 959 976 993 1014 1031 1048 1066 1083 1100 1117 844 850 :::: 995 1003 993 1004 1015 1026 1037 40 36 7/0 7/0 2 ftM 1 1.40 : 16 18 20 22 24 26 28 16 18 20 22 24 26 28 .... '895 901 '899 907 915 924 932 902 913 924 935 946 957 968 926 940 953 967 981 995 1009 1048 1062 1076 1089. 1103 1117 1131 952 969 986 1003 1020 1038 1055 1074 1091 1108 1125 1143 1160 1177 1637 1046 1054 i646 1057 1068 1079 1090 11 37 7/0 7/0 2 IK 1.36 16 18 20 22 24 26 28 16 18 20 22 24 26 28 936 944 953 961 970 978 948 959 970 981 992 1003 1014 i086 1097 1108 1119 1130 971 985 999 1013 1027 1041 1055 1088 1101 1115 1129 1143 1157 1171 998 1015 1032 1049 1066 1083 1101 1114 1131 1148 1165 1182 1200 1217 *934 941 947 1086 1094 121 COLUMNS TABLE 35 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS Column size 2000-lb. concrete 1:6 mixture n = 15 f c =500 ,_ /unsupported length\ Max.\ - jr; - - - I =15 \ diameter / Spirals Size of vertical round rods Size of Diam- eter Number -r | column (inches) of core (inches) Size No. i (A. S. & W. Co.) Pitch (inches) Per cent of core OI rods K H K 1 1H 1>4 42 38 7/0 2 1 16 995 1019 1045 18 1006 1032 1062 20 99i 1017 1046 1079 22 1000 1028 1060 1096 24 1008 1039 1074 1113 26 988 1017 1050 1088 1131 28 '.'.'.'. 994 1025 1061 1102 1148 30 1000 1033 1072 1116 1165 7/0 IK 1.32 16 1127 1154 18 I 1141 1170 20 ii26 1155 1188 22 .... ! . . . . 1137 1169 1205 24 .... 1148 1183 1222 , 26 ii26 1159 1197 1239 28 1134 1170 1211 1257 30 i - - 1142 1181 1225 1274 43 39 7/0 l% 1 16 1044 1067 1093 18 1055 1081 1110 20 1640 1066 1095 1127 22 1048 1077 1109 1145 24 1057 1088 1123 1162 26 1065 1099 1137 1179 28 1042 1073 1110 1151 1196 30 '.'.'.'. 1048 1082 1121 1164 1213 7/0 IK 1.29 16 1171 1197 I 18 1185 1214 j 20 ii7o 1199 1231 22 1181 1213 1249 24 1192 1227 1266 26 ii69 1203 1241 1283 28 1177 1214 1254 1300 30 1186 1225 1268 1317 44 40 7/0 IH 1 16 1093 1117 1143 18 1104 1130 1160 20 1115 1144 1177 22 io98 1126 1158 1194 24 1106 1137 1172 1211 26 1115 1148 1186 1229 28 i692 1123 1159 1200 1246 30 1098 1132 1170 1214 1263 7/0 IX 1.25 16 1211 1237 18 1225 1254 20 1209 1239 1271 22 1220 1253 1288 24 1231 1266 1306 26 1242 1280 1323 28 i217 1253 1294 1340 30 1226 1264 1308 1357 122 TABLE 36 COLUMNS Ca/umn size ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS P=Af c ((l+4np')+(n-l)p] .. (unsupported length\ Max. I -=-: 1 =15 \ diameter J 2500 -Ib. concrete 1:4% mixture n = 12 f c =625 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core M H K 1 IH IH 12 8 6 1M 1 6 59 13 9 g 1^ 1 6 8 71 76 14 10 4 1M 1 6 8 85 89 91 15 11 3 IH 1 6 8 10 100 105 109 106 112 113 16 12 2 3/0 IH IH 1 2 6 8 10 6 8 10 117 121 126 'i55 160 123 129 135 157 163 169 129 163 17 13 1 4/0 IX IK 1 2 6 8 10 6 8 10 135 140 144 'i84 141 147 153 181 187 193 148 156 187 196 195 18 14 4/0 l IH 2 6 8 10 12 6 8 10 12 155 159 163 168 '210 214 161 167 173 179 '2i3 219 225 167 175 184 213 222 230 175 221 19 15 5/0 IK 1J4 1 2 6 8 10 12 6 8 10 12 176 180 184 189 "242 182 188 194 200 '24i 247 253 188 196 205 241 250 258 196 207 249 260 204 258 20 16 2/0 6/0 2H 2 2 8 10 12 14 8 10 12 14 203 207 211 216 '276 210 216 222 229 '277 283 289 219 227 236 279 288 296 229 240 289 300 241 301 123 COLUMNS TABLE 36 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS ^Column size 2500-lb. concrete 1:4% mixture n = 12 f c =625 ,_ (unsupported length\ _ IrlttX* I -j7 7 ~- I 15 \ diameter / Spirals Size of vertical round rods Size of Diam- eter Number . column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core of rods H H H 1 IK IK 21 17 2/0 2 1 8 227 234 243 253 265 10 231 240 251 264 12 235 246 260 14 240 253 268 6/0 1% 2 8 311 321 333 10 .... 319 332 12 314 328 14 321 336 22 18 3/0 2^ 1 8 260 268 279 290 303 10 '257 266 277 289 304 12 261 272 285 300 14 265 278 293 7/0 2 2 8 355 366 379 10 '353 366 380 12 '348 361 377 14 354 370 23 19 3/0 2K 1 8 286 295 305 317 330 10 '283 293 304 316 331 12 288 299 312 327 14 292 305 320 338 16 296 311 328 7/0 IK 2 8 391 402 415 10 '389 401 416 12 397 412 14 '390 405 423 16 396 414 24 20 3/0 2 1 8 315 324 334 345 358 10 321 332 345 359 375 12 '316 327 340 355 373 14 320 333 348 366 16 324 339 357 377 7/0 IK 2 8 428 440 452 10 439 453 469 12 '435 450 467 j 14 443 461 16 434 451 471 25 21 4/0 ty* 1 10 350 361 374 388 404 12 '345 356 369 385 402 14 349 362 378 395 16 354 368 386 406 7/0 ix 2 10 478 492 508 12 '474 489 506 14 482 500 16 473 490 510 124 TABLE 36 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS P=Af c [(l+4np')+(n-l)p] Max. 'unsupported length\ diameter = 15 2500 -Ib. concrete 1:4% mixture n = 12 f c =625 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core % H H 1 IH IX 26 22 4/0 7/0 zy* i% 1 2 10 12 14 16 18 10 12 14 16 18 '38i 385 389 382 388 394 400 406 393 401 409 418 426 405 416 427 438 449 520 531 542 552 563 420 433 447 534 548 562 435 453 550 567 524 532 540 *52i 27 23 4/0 7/0 2H 1% 2 10 12 14 16 18 10 12 14 16 18 '4i4 418 422 414 420 427 433 439 425 434 442 450 458 438 449 460 470 481 452 466 480 493 576 590 604 617 468 485 592 609 I .'.' : '566 574 582 573 584 594 605 28 24 4/0 7/0 2 IX 1 2 10 12 14 16 18 10 12 14 16 18 460 468 476 484 493 472 483 494 505 515 487 500 514 527 541 623 637 650 664 678- 503 519 536 639 656 673 "452 456 455 461 467 473 .... 619 630 641 652 .... 621 629 29 25 5/0 7/0 Wt iy* 1 2 10 12 14 16 18 20 10 12 14 16 18 20 '487 492 496 '490 496 502 508 514 495 503 512 520 528 537 508 519 529 540 551 562 522 536 549 563 577 670 683 697 711 724 686 703 719 736 .. ; :::: '676 684 677 688 699 709 30 26 5/0 7/0 w IX 1 1.93 12 14 16 18 20 12 14 16 18 20 '529 533 528 534 540 546 552 541 549 557 566 574 556 567 578 589 599 '715 725 736 747 573 587 601 614 628 721 735 748 762 776 593 609 626 740 757 774 .... .... '7i3 722 125 COLUMNS TABLE 36 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS Column Size 2500 -lb. concrete 1:4% mixture n = 12 f c =625 /unsupported length\ Max. I - -j-; - - - } = 15 \ diameter / Spirals Size of vertical round rods Size of Diam- eter Number _ e column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core OI rods H H Ys 1 1H IK 31 27 5/0 2^ 1 12 579 594 612 631 14 '572 587 605 625 648 16 578 596 616 639 664 18 584 604 627 653 681 20 '572 590 612 638 666 22 576 596 621 648 680 7/0 1H 1.86 12 759 778 14 .... '753 773 795 16 764 787 812 18 '752 774 800 829 20 760 785 814 22 768 796 828 32 28 5/0 2 1 12 619 634 651 670 14 ei2 627 645 665 687 16 618 635 656 679 704 18 .... 624 644 666 692 721 20 630 652 677 706 738 22 616 636 660 688 720 7/0 IK 1.80 12 799 819 14 793 813 835 16 804 827 852 18 815 840 869 20 800 825 854 886 22 808 836 868 33 29 6/0 2>i 1 12 660 675 693 712 14 669 686 706 729 16 659 677 697 720 746 18 665 685 708 734 763 20 671 693 719 747 779 22 '667 677 702 729 761 7/0 IK 1.73 12 837 856 14 851 873 16 '84i 864 890 18 852 878 907 20 '838 863 892 924 22 846 874 905 34 30 6/0 2>i 1 12 704 719 736 755 14 712 730 750 772 16 703 720 740 763 789 18 709 728 751 777 806 20 715 737 762 791 823 22 721 745 773 804 840 24 '705 727 753 784 718 7/0 IK 1.67 12 878 897 14 891 914 16 '882 905 931 18 893 919 948 20 '878 904 932 964 22 887 914 946 981 ! 24 895 925 960 126 TABLE 36 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS ,_ /unsupported length\ 1C Max. \ 7^ I = lo \ diameter 2500-lb. concrete 1:4% mixture n = 12 Spirals Size of vertical round rods Size of Diam- j eter Number f. column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core OI rods H K ft 1 IH 1H 35 31 6/0 2M 1 14 756 774 794 816 16 764 784 807 833 18 753 772 795 821 850 20 759 781 806 835 867 22 765 789 817 848 884 24 771 797 828 862 901 7/0 1H 1.62 14 933 956 16 '. '. '. '. 924 947 972 , 18 935 961 989 20 946 974 1006 22 '929 956 988 1023 24 937 967 1002 1040 36 32 6/0 2 1 14 802 820 840 862 16 810 830 853 879 18 818 841 867 896 20 '805 827 852 881 913 22 811 835 863 894 930 24 817 843 874 908 947 7/0 IH 1.57 14 977 999 16 '968 991 1016 18 979 1004 1033 20 989 1018 1050 22 "972 1000 1032 1067 24 981 1011 1045 1084 37 33 7 2> 1 14 867 887 909 16 857 878 901 926 18 866 888 914 943 20 '852 874 899 928 960 22 858 882 910 942 977 24 864 890 921 955 994 26 870 899 932 969 1011 f/0 1M 1.52 14 1020 1042 16 1033 1059 18 io2i 1047 1076 20 1032 1061 1093 22 iois 1043 1074 1110 24 1023 1054 1088 1127 26 1031 1064 1102 1144 38 34 7/0 2H 1 14 .... I .... 916 936 958 16 '906 926 949 975 18 914 937 963 992 20 923 948 977 1009 22 '967 931 959 990 1026 24 913 939 970 1004 1043 26 919 947 980 1018 1059 7/0 iy z 1.48 14 1065 1088 16 1079 1104 18 i067 1093 1121 20 1078 1106 1138 22 1088 1120 1155 24 1669 1099 1134 1172 26 1077 1110 1147 1189 127 ^> , ! COLUMNS ] & SAI <-/ ',500 -Ib. concrete \J ':4% mixture V TABLE 36 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS Column size ^ P=Af c [(l+4np') + (n- ., max, (unsupported length\ f c =625 diameter / ** m * V } :> ^- Size of column (inches) Diam- Spirals Number of rods Size of vertical round rods eter of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core H H H 1 IH U4 39 35 7/0 7/0 2H IH 1 1.43 14 16 ' 18 20 22 24 26 14 16 18 20 22 24 26 '963 969 '956 964 973 981 989 997 966 976 987 998 1009 1020 1030 986 999 1013 1026 1040 1054 1068 1109 1122 1136 1150 1163 1177 1191 1008 1025 1042 1059 1076 1093 1109 1131 1148 1165 1182 1199 1216 1233 iii2 1120 iiio 1121 1132 1143 1153 40 , 36 7/0 7/0 2 IH 1 1.40 16 18 20 22 24 26 28 16 18 20 22 24 26 28 i020 1027 i024 1033 1041 1049 1057 1028 1039 1050 1060 1071 1082 1093 1051 1065 1078 1092 1106 1119 1133 1173 1187 1200 1214 1228 1241 1255 1076 1093 1110 1127 1144 1161 1178 1198 1215 1232 1249 1266 1283 1300 '.'.: lies 1171 1179 ii72 1182 1193 1204 1215 V 41 H> ^ V * 37 7/0 7/0 ' ! 2 \H j 1 1.36 16 18 20 22 24 26 28 16 18 20 22 24 26 28 1067 1073 1080 1669 1077 1086 1094 1102 1110 1081 1092 1103 1113 1124 1135 1146 1104 1118 1131 1145 1159 1172 1186 1219 1233 1246 1260 1274 1287 1301 1129 1146 1163 1180 1197 1214 1231 1244 1261 1278 1295 1312 1329 1346 1217 1225 1218 1228 1239 1250 1261 TABLE 36 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS P=Af e ((l+4np' ,_ /unsupported length\ Max '( diameter ) 15 2500 -Ib. concrete 1:4% mixture n = 12 f e =625 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core M H M 1 IK IK 42 38 7/0 7/0 2 1^ 1 1.32 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 1136 1147 1158 1168 1179 1190 1201 1212 1159 1173 1186 1200 1214 1227 1241 1255 1268 1282 1296 1309 1323 1337 1350 1364 1184 1201 1218 1235 1252 1269 1286 1303 1294 1311 1328" 1345 1362 1378 1395 1412 .... ii28 1135 1141 1132 1141 1149 1157 1165 1174 .... 1267 1278 1289 1299 1310 1321 i266 1274 1283 43 39 7/0 7/0 IK IX 1.29 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 '. '.'. iiss 1196 1204 1212 1220 1229 1191 1202 1213 1224 1235 1245 1256 1267 1214 1228 1242 1255 1269 1283 1296 1310 1318 1332 1345 1359 1373 1386 1400 1414 1240 1257 1274 1291 1308 1324 1341 1358 1344 1361 1377 1394 1411 1428 1445 1461 '.'.'.'. iioo 1196 1317 1327 1338 1349 1360 1371 1316 1324 1333 44 40 7/0 7/0 1H IX 1 1.25 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 !!!? .... i253 1261 1269 1277 1286 1248 1259 1270 1280 1291 1302 1313 1324 1271 1285 1298 1312 1326 1339 1353 1367 1366 1380 1393 1407 1421 1434 1448 1462 1296 1313 1330 1347 1364 1381 1398 1415 1392 1409 1425 1442 1459 1476 1493 1510 .... 1247 1253 1365 1375 1386 1397 1408 1419 1372 1381 129 COLUMNS TABLE 37 3000-lb. concrete 1:3 mixture n=12 f c =750 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS P=Af c [(l+4np')+(n-l)p] ,_ /unsupported length\ Max. I ^-. I =25 \ diameter I Column size * Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A.S.&W. Co.) Pitch (inches) Per cent of core H H K 1 .IM 1H 12 8 6 IK 1 6 71 13 9 5 IH 1 6 8 86 91 14 10 4 iH 1 6 102 8 107 109 15 11 3 IH 1 6 121 8 126 10 131 127 135 135 16 12 2 3/0 1% IH 1 2 6 8 10 6 8 10 141 146 151 'ise 191 147 155 162 188 195 203 155 196 17 13 1 4/0 1% m 1 2 6 8 10 6 8 10 162 167 172 '226 169 176 184 217 224 231 177 187 225 235 186 234 18 14 1 4/0 1% iH 1 2 6 8 10 12 6 8 10 12 186 191 196 201 '251 257 193 200 207 215 255 263 270 201 210 220 256 266 276 210 265 19 15 5/0 1% i% 1 2 6 8 10 12 6 8 10 12 211 216 221 226 '290 218 225 233 240 '289 296 303 226 236 246 289 299 309 235 248 299 312 245 309 20 16 2/0 6/0 2y* 2 1 2 8 10 12 14 8 10 12 14 243 248 254 259 '331 252 260 267 274 332 339 347 263 273 283 335 345 355 275 288 347 360 289 361 130 TABLE 37 COLUMNS Column ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS P=Af e ((l+4np' /unsupported length\ * \ diameter / 3000-lb. concrete 1:3 mixture n = 12 f e =750 Spirals Size of vertical round rods Size of Diam- eter Number nf column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core OI rods M K K 1 IK 1H I ! 21 17 2/0 2 1 8 272 281 292 304 318 10 277 288 302 317 12 282 296 312 14 287 303 321 6/0 IK 2 8 373 385 399 10 383 398 12 '377 393 14 385 403 22 18 3/0 2K 1 8 312 322 334 348 363 10 308 319 332 347 364 12 313 326 342 360 14 318 333 352 7/0 2 2 g 426 440 455 10 424 439 456 12 iis 434 452 14 425 444 23 19 3/0 2K 1 8 344 354 366 380 396 10 340 351 364 379 397 12 345 358 374 392 14 350 366 384 405 16 355 373 394 7/0 IK 2 8 469 482 498 10 .... '466 481 499 12 476 494 14 "468 486 507 16 475 496 24 20 3/0 2 1 8 378 388 401 414 430 10 385 398 413 431 450 12 379 392 408 426 447 14 384 400 418 439 16 389 407 428 452 7/0 IK 2 8 514 528 543 10 527 544 563 12 '522 540 560 14 531 553 16 520 541 566 25 21 4/0 2K 1 10 421 434 449 467 486 12 415 428 444 462 483 14 420 436 454 475 16 425 443 464 488 7/0 1% 2 10 574 591 610 12 "570 587 60S 14 579 600 16 '568 589 613 131 COLUMNS TABLE 37 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS ^Column )-lb. concrete 1:3 mixture n = 12 f c = 750 P=Af c [(l+4np') + (n- ,_ /unsupported length\ ,_ Max. I - ^ - I =J.o \ diameter / Spirals Size of vertical round rods Size of Diam- eter Number _r column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core of rods H H H 1 iy* 1M 26 ! 22 4/0 2H 1 10 458 472 487 504 523 12 466 481 500 520 543 14 '457 473 491 513 537 16 462 480 501 526 18 467 488 511 539 7/0 \*A 2 10 623 641 660 A /8 12 636 657 680 14 '628 649 674 16 .... 638 662 18 624 648 675 27 23 4/0 2H 1 10 498 511 526 543 562 12 505 521 539 560 583 14 '497 512 531 552 576 16 502 520 541 565 592 18 507 527 551 578 7/0 1% 2 10 693 712 12 688 709 732 14 680 701 726 16 690 714 742 18 700 727 28 24 4/0 2 1 10 552 567 584 603 12 546 562 580 601 623 14 553 572 593 617 644 16 543 560 581 606 633 18 548 568 591 619 650 7/0 IK 2 10 747 766 A /2 12 743 763 786 14 756 780 806 16 '744 769 796 18 754 782 813 29 25 5/0 2M 1 10 594 610 627 646 12 '589 604 623 643 f>60 14 596 614 636 660 687 16 '585 603 624 648 676 707 18 590 610 634 661 692 20 595 618 644 674 7/0 114 2 10 804 823 * /2 12 820 843 14 '812 836 863 16 825 853 884 18 'sii 838 869 20 821 851 30 26 5/0 2?6 i 14 907 929 953 980 16 .... 917 941 969 1000 18 '963 927 954 985 1020 20 911 937 967 1002 1040 22 918 947 980 1018 1061 24 925 957 993 1035 1081 7/0 1H ].62 14 1123 1150 16 iiii 1139 1170 18 .... 1124 1155 1190 20 1137 1172 1210 22 iii7 1150 1188 1231 24 1127 1163 1205 1251 36 32 6/0 2 1 14 962 983 1007 1034 16 972 996 1024 1055 18 982 1009 1040 1075 20 '965 992 1022 1056 1095 22 973 1002 1035 1073 1115 24 980 1012 1048 10.89 1136 7/0 IK 1.57 14 1173 1200 16 ii<52 1189 1220 18 1175 1206 1240 20 1187 1222 1260 22 ii67 1200 1239 1280 \ 24 I .... 1177 1213 1256 1301 37 33 7/0 2M 1 14 1040 1064 1091 16 , i028 1053 1080 1111 18 .... 1038 1066 1097 1131 20 .... 1022 1048 1079 1113 1151 22 1029 1058 1092 1130 1172 24 1037 1068 1105 1146 1192 26 1044 1078 1118 1164 1212 7/0 U2 1.52 14 1225 1251 16 1241 1272 18 i226 1257 1292 20 .... 1239 1274 1312 22 i2ij> 1252 1290 1332 24 1229 1265 1307 1353 26 1239 1278 1323 1373 38 34 7/0 2Y& 1 14 1098 1123 1149 16 io87 1111 1139 1170 18 : .... 1097 1124 1155 1190 20 .... 1107 1137 1172 1210 22 .... 1088 1117 1150 1188 1230 24 1095 1127 1163 1205 1251 26 1102 1137 1176 1221 1271 7/0 1>2 1.48 14 1279 1306 16 1296 1326 18 . . . . i2si 1312 1347 20 1294 1328 1367 22 1307 1345 1387 24 1283 1320 1361 1407 26 1293 1333 1378 1428 134 TABLE S7 COLUMNS ROUND .CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS -- /unsupported length\ ,_ Max. [ - j-. - - - J = 15 \ diameter / 3000-lb. concrete 1:3 mixture n = 12 f f =750 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods i Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core K H % 1 IX 1M 39 35 7/0 7/0 2K l)i 1 1.43 14 16 18 20 22 24 26 14 16 18 20 22 24 26 il47 1157 1167 1177 1187 1197 1158 1172 1185 1197 1210 1223 123G 1183 1199 1216 1232 1248 1265 1281 1334 1351 1367 1383 1400 1416 1433 1210 1230 1250 1270 1291 1311 1331 1361 1381 1402 1422 1442 1462 1483 1148 1155 1163 1336 1349 1362 1375 1388 1339 1348 40 36 7/0 7/0 cy 1H 1.40 16 18 20 22 24 26 28 16 18 20 22 24 26 28 1233 1246 1259 1272 1285 1298 1311 1261 1277 1294 1310 1327 1313 1359 1406 1423 1439 1455 1472 1488 1505 1292 1312 1332 1353 1373 1393 1413 1437 1457 1477 1498 1518 1538 1558 i225 1231 1229 1239 1249 1259 1269 1404 1417 1430 1443 1456 1394 1404. 1414 41 37 7/0 7/0 2 1H 1.36 16 18 20 22 24 26 28 16 18 20 22 24 26 28 i2si 1288 1295 .... i283 1293 1303 1312 1322 1332 i4o9 1469 1297 1310 1323 1336 1349 1361 1375 i-iso 1473 I486 1499 1512 1325 1341 1357 1374 1390 1407 1423 1462 1478 1495 1511 1527 1544 1560 1355 1376 1396 1416 1436 1457 1477 1492 1513 1533 1553 1573 1594 1614 135 COLUMNS TABLE 37 3000 -lb. concrete 1:3 mixture ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS = Af c [(l+4np')+(n-l}p] (unsupported length\ _ ' \ diameter / Column Size ^ Spirals Size of vertical round rods Size of Diam- eter Number column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core of rods H H % 1 IH IK 42 38 7/0 2 1 16 ! ... 1362 1390 1421 18 1375 1406 1441 20 i358 1388 1423 1461 22 1368 1401 1439 1482 24 1378 1414 1456 1502 26 1354 1388 1427 14*72 1522 28 1360 1398 1440 1488 1542 30 1368 1408 1453 1504 1563 7/0 IK 1.32 16 1520 1551 18 1537 1571 20 1519 1553 1591 22 1532 1570 1612 24 1545 1586 1632 26 isis 1558 1603 '1652 28 1528 1571 1619 1673 30 1538 1583 1635 1693 43 39 7/0 iy* 1 16 1430 1457 1488 18 1443 1474 1508 20 1425 1456 1490 1528 22 1435 1469 1506 1549 24 1445 1482 1523 1569 26 1455 1494 1539 1589 28 i428 1465 1507 1556 1609 30 1435 1475 1520 1572 1630 7/0 IK 1.29 16 1583 1613 18 1599 1634 20 1581 1615 1654 22 1594 1632 1674 24 1607 1648 1694 26 isso 1620 1665 1715 28 1590 1633 1681 1735 30 1600 1645 1697 1755 44 40 7/0 1% 1 16 1498 1526 1557 18 1511 1542 1577 20 1524 1559 1597 22 is b-4 1537 1575 1618 24 1514 1550 1592 ] 638 26 1524 1563 1608 1658 28 1496 1534 1576 1624 1678 30 1504 1544 1589 1641 1699 7/0 IK 1.25 16 1639 1670 18 1656 1690 20 1(337 1672 1710 22 1650 1688 1731 24 1663 1705 1751 26 1670 1721 1771 28 1647 1689 1738 1791 30 1657 1702 1754 1812 130 TABLE 38 COLUMNS Column size ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS P =Af c (l + (n -l)p] +2f s p'A f t =20,000 1:6 mixture n = 15 f e =500 Size of column (inches) Diam- Spirals Number of rods Size of vertical round rods eter of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core X K H 1 1H IK 12 8 6 IK 1 6 58 13 9 5 1M 1 6 8 70 74 14 10 4 IK 1 6 8 83 88 89 15 11 3 IH 1 6 8 10 98 103 107 104 110 ill 16 12 2 3/0 IK 1H 1 2 6 8 10 6 8 10 115 119 123 'iei 168 120 126 133 166 172 178 127 172 17 13 1 4/0 IK IVs 1 2 6 8 10 6 8 10 132 137 141 'i94 138 144 150 191 197 203 145 153 198 206 152 205 18 14 1 4/0 IK IK 1 2 6 8 10 12 6 8 10 12 151 156 160 164 "222 226 157 163 169 176 '225 231 237 164 172 181 225 234 242 171 233 19 15 5/0 Ul 1% 1 2 6 8 10 12 6 8 10 12 172 176 180 185 '255 178 184 190 196 '254 261 267 184 193 201 255 263 272 192 203 263 274 201 271 20 16 2/0 6/0 2H 2 1 2 8 10 12 14 8 10 12 14 198 202 207 211 '29i 206 212 218 224 '292 299 305 215 223 231 295 303 312 225 236 305 316 237 317 137 COLUMNS TABLE 38 1:6 mixture n = 15 f c =500 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS -l)p]+2f,p'A f s = 20,000 Spirals Size of vertical round rods Size of Diam- eter Number column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core rods M M 14 1 IK IX 21 17 2/0 1 8 221 229 238 248 260 10 226 235 246 259 12 230 241 255 14 234 248 263 6/0 114 2 8 329 339 351 10 337 350 12 '332 346 14 338 354 22 18 3/0 2>4 1 8 254 263 273 285 298 10 '256 260 271 284 299 12 255 266 280 295 14 259 272 288 7/0 2 2 8 375 386 400 10 '373 386 400 12 '368 381 397 14 374 390 23 19 3/0 2V & 1 8 280 289 299 311 324 10 '277 286 297 310 325 12 281 292 306 321 14 285 298 314 332 16 289 305 322 7/0 114 2 8 412 424 437 10 411 423 438 12 419 434 14 '412 427 445 16 418 436 24 20 3/0 2 1 8 307 316 327 338 351 10 314 325 338 352 369 12 '308 320 333 349 366 14 313 326 342 360 i ! 16 317 332 350 371 7/0 114 2 8 452 464 477 10 . 463 478 494 12 '459 474 492 14 467 485 16 '458 476 496 25 21 4/0 2K 1 10 343 354 367 381 398 12 '337 349 362 378 395 1 14 342 355 371 389 16 346 361 379 400 7/0 1?4 l' 10 505 520 536 12 'soi 516 534 14 509 527 16 500 518 538 138 TABLE 88 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS f , 1:6 mixture 71=15 f e =500 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Percent of core K H H 1 I.H 1>4 26 22 4/0 7/0 2 ?-8 1 1 2 10 12 14 16 18 10 12 14 16 18 '372 376 381 373 379 385 391 398 384 393 401 409 418 397 408 419 430 441 549 560 571 582 593 412 425 439 564 578 592 428 445 580 597 550 '553 561 570 27 23 1 4/0 7/0 2H 1^ 2 10 12 14 16 18 10 12 14 16 18 "404 408 413 405 411 417 423 430 416 424 433 441 450 429 440 451 462 473 443 457 171 485 610 624 638 651 460 477 626 643 '599 607 616 606 617 628 639 28 24 4/0 7/0 2 IH 1 2 10 12 14 16 18 10 12 14 16 18 10 12 14 16 18 20 10 12 14 16 18 20 441 446 444 450 457 463 449 458 466 474 483 '655 664 462 473 484 495 506 '654 665 676 687 477 491 505 518 532 658 672 686 699 713 493 510 527 674 691 708 29 25 5/0 7/0 2X iy z 1 2 '476 480 485 479 485 491 497 504 484 492 501 509 518 526 497 508 519 530 541 551 511 525 539 553 567 708 722 736 749 763 528 545 562 579 724 741 758 776 '714 722 715 726 737 748 30 26 5/0 7/0 2 1H 1 1.93 12 14 16 18 20 12 14 16 18 20 'sie 521 515 521 527 533 540 528 537 545 554 562 544 555 566 577 588 '752 763 774 785 501 575 589 603 759 773 787 801 815 581 598 615 778 796 813 '75i 760 139 COLUMNS TABLE 38 1:6 mixture n=15 f c =500 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS -l)p]+2f s p'A f s =20,000 length \ * \diameterl = 15 ! Spirals Size of vertical round rods Size of Diam- eter Number column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core of rods H % % 1 Ui 1M 31 27 5/0 2V 1 12 566 581 599 618 ^7a 14 559 574 592 613 636 16 565 583 603 627 653 18 571 591 614 641 670 20 '558 577 599 625 654 22 563 583 608 636 668 7/0 1M 1.86 12 796 816 14 '796 810 833 16 801 824 850 18 '789 812 838 868 20 797 823 852 22 806 834 866 32 28 5/0 2 1 12 605 620 638 657 14 '597 613 631 652 674 16 604 622 642 666 692 18 610 630 653 679 709 20 616 638 664 693 726 22 'eoi 622 647 675 707 7/0 1H 1.80 12 834 854 14 '827 ' 848 871 16 838 862 888 18 849 876 905 20 '835 860 890 922 22 843 871 904 33 29 6/0 2H 1 12 645 660 678 697 14 653 671 692 715 16 '644 662 682 706 732 18 ! ! . . 650 670 693 720 749 20 656 679 704 734 766 22 *642 662 687 715 747 7/0 1H 1.73 12 869 889 14 883 906 16 '874 897 923 18 885 911 940 20 '870 896 925 958 22 878 907 939 34 30 6/0 2X 1 12 687 702 720 739 14 695 713 734 756 16 '686 704 724 748 774 18 692 712 735 761 791 20 698 720 746 775 808 22 704 729 757 789 825 24 '688 710 737 768 803 7/0 \H 1.67 12 908 928 14 922 945 16 '913 936 962 18 924 950 980 20 909 935 964 997 22 917 946 978 1014 24 926 957 992 140 TABLE 38 COLUMNS Column size ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS P = Af e [l + (w -l)p] +2f s p'A f,=20,000 I length \ Max. \diameteri = 15 1:6 mixture n = 15 f e =500 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core *A H H 1 1H t# 35 31 6/0 7/0 2^ 1H 1 1.62 14 16 18 20 22 24 14 16 18 20 22 24 '735 741 747 754 738 747 755 763 772 780 756 767 778 789 800 811 777 791 805 818 832 846 964 978 992 1006 1020 1033 800 817 834 851 868 885 987 1004 1021 1038 1055 1073 954 965 976 987 998 959 967 36 32 6/0 7/0 2 IK. 1 1.57 14 16 18 20 22 24 14 16 18 20 22 24 '786 792 798 783 791 799 808 816 825 801 812 823 834 845 856 '994 1005 1016 1026 1038 821 835 849 863 877 891 1003 1017 1031 1045 1059 1073 844 861 878 896 913 930 1026 1043 1060 1078 1095 1112 '999 1007 37 33 7/0 7/0 2tf 1H 1 1.52 14 16 18 20 22 24 26 14 16 18 20 22 24 26 847 858 869 880 891 902 913 867 881 895 909 923 937 951 1043 1057 1071 1085 1099 1113 1127 890 907 924 942 959 976 993 1066 1083 1101 1118 1135 1152 1169 .... '832 838 844 850 837 845 854 862 871 879 1045 1056 1067 1078 1089 1039 1047 1055 68 34 7/0 7/0 2H 1>2 1 1.4S 14 16 18 20 22 24 26 14 16 18 20 22 24 26 '885 891 898 .... '884 893 901 909 918 927 1692 1100 894 905 916 927 938 949 960 1690 1101 1112 1123 1134 915 928 942 956 970 984 998 1088 1102 1116 1130 1144 1158 1171 937 955 972 989 1006 1023 1-040 1111 1128 1146 1163 1180 1197 1214 141 COLUMNS TABLE 38 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS Cofumn size ^ 1:6 mixture n = 15 f c =500 -l)p]+2f s p'A f s =20,000 / length \ \diameter Spirals Size of vertical round rods Size of Diam- eter kT 1 ' Number ~ nf column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core rods ^ ^ 7 A 1 1H 1>4 39 35 7/0 2> 1 14 1 943 963 986 16 933 954 977 1003 j | 18 942 964 991 1020 20 950 975 1005 1038 22 934 958 986 1019 1055 24 940 967 997 1033 1071 26 ' i 946 975 1008 1047 1089 7/0 \Y 2 1.43 14 1129 1152 16 1143 1169 18 iisb 1157 1187 20 1141 1171 1204 22 1152 1185 1221 24 iis3 1164 1199 1238 26 1141 1175 1213 1255 40 36 7/0 2 1 16 1005 1028 1055 18 '992 1016 1042 1072 20 1001 1027 1056 1089 22 1010 1038 1070 1106 24 990 1018 1049 1084 1123 26 997 1027 1060 1098 1140 28 1004 1035 1071 1112 1158 7/0 IH 1.40 16 1190 1216 18 .... 1204 1234 20 iis9 1218 1251 22 1200 1232 1268 24 iisb 1211 1246 1285 26 1188 1222 1260 1302 28 ' 1197 1233 1274 1320 41 37 7/0 2 1 16 1056 1079 1105 18 1643 1067 1093 1122 20 1052 1078 1107 1139 22 1060 1089 1121 1157 24 1042 1069 1100 1135 1174 26 1048 1077 1111 1149 1191 28 1054 1085 1122 1162 1208 ! , 7/0 \K 1.36 16 1233 1259 ! 18 1247 1277 20 1232 1261 1294 22 1 1 1243 1275 1311 24 1254 1289 1328 26 i23i 1265 1303 1345 28 1240 1276 1317 1362 142 TABLE 38 COLUMNS Column Size ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS f,=20, 1:6 mixture n=15 f c =500 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch {.inches) Per cent of core H y* 1 IX M 42 38 7/0 7/0 2 1 1 1.32 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 hoi 1107 1113 iios 1113 1122 1130 1138 1147 1109 1120 1131 1142 1153 1164 1175 1186 1132 1146 1160 1174 1188 12D2 1215 1229 1277 1291 1305 1319 1333 1347 1361 1375 1158 1175 1192 1210 1227 1244 1261 1278 1303 1321 1338 1355 1372 1389 1407 1424 1276 1287 1298 1309 1320 1331 1275 1284 1292 43 39 7/0 7/0 IH IX 1 1.29 11 20 22 24 26 28 30 16 18 20 22 24 26 28 30 iie2 1168 il59 1168 1176 1185 1193 1201 1163 1174 1185 1196 1207 1218 1229 1240 1186 1200 1214 1228 1242 1256 1270 1284 1323 1337 1351 1365 1379 1392 1407 1421 1212 1230 1247 1264 1282 1298 1316 1333 1349 1367 1384 1401 1418 1435 1453 1470 i32i 1330 1338 1322 1333 1344 1355 1366 1377 44 40 7/0 7/0 IK 1H 1 1.25 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 1219 1230 1241 1252 1263 1274 1285 1296 1242 1256 1270 1284 1298 1312 1326 1340 1367 1381 1395 1409 1423 1437 1451 1465 1268 1286 1303 1320 1337 1354 1371 1389 1393 1411 1428 1445 1462 1479 1497 1514 1224 1232 1240 1249 1257 1217 1224 i,374 1382 1366 1377 1388 1399 1410 1421 143 COLUMNS TABLE 39 1:4Y 2 mixture n=12 f c =600 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS n-l)p]+2f s p'A f s =20,000 }=15 ,^ Column size o Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core *A H 14, 1 1M Ui 12 8 6 IK 1 6 62 13 9 5 lYz 1 6 8 76 80 14 10 4 iy* 1 6 8 91 95 96 15 11 3 IK 1 6 8 10 107 111 115 112 118 119 16 12 2 3/0 IK IH 1 2 6 8 10 6 8 10 125 129 133 'i75 179 131 136 142 176 182 187 J37 182 17 13 1 4/0 1H IK 1 2 6 8 10 6 8 10 145 149 153 '206 150 156 162 203 209 215 157 164 210 217 164 217 18 14 1 4/0 1H 1% 1 2 6 8 10 12 6 8 10 12 166 170 174 178 '236 240 171 177 183 189 '239 245 250 178 186 194 239 247 255 185 247 19 15 5/0 IK IK 1 2 6 8 10 12 6 8 10 12 189 193 197 201 '272 194 200 206 212 '27i 276 282 201 208 216 271 279 287 208 218 278 289 216 237 20 16 2/0 6/0 2^ 2 1 2 8 10 12 14 8 10 12 14 217 221 225 229 'SIO 224 230 236 242 'sii 316 322 233 241 249 313 321 329 243 253 323 333 254 334 144 TABLE 39 COLUMNS Column size > ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS -l)p]+2f,p'A f,= 1:4]4 mixture n = 12 f c =600 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core *8 H H 1 IK iy* 21 17 2/0 6/0 2 IK 2 8 10 12 14 8 10 12 14 243 247 251 255 250 256 262 268 353 359 259 267 275 283 350 357 365 373 268 289 359 370 279 370 22 18 3/0 7/0 2H 2 1 2 8 10 12 14 8 10 12 14 '275 279 283 278 284 289 295 286 294 302 310 296 306 317 398 408 419 307 320 409 422 319 421 396 404 412 391 397 23 19 3/0 7/0 2H IK 1 2 8 10 12 14 16 8 10 12 14 16 *304 308 312 316 307 313 318 324 330 315 323 331 339 347 '437 445 452 460 325 335 346 366 438 449 459 469 336 349 449 463 348 462 ' '438 444 24 20 3/0 7/0 2 IK 1 2 8 10 12 14 16 8 10 12 14 16 '338 343 347 337 343 349 355 361 346 354 362 370 378 356 366 376 387 397 481 492 502 512 523 367 380 393 492 505 519 379 395 505 521 487 495 503 :::: '486 25 21 4/0 7/0 2x '*. 1 2 10 12 14 16 10 12 14 16 37i 375 379 376 381 387 393 386 394 402 410 '533 540 548 398 409 419 429 537 547 557 568 412 425 551 564 427 566 532 145 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS 1:4}^ mixture n = 12 f c =600 f g =20,000 I length \ Max. ( -T-. ) = 15 \diameterj Spirals Size of vertical round rods Size of Diam- eter Number r I ^ column (inches; of core (inches) Size No. (A. S. & W. Co.) Pitch (inches^ Per cent of core OI rods y* H 1H 26 22 4/0 2Ys, 1 10 409 420 432 446 461 12 415 428 442 459 477 14 '408 421 436 453 472 16 412 427 444 463 18 417 433 452 473 7/0 IH 2 10 584 598 613 12 594 611 629 14 '588 605 624 16 596 615 18 585 ! 604 625 27 23 4/0 2K 1 10 445 455 467 481 496 12 450 463 478 494 513 14 444 456 471 488 507 16 448 462 479 498 520 18 452 468 487 509 7/0 1% 2 10 647 663 12 '644 660 679 14 037 654 673 16 * 645 ! 665 686 18 653 ! 675 28 24 4/0 2 1 10 492 504 518 533 12 487 500 515 531 550 14 493 508 525 544 566 16 '485 499 516 535 557 18 489 505 | 524 546 570 7/0 IK 2 10 699 714 12 i 696 712 14 706 725 1 747 16 697 716 738 1 18 705 727 751 ! 29 25 5/0 2> 1 10 531 543 557 572 1 1 12 526 539 553 570 588 14 532 546 ! 563 583 604 16 523 538 554 574 596 620 18 527 543 562 584 609 20 531 549 570 595 7/0 IK 2 10 753 768 12 766 784 14 '760 779 801 16 770 792 817 18 759 781 805 20 767 791 30 26 5/0 2% 1 12 .... I 566 579 593 010 628 14 572 586 603 023 644 16 578 594 614 636 660 18 '567 583 602 624 649 20 571 589 610 635 662 7/0 IK 1.93 12 807 825 14 1 .... '800 820 841 16 ! .... 811 833 857 18 799 821 846 20 807 832 859 146 TABLE 39 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS (n-l)p]+2f s p'A f g =20,000 ,_ / length \ Max - (diameter) =K mixture n = 12 f c =60 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core i H H 1 IK Ifc 31 27 5/0 7/0 2M 1M 1 1.86 12 14 16 18 20 22 12 14 16 18 20 22 eis 617 6i3 619 625 631 637 620 628 636 644 652 660 635 645 656 666 676 687 651 664 678 691 704 717 848 861 875 888 901 914 670 686 702 718 867 883 899 915 842 853 863 873 884 '841 849 857 32 28 5/0 7/0 2 IX 1 1.80 12 14 16 18 20 22 12 ' 14 16 18 20 22 660 657 662 668 674 680 663 671 679 687 695 703 678 688 699 709 719 730 '885 896 906 916 927 695 708 721 734 747 760 892 905 918 931 944 957 713 729 745 762 778 910 926 942 959 975 ::: "892 900 33 29 . 6/0 7/0 2M IX 1.73 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 24 12 14 16 18 20 22 24 705 "707 713 719 725 708 716 724 732 740 748 723 733 743 754 764 775 739 752 765 778 792 805 932 945 958 971 985 998 758 774 790 806 822 951 967 983 999 1015 1 . 936 947 957 967 i ;;;; ;;;; '934 941 34 30 6/0 7/0 *K IX 1 1.67 .... 755 754 759 765 771 777 755 762 770 778 786 794 802 769 779 790 800 811 821 831 786 799 812 825 838 851 864 975 988 1001 1014 1028 1041 1054 804 820 836 853 869 885 994 1010 1026 1042 1058 1075 '.'.'.'. '976 984 992 979 990 1000 1010 1021 147 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS .^ Column size ^ % mixture 12 600 Max. -l)p]+2f t p'A f ,=20, 000 I length \ \diameter 15 Spirals Size of vertical round rods Size of Diam- eter Number ~f column (inches) of core (inches) Size No. (A. S. & \\ . Co.) Pitch (inches) Per cent of core OI .rods H X V* 1 1H IK 35 31 6/0 2H 1 14 1 810 827 847 868 16 818 838 860 884 18 '807 826 848 873 901 20 813 834 858 886 917 22 819 842 869 899 933 24 825 850 879 912 949 7/0 1H 1.62 14 1034 1055 16 1625 1047 1072 18 1035 1060 1088 20 1046 1073 1104 22 i029 1056 1086 1120 24 1037 1066 1099 1136 36 32 6/0 2 1 1 : 14 860 877 896 918 16 868 887 909 934 18 876 898 922 950 20 '863 884 908 935 966 22 868 892 j 918 949 982 24 874 899 i 929 962 999 7/0 1H 1.57. 14 1079 1101 16 io7o 1092 1117 18 i . . . . 1081 1106 1133 20 1091 1119 1149 22 i675 1102 1132 1166 24 i 1083 : 1112 1145 1182 37 33 7/0 2H 1 14 : 928 947 969 16 ! 919 938 960 985 18 927 949 973 1001 20 914 935 959 987 1017 22 919 943 969 1000 1033 24 925 951 980 1013 1050 26 931 958 | 990 1026 1066 7/0 1H 1.52 14 1125 1146 16 1138 1163 18 1126 1151 1179 20 1137 1164 1195 22 ii20 1147 1177 1211 24 ... 1128 1157 1190 1227 1 26 1 .... 1136 1168 1204 1243 38 34 7/0 2H 1 14 980 1000 1021 16 971 991 1013 1037 18 ' 979 1001 1026 1054 20 987 j 1012 1039 1070 22 ... 972 995 1022 1052 1086 24 978 1003 1032 1065 1102 26 984 1011 1013 1078 1118 7/0 IH 1.48 14 1174 1196 16 1187 1212 18 ii"6 1200 1228 20 1186 1214 1244 22 1196 1227 12G1 24 ii78 1207 1240 1277 26 1186 1217 1253 1293 148 TABLE 39 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS n-l)p]+2f e p'A f s =20,000 length \ ,_ - mixture f c =600 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core H X % 1 IH IK 39 35 7/0 7/0 2H 1>* 1 1.43 14 16 18 20 22 24 26 14 16 18 20 22 24 26 i026 1034 1041 1049 1057 1065 1035 1045 1055 1066 1076 1087 1097 1054 1067 1080 1093 1106 1120 1133 1219 1232 1245 1258 1271 1284 1298 1075 1092 1108 1124 1140 1156 1173 1240 1257 1273 1289 1305 1321 1338 1626 1032 1038 . . . .* 1220 1231 1241 1251 1262 i222 1230 40 36 7/0 7/0 2 IH 1 1.40 16 18 20 22 24 26 28 16 18 20 22 24 26 28 .... 1101 1111 1122 1132 1142 1153 1163 1123 1136 1149 1162 1175 1188 1202 1286 1299 1312 1325 1338 1352 1365 1147 1164 1180 1196 1212 1228 1245 1311 1327 1343 1359 1375 1392 1408 i094 1100 1097 1105 1113 1121 1129 i284 1295 1305 1316 1326 1276 1284 1292 41 37 7/0 7/0 2 m 1 1.36 16 18 20 22 24 26 28 16 18 II 11 28 ii47 1155 1163 1170 1178 1186 1158 1169 1179 1189 1200 1210 1220 1180 1193 1206 1220 1233 1246 1259 1334 1347 1360 1373 1386 1399 1413 1205 1221 1237 1253 1270 1286 1302 1359 1375 1391 1407 1423 1440 1456 .... ii4o 1151 1157 1333 1343 1353 1364 1374 i.332 1340 149 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS Column size 1:4% mixture n = 12 f c =600 f, = 20,000 Max (tewth\ 15 \diameter) Spirals Size of vertical round rods Size of Diam- eter Number f\f column (inches) of core (inches) Size No. (A. S. & W. Co-.) Pitch (inches) Per cent of core OI rods : % K H 1 1H IK 42 38 7/0 2 1 16 1217 1239 1264 18 1227 1252 1280 20 1213 1238 1265 1296 22 1221 1248 1278 1312 24 1229 1259 1292 1328 26 i2ib 1237 1269 1305 1345 28 1216 1245 1279 1318 1361 30 1222 1253 1290 1331 1377 ' 7/0 IK 1.32 16 1362 1384 1409 18 1372 1397 1425 20 1358 1383 1410 1441 1 22 1366 1393 1423 1457 i 24 1374 1403 1436 1473 26 1382 1414 1450 1490 28 isei 1390 1424 1463 1506 30 1366 1398 1435 1476 1522 43 39 7/0 l 7 ^ 1 16 1278 1300 1324 18 1288 1313 1340 20 . 1274 1298 1326 1357 22 1282 1309 1339 1373 24 1290 1319 1352 1389 26 1298 1329 1365 1405 28 1276 1306 1340 1378 1421 30 1282 1314 1350 1391 1438 7/0 V/4 1.29 1T> 1438 1463 18 1451 1479 20 1437 1464 1495 22 1447 1477 1511 24 1457 1490 1527 26 i436 1468 1504 1543 28 1444 1478 1517 1560 30 1452 1489 1530 1576 44 40 7/0 1J 8 ' 1 16 1340 1362 1386 18 1350 1375 1402 1 20 1360 1388 1419 22 1344 1371 1401 1435 24 1352 1381 1414 1451 26 1360 1391 1427 1467 28 1338 1368 1402 1440 1483 30 1344 1376 1412 1453 1499 7/0 1> 1-25 16 1487 1511 1 18 1500 1528 20 i .... '. '. '. i486 1513 1544 22 1496 1526 1560 24 1506 1539 1576 26 1517 1553 1593 28 1493 1527 1566 1609 30 1501 1538 1579 1625 150 TABLE 40 COLUMNS Column size ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS / length \ MaxA-T^ I =12 \diameter 1:2:4 mixture n = 15 f c =500 Size of column (inches) Spirals Size of vertical round rods eter of core Size No. (inches) (A. S. & W. Co.) ! Pitch (inches of Per cent rods of core H % K 1 ix iy* 15 12 9 IK 0.5 8 10 88 93 97 104 16 13 8 Hi 0.5 8 10 99 104 108 115 119 17 14 7 \X IX 0.5 8 10 12 1.5 8 10 I 12 112 117 122 147 154 161 121 128 135 159 168 178 131 141 173 186 1 - 18 15 6 2/0 IX IX 0.5 8 10 12 1.5 8 10 12 125 130 136 'i72 178 134 142 149 177 186 196 145 155 191 204 157 207 19 16 G 3/0 \H ix 0.5 8 10 12 14 1.5 8 10 12 14 140 145 150 155 igi 197 204 149 156 164 171 196 205 215 225 159 169 179 210 223 236 172 185 226 243 185 244 ' 20 17 5 3/0 IX IX 0.5 8 10 If 1.5 8 10 12 14 155 160 165 170 "2is 224 164 171 179 186 216 226 235 245 175 185 195 205 230 243 256 269 187 200 246 263 201 264 21 18 4 3/0 i?i ' ' '. IX 0.5 8 10 12 14 1.5 8 10 12 14 172 177 182 187 180 188 195 203 191 201 211 221 251 265 278 291 203 216 230 268 285 302 217 233 234 286 306 307 246 "247 257 266 151 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS TABLE 40 . Column size yi 1:2:4 mixture n = 15 f c =500 = Af c (l+2.5np' 12 Spirals Size of vertical round rods Size of Diam- eter Number f column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core ot rods y& H + H 1 IK IK 22 19 4 IH 0.5 8 189 198 208 221 234 250 10 194 205 218 234 251 12 199 213 228 247 14 204 220 238 260 16 ! 209 227 248 4/0 IH 1.5 8 i 274 290 308 329 10 270 287 307 330 12 280 301 325 14 268 289 314 342 16 275 299 327 i 2.3 20 3 1M 0.5 8 207 216 226 239 253 268 j , : 10 212 223 236 252 269 289 12 217 231 246 265 277 14 222 238 257 278 16 227 245 267 291 5/0 1% 1.5 8 298 314 332 353 10 311 331 354 379 12 'SOS 324 349 376 14 313 337 366 i 16 '299 323 351 383 24 21 3 iH 0.5 10 231 242 256 271 288 308 12 236 250 266 284 305 14 241 257 276 297 16 I 246 264 286 310 5/0 IH 1.5 10 336 357 379 405 1 12 '329 350 374 401 14 338 363 391 I 16 348 376 408 25 22 2 IK 0.5 10 251 262 276 291 308 328 12 256 270 286 304 325 348 II 14 261 277 296 317 341 16 267 284 306 330 18 272 292 316 343 0/0 2 1.5 10 363 383 406 431 12 376 400 427 458 14 '365 369 417 449 16 374 402 435 ! || 18 384 416 452 26 23 2 Ui 0.5 10 272 283 297 312 329 349 12 277 291 307 325 346 369 14 283 298 317 338 362 16 288 305 327 351 379 18 293 313 337 364 6/0 1% 1.5 10 411 433 459 12 '464 428 455 486 14 417 445 477 16 '462 430 462 499 ! 18 411 443 479 152 TABLE 40 COLUMNS Column Size <. ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS I length \ A-r. ) =12 \diameterj 1:2:4 mixture n = 15 f e =500 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core H H H 1 IX IH 27 24 7/0 2 2 0.5 1.5 10 12 14 16 18 10 12 14 16 18 294 299 304 310 315 305 313 320 327 335 318 329 339 349 359 '432 446 459 472 334 347 360 373 386 439 457 474 491 508 351 368 384 401 417 462 484 506 527 549 370 391 411 487 514 541 431 440 28 25 1 7/0 2 2 0.5 1.5 10 12 14 16 18 20 10 12 14 16 18 20 317 322 327 332 337 343 328 335 343 350 358 365 341 351 361 371 381 391 '476 489 502 515 357 370 383 396 409 422 469 487 504 521 538 555 374 391 407 424 440 492 514 536 558 579 393 414 434 455 518 545 571 598 470 480 29 26 7/0 2K m 0.5 1.5 12 14 16 18 20 12 14 16 18 20 346 351 356 361 366 359 366 374 381 389 502 512 375 385 395 405 415 '507 520 533 546 393 407 420 433 446 518 536 552 570 588 414 431 447 464 481 545 567 589 610 632 438 458 478 576 602 630 30 27 7/0 2X IH 0.5 1.5 12 14 16 18 20 22 12 14 16 18 20 22 371 376 381 386 391 396 384 391 399 406 413 421 400 410 420 430 440 450 418 431 445 457 471 484 550 568 585 602 620 636 439 456 472 489 505 522 578 600 622 643 664 686 462 483 503 524 608 635 662 689 '552 566 579 592 544 554 153 COLUMNS TABLE 40 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS Column siz 1:2:4 mixture n=15 f c =500 ,_ / length \ Max. T - ) =12 \diameter Spirals Size of vertical round rods Size of Diam- ' -vr eter 1 Number column of core Size No. p- h P t H (inches) (inches) $-S.& (inches) oTcor" H % ^ l 1M 1>4 I i 31 28 2/0 2?^ 0.5 12 '396 410 425 444 465 488 14 401 417 435 457 481 i 508 16 407 424 445 470 498 529 18 312 432 455 483 514 549 20 417 439 466 496 531 569 22 422 447 476 509 548 7/0 ] 1.5 12 584 612 642 14 602 633 669 i 16 '586 619 655 696 18 600 646 677 722 20 613 653 698 749 22 .... | 588 626 670 720 32 29 2/0 2*4 0.5 12 423 436 452 471 491 514 14 428 444 462 484 508 535 16 433 451 472 497 524 556 18 438 458 482 509 541 576 20 443 466 492 523 557 596 22 448 473 502 536 574 7/0 \% 1.5 12 646 677 || 14 637 668 704 16 ! 654 690 731 18 '635 670 712 758 20 648 688 734 784 22 .... 661 705 755 33 30 2/0 2^ 0.5 12 450 464 479 498 519 542 14 456 471 490 511 537 563 16 461 479 500 524 552 583 18 466 486 510 537 568 603 20 471 493 520 550 585 624 22 476 500 530 563 602 644 24 481 508 540 576 618 7/0 16 1-5 12 672 713 14 '672 704 740 16 690 726 767 18 670 707 748 794 20 684 724 770 821 22 .... 697 741 791 847 24 i '668 710 758 813 34 31 3/0 2^ 0.5 14 || 484 500 518 540 564 591 16 ! 489 507 528 552 581 611 18 494 514 538 566 597 632 20 499 522 548 579 613 652 ; 22 504 529 558 592 630 672 24 510 536 568 605 (346 693 : 7/0 l$i 1.5 14 710 742 778 | 16 727 764 805 18 '708 744 785 832 20 722 762 807 858 22 734 779 829 885 24 748 796 851 912 154 TABLE 40 COLUMNS Column size ^ ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS Af e (l+2.5np')(l + (n- / length \ = Max. \diameter 12 1:2:4 mixture n = 15 f c = 500 Spirals Size of vertical round rods Size Diam- : I %__i of eter rxumuer ^r column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core OI rods X H X 1 IK IK 35 32 3/0 2K 0.5 14 513 529 547 569 593 620 16 518 536 557 582 610 641 18 524 544 567 595 626 661 20 529 551 577 608 642 681 22 534 558 587 621 659 702 24 539 566 597 634 676 722 7/0 iX 1.5 14 780 816 16 '766 802 843 18 782 824 870 20 800 846 896 22 '773 818 867 924 24 786 834 889 950 36 33 3/0 2^ 0.5 14 544 559 578 599 623 650 16 549 566 588 612 640 671 18 , 554 574 598 625 656 691 20 559 581 608 | 638 673 712 22 564 589 618 ! 651 690 732 24 569 596 628 1 664 706 752 26 574 603 638 677 723 772 7/0 IK 1.5 14 820 856 16 842 883 18 823 864 910 20 840 886 936 22 . . sis 857 907 963 , 24 826 874 929 990 : 26 839 892 951 1017 37 34 3/0 2H 0.5 14 591 609 630 655 682 16 580 598 619 644 671 702 18 585 605 629 657 688 723 20 590 613 ! 639 669 704 743 22 595 620 649 683 721 763 24 600 627 659 696 737 784 26 606 635 669 709 754 804 7/0 IX 1.48 14 857 893 16 879 920 18 860 901 946 20 876 922 973 22 894 944 1000 24 863 911 | 966 1027 26 .... 876 928 I 988 1053 38 35 3/0 2H 0.5 14 623 641 663 687 714 16 1 612 630 651 676 703 734 18 617 638 661 689 720 755 20 622 645 671 702 737 775 22 628 652 681 1 715 753 795 24 633 660 691 728 769 816 26 638 667 701 ! 741 786 836 7/0 IK 1.43 14 1 890 925 16 911 951 18 892 932 977 20 909 954 1003 22 926 975 1031 24 895 943 996 1057 26 , .... 908 959 1018 1082 155 COLUMNS TABLE 40 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS Column Size 1:2:4 mixture n=75 f c =500 / length \ \diameterj Spirals Size of vertical round rods Size of Diam- eter Number column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core of rods *A H 14 1 IK iy* 39 36 4/0 2% 0.5 16 663 684 709 735 768 18 '65i 671 694 722 753 788 20 656 678 704 735 769 808 22 661 685 714 748 786 829 24 666 693 724 761 803 849 26 ! 671 700 734 774 819 870 28 676 707 744 787 836 890 7/0 m 1.40 16 943 985 18 ' . .. . 966 1012 20 943 987 1037 22 959 1008 1063 24 || . 930 976 1030 1089 26 .... 942 993 1051 1116 28 955 1010 1072 1142 40 37 4/0 2*A 0.5 16 697 718 743 771 802 18 '685 705 728 756 787 822 20 690 712 738 769 803 842 22 695 719 748 782 820 863 24 700 727 758 795 837 884 26 . 705 734 768 808 854 905 28 710 741 778 821 869 925 7/0 1M 1.36 ! 16 980 1019 18 1001 1045 j 20 '978 1022 1071 22 994 1043 1097 24 1011 1064 1123 26 '976 1027 1085 1148 I 28 989 1044 1105 1174 41 38 4/0 2H 0.5 16 732 753 778 806 836 18 740 763 791 822 857 20 725 747 773 804 839 877 22 730 754 783 817 856 898 24 735 762 793 830 873 919 26 740 769 803 843 889 939 28 745 776 813 856 906 960 30 750 784 823 870 922 980 7/0 iy 2 1.32 16 1015 1054 18 1035 1079 20 .... i6l2 1057 1105 22 1029 1077 1131 24 1045 1098 1157 26 ioi2 1062 1118 1183 28 1024 1078 1140 1209 30 1037 1095 1101 1234 156 TABLE 40 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS ,_ / length \ Max. [-T-. -) =12 \dianieteri 1:2:4 mixture n=15 f c = 500 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitc-h (inches) Per cent of core K H H 1 1^ IH 42 39 4/0 7/0 2H 1H 0.5 1.29 | i 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 '76i 766 771 776 781 786 768 776 783 790 798 805 812 820 789 799 809 819 829 839 849 859 813 827 840 853 866 879 892 905 841 858 875 892 908 924 941 957 1052 1073 1093 1114 1134 1155 1175 1196 873 894 914 934 954 975 996 1016 1091 1117 1142 1167 1193 1218 1244 1269 1649 1065 1082 1098 1115 1131 :::: 1648 1061 1074 43 40 4/0 7/0 2H IK 0.5 1.25 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 803 808 813 818 823 805 813 820 827 835 842 849 857 826 836 846 856 866 876 886 896 851 864 877 890 903 916 929 942 879 895 911 928 944 961 978 995 1087 1107 1127 1147 1168 1188 1208 1228 909 930 950 970 991 1011 1032 1052 1124 1150 1175 1200 1225 1250 1275 1300 i096 1108 i085 1100 1116 1133 1148 1164 157 COLUMNS TABLE 41 mixture ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS P = Af c (l+2.5np'}[l + (n- Column Size * 12 600 \diameterl Spirals Size of vertical round rods Size of Diam- eter Number _r column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core OI rods H H H 1 1H 1M 15 12 9 Us' 0.5 8 97 105 10 101 112 10 13 8 IM 0.5 8 110 118 10 115 125 17 14 7 IH 0.5 8 125 133 143 10 130 140 152 . 12 134 146 \H 1.5 8 157 168 180 10 163 176 191 12 169 185 IS 15 6 1> 0-5 8 141 149 158 170 ! 10 145 155 168 ! 12 150 162 2/0 Ik' 1.5 8 188 200 214 10 'l83 196 211 12 189 204 19 16 6 ]? j 0.5 8 157 166 175 186 199 10 162 172 184 198 1 1 12 167 179 194 14 ; 171 186 3/0 1% l!5 8 209 221 235 251 10 '264 217 233 250 12 210 226 244 | 14 1 216 234 20 17 5 1>2 0.5 8 175 183 193 204 217 10 ISO 190 202 216 12 185 197 211 14 189 204 221 1 3/0 IH 1.5 8 231 244 258 274 10 240 255 273 12 233 248 267 | 14 239 257 278 21 18 4 iH 0.5 8 194 202 212 224 236 250 10 199 209 221 235 251 12 204 216 230 247 14 208 223 239 3/0 1>2 1.5 8 267 282 298 315 10 '264 279 297 317 12 272 290 312 14 '263 281 302 158 TABLE 41 COLUMNS Column size ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS 12 ._ A/ax. / length \ (-^ ) \diameterl 1:1%:3 mixture n = 12 f c =600 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core K K 1 IH IK 22 19 4 4/0 1^ I* 0.5 1.5 10 12 14 16 8 10 12 14 16 214 219 224 228 233 '288 294 222 229 236 243 249 '289 297 306 314 232 241 250 259 269 293 304 316 327 339 243 255 267 279 307 322 337 352 256 271 323 342 270 341 23 20 3 5/0 IK IK 0.5 1.5 8 10 12 14 16 8 10 12 14 16 227 231 ' 245 249 254 244 250 257 264 270 253 263 271 281 290 319 331 342 354 365 265 276 288 300 312 333 349 364 379 394 277 292 307 349 368 388 291 310 367 391 "326 324 333 341 24 21 3 5/0 1 1 0.5 1.5 10 12 14 16 10 12 14 16 262 267 272 276 272 279 286 293 '352 361 369 285 294 303 313 359 370 382 393 299 311 322 334 377 392 407 422 314 330 396 416 332 419 25 22 2 6/0 IK 2 0.5 1.5 10 12 14 16 18 10 12 14 16 18 286 290 295 299 304 296 302 309 316 322 308 317 326 335 344 388 400 411 423 434 322 334 346 358 370 406 421 436 451 466 338 353 368 426 445 464 356 374 -448 472 1 390 398 407 26 23 2 6/0 IK IK 0.5 1.5 10 12 14 16 18 10 12 14 16 18 310 315 319 324 329 320 327 334 340 347 332 342 350 360 369 346 358 370 382 394 437 452 467 482 497 362 377 392 408 457 476 495 514 380 398 479 502 .' : : : '429 438 431 442 454 465 159 TABLE 41 COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS Column size mixture = 600 Spirals Size of vertical round rods Size of Diam- eter Number column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core of rods H H H 1 1H IK 27 24 1 2 0.5 10 335 346 358 372 388 405 12 340 352 367 384 403 424 14 345 359 376 396 418 443 16 849 366 385 408 433 18 354 372 394 420 448 7/0 2 1.5 10 469 489 511 12 463 484 508 535 14 474 499 527 558 16 461 486 514 546 ; 18 470 497 529 565 28 25 1 1 2 0.5 10 362 372 384 399 414 432 12 367 379 394 410 429 451 14 371 386 403 423 444 469 16 376 392 412 434 459 488 18 380 399 421 446 474 20 i 385 406 430 458 7/0 2 1.5 10 502 522 545 12 517 541 568 14 j '508 532 560 592 16 .... 519 547 579 615 18 '503 531 562 598 20 | 512 542 577 29 26 2M 0.5 12 394 407 421 438 457 478 14 399 413 430 450 472 497 16 404 420 439 462 487 516 i 1 1 18 408 427 448 473 502 20 413 433 458 485 516 7/0 1H 1.5 12 j . .. 552 576 603 14 '542 567 595 626 I j 16 li . .. 554 582 614 650 ! 1 is :j . .. '538 565 597 633 i 20 ! . .. 546 577 612 652 30 27 2H 0.5 12 423 435 450 467 486 507 14 ! 428 442 459 479 501 525 16 432 449 468 491 516 544 i 18 437 455 477 502 . 531 563 1 20 442 462 486 514 546 22 446 469 495 526 561 7/0 IK 1.5 12 588 612 639 14 |i 603 631 663 16 '596 618 650 686 18 .... 602 633 669 710 20 '583 613 648 688 22 591 624 664 707 160 TABLE 41 Column size ^ COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS P = Af c (l +2.5np')U + (n - I length \ Max. -;-. \diameterj 12 1:1)4:3 mixture n = 12 f c =600 Size 'of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods I Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core % \ K H 1 IX IK 31 1 28 2/0 7/0 2H IK 0.5 1.5 12 14 16 18 20 22 12 14 16 18 20 22 453 458 462 467 471 476 465 472 479 485 492 499 480 489 498 507 516 525 497 508 520 532 544 556 626 641 656 671 686 701 515 530 546 561 576 591 650 669 688 707 726 745 545 555 574 593 611 687 700 724 747 771 628 639 651 662 '629 32 29 2/0 7/0 2H IM 0.5 1.5 12 14 16 18 20 22 12 14 16 18 20 22 484 488 493 498 502 507 496 503 509 516 523 530 510 520 529 538 546 556 527 539 551 563 575 587 547 562 577 592 606 622 689 708 727 746 765 784 568 586 605 624 642 716 739 763 786 810 680 695 710 725 740 678 690 701 33 30 2/0 7/0 2K i* 0.5 1.5 12 14 16 18 20 22 24 12 14 16 18 20 22 24 516 520 525 530 534 539 544 528 535 541 548 555 562 568 542 552 561 570 579 588 597 559 571 583 595 607 619 631 578 593 608 624 639 654 669 729 748 767 786 805 824 843 599 618 637 656 674 693 756 779 803 826 850 873 720 735 750 765 780 795 .... .... 719 730 742 753 716 34 31 3/0 7/0 2H l)i 0.5 1.5 14 16 18 20 22 24 .14 16 18 20 22 24 553 558 563 567 572 577 568 574 581 588 595 602 585 594 603 612 622 631 605 617 629 641 653 665 762 777 792 807 822 837 627 642 657 672 687 702 790 809 828 847 866 885 651 670 688 707 726 745 821 845 868 892 915 939 '7ei 772 784 795 ( ' 11 161 COLUMNS TABLE 41 1:1^4:3 mixture n = 12 f c = 600 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS P=Af c (l+2.5np' Max. , Column si. Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core % H % 1 IH IK 35 32 3/0 7/0 2H IK 0.5 1.5 14 16 18 20 22 24 14 16 18 20 22 24 587 592 597 601 606 611 602 608 615 622 629 635 619 628 637 646 655 664 638 650 662 674 686 698 661 676 691 706 721 736 833 852 871 890 909 928 685 704 722 741 760 779 864 888 911 935 958 982 '826 838 820 835 850 865 880 36 33 3/0 7/0 2M IX 0.5 1.5 14 16 18 20 22 24 26 14 16 18 20 22 24 26 623 627 632 637 641 646 652 637 644 650 657 664 670 677 654 663 673 682 691 700 709 674 685 697 709 721 733 745 696 711 726 741 756 771 786 877 896 915 934 953 972 991 721 739 758 777 795 813 832 909 932 956 979 1002 1026 1049 .... '87i 882 894 '879 894 909 925 940 37 34 3/0 7/0 2H 1H 0.5 1.48 14 16 18 20 22 24 26 14 16 18 20 22 24 26 ' '664 ; 668 673 678 682 687 673 680 687 693 700 707 714 690 699 708 717 727 736 745 710 722 734 746 758 770 782 732 747 76? 777 792 807 822 919 937 956 975 994 1013 1031 757 775 794 813 831 850 868 949 973 996 1019 1042 1065 1089 '923 935 921 936 950 965 980 38 35 3/0 7/0 2H IH 0.5 1.43 14 16 18 20 22 24 26 14 16 18 20 22 24 26 '761 706 710 715 720 725 711 717 724 731 738 744 751 727 737 746 755 764 773 782 747 759 771 783 794 806 819 769 784 800 815 830 845 860 956 975 994 1013 1031 1050 1069 794 813 832 851 869 887 906 987 1010 1033 1056 1080 1103 1126 '96i 973 958 973 988 1003 1018 162 TABLE 41 COLUMNS Column Size ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS P=Af c (l+2.5np')[l + (n- Max. I length \ {diameter/ 12 %: 3 mixture 12 600 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical raund rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core H H H 1 iM 1M 39 36 4/0 7/0 *M iK 0.5 1.40 16 18- 20 22 24 26 28 16 18 20 22 24 26 28 16 18 20 22 24 26 28 16 18 20 22 24 26 28 '744 749 754 758 763 768 756 763 769 776 783 789 796 775 784 794 803 812 821 830 798 810 821 833 845 857 869 823 838 853 869 884 899 914 1016 1035 1054 1073 1092 1110 1129 851 870 889 908 926 945 964 1052 1075 1098 1121 1145 1168 1191 - iois 1030 1044 1059 1074 ; ;;; ioos 1014 1025 40 37 4/0 7/0 2% IH 0.5 1.36 "784 788 793 798 803 807 795 802 809 816 822 829 836 815 824 833 842 851 860 869 837 850 861 873 885 897 909 863 878 893 909 924 939 954 1056 1074 1093 1111 1130 1148 1167 891 909 928 947 965 984 1003 1091 1113 1136 1159 1182 1205 1228 ;; : 1054 1065 1055 1070 1084 1098 1113 41 38 1 4/0 7/0 *H IK 0.5 1.32 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 '829 834 839 844 , 848 852 836 843 850 856 863 870 876 883 856 865 874 883 892 901 910 919 879 890 902 914 926 938 950 962 903 918 934 949 964 979 994 1009 1096 1115 1133 1152 1170 1188 1207 1225 932 951 970 988 1007 1025 1044 1063 1131 1154 1176 1199 1221 1244 1267 1289 ' i094 1105 1116 16&5 1109 1124 1138 1153 1167 163 COLUMNS TABLE 41 1:1%:3 mixture n = 12 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS 12 fnlnmrt size %. Max. Size of. column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (.inches) Per cent of core ys H 7 A 1 IH IK 42 39 4/0 7/0 2M 1}'2 0.5 1.29 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 'S71 876 880 885 889 894 878 885 891 898 905 911 918 924 897 906 916 925 934 943 953 962 920 932 944 956- 967 979 991 1003 945 960 975 990 1004 1019 1034 1050 1140 1158 1176 1194 1212 1230 1249 1267 973 992 1010 1029 1048 1066 1084 1103 1172 1196 1219 1241 1264 1286 1309 1331 ii37 1148 1159 li38 1152 1167 1181 1195 1210 43 40 4/0 7/0 2H IH 0.5 1.25 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 "gis 923 928 932 1 937 921 927 934 941 947 954 961 968 940 949 958 968 977 986 995 1004 962 974 986 998 1010 1022 1034 1046 988 1003 1018 1033 1048 1062 1077 1092 1181 1199 1217 1235 1253 1271 1289 1307 1016 1035 1053 1072 1090 1109 1128 1146 1215 1237 1259 1282 1304 1326 1348 1371 1179 1193 1207 1222 1236 1250 .... ii90 1200 164 TABLE 42 Column size COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS 1:1:2 mixture n=10 f c =725 Spirals Size of vertical round rods Size of Diam- eter Number column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core of rods H H H 1 IX IH 15 12 9 1H 0.5 8 110 118 1 10 115 125 16 13 8 IH 0.5 8 126 134 ! 10 ; 131. 141 17 14 7 IK 0.5 8 144 151- 161 10 148 158 170 12 153 164 IH 1.5 8 175 185 197 10 181 193 207 12 186 201 18 15 .6 1H 0.5 8 162 170 179 190 10 167 177 188 12 171 183 2/0 1H 1.5 8 208 219 233 10 '264 216 230 12 209 224 19 16 6 IH 0.5 8 182 190 199 210 223 10 186 196 208 222 12 191 203 217 14 195 211 3/0 i^ 1.5 8 232 244 257 272 10 '228 240 254 271 12 233 248 265 14 239 257 20 17 5 1H 0.5 8 203 211 220 231 243 10 208 217 229 243 12 212 224 238 14 217 231 247 3/0 m 1.5 8 258 269 283 298 10 266 280 296 12 '259 274 291 14 265 282 302 21 18 4 IK 0.5 8 225 234 243 254 266 280 10 230 240 252 265 280 12 235 247 260 277 14 239 254 269 3/0 IK 1.5 8 297 310 325 342 10 '293 308 324 343 12 301 318 338 1 14 '292 310 329 165 COLUMNS TABLE 42 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS Column size 1:1:2 mixture 'ri = 10 f c = 725 Max l lw"L\ =12 \diameter / Spirals Size of vertical round rods Size of Diam- eter Number _r column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core OI rods *A H V* 1 IH IH 22 19 4 IH 0.5 8 249 257 266 277 290 303 10 254 264 275 289 304 12 258 270 284 300 14 263 277 293 312 16 267 283 302 4/0 1% 1.5 8 326 339 354 370 10 '322 336 353 372 12 330 347 367 14 '321 338 358 381 16 327 346 369 23 20 3 IH 0.5 8 i 274 282 291 302 315 328 10 i 279 289 300 314 329 346 12 ; 283 295 309 326 344 14 i 288 302 318 337 16 292 808 327 349 5/0 1% 1.5 8 356 369 384 401 10 367 384 402 423 12 'sei 378 398 420 14 369 389 412 1 i 16 357 377 399 426 24 21 3 1% 0.5 10 305 315 326 340 356 372 12 309 321 335 352 370 14 ' 314 328 344 363 16 319 334 353 375 5/0 IM 1.5 10 399 416 435 455 12 393 410 430 452 14 401 421 444 16 409 432 458 25 22 2 1% 0.5 10 333 342 354 1 368 383 400 12 337 349 363 379 398 418 : j 14 341 356 372 391 412 16 346 362 381 402 18 350 368 389 414 6/0 2 1.5 10 433 449 468 490 12 444 463 486 511 14 '434 454 478 504 16 442 465 492 18 450 476 506 1 26 23 2 IH 0.5 10 i 361 372 383 396 412 429 12 366 378 392 408 427 447 14 370 385 401 420 442 16 375 391 410 431 456 18 1 379 397 418 443 6/0 1% ' 1.5 10 485 503 525 12 '479 499 521 546 14 490 513 539 16 '478 501 527 557 18 |; .... 485 512 541 . lf>6 TABLE 42 COLUMNS Column size ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS Max. -- =12 n=10 f c = 725 Size of column (inches) Diam- eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent 1 of core *A H H 1 IK in 27 24 7/0 Q 2 0.5 1.5 10 12 1 4 6 18 10 12 14 16 18 392 396 401 305 410 401 408 415 421 428 413 422 431 440 449 '515 526 537 548 427 438 450 461 473 522 536 550 564 578 442 457 471 486 500 540 558 576 594 612 459 477 495 561 583 605 :::.' 'si 5 522 28 25 1 7/0 2 0.5 1.5 10 12 14 16 18 20 10 12 14 16 18 20 423 428 432 437 441 446 433 440 447 453 459 465 445 453 462 471 480 489 458 470 481 493 504 516 560 574 588 602 616 630 473 488 503 517 532 578 596 614 632 650 490 508 527 545 599 621 644 666 '56i 569" '565 576 587 597 29 26 7/0 2M m 0.5 1.5 12 14 16 18 20 12 14 16 18 20 460 464 469 473 478 472 479 485 491 498 'eoi 608 486 495 504 512 521 '605 616 626 637 502 513 525 537 548 613 628 642 656 670 521 535 550 564 579 636 654 672 690 707 541 559 577 662 683 705 30 27 7/0 2H IH 0.5 1.5 12 14 16 18 20 22 12 14 16 18 20 22 494 499 503 508 512 517 506 513 519 525 531 538 520 529 537 546 555 564 536 548 559 570 582 593 655 670 684 698 712 726 554 569 583 598 613 628 678 696 714 731 749 767 575 593 611 629 703 725 747 769 "650 658 '657 668 679 689 167 COLUMNS 1:1:2 mixture n=10 f c=7 25 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS P=Af c (l+2.5np'j[l+(n-l)p] Max. t-- =12 TABLE 42 i^ Co/if 777/7 size y. Spirals Size of vertical round rods Size of Diam- eter Number _* column (inches) of core (inches) Size No. (A. S. &. W. Co.) Pitch (inches) Per cent of core OI rods H H % 1 IK IX 31 28 2/0 2% 0.5 12 530 541 555 571 590 610 14 534 548 564 583 605 628 16 539 554 573 595 619 647 18 543 560 582 606 633 665 20 548 567 590 618 648 682 22 552 573 599 629 663 7/0 IK 1.5 12 698 721 746 14 713 739 768 16 '766 727 757 790 18 711 741 775 812 20 722 755 792 834 22 '76! 733 769 810 32 29 2/0 2H 0.5 12 565 577 592 608 626 647 14 570 584 600 620 641 665 16 ' 574 590 609 631 655 683 18 579 597 618 642 670 701 20 583 603 627 654 685 718 22 588 610 636 666 699 7/0 . IK 1.5 12 765 792 14 '757 783 813 16 771 801 835 18 '756 785 819 857 20 767 800 837 879 22 777 814 855 33 30 2/0 2H 0.5 12 604 616 629 646 664 685 14 608 622 638 657 678 702 16 613 628 647 669 693 720 18 617 635 656 680 708 738 20 622 641 665 691 723 757 22 526 648 674 703 737 775 24 631 654 683 715 752 7/0 IK 1.5 12 812 836 14 '803 830 858 16 817 848 880 18 '802 832 866 902 ' 20 813 846 883 925 22 824 860 901 947 24 '800 834 873 919 34 31 3/0 2% 0.5 14 647 661 677 696 718 742 16 652 668. 686 708 733 760 18 656 674 695 720 747 778 20 661 680 704 731 762 796 22 665 687 713 743 777 813 24 670 693 722 754 791 831 7/0 IK 1.5 14 851 878 907 1 16 ! 865 895 929 18 '850 880 913 951 20 861 894 931 973 22 872 908 949 995 24 882 922 966 1017 168 TABLE 42 Column size <. COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS P=Af c (l+2.5np')(l + (n- I length \ ) = 12 Max ' diameter 1:1:2 mixture n=10 f c = 725 Size of column (inches) Diam- eter of core (inches) j Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) ! Pitch (inches) Per cent of core K % H 1 IX IH 35 32 3/0 7/0 2K IK 0.5 1.5 14 16 18 20 22 24 14 16 18 20 22 24 688 692 697 701 706 710 702 708 715 721 728 734 717 727 736 745 753 762 737 748 760 771 782 795 758 773 787 802 817 831 927 945 963 981 998 1016 782 800 818 836 854 872 956 978 1000 1022 1045 1067 915 929 943 957 972 .... '921 931 36 33 3/0 7/0 2K IK 0.5 1.5 14 16 18 20 22 24 26 14 16 18 20 22 24 26 729 734 738 743 747 752 756 743 749 756 762 769 775 782 759 768 777 786 795 804 812 778 790 801 813 825 836 848 800 814 829 843 858 873 887 978 996 1013 1031 1049 1067 1086 824 842 860 878 896 914 932 1007 1029 1051 1073 1095 1117 1140 '972 983 993 980 994 1008 1022 1036 37 38 34 3/0 7/0 99i IK 0.5 1.48 14 16 18 20 22 24 26 14 16 18 20 22 24 26 '778 782 787 791 796 800 787 793 800 806 813 819 826 803 812 820 829 838 846 855 821 833 844 856 867 879 890 843 858 872 886 900 915 930 1027 1044 1061 1079 1097 1114 1132 867 885 903 920 938 956 975 1054 1077 1099 1121 1143 1165 1187 1628 1042 1056 1070 1084 ioso 1041 35 3/0 7/0 2H IK 0.5 1.43 14 16 18 20 22 24 26 14 16 18 20 22 24 26 "82i 826 830 835 839 844 830 837 843 850 856 863 869 846 854 863 872 881 890 899 866 877 888 900 912 923 935 887 901 916 930 945 960 975 1072 1089 1107 1125 1142 1160 1178 911 929 947 965 983 1000 1018 1100 1122 1144 1166 1188 1209 1231 1673 1087, 1101 1115 1129 :::: | i075 1086 169 COLUMNS TABLE 42 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS Column size .^i P 1:1:2 mixture n = 10 Af e (l+2.5np')[l+(n-l)p] Spirals Size of vertical round rods Size Diam- t of eter JN umber of column (inches) of core (inches) Size No. (A. S. & W. Co.) Pitch (inches) Per cent of core j OI rods H ! 2i H 1 IH IX 39 36 4/0 2H 0.5 16 866 882 901 922 947 974 I 18 871 888 910 934 961 992 20 875 895 919 945 976 1010 22 880 901 928 957 991 1028 24 884 908 936 969 1005 1046 26 889 914 945 980 1020 1064 28 893 920 954 992 1034 1082 7/0 iy 2 1.40 16 1133 1167 18 1151 1188 20 ii32 1168 1210 22 1146 1186 1232 24 ii2i 1159 1204 1254 26 1131 1173 1221 1275 28 1141 1187 1239 1297 40 37 4/0 2H 0.5 16 929 948 968 993 1021 18 '6i8 935 956 980 1008 1039 20 922 942 965 991 1023 1057 22 927 948 974 1003 1037 1075 24 931 955 983 1015 1052 1093 26 936 961 991 1026 1066 1111 28 940 967 1000 1038 1081 1129 7/0 1>2 1.36 16 1183 1216 18 1201 1237 20 1181 1219 1259 22 1195 1236 1280 24 1209 1253 1302 26 iisi 1223 1271 1323 28 | 1191 1237 1289 1345 41 38 4/0 2^ 0.5 16 978 996 1017 1041 1069 18 984 1005 1029 1056 1087 20 97i 991 1013 1040 1071 1105 22 976 997 1022 1052 1086 1123 24 980 1004 1031 1063 1100 1141 26 985 1010 1040 1075 1115 1159 1 28 989 1016 1049 1086 1130 1177 30 994 1022 1058 1098 1144 1196 7/0 ll 1.32 16 1232 1264 * 7z 18 1249 1285 20 1230 1266 1306 22 1244 1284 1328 24 1257 1301 1350 26 1230 1271 1318 1371 28 . 1240 1285 1336 1393 30 1251 1298 1353 1415 170 TABLE 42 Column size COLUMNS ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS CHICAGO BUILDING CODE REQUIREMENTS 19 12 .f-. \diameter 1:1:2 mixture n = 10 f e =725 Size of column (inches) Diam- i eter of core (inches) Spirals Number of rods Size of vertical round rods Size No. (A. S. & W. Co.) Pitch (inches) Per cent j of core ! X H H 1 IH I 42 39 4/0 7/0 2H 1H 0.5 1.29 16 18 20 22 24 26 28 30 16 18 20 22 24 26 28 30 1620 1025 1029 1034 1038 1042 1027 1033 1040 1046 1053 1059 1065 1072 1045 1054 1063 1071 1080 1089 1098 1107 1067 1078 1090 1101 1112 1124 1136 1147 1091 1106 1120 1135 1149 1163 1178 1193 1283 1300 1317 1334 1351 1368 1386 1403 1118 1136 1154 1172 1190 1208 1226 1244 1315 1336 1357 1378 1399 1420 1441 1463 1281 1294 1308 1321 1335 1349 '.'.'.'. i 1280 1290 1300 43 40 4/0 7/0 2H 1H 0.5 ,. 16 18 ^0 22 24 26 28 30 16 18 20 22 24 26 28 30 i073 1078 1083 1088 1092 1 1077 1083 1090 1096 1103 1109 1116 1122 1096 1104 1113 1122 1131 1140 1149 1158 1117 1129 1140 1152 1163 1175 1186 1198 1142 1156 1171 1186 1200 1215 1229 1244 1333 1350 1367 1385 1402 1419 1436 1453 1169 1187 1205 1223 1241 1259 1277 1295 1366 1387 1408 1429 1450 1471 1492 1513 1332 1345 1359 1372 1386 1400 i 1340 1350 171 COLUMNS TABLE 43 71=15 f c =800 ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS LOS ANGELES AND MILWAUKEE BUILDING CODE REQUIREMENTS P=Af c [l+(n-l)p] Cotumn size Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods IK 1M H H | H 1 IK 134 H H H 1 10 7 6 *57.0 *51.4 *60.5 11 8 6 *66.4 *78 . . . 60.8 *69.9 c *7* 2; *67.7 *79.8 12 9 6 77.1 71.5 8 ' 78.4 13 10 6 j 89 83 4 92.5 8 j 97.8 90.3 14 11 6 102 2 1138 96.6 105.7 116.4 8 1111. 103.5 115.6 10 110.4 15 12 6 116.7 128.3 111.1 120.2 130.9 8 125.5 140.9 118.0 130.1 10 134 3 124.9 140.0 10 13 6 132.4 144.0 157.6 126.8 135.9 146.6 159.0 8 141.2 156.6 133.7 145.8 160.1 10 150.0 140.6 155.7 17 14 6 8 149.3 158.1 160.9 174.5 173.5 191.7 190.3 143.7 150.6 152.8 162.7 163.5 177.0 175.9 189.9 10 166.9 186.1 i , 157.5 172.6 190.4 12 175.6 164.3 182.5 18 15 6 167.6 179.2 192.8 208. G ! 162.0171.0 181.8 194.2 . 8 176.4 191.8 210.0 168.9 181.0 195.3 211.8 10 185.2 204.4 175.8 190.9 208.7 12 193.9 217.0 182.6 200.8 19 10 8 195.9 211.3 229.5 250.5 188.4 200.5 214.8 231.3'250.0 10 204.7 223.9 246.6 195.3 210.4 228.2 248.9 12 213.4 236.5 202.1 220.3 241.7 14 222.2 249.1 209.0 230.2 20 17 8 216.6 232.0 250.2 271.2 .. 209.1 221.2235.5 252.0270.7 10 225.4 244.6 267.3) 216.0 231.1 248.9 269.6, 12 234.1 257.2 ...... 1 222.8 241.0 262.4 14 242.9 269.8 229.7 250.9 275.9 I 21 18 8 238.6 254.0 272.2 293.2'317.0 243.2 257.5 274.0292.7 313.5 10 247.4 266.6 289.3 315. 6j 238 '. 6 253.1 270.9 291.6314.9 12 256.1 279.2 306.5 244.8 263.0 984 4 309.2 14 264.9 291.8 251.7 272.9 297.9 22 19 8 261.8 277.2 295.4 316.4340.2 266.4 280.7 297.2315.9 336.7 10 270.6 289.8 312.5 338.8 ..-.[.I 26i!2 276.3 294.1 314.8338.1 12 279.3 302.4 329.7 1 268.0 286.2 307.6 332.4 14 16 288.1 296.8 315.0 327.6 346 8 274.9 281.8 296.1 306.0 321.1 334.6 350.0 23 20 8 10 286.4 295.2 301.8320.0341.0364.8 314.41337.1 363.4393.1 391.4 291.0 300.9 305.3 318.7 321.8340.5361.3 339.4362.7388.8 12 303.9 327. 0354.31 385. 8 262! 6 310.8 332.2 357.0 385. Oj 14 312.7 16 321.4 339.6 352.2 371.4 388.6 299.5 306.4 320.7(345.7 330.6359.2 374.6 392.1 These columns contain more than 4 % of steel. 172 TABLE 43 COLUMNS i^ Column size ^ ROUND CORED HOOPED COLUMNS SAFE LOAD IN THOUSANDS OF POUNDS LOS ANGELES AND MILWAUKEE BUILDING CODE REQUIREMENTS = 15 \ \ 1/4^^-?^ i k **&& oUU Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods H H M 1 IK IK .* H M 1 IK IX 24 25 26 27 28 29 30 31 32 33 21 22 23 24 25 26 27 28 29 30 10 12 14 16 10 12 14 16 18 10 12 14 16 18 10 If 16 18 10 12 14 16 18 20 12 14 16 18 20 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 12 14 16 18 20 22 24 320.9 329.6 338.4 347.1 347.9 356.6 365.4 374.1 382.9 340.1 352.7 365.3 377.9 367.1 379.7 392.3 404.9 417.5 395.4 408.0 420.6 433.2 445.8 424.9 437.5 450.1 462.7 475.3 455.7 468.3 480.9 493 . 5 506.1 518.7 500.3 512.9 525.5 538.1 550.7 533.7 362.8 380.0 397.1 414.3 389.8 407.0 424.1 441.3 458.4 418.1 435.3 452.4 469.6 486.7 447.6 464.8 481.9 499.1 516.2 478.4 495.6 512.7 529.9 547.0 564.2 527.6 544.7 561.9 579.0 596.2 561 . 389.1 411.5 418.8 318.3 325.2 332.1 326.6 336.5 346.4 356.3 353.6 363.5 373.4 383.3 393.2 381.9 391.8 401.7 411.6 421.5 42i!3 431.2 441.1 451.0 344.4 357.9 371.4 384.9 371.4 384.9 398.4 411.9 425.3 399.7 413.2 426.7 440.2 453.6 429.2 442.7 456.2 469.7 483.1 460.0 473.5 487.0 500.5 513.9 527.4 505.5 519.0 532.5 545.9 559.4 538.9 552.4 565.9 579.3 592.8 606.3 573.4 586.9 600.4 613.8 627.3 640.8 609.2 622.7 636.2 649.6 663.1 676.6 646.3 659.8 673.3 686.7 700.2 713.7 727.1 265.1 382.7 400.3 417.8 392.1 409.7 427.3 444.8 462.4 420.4 438.0 455.6 473.1 490.7 449.9 467.5 485.1 502.6 520.2 480.7 498.3 515.9 533 . 4 551.0 568.6 530.3 547.9 565.4 583.0 600.6 563.7 581.3 598.8 616.4 634.0 651.6 598.2 615.8 633.3 650.9 668.5 686.1 634.0 651.6 669.1 686.7 704.3 721.9 671.1 688.7 706.2 723.8 741.4 759.0 776.6 388.4 410.7 415.4 437.7 460.0 443.7 466.0 488.3 510.5 473 . 2 495.5 517.8 540.0 562.3 504.0 526.3 548.6 570.8 593.1 558.3 580.6 602.8 625.1 647.4 591.7 614.0 636.2 658.5 680.8 703.0 626.2 648.5 670.7 693.0 715.3 737.5 662.0 684.3 706.5 728.8 751.1 773.3 699.1 721.4 743.6 765.9 788.2 810.4 832.7 414.5 441.5 469.0 469.8 497.3 499.3 526.8 554.3 530.1 557.6 585.1 612.6 589.6 617.1 644.6 623.0 650.5 678.0 705.5 657.5 685.0 712.5 740.0 767.4 693.3 720.8 748.3 775.8 803.2 730.4 757.9 785.4 812.9 840.3 867.8 416.1 438.5 460.9 445.8 474.2 507.4 352.2 359.1 366.0 444.4 466.8 489.2 511.6 473.9 496.3 518.7 541.1 563.5 504.7 527.1 549.5 571.9 594.3 559.1 581.5 603.9 626.3 648.7 592.5 474.1 502.5 503.6 532.0 560.3 536.9 534.4 562.8 591.1 567.7 602.7 452.1 462.0 471.9 481.8 491.7 484.1 494.0 503.9 513.8 523.7 594.8 623.1 651.5 628.2 634.7 668. 1 ::::: 546.3578.1 558.9595.3 571.5612.4 584.1J629.6 596.7i646.7 568.2595.5 580.8612.6 593.4629.8 606.0;646.9 618.6664.1 631.2 681.2 604.0631.3 616.6 648.4 614.9 637.3 659.7 682.1 704.5 627.0 649.4 671.8 694.2 716.6 739.0 662.8 685.2 656.5 684.9 713.2 703.1 527.4 537.3 547.2 557.1 567.0 561 .9 571.8 581.7 591.6 601.5 ::::: 662.7 691.0 719.4 747.7 698.5 726.8 702.6 737.6 738.4 773.4 ! '.'.'. : : : : : 629.2 641.8 654.4 667.0 665.6 682.7 699.9 717.0 66S 4 707.6 730.0 752.4 774.8 699.9 755.2 783.5 811.9 735.6 808.4 607.6 617.5 627.4 637.3 775.5 g 653.7685.5 666.3702.7 678.91719.8 691.51 737.0 704.1 754.1 716.7771.3 722.3 744.7 767.1 789.5 811.9 834.3 763.9 792.3 820.6 849.0 877.3 810.5 845.5 880.5 644.7 654.6 664.5 674.4 684.3 173 COLUMNS TABLE 43 SAFE LOAD IN THOUSANDS OF POUNDS LOS ANGELES AND MILWAUKEE BUILDING CODE REQUIREMENTS f c =800 jgaa* IP I Size of column (inches) Diameter Number of of (inches) rod8 ! Square rods Round rods M H K 1 IK I* M K H 1 1M 1M 34 35 36 37 38 3!) 40 41 31 14 16 18 20 22 24 32 14 16 18 20 22 24 33 14 16 18 20 22 24 26 34 14 16 18 20 22 24 26 35 14 16 18 i 20 22 24 26 36 16 18 20 ; 22 24 26 28 37 16 18 20 22 24 26 28 38 16 18 ! 20 22 24 26 28 30 ::::: 692.0 704.6 717.2 729.8 742.4 755.0 723.8 741.0 758.1 775.3 792.4 809.6 763.4 780.6 797.7 814.9 832.0 849.2 804.2 760.6 783.0 805.4 827.8 850.2 872.6 800.2 822.6 845.0 867.4 889.8 912.2 841.0 802.2 830.6 858.9 887.3 915.6 848.8 883.8 918.8 692! 9 702.8 712.7 722.6 698.1 711.6 725.0 738.5 752.0 765.4 737.7 751.2 764.6 778.1 791.6 805.0 727.0 744.5 762.1 779.7 797.3 814.9 766.6 784.1 801.7 819.3 836.9 854.5 807.4 824.9 842.5 860.1 877.7 895.3 912.9 849.5 867.0 884.6 902.2 919.8 937.4 955.0 892.9 910.4 928.0 945.6 963.2 980.8 998.4 955.0 972.6 990.2 1008 1025 1043 1061 1001 1019 1036 1054 1071 1089 1107 1048 1066 1083 1101 1118 1136 1154 1171 759.7 781.9 804.2 826.5 848.7 871.0 799.3 821.5 843.8 866.1 888.3 920.6 840.1 862.3 884.6 906.9 929.1 951.4 973.7 882.2 904.4 926.7 949.0 971.2 993.5 1016 925.6 947.8 970.1 992.4 1015 1037 1059 992.4 1015 1037 1059 1082 1104 1126 1038 1061 1083 1105 1127 1150 1172 1085 1108 1130 1152 1175 1197 1219 1241 796.2 823.7 851.2 878.6 906.1 933.6 835.8 863.3 890.8 918.2 945.7 973.2 876.6 904.1 931.6 959.0 986.5 1014 1041 918.7 946.2 973.7 1001 1029 1056 1084 962.1 989.6 1017 1045 1072 1100 1127 1034 1062 1089 1117 1144 1172 1199 1080 1108 1135 1163 1190 1218 1245 1127 1155 1182 1210 1237 1265 1292 1320 841.8 870.2 898.5 926.9 955.2 983.6 882.6 888.4 923.4 958 4 993.4 929.2 821.4 838.5 855.7 872.8 890.0 907.1 846.3 863.5 880.6 897.8 914.9 932.1 949.2 889.7 906.9 924.0 941.2 958.3 975.5 992.6 951.5 968.6 985.8 1003 1020 1037 1054 997.4 1015 1032 1049 1066 1083 1100 1045 1062 1079 1096 1113 1130 1147 1165 863.4 885.8 908.2 930.6 953.0 975.4 883.1 905.5 927.9 950.3 972.7 995.1 1018 926.5 948.9 971.3 993.7 1016 1039 1061 993.5 1016 1038 1061 1083 1106 1128 1039 1062 1084 1107 1129 1151 1174 1087 1109 1131 1154 1176 1199 1221 1243 911.0 939.3 967.7 996.0 1024 1053 924.7 953.1 981.4 1010 1038 1067 1095 968.1 996.5 1025 1053 1082 1110 1138 1041 1069 1098 1126 1155 1183 1211 1087 1115 1144 1172 1200 1229 1257 1134 1162 1191 1219 1248 1276 1304 1333 964.2 999.2 1034 971.3 1006 1041 1076 1111 792.0 805.4 818.9 832.4 845.8 859.3 834 !i 847.5 861.0 874.5 887.9 901.4 877 '.5 890.9 904.4 917.9 931.3 944.8 1015 1050 1085 1120 1155 1190 1094 1129 1164 1199 1234 1269 1140 1175 1210 1245 1280 1315 935.5 949.0 962.5 975.9 989.4 1003 981.4 994.9 1008 1022 1035 1049 1187 1222 1257 1292 1327 1362 1397 1042 1056 1069 1082 1096 1109 174 TABLE 43 COLUMNS ROUND CORED HOOPED COLUMNS -srr^ SAFE LOAD IN THOUSANDS OF POUNDS LOS ANGELES AND MILWAUKEE BUILDING CODE REQUIREMENTS P = Af e [l + (n-l)p] ? fc = 15 snn IP ^^j&r ouv Size of column (inches) Diameter of core (inches) Number of rods Square rods Round rods H H H 1 IK IK H H H ' i m lA 42 43 44 45 46 47 48 49 39 40 41 42 43 44 45 46 16 18 20 22 24 26 28 30 16 18 20 22 24 26 1093 1110 1127 1144 1162 1179 1196 1213 1135 1157 1180 1202 1225 1247 1269 1292 1185 1207 1229 1252 1274 1297 1319 1341 1258 1280 1303 1325 1347 1370 1392 1310 1332 1355 1377 1400 1422 1444 1363 1386 1408 1431 1453 1475 1498 1418 1440 1463 1485 1508 1530 1552 1474 1496 1519 1541 1563 1586 1608 1554 1576 1598 1621 1643 1666 1183 1211 1239 1268 1296 1324 1353 1381 1232 1260 1289 1317 1346 1374 1402 1431 1311 1340 1368 1396 1425 1453 1481 1363 1392 1420 1449 1477 1505 1534 1417 1445 1474 1502 1530 1559 1587 1472 1500 1528 1557 1585 1613 1642 1527 1556 1584 1613 1641 1669 1698 1613 1641 1670 1698 1726 1755 1236 1271 1306 1341 1376 1411 1446 1481 1285 1320 1355 1390 1425 1460 1495 1530 1371 1406 1441 1476 1511 1546 1581 1423 1458 1493 1528 1563 1598 1633 1477 1512 1547 1582 1617 1652 1687 1531 1566 1601 1636 1671 1706 1741 1587 1622 1657 1692 1727 1762 1797 1680 1715 1750 1785 1820 1855 I 1096 1114 1132 1149 1167 1184 1202 1220 1146 1164 1181 1199 1216 1234 1252 1269 1215 1232 1250 1267 1285 1303 1320 1267 1284 1302 1319 1337 1355 1372 1134 1156 1178 1201 1223 1245 1267 1290 1183 1206 1228 1250 1273 1295 1317 1339 1257 1279 1301 1323 1346 1368 1390 1309 1331 1353 1376 1398 1420 1442 1362 1385 1407 1429 1451 1474 1496 1417 1439 1461 1484 1506 1528 1550 1473 1495 1517 1540 1562 1584 1606 1552 1574 1597 1619 1641 1664 1176 1203 1231 1258 1286 1313 1341 1368 1225 1253 1280 1308 1335 1363 1390 1418 1304 1331 1359 1386 1414 1441 1469 1356 1383 1411 1438 1466 1493 1521 1409 1437 1464 1492 1519 1547 1574 1464 1491 1519 1546 1574 1601 1629 1520 1547 1575 1602 1630 1657 1685 1604 1632 1659 1687 1714 1742 ' 1104 1117 1131 1144 1158 1160 1177 1194 1211 1228 1245 1262 1211 1228 1245 1262 1279 1296 1313 1154 1167 1180 1194 1207 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 18 20 22 24 26 28 30 20 22 24 26 28 30 ..... 1204 1218 1231 1245 1258 - 1280 1297 1314 1331 1348 1366 'i270 1283 1297 1310 | :::! :::. 1333 1350 1368 1385 1402 1419 :::::;:::: 'i337 1351 1364 1338 1355 1373 1391 1408 1426 1388 1405 1422 1439 1457 1474 1392 1410 1428 1445 1463 1480 1392 1405 1418 1461 1478 1495 1512 1530 1466 1483 1501 1519 1536 ::::: ::::: 1461 1474 i 1518 1535 1552 1570 1587 1523 1541 1558 1576 1593 1518 1532 175 COLUMNS TABLE AREAS AND WEIGHTS OF COLUMN RODS Number of rods Area of column rods Number of rods Weight of column rods per linear foot Size of rods Size of rods H H M 1 IK IH H K H 1 IH i* 4 1.56 2.25 3.06 4.00 5.06 6.25 4 5.313 7.650 10.41 13.60 17.21 21.25 6 2.34 3.38 4.59 6.00 7.59 9.38 6 7.969 11.48 15.62 20.40 25.82 31.88 8 3.13 4.50 6.12 8.00 10.1 12.5 8 10.63 15.30 20.82 27.20 34.42 42.50 10 3.91 5.63 7.66 10.0 12.7 15.6 10 13.28 19.13 26.03 34.00 43.03 53.13 1 12 14 4.69 5.47 6.75 7.88 9.19 10.7 12.0 14.0 15.2 17.7 18.8 21.9 12 14 15.94 18.59 22.95 26.78 31.24 36.44 40.80 47.60 51.64 60.24 63.75 74.28 16 6.25 9.00 12.2 16.0 20.2 25.0 16 21.25 30.60 41.65 54 . 40 68.85 85.00 1 18 20 7.03 7.81 10.1 11.3 13.8 15.3 18.0 20.0 22.8 25.3 28.1 31.3 18 20 23.91 26.56 34.43 38.25 46.85 52.06 61.20 68.00 77.45 86.06 95.63 106.3 22 8.59 12.4 16.8 22.0 27.8 34.4 22 29.22 42.08 57.27 74.80 94.67 116.9 24 9.38 13.5 18.4 24.0 30.4 37.5 24 31.88 45.90 62 47 81.60 103.3 127.5 26 10.2 14.6 19.9 26.0 32.9 40.6 26 34.53 49.73 67.68 88.40 111.9 138.1 28 10.9 15.8 21 .4 28.0 35.4 43.8 28 37.19 53 . 55 72.89 95.20 120.5 148.8 30 11.7 16.9 23.0 30.0 38.0 46.9 30 39.84 57.38 78.09 102.0 129.1 159.4 4 1.23 1.77 2.41 3.14 3.98 4.91 4 4.172 6.008 8.178 10.68 13.52 16.09 6 1.84 2.65 3.61 4.71 5.96 7.36 6 6.259 9.013 12.27 16.02 20.28 25.03 8 2.45 3.53 4.81 6.28 7.95 9.82 8 8.345 12.02 16.36 21.36 27.04 33.37 10 3.07 4.42 6.01 7.85 9.94 12.3 10 10.43 15.02 20.44 26.70 33.80 41.72 12 3.68 5.30 7.22 9.42 11.9 14.7 12 12.52 18.03 24.53 32.04 40.56 50.06 14 4.30 6.19 8.42 11.0 13.9 17.2 14 14.60 21.03 28.62 37.39 47.31 58.41 16 4.91 7.07 9.62 12.6 15.9 19.6 16 16.69 24.03 32.71 42.73 54.07 66 . 75 c 18 5.52 7.95 10.8 14.1 17.9 22.1 18 18.78 27.04 36.80 48.07 60.83 75 09 o tf 20 6.14 8.84 12.0 15.7 19.9 24.5 20 20.86 30.04 40.89 53.41 67.59 83.44 22 6.75 9.72 13.2 17.3 21.9 27.0 22 22.95 33.05 44.98 58.75 74.35 91.78 24 7.36 10.6 14.4 18.8 23.9 29.4 24 25.03 36.05 49 07 64.09 81.11 100.1 26 7.98 11.5 15.6 20.4 25.8 31.9 26 27.12 39.06 53.15 69.43 87.87 108.5 28 8.59 12.4 16.8 22.0 27.8 34.4 28 29.21 42.06 57.24 74.77 94.63 116.8 30 9.20 13.3 18.0 23.6 29.8 36.8 30 31.29 45.06 61.33 80.11 110.4 125.2 176 TABLE 45 COLUMNS AREA, VOLUME, WEIGHT AND PERIMETER OF SQUARE, ROUND AND OCTAGONAL COLUMNS Square columns Round columns Octagonal columns Diam- eter of Area Volume Weight Perim- Area Volume Weight Perim- Volume Weight Perim- (sq. (c. f. (Ib. eter (sq. (c.f. (Ib. eter (c.f. (Ib. eter in.) per ft.) per ft.) (ft.) in.) per ft.) per ft.) (ft.) per ft.) per ft.) (ft.) 10 100 0.69 104 3.3 78.54 0.55 82 2.62 0.58 86 2.76 11 121 0.84 126 3.7 95.03 0.66 99 2.88 0.70 104 3.14 12 144 1.00 150 4.0 113.1 0.79 118 3.14 0.83 124 3.31 13 169 1.17 175 4.3 132.7 0.92 138 3.40 0.97 146 3.57 14 196 1.36 204 4.7 153.9 1.07 160 3.66 1.13 169 3.87 15 225 1.56 234 5.0 176.7 1.23 184 3.93 1.29 194 4.14 16 256 1.78 267 5.3 201.1 1.40 209 4.18 1.47 221 4.42 17 289 2.01 302 5.7 227.0 1.58 236 4.45 1.66 249 4.70 18 324 2.25 338 6.0 254.5 1.77 265 4.71 1.86 280 4.97 19 361 2.51 377 6.3 283.5 1.97 295 4.97 2.08 312 5.25 20 400 2.78 417 6.7 314.2 2.18 327 5.23 2.30 345 5.52 21 441 3.06 459 7.0 346.4 2.41 361 5.50 2.54 381 5.80 22 484 3.36 504 7.3 380.1 2.64 396 5.76 2.78 418 6.08 2.3 529 3.68 552 7.7 415.5 2.89 433 6.02 3.04 457 6.35 24 ! 576 4.00 600 8.0 452.4 3.14 471 6.28 3.31 497 6.63 2.~> 025 4.34 651. 8.3 490.9 3.41 511 6.55 3.60 539 6.90 2(i 676 4.69 704_ 8.7 530.9 3.69 553 6.81 3.89 583 7.18 27 729 5.06 758 9.0 572.6 3.98 596 7.07 4.19 629 7.45 28 784 5.44 816 9.3 615.8 4.28 641 7.33 4.51 677 7.73 29 841 5.84 877 9.7 660.5 4.59 688 7.58 4.84 726 8.01 30 900 6.25 938 10.0 706.9 4.91 736 7.86 5.18 777 8.29 31 961 6.67 1000 10.3 ! 754.8 5.24 786 8.12 5.53 829 6.56 32 1024 7.12 1067 10.7 804.2 5.58 838 .8.38 5.89 884 8.84 33 1089 7.56 1134 11.0 855.3 5.94 891 8.64 6.27 940 9.11 34 1156 8.02 1203 11.3 1 907.9 6.30 946 8.89 6.55 983 9.39 35 1225 8.50 1275 11.7 I 962.1 6.68 1002 9.16 7.05 1057 9.67 36 1296 9.00 1350 12.0 1018 7.07 1060 9.42 7.46 1118 9.94 37 1369 9.50 1425 12.3 1075 7.47 1120 9.68 7.88 1181 10.22 38 1444 10.03 1505 12.7 1134 7.88 1181 9.95 8.31 1246 10.50 39 1521 10.57 1586 13.0 1195 8.30 1244 10.21 8.75 1313 10.78 40 1600 11*11 1666 13.3 1257 8.73 1309 10.47 9.21 1381 11.05 41 1681 11.68 1753 13.7 1320 9.17 1375 10.72 9.67 1451 11.33 42 1764 12.25 1839 14.0 1385 9.62 1443 10.99 10.15 1522 11.60 43 1849 12.84 1926 14.3 1452 10.08 1513 11.26 10.64 1596 11 88 44 1936 13.45 2020 14.7 1520 10.56 1584 11.52 11.14 1671 j 12.17 45 2025 14.06 2110 15.0 1590 11.04 1657 11.79 11.65 1748 12.43 46 2116 14.69 2202 15.3 1662 11.54 1731 12.04 ! 12.17 : 1826 12.70 47 ; 2209 15.34 2300 15.7 1735 12.05 1807 12.31 I 12.71 1906 12.98 48 2304 16.01 2400 16.0 1810 12.57 1885 12.57 j 13.26 1988 13.26 49 2401 16.68 2502 16.3 1886 13.10 1964 12.83 j 13.81 2072 13.53 50 2500 17.36 2604 16.7 1964 13.64 2045 13.10 1 14.38 2158 13.81 j 177 COLUMNS TABLE 46 COLUMN SPIRALS PERCENTAGE OF VOLUME OF CORE AND WEIGHT IN POUNDS PER FOOT OF COLUMN HEAVY TYPE GIVES PERCENTAGES WEIGHTS DO NOT INCLUDE SPACERS LIGHT TYPE GIVES WEIGHTS WIRE SIZES ARE A. S. & W. CO. GAGE o S o CO CD O 5 i S d CO o 1C 0* d ' 3 o , S C4 to 1C Tfl o 00 CN d I i-O re s tc en TH S3 en oo TH TH ^S ^ ^ co \oo o 1C co d o o II CO* i 10 t- " S TH TH M< ^ CO* Co' "V, I co O IN S d im iH TH CO Tf os ic co co co (N CQ C4 00 TH o en i O CN t to 10 os 1C CO IN 03 CO CO CN X CC CM -r oo TH o TH en I en S IE ^b 00 ^H rH co co o t^ CO CO CO CM N 1H T-l TH sf eo TH TH' ^J^' ^(0 IN CO o o S 5 S S |S g TH en t~ 10 eo t> 03 CM CO IN OS CO OS 1 en ^ eo TH in * eo CM IN cs TH C3 OJ CO 00 >C 00 CO CM OS CO Tf o i i S!53|38 CO T-l CO I-H 00 1C O CO ^ 10 00 iH " S GO (0 s eo eo co eo en en ^ o ic TH O 1^ 10 "safe ^ J.H' ^ TH'rn" 1-4 o o> t^ p co IN CO 1C co o oo $3 S i 1 i d DO 00 rH TJH OS CO CO O OC t^ THTH_ ^ c- O O -^ CO (N CM (N CN rH rH S 1 o i o Islallss s o r^ oo rH 00 CO s gi E- en w 30 ^< t- en w oo ic o co t- t- f~ rH l> CO O OS C- 1C s CO o d 2SSet5^ Os co oc ooioeoiHOOoot- THCOCN O l> O t^ CO 3 oo CO Kg o eo 00 TH eo 3 IB! 8883 os os co o 03 l> CO 1C s CN O 1 d toloocot-ooinift 1 OtlMMOtCOOlMtO CO 00 >C loleOTHOOt-t-iD J> >C t*< OOt-OlOlO'* C3 - rt< Tj* OS CO C^ rH OS OS lOO CO * CQ <0 SSS5S y> . COCOOOTjHINrH * CO 10 CO 10 IS c- CN IO (0 eo 04 1 \OJ 1C t^ d 1C o d rH L-H CO CO CO TH 5 3 ,H 9 CO D CO CO TH 00 OS Tf< TH OS CN S S S 2 TH . . | . . . X. 00 c5 8 d 1 d 1 ~ TH 00 CO rH oo ic co os co IM CM CO Tf< t- 10 00 IrH O 0) TH TH 00 TH t- IO IO TH CO 10 Ml 04 TH O GO O GC CN T so CO S Ol t- (O ii" S 1 00 U> CO 1C 1C <*'* C, _ TH |TH ,H TH TH O) 00 l> co 10 10 t V, o CO CO o CO 00 o TH CO rH CM rH CM CO S S CO TH < n co CN S sb CO 00 1- CO 00 08 iiii O CO to o rH CO d o 1 o d 00 1C CO OS CO G> gs S3S3: us co TH o e SSg rH 1 rH CO t^ j TH 04 10 10 H a d e t- S d o =*= i CO d 00 CO d O CO TH l> CM l> * co * > O O i rH O> CO TH C 10 04 iH O C e- t- 04 IO n co t- X CO CO 00 rH iO rH Tj< CN O O IO at TH TH CO 2 l> CO 1C T}< Tfl CO 00 00 TH TH TH TH 500 CO 1C 1C Tfl * CO CO TH TH TH o =* d I d CO OS CM TH OS CO TH CO CO 1C CM TH OS OS CD Isissls co oo t^ CO 8. o iO 00 b 01 TH ii CO t- TH in CO 1C Tf< T}< CO CO CM CN iH TH O O C 300 >0 1C T* CO CO CO t>- OS 00 1C CD OS TH O l^ CO CM 1C 00 TH C4 O> 00 f 10 CN o o co co t> ss o a 10 1 IE 2 S 1 ! O * CO CO CO CN CM CN TH O O O C O O 10 Th CO CO CO CN 0-1 TH o o o o o < ft; \MI i-K o 1 d cs d 1C rH 1C rH CM O CN CO rH 00 C 1C TH CO* CO* CM' CM 32 O 00 B . OS TH O CO TH 00 OS 1-H OS o o> t- t- eo TH loo 10 TH TH CO C- CN t- o oo e- e 10 u * co 00 CO oi OS CO CO 1C CO rH CO TH 10 04 ssss CM S TH Tt* CO CO 00 CM CM (N rH d d d o' o" o' |d -* CN CN|CM 00000 o CO o CN d d CM CO CO 00 1C rH TH OS 1C CM O CO rH 30 t>* CO * r rH O rH TH co e- to ie x H 10 ! TJH > 00 S c^S : O TH O 10 t- e- CO CO CN CJ CN 3 OS CO CM CO OS 2 00 8 1 to TH 10 TH TH 8 TH g TH TH ,H TH TH CN OS re t" 00 CO 09 s s. s. to eo to to 1 en o CO OS 00 * co co co s. T X o CM CO CO TH to to i TH 01 ce C) CO 00 **< o os o OS CS CO 00 11 co s liSJ r i 1 - THCNTH 9 CO CO 00 C5 10 5 1 s ilse SB3 1- SP S i ssslsi TH CO ^f CN CO to 10 en to 35SS O cn -f OS -s. ^ CO CO MJTH disc a|oo i- t. * JjM TH TH TH TH TH CO 8 S s o |os' 00 t i" CO co M a O) o 1- Is N CO TH 1 M S 532 o "* OS 3S TH N s I c '*. e 338 99 S 1 to to TH e- OS 00 * CO CO 10 CN 05 00 t- co D CO d 10 CO $ 2 3 5 s E i i S S3 sss S fel 3 1 1 TH Ok Tj( CO rH 00 00 t> CO s en S2| Sis at 2 00 |l> CO re 5 cs en CM TH TH eo t- *< TH g s i S oas t* ^1 00 o ^ CM o CO co en eo N t to en 1 t- C- y: 5 CO O 00 to O S m c- 10 TH CM 1 5 O - o OS t^ CO CO to to ^ TH TH TH s" at 00 b. CO IO to rt* TH TH TH o *s| Q s y. s co m en TH CO i 1 33 IO CO CM TH Tf< CS X Si 1 t- t- i CO t> o > $ t 00 O S -M s GO c CO m co s TH i d o d d io o co OS t^ o i> d (N CO TjH OS o -^ * eo TH TH to * * TH d o' d d d d 1 00 C>1 d to * 2 CO CO BO* eo TH TH en en eo CO 10 <> TH 10 - O 00 CO Tj* e re ii g i i s i z 2 8 O TH co os X I 1 2 I i co i TH 1" o o : 3 - ro -T re OS M o M i s iH c- t- 10 I 3 CO 00 * TH OS 00 IS g TH TH 10 TH en s 00 o re ss CO OS d oo d io O 1 d o TH e d o o o CO CN O 71 g : o o oo eo t- to t- TH 3 : ' CO re e. M N o o o o o o * CO CO CO * OS to 30 TH t- CO M CM ^ t- S 10 3 ; "* CO CO CO (N IN o o o -* -<*< co co | * S . 8 . ro en d IO 00 d 3 05 ^* i" fe ^QO CON o CO d 2 d r-l d co co o rH s S s S 1 rH c 00 * T}< rH Tf* O i S s co co e- e- CO r-l o 00 00 t^ CO 00~ f O CO "fa 1 2 co co X 00 IO Tf* CD CO CO 05 (N CO rH 00 en CO 00 1 I o o co co d O d o d CO IO * O5 CO CN O3 rH CO CN i 1 1 d o s d 10 S3 d d co OS 00 CO CO CO CO O a c- rH i ro ! I O Tl< o s o i d d oo' "> E CD 10 10 00 t> CO CO 5 r-t CO d 00 OS l^ X CM CO X 10' CO 10 Tfl 2 f- S 8 o C4 O CO sss OC !g 05 CO CD 10 rH X CO 05 00 05 t- C- 1 s o c- s s o 000 05 X t> (D 10 iO * rt O o o o i CO d 8 d 10 t^ i-l 05 CO l^ 00 |t> co' 8 r- 10 X X fj 1 TH i 10 t- 1 s^gssl X -f N CO 00 t>- CD 1-1 t| s i c- ^ d rH rH 10 00 05 (N (0 TH (0 (0 10 10 o o o 000 03 oo CN O CO iO 00 CO iO iO * 1 rH o d 1 d CO IO ^ 10 2 1 1 O 0) rH 83 d d life O |0 g 5 CO to SS 1 00 O SCO 10 S3 t>. CO "5 10 TH oo CD CO o o o 3 a 1 d 1 d CO CO CO O CD O5 X CO s 00 t> rH 10 oo o n CO to 10 rH a 3 O5 O5 CN co' 10' 10' 2 -f- > * CO sssg e- o 10 10 d o' o' o : : d CD IO * co" 10 * N en TH to 00 Cn rH (O IO IO d d d 1 D 10 IO * co o 000 = IN d co~ >o (N d CO CO S d 10 IO Tj* CO X O -. TfH Tj< s ii 3 1 ' CQ OS U* . rH CO X o S i : I 1 => . . . iO ^ |CO ; ; ; 5 o 85 Diameter (inches). .S I < '& '! <; ~' *** r1\ -\ -' c S? \N V^l \T)I \N Vf< SX r^r^^ 1 5 2 ~ j 00 05 182 TABLE 46 COLUMNS COLUMN SPIRALS PERCENTAGE OF VOLUME OF CORE AND WEIGHT IN POUNDS PER FOOT OF COLUMN HEAVY TYPE GIVES PERCENTAGES LIGHT TYPE GIVES WEIGHTS WEIGHTS DO NOT INCLUDE SPACERS WIRE SIZES ARE A. S. & W. CO. GAGE r. ,-: 8 s .N *' CO 1 o :- 10 pi ~ s- M X C CO s CO 3 pi t- CN a c ~ Tj< 1C rH CO b. SS S 3 ss ~. 5 T) ro OS s S g ss CO CN X s S3 i (0 3> t- s t- (0 i r. CO IN SS3 iS is CN t~ M 3 00 CO eo co CN e i 1 t- TH TH C4 TH a 00 -r r M OS e g 5 8 M s M TH tig X * O 00 3 gs| e- co i- ss eo t- n 23 ~. re N 1C -r CO 1-1 CN h iH TH TH -Ul rl 00 S 1C CO CN C4 TH TH TH TH TH TH o X 8 3 S CN cs I i 1 1 ii ^r c co 8 2 1 1 3 s 33 1 a = ~ ^-( OS t-- 1C . 00 O OS s n i s s lp ~ s 8 z CO T 1-H i-C CO 00 CO CO en s 30 co TH co CN 11 CN re 2 OS gsl E:g TH O is 1C re .=_ C-J 3 ~. OS OS 00 s s eo 2. iH c- en 3.3 S - r. g 1-1 ,-t t>. 00 - S 1-1 8 1-1 M d d CN S CN t CM O 00 C 8' eo ci OS CS SHs ii IO 00 O O) X x t ; r-. ~ 00 OS CO S to ;o I IB =_ - x C; ^ 00 CO 00 co i i 1 Si 1 s C: S S!8 3 CO TH O ss CO CO HI 2 71 ~ OS 00 00 t* 1- re ^; 5 CS :! ~ OS CS 00 o g ss s 8 CO en c- CN CO Si e 8 8 CO X * ^ t* O CO iH eo co CN i 2 10 10 3 ^ S ^ re 00 * * ff M C4 O <* TH 8S ii ZH .I.' 2 ' _ ^i _ J ~ 00 t> ^ 1 ' ^1 __ J_ OS 00 l> 1C ~ - <: s CO 00 c- 1-1 s o CO *3* P S 5S s e ~i X g S2 i co en iH co 1 ii i 8 2 D r. to N W ^J iii S3 ii ^ ~ X ^ CO CO iC 1-1 c-j f BO N CO CO o SJ 00 t^ ts> CO TH jd o o o co t- c- M t> CO TH j * en -r TH s "s o t- 10 10 O co d It - OS T}< en CO c- <> S Cfl CT s ^ X ~ 2 00 CN t>. s s s s s 86 x '- CO CO iC iC 1-1 e ~. 00 * (O 1C 1C Oft 00 * CO CO iO 000 o o O p o 1- C: i- j i CO i eo CO so o (D sir S re c-. ~. ej 00 1C CO t- S? 1 i 1 STH 10 10 1 r. ~i ^ CO CO CO So e> t- (0 ss 3 : 00 '- CO CO 1C 1C o |o Ok t- ** CO ic bo e o I-" Oft 00 t- CO CO 1C 000 00 CN 1C n 8 ~ 3 i en t- s en i 5 Oft 8 5 X c. X CO 8 : g s s co ^ : TH -- s X ^ : Sow l|i I :" 00 N CO M9 1C T*. * o 00 t- ae to TJH o OS BO N CO iC iC 000 o]o CO c: CO C: O 5. 5 E cn <> s S 3 g y Oft C J t- en 10 t0 s o e - x ~ ss| 3 S S t- . 09 ^ - '" - o k> ' o o 00 - o o o o o CO rH <# i i 1-1 * * S o e BfJ * s s 5 co - Tti o r o l- <*< . *- '-t . o o o : * - e o o o CO 5 r- i i 1 ; 'i 8 ~ s 1 ; 1 s t- s : 2? * 90 II CO i* F * CO id * o 1 CO d ~ d |d _ g *> o 5 c- : oo 1 D S : : : 2 . . . r ^ ct - - vf~ - - - - S! ^ -. -K K I -\ -^ \ rA. : -\ -N rt\ "N Ctf\ -\^' ~. ' =; O) a CN CM- 183 COLUMNS TABLE 46 COLUMN SPIRALS PERCENTAGE OF VOLUME OF CORE AND WEIGHT IN POUNDS PER FOOT OF COLUMN HEAVY TYPE LIGHT TYPE GIVES PERCENTAGES GIVES WEIGHTS WEIGHTS DO NOT INCLUDE SPACERS WIRE SIZES ARE A. S. & W. CO. GAGE i O o iO d 05 d co " IN iO O3 ^rH c- t- gTH CO 99 C^ t^ 00 CO 00 rH s s 10 en TH TH 10 o o en re CO 00 IN (N rH CO 10 N ^ a 05 d d gg TH rH 00 c- 00 iH s o 8 CN TH 85U TH O 05 O (N CD CO (N IN is X 00 l> co' 10 CO SS *H TH wGT si a 04 vi o 1 TH' TH' -i Id CO 1 SSL. >o CO TH co co IO 35 IO O5 CO IN rH ss en o to eo S to TH en TH 3 8 ce " 00 00 ^<0 >o co CO o 10 IN O5 CO Cl C) o 03 IN 10 TH O 00 00 co 2 c- eo S i 1 (N S B co en co co rf ei 3 00 5S 1 co CO IO TH 1 _l H CO en co d d o IQ >o CO CO 10 10 00 CO 00" X 33 OS eo re 0$ 00 TH 10 oo eo eo 00 3 en O TH 05 00 IN L . MOO TH TH TH CM O TH t- X 00 sss CO rH t S . OJ CO TH 00 CO O TH TH en s 00 e (O O TH CO odd 06 ei id 8 CN X X o" 05 05 !-!| 00 CO d d CO (O 0* 0* CO 10 (N co d d (N CO re 00 rH TH rH 00 t^ (N rH (N TH TH i i to d SS O 00 CD 2! CO CO 1> t>i CO* en o CO d 1 i CO o 10 sis s as o & <=> cc 00 ;fc i TH 00 o s e IO d !* CO rH rH 05 00 o |d TH 2 OS \ 10 (N CO d co d d CO o re rH rH TH O O - CO CO o o o o O CN o OS O i d 00 TH O5 CO CO IO OS CO l> C5 CO co IO t? 1 i eo to | 'o 00 t^.' O co CO 1 eo d to 3 o I I S C5 00 t^ CO CO o o o o O 0 IN d 05 d rH t* CO 03 ' ' '. ' en IP us ' O 05 I'.'.!! ! 1" : : : : t> CD J to" : : : : o O 00 CO o co 10 CO IN d co 1 d rH co 1 s : : S s 3 - o t Diameter(inches).. 0.2253 O5 d HI SiiMM CO CN ri pi\ : : S '. '. CD eo o 09 CD d t \ o S a X -x CO o 3 s 1 s s t- ~- i $ Z c ~. el J c- e s 5 1 11 d d CO o B ei re 8 d ei X ^ rH iO D IO s. TH s rH s s (N CO s 3 CO i- -r - r^ 1 2 i 1 1 2 1 et a e 8 i o i TH IN CO t- 10 TH 1 1 TH TH eo S ei I ei ei X re = t- * ?s i s eo TH i rH s N Ij c-. ei ei It ei CO o - 90 ej 5 o re --^ ei i :o s s s 6 N. re X S5 00 Ok i 1 g f> 03 CO ** e- O O s- 10 eo iO ei o X o r ei r ~ " O ~ IO J< CO TH s TH TH oo IO CT> s CO d 10 d 0> g 00 90 S = re eo i TH I t- I 1 SL ei ?j -x 8 IO X CO 00 N g i 1 TH *# 2 r CO -i. s >H r 08 1 TH 1 1 t- i t- 1C re ei '- * ^ o o o ei r. 2 re - C: H TH S c: a id re : H S r-l TH X ei M to r: I ei CO d ci TH TH i * d d 2 ^ CS 90 M re ei 90 d x" Ok eo TH (N d L-3 eo <> IO C- d oo e- o d a d ei c t- eo re o ; eo ei - O H M H d r-l TH 10 o s o I d IO d S o 0* r^ ~ el BO co S CO 00 o i s s is o to 10 3 > v: ^ ei 1 S I S 11 ^ g X ' # t o c- 00 I 1 t- o re o 9 00 ^ o a d re 2 3 Ok- H O r. - - ei ^ OS TH o o o o o o S CO cr Bt - 2 D CO s s s 1 TH s a ? CO ei fi So e 1 i i 1 TH TH 00 ^j O ^ ?. S 5 00 - o i 1 e- S 1 1 i 3 T* (N - ~ 00 "> o IO re c: Ok X '- O o o o O O S re - -. -. t o o o o CO a ei IO oo O a r s TH H s TH 3 S c ei ei g s 1 1 5 s ~ 5 -f - j I 1 1 1 3 eo CT. X ^ ^ =; Ok X d o S eo M s t~ ?- 1 s N \_ s 5 - e- 1 i 1 S g g t* ei I 1 s 1 1 e- 10 (0 i 2 ~ Ok X t~ * o o o o o eo z Ok BC o re ~ ~ 90 fc vr C: [^ ; ': (C i c- <- TJ< s 9' 5 X s 2 i fe |2 X i 3 1 o Ok BE f* ; o o o 3 O> t o 3 c: X) O ei s ~ * o 10 3 i S ei IO ei s = s 3 o ^ to * o r. BO r- d 30 = ei - 1 1 ;: = 1 3 : 00 * r. t il : 00 * o c- -, o 10 f *. . * i-N 5 - s 5 ~. -i eo . - ' rH i? - - - 5 -: C4 - - - - - B4- - ' - 1 eo - TH ^ (N - 5 S- - ei - - ei - ; ' r- ei e % 4 CO iH\ rH - - TH IN - d - 1 N s eo a r n Si 185 COLUMNS TABLE 46 COLUMN SPIRALS PERCENTAGE OF VOLUME OF CORE AND WEIGHT IN POUNDS PER FOOT OF COLUMN HEAVY TYPE LIGHT TYPE GIVES PERCENTAGES GIVES WEIGHTS WEIGHTS DO NOT INCLUDE SPACERS WIRE SIZES ARE A. S. & W. CO. GAGE * o o 03 co CO 01 CO S CO ^H !>. CO C3 gg S3 CO ** C4 go to eo co rH o en CN Ol -t* >o ^ to 1 i eo 1 I 2 en en o o w Ol CO X >o CN O 00 04 CM -H 3 ol CD Ol CO Ol 01 cr o o o o o 1 CO -H 01 S t> 00 rH > 10 eo 1-1 o en co o Ol 10 04 ^ o CO X eo c- i rH eo tr- io rH Ol 10 co S eo S t- S N eo CO si ^ d d * Ol Ol I> IO * 1-4 ^ t-4 000 ol Ol 0) o Ol GO CD >0 rH rH rH 1 O o co o CO CM CO CO ssli 00 t^ tO O CO GO cr CO 10 CD X LO i t- rH 1 i 1 eo c0 fc d d 00 CM Ol O4 X 000 03 "t 1 01 cr 1-H 10 "* rH rH rH 00 CN 00 CM CO I S CO O CO 00 1> ^ en co t^ S8S co ID 10 10 CO 10 X 01 04 01 CD ol CD rH g en S CO g rIS O 10 =*= d o CN 1 5 10 * CM rH r-i 000 -* X CD ^ CO 04 rH o o o % o S 00 CN -t O4 CD rH CD CD i ill S5S o Ol cr :H ^ S S rH co S 1 3 SSI >0 10 M\ d d 3 X 10 s CN rH rH 000 c^ X CD Th co 01 3 rH o o d ol i CN 00 o cr. 01 O3 00 03 iiBI O CO ItN ssp s CD CO 1^ 01 CO 1 rH CO rH i 00 ]* rH t- 10 kjl t. d d O3 '^ -* co rH 03 o o o o oo|o o J 10 co- Ol ^ o o o d jo o o CD X S o Ol S ^ co oo 03 04 sis! i?3 : 2 Ol X X '-5 g ! S to c- o 5 M eo =*= d d CO rt S ^ O3 03 GO o o o o I> S Ol ^ 2 cr o o %J t~- j: X X rH t- 00 t- SSS 3 : : : co CO' cr t O4 i 10 en S 5 \ d d S 01 ^ cr 00 0000 . . . >O co ^ O o 1 CN X \ X eo eo t~ en ssss : : : a S i co X g 1 to OJ IO o d rH 01 cr. O O O O : : : S 01 ^ 03 o o o S o CO 00 Ol d 03 O) i o CO CN X o i cr S IS p : d d jo . . . CO . . . 10 ' CN : ~ d O4 cr g o CO Tj( d a CN O I d 2 CO cr 00* 10 |C4 10 UK i ' d |d 00 ! ; ; d cr t- 8: O O 10 d o CO 03 5 j j j o X S, CN d CD CD d S 1 CN d c? CO o o (inches). -4 CM 'H.ir l , M S Vjl 01 V* CN CN CO rH rH 04 C4 etc?* 5 - Ol f 01 N V* Ol" ec rH H N - N -\ w\ N eo Size of w o S CO .5*0 S Q u CM . OS 01 186 TABLE 46 COLUMNS COLUMN SPIRALS PERCENTAGE OF VOLUME OF CORE AND WEIGHT IN POUNDS PER FOOT OF COLUMN HEAVY TYPE GIVES PERCENTAGES LIGHT TYPE GIVES WEIGHTS WEIGHTS DO NOT INCLUDE SPACERS WIRE SIZES ARE A. S. & W. CO. GAGE s 71 X ^ S 00 re 2 CO tO CM TH 10 Ti< IO t- i8 s = 71 CO 71 7! 00 I- -* i-l H o oo ioococoTHor* CO CO CN s ! CN TH i { re eo C i to t- c- O$ Or-ttt^t.0000 t"O THt|cOt-t>-OiO s i 1 s iH IO e- i s e $STH III Ills O co 71 71 71 = X 2 2 - o 71 re 71 CM CM TH ^H TH ^ TH 0000 ?- X 71 s iH co K s S< l^-*lOOOTj<(NCO IO OCOOCOOCNO 2 1 1 1 i 1 i re S N O TH CO *< sis SSSSI (0 10 10 o - X - 10 CO CM - 1 o o OO CO TJ< o o> o 01 ^1 CO(Nt^t^T-iO500 1 s o H 1 CO iH to 10 c- s r. "0 C5 O5 CO IcM CM CO CO CM iH O TH gss sill IN r-. t- re s 05 OC5o2 tO CO ICM sll o o o o en t- iH tO 10 10 Ti< o o o . 00 en X s I 10 IO ^ ^1 CO 05 o 10 IO . O 00 IO CO TH 1 o I 5 a s re CM .... 10 r- rH 3 g % o' o o' g : 1 ; . . CO * - Tf 10 iH o ^ if : eo ~ CO a IO 1-1 * - 3 J5 : : :::::: o a . -i. i - r; - y X* oj\ y. s -. x a *a ss >t c-' - \ X Vf v r . S^C,,. -M V* ^ I-K 0^. - re CO 1 . 187 COLUMNS TABLE 46 COLUMN SPIRALS PERCENTAGE OF VOLUME OF CORE AND WEIGHT IN POUNDS PER FOOT OF COLUMN HEAVY TYPE LIGHT TYPE GIVES PERCENTAGES GIVES WEIGHTS WEIGHTS DO NOT INCLUDE SPACERS WIRE SIZES ARE A. S. & W. CO. GAGE % a. 3 CO i! 55 o ^? O) g o CO co s co m I to <4< t- X e- to co t> sfesss CN rH CO in tN rH 1 00 c- 38 t- to ** d d 3 Ol CO 2JL iO 01 o! 01 co co o^ |o co ^-i o C^J lo* (N (N i-H rH rH fe o 10 CO co o 10 CO c Tf CO X S l rH rH cn rH 00 a CO t- to o x co to to co co ^g^og i i t- 11 d d 55 oi 01 Ol o 01 X TH rH O o o O Q 1C O co co CO CO' rH O5 t>J CM CM IM rH rH rH rH o o o o CO i CM OS co a CO 01 s 1 s eo i 3S KOO tO 10 CM CO rH 1C CO O Tf( t> X 1C t- rH 5 cn CO in 00 s 1 s s =*= * d o co co CC 01 -H Ol Ol 2 X to rH rH o o 00 3% 1C CM O X |> CM CM (M rH rH TH o o X CM g 00 CM X $ X 2 X CO rH o cr. s oo t- 1 s te ^x in ki co ic rH Tt< LH 10 rH . 10 * . O o o o o o O 1C i CO 1C t> o co 5 i in 8 i m n os CM ^< CM X C^ C5 X 1C CM rH 10 CM rH co 1 c- s en CO in o d CO CM Ol t~ 1 1 10 2 01 o o O o o O TtH CM CM X CO TJ< CO O Ol co o CO co co X 01 X s s i 3 c- rH Tj* 1C CM CO X O 1C i in c- in CO TH d d to -f CO s o o t^ CM rH 1C CO CM o o o ; % C CO IN CN (N i-i TH H O 9 sfe a CO * CN CN i-l i-l iH b b b b 00 1C X M S >*< Tf g N S Isfl R S3 s SS N 1 I 1 H ii - g ~ C 1 M CO in ssss DO t- tO tO 1< * 77 71 * CN CN CN O 71 coJeo IN CN CN 71 g 71 -J i CO 71 CO i-l CN CN iH i-l 0000 5 71 g S 00 00 OO CO 71 Sll glli s o * N t^ CO CN rH i-i 1 1 s 1 ii Ok s c y - - 71 1 iH <* 00 (N I'M N O iH M N 10 en * c- to to 10 eo g 7! 71 CN <-< X s?s VI N S 2 i-l o i 71 -7 71 7 re 71 2 iH oooo CO 7~1 5 S 2 CO CO 511 gin s -H CN CO CN i-l CO 00 X 00 i-l i i 1 i ii 77 S o / ~ J S l^ 1C CO CC en en t- Sen co CO t> ills c^ O CO 71 77 71 S2 [N. i-l O O oooo o eo c5 - i-i O> 00 H b q x - 71 7 71 71 00 (N i T-l oooo s 77 2 N ^ N 85$ a t- o SSSfe 5 S SB n t* 00 C^ ggjg 1 n 5 I in 55 - C C - v S CO CO N 00 t- 10 10 CO t- * 10 CO CN CN X CO iC 00 71 71 y 71 - t- 000 o o CO r- 8 2 : (- * O S5S IS ': fc 00 IN CO i CO s 3 2 1 " 5; = Tt* 1^ X U s III . . . s CN X cc c 000 00 : S CN O CN -H r- 2 O ~ 7) 71 r. ^ - 000 o co 00 00 X 3 ssg <0 10 * S ; : 5 re t IS IS co 1< i to c S 4* * - t- 1 . isi o IN t- 2 2 000 : : S 00 CO - o 71 71 y. - - t . 000 _ CO * . . . t- s s CO c. - 223 . . . .-i ^ CO . ^ C S 5 : 00 1-1 It 77 o o [o : : : 2 cc ** o a o - * 11 : . ' CO ' 30 s 1 PC - ii ; 5: o - - - 00 . . . . ,-t iC o X E CO g : : o s 00 s 1C o . . . - 1C ** b X r.l 3\ e$s : x J5* s; vff \- X :' - - - V* o\ -' !*k < - 3 - - rj - * x* 1C CO eo . s 22 189 COLUMNS TABLE 46 COLUMN SPIRALS PERCENTAGE OF VOLUME OF CORE AND WEIGHT IN POUNDS PER FOOT OF COLUMN HEAVY TYPE LIGHT TYPE GIVES PERCENTAGES GIVES WEIGHTS WEIGHTS DO NOT INCLUDE SPACERS WIRE SIZES ARE A. S. & W. CO. GAGE % o o O3 ^ CO 00 CO t^ CM iO TH CN 03 S TH CO TH eo eo O si S 1 ^ 2 CO 05 TH T* CN O3 <*< O3 O CO i 10 TH i 1 IBS i-K d d S 3 co tl i-H 00 lO CO CO CM CN TH TH TH o o O O CO if O3 lO rH O5 CO CO CO CO CM CN TH ^ TH 000 o o 0: 1 00 CO CO t^ CO CO O3 t^ IO O3 rH OO TH 00 eo TH eo en en is SS CMC, t- tO rH OC ^ 00 b- O3 CO CO O CO 00 IO S I i CO co eo TH SS3 =*, d d 05 CN b- * * co_ iO CN CN CN TH iH O 00 S3 00 >*< O N. IO CO CO CO CM CM TH ^ o 000 o 10 CO CO CO lO CN rH 00 i-H rt< 05 05 00 ^ Tt^ O O S O 00 il si %$ O CM CN b- CO TH i i S sis "*= d d Tt* co co 03 CO M< CN CN CN CN CN TH ^ 00 3g co co CN CM CM TH o o o 10 CO * TH S S { 2 -, M 00 TH TH to t- TH TH co 10 co o i> TJ< CO CO 00 en S ? S K S r- r 10 rH T* CM CO O CO t- S (O IO 10 f\ d d CO CO CN co co TH 05 TH O O O o * t^ T}< CN CO CM CM CN CM" TH O d d d co CO 10 3 S 00 N CO CO i-H CO 05 CN i io s is IS ss O i-H 00 CO CO I eo S S i life -*= d d CO CO CN CM CN O O i CM eo t- is 55 C.O * Tf O CC CO rH 1-H rH 1-H 1> 00 10 i eo TH t- 2 i II ; =*5 d d (N b- TH CO CN CN rH 05 l> CO CM ,-H rH rH o O O CO OC CO O " CM 05 00 CO o o o * iO 10 o b- 00 rH 00 ?b ': : (0 10 (O to i Sfe ' '. CO t^ . . O5 CC CO l> t^ ' ' S oo i g i ; : CSS d d 03 IO TH CN CN CN OS t^ o d |o O5 IO CN CM CM O3 t- CN rH rH . . 0- o o CN CO i CO IO CO CN CO Tj< S : : : 2 i S 3 : : : S? gb : ' : 1 IA cn S TH ft, d d CM i d in o S o ' ' rH 00 CO 03 '. '. CN n o S o TH d *<> 10 CM tf iO CN CO i S i i O5 CN 1> 00 ::"::: 1 3 \ d d t- . . t> CN rH o 1 00 CO 00 00 5 ' ' O r^ I i I d d 03 CO o t^ C3_rH i co d 1 d : : TH 0* 10 _i CN =*= CO CM 1 o o lH i-N CM d CO co co co S d d co O3 =*a CM CN d co o d 0) (inches). 4 Hi \N \* rt\ eo\ H\ lJ\ C0\ N (N oo 04 10 -r re re ^r re t~ ~i CO C- C- OOOCOCOiCO 5 8 J> N t- 0> 1 JCOt>So ^WOMTt 2iBS2i3 *o CC O CO CM OS l> * -tfjeo CO IN .COOOO 1C TJH <-ioic iiii~ii M Tf< O ^ i i 00 CO Tf CO CO CO IN IN 1C rp * CO CO (N -n os o os co IN 1 S 5?SS ^ M -c,^^r. t>ooie tosoooocoooo 1 eo t- to eo TJ ^< rt IN W * COTjtOINCOOSl^ oo c- o 10 ie o os i> co co -o * N O t- en oo en IH i o 1-1 en o eo t- eo o at t- t- o M 10 1 5 CO CO CO i-l SSSS SS2?3^4: i 1 50 S 00 CO S COOOt^^-lOOOOOO t- 10 10 -^ OOCOOSCOCOOSOS 10 CO t- CO rH t- 10 IH -i eo t- t- 00 t~ 10 10 ^ q| 1C <-H . 1C M O CO CO C ^ CO O CO O C<1 I M CO CO 90 5SSS ^^oococo^ (0 10 10 Tt< iCcOi-it^CSCC> I 1-1 1-1 eo S IH " ooo-^osiccocs t- I>CO'* 1 eo m en w * 04 w OS 10 hf . CO SSSte : : O . . . ^H t^ CO <-H . CO . . . . .... SB : : : : : 8 _fe : : : . . . . -tf ^ 00 : : : : ^_b 22 : : : : | : : : : : CO B : : : : 1-1 30 ; ; ; i oo co i i ' i . . . . oo > .... en ;;:;; co * 5 : : : i S 00 . . . . ,-H 00 o : : : : : 8 :::::: o . S S ; . .1 % ::::::::: 0} ^ ; ; ; ; '.'.'.'. c^ '.'.'.'.'. ; ; '. ; ::::::: S-* V* NN \^i S s sxx yx xxx x: : ' axa ^^ ^^^ xa ^^^ 3 s , 191 COLUMNS TABLE 46 COLUMN SPIRALS PERCENTAGE OF VOLUME OF CORE AND WEIGHT IN POUNDS PER FOOT OF COLUMN HEAVY TYPE GIVES PERCENTAGES LIGHT TYPE GIVES WEIGHTS WEIGHTS DO NOT INCLUDE SPACERS WIRE SIZES ARE A. S. & W. CO. GAGE \(N o co 323323 ss rHTHeOtOp Tt N at TH 00 Ss ii o o $ S 3 co n co CM TH TH OOOOO OrHiOOCOCMO iH TH o o o o O o 1 S^c^cSSSS T-l O sills ggcSksScS TH en OQ SI eo TH SB * d d iO Tj< rt< CO CO CO .O3COOOTt(rHOO iO Tf Tf CO CO CO CM TH o o o 10 co CO IO iO Tf CO CO CM (M TH OOOOO t-H M 00 Jjj O t Jg TH O O o o \3 Is. CO CO CO O C<1 (N CO rH O CO O O IO iO i a i-i cr oo | GO eo C-o5 IO rH CO CO t-- rH CO CO O ii SB;- o 10 ScOOO -4u3M3ooeq o d TH 00 t- 10 t(NCOCSCOrHCM w (O oo t- sssssss T-H CM CO I-H O CO O co o * * co eo co rHOOOOOO CO^t-CMb.^.-; O "O "^ "^ CO CO CO ^OOOOOO SS^^c^c^S ^OOOOOO O rft O O CM O O CM > rjt T}< 10 CM CO S2S3SSS ^os^cocsc^ ^HOOOt-0eiO iCOO^COCOOCM OD O CD en *3 kn ocoooocMOsko Oi 00 t- D 10 W p t^O(NOO(NCMpO SSS5S|~ oo^o^^U S 3 I- B 5 B cso^cocsoF* g^sssste 0) 00 f O 10 M9 M CM 10 OS >O ^H 00 CO 1C ^ CO CO CM CM o o o d o o p co co cs 10 CM cs =0 I 10 ^ ^ co co c^ Ic^i OOOOOO |d S^^c^c^iJ^ d d d d d d d I-H TJ< eo * eo > >o Sto to e> n to vr r: t^- i" ri t>oioie^i cMcoi-i^iosco S3SSSS : c^osoooso : t- vo 10 10 TH . eocMCsooioos isllsl : t>. O U5 1-1 OO >O CO tf <*< CO CO CM CM CM OOOOOO GOi-tCOCMOOcO Tt< * CO CO CM IN OOOOOO ; OCMOCSOCO . OOOOOO O b- b- t- O*)OOOOOw gSS3 : : Lt C! * O t * T}< CO CO CO C^ M OOOOOO ; OOjCjHOO^ . OOOOOO "J^^^ScM ' CO l> l> O * CM t^ O *J< O C^i-l^'OOCO Oi-ICMCOO J>oio^'* ,Hoeoo^ HISS : i SSg : : IISS : ': cSScSSS : : o o ojd o . o eo c^ o co . . O oo_oo - : j*_g : ; 0000 S2 : SS3 : : : : ^5 : : : : iH O IrH .... SS3 : : : : S2 : : : : t- 00 O - . . SS5 : : : : Tf OS CO CO i \* 3 s ' 193 COLUMNS TABLE 46 COLUMN SPIRALS PERCENTAGE OF VOLUME OF CORE AND WEIGHT IN POUNDS PER FOOT OF COLUMN HEAVY TYPE GIVES PERCENTAGES LIGHT TYPE GIVES WEIGHTS WEIGHTS DO NOT INCLUDE SPACERS WIRE SIZES ARE A. S. & W. CO. GAGE X o o d o iO * O5 O ^H (N CN 00 * CO O5 IO O5 O5 10 d 05 CO 05 10 t>.' o * d co co g o d d CO O * i-H t> 00 to 00 O> TH TK 1 1 WO>COO>t-NOO>OCOiOrt(N(N TH O O O O O O \ ^ iO CO Co' 00 10 (N 1 co 10 ^ * co co ro 1 \ 10 CO CO 00 1> O5 CO O Tf< O O CO CO CO O O t- b* O CO t> JIO eoo>0>o4iooto 00 o o OJ rH K* O>t(O(OIOIOMI (Ni-iO5T-ICO(NCO o d 10 rt< Tt< CO CO CO IN , 1 iO Tt* TJH CO CO CO I 00 t- 1C US ^1 ^ TH ^ CO 00 JO f\ d d O CO t>- CO O f 10 Tt< co co co N OOOOOO i-H^OOTtHOOO iO Tt< CO CO CO '(N 10 o co TH d I d 00 00 CO 10 eo to o> lio O O CO 00 >OCOO5Tt CO OJ o 00 co d 00 h. . . . . CO CO Tf . 5000 ! 0.19635 0.6668 3,521.0 1.500 7/0 0.4900 0.18857 0.6404 3,381.0 1.562 % 0.46875 0.17257 0.5861 3,094.0 1.706 6/0 0.4615 0.16728 0.5681 2,999.0 1.760 He 0.4375 0.15033 0.5105 2,696.0 1.959 5/0 0.4305 0.14556 0.4943 2,610.0 2.023 13| 2 0.40625 0.12962 0.4402 2,324.0 2.272 4/0 0.3938 0.12180 0.4136 2,184.0 2.418 H . 3750 0.11045 0.3751 1,980.0 2.666 3/0 0.3625 0.10321 0.3505 1,851.0 2.853 11,^2 0.34375 0.092806 0.3152 1,664.0 3.173 2/0 0.3310 0.086049 0.2922 1,543.0 3.422 Me 0.3125 0.076699 0.2605 1,375.0 3.839 . 3065 0.073782 0.2506 1,323.0 3.991 1 0.2830 0.062902 0.2136 1,128.0 4.681 %a 0.28125 0.062126 0.2110 1,114.0 4.74 2 0.2625 0.054119 0.1838 970.4 5.441 ^ . 2500 0.049087 0.1667 880.2 5.999 3 0.2437 0.046645 . 1584 836.4 6.313 4 0.2253 0.039867 0.1354 714.8 7.386 3-32 0.21875 0.037583 0.1276 673.9 7.835 ] 5 0.2070 0.033654 0.1143 603.4 8.750 6 0.1920 0.028953 0.09832 519.2' 10.17 He 0.1875 0.027612 0.09377 495.1 10.66 7 0.177( 0.024606 0.08356 441.2 11.97 8 0.162C 0.020612 0.07000 369.6 14.29 %2 0.15625 0.019175 0.06512 343.8 15.36 9 G.1483 0.017273 0.05866 309.7 17.05 10 0.1350 0.014314 0.04861 356.7 20.57 0.125 0.012272 0.04168 220.0 24.00 If 0.1205 0.011404 0.03873 204.5 25.82 12 0.1055 0.0087417 0.02969 156.7 33.69 Ma 0.09375 . 0069029 0.02344 123.8 42.66 13 0.0915 0.0065755 0.02233 117.9 44.78 14 0.0800 . 0050266 0.01707 90.13 58.58 15 0.0720 0.0040715 0.01383 73.01 72.32 16 0.0625 0.0030680 0.01042 55.01 95.98 17 0.0540 . 0022902 0.007778 41.07 128.60 196 JJ1AUKAM 42 WEIGHT OF TYPICAL SQUARE PANEL OF THREE-BE FLOOR SYSTEM DESIGNED IN ACCORDANCE WITH J RECOMMENDATIONS (FOR ESTIMATING COLUMN LOADS COLUMNS AM-AND-GIRDER OINT COMMITTEE ) (0 10 / / / t / f / / j / j f j J j j 1 j 1 f j j f 1 f ^f f j / j i I f / ~f^ J J f / / j f i f f i j i } j I f 1 / J 1 / i C 4- CO 1 90 f A / / f 1 / / j / / / r f j / / J j / / 80 j f f f i j j * j 1 f f / / j j j / f f f / f / t f f A / I j f / / / i I J / 1 f / f I T ' f J y J I / J ^ f ) f j 1 f / / *} f j y j / I / ^^ / i / J / / / / f / / / i I J f J / / / Y X 1 j f J / j J y n I 1 f / / f / f f / / J / j /^ 1 dead panel load in thousands of 60 f / j / f j j J / 'y / / J J -/ ^ J/ f j / j / -fa >>v J7^~ 1 ^ f (Si f y f ^ if\ $ f f f J fkj. y j f / <&- f -Q* 1 / / / A t ^ ^ 7 / / P^ Sfi / 2 P> f~ ~X -p Y , y / V / 4V y^ f y^ /* y .v^ s^L. KX f -f y _ /: 1 ' >^ 1* f y j / f / y jr f f f y yj / y y jf A / f / f J f j / J / j f J / f 3D ,/^ Xy / / / / / / AO 7 J -/ f 7 r { / / / / / / y ^x 1 / f/ / + / / / t y -v y_ ~~7T ^ f- -/ -/ X- ^- 50 y^ ~f~ -f~ --f- / -} * 7* ; ' t 1 - t / / / y . ^~ / '/" y / I ; s\ 1*f -y^ ^ y?* ~^T~ f ^ ^ ./ t*t- ^ 20 j-> ^ "7^ -/ -/> ^^ -^^ ^- .. ^^ ^ ^ ^| r ^^^f ^^* ^^ ^f) ^^ ^^r ^r _^^ ^ ^r ^ ^ ^ ^^ ^ pj ~.( ^ _^^ ^*^ s^ ^^^ ^s^ ^s s ^r ^^^ .^ . x^^ rfX ^ -] 10 * t 2 $ s K (VJ (VI S3 s 10 OJ s l^ S Column spacing in feet 197 COLUMNS DIAGRAM 43 WEIGHT OF TYPICAL FLOOR PANEL OF FLAT SLAB CONSTRUCTION DESIGNED IN ACCORDANCE WITH CHICAGO BUILDING CODE (FOR ESTIMATING COLUMN LOADS) Column spacing in feet SECTION 8 BENDING AND DIRECT STRESS Rectangular Sections The following notation is used : R = resultant thrust. N = vertical component of R. x = eccentricity of thrust. t = thickness or depth of section. 6 = breadth of section. d' = embedment of steel top and bottom. As = area of steel on tension side. A' = area of steel on compression side. Ao = total area of steel = A a + A'. p = total percentage of steel = r-r- f c = maximum unit compression in concrete. f a = maximum unit tension in steel. // = maximum unit compression in steel. Case I. Compression Over Whole Section (A' = A s }. ir$ Diagrams 44 to 49 inclusive give values of K for various values of p , -~i and-, and for both n = 12 and n = 15. For values of ~ beyond the termination of the curves, tension occurs over part of the section and the diagrams for Case II should be used. Case n. Tension Over Part of Section (A' = A s ). Diagrams 50, 51, 52, 54, 55 and 56 give values of k for various values of p , , and y> and for both n = 12 and n = 15. Diagrams 53 and 57 give values of L. The method of procedure in solving problems is as follows: (1) Determine k from the proper diagram; (2) find L from Diagram 53 or 57; (3) solve equation (2) for/ c ; (4) find unit stresses in the steel from the formulas (3) (4) 199 - BENDING AND DIRECT STRESS Case III. Tension Over Part of Section (A' = 0). Notation is given on Dia- grams 58 and 59. k* -2pn(l - A;) = k*j d e , (5) 3 = 1- l Ak (6) (8) / - /c (10) Diagrams 58 and 59 may be used as shown in two of the examples which follow. Examples for Rectangular Sections A beam is 9 in. wide and 20 in. deep. The reinforcement both above and below consists of one steel rod 1 in. in diameter embedded at a depth of 2 in. At a certain section, the normal component of the resultant force is 60,000 lb., acting at a distance of 3 A in. from the gravity axis. Assume n 15. Compute the maximum unit compressive stress in the concrete. A _ (2) (0.7854) _ __ Po ~ ~ bt ~ (9)(20 d r = O.lOi For these values of p and , Diagram 48 gives K = 1.70 and shows that the problem falls under Case I. Then by formula (1) NK (60, 000) (1.70) (9) (20) = 567 Ib. per sq. in. Change the eccentricity of the preceding problem to 6 in. and solve. / , /v For p, = 0.0087 and -r = 0.30, Diagram 48 shows that y is too great for the problem to come under Case I. The method of procedure for Case II must then be followed. Diagram 55 gives k = 0.73 for the values of p and -y given above. With k = 0.73 and p = 0.0087, Diagram 57 shows L to be 0.123. Solving equation (2) M (60,000;(6) fc = LbT* = (0.123)(9)(20) = 815 lb ' Per Sq ' in ' Using formula (3) /. - nf c (~- t - l) = (15) (815) (0-7320 - l ) = 283 lb - P er sq- in. The stress /,' may be found by formula (4) but is always less than n X fc- An arch is 20 in. deep and is reinforced with three rods % in. in diameter to each foot of width, both above and below. If the rods are embedded to a depth of 2 in. and the normal component of the resultant thrust on a section is 100,000 lb. for 1-ft. width of arch. 200 BENDING AND DIRECT STRESS ivith an eccentricity of 3.4 in., determine the maximum intensity of compressive stress on the concrete. Assume n 15. (6) (0.4418) Po= - Diagram 48 gives K = 1.63 and the problem comes under" Case I. Then by formula (1) NK (100,000)(1.63) a _ nlu '- ! The vertical wall of a cantilever retaining wall is subjected to an earth pressure of 2400 Ib. applied at a distance of 4.54 ft. above the top of footing. The weight of vertical wall is 2200 Ib. which can be considered as applied 5 in. in front of the steel. Determine the unit stresses f c andf s , assuming n = 15, p = 0.0077 and d = 10.5 in. The moment at the top of footing M = (2400) (4.54) (12) + (2200) (5) = 141,700 in. - Ib. = _141,700_ (12)(10.5) 2 e^ 141,700 d (2200) (10.5) Entering Diagram 59 with a value of p = 0.0077 on the lower right-hand margin pt and tracing vertically to a value of -r = 6.1, then horizontally to the left to a point vertically above K = 107, we find /. = 14,000 and f c = 610. Design the vertical watt of the retaining wall described in the preceding problem so thatf f = 750 and /, = 16,000. Assume the weight. of wall to be 2000 Ib. For these unit stresses the left-hand part of Diagram 59 shows K = 133.8. Then d = V(133!s)(12) = 9 ' 4 ^ Say 9 ^ in ' : = _Hi,70o_ d (2000) (9.5) Following across the diagram horizontally to the right to a value of -r = 7.45 and then vertically downward to the lower right-hand margin, we find p = 0.0085. Round Columns Concrete outside of the hooping is neglected. The following notation is used: P = direct load (compression). e = eccentricity of load. r = radius of column core. p = total percentage of steel. f e = maximum unit compression in concrete. fc = minimum unit compression in concrete. f s = maximum unit tension in steel. /.' = maximum unit compression in steel. Case I. Compression Over Whole Section. Diagram 60 gives values of for various values of p and , and for both n = 12 and n = 15. 201 BENDING AND DIRECT STRESS Case II. Tension Over Part of Section. *- r> The right-hand side of Diagrams 61 and 62 gives values of 7- in formula (11) for Jc various values of p and , and the left-hand side of these diagrams gives values of ^ in R formula (12). Case III. Bending Only. *- ff f? Values of j and -7- in the preceding equations are given in Diagram 63. Diagram J c J s 64 gives the concrete and steel stresses in solid circular sections in the same manner as the familiar diagrams for rectangular sections with steel in tension side only. In the present case the value of ; is used instead of T-TO' irr 3 bd 2 Examples for Round Columns Assuming a column with 2Q-in. core reinforced with ten l-in. square rods and sus- taining a load of 200,000 Ib. applied 2 in. off center, determine the maximum unit stress in the concrete, n = 15. 10 e 2 r = 10 in. - (angexioy = 0.0318 r = Fd - - 2 From Diagram 60 or 1.12P 224,000 ~i^~ " "31TT6 = 712 lb ' PW * Sq " m - Find the maximum unit stresses in the concrete and steel of the column in the preceding problem if the eccentricity of the load is 8 in. r = 10 in. p = 0.0318 - = = 1.25 8 From Diagram 62 ? = 0.325 R - ^ - 1 > 600 > 000 - r ) " irr* ~ 3141.6 fc = ~ = 0^25 = 1)56 /, = 25R = (25) (509) = 12,720 lb. per sq. in. f/ = nf c = 23,500 lb. per sq. in. 202 44 BENDING AND DIRECT STRESS OCTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTION btf d'= 0.051 VALUES OF ^ n =12 " A' = A. Compression Over Whole Section and A 1 =A S Values of K in formula f t -|r M- O (Ti 0) 1 1 ^ SL ^s ^ X \ s v \ N 1 1 N ^ v 5 S > *- m \ \ k x A \, N N s, N s 1 \ \ N s s 1 ! \ \ \ s \ vv 1 s \ \ x, yiu s s \ , S s S \, s S s \ \ s \ \ V\ ' V N s s \1 -\ x^~ Sy \ \ s \ $T \. s" 1 s, \ "v \ S \ \ s V \ \ *& \ \ ^t s S *v \ s. s s S \ S s V s s \ N s S V\v V N sc o\ s \ yu; \ N ^ x s s s \ x S s s s s $ \J\ s& v\ 1 \ s yiu J ^s s \ \ \ N . 1 s XL > s V s ? N S \^ 1 \ V \ \A X- v\ s/\ -\ s m S X - X IS" \ ( \ V i s \ e. 1 \i 1 k X/" x\ x. sb S _\ y wu tlX) 2 I'D s E \ \ \ \ v X \J \ s S V 3 xV *x \ x s s x - V 1 X x v^ 4- -s ^v \ s s ^ 1 \ \ ^ x, x \ c '> s^ x \1 ^ N. 1 x X S ^N V 1 X ' x \- S^~ X J \ XT ^sr x. ^^ *^ ~x^ 37 \y'X ^y N V^ s N X N^ x^ : 'xP X x -X ^x N, \! i X7 3s % s v Bending and Direct Stress- ed 0.05 1 Based on n-l UIC X S,. X b ^ ^ s N. V >^- r^ ^ (ill * s, X x ^>^ t C S s X 5 X \ S -X ^* xi Sjj s s -^ ^ x^ x^ i x s, X x rl \7 \ j ,-x. X^ N^ s^-^ s^ ^ N N X N N N \ x^ \ x^*^ \ PC ;- s 5 5 N x S N s N X X xJ ? s X x-' s S s x^ si X" x. 5' S X N- - HZ X^" S X 9C 1 ! X \ r j \ \ \[ s 1 s "^ \ x^ x \^ \ ^^ x^ \ x ^^ X \ _ ^ x X x, N, x M- \ x x i X s, ^ x N N x S x N X X E 5 x x 5 S x x X S N. X 1 x^ R 90 1 - x, x. ^^ S ^ X, "^x ^xj X ^- s _/x. X x x X X v - ^s s "- x X, X ^*X, x -* x; ~ v v x X j 2 * rj XT N^ X. ^x ^-*< x^ j'OC ^^v, ^x. ^x \^^ ' x^ x^ \ ^^ \ \^ x^_ ijUt. ,-.-- ^s N x x x X 5s J X X _5 ^p i _X Sj 5 5 - s _ s 5 x 1 ^ S - x v -X x X ^ b , __ ^-x. S E | i 5 - x~ s^ r^- x; c.00 X . ^\ : x - X X, ^ X s ^ ^ \ 20C 1 s ^ ( ^ s 1 x i x -, S -X ? ^^ == k ^ ^"X ^ <* $ ^v 51 5 -- ^ s j * ^ p 55 s: ^, ""-x, ICC ^ 5 p -4- X 5 -^. 5s^, E 0,020 (D c c d c c C5| Q C c i c 1 C OO'O *ti j.o sanity^ ono BENDING AND DIRECT STRESS DIAC ] d' = 0.1( n = 12 A'=A, * RECTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTIOly VALUES OF ^~ Bending and Direct Stress- Compression Over Whole Section 1 d'=O.IOt Based on n -IE and A' = A s Values of K in formula *$ 4~ X in (U I 1 1 ceo i s ; d c> 1 1 1 1 1 020 0210 S "--V _ S S^x N x^r ^- ^ " - "s "" IS "" S S ^^^S^^" 61*0 S S X x X^sr^ ^^ ^^, ^ X ^ S ^ s ^ \ s^ x S^ SIO S ^^X^S~^ 5 x-S-x 5 S S S ^; ;^^x N 3 s ^^^x s^ ^ Fcx s ^ y x x, x _S_S_S S x -!> x x x^s x " r x : "x^-TS^^ ^^N x S ^|'( X ^ v V. *\ N S JSk. ! X X X, s X ^J "X xP* s. ^ s. X N. >W v S ^ ^ ^ N x. \ v \ X. ^ ^ J|"^ *S v *x ^ "S ^ \ \ ^, iy Vv 1 * X "X X v, \ v *\ v ^ x x! s^ \ v "X *\ ^ h -v v ^ ^ *x *X x ^ ^ X \ v s^ ^^ ^ ^ X _S^SZ_I^ N ^" - * 5 ^ S ^ ra ^ ~x ~s s ^s ^~ S s^N X X--^\^ "^ ^ ^ ^^ x x ^ ^ *^ N v S XX^ x"^-v S -X-x^r^F ^x^ re 1Z ^ s s, -\-v-S rs^s_. - ^ ^ s; *x- *N X^ S X, S^XN II'O S X. ^ ^^c*^ S ^ ^. x. X 'x ' x ^^ ^v ^~^~ S S~H -^- Nr^^; S S~" s ^S^N ~x;^ ^X^ ^~X^ \ SL 2 <5i6_x__x-^ s x S ^ x. "x^ ^-X-^-X;-- s s s s^s^ 5 s~^ x 01 '( ^ : 2bt-x- s x ^ v ^s ^ S 5> ^ x; s ^ x-x^x^ixX nN^^ jO"'C x ^*Cs x s -^x-^^-x-s-" N ^-^-X-X : X-X- x;^^^ -X ^js 60U ^^ ^ x ^*s S S H x, "^^^^ * N ^^ x ^ x x-^ K^ x-^^^ S s S ^X ^S X S<_^_^,_ X s - ""^ - s x s Xps ^X X; _. ^_ J^_ __S_ -Ss;-!^^- S;- - ^s; ^s; "x * ^s^ N x^s!^ s ^ -^--X^^ix ^s, ^ S ^ ^ x V, ** S V X X x, S S^S ."(^C s s ^ x, X --^- ^^-^ ^ S "s; "^xf^'T^R/ "*x *^T LOO x x ^ s. *** ^ . x "*** ^ * ^ X X X ^ \ ^ x X X v *** x X X x^ *^ ^ X ^ s. s 'S ^ "^ . . ^ **% ^x^"^ ^"^ s v~ v xc**> ~^x" *x ~ ^ ~ ^X ^S X^-X^ 900 x x ^ Sh *X "^ s ^- * i* *** !^ ^ ^ X ^ ^ ^x^ v ^ ** ^-^ -^ x ^S ^^ V<5 - **" ~^ V ^ s ^x x ^ ^^ 5O*u x "^ ^ \ X *N ^^" *" "^ X % *x ^ ^ X ^ v ^ -x^ s "*^ "** s.^ ^ S 1X1 ^ **> *** v^ S ^ . x ^ v ; ^ n; '*'*> ^ X ^ ^ -xa^- "* * s v x ^ ^ v x ^ S ^ ^J "^-^ S "^ k, ^ * _ E "^ ^^ x ^ "* *N ^ ^ ^ ^ ^ * "^ *s *V "^ V, **"* s^ X "*** w - **" -X - v N S ^X; "** X. - ^5x ^ iv "* S x ** ^"v, "*> ^^ ^ SSB ~ ^> ^Z "'"^L^Hv^ ^^I^" """s. "^^ ^ ^^x 90Y _x_ s **-^- "*" *i "** ^. "^^ = ^-v "^ *i v>> ^ *> ""Si "** ^^x v K^ *=>;- "" - ^^ ^^ "*" * ^-^ "^-^ ^"^ "^ ^ *"' S x x TO ^ > N *** , *"*^ ^ "*> " t: - ^**^ ^ v " "-x *" -^ ""x ZCK. ' ^ v v. ^oV " ""** ^ ^^<=^^ x ' ^^- ^^ ^ ^"-^ --x.^'*" TSfl-"^--^ 1 - ^k _ "-a ^. ^s. .^^^- --^, "' ;;s >. ^^^" -=^""^ ot -^ ^^j *** -^ ***''* ^^ '^-^^ --^^ --^-=^* 51 ^^ -^._^ ^5i^ ^**^; "^"""'Xi "*"" . "*">*. "*- "^^- ^^'v "^5. ^ ill ! _J i 1 I _J 1 OO'O d jo ssnjDA 204 DIAGRAM 46 BENDING AND DIRECT STRESS RECTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTION VALUES OF ~~ d'=0.15t n=12 A'=A S :ssion Over Whole Section Values of K in formula f c 7FF 1 yi'u s, 4) (V o r S OJ o J I 1 1 o - zn on SO) 5 s s i si s ^ - N s N s S \ ^ s S N s s s s J x s x * - % 1 v sj S, ^ bllj t Jx ^ ^ l s x x ' X ~^ ^ *sJ^ x^ \ \ s ^x ^ \ x \ K^ x Si s : s 5 S S s ^ '"S, X s x; ^ s^ x *v. x *=^ ^ X" r^ ^ x x > 5; N x x "^ * X* 2 S x ^> ^ x. .00 ^ X, ^r x^ ^ 5Z S x ^ ^ 2 s. " S s ^ -V X 2 x ^ ^ x ^ "- ^ x ^ \ ^ ^ 5 5 ~ X x ^ ^ -^ x N v __ ^ - -*" XT ^7 x^ - N ^ ^; x ^ I'UL ; "s x *x -v. ^^ ^ *^^ s^ 1^ ^, X 5 J rOO ' S s S! ( ^ ^> -, x 5 ^s ^ s 9<)'( "X, ^ ^; ^ X ,^- L^ "S^ ~^ - ^ *s ^ *^~ ^> ^ ^v^ *N ^ ^*, N^ ^^ N ^ *^s. -*, X x ^ ' ~~ *^ x; x; x ^ ~ * *"v X ^ |j ==^7 S - K; 1 3i ^ ^^ V | ^ --^ -^ "^^ ^ ^ * X. ^ --*. V x -^ >, S -> < f -> -, X. luu s^ >, lO'O ~-^ '**--. ---. ^^ ~^ ^, ^ ^^ * s^ X S 5 5 x -> -^, 5 >* _ p 5 OJ 8 o 8 8 8 1 wo "U j.o sen IDA 205 BENDING AND DIRECT STRESS DIAGRAM 47 RECTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTION n=15 A'=A S VALUES OF N ^ I f 1 0. o c 1 i ^ 1 1 1 H-i 1 m s | \ \ A \ w,; / / - * * j 120 V N \ v^~ / ? i do H- s L s s L ^ f ;4 . N C s \ V \ ^ / r -*-* . X 0771 r- v\ 7 I ^_ i- V : rnr t \ \ \s ^^rv \\ y__s K ^ -- fc 0) S 3 blU 9TO ^ s s s ^ L rn y^ ^ s^ \ \ - ^-\ V S v s r s V ? s r~* 1 m m I f ~> LK yit S s s, \ \ 5 \ S ly \ M- \ , ^ r !|s s s \ \ \ X \ \ s s^ s \ * \ \ s \ \ s\ \ S \ A X \\ 1 1 /.I'C > _ s ^ -^ \ y r^r^ A-V \\ v\ S \ SS ^ Q> SIO S^ \ \ \ * V \o^ ~ s^ ^ y^ \ \ -^ -v s v \\ \\' SulU > V \ ^ s . \ \ ^ X N s >_ \ \ \ V V s \ \\ \ V s \ v^ \ s O s S \ ^ \ N ^ S; s 5 y y\ \ A' XV 8 ho \ s s \ \- s \ _\ ' A \ s \ \\ \S \ x \ | v\ Wo (n IT) > ^. s~ s y ^ N \ y N s >' s ,v N+- < -1C N N s X. V\ S ^^- s:^^ y \ s ~y s\ V s \ \ ^v* \ ^ \\ tl'U o\ X Q. ii CVf s \ \ N v / S^f S ^ ^N y \ -^ V y y \s \\ \ \ \ X. \ r> 8? c x^ \ y S \ s ^-vj X- s y \ s,^ sS y\ u5 QIC \ s^\- X ^ s \ _ \ j ^ s \_y Ol( Jp s s X s^ V \ NV s^ \ ^ N \ \ s 4 -J? ^ \ s 5 \ \ >^ s ^ \ X m D y s s ^ S S \ \ s v ^ N ^ 00 >U; v \ s ^ ^ v?S v 600 Q -* v ^ s 5; S ~ \ -^ ^v s - \ ^ 5? s s T3 s s s 5s_ s S y . S ^ X s, \ \ k \ \ v C Q !0fl \ s N 5 ^ v S x X s t y ' S N y ' WO s, "s X, V -^^ -S; X s, S S v *> \ LA x^ ' k\ O> \ ^ ^ ^ V > N S. * . s. \ s s C ,oc ^ s -^^ S, S, ^ ' (K ? ^ S^ * ^ -%-] S ~~ ;s^> x^ ' S 5 S,-^ \ ^-s^ N s \ \ s^ ^ s s ^ ^ s, \ ^ X N. V ^ \ v^N^ Q) rn N x, s ; v~ ^ *\ ^ V s N s S -^ S (| N \ x~ s 5 \ X^ -^ - S^ s 5> -^- ^ S - S x Ns^ X \As ^v lOu -^ "^S r x L r r^ "V v^ bUU X ^ s S -N v ^ \ N S 5 x x^ R5T5 C X" N~ ~*^ --ft ^-^ s~ S ~ r s^ m V S 5 ^s. /' x NX p ^, S s X s X X X \ \ v ^ s7 ^- ^s v > ^ ~x ^ ^ x^ s s\ x^ s^ x, x^ ^CW ^* X^ X ^ \ x, ^ s^ N X. x. X x. X. 'r'lX x. X, s . X ^ s . X. Xa x ^x s "S x^ x X X. S -K is <- x 5 X. "^^ X s X ZO'O i I 6 *ii - ^x ^x Wfi ^ X - ^ v> ^. N x x S, ^x ^ s. X X s^ -t- TTT - N ^J. _L N. |sj [JJ S s . i^ 51 N " 1 X X (70 1O *^\ SN^ x ^ ^s^ Ss,, s^ ^ ^Xv^ ^^x^ o * ^x. "X ^ "X N s x 1 ou 1 cu o ] t, z 4 1 ru " 1 1C ) sar ^OA DIAGRAM 48 BENDING AND DIRECT STRESS RECTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTION VALUES OF BENDING AND DIRECT STRESS DIAC ] i'=O.L n = 15 l'=A a RECTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTIOI 5 * btf VALUES OF ~~ c Bending and Direct Stress -Compression Over Whole Section d'=O.I5f Based on n = l5 and A =A S Values of K infbrmula f c = FT i 5 o i CVJ O a 1 g 1 1 I S 5R5 LIO \^ V 5 9fO L\'0 X \ c \ x s^ ^ " -^ s ^ *v ,. \ s X S s s s V i ^^^ k 31 X w* \ \ >* s X 1 ^-- ^^ xl x 1 TV V s \ S a ? fe t!) s x, \ s Sj ' \ -^ \ \ s s $ XT_ s \ \ \ \ K^- i ^ c F* _s \ x ^ s s X sfe S s^- s \ N \ \ y v.\ A- s \ s r\ ylu "~\ X 1 X X S \ s ^S X ft s 3Z \ s ^ s ^ 's \ A 9I'0 \ N X Xi s \ N x, ~^v \ N V \ \ s N 5 \. N ^ s 5> S S Xv. -X X X 5 V > \ -X- 5 X ' o s ^ \ ^ N \x \ s\ slU FH3 \ N -X S s N x \ \ s x \ V s \, i p^ S, 3 \ , .\ \\ N S SIO WQ- s X \ -\- V s N ^ ^ > s ^\ s S \l S \ \ S, \ X -Ni X- \ x ^t X _ S3 S s X \ X^ s s i x, X X X \ X s S s 1 x s N s k-\ \ S tiu ^i x X V v X Ny Is S S> x s x^ 5j_ K >v \ V N s X ero ^\ s \ X \ x 1 1 \ x Xv X s V \ X x N X \ s. X. s s X s X x N ^ s. x^ X ^ ^N s, X ^ 210 X S^ 5 NT- x X ^ ^ s \ x. s. " ^v \ \ \ s N. \ \ ^ x^ X s 1 ^ El'O UU s s x x ~X X, V s - X 1 x X N \ \ N s \ s, - X x x -x S \ >-- s V N \ X s^ \ I ^x s\ h'oxt: K 1 ^ X' ^N r> Nw \ X X \ XI X X x ^N X- x. \ X \ X, 1 \ x x s 1 ^01 0> 2 bUU s x^ V ^ sH x x X x X X. X x X ^^ K \ x >v N x_ 5 x^ 6ff s X. -s X X s N X t^. s. >sj ^ \ 2 x, X^ S X X s s N N & X. s x ^ X V, \ x \ X N i s. s. x s. X, N ^s X \ X, \ s \ x^ x^ ^x s x ^x. 9(70 S "V s x^ X x X | X X X \ x x $ 90'0 "x. s, 5 X x X X; x s S x 5 > s< ^> sJ X x ; X. X x x x \ ^X > x x^ |X, s^ X x Xy_ x /uo X x^ x ^> X . s, 5 5 X X x s . x x X LOV ^ X ^S 1 ^ X x X^ s s^ N x x x ^ x_ - s x y \ x. X ^s X X^ ^x^ s x, x ^ u ? s, X x^ X X s X, V X N, x^ 5 ^ - yc'o s "X 1\ x, X X X. , | - s x >. X 5 xN 900 s^ \ s X s v ^X s v \ X. 1 S "X X s x X 5^ s X ^x 5 ^x s x "V x x X s S s X ^^ x \ s v' X X N x. Xv N x x V X Sffij V ^ 1 *x X X 5 -9 s X X . k x, SffO x 4r s x 5 x. , X x ^ x X, s, x * ^N s ^x s s N \ S i "S X X x. \ x x^ X * ^^ ^ s,. v - S V x s x x^ ^s FOC =s i 4- - 3 fy x. 5 x X ^ s^ > ** X x 5 *x _^ s x : x^ ^ X; s 5 x *s ^ X ^ x ' vo'o <^0(J "^s, X, 5r jr 5 s X s V, V "X,* . X* "X^^ 00 iOO *s; N X x , s S X, X Xx. s x^ 35 s. s X 5 \ S 5 ^;C *)* ^v v^ x X ^> s x^ ^ x - i X V _x % s X x. ^^ "N x ""^ ^*s, I IUU =1 5 5 ^ - ~ x ^ s> X H 5 x^ ^ x. - ^V x x ' % v v v. IUU x. X > -x "^w J c | c Q 1 1 1 1 1 | ooO "d J.O sanpA 208 DIAGRAM 50 BENDING AND DIRECT STRESS RECTANGULAR SECTIONS TENSION OVER PART OF SECTION d'=0.05t VALUES OF k n = 12 BENDING AND DIRECT STRESS DIAGRAM 51 d'=0.10t RECTANGULAR SECTIONS TENSION OVER PART OF SECTION VALUES OF k Ofr'O 00 vD ^ W o o o o DIAGRAM 52 BENDING AND DIRECT STRESS RECTANGULAR SECTIONS TENSION OVER PART OF SECTION d'=0.15t VALUES OF k n =12 211 BENDING AND DIRECT STRESS DIAGRAM 53 RECTANGULAR SECTIONS TENSION OVER PART OF SECTION d'=0.10t M n=12 VALUES OF -^ j.0 san t o A a v i 1 g > ii ii 'c c o o Oi ^^ d i-< a> o -d 'd *> '> O O IT) O IO Ol O| O in 10 ^j- ^- co ro| w| (\. [\[\ \ ' ' ( V 1 ' 1 V "\"'\ ^ i \ s x ^ ^ > ' 1 1 ' \ 1 \l \l \ \^" ""x ^2C k M L V \ > v -u \ ^ II. 5 o) M ^ \ $:i::~::::_i:s:S::: s ^ ^ S v \J x Q\ > f?\^ < ^^ KI ' 3 \ ii] '"_: si:i KIIS is" :i_s is; ^ S ^^'^\ ^ V N i 1 ^\ -\" ' l r ' 5ll*O lott nk L\ ' M k \ \ L V i V . N \ N \ ^ hi ^ ^ ii ^ ^ < ~A. ^ , r i .1^ ^^- -^ \ M\ 1 L \ I S ^ ! ""s, ^ 5v^ s ^s^ 1 ~r. \ [ . L |jj R ei^f 1\ * i i L v \ L y \ s v ^ r\ \ ' s i ^ III.IZ-5I s s . v X .^^^ L 1 \ i ^ \ \ L sJe 1\ L \ \ i .11: N. . ^ s ^ s ^\S^C^ f^ --r-* < \ ^ri W-\ 1 \ \ - \ ^ " *. ' ^ ' S v \ , S S "^ oxj^^^ S jl ^ L ^ J L L m!:! 2 ::: :s:^ :s::si:s :.s :.5 :.i : - ^ N - v ^CiT s ^c-JI!--^" \-f i fc M " " '^ P s j "~ V \ ~ ^raLfj' s ~" v "~^Tv~S~" i - - 3 - J -'-^1 J --- IV ! . . L i s i . S s s ^ ^ " s v ja-i i *^ *. ^^H-VS S - S \\ mS: !:a :.:.::!:.;:.; :_v is; i:s;:::; i:.! :5;3biiii55ii5s$-sjsi[i5:ii E [(si 11 ' \ kill !II[I j !S^ ISII. N \ N ^~ S& i s .51 I5l5 k S:[ i i* LA^ l\I ^l^^v ^ s ; _L^ s > : _ ; ; sip ^^ ^ y ~ ; 3 : 5 S . J u p|:i!j!j:i:jj:j;!j:!jj:i|::;|j:||:j:!|i -&* - "* * -*"-->TK-S-|-*cs5"S \* " ^ ag:_:;;; i_:s; i^s; j;s^;s s 55 ^13" ^n! C" Li ^L^ \ ^ S s ^ ^ s s V ^;-;S-- J-j-J-S-rj jjj-VJ-Jrt o ti- r -S k SS v ^ " * % 5t I:!sl" > ^^1 A . SS 5 S Cv sra N \\ \ \ \ v V i v s: "^ s ^ + ?;;:: :. *s; ^::i"\ ^ v ;^ :: k :]_ : +r pp3i 3i3".iisi a". \ - v s" r!s; - !sI5:_i:s:[S5;;3 i in o \ ^ \ \ \ s v \ s ^; *> ^ " _:; " ** ~4 \ ^J^^S^i^V in ffi!-!::::;iS"S":s;"s;::s;i:^s;i:^; :;;: =*:^;-i*4jis;^i|s^^5 jj?jj H\r s " J " j " --^--^--s- -^- s S--T<^V Sv 1..U., . -:^ H^y,_ s ' |\N s V\ v\L ' -i i \ \ i \ ^ \ ' j [ L^ ILA r \ SI.IIXI.; S _ S- s , ,qc-+^. ff* L\-^- r \-^--\--v--^--^-^s----^l ;; -. """"" ^*"" i > ~r ~ ^" " ^~ ^ r v\*s ^AsvS L. r^ ' L ^ " " J \ ^ ^ ** ^ 1 I ^ *" "* o> g_yi_\_]! .^__^__S^_A--- -s-----=yj--- Q wLx-L.L.^,. v'lLb" S ^^il r- rPr i~i \ r " "" s~n~M ~ ~ ^j ~ i*z s s ^ X\K \\i\v\ '"p"""" "'"T ^xjx/ iNVvA 1 10 v--" kj \ \ \--\- S, s S H_s I '^v^--. 8cffi^ : ^^ :! r| ;: ^ :: -^ ::: " : p- ;:::: ^l|p;|^|;^l^SiH^ =|-:!::|;l;:::;;;i:|!|::l:[=l^!:|j:|^ H sIMllHK^Ifllifli^iff rffljtifffijMllffl tfttBMSiH xj 3_ j_. |.j._j___s \ ?UJ ^ ^"' .,* ' ^ _ *i '!_.,<'- '. e .'"-* 900 O t t -V L IjIII.S" ^&?> * - ~r^' ---?*---?*-- '*~~y(~~'s' "~^ p " II ^I 55 "^ g' n \ \ \ 1 S* ' / S \4~' s ' * * " *" x "c J^-j^p-^j--s:ii-kiiOT-=s: ===::: n 3' j:s":s';:;:: .ij::^; :;;=;; ;;:;:=:.: B^ : :i : :j : ^r:;jj:::^::::::::f:iii;s 1^^^%^^/^ X '^^ 200 2 d d II II - ~ ol 1 1 III 1 Pkll IH III ITRLI III! liiifMI H; LOO loolio omo loin ^M-|f> cr ? (V !'V M ^o san|D A 212 DIAGRAM 54 BENDING AND DIRECT STRESS RECTANGULAR SECTIONS TENSION OVER PART OF SECTION VALUES OF k d n=15 5t A'=A, S3HIDA 1 N ^ IT O< (D 4- - u a B Q -o lAI i ft* \rv\ su Ju \\ -o (U CD w x 22 91 Q c? . vO ^ ^ < vO 5* OJ O COI \O -d- P o o P g g 8 o- o c> c> c> O Q - - N -- - -- - :: 4H >j ^0 S3 n|D A SOO s ^ - - 1 - - i:^:::: - 5 l!|j;;j|!ll!l|j||!l|jj|l 8 S || o <=> ^ In - S ^-- IBM &OC i ^\ \ s * 1 if} : : :.; ; ; AM \ \ 1 >> II ::::::::::::^-:s^:::::: t :::::: :: Cf :::::::::::::V5s::::::F s \_ \ WW V O^~ rii - - ~: ^^ . ^ ^ 1 -JU | -:: :::::: ^,5" ::^LfA:::::: :: """"J^|H^~"" TW ^r^ ; > ITKJ::::: :: Hd+"J" t^Y/" 1 Percentage of vertical ^*^ Mvl ^ S - lyy ^3 Mr >\ s UU ^cS-- -- rt^ hfft~t ^~ - _S_ i*j i - III -i * 5 ^ ^ r\fv/i ' + 5- 1 L i 1 J_ IT" " " " " ~ * " CAn (D - - -s - \ n ; ; " aC/v, w " s 4 11 C I-5 S . --X-. C TV r-. r- . -SI- V V> v \ I _L. . D s : ; :.: :;;_:: :__: :._ :: ; 5' r : O- - ^ ::5::: < \ **> 1 OS :_ .: :_i>: ::_:: lA^I^^ J^ :_:.:: _I :i i . iijfci. { j. .'^ yt -rr s, r^_ ii i - 1 i 1 U : i r INI 111 L. .. 3 "s "S ffi :: = :::: - _SI ^__ m ^ f :: ^lsS^- S s ::x B!E!! II _ :iss : ::::S ttf ====:== Clj: M^ ao'o ::: = -::::::- = ::::: = | - 100 S J "^ ^- 10 (vj O 0] oOOO o **/& j-o sanfDA 222 DIAGRAM 64 BENDING AND DIRECT STRESS ROUND COLUMNS BENDING ONLY VALUES OF R, f s , f e AND p = 12 = 15 223 SECTION 9 FOOTINGS Diagram 65 makes it possible to find readily the bending moments which occur at each face of column for both square and rectangular footings. The illustrations above this diagram show how the diagram is used. For example, suppose the bending moment is required at the face of a 24-in. column supporting a load of 300,000 Ib. and resting on a footing 9 ft. 2 in. square. From the upper part of Diagram 65, C\ = 6.2 and M = (6.2) (300,000) = 1,860,000 in.-lb. Tables 49, 50 and 51, based on the recommendations contained in Bulletin 67 of the University of Illinois Engineering Experiment Station, give the design of square reinforced footings for different loads, column sizes and soil pressure. These footings are without offsets and for large footings it will usually be found more economical to use one or two offsets. These tables are computed for square columns. If round columns are used, multiply the diameter by 0.7854 to get the size of square columns of equivalent perimeter and enter the table with that size. The recommendations in the bulletin mentioned above are as follows: Width of Footing to Use in Flexure Computations for Two-way Reinforcement. With two-way reinforcement evenly spaced over the footing, it seems that the tensile stress is approximately the same in bars lying within a space somewhat greater than the width of the pier and that there is also considerable stress in the bars which lie near the edges of the footing. For intermediate bars stresses intermediate in amount will be developed. For footings having two-way reinforcement spaced uniformly over the footing, the method proposed for determining the maximum tensile stress in the reinforcing bars, is to use in the calculation of resisting moment at a section at the face of the pier the area of all the bars which lie within a width of footing equal to the width of pier plus twice the thickness of footing, plus half the remaining distance on each side to the edge of the footing. This method gives results in keeping with the results of tests. When the spacing through the middle of the width of the footing is closer, or even when the bars are concentrated in the middle portion, the same method may be applied without serious error. Enough reinforcement should be placed in the outer portion to prevent the concentration of tension cracks in the concrete and to provide for other distribution of stress. No failures of concrete have been observed in tests and none would be expected with the low percentages of reinforcement used. Bond Stresses. The method proposed for calculating maximum bond stress in column footings having two-way reinforcement evenly spaced, or spaced as npted in the preceding paragraph, is to use the ordinary bond stress formula, and to consider the circumference of all the bars which were used in the calculation of tensile stress, and to take for the external shear that amount of upward pressure or load which was used hi the calculation of the bending moment at the given section. Bond resistance is one of the most important features of strength of column footings, and probably much more important than is appreciated by the average 225 FOOTINGS designer. The calculations of bond stress in footings of ordinary dimensions- where large reinforcing bars are used show that the bond stress may be the governing element of strength. Tests show that in multiple-way reinforcement a special phenomenon affects the problem and that lower bond resistance may be found in footings than in beams. Longitudinal cracks form under and along the reinforcing bar due to the stretch in the reinforcing bars which extend in another direction, and these cracks act to reduce the bond resistance. The development of these cracks along the reinforcing bars must be expected in service under high tensile stresses, and low working bond stresses should be selected. An advantage will be found in placing under the bars a thickness of concrete of 2 in., or better 3 in., for footings of the size ordinarily used in buildings. Difficulty may be found in providing the necessary bond resistance, and this points to an advantage in the use of bars of small size, even if they must be closely spaced. Generally speaking, bars of %-in. size or smaller will be found to serve the purpose of footings of usual dimensions. The use of large bars, because of ease in placing, leads to the construction of footings which are insecure in bond resistance. Column footings reinforced with deformed bars develop high bond resistance. Curving the bar upward and backward at the end increases the bond resistance, but this form is awkward in construction. Reinforcement formed by bending long bars in a series of horizontal loops covering the whole footing gives a footing with high bond resistance. The use of short bars placed with their ends staggered increases the tendency to fail by bond and cannot be considered as acceptable practice in footings of ordinary pro- portions. In footings in which the projection is short in comparison with the depth, the objection is very great. Diagonal Tension. As a means of measuring resistance to diagonal tension failure, the vertical shearing stress should be calculated by using the vertical sections formed upon the square (assuming square column) which lies at a distance from the face of the pier equal to the depth of the footing. This calculation gives values of the shearing stress, for footings which failed by diagonal tension, which agree fairly closely with the values which have been obtained in tests of simple beams. The formula used in V this calculation is v = rrj? where V is the total vertical shear at this section taken to ojd' be equal to the upward pressure on the area of the footing outside of the section con- sidered, b is the total distance around the four sides of the section, and jd is the dis- tance from the center of reinforcing bars to the center of the compressive stresses. The working stress now frequently specified for this purpose in the design of beams, 40 Ib. per sq. in., for 1:2:4 concrete, may be applied to the design of footings. 226 DIAGRAM 65 BENDING MOMENTS FOR SINGLE COLUMN FOOTINGS .- d M=C,P *. EH LJi M-QdP M=CjdP Square footings with square or round columns M = C,P (in.-lh) Length of footing, side (b) in feet Rfictungjlar fbalrnqs-for squan- or round cofumns M-CjdP far rectanular columns Values of a /d (or 227 FOOTINGS DESIGN OF SINGLE SQUARE FOOTINGS Punching shear = 120 Bond stress =100 Tension in steel = 16, 000 2 TONS ON SOIL TABLE 49 Squart column Footing size b Column size a (in.) Allowable load P (thousands of pounds) Total depth (in.) Steel Volume of concrete (cu. ft.) Size (in.) No. rods each way Weight of sq. rods Ub.) (ft.) (in.) Square Round 3 10 34.8 11 H 8 10 37.4 8.3 12 " 34.9 10 9 12 42.0 7.5 14 35.0 9 10 13 46.7 6.8 3 6 10 46.9 14 M 8 10 44.2 14.3 12 47.2 12 10 12 55.2 12.3 14 47.3 11 11 13 60.7 ,11.3 4 10 60.6 17 H 8 10 51.0 22.7 12 61.2 14 10 13 63.7 18.7 14 61.4 13 11 14 70.1 17.3 16 61.6 12 12 15 76.5 16.0 4 6 10 75.9 20 H 8 10 57.7 33.8 12 76.7 17 10 12 72.2 28.7 14 77.2 15 12 15 86.6 25.3 16 77.7 13 14 18 101.0 22.0 5 10 92.7 23 H 8 10 64.6 47.9 12 93.7 20 10 12 80.7 41.7 14 94.4 18 11 14 88.8 37.5 16 95.0 16 13 16 105 33.4 18 95.6 14 16 20 129 29.2 5 6 10 110.8 27 2 8 10 71.4 68.0 12 112.8 23 10 12 89.2 58.0 14 113.4 20 12 15 107 50.4 16 114.2 18 13 17 116 45.4 18 114.6 17 14 18 125 42.8 6 10 130.1 31 H 7 9 68.4 93.0 12 131.8 27 9 11 88.0 81.0 14 133.2 24 11 14 108 72.0 16 134.5 21 13 16 127 63.0 18 135.4 19 15 19 147 57.0 20 22 136.3 136.8 17 16 & 17 18 22 23 166 176 51.0 48.0 6 6 10 150.5 35 M 8 10 85 123.0 12 153.1 30 10 12 106 106.0 14 154.7 27 11 14 117 95.0 16 156.3 24 13 16 138 84.5 18 157.3 22 14 18 149 77.5 20 158.4 20 16 20 170 70.4 22 158.9 19 17 21 181 67.2 228 TABLE 49 FOOTINGS DESIGN OF SINGLE SQUARE FOOTINGS 2 TONS ON SOIL Punching shear = 120 Bond stress =100 Tension in steel = 16,000 Footing size b Column size a (in.) Allowable load P (thousands of pounds) Total depth D (in.) Steel Volume of concrete (cu. ft.) Size (in.) No. rods each way Weight of sq. rods db.) (ft.) (in.) Square Round 7 12 175.1 34 H 10 12 115 139 14 177.6 30 12 15 138 123 16 179.5 27 13 17 149 110 18 181.3 24 14 18 161 98 20 182.5 22 17 21 195 90 22 183.1 21 17 22 195 86 24 184.4 19 . - 20 25 230 78 7 6 12 198.3 38 H 11 14 136 178 14 201.1 34 13 16 160 160 16 203.9 30 15 18 185 141 18 206.0 27 16 21 197 127 20 207.4 25 . 17 22 210 117 22 208.8 23 19 24 234 108 24 210.2 21 20 26 246 99 8 14 226.4 37 M 14 17 185 198 16 229.6 33 16 ' 20 211 176 18 232.0 30 17 22 224 160 20 233.6 28 18 . 23 237 149 22 235.2 26 20 25 264 139 24 236.8 24 21 27 277 128 26 238.4 22 23 29 303 117 8 6 14 252.0 41 H 14 18 196 247 16 255.6 37 16 21 224 223 18 259.2 33 19 24 267 199 20 261.9 30 21 26 294 181 22 263.7 28 22 28 309 169 24 265.5 26 24 30 337 156 26 267.3 24 25 32 351 145 9 16 283.5 40 H 11 14 256 270 18 286.5 37 12 16 279 250 20 289.5 34 14 17 325 230 22 292.7 31 15 19 349 209 24 294.4 29 16 20 372 197 26 296.6 27 17 22 395 182 28 298.7 25 19 24 442 169 9 6 16 311.3 44 H 12 15 295 331 18 315.8 40 13 17 319 301 20 319.3 37 14 18 344 278 22 322.6 34 16 20 393 256 24 326.0 31 17 22 418 233 26 328.7 29 18 23 442 218 28 330.6 27 20 25 491 203 229 FOOTINGS DESIGN OF SINGLE SQUARE FOOTINGS 2 TONS ON SOIL Punching shear = 120 Bond stress =100 Tension in steel = 16,000 TABLE 49 Square column. Footing size b Column size a vin.) Allowable load P (thousands of pounds) Total depth (in.) Steel Volume of concrete (cu. ft.) Size (in.) No. rods each way Weight of sq. rods Ob.) (ft.) (in.) Square Round 10 16 340.0 48 % 12 16 310 400 18 346.3 43 14 18 362 358 20 349.9 40 15 19 388 334 22 353.8 37 17 21 440 308 24 357.4 34 18 23 466 284 26 360 . 32 19 25 492 267 28 362.5 30 20 26 518 250 30 365.0 28 22 28 565, 233 10 6 16 369.3 52 H 14 17 381 478 18 376.1 47 15 19 408 432 20 381.8 43 16 21 435 395 22 386.0 40 . 18 23 490 367 24 390.0 37 19 25 517 340 26 392.9 35 20 26 544 321 28 395.5 33 21 27 571 303 30 398.2 31 22 28 599 285 11 18 406.9 51 H 15 19 419 514 20 414.5 46 17 22 486 463 22 419.0 43 19 24 543 433 24 423.5 40 20 26 572 403 26 428.0 37 22 28 629 373 28 431.0 35 23 29 658 353 30 434.0 33 24 31 686 333 32 437.2 31 26 33 743 312 34 438.7 30 26 33 743 302 11 18 439.7 54 H 16 21 478 595 20 446.3 50 18 23 538 551 22 452.8 46 20 25 598 507 24 457.8 43 21 27 628 474 26 462.9 40 23 29 687 441 28 466.3 38 24 31 717 418 30 469.4 36 25 32 747 397 32 472.7 34 26 34 111 375 34 476.0 32 28 35 837 353 12 18 471.4 58 H 17 22 530 697 20 480.5 53 19 24 593 636 22 486.0 50 20 26 624 600 24 493.2 46 22 28 686 552 26 498.6 28 502 . 1 43 41 24 25 31 32 748 780 516 492 30 507.6 38 27 35 841 456 32 511.1 36 28 36 873 432 34 514.8 34 30 38 936 408 36 518.4 32 31 40 967 384 230 TABLE 50 FOOTINGS DESIGN OF SINGLE SQUARE FOOTINGS 3 TONS ON SOIL Punching shear = 120 Bond stress = 100 Tension in steel = 16,6 Footing size b Column size (in.) Allowable load P (thousands of pounds) Total depth (in.) Steel Volume of concrete (cu. ft.) Size (in.) No. rods each way Weight of sq. rods Ub.) (ft.) ! (in.) Square Round 3 10 52.4 14 H 8 10 37.4 10.5 12 52.5 13 8 11 37.4 9.8 14 52.8 11 11 14 51.5 8.3 16 52.9 10 12 15 56.1 7.5 3 6 10 70.7 18 M 7 9 38.7 18.4 12 71.1 16 9 11 49.7 16.3 14 71.4 14 10 13 55.2 14.3 16 71.7 12 13 16 71.8 12.3 4 10 91.4 23 M 7 9 44.6 30.7 12 92.2 19 10 12 63.7 25.3 14 92.6 17 10 13 63.7 22.7 16 93.0 15 12 16 76.5 20.0 18 93.2 14 13 17 82.9 18.7 20 93.4 13 14 18 89.2 17.3 4 6 10 114.7 27 y* 7 9 50.6 45.6 12 115.7 23 9 11 65.0 38.8 14 116.2 21 10 13 72.2 35.5 16 116.9 18 12 16 86.7 30.4 18 117.2 17 13 16 94.0 28.7 20 117.7 15 15 19 108.0 25.3 5 12 141.2 28 H 8 11 64 . 6 58 . 3 14 142.2 25 10 12 80.7 i 52 1 J6 143.1 22 12 15 97.0 45.8 18 143.7 20 13 16 105 41.7 20 144.4 18 15 19 121 37.5 22 145.0 16 16 22 129 33.3 5 6 12 169.0 33 H 8 11 71.4 83.2 14 170.5 29 10 12 89.2 73.1 16 172.0 25 13 16 116.0 63 18 172.8 23 13 17 116 58.0 20 173.6 21 15 19 134 52 9 22 174.3 19 17 21 152 47.9 6 12 198.9 38 H 8 11 78.2 114.0 14 201.2 33 10 12 97.8 i 99.0 16 202.5 30 11 14 108 90 . 18 203.8 27 13 16 127 81.0 20 205.2 24 15 19 147 72.0 22 206.1 22 17 21 166 66.0 24 207 . . 20 19 24 186 60.0 26 207.4 19 20 25 195 57.0 6 6 12 230.8 43 M 9 11 95.7 152.0 14 233.5 38 10 12 106 134.0 16 235.6 34 11 14 117 120.0 18 237.7 30 13 17 138 106.0 20 238.7 28 14 18 149 98.5 22 240.3 25 17 21 181 88 24 241.4 23 18 23 192 81.0 26 241.9 22 19 24 202 77.4 231 FOOTINGS Punching shear = 120 Bond stress =100 Tension in steel = 16,0 DESIGN OF SINGLE SQUARE FOOTINGS 3 TONS ON SOIL Footing size Column Allowable i -_ j Total Steel Volume b size a (in.) load P (thousands of uounds) depth (in.) Size (in.) No. rods each way Weight of sq. rods of concrete (cu. ft.) (ft.) (in.) Square Round db.) 7 14 267.7 43 H 11 14 121 176 16 270.2 39 12 15 138 159 18 272.6 35 13 16 149 143 20 275.0 31 15 19 172 126 22 276.3 29 16 20 184 118 24 277.5 27 18 22 207 110 26 278.7 25 19 24 218 102 28 279.9 23 21 27 241 94 7 6 14 303.7 48 y* 12 .15 148 225 16 307.4 43 13 16 160 202 18 310.0 39 14 18 173 183 20 312.9 35 16 20 197 164 22 315.0 32 17 22 210 150 24 316.3 30 18 22 222 141 26 317.8 28 19 24 234 131 28 319.2 26 21 27 257 122 8 16 345.6 48 H 14 17 185 256 18 349.6 43 15 19 198 229 20 352.8 39 17 21 . 224 208 22 . 355.2 36 18 23 237 192 24 357.6 33 20 25 264 176 26 359 . 2 31 21 26 277 165 28 360.7 29 21 27 ! 277 155 30 362.4 27 23 29 303 144 8 6 16 386.6 53 y* 15 19 211 319 18 390.1 48 16 21 224 289 20 393.7 44 18 22 ' 252 265 22 397.3 40 19 24 266 241 24 400 . 1 37 21 27 294 223 26 401.9 35 22 28 309 211 28 404.5 32 24 30 337 193 - 30 406.3 30 25 32 351 181 9 18 432.2 53 y% .11 14 256 358 20 437.3 48 12 15 279 324 22 441.4 44 13 17 302 297 24 444.4 41 14 18 325 277 26 447.4 38 15 20 349 257 28 449.5 36 16 21 372 243 30 452.5 33 18 23 418 223 32 454.6 31 20 25 465 209 34 456.6 29 21 27 488 196 9 6 18 476.1 58 H 12 15 295 436 20 481.6 53 13 16 319 399 22 486.1 49 14 18 344 369 24 490.6 45 15 19 369 339 26 494.1 42 16 21 393 316 28 497.5 39 17 22 418 293 .-30 499.8 37 18 23 442 278 32 502 . 35 19 24 467 263 34 504.3 33 20 26 492 248 232 TABLE 50 FOOTINGS DESIGN OF SINGLE SQUARE FOOTINGS 3 TONS ON SOIL Punching shear = 120 Bond stress =100 Tension in steel = 16, 000 Footing size 6 Column size a (in.) Allowable load P (thousands of pounds) Total depth (in.) Steel Volume of concrete (cu. ft.) Size (in.) No. rods each way Weight of sq. rods Ob.) (ft.) (in.) Square Round 10 18 521.3 63 H 13 16 336 525 20 527.5 58 14 17 362 483 22 533.7 53 15 19 388 442 24 538.9 49 16 20 414 408 26 542.5 46 17 22 440 383 28 546.3 43 18 23 465 358 30 550.0 40 19 25 492 333 32 552.5 38 20 25 518 317 34 555.0 36 21 27 544 300 36 557.5 34 22 28 569 283 10 6 18 566.3 69 K 14 17 381 634 20 574.5 63 15 18 408 , 579 22 581.5 58 16 20 435 533 24 . 587.1 54 17 21 463 496 26 593 . 2 50 18 23 490 456 28 596 . 6 47 19 24 517 432 30 600.8 44 20 26 544 404 32 604 . 9 41 22 28 599 377 34 608 . 8 39 23 29 626 358 36 610.5 37 23 30 626 340 38 613.2 35 24 31 653 322 11 20 623.2 68 M 15 20 458 686 22 630 . 8 63 17 21 486 635 24 638 . 3 58 18 22 515 585 26 644.4 54 19 24 543 544 28 648.9 51 20 25 582 514 30 653.4 48 21 27 600 484 32 657.9 45 23 29 658 454 34 662.5 42 24 31 686 423 36 665 .5 40 25 32 715 403 38 668.5 38 26 33 743 383 40 671.5 36 27 34 772 363 11 6 20 672.9 73 H 16 21 478 804 22 682.8 67 18 23 538 738 24 689.5 63 19 24 568 694 26 696.0 59 20 25 598 650 28 702 . 6 55 21 27 628 606 30 709 . 1 51 23 29 687 562 32 714.1 48 24 31 717 529 34 717.5 46 25 32 747 507 36 722.3 43 26 34 777 474 38 725 . 7 41 27 35 807 452 40 729 . 1 39 28 36 837 429 42 732.3 37 29 37 866 408 12 22 734.4 72 M 19 24 593 864 24 743.4 67 20 25 614 804 26 750 . 6 63 21 27 655 756 28 757 . 8 59 22 28 686 708 30 765.0 55 24 31 748 660 32 770.4 52 25 32 780 624 34 775.8 49 27 34 842 588 36 779.4 47 27 35 842 564 38 784.8 44 29 37 904 528 40 788 . 4 42 30 38 936 504 42 792 . 40 31 39 967 480 44 793.8 39 31 39 967 468 233 FOOTINGS Square column DESIGN OF SINGLE SQUARE FOOTINGS A J I ^ 4 TONS ON SOIL Punching shear = 120 m Iff I Bond stress =100 HfH Q * Tension in steel - 16,000 5 gFi 1 Footing size b Column size a (in.) Allowable load P (thousands of pounds) Total depth D (in.) Steel Volume of concrete (cu. ft.) Size (in.) No. rods each way Weight of sq. rods Ob.) (ft.) (in.) Square Round 3 10 70.0 18 H 7 9 32.8 13.5 70.3 15 9 11 42.0 11.3 14 70.5 13 10 13 46.7 9.8 16 70.6 12 11 14 51.5 9.0 18 70.8 11 12 15 56.1 8.3 3 6 10 94 . 5 23 M 7 9 38.7 23.5 12 94.9 20 8 10 44.2 20 4 14 95.4 17 10 12 55.2 17.4 16 95.7 15 11 15 60.7 15.3 18 95.9 14 12 15 66.3 14.3 20 96.2 ' 12 15 19 82.9 12.3 4 10 122.2 29 H 7 9 44 . 6 38 7 12 123.0 25 8 10 51.0 33 . 3 14 123.8 21 10 12 63.7 28.0 16 124.1 19 11 14 70.1 25.3 18 124.6 ' 17 13 16 82.9 22.7 20 125.0 15 15 19 95.6 20.0 22 125.3 14 15 19 95.6 18.7 4 6 10 153.1 35 H 7 9 50 . 6 59 . 12 154.4 30 8 10 57 . 7 50 . 6 14 155.4 26 10 12 72 . 2 . 43 . 8 1 16 156.2 23 11 14 79.5 38.8 1 18 156.7 21 12 15 86.7 35.4 20 157.2 19 14 17 101.0 32.0 22 157.7 17 16 20 116.0 28.7 5 12 188.7 36 M 8 11 64.6 75.0 14 190.3 31 10 12 80.7 64.6 16 191.6 27 11 14 88.8 56.2 18 192.2 25 12 15 97.0 52.1 20 193 . 1 22 14 18 113 45.8 22 193.7 20 16 20 129 41.7 24 194.1 19 17 21 137 39.6 5 6 12 226.1 42 H 9 11 80.2 106.0 14 228.0 37 10 12 89.2 93.2 16 229.9 32 11 14 98.2 80.7 18 231 .0 29 13 16 116 73.1 20 232.2 26 14 18 125 65.5 22 232.9 24 15 19 134 60.5 24 233 . 7 22 17 22 152 55.4 26 234.4 20 19 24 170 50.4 6 14 268.6 43 H 9 12 88.0 129.0 16 270.6 38 11 14 108 116.0 18 272.7 34 12 16 117 102.0 20 274.0 31 14 17 137 93.0 22 275 . 4 28 15 19 147 84.0 24 276.3 26 17 21 166 78.0 26 277.2 24 18 23 176 72.0 28 278.1 22 20 26 195 66.0 6 6 14 312.1 49 y* 10 13 106 172.0 16 314.7 44 11 14 117 155.0 18 317.5 39 13 16 138 137.0 20 319.5 35 14 18 149 123.0 22 321.1 32 15 19 160 112.0 24 322.2 30 17 21 181 106.0 26 323 . 2 28 18 23 192 98.5 28 ,", > 1 : . 3 26 i/ 19 25 202 91 .5 30 325 . 3 24 21 27 223 84.5 234 TABLE 51 FOOTINGS 5quar 238 TABLE 52 MISCELLANEOUS BUILDING CODE REQUIREMENTS FOR LIVE LOAD Structure i Boston Buffalo Chicago Cincinnati Indianapolis Milwaukee Minneapolis ! 1 New York Philadelphia Pittsburgh .2 1 San Francisco A 1 Washington \partments 60 50 70 40 40 50 30 50 40 70 50 60 40 50 100 100 70 75 100 100 100 125 125 100 120 150 100 Fxd seat auditoriums 75 100 50 75 75 Mov. seat auditoriums Churches 125 100 100 1?5 80 50 75 125 100 75 Dance halls ?00 100 150 100 150 100 200 100 150 250 Theaters 100 100 100 125 50 100 75 75 Theater balconies Theater stairways 80 100 Dwellings 60 50 40 40 40 50 30 50 40 40 70 70 50 60 40 50 Hospitals 70 50 50 30 50 70 50 60 50 Hotels 60 70 50 40 75 30 50 40 70 50 60 40 50 First floors 100 100 75 Corridors 125 100 75 Office rooms 50 75 Manufacturing ........ 175 150 ?00 150 200 150 250 Light manufacturing Mercantile 125 m 125 ?50 120 100 100 100 100 100 100 125 ?00 120 100 150 125 125 Retail stores Heavy storehouses 125 250 125 250 120 100 100 150 100 200 100 100 125 120 120 150 150 125 250 125 110 150 Warehouses . . 250 150 150 ?00 200 150 200 150 250 150 Offices 75 100 70 50 50 75 40 75 70 60 100 60 60 50 75 First floor 150 100 150 80 100 100 125 Corridors 100 110 100 125 100 110 Schools class rooms 75 60 60 100 40 100 60 75 75 50 75 Assembly rooms .... 125 100 75 60 125 75 Corridors 60 125 100 Stairways 60 Sidewalks ?00 300 300 150 300 300 300 150 Stables, carriage houses, garages 100 120 100 75 85 80 85 100 75 75 Stairways, general 70 100 80 60 70 100 Fire escapes . . . 70 70 100 Roofs slope under 20 Over 20 (hor. proj.) Wind pressures 30 40 40 30 25 20 25 20 30 30 30 50 50 30 30 40 30 30 30 30 50 30 30 30 20 20 40 40 25 25 30 239 TABLE S3 MISCELLANEOUS CONTENTS OF STORAGE WAREHOUSES Material Pounds cubic foot of space Height of pile, feet Pounds per square foot of floor Recommended live loads, pounds per square foot Produce, Grain, Fruit, Etc. Grain, in bulk Barley and corn 37 8 296 * Oats 26 8 208 Rye and wheat 48 8 384 Fruit and vegetables, in bulk Apples, pears, etc . . . 38 8 304 Potatoes, turnips, etc Miscellaneous produce, packed Beans, in bags .... 44 40 8 8 352 320 Corn, in bags 31 8 248 250 to 300 Cornmeal, in barrels 37 26 6H 240 234 Rice, in bags Wheat, in bags 58 39 5 8 290 312 Wheat flour, in barrels Hay, in bales, not compressed Hay, in bales, compressed Straw, in bales, compressed Groceries Miscellaneous articles, packed 40 14 24 19 7 9 9 9 280 126 216 171 Butter, lard, etc., in carrels Canned goods, preserves, etc., in cases. . Cheese 32 58 30 6 6 8 '-- 192 348 240 Coffee, green, in bags 39 8 312 Coffee, roasted, in bags 33 8 264 Dates and figs, in cases, average Meat, beef, pork* etc., in barrels Molasses, in barrels Salt, finely ground in sacks 65 37 48 60 5 5 5 5 325 185 240 300 250 to 300 Soap powder, in cases Starch, in barrels 38 25 8 7 288 175 Sugar, in barrels 43 5 215 Tea, in chests Wines, liquors, etc., in barrels Dry Goods, Cotton, Wool, Etc. Cotton, in bales, compressed, average. . . . Cotton, unbleached goods, in bales Cotton, tickings and duck, in bales Cotton, printed goods, in bales 25 48 25 24 35 19 8 5 9 9 8 9 200 240 225 216 280 171 Cotton, printed goods, in cases Cotton, quilts and flannels, in cases 31 16 8 9 248 144 Cotton, yarn, in cases Hemp, in bales, compressed Hemp, manila, in bales, compressed Hemp, sisal, in bales, compressed Hemp, tow, in bales, compressed. Hemp, burlaps, in bales, compressed 25 22 26 24 29 43 41 8 8 9 9 9 6 6 200 176 234 216 261 258 246 200 to 250 Linen, bleached goods, in cases 35 7 245 Linen, damask goods, in cases . . 50 5 250 Wool, in bales, not compressed 13 9 117 Wool, in bales, compressed Wool, dress goods, flannels, in cases Wool, worsted goods, in cases 48 18 27 5 9 9 240 162 243 19 9 171 Excelsior, in bales, compressed 19 9 171 240 TABLE 63 MISCELLANEOUS CONTENTS OF STORAGE WAREHOUSES Material Pounds per cubic foot of space Height of pile, feet Pounds per square foot of floor Recommended live loads, pounds per square foot Drugs, Oils, Paints, Etc. Chemicals: Acids, muriatic and nitric, in carboys. . . Acids, sulphuric, in carbovs. . . 45 60 m 75 100 Ammonia, in carboys . . 30 1?1 50 Alum, pearl alum, in barrels Bleaching powder, in hogsheads Copper sulphate, blue vitriol, in bbls. . . Soda, caustic soda, in iron drums Soda, soda ash, in hogsheads 33 31 45 88 62 7 I* $ 231 103 225 294 170 Soda crystals, sal soda, in barrels Soda nitrate, niter, in barrels Soda silicate, in barrels 30 45 53 5 5 5 150 225 265 Zinc sulphate, white vitriol, in barrels . . Oils, fats, resins, etc.: Glycerine, in cases 40 52 5 6 200 312 Oils, animal, lard, etc., in barrels. . . 34 6 204 200 to 250 Oils, vegetable, linseed, in barrels Oils, mineral, lubricants, in barrels. . . . Oils, petroleum, kerosene, in barrels. . . . Oils, naphtha, gasolene, in barrels Rosin, in barrels 36 35 33 28 48 6 6 6 6 216 210 198 168 288 Shellac gum in boxes . . 38 & 228 Tallow, in barrels 37 g 222 Dye stuffs, paints, etc.: 43 6 258 Logwood extract, in boxes 70 4H 315 Sumac, in boxes 39 5 195 Red lead, litharge, dry, in barrels White lead, dry in barrels 132 86 3% 4% 495 409 White lead, paste, in cans Building Materials Cement, natural, in barrels 174 59 3>I 6 609 354 ) Cement, Portland, in barrels Lime, quick lime, ground, in barrels. . . . 73 50 6 5 438 250 300 to 400 Plaster of Paris, ground, in barrels. . 53 5 265 1 Sheet Metal and Wire Sheet tin, in boxes 278 1 LZ 417 Wire, insulated copper, in coils 63 5 315 Wire, galvanized iron in coils 74 414 333 300 to 400 Wire, magnet wire, on spools. . . . 75 g 450 Miscellaneous Chinawarc, glassware, in crates 40 g 320 Chinaware, glassware, in casks ..... 14 g 126 Glass, in boxes 69 g 360 Hardware, door and sash checks, in cases. Hardware, hinges, in cases. .'.. 46 64 6 g 276 384 Hardware, locks, in cases 31 6 186 Hardware, screws, in boxes Hides, raw, not compressed, in bales Hides, raw, conipressed, in bales Leather in bales 101 13 23 16 4 10 10 10 404 130 230 160 300 to 400 Paper, calendered paper \ Paper, newspaper, manila, strawboards. . . Paper writing paper 50 35 64 6 6 g 300 210 384 Rope in coils 42 g 252 241 MISCELLANEOUS TABLE 54 WEIGHTS OF BUILDING MATERIALS Kind Weight in Ib. per sq. ft. FLOORS . maple finish floor and %-in. spruce under floor on 2 X 4-in. sleepers, 16-in. centers, with 2-in. dry cinder concrete filling Cinder concrete filling per inch of thickness Cement finish per inch of thickness Asphalt mastic flooring IJ-^ in. thick 3-in. creosoted wood blocks on H-in. mortar base Solid flat tile on 1-in. mortar bed CEILINGS Plaster on tile or concrete Suspended metal lath and plaster ROOFS Five-ply felt and gravel Four-ply felt and gravel Three-ply ready roofing Cement tile Slate, \i in. thick Sheathing, 1 in. thick, yellow pine 2-in. book tile 3-in. book tile Skylight with galvanized iron frame, 2s~i n - glass 18 7 12 18 21 1 16 J* 12 20 Kind Weight in Ib. per sq. ft. Unplastered One side plastered Both sides plastered WALLS 9-in. brick wall 84 121 168 205 243 60 75 102 33 45 17 18 25 31 35 10 12 14 16 89 126 173 210 248 65 80 107 38 50 22 23 30 36 40 15 17 19 21 43 55 27 28 35 41 45 20 22 24 26 20 32 22 13-in. brick wall 18-in. brick wall 22-in. brick wall 26-in. brick wall 4-in brick 4-in tile backing 4-in. brick, 8-in. tile backing 9-in. brick, 4-in. tile backing 8-in. tile 12-in. tile PARTITIONS 3-in. clay tile 4-in. clay tile 6-in. clay tile 8-in. clay tile 10-in. clay tile. 3-in. gypsum block 4-in. gypsum block 6-in. gypsum block 2-in. solid plaster 4-in. solid plaster 4-in. hollow plaster Kind Weight in Ib. per cu. ft. Kind Weight in Ib. per cu. ft. Beech Birch Brickwork Concrete, cinder, structural 42 42 120 108 Limestone Maple Marble Oak 150 42 168 48 Concrete, cinder, floor filling Concrete, stone Concrete, stone, reinforced Douglas fir . 96 144 150 36 Pine, southern yellow Sandstone Spruce 42 144 30 Granite Granolithic surface 168 144 unfilled 72 120 242 APPENDIX RULINGS PERTAINING TO DESIGN AND WORKING STRESSES Joint Committee Recommendations* Design Massive Concrete. In the design of massive or plain concrete, no account should be taken of the tensile strength of the material, and sections should usually be proportioned so as to avoid tensile stresses except in slight amounts to resist indirect stresses. This will generally be accomplished in the case of rectangular shapes if the line of pressure is kept within the middle third of the section, but in very large structures, such as high masonry dams, a more exact analysis may be required. Structures of massive concrete are able to resist unbalanced lateral forces by reason of their weight; hence the element of weight rather than strength often determines the design. A leaner and relatively cheap concrete, therefore, will often be suitable for massive concrete structures. It is desirable generally to provide joints at intervals to localize the effect of contraction. Massive concrete is suitable for dams, retaining walls, and piers in which the ratio of length to least width is relatively small. Under ordinary conditions this ratio should not exceed four. It is also suitable for arches of moderate span. Reinforced Concrete. The use of metal reinforcement is particularly advantageous in members such as beams in which both tension and compression exist, and in columns where the principal stresses are compressive and where there also may be cross-bending. Therefore, the theory of design here presented relates mainly to the analysis of beams and columns. General Assumptions, (a) Loads. The forces to be resisted are those due to: 1. The dead load, which includes the weight of the structure and fixed loads and forces. 2. The live load, or the loads and forces which are variable. The dynamic effect of the live load will often require consideration. Allowance for the lattter is preferably made by a proportionate increase in either the live load or the live load stresses. The working stresses hereinafter recommended are intended to apply to the equivalent static stresses thus determined. In the case of high buildings the live load on columns may be reduced in accordance with the usual practice. (6) Lengths of Beams and Columns. The span length for beams and slabs simply supported should be taken as the distance from center to center of supports, but need not be taken to exceed the clear span plus the depth of beam or slab. For continuous or restrained beams built monolithically into supports the span length may be taken as the clear distance between faces of supports. Brackets should not be considered as reducing the clear span in the sense here intended, except that when brackets which make an angle of 45 degrees or more with the axis of a restrained beam are built monolithically with the beam, the span may be measured from the section where the combined depth of beam and bracket is at least one-third more than the depth of the beam." Maximum negative moments are to be considered as existing at the end of the span as here defined. When the depth of a restrained beam is greater at its ends than at midspan and the slope of the bottom of the beam at its ends makes an angle of not more than 15 degress with the direction of the axis of the beam at midspan, the span length may be measured from face to face of supports. The length of columns should be taken as the maximum unstayed length. (c) Stresses. The following assumptions are recommended as a basis for calculations: 1. Calculations will be made with reference to working stresses and safe loads rather than with reference to ultimate strength and ultimate loads. 2. A plane section before bending remains plane after bending. * From Final Report of the Special Committee on Concrete and Reinforced Concrete of the Ameri- can Society of Civil Engineers, presented before the Society, Jan. 17, 1917. 243 3. The modulus of elasticity of concrete in compression is constant within the usual limits of working stresses. The distribution of comprefisive stress inbeams is, therefore, rectilinear. 4. In calculating the moment of resistance of beams the tensile stresses in the concrete are neglected. 5. The adhesion between the concrete and the reinforcement is perfect. Under compressive stress the two materials are, therefore, stressed in proportion to their moduli of elasticity. 6. The ratio of the modulus of elasticity of steel to the modulus of elasticity of concrete is taken at 15, except as modified in section on "Working Stresses." 7. Initial stress in the reinforcement due to contraction or expansion of the concrete is neglected. It is recognized that some of the assumptions given herein are not entirely borne out by experimental data. They are given in the interest of simplicity and uniformity, and variations from exact conditions are taken into account in the selection of formulas and working stresses. The deflection of a beam depends upon the strength and stiffness developed throughout its length. For calculating deflection a value of 8 for the ratio of the moduli will give results corresponding approximately with the actual conditions. T-Beams. In beam and slab construction an effective bond should be provided at the junction of the beam and slab. When the principal slab reinforcement is parallel to the beam, transverse reinforcement should be used extending over the beam and well into the slab. The slab may be considered an integral part of the beam, when adequate bond and shearing resistance between slab and web of beam is provided, but its effective width shall be determined by the following rules: (a) It shall not exceed one-fourth of the span length of the beam. (6) Its overhanging width on either side of the web shall not exceed six times the thickness of the slab. In the design of continuous T-beams, due consideration should be given to the com- pressive stress at the support. Beams in which the T-form is used only for the purpose of providing additional com- pression area of concrete should preferably have a width of flange not more than three times the width of the stem and a thickness of flange not less than one-third of the depth of the beam. Both in this form and in the beam and slab form the web stresses and the limitations in placing and spacing the longitudinal reinforcement will probably be control- ling factors in design. Floor Slabs Supported Along Four Sides. Floor slabs having the supports extending along the four sides should be designed and reinforced as continuous over the supports. If -the length of the slab exceeds 1.5 times its width the entire load should be carried by transverse reinforcement. For uniformly distributed loads on square slabs, one-half the live and dead load may be used in the calculations of moment to be resisted in each direction. For oblong slabs, the length of which is not greater than one and one-half times their width, the moment to be resisted by the transverse reinforcement may be found by using a proportion of the live and dead load equal to that given by the formula r = r 0.5, where I = length and b = breadth of slab. TJie longitudinal reinforcement should then be proportioned to carry the remainder of the load. In placing reinforcement in such slabs account may well be taken of the fact that the bending moment is greater near the center of the slab than near the edges. For this purpose two-thirds of the previously calculated moments may be assumed as carried by the center half of the slab and one-third by the outside quarters. Loads carried to beams by slabs which are reinforced in two directions will not be uniformly distributed to the supporting beams and the distribution will depend on the relative stiffness of the slab and the supporting beams. The distribution which may be expected ordinarily is a variation of the load in the beam in accordance with the ordinates of a parabola, having its vertex at the middle of the span. For any gn en design, the prob- able distribution shlould be ascertained and the moments in the beam calculated accordingly. Continuous Beams and Slabs. When the beam or slab is continuous over its supports, reinforcement should be fully provided at points of negative moment; and the stresses in concrete recommended in the section on "Working Stresses" should not be exceeded. In computing the positive and negative moments in beams and slabs? continuous over several supports, due to uniformly distributed loads, the following rules are recommended: (a) For floor slabs the bending moments at center and at support should be taken at jo" f r both dead and live loads, where w represents the load per linear unit and I the span length. 244 (6) For beams the bending moment at center and at support for interior spans should icl~ wl~ be taken at y^"' anc ^ f r en d spans it should be taken at -r/r for center and interior support, for both dead and live loads. (c) In the case of beams and slabs continuous for two spans only, with their ends re- strained, the bending moment both at the central support and near the middle of the span /2 should be taken at r-Tr* (d) At the ends of continuous beams the amount of negative moment which will be developed in the beam will depend on the condition of restraint or fixedness, and this will depend on the form of construction used. In the ordinary cases a moment of may 10 be taken; for small beams running into heavy columns this should be increased, but not to .wP exceed-- For spans of unusual length, or for spans of materially unequal length, more exact calculations should be made. Special consideration is also required in the case of con- centrated loads. Even if the center of the span is designed for a greater bending moment than is called for by (a) or (6), the negative moment at the support should not be taken as less than the values there given. Where beams are reinforced on the compression side, the steel may be assumed to carry its proportion of stress in accordance with the ratio of moduli of elasticity, as given in the section on "Working Stresses." Reinforcing bars for compression in beams should be straight and should be two diameters in the clear from the surface of the concrete. For the positive bending moment, such reinforcement should not exceed one per cent of the area of the concrete. In the case of cantile"\er and continuous beams, tensile and compressive reinforcement over supports should extend sufficiently beyond the support and beyond the point of inflection to develop the requisite bond strength. In construction made continuous over supports it is important that ample foundations should be provided; for unequal settlements are liable to produce unsightly, if not danger- ous cracks. This effect is more likely to occur in low structures. Girders, such as wall girders, which have beams framed into one side only, should be designed to resist torsional moment arising from the negative moment at the end of the beam. Bond Strength and Spacing of Reinforcement. Adequate bond strength should be provided. The formula hereinafter given for bond stresses in beams is for straight longitudinal bars. In beams in which a portion of the reinforcement is bent up near the end, the bond stress at places, in both the straight bars and the bent bars, will be consider- ably greater than for all the bars straight, and the stress at some point may be several times as much as that found by considering the stress to be uniformly distributed along the bar. In restrained and cantilever beams full tensile stress exists in the reinforcing bars at the point of support and the bars should be anchored in the support sufficiently to develop this stress. In case of anchorage of bars, an additional length of bar should be provided beyond that found on the assumption of uniform bond stress, for the reason that before the bond resistance at the end of the bar can be developed the bar may have begun to slip at another point and "running" resistance is less than the resistance before slip begins. Where high bond resistance is required, the deformed bar is a suitable means of supply- ing the necessary strength. But it should be recognized that even with a deformed bar initial slip occurs at early loads, and that the ultimate loads obtained in the usual tests for bond resistance may be misleading. Adequate bond strength throughout the length of a bar is preferable to end anchorage, but, as an additional safeguard, such anchorage may properly be used in special cases. Anchorage furnished by short bends at a right angle is less effective than by hooks consisting of turns through 180 degrees. The lateral spacing of parallel bars should be not less than three diameters from center to center, nor should the distance from the side of the beam to the center of the nearest bar be less than two diameters. The clear spacing between two layers of bars should be not less than one inch. The use of more than two layers is not recommended, unless the layers are tied together by adequate metal connections, particularly at and near points where bars are bent up or bent down. Where more than one layer is used, at least all bars above the lower layer should be bent up and anchored beyond the edge of the support. Diagonal Tension and Shear. When a reinforced concrete beam is subjected to flexural action, diagonal tensile stresses are set up. A beam without web reinforcement will fail if these stresses exceed the tensile strength of the concrete. When web reinforcement, made up of stirrups or of diagonal bars secured to the longitudinal reinforcement, or of longitudinal reinforcing bars bent up at several points, is used, new conditions prevail, but 245 even in this case at the beginning of loading the diagonal tension developed is taken princi- pally by the concrete, the deformations which are developed in the concrete permitting but little stress to be taken by the web reinforcement. When the resistance of the concrete to the diagonal tension is overcome at any point in the depth of the beam, greater stress is at once set up in the web reinforcement. For homogeneous beams the analytical treatment of diagonal tension is not very complex, the diagonal tensile stress is a function of the horizontal and vertical shear- ing stresses and of the horizontal tensile stress at the point considered, an as the intensity of these three stresses varies from the neutral axis to the remotest fibre, the intensity of the diagonal tension will be different at different points in the section, and will change with different proportionate dimensions of length to depth of beam. For the composite structure of reinforced concrete beams, an analysis of the web stresses, and particularly of the diagonal tensile stresses, is very complex; and when the variations due to a change from no horizontal tensile stress in the concrete at remotest fibre to the presence of hori- zontal tensile stress at some point below the neutral axis are considered, the problem becomes more complex and indefinite. Under these circumstances, in designing recourse is had to the use of the calculated vertical shearing stress as a means of comparing or measuring the diagonal tensile stresses developed, it being understood that the vertical shearing stress is not the numerical equivalent of the diagonal tensile stress, and that there is not even a constant ratio between them. It is here recommended that the maximum vertical shearing stress in a section be used as the means of comparison of the resistance to diagonal tensile stress developed in the concrete in beams not having web reinforcement. Even after the concrete has reached its limit of resistance to diagonal tension, if the beam has web reinforcement, conditions of beam action will continue to prevail, at least through the compression area, and the web reinforcement will be called on to resist only a part of the web stresses. From experiments with beams it is concluded that it is safe practice to use only two-thirds of the external vertical shear in making calculations of the stresses that come on stirrups, diagonal web pieces, and bent-up bars, and it is here recommended for calculations in designing that two-thirds of the external vertical shear be taken as producing stresses in web reinforcement. It is well established that vertical members attached to or looped about horizontal members, inclined members secured to horizontal members in such a way as to insure against slip, and the bending of a part of the longitudinal reinforcement at an angle, will increase the strength of a beam against failure by diagonal tension, and that a well- designed and well-distributed web reinforcement may under the best conditions increase the total vertical shear carried to a value as much as three times that obtained when the bars are all horizontal and no web reinforcement is used. When web reinforcement comes into action as the principal tension web resistance, the bond stresses between the longitudinal bars and the concrete are not distributed as uniformly along the bars as they otherwise would be, but tend to be concentrated at and near stirrups, and at and near the points where bars are bent up. When stirrups are not rigidly attached to the longitudinal bars, and the proportioning of bars and stirrups spacing is such that local slip of bars occurs at stirrups, the effectiveness of the stirrups is impaired, though the presence of stirrups still gives an element of toughness against diagonal tension failure. Sufficient bond resistance 'between the concrete and the stirrups or diagonals must be provided in the compressing area of the beam/ The longitudinal spacing of vertical stirrups should not exceed one-half the depth of beam, and that of inclined members should not exceed three-fourths of the depth ef beam. Bending of longitudinal reinforcing bars at an angle across the web of the beam may be considered as adding to diagonal tension resistance for a horizontal distance from the point of bending equal to three-fourths of the depth of beam. Where the bending is made at two or more points, the distance between points of bending should not exceed three- fourths of the depth of the beam. In the case of a restrained beam the effect of bending up a bar at the bottom of the beam in resisting diagonal tension may not be taken as extending beyond a section at the point of inflection, and the effect of bending down a bar in the region of negative moment may be taken as extending from the point of bending down of bar nearest the support to a section not more than three-fourths of the depth of beam beyond the point of bending down of bar farthest from the support but not beyond the point of inflection. In case stirrups are used in the beam away from the region in which the bent bars are considered effective, a stirrup should be placed not farther than a distance equal to one-fourth the depth of beam from the limiting sections defined above. In case the web resistance required through the region of bent bars is greater than that furnished by the bent bars, sufficient additional web reinforcement in the form of stirrups or attached diagonals should be provided. The higher resistance to diagonal tension stresses given by unit frames having the stirrups and bent-up bars securely connected together both longi- tudinally and laterally is worthy of recognition. It is necessary that a limit be placed 246 on the amount of shear which may be allowed in a beam; for when web reinforcement sufficiently efficient to give very high web resistance is used, at the higher stresses the concrete in the beam becomes checked and cracked in such a way as to endanger its dura- bility as well as its strength. The section to be taken as the critical section in the calculation of shearing stresses will generally be the one having the maximum vertical shear, though experiments show that the section at which diagonal tension failures occur is not just at a support even though the shear at the latter point be much greater. In the case of restrained beams, the first stirrup or the point of bending down of bar should be placed not farther than one-half of the depth of beam away from the face of the support. It is important that adequate bond strength or anchorage be provided to develop fully the assumed strength of all web reinforcement. Low bond stresses in the longitudinal bars are helpful in giving resistance against diagonal tension failures and anchorage of longitudinal bars at the ends of the beams or in the supports is advantageous. It should be noted that it is on the tension side of a beam that diagonal tension develops in a critical way, and that proper connection should always be made between stirrups or other web reinforcement and the longitudinal tension reinforcement, whether the latter is on the lower side of the beam or on its upper side. Where negative moment exists, as is the case near the supports in a continuous beam, web reinforcement to be effective must be looped over or wrapped around or be connected with the longitudinal tension reinforcing bars at the top of the beam in the same way as is necessary at the bottom of the beam at sections where the bending moment is positive. Inasmuch as the smaller the longitudinal deformations in the horizontal reinforce- ment are, the less the tendency for the formation of diagonal cracks, a beam will be strength- ened against diagonal tension failure by so arranging and proportioning the horizontal reinforcement that the unit stresses at points of large shear shall be relatively low. It does not seem feasible to make a complete analysis of the action of web reinforce- ment, and more or less empirical methods of calculation are therefore employed. Limiting values of working stresses for different types of web reinforcement are given in the section on "Working Stresses." The conditions apply to cases commonly met in design. It is assumed that adequate bond resistance or anchorage of all web reinforcement will be provided. When a flat slab rests on a column, or a column bears on a footing, the vertical shearing stresses in the slab or footing immediately adjacent to the column are termed punching shearing stresses. The element of diagonal tension, being a function of the bending moment as well as of shear, may be small in such cases, or may be otherwise provided for. For this reason the permissible limit of stress for punching shear may be higher than the allowable limit when the shearing stress is used as a means of comparing diagonal tensile stress. The working values recommended are given in the section on "Working Stresses." Columns. By columns are meant compression members of which the ratio of unsup- ported length to least width exceeds about four, and which are provided with reinforcement of one of the forms hereafter described. It is recommended that the ratio of unsupported length of column to its least width be limited to fifteen. The effective area of hooped columns or columns reinforced with structural shapes shall be taken as the area within the circle enclosing the spiral or the polygon enclosing the structural shapes. Columns may be reinforced by longitudinal bars; by bands, hoops, or spirals, together with longitudinal bars; or by structural forms which are sufficiently rigid to have value in themselves as columns. The general effect of closely spaced hooping is to greatly increase the toughness of the column and to add to its ultimate strength, but hooping has little effect on its behavior within the limit of elasticity. It thus renders the concrete a safer and more reliable material, and should permit the use of a somewhat higher working stress. The beneficial effects of toughening are adequately provided by a moderate amount of hooping, a larger amount serving mainly to increase the ultimate strength and the deforma- tion possible before ultimate failure. Composite, columns of structural steel and concrete in which the steel forms a column by itself should be designed with caution. To classify this type as a concrete column reinforced with structural steel is hardly permissible, as the steel, generally, will take the greater part of the load. When this type of column is used, the concrete should be adequately tied together by tie plates or lattice bars, which, together with other details, such as splices, etc., should be designed in conformity with standard practice for structural steel. The concrete may exert a beneficial effect in restraining the steel from lateral deflection and also in increasing the carrying capacity of the column. The proportion of load to be carried by the concrete will depend on the form of the column and the method of 247 construction. Generally, for high percentages of steel, the concrete will develop relatively low unit stresses, and caution should be used in placing dependence on the concrete. The following recommendations are made for the relative working stresses in the concrete for the several types of columns: (a) Columns with longitudinal reinforcement to the extent of not less than 1 per cent and not more than 4 per cent, and with lateral ties of not less than 34 inch in diameter 12 inches apart, nor more than 16 diameters of the longitudinal bar: the unit stress rec- ommended for axial compression, on concrete piers having a length not more than four diameters, in section on "Working Stresses." (6) Columns reinforced with not less than 1 per cent and not more than 4 per cent of longitudinal bars and with circular hoops or spirals not less than 1 per cent of the volume of the concrete and as hereinafter specified : a unit stress 55 per cent higher than given for (a), provided the ratio of unsupported length of column to diameter of the hooped core is not more than 10. The foregoing recommendations are based on the following conditions: It is recommended that the minimum size of columns to which the working stresses may be applied be 12 inches out to out. In all cases longitudinal reinforcement is assumed to carry its proportion of stress in accordance with (c) Stresses, page 243. The hoops or bands are not to be counted on directly as adding to the strength of the column. Longitudinal reinforcement bars should be maintained straight, and should have suffi- cient lateral support to be securely held in place until the concrete has set. Where hooping is used, the total amount of such reinforcement shall be not less than 1 per cent of the volume of the column, enclosed. The clear spacing of such hooping shall not be greater than one-sixth the diameter of the enclosed column and preferably not greater than one- tenth, and in no case more than 2% in. Hooping is to be circular and the ends of bands must be united in such a way as to develop their full strength. Adequate means must be provided to hold bands or hoops in place so as to form a column, the core of which shall be straight and well centered. The strength of hooped columns depends very much upon the ratio of length to diameter of hooped core, and the strength due to hooping decreases rapidly as this ratio increases beyond five. The working stresses recommended are for hooped columns with a length of not more than ten diameters of the hooped core. The Committee has no recommendation to make for a formula for working stresses for columns longer than ten diameters. Bending stresses due to eccentric loads, such as unequal spans of beams, and to lateral forces, must be provided for by increasing the section until the maximum stress does not exceed the values above specified. Where tension is possible in the longitudinal bars of the columns, adequate connection between the ends of the bars must be provided to take this tension. Reinforcing for Shrinkage and Temperature Stresses. When areas of concrete too large to expand and contract freely as a whole are exposed to atmospheric conditions, the changes of form due to shrinkage and to action of temperature are such that cr cks may occur in the mass unless precautions are taken to distribute the stresses so as to prevent the cracks altogether or to render them very small. The distance apart of the cracks, and consequently their size, will be directly proportional to the diameter of the reinforcement and to the tensile strength of the concrete, and inversely proportional to the percentage of reinforcement and also to its bond resistance per unit of surface area. To be most effective, therefore, reinforcement (in amount generally not less than one-third of 1 per cent of the gross area) of a form which \vill develop a high bond resistance should be placed near the exposed surface and be well distributed. Where openings occur the area of cross-section of the reinforcement should not be reduced. The allowable size and spacing of cracks depends on various considerations, such as the necessity for water-tightness, the importance of appearance of the surface, and the atmospheric changes. The tendency of concrete to shrink makes it necessary, except where expansion is - provided for, to thoroughly connect the component parts of the frame of articulated structures, such as floor and wall members in buildings, by the use of suitable reinforcing material. The amount of reinforcement for such connection should bear some relation to the size of the members connected, larger and heavier members requiring stronger connec- tions. The reinforcing bars should be extended beyond the critical section far enough, or should be sufficiently anchored to develop their full tensile strength. Flat Slab. The continuous flat slab reinforced in two or more directions and built monolithically with the supporting columns (without beams or girders) is a type of construc- tion which is now extensively used and which has recognized advantages for certain types of structures as, for example, warehouses in which large, open floor space is desired. In its construction, there is excellent opportunity for inspecting the position of the re- inforcement, The conditions attending deposition and placing of concrete are favorable to 24S securing uniformity and soundness in the concrete. The recommendations in the following paragraphs relate to flat slabs extending over several rows of panels in 'each direction. Necessarily the treatment is more or less empirical. The co-efficients and moments given relate to uniformly distributed loads. (a) Column Capital. It is usual in flat slab construction to enlarge the supporting columns at their top, thus forming column capitals. The size and shape of the column capital affect the strength of the structure in several ways. The moment of the external forces which the slab is called upon to resist is dependent upon the size of the capital; the section of the slab immediately above the upper periphery of the capital carries the highest amount of punching shear; and the bending moment developed in the column by an eccentric or unbalanced loading of the slab is greatest at the under surface of the slab. Generally the horizontal section of the column capital should be round or square with rounded corners. In oblong panels the section may be oval or oblong, with dimensions proportional to the panel dimensions. For computation purposes, the diameter of the column capital will be considered to be measured where its vertical thickness is at least lj^ inches, provided the slope of the capital below this point nowhere makes an angle with the vertical of more than 45 degrees. In case a cap is placed above the column capital, the part of this cap within a cone made by extending the lines of the column capital upward at the slope of 45 degrees to the bottom of the slab or dropped panel may be considered as part of the column capital in determining the diameter for design purposes. Without attempting to limit the size of the column capital for special cases, it is recommended that the diameter of the column capital (or its dimensions parallel to the edge of the panel) generally be made not less than one-fifth of the dimension of the panel from center to center of adjacent columns. A diameter equal to 0.225 of the panel length has been used quite widely and acceptably. For heavy loads or large panels especial attention should be given to designing and reinforcing the column capital with respect to compressive stresses and bending moments. In the case of heavy loads or large panels, and where the conditions of the panel loading or variations in panel length or other conditions cause high bending stresses in the column, and also for column capitals smaller than the size herein recom- mended, especial attention should be given to designing and reinforcing the column capital with respect to compression and to rigidity of connection to floor slab. (6) Dropped Panel. In one type of construction the slab is thickened throughout an area surrounding the column capital. The square or oblong of thickened slab thus formed is called a dropped panel or a drop. The thickness and the width of the dropped panel may be governed by the amount of resisting moment to be provided (the com- pressive stress in the concrete being dependent upon both thickness and width), or its thickness may be governed by the resistance to shear required at the edge of the column capital and its width by the allowable compressive stresses and shearing stresses in the thinner portion of the slab adjacent to the dropped panel. Generally, however, it is recommended that the width of the dropped panel be at least four-tenths of the correspond- ing side of the panel as measureU from center to center of columns, and that the offset in thickness be not more than five- tenths of the thickness of the slab outside the dropped panel. (c) Slab Thickness. In the design of a slab, the resistance to bending and to shear- ing forces will largely govern the thickness, and, in the case of large panels with light loads, resistance to deflection may be a controlling factor. The following formulas for minimum thicknesses are recommended as general rules of design when the diameter of the column capital is not less than one^fifth of the dimension of the panel from center to center of adjacent columns, the large dimension being used in the case of oblong panels. For notation, let t = total thickness of slab in inches. L = panel length in feet. w = sum of live load and dead load in pounds per square foot. Then, for a slab without dropped panels, minimum t = 0.024L\/w -f 1^; for a slab with dropped panels, minimum I = Q.Q2L'vw + 1; for a dropped panel whose width is four- tenths of the panel length, minimum t = 0.03L\A0 + lM- In no case should the slab thickness be made less than six inches, nor should the thick- ness of a floor slab be made less than one-thirty-second of the panel length, nor the thick- ness of a roof slab less than one-fortieth of the panel length. (d) Bending and Resisting Moments in Slabs. If a vertical section of a slab be taken across a panel along a line midway between columns, and if another section be taken along an edge of the panel parallel to the first section, but skirting the part of the periphery of the column capitals at the two corners of the panels, the moment of the couple formed by the external load on the half panel, exclusive of that over the column capital (sum of dead and live load) and the resultant of the external shear or reaction at the support at the 249 two column capitals (see Fig. 1), may be found by ordinary static analysis. It will be noted that the edges of the area here considered are along lines of zero shear except around the column capitals. This moment of the external forces acting on the half panel will be resisted by the numerical sum of (a) the moment of the internal stresses at the section of the panel midway between columns (positive resisting moment) and (b) the moment of the internal stresses at the section referred to at the end of the panel (negative resisting moment). In the curved portion of the end section (that skirting the column), the stresses considered are the components which act parallel to the normal stresses on the straight portion of the section. Analysis shows that, for a uniformly distributed load, and round peripheries of -fin column caprta/s ...7 section section FIG. 1. FIG. 2. columns, and square panels, the numerical sum of the positive moment and the negative moment at the two sections named is given quite closely by the equation In this formula and in those which follow relating to oblong panels: w = sum of the live and dead load per unit of area. I = side of a square panel measured from center to center of columns. h = one side of the oblong panel measured from center to center of columns. fa = other side of oblong panel measured in the same way. c = diameter of the column capital. M x = numerical sum of positive moment and negative moment in one direction. My = numerical sum of positive moment and negative moment in the other direction. (See paper and closure, Statical Limitations upon the Steel Requirement in Reinforced Concrete Flat Slab Floors, by John R. Nichols, Jun. Am. Soc. C. E., Transactions Am. Soc. C. E. Vol. LXXVII.) For oblong panels, the equations for the numerical sums of the positive moment arid the negative moment at the two sections named become -! *(,.-!)' Where M x is the numerical sum of the positive moment and the negative moment for the sections parallel to the dimensions fa, and M y is the numerical sum of the positive moment and the negative moment for the sections parallel to the dimensions h. What proportion of the total resistance exists as positive moment and what as negative moment is not readily determined. The amount of the positive moment and that of the negative moment may be expected to vary somewhat with the design of the slab. It seems proper, however, to make the division of total resisting moment in the ratio of three-eighths for the positive moment to five-eighths for the negative moment. With reference to variations in stress along the sections, it is evident from condi- tions of flexure that the resisting moment is not distributed uniformly along either the section of positive moment or that of negative moment. As the law of the distribution is not known definitely, it will be necessary to make an empirical apportionment along the sections; and it will be considered sufficiently accurate generally to divide the sections into two parts and to use an average value over each part of the panel section. The relatively largebreadth of structure in a flat slab makes the effect of local variations in the concrete less than would be the case for narrow members like beams. The tensile resistance of the concrete is less affected by cracks. Measurements of deformations in 250 buildings under heavy load indicate the presence of considerable tensile resistance in the concrete, and the presence of this tensile resistance acts to decrease the intensity of the compressive stresses. It is believed that the use of moment coefficients somewhat less than those given in a preceding paragraph as derived by analysis is warranted, the calcula- tions of resisting moment and stresses in concrete and reinforcement being made according to the assumptions specified in this report and no change being made in the values of the working stresses ordinarily used. Accordingly, the values of the moments which are recommended for use are somewhat less than those derived by analysis. The values given may be used when the column capitals are round, oval, square or oblong. (e) Names for Moment Sections. For convenience, that portion of the section across a panel along a line midway between columns which lies within the middle two quarters of the width of the panel (HI, Fig. 2), will be called the inner section, and that portion in the two outer quarters of the width of the panel (GH and IJ, Fig. 2) will be called the outer sections. Of the section which follows a panel edge from column capital to column capital and which includes the quarter peripheries of the edges of two column capitals, that portion within the middle two quarters of the panel width (CD, Fig. 2) will be called the mid- section, and the two remaining portions (ABC and DEF, Fig. 2), each having a projected width equal to one-fourth of the panel width, will be called the column-head sections. (/) Positive Moment. For a square interior panel, it is recommended that the positive moment for a section in the middle of a panel extending across its width be taken as wl[ I TT ) . Of this moment, at least 25 per cent should be provided for in the 25 \ 6 / inner section; in the two outer sections of the panel at least 55 per cent of the specified moment should be provided for in slabs not having dropped panels, and at least 60 per cent in slabs having dropped panels, except that in calculations to determine necessary thickness of slab away from the dropped panel at least 70 per cent of the positive moment should be considered as acting in the two outer sections. (Q) Negative Moment. For a square interior panel, it is recommended that the negative moment for a section \\ hich follows a panel edge from column capital to column capital and which includes the quarter peripheries of the edges of the two column capitals (the section 1 / 2c\ 2 altogether forming the projected width of the panel) be taken as u-ll I- \ . Of this negative moment, at least 20 per cent should be provided for in the mid-section and at least 65 per cent in the two column-head sections of the panel, except that in slabs having dropped panels at least 80 per cent of the specified negative moment should be provided for in the two column-head sections of the panel. (h) Moments for Oblong Panels. When the length of a panel does not exceed the breadth by more than 5 per cent, computation may be made on the basis of a square panel with sides equal to the mean of the length and the breadth. When the long side of an interior oblong panel exceeds the short side by more than one-twentieth and by not more than one-third of the short side, it is recommended that the positive moment be taken as wlz l/i 5- J on a section parallel to the dimension h, and wl\ (h TT ) on a section parallel to dimension Zi; and that the negative moment 25 V / be taken as - wh [h ^ ) on a section at the edge of the panel corresponding to the 2c2 dimension h, and irli (h ^ 1 at a section in the other direction. The limitations of the apportionment of moment between inner section and outer section and between mid- section and column-head sections may be the same as for square panels. (t) Watt Panels. The coefficient of negative moment at the first row of columns away from the wall should be increased 20 per cent over that required for interior panels, and likewise the coefficient of positive moment at the section halfway to the wall should be increased by 20 per cent. If girders are not provided along the wall or the slab does not project as a cantilever beyond the column line, the reinforcement parallel to the wall for the negative moment in the column-head section and for the positive moment in the outer section should be increased by 20 per cent. If the wall is carried by the slab this concen- trated load should be provided for in the design of the slab. The coefficient of negative moments at the wall to take bending in the direction perpendicular to the wall line may be determined by the conditions of restraint and fixedness as found from the relative stiffness of columns and slab, but in no case should it be taken as less than one-half of that for interior panels. 0') Reinforcement. In the calculation of moments all the reinforcing bars which cross the section under consideration and which fulfill the requirements given under paragraph (I) of this chapter may be used. For a column-head section reinforcing bars parallel to the 251 straight portion of the section do not contribute to the negative resisting moment for the column-head section in question. In the case of four-way reinforcement the sectional area of the diagonal bars multiplied by the sine of the angle between the diagonal of the panel and straight portion of the section under consideration may be taken to act as reinforcement in a rectangular direction. (k) Point of Inflection. For the purpose of making calculations of moments at sections away from the sections of negative moment and positive moment already specified, the point of inflection on any line parallel to a panel edge may be taken as one-fifth of the clear distance on that line between the two sections of negative moment at the opposite ends of the panel indicated in paragraph (e), of this chapter. For slabs having dropped panels the coefficient of one-fourth should be used instead of one-fifth. (1) * Arrangement of Reinforcement. The design should include adequate provision for securing the reinforcement in place so as to take not only the maximum moments, but the moments at intermediate sections. All bars in rectangular bands or diagonal bands should extend on each side of a section of maximum moment, either positive or negative, to points at least twenty diameters beyond the point of inflection as defined herein or be hooked or anchored at the point of inflection. In addition to this provision bars in diagonal bands used as reinforcement for negative moment should extend on each side of a line drawn through the column center at right angles to the direction of the band at least a distance equal to thirty-five one-hundredths of the panel length, and bars in diagonal bands used as reinforcement for positive moment should extend on each side of a diagonal through the center of the panel at least a distance equal to thirty-five one-hundredths of the panel length; and no splice by lapping should be permitted at or near regions of maximum stress except as just described. Continuity of reinforcing bars is considered to have advantages, and it is recommended that not more than one-third of the reinforcing bars in any direction be made of a length less than the distance center to center of columns in that direction. Continuous bars should not all be bent up at the same point of their length, but the zone in which this bending occurs should extend on each side of the assumed point of inflection, and should cover a width of at least one-fifteenth of the panel length. Mere draping of the bars should not be permitted. In four-way reinforcement the position of the bars in both diagonal and rectangular directions may be considered in determining whether the width of zone of bending is sufficient. (ra) Reinforcement at Construction Joints. It is recommended that at construction joints extra reinforcing bars equal in section to 20 per cent of the amount necessary to meet the requirements for moments at the section where the joint is made be added to the reinforcement, these bars to extend not less than 50 diameters beyond the joint on each side. (n) Tensile and Compressive Stresses. The usual method of calculating the tensile and .compressive stresses in the concrete and in the reinforcement, based on the assump- tions for internal stresses given in this chapter, should be followed. In the case of the dropped panel the section of the slab and dropped panel may be considered to act integrally for a width equal to the width of the column-head section. (o) Provision for Diagonal Tension and Shear. In calculations for the shearing stress which is to be used as the means of measuring the resistance to diagonal tension stress, it is recommended that the total vertical shear on two column-head sections constituting a width equal to one- half the lateral dimensions of the panel, for use in the formula for deter- mining critical shearing stresses, be considered to be one-fourth of the total dead and live load on a panel for a slab of uniform thickness, and to be three-tenths of the sum of the dead and live loads on a panel for a slab with dropped panels. The formula for shearing unit stress may then be written v = for slabs of uniform thickness, and v = ' . bjd bjd for slabs with dropped panels, where W is the sum of the dead and live load on a panel, 6 is half the lateral dimension of the panel measured from center to center of columns, and jd is the lever arm of the resisting couple at the section. The calculation of what is commonly called punching shear may be made on the assump- tion of a uniform distribution over the section of the slab around the periphery of the column capital and also of a uniform distribution over the section of the slab around the periphery of the dropped panel, using in each case an amount of vertical shear greater by 25 per cent than the total vertical shear on the section under consideration. The values of working stresses should be those recommended for diagonal tension and shear in the section on "Working Stresses." (p) Walls and Openings. Girders or beams should be constructed to carry walls and other concentrated loads which are in excess of the working capacity of the lab. Beams should also be provided in case openings in the floor reduce the working strength of the slab below the required carrying capacity. (q) Unusual Panels. The coefficients, apportionments, and thicknesses recom- mended are for slabs which have several rows of panels in each direction, and in which 252 the size of the panels is approximately the same. For structures having a width of one, two, or three panels, and also for slabs having panels of markedly different sizes, an analysis should be made of the moments developed in both slab and columns, and the values given herein modified accordingly. Slabs with paneled ceiling or with depressed paneling in the floor are to be considered as coming under the recommendations herein given. (r) Bending Moments in Columns. Provision should be made in both wall columns and interior columns for the bending moment which will be developed by unequally loaded panels, eccentric loading, or uneven spacing of columns. The amount of moment to be taken by a column will depend upon the relative stiffness of columns and slab, and com- putations may be made by rational methods, such as the principal of least work, or of slope and deflection. Generally, the larger part of the unequalized negative moment will be transmitted to the columns, and the column should be designed to resist this bending moment. Especial attention should be given to wall columns .and corner columns. Working Stresses General Assumptions. The following working stresses are recommended for static loads. Proper allowances for vibration and impact are to be added to live loads where necessary to produce an equivalent static load before applying the unit stresses in propor- tioning parts. In selecting the permissible working stress on concrete, the designer should be guided by the working stresses usually allowed for other materials of construction, so that all structures of the same class composed of different materials may have approximately the same degree of safety. The following recommendations as to allowable stresses are given in the form of per- centages of the ultimate strength of the particular concrete which is to be used ; this ultimate strength is that developed at an age of twenty-eight days, in cylinders 8 inches in diameter and 16 inches long, of proper consistency* made and stored under laboratory conditions. In the absence of definite knowledge in advance of construction as to just what strength may be expected, the committee submits the following values as those which should be obtained with materials and workmanship in accordance with the recommendations of this report. Although occasional tests may show higher results than those here given, the Committee recommends that these values should be the maximum used in design. TABLE OF COMPRESSIVE STRENGTHS OF DIFFERENT MIXTURES OF CONCRETE (In Pounds per Square Inch) Aggregate Granite trap rock l:3t 3300 1 :4M t 2800 l:6f 2200 l:7Mt 1800 l:9t 1400 Gravel, hard limestone and hard sandstone . . Soft limestone and sandstone Cinders 3000 2200 800 2500 1800 700 2000 1500 600 1600 1200 500 1300 1000 400 . NOTE. For variations in the moduli of elasticity see 254. Bearing. When compression is applied to a surface of concrete of v at least twice the loaded area, a stress of 35 per cent of the compressive strength may be allowed in the area actually under load. Axial Compression. For concentric compression on a plain concrete pier, the length of.wnich does not exceed four diameters, or on a column reinforced with longitudinal bars only, the length of which does not exceed 12 diameters, 22.5 per cent of the compressive strength may be allowed. For other forms of columns the stresses obtained from the ratios given in the preceding section on " Design" may govern. . Compression in Extreme Fiber. The extreme fiber stress of a beam, calculated on the assumption of a constant modulus of elasticity for concrete under working stresses may be allowed to reach 32.5 per cent of the compressive strength. Adjacent to the support of continuous beams stresses 15 per cent higher may be used. Shear and Diagonal Tension. In calculations on beams in which the maximum shearing stress in a section is used as the means of measuring the resistance to diagonal tension stress, the following allowable values for the maximum vertical shearing stress in concrete, calculated by the method given in formula on page 4, v = J-TJ, are recommended: * The materials should be mixed wet enough to produce a concrete of such a consistency as will flow sluggishly into the forms and about the metal reinforcement, and which, at the same time, can be conveyed from the mixer to the forms without separation of the coarse aggregate from the mortar. The quantity of water is of the greatest importance in securing concrete of maximum strength and density; too much water is as objectionable as too little. t Combined volume fine and coarse aggregate measured separately. 253 (a) For beams with horizontal bars only and without web reinforcement, 2 per cent of the compressive strength. (6) For beams with web reinforcement consisting of vertical stirrups looped' about the longitudinal reinforcing bars in the tension side of the beam and spaced horizontally not more than one-half the depth of the beam; or for beams in which longitudinal bars are bent up at an angle of not more than 45 degrees or less than 20 degrees with the axis of the beam, and the points of bending are spaced horizontally not more than three-quarters of the depth of the beam apart, not to exceed 4)^ per cent of the compressive strength. (c) For a combination of bent bars and vertical stirrups looped about the reinforcing bars in the tension side of the beam and spaced horizontally not more than one-half of the depth of the beam, 5 per cent of the compressive strength. (d) For beams with web reinforcement (either vertical or inclined) securely attached to the longitudinal bars in the tension side of the beam in such a way as to prevent slipping of bar past the stirrup, and spaced horizontally not more than one-half of the depth of the beam in case of vertical stirrups and not more than three-fourths of the depth of the beam in the case of inclined members, either with longitudinal bars bent up or not, 6 per cent of the compressive strength. The web reinforcement in case any is used should be proportioned by using two-thirds of the external vertical shear in formulas (a) and (6) on page 4. The effect of longitu- dinal bars bent up at an angle of from 20 to 45 degrees with the axis of the beam may be taken at sections of the beam in which the bent up bars contribute to diagonal tension resistance (see "Diagonal Tension and Shear," page 245) as reducing the shearing stresses to be otherwise provided for. The amount of reduction of the shearing stress by means of bent up bars will depend upon their capacity, but in no case should be taken as greater than 4 % per cent of the compressive strength of the concrete over the effective cross-section of the beam.* The limit of tensile stress in the bent up por- tion of the bar calculated by formula (6) on page 4, using in this formula an amount of total shear corresponding to the reduction in shearing stress assumed for the bent up bars, may be taken as specified for the working stress of steel, but in the calculations the stress in the bar due to its part as longitudinal reinforcement of the beam should be considered. The stresses in stirrups and inclined members when combined with bent up bars are to be determined by finding the amount of the total shear which may be allowed by reason of the bent up bars, and subtracting this shear from the total external vertical shear. Two-thirds of the remainder will be the shear to be carried by the stirrups, using formulas (a) or (6) on page 4. Where punching shear occurs, provided the diagonal tension requirements are met, a shearing stress of 6 per cent of the compressive strength may be allowed. Bond. The bond stress between concrete and plain reinforcing bars may be assumed at 4 per cent of the compressive strength, or 2 per cent in the case of drawn wire. In the best types of deformed bar the bond stress may be increased, but not to exceed 5 per cent of the compressive strength of the concrete. Reinforcement. The tensile or compressive stress in steel should not exceed 16,000 pounds per square inch. In structural steel members the working stresses adopted by the American Railway Engineering Association are recommended. Modulus of Elasticity. The value of the modulus of elasticity of concrete has a wide range, depending on the materials used, the age, the range of stresses between which it is considered, as well as other conditions. It is recommended that in computations for the position of the neutral axis, and for the resisting moment of beams and for compression of concrete in columns, it be assumed as: (a) One-fortieth that of steel, when the strength of the concrete is taken as not more than 800 pounds per square inch. (6) One-fifteenth that of steel, when the strength of the concrete is taken as greater than 800 pounds per square inch. (c) One-twelfth that of steel, when the strength of the concrete is taken as greater than 2,200 pounds per square inch, and less than 2,900 pounds per square inch. (d) One-tenth that of steel, when the strength of the concrete is taken as greater than 2,900 pounds per square inch. Although not rigorously accurate, these assumptions will give safe results. For the deflection of beams which are free to move longitudinally at the supports, in using formulas for deflection which do not take into account the tensile strength developed in the concrete, a modulus of one-eighth of that of steel is recommended. 254 AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS* 1. Conditions. All reinforced-concrete construction shall be designed to meet the conditions of loading (including bending in columns) without stressing the materials used beyond the safe working stresses specified. 2. Dead-Loads. The dead-loads shall be the weight of the permanent structure. The weight of reinforced stone, gravel or slag concrete shall be taken as 144 Ib. per cu. ft.; the weight of cinder concrete as 100 Ib. per cu. ft. 3. Live-Loads. The live-load shall be the working or variable load for which the structure is designed. 4. Reduction of Loads. All parts of a structure shall be designed to carry safely the entire combined dead- and live-loads with the exception that the loads on columns and foundations may be reduced by considering that columns in top story carry the total live- and dead-load above them; columns in next to top story carry the total dead-load and eighty-five (85) per cent of the total live-load above; columns in the next lower story, the total dead-load and eighty (80) per cent of the total live-load above: and thus on downward reducing at each story the percentage of total live-loads carried, by 5, until a reduction of fifty (50) per cent is reached. The columns in this and in every story below this point shall be proportioned to carry the total dead-load and at least fifty (50) per cent of the total live-load of all the floors and roofs above them. For warehouses the increment of reduction per story shall be 2^ per cent instead of 5 per cent. 5. General Assumptions. As a basis for calculations for the strength of reinforced- concrete construction the following assumptions shall be made: (a) Calculations shall be made with reference to working stresses and safe loads rather than with reference to ultimate strength and ultimate loads. (6) A plane section before bending remains plane after bending. (c) The modulus of elasticity of concrete in compression within the usual limits of working stresses is constant. (d) In calculating the moment of resistance of beams, the tensile stresses in the concrete are neglected. (e) Perfect adhesion is assumed between concrete and reinforcement. Under compressive stresses the two materials will, therefore, be stressed in proportion to their moduli of elasticity. (/) The ratio of the modulus of elasticity of concrete shall be taken as follows : 1. One-fortieth that of steel when the strength of the concrete is taken as not more than eight hundred (800) Ib. per sq. in. 2 One-fifteenth that of steel when the strength of the concrete is taken as greater than twelve hundred (1200) Ib. per sq. in. or less than twenty-two hundred (2200) Ib. per sq. in. 3. One-twelfth that of steel when strength of the concrete is taken as greater than twenty- two hundred (2200) Ib. per sq. in. or less than thirty- three hundred (3300) Ib. per sq. in. 4. One-tenth that of steel when the strength of the concrete is taken as greater than thirty-three hundred (3300) Ib. per sq. in. 6. Strength of Materials. The ultimate strength of concrete shall be that developed at an age of 28 days, in cylinders 8 in. in diameter and 16 in. in length or 6 in. in diameter and 12 in. in length, of the consistency and proportions to be used in the work, made and stored under laboratory conditions, but in no case shall the values exceed those allowed in the table below. In the absence of definite knowledge in advance of construction as to just what strength may be developed, the following values may be used: * Passed by letter-ballot of the Institute, April 17, 1920. ' 255 TABLE OF STRENGTHS OF DIFFERENT MIXTURES Proportion of cement to aggregate Aggregate 1:3* 1:4> 2 * 1:6* 1:7^* 1:9* For stone, gravel or slag with water-cement ratiot of : 0.8 0.9 1.0 1.11 1.22 Strength of concrete 3000 2500 2000 1600 1300 Cinders SDO 700 600 500 400 7. Safe Working Stresses. Reinforced-concrete structures shall be so designed that the stresses, figured in accordance with these regulations, in pounds per square inch, shall not exceed the following: (a) Extreme fiber stress in concrete in compression 37^ per cent of the compressive strength specified in Section 6. Adjacent to the support of continuous members, 41 per cent provided the member frames into a mass of concrete projecting at least 50 per cent of the least dimension of the member on all sides of the compression area of the member. (6) Concrete in direct compression 25 per cent of the compressive strength specified in Section 6. (c) Shearing stress in concrete when main steel is not bent and when steel is not provided to resist diagonal tension, as specified in Section 10. (d) Where punching shear occurs, provided the diagonal tension requirements are met, a shearing stress as specified in Section 10 will be allowed. (e) Vertical shearing stresses, as specified in Section 10. (/) Bond stress between concrete and plain reinforcing bars 4 per cent of the compressive strength. (fir) Bond stress between concrete and approved deformed bars 5 per cent of the compressive strength. (ft) Compression applied to a surface of concrete of at least twice the loaded area, a stress of 50 per cent of the compressive strength shall be allowd over the area actually under load. (?') Tensile stress in steel 16,000 Ib. per sq. in., except that for steel having an elastic limit of at least 50,000 Ib., a working stress of 18,000 Ib. per sq. in. will be allowed. 8. Girder, Beam, and Slab Construction. In determining the bending moment in slabs, beams and girders, the load carried by the member shall include both the dead- and the live-loads. The span of the member shall be the distance center to center of supports, but not to exceed the clear span plus the depth of the member, except that for continuous or fixed members framing into other reinforced-concrete members the clear span may be used. For continuous members supported upon brackets making an angle of not more than 45 degrees with the vertical, and having a width not less than the width of the member supported, the span shall be the clear distance between brackets plus one-half the total depth of the member. If the brackets make a greater angle than 45 degrees with the vertical, only that portion of the bracket within the 45 degrees slope shall be considered. Maximum negative mo- ments are to be considered as existing at the end of the span as here defined. ~WJ For members uniformly loaded the bending moment shall be assumed as -=r- > where b W = total load; L = span; and F = 8 for members simply supported, 10 for both negative and positive bending moment for members restrained at one end and simply supported or partially restrained at the other, and 12 for both negative and positive bend- ing moment for members fixed or continuous at both supports. The above bending mo- ments for continuous members apply only when adjacent spans are approximately equal. A special condition of loading to be reduced to equivalent uniformly distributed loading in accordance with approved engineering practice. For members having one end simply supported or partially restrained, at least fifty (50) per cent of the tension reinforcement required at center of span shall be bent up and adequately anchored to take bending moment at exterior support. At the ends of continuous beams, the amount of negative moment which will be devel- oped in the beam will depend on the condition of restraint or fixedness, and this will depend on the form of construction used. In the ordinary cases a moment of ,-- may be taken: ID for small beams running into heavy columns this should be increased but not to exceed ^ * Total volume of fine and coarse aggregate, measured separately, t Water-Cement Ratio = Ratio of water to cement by volume. 256 9. Slabs. The main tensile reinforcement shall not be farther apart than two times the thickness of the slab. For slabs designed to span one way, steel having an area of at least two-tenths of one per cent (0.2 %) of section of slab shall be provided transverse to main reinforcement, and this transverse reinforcement shall be further increased in the top of the slab over girders to prevent cracking, and the main steel in slabs parallel and adjacent to girders may be reduced accordingly. Where openings are left through slabs, extra reinforcement shall be provided to prevent local cracks developing. This reinforcement shall in no case be less than Y sq. in. in section and must be securely anchored at ends. Floor finish when placed monolithic may be considered part of the structural section. Where adequate bond and shearing resistance between slab and web of beam is provided, the slab may be considered as an integral part of the beam, but its effective width shall not exceed on either side of the beam one-sixth of the span length of the beam nor be greater than six times the thickness of the slab on either side of the beam, nor greater than one-half of the distance between beams on either side, the measurements being taken from edge of web. 10. Shear and Diagonal Tension. (a) The notation used in this section is as follows: V = total vertical shear at any section. V = vertical shear carried by the web reinforcement. v = V/bjd = Unit vertical shearing stress. d = depth from compressive face to c. g. of tensile steel in inches. b = breadth of beam. b f = breadth of stem of T-beam or web of I-beam. As = area of longitudinal steel. A v = area of shear steel in section of beam considered. j = ratio of lever arm of resistance couple to depth d. p = Ag/bd = Longitudinal steel ratio. r = A v /ba = Shear steel ratio. a = spacing of shear steel measured perpendicular to its direction. f e ' = ultimate strength of concrete cylinders at 28 days (or at time of test in considering test data). / = tensile stress in web reinforcement. Except where v is noted as the unit punching shearing stress, it is used as a shearing stress index governing the v alue of the diagonal tension in the web as is the present common practice. (6) All allowances for design unit shearing stresses in the following sections are predicated on proper design of the longitudinal reinforcement to effectively resist all positive and negative moments, as prescribed in other sections of these standards. Wherever web reinforcement is used it must be adequately anchored at both ends. (c) Members with Web Reinforcement. When adequate mechanical anchorage of both web and longitudinal rods is provided, the concrete may be figured to carry a unit vertical shearing stress equal to 0.025/ c ' and the remainder of the shear shall be carried by web bars designed according to the formula: A - V ' a ~m Properly anchored bent-up longitudinal bars may be considered as web reinforcement. The maximum unit shearing stress shall not exceed 0.12/ c ' in any case. (d) When adequate mechanical anchorage of the longitudinal rods as defined in the next paragraph is not provided, the maximum unit shearing stress shall not exceed 0.06/ c ', of which 0.02// may be considered to be taken by the concrete and the remainder of the shear taken by the web bars designed as above. Web rods must be adequately anchored in all cases. (e) Adequate mechanical anchorage of the bottom longitudinal steel for positive moments shall consist of carrying the reinforcement a sufficient distance beyond the point of inflection to develop the assumed tension in the reinforcement at the point of inflection by bond between the end of the bar and the point of inflection of the member (never to a less distance than one inch from the center of the support or in case of wide supports to not less than 12 in. of embedment in the support), or of bending the end of the bars over the support to a half circle of diameter not less than 8 times the diameter of the bar, or by any device that will transmit the tension on the bar to the concrete over the support at a compressive stress of not over 0.50/ c '. The tension in the bar, at the point of inflection to be resisted by the anchorage, shall be taken for this computation as not less than one- third of the maximum safe tension in the bar. Reinforcement for negative moment shall be thoroughly anchored at the support and extend into the span a sufficient distance to adequately provide for negative tension by bond. Simply supported beams shall have the longitudinal steel anchored by hooks of diameter specified above or by an equivalent anchor- 257 age, the tensile stress at the edge of the support being taken as one-third of the maximum safe tension in the bar. (Figs. 1, 2 and 3.) (/) Anchorage of the web steel shall consist of continuity of the web member with the longitudinal member, or of carrying the web member about at least two sides of a longitudi- nal bar at both ends, or of carrying the web member about at least two sides of a longitudinal member at one end and making a half circular hook at the other end of a diameter not less than eight times the diameter of the web rod. In all cases, the bent ends of web bars shall extend at least eight diameters below or above the point of extreme height or depth of the "^JT ^ _^L_ Steel from %&$('* Vertical stirrups adjacent only span not shown FIG. 1, Bent up rods i-j and vertical stirrups Steel from % adjacent span not shown Bent up bars and inclined stirrups FIG. 2. Plate must be rigid- ly connected to rod FIG. 3. :;* ; >'., : >>'; * ' ^ \ - $ po * P5l Hook must engage a substantial block of concrete ' . 4 _' A . **Gd "'This dimension limited by bond value unless wffb * ^ ste*l is integral with longitudinal steel ;:.?: W ''' 4 FIG. 4. on this section must not exceed .02 f, unless steel is provided in top of beam at support FIG. 5. bar. In case the end anchorage is not in bearing on other reinforcing steel, the anchorage shall be such as to engage an adequate amount of concrete to prevent the bar from pulling off a portion of the concrete. In all cases the stirrups shall be carried as close to the upper and lower surfaces as fireproofing requirements will permit. The size of web reinforcing bars which are not either a part of the longitudinal steel or welded thereto shall be such that not less than two-fifths of the maximum design tensile stress in the bar may be developed at design bond stresses in a length of rod equal to 0.4d. This condition is satisfied for plain 258 round stirrups when the diameter of the bar does not exceed d/50. The balance of the tensile stress in the bar may be considered as taken by adequate end anchorage as specified above. (Fig. 4.) (0) Beams in which no longitudinal reinforcement is provided in the upper portion of the beam adjacent to the support and in which the ends of the beam are built monolithic with other parts of the concrete structure, shall not carry a unit shearing stress in excess of 0.02//, regardless of amount of web reinforcement provided. (Fig. 5.) (A) When the shear reinforcement consists of bars bent up at an angle so as to rein- force all sections of the beam in which the unit shearing stress exceeds 0.02/ c ' the design may be made as follows: Atf v = V sec a. Where A v = area of bent-up shear bars. / = stress in bent-up shear bars. V' = total shear at end of span as prescribed for moment less the shearing resistance of the concrete at a unit stress of 0.02/ c ' over the area b'jd. a = angle between bent-up rod and the vertical. (F^g. 6.) FIG. 6. The maximum unit shearing stress shall not exceed 0.06 f c f with this arrangement of web steel and the longitudinal steel shall be adequately anchored as defined above in all cases. (i) In case the web reinforcement consists solely of inclined shear bars the first bent bar shall bend downward from the plane of the upper reinforcement directly over or within the edge of the support. 0') Where additional web reinforcement is provided the same may be figured in accord- ance with Section 10 (c). The total shearing resistance of the beam shall be taken as the sum of the resistances under Section 10 (c) and 10 (h). (k) Beams without Web Reinforcement. When the longitudinal steel is not fully an- chored, as prescribed above, the unit shearing stress shall not exceed 0.02//. When the longitudinal steel is fully anchored, as prescribed above, the unit shearing stress shall not exceed 0.03//. (I) Critical Section for Shear in Beams. The critical section for shear as governing diagonal tension shall be taken at a distance not greater than one-half the effective depth of the beam O^d), from the end of the span as prescribed for moment. C.G. Shear governing diagonal tension Critical sections (IJ following per- iphery of drop panel, and (2) sur- face of frustum of cone thru e> of column capital; base Punching shear: - Critical section follows per- iphery of column capital The effective depth of the critical section for shear as governing diagonal tension shall be taken as the depth jd of the beam in the plane of the critical section. The breadth of the critical section shall be the full breadth of rectangular beams or the breadth of the stem of T-beams or the thickness of the web in beams of I section. (m) TUe and Concrete Joist Construction. The shearing stresses in tile and concrete joist construction shall not exceed those in beams or slabs of similar reinforcement. The breadth of the effective section for shear, as governing diagonal tension, may be taken as the thickness of the concrete joist plus one-half the thickness of the vertical webs of the tile, provided that the joints in one row come opposite the centers of tile in adjoining rows on either side. Where the tile joints are not staggered, only the concrete joists may be considered effective in resisting shear. 259 (n) Flat-slab Construction. In flat-slab construction where a drop panel is used ad- joining the column, the shearing stress, as governing diagonal tension, figured on the jd depth on a vertical section along the periphery of the drop, shall not exceed 0.03/ c '. (See Fig. 7.) (o) In flat-slab construction, with or without drop panels, the shearing stress, as govern- ing diagonal tension, figured between the compression face of the slab or drop and the level of the center of gravity of the reinforcing steel, on the surface of the frustum of a cone or pyramid passing through the periphery of the column capital and having a base angle of 45 degrees, shall not exceed 0.035/ c '. (p) Footings. In footings carrying a single column or load, the shearing stress, as governing diagonal tension, figured between the level of the centroid of the compressive stresses and the level of the center of gravity of the reinforcing steel on the surface of the frustum of a cone or pyramid passing through the base of the supported column or loaded member and having a base angle of 45 degrees the unit stresses shall not exceed those in beams without web reinforcement. Especial attention shall be given to bond in footings. The total vertical shear on this section shall be taken as the upward pressure on the area of the footing outside the base of this section. (q) If adequate anchorage is provided for the tensile steel arid adequately anchored web reinforcement is also provided such web reinforcement may be figured in accordance with the formula given in Section 10 (c) above. Such calculations may be made for vertical sections concentric with the supported column. (r) For footings supporting two or more columns, the shearing stresses shall be figured as for beams or slabs. (s) Arrangement of Web Reinforcement. The spacing of web reinforcement as measured perpendicular to their direction shall not exceed 3d/4 in any case where web reinforcement is necessary. Where vertical stirrups or web members inclined less than 30 degrees to the Shear governing diagonal tension :-} \ Punching shear :- Critical section follows periphery-' ^- Critical 'section follows periphery of supported portion at top of of supported portion, footing; base angle 45 FIG. 8. vertical are used, the spacing shall not exceed d/2. When the unit shearing stress exceeds 0.06/c' the spacing of the web reinforcement shall not exceed d/2 in any case, nor d/3 for vertical stirrups or web steel inclined less than 30 degrees with the vertical. The first vertical stirrup shall be placed not farther than d/2 from the face of the support in any case. The first inclined stirrup or bent-up rod shall reach the level of the upper longitudinal steel at a distance not greater than d/2 from the edge of the support if the bottom longitudinal steel is adequately anchored and at the edge of the web support if the longitudinal steel is not anchored. Web members may be placed at any angle between and 60 degrees with the vertical, provided that, if inclined, they shall be inclined in the proper direction to take tension, rather than compression, in the web. (t) Punching Shear. Punching shear shall be figured on a vertical section through the periphery of the smaller member. The unit shearing stress in punching shear, figured on the full depth d to the center of gravity of the reinforcement, shall not exceed 0.1/ c '. (u) When the depth of the supported or supporting member is less than one-fifteenth of the span in the case of beams or slabs, or less than one-third of the overhang in the case of cantilevers (including footings), the unit shearing stress in punching shear shall not exceed 0.06/c'. 11. Tile and Joist Floors. Wherever floors are built with a combination of tile or other fillers between reinforced-concrete joists, the following rules regarding the dimensions and methods of calculations of construction shall be observed: (a) Wherever a portion of the slab above the fillers is considered as acting as a T-beam section, the slab portion must be cast monolithic with the joist and have a minimum thick- ness of two (2) inches. (6) Wherever porous fillers are used which will absorb water from the concrete, oare must be taken thoroughly to saturate same before concrete is placed. 260 (c) All regulations given above for beam and girder floors shall apply to tile and joist floors. (d) The sections of fillers shall be together and all joints reasonably tight before concrete is placed. 12. Flat -slab or Girderless Floors, Continuous flat-slab floors, reinforced with steel rods or mesh and supported on spaced columns in orderly arrangement, shall conform to the following requirements: FIG. 9. (a) Notation and Nomenclature. In the formula let w = total dead-and live-load in pounds per square foot of floors. l\ ='span in feet center to center of columns parallel to sections on which moments are considered. lz = span in feet center to center of columns perpendicular to sections on which moments are considered. C = average diameter of column capital in feet at plane where its thickness is 1% in. q = distance from center line of the capital to the center of gravity of the periphery of the half capital divided by %c. For round capitals q may be considered as two-thirds and for square capitals as three-quarters. t = total slab thickness in inches. L = average span in feet center to center of columns, but not less than 0.9 of the greater span. (a) Drop construction (f>s Cop construct kjf > 7 \_i_/ i- TF-- - - (c) Poneifed ceiling consfPtocficn FlG. 10. The column head section, mid section, outer section, and inner section are located and dimensioned as shown in Fig. 9. Corresponding moments shall be figured on similar sections at right angles to those shown in Fig. 9. (b) Structural Variations. Flat-slab floors may be built with or without caps, drops or paneled ceilings. These terms are illustrated in Fig. 10. Where caps are employed they shall be considered a part of the columns and the column 261 capital dimension c shall be found by extending the lines of the capital to an intersection with the plane of the under surface of the slab as indicated in Fig. 10&. The cap shall be large enough to enclose this extension of the capital lines. The column capital profile shall not fall at any point inside an inverted cone drawn, as shown in Fig. 10a, from the periphery of the designed capital of diameter c and with a base angle of 45 degrees. The diameter of the designed capital c shall be taken where the verti- cal thickness of the column capital is at least 1% in. The drop, where used, shall not be less than 0.3 L in width. Where paneled ceilings are used the paneling shall not exceed one-half of the slab thickness in depth and the dimension of the paneling shall not exceed 0.8 of the panel dimen- sion. (See Fig. lOo.) (c) Slab Thickness. The slab thickness shall not be less than t = 0.02L ^/w + 1 in. In no case shall the slab thickness be less than ^ 2-^ f r floor slabs nor less than Y oL for roof slabs. (d) Design Moments. The numerical sum of the positive and negative moments in foot pounds shall not be less than 0.09wli(l gc) 2 . Of this total amount not less than 40 per cent shall be resisted in the column head sections. Where a drop is used, not less than 50 per cent shall be resisted in the column head sections. Of the total amount not less than 10 per cent shall be resisted in the mid section. Of the total amount not less than 18 per cent shall be resisted in the outer section. Of the total amount not less than 12 per cent shall be resisted on the inner sections. The balance of the moment shall be distributed between the various sections as required by the physical details and dimensions of the particular design employed. (c) Exterior Panels. The negative moments at the first interior row of columns and the positive moments at the center of the exterior panel on sections parallel to the wall, shall be increased 20 per cent o\er those specified above for interior panels. If girders are not provided long the column line, the reinforcement parallel to the wall for negative moment in the column head section and for positive moment in the outer section adjacent to the wall, shall be altered in accordance with the change in the value of c. The negative moment on sections at the wall and parallel thereto should be determined by the conditions of restraint, but must never be taken less than 80 per cent of those for the interior panels. (/) Reinforcement. In the calculation of moments all the reinforcing bars which cross the section under consideration and which fulfill the requirements given under "Arrange- ment of Reinforcement" may be used. For a column head section reinforcing bars parallel to the straight portion of the section do not contribute to the negative resisting moment for the column head section in question. The sectional area of bars, crossing the section at an angle, multiplied by the sine of the angle between these bars and the straight portion of the section under consideration may be taken to act as reinforcement in a rectangular direction. Calculations for shearing stress shall be made in accordance with Section 10. (g) Point of Inflection. For the purpose of making calculations of moment at sections away from the sections of negative moment and positive moment already specified, the point of inflection shall be taken at a distance from center line of columns equal to /&(k ?c) + %qc. This becomes K(^2 + c) where capital is circular. For slabs having drop panels the coefficient of Y should be used instead of Jo- (h) Arrangement of Reinforcement. The design should include adequate provision for securing the reinforcement in place so as to take not only the maximum moments but the moments of intermediate sections. If bars are extended beyond the column capital and are used to take the bending moment on the opposite side of the column, they must extent to the point of inflection. Bars in diagonal bands used as reinforcement for negative moment should extend on each side of the line drawn through the column center at right angles to the direction of the band a distance equal to 0.35 of the panel length, and bars in the diagonal bands used as reinforcement for positive moment, should extend on each side of the diagonal through the center of the panel a distance equal to 0.35 of the panel length. Bars spliced by lapping and counted as only one bar in tension shall be lapped not less than 80 diameters if splice is made at point of maximum stress and not more than 50 per cent of the rods shall be so spliced at any point in any single band or in any single region of tensile stress. Continuous bars shall not all be bent up at the same point of their length, but the zone in which this bending occurs should extend on each side of the assumed point of inflection. (i) Tensile and Compressive Stresses. The usual method of calculating the tensile and compressive stresses in the concrete and in the reinforcement, based on the assumptions for internal stresses, should be followed. In the case of the drop panel, the section of the slab and drop panel may be considered to act integrally for a width equal to a width of the column head section. Within the column head section the allowable compression may be increased as prescribed in Section 7 for continuous members. 0') Provision for Diagonal Tension and Shear. In calculations for the shearing stress which is to be used as the means for measuring the resistance to diagonal tension stress, it 262 shall be assumed that the total vertical shear on a column head section constituting a width equal to one-half the lateral dimension of the panel, for use in determining critical shearing stresses, shall be considered to be one-fourth of the total dead- and live-load on a panel for a slab of uniform thickness, and to be 0.3 of the sum of the dead- and live-loads on a panel for a slab with drop panels.^ The formula for shearing unit stress shall be v = f\ *) ^ TV 0^0 TV ' . for slabs of uniform thickness and v = ' , - for slabs with drop panels, where W is bjd bja the sum of the dead- and live-load on a panel, 6 is half the lateral dimension of the panel measured from center to center of columns, and jd is the lever arm of the resisting couple at the section. The calculation for punching shear shall be made on the assumption of a uniform distri- bution over the section of the slab around the periphery of the column capital and also of a uniform distribution over the section of the slab around the periphery of the drop panel, using in each case an amount of vertical shear greater by 25 per cent than the total vertical shear on the section under consideration. The values of working stresses should be those recommended for diagonal tension and shear in Section 10. (k) Walls and Openings. Additional slab thickness, girders, or beams shall be provided to carry walls and other concentrated loads which are in excess of the working capacity of the slab. Beams should also be provided in case openings in the floor reduce the working strength of the slab below the required carrying capacity. Where lintels are used with flat-slab construction the depth of the lintels being greater than the combined depth of the slab and depressed panel, they shall be designed to carry a uniformly distributed load equal to /- of the total panel load in addition to any other loads superimposed upon the lintel and the dead weight of the lintel. (1) Unusual Panels. The coefficients, steel distribution, and thicknesses recommended are for slabs which have three or more rows of panels in each direction and in which the sizes of the panels are approximately the same. For structures having a width of one or two panels, and also for slabs having panels of markedly different sizes, an analysis should be made of the moments developed in both slab and columns and the values given herein modified accordingly. (m) Oblong Panels. The requirements of design herein given for flat-slab floors do not apply for oblong panels where the long side is more than four-thirds of the short side. (n) Bending Moments in Columns. Provision shall be made in both wall columns and interior columns for the bending moment which will be developed by unequally loaded panels, eccentric loading, or uneven spacing of columns. The amount of moment to be taken by a column will depend on the relative stiffness of columns and slab, and computa- tions may be made by rational methods such as the principle of least work or of slope and deflection. Generally the largest part of the unequalized negative moment will be trans- mitted to the columns and the columns shall be designed to resist this bending moment. Especial attention shall be given to wall columns and corner columns. Column capitals shall be designed, and reinforced where necessary, with these conditions in mind. The resistance of any wall column to bending in a direction perpendicular to the wall shall be not less than 0.04 ivl\(li gc) 2 in which h is the panel dimension perpendicular to the wall. The moment in such wall column may be reduced by the balancing moment of the weight of the structure which projects beyond the center line of the supporting wall column. Where the column extends through the story above, the resisting moment shall be divided between the upper and the lower columns in proportion to their stiffness. Calcu- lated combined stresses due to bending and direct load shall not exceed by more than 50 per cent the stresses allowed for direct load. 13. Columns General. Reinforced-concrete columns, for the working stresses here- inafter specified, shall have a gross width or diameter not less than one-fifteenth of the unsupported height nor less than twelve (12) in. All vertical reinforcement shall be secured against lateral displacement by steel ties not less than j in. in diameter, placed not farther apart than 15 diameters of the vertical rods or more than 12 in. For columns supporting flat-slab floors or roofs, the diameter shall be not less than one-thirteenth of the distance between columns. The length of columns shall be taken as the maximum unstayed length. 14. Columns with Longitudinal Reinforcement. For columns having not less than 0.5 per cent nor more than 4 per cent of vertical reinforcement, the allowable working unit stress for the net section of the concrete shall be 25 per cent of the compressive strength specified in Section 6, and the working unit stress for the steel shall be based upon the ratio of the moduli of elasticity of the concrete and steel. Concrete to a depth of 1 3^ in. shall be considered as protective covering and not a part of the net section. 15. Columns with Longitudinal and Lateral Reinforcement. Columns, having not less than 1 per cent nor more than 4 per cent of vertical reinforcement and not less than 0.5 per 263 cent nor more than 2 per cent of lateral reinforcement in the form of hoops or spirals spaced not farther apart than one-sixth of the outside diameter of the hoops or spirals nor more than 3 in. shall have an allowable working unit stress for the concrete within the outside diameter of the hoops or spirals equal to 25 per cent of the compressive strength of the concrete, as given in Section 6, and a working unit stress on the vertical reinforcement equal to the working value of the concrete multiplied by the ratio of the specified moduli of elasticity of the steel and concrete, and a working load for the hoops or spirals determined by considering the steel in hoops or spirals as four times as effective as longitudinal rein- forcing steel of equal volume. The percentage of lateral reinforcement shall be taken as the volume of the hoops or spirals divided by the volume of the enclosed concrete in a unit length of column. The hoops or spirals shall be rigidly secured at each intersection to at least four (4) verticals to insure uniform spacing. The percentage of longitudinal reinforce- ment used shall be not less than the percentage of the lateral reinforcement. Spirals shall be manufactured of steel having a yield point of not less than 50,000 Ib. per square inch. 16. For steel columns filled with concrete and encased in a shell of concrete at least 3 in. thick, where the steel is calculated to carry the entire load, the allowable stress per square inch shall be determined by the following formula: 18,000 70^, but shall not exceed 16,000 Ib. where L = unsupported length in inches and R = least radius of gyration of steel section in inches. The concrete shell shall be reinforced with wire mesh or hoop weighing at least 0.2 Ib. per square foot of surface of shell. When the details of the structural steel are such as to fully enclose or encase the concrete, or where a spiral of not less than one-half of 1 per cent of the core area, and with a pitch of not more than 3 in., is provided for this purpose, the concrete inside the column core or spiral may be loaded to not more than 25 per cent of the ultimate strength specified in Section 6, in addition to the load on the steel column figured as above. Composite columns having a cast iron core or center surrounded by concrete which is enclosed in a spiral of not less than one-half of 1 per cent of the core area, and with a pitch of not more than 3 in. may be figured for a stress of 12,000 60L/R, but not over 10,000 Ib. per square inch on the cast iron section and of not more than 25 per cent of the com- pressive strength specified in Section 6 on the concrete within the spiral or core. The diameter of the cast iron core shall not exceed one-half of the diameter of the spiral. 17. Footings General. Symmetrical, concentric column footings shall be designed for punching shear, diagonal tension, and bending moment. 18. Punching Shear in Footings. Punching shear shall be figured in accordance with Section 10. 19. Diagonal Tension in Footings. Shearing stresses shall be figured in accordance with Section 10. 20. Bending Moment in Footings. The bending moment in isolated column footings at a section taken at edge of pier or column shall be determined by multiplying the load on the quarter footing (after deducting the quarter pier or column area) by six-tenths of the distance from the edge of pier or column to the edge of footing. The effective area of concrete and steel to resist bending moment shall be considered as that within a width extending both sides of pier or column, a distance equal to depth of footing plus one-half the remaining distance to edge of footing, except that reinforcing steel crossing the section other than at right angles, shall be considered to have an effective area determined by multiplying the section area by the line of the angle between the bar and the plane of section. 21. Bond Stresses in Footings. In designing footings, careful consideration must be given to the bond stresses which will occur between the reinforcing steel and the concrete. 22. Walls General. Walls shall be reinforced by steel rods running horizontally and vertically. Walls having an unsupported height not exceeding fifteen times the thickness may be figured the same as columns. Walls having an unsupported height not more than twenty-five times the thickness may be figured to carry safely a working stress of 12% per cent of the compressive strength specified in Section 6. 23. Exterior Walls. Exterior walls shall be designed to withstand wind loads or loads from backfill. The thickness of wall shall in no case be less than 4 in. 24. Protection. The reinforcement in columns and girders shall be protected by minimum thickness of 2 in. of concrete; in beams and walls by a minimum of lj^ in. in floor slabs by a minimum of Y in. ; in footings by a minimum of 3 in. 264 NEW YORK BUILDING CODE REQUIREMENTS Working Stresses. Reinforced concrete structures shall be so designated that the stresses in pounds per square inch shall not exceed the following: Extreme fibre stress on concrete in compression 650 Concrete in direct compression 500 Shearing stress in concrete when all diagonal tension is resisted by steel 150 Shearing stress in concrete when diagonal tension is not resisted by steel 40 Bond stress between concrete and plain reinforcement 80 Bond stress between concrete and approved deformed bars 100 Tensile stress in steel reinforcement 16,000 Tensile stress in cold drawn steel wire or fabric, 35 per cent of the elastic limit but not more than 20,000 In continuous beams the extreme fiber stress on concrete in compression may be in- creased 15 per cent, adjacent to supports. The ratio of the moduli of elasticity of 1 : 2 : 4 stone or gravel concrete and steel shall be taken as one to fifteen. The ratio of the moduli of elasticity of 1 : 1^ : 3 stone or gravel concrete and steel shall be taken 'as one to twelve. Slabs and Beams, (a) Thickness. Slabs shall not be less than 4 in. in thickness for floors and 3% in. for roofs. (b) Tee-Beams. Where adequate bond between slab and web of beam is provided, the slab may be considered as an integral part of the beam provided its effective width shall not exceed on either side of the beam one-sixth of the span length of the beam, nor be greater than six times the thickness of the slab on either side of the beam, the measure- ments being taken from edge of web. (c) Placing of Reinforcement. All reinforcement shall be accurately located and secured against displacement. The reinforcement for slabs shall not be spaced farther apart than two and one- half times the 'thickness of the slab. (d) Web Reinforcement. Members of web reinforcement shall be so designed as ade- quately to take up throughout their length all stresses not taken up by the concrete. They shall not be spaced to exceed three-fourths of the depth of the beam in that portion where the web stresses exceed the allowable value of concrete in shear. Web reinforcement, unless rigidly attached, shall be placed at right angles to the axis of the beam and carried around the tension members. Use of Fillers in Floor Construction. When hollow tile, concrete blocks or other acceptable fillers are used in any reinforced concrete floor construction, the reinforced con- crete members of such floor construction shall be designed in accordance with the provisions of this article to take the entire loads, provided, however, that when the fillers do not exceed 60 per cent of the construction, not more than 2^ in. of concrete shall be required over the fillers. Columns, (a) With Longitudinal Reinforcements Only. In concrete columns, having not less than one-half nor more than 4 per cent of vertical reinforcement secured against displacement by 24-in. steel ties placed not farther apart than 15 diameters of the verti- cal rods nor more than 12 in., the allowable load shall be 500 lb. per square inch on the concrete, plus 7,500 lb. on the vertical reinforcement. (6) With Longitudinal and Lateral Reinforcement. In concrete columns, having not less than one-half nor more than 2 per cent of hoops or spirals spaced not farther apart than one-sixth of the diameter of the enclosed column nor more than 3 in., and having not less than 1 nor more than 4 per cent of vertical reinforcement, the allowable load shall be 500 lb. per square inch on the effective area of the concrete, plus 7,500 lb. per square inch on the vertical reinforcement, plus a load per square inch on the effective area of the concrete equal to two times the percentage of lateral reinforcement multiplied by the tensile stress in the lateral reinforcement prescribed under " Working Stresses," the percentage of lateral reinforcement being the volume of the hoops or spirals divided by the volume of the en- 265 closed concrete in a unit length of column. The hoops or spirals shall be rigidly secured to at least four verticals to insure uniform spacing. (c) Structural Steel and Concrete. In columns of structural steel, thoroughly encased in concrete not less than 4 in. thick and reinforced with not less than 1 per cent of steel, the allowable load shall be 16,000 lb. per square inch on the structural steel, the percentage of reinforcement being the volume of the reinforcing steel divided by the volume of the con- crete enclosed by the reinforcing steel. Not more than one-half of the reinforcing steel shall be placed vertically. The reinforcing steel shall not be placed nearer than 1 in. to the structural steel or to the outer surface of the concrete. The ratio\>f length to least radius of gyration of structural steel section shall not exceed one hundred and twenty. (d) When Richer Concrete is Used. In concrete columns the compression on the concrete may be increased 20 per cent when the fine and coarse aggregates are carefully selected and the proportion of cement to total aggregate is increased to one part of cement to not more than four and one-half parts of aggregate, fine and coarse, either in the proportion of one part of cement, one and one-half parts of fine aggregate and three parts of coarse aggregate*, or in such proportion as will secure the maximum density. In such cases, however, the compressive stress in the vertical steel shall not exceed 7,200 lb. per square inch. (e) Eccentric Loads. Bending stresses due to eccentric loads shall be provided for by increasing the section of concrete or steel until the maximum stress shall not exceed the allowable working stress. (/) Length. In columns, the ratio of length to least side or diameter shall not exceed fifteen, but in no case shall the least side or diameter be less than 12 in. Walls. Enclosure walls of reinforced concrete shall be securely anchored at all floors. The thickness shall not be less than one-twenty-fifth of the unsupported height, but in no case less than 8 in. The steel reinforcement, running both horizontally and vertically, shall be placed near both faces of the wall; the total weight of such reinforcement shall be not less than }4, lb. per square foot of wall. Protection of Reinforcement. The reinforcement in columns and girders shall be protected by a minimum of 2 in. of concrete; in beams and walls by a minimum of 1^ in.; in floor slabs by a minimum of 1 in.; and in footings by a minimum of 4 in. of concrete. Flat Slabs* Application. The rules governing the design of reinforced concrete flat slabs shall apply to such floors and roofs, consisting of three or more rows of slabs, without beams or girders, supported on columns, the construction being continuous over the columns and forming with them a monolithic structure. Compliance with Building Code. In the design of reinforced concrete flat slabs, the provisions of the preceding articles of the building code shall govern with respect to such matters as are specified therein. Assumptions. In calculations for the strength of reinforced concrete flat slabs, the following assumptions shall be made: (a) A plane section before bending remains plane after bending. (6) The modulus of elasticity of concrete in compression within the allowable working stresses is constant. (c) The adhesion between concrete and reinforcement is perfect. (d) The tensile strength of concrete is nil. (e) Initial stress in the reinforcement due to contraction or expansion in the concrete is negligible. Stresses. (a) The allowable unit shear in reinforced concrete flat slabs on the bd section around the perimeter of the column capital shall not exceed 120 lb. per square inch; and the allowable unit shearing stress on the bjd section around the perimeter of the drop shall not exceed (60) lb. per square inch, provided that the reinforcement is so arranged or anchored that the stress may be fully developed for both positive and negative moments. The extreme fibre stresses to be used in concrete in compression at the column head section shall not exceed 750 lb. per square inch. Columns. For columns supporting reinforced concrete flat slabs, the least dimension of any column shall be not less than one-fifteenth of the average span of any slabs supported by the columns; but in no case shall such least dimension of any interior column supporting a floor or roof be less than 16 in. when round, nor 14 in. when square; nor shall the least dimension of any exterior column be less than 14 in. Column Capital. Every reinforced concrete column supporting a flat slab shall be provided with a capital whose diameter is not less than 0.225 of the average span of any slabs supported by it. Such diameter shall be measured where the vertical thickness of the capital is at least 1^ in., and shall be the diameter of the inscribed circle in that horizontal * Adopted July 8, 1920. 266 plane. The slope of the capital considered effective below the point where its diameter is measured shall nowhere make an angle with vertical of more than 45. In case a cap of less dimensions than hereinafter described as a drop, is placed above the column capital, the part of this cap enclosed within the lines of the column capital extended upwards to the bottom of the slab or drop at the slope of 45 may be considered as part of the column capital in determining the diameter for design purposes. Drop. When a reinforced concrete flat slab is thicker in that portion adjacent to or surrounding the column, the thickened portion shall be known as a drop. The width of such drop when used, shall be determined by the shearing stress in the slab around the perimeter of the drop, but in no case shall the width be less than 0.33 of the average span of any slabs of which it forms a part. In computing the thickness of drop required by the negative moment on the column head section, the width of the drop only shall be considered as effective in resisting the compressive stress, but in no case shall the thickness of such drops be less than 0.33 of the thickness of the slab. Where drops are used over interior columns, corresponding drops shall be employed over exterior columns and shall extend to the one-sixth point of panel from the center of the column. Slab Thickness. The thickness of a reinforced concrete flat slab shall be not less than that derived by the formulae t = 0.024Z/\/w + I'M f r slabs without drops, and t = 0.02 L\A0 + 1 for slabs with drops, in which t is the thickness of the slab in inches, L is the average span of the slab in feet, and w is the total live- and dead-load in pounds per square foot; but in no case shall this thickness be less than one-thirty-second of the average span of the slab for floors, nor less than one-fortieth of the average span of the slab for roofs, nor less than 6 in. for floors nor less than 5 in. for roofs. Reinforcement. (a) In the calculation of moments at any section, all the reinforcing bars which cross that section may be used, provided that such bars extend far enough on each side of such section to develop the full amount of the stress at that section. The effective area of the reinforcement at any moment section shall be the sectional area of the bars crossing such section multiplied by the sine of the angle of such bars with the plane of the section. The distribution of the reinforcement of the several bands shall be arranged to fully provide for the intermediate moments at any section. (fe) Splices in bars may be made wherever convenient but preferably at points of mini- mum stress. The length of any splice shall be not less than 80 bar diameters and in no case less than 2 ft. The splicing of adjacent bars shall be avoided as far as possible. Slab bars which are lapped over the column, the sectional area of both being included in the calcula- tion for negative moment, shall extend to the lines of inflection beyond the column center. (c) When the reinforcement is arranged in bands, at least 50 per cent of the bars in any band shall be of a length not less than the distance center to center of columns measured rectangularly and diagonally; no bars used as positive reinforcement shall be of a length less than half the panel length plus 40 bar diameters for cross bands, or less than seven-tenths of the panel length plus 40 bar diameters for diagonal bands and no bars used as negative reinforcement shall be of a length less than half the panel length. All reinforcement framing perpendicular to the wall in exterior panels shall extend to the outer edge of the panel and shall be hooked or otherwise anchored. (d~) Adequate means shall be provided for properly maintaining all slab reinforcement in the position assumed by the computations. Line of Inflection. In the design of reinforced concrete flat slab construction, for the purpose of making calculations of the bending moments at sections other than defined in these rules, the line of inflection shall be considered as being located one-quarter the distance, center to center, of columns, rectangularly and diagonally, from center of columns for panels without drops, and three-tenths of such distance for panels with drops. Moment Sections. For the purpose of design of reinforced concrete flat slabs, that portion of the section across a panel, along a line midway between columns, which lies within the middle two quarters of the width of the panel shall be known as the inner section, and those portions of the section in the two outer quarters of the width of the panel shall be known as the outer sections. Of the section which follows a panel edge from column to column and which includes the quarter perimeters of the edges of the column capitals, that portion within the middle two quarters of the panel width shall be known as the mid section and the two remaining portions, each having a projected width equal to one-quarter of the panel width shall be known as the column head sections. Bending Moments. In the design of reinforced concrete flat slabs the following provi- sions with respect to bending moments shall be observed. In the moment expressions used: W is the total dead- and live-load on the panel under consideration, including the weight of drop whether a square, rectangle or parallelogram. Wi is the total live-load on the panel under consideration. L is the length of side of a square panel center to center of columns; or the average span of a rectangular panel which is the mean length of the two sides. 267 n is the ratio of the greater to the less dimension of the panel. h is the unsupported length of a column in inches, measured from top of slab to base of capital. / is the moment of inertia of the reinforced concrete column section. A. Interior Square Panels. The numerical sum of the positive and negative moments shall be not less than Y\ 7 WL. A variation of plus or minus 5 per cent shall be permitted in the expression for the moment on any section, but in no case shall the sum of the negative moments be less than 66 per cent of the total moment, nor the sum of the positive moments be less than 34 per cent of the total moment for slabs with drops; nor shall the sum of the negative moments be less than 60 per cent of the total moment, nor the sum of the positive moments be less than 40 per cent of the total moment for slabs without drops. In two-way systems, for slabs with drops, the negative moment resisted on two column head sections shall be^2^L; the negative moment on the mid section shall be Ms3 WL; the positive moment on the two outer sections shall be + %oWL and the positive moment on the inner section shall be + Mss^FL; and for slabs without drops, the negative moment resisted on two column head sections shall be %sWL, the negative moment on the mid section shall be ^33 WL, the positive moment on the two outer sections shall be + }^^WL and the positive moment on the inner section shall be + M.ssWL, In four- way systems, the negative moments shall be as specified for two-way systems; the positive moment on Ijie two outer sections shall be + HooWL, and the positive moment on the inner section shall be + ^looWL for slab with drops; and the positive moment on the two outer sections shall be + ^j.^WL, and the positive moment on the inner section shall be + ^ooWL, for slabs without drops. In three-way systems, the negative moment on the column head and mid sections and the positive moment on the two outer sections, shall be as specified for four-way systems. In the expression for the bending moments on the various sections, the length L shall be assumed as the distance center to center of columns, and the load W as the load on the panel parallelogram. B. Interior Rectangular Panels. When the ratio n does not exceed 1.1, all computa- tions shall be based on a square panel of a length equal to the average span, and the rein- forcement shall be equally distributed in the short and long directions according to the bending moment coefficients specified for interior square panels. When the ratio n lies between 1.1 and 1.33, the bending moment coefficients specified for interior square panels shall be applied in the following manner: (a) In two-way systems, the negative moments on the two column head sections and the mid section and the positive moment on the two outer sections and the inner section at right angles to the long direction shall be determined as for a square panel of a length equal to the greater dimension of the rectangular panel; and the corresponding moments on the sections at right angles to the short direction shall be determined as for a square panel of a length equal to the lesser dimension of the rectangular panel. In no case shall the amount of reinforcement in the short direction be less than two-thirds of that in the long direction. The load W shall be taken as the load on the rectangular panel under consideration. (6) In four-way systems, for the rectangular bands, the negative moment on the column head sections and the positive moment on the outer sections shall be determined in the same manner as indicated for the two-way systems. For the diagonal bands, the negative moments on the column head and mid sections and the positive moment on the inner section shall be determined as for a square panel of a length equal to the average span of the rectangle. The load W shall be taken as the load on the rectangular panel under consideration. (c) In three-way systems, the negative and positive moments on the bands running parallel to the long direction shall be determined as for a square whose side is equal to the greater dimension; and the moments on the bands running parallel to the short direc- tion shall be determined as for a square whose side is equal to the lesser dimension. The load W shall be taken as the load on the parallelogram panel under consideration. C. Exterior Panels. The negative moments at the first interior row of columns and the positive moments at the center of the exterior panels on moment sections parallel to the wall, shall be increased 20 per cent over those specified above for interior panels. The negative moment on moment sections at the wall and parallel thereto shall be deter- mined by the conditions of restraint, but the negative moment on the mid section shall never be considered less than 50 per cent and the negative moment on the column head section never less than 80 per cent of the corresponding moments at the first interior row of columns. D. Interior columns shall be designed for the bending moments developed by un- equally loaded panels, eccentric loading or uneven spacing of columns. The bending moment resulting from unequally loaded panels shall be considered as YW\L, and shall be resisted by the columns immediately above and below the floor line under consideration in direct proportion to the values of their ratios of I /h. E. Wall columns shall be designed to resist bending in the same manner as interior 268 columns, except that W shall be substituted for Wi in the formula for the moment. The moment so computed may be reduced by the counter moment of the weight of the structure which projects beyond the center line of the wall columns. F. Roof columns shall be designed to resist the total moment resulting from unequally loaded panels, as expressed by the formulae in paragraphs (D) and (E) of this rule. Walls and Openings. In the 'design and construction of reinforced concrete flat slabs, additional slab thickness, girders or beams shall be provided to carry any walls or concen- trated loads in addition to the specified uniform live- and dead-loads. Such girders or beams shall be assumed to carry 20 per cent of the total live and dead panel load in addition to the wall load. Beams shall also be provided in case openings in the floor reduce the working strength of the slab below the presciibed carrying capacity. Special Panels. For structures having a width of less than three rows of slabs, or in which exterior drops, capitals or columns are omitted, or in which irregular or special panels are used, and for which the rules relating to the design of reinforced flat slabs do not directly apply, the computations in the analysis of the design of such panels, shall, when so required, be filed with the superintendent of buildings. 269 CHICAGO BUILDING CODE REQUIREMENTS Ratio of Moduli of Elasticity Adhesion Bond, (a) The calculations for the strength of reinforced concrete shall be based on the assumed ultimate compressive strength per square inch designated by the letter " C7" given in the table below for the mixture to be used. (b) The ratio designated by the letter "#" of the modulus of elasticity of steel to that of the different grades of concrete shall be taken in accordance with the following table: Mixture U R cement, 1 sand, 2 broken stone, gravel or slag 2,900 10 cement, 1% sand, 3 broken stone, gravel or slag 2,400 12 cement, 2 sand, 4 broken stone, gravel or slag 2,000 15 cement, 2^ sand, 5 broken stone, gravel or slag 1,750 18 cement, 3 sand, 7 broken stone, gravel or slag 1,500 20 Unit Stresses for Steel and Concrete, (a) The stresses in the concrete and the steel shall not exceed the following limits: (6) Tensile stress in steel shall not exceed one-third of its elastic limits and shall not exceed 18,000 Ib. per square inch. (c) Shearing stress in steel shall not exceed 12,000 Ib. per square inch. (d) The compressive stress in steel shall not exceed the product of the compressive stress in the concrete multiplied by the elastic modulus of the steel and divided by the elastic modulus of the concrete. (e) Direct compression in concrete shall be one-fifth of its ultimate strength. Bending in extreme fiber of concrete shall be thirty-five one-hundredths of the ultimate strength. (/) Tension in concrete on diagonal plane shall be one-fiftieth of the ultimate compres- sive strength. ((/) For a concrete composed of one part of cement, two parts of sand and four parts of broken stone, the allowable unit stress for adhesion per square inch of surface of imbedment shall not exceed the following: Pounds per sq. in. On plain round or square bars of structural steel 70 On plain round or square bars of high carbon steel 50 On plain flat bars in which the ratio of the sides is not more than 2 to 1 . . 50 On twisted bars when the twisting is not less than one complete twist in 8 diameters 100 (h) For specially formed bars, the allowable unit stress for bond shall not exceed one- fourth of the ultimate bond strength of such bars without appreciable slip which shall be determined by tests made by the person, firm or corporation to the satisfaction of the Commissioner of Buildings, but provided that in no case shall such allowable unit stress exceed 100 Ib. per square inch of the specially formed bars. Design for Slabs, Beams and Girders. Reinforced concrete slabs, beams and girders shall be designed in accordance with the following assumptions and requirements. (a) The common theory of flexure shall be applied to beams and members resisting bending. (b) The adhesion between the concrete and the steel shall be sufficient to make the two materials act together. (c) The steel to take all the direct tensile stresses. (d) The stress strain curve of concrete in compression is a straight line. (e) The ratio of the moduli of elasticity of concrete to steel shall be as specified in the table in preceding article. Moments of External Forces, (a) Beams, girders, floor or roof slabs and joists shall be calculated as supported, or with fixed ends, or with partly fixed ends, in accordance with the actual end conditions, the number of spans and the design. (b) When calculated for ends partly fixed for intermediate spans with an equally distri- buted load where the adjacent spans are of approximately equal lengths: 270 Bending moment at center of spans shall not be less than that expressed in the formula -TO~ for intermediate spans and -^ for end spans. WL* (c) The moment over supports shall not be less than the formula =- and the sum of lo the moments over one support and at the center of span shall be taken not less than the . WL* formula 5 o In the formula hereinabove given "TF" is the load per lineal foot and "L" the length of span in feet. (d) In case of concentrated or special loads the calculations shall be based on the critical condition of loading. (e) For fully supported slabs, the free opening plus the depth, for continuous slabs, the distance between centers of supports, is to be taken as the span. (/) Where the vertical shear, measured on the section of a beam or girder between the centers of action of the horizontal stresses, exceeds one-fiftieth of the ultimate direct compressive stress per square inch, web reinforcement shall be supplied sufficient to carry the excess. The web reinforcement shall extend from top to bottom of beam, and loop or connect to the horizontal reinforcement. The horizontal reinforcement carrying the direct stresses shall not be considered as web reinforcement. (0) In no case, however, shall the vertical shear, measured as stated above, exceed one- fifteenth of the ultimate compression strength of the concrete. (h) For T-beams the width of the stem only shall be used in calculating the above shear. (t) When steel is used in the compression side of beams and girders, the rods shall be tied in accordance with- requirements of vertical reinforced columns with stirrups connecting with the tension rods of the beams or girders. 0') All reinforcing steel shall be accurately located in the forms and secured against displacement; and inspected by the representative of the architect or engineer in charge before any surrounding concrete be put in place. It shall be afterwards completely in- closed by the concrete, and such steel shall nowhere be nearer the surface of the concrete than \}^ inches for columns, lj^ inches for beams and girders, and } inch, but not less than the diameter of the bar, for slabs. (fc) The longitudinal steel in beams and girders shall be so disposed that there shall be a a thickness of concrete between the separate pieces of steel of not less than one and one-half times the maximum sectional dimension of the steel. (1) For square slabs with two-way reinforcements the bending moment at the center of WL 2 the slab shall be not less than that expressed in the formula - (> -.~ for intermediate spans, and . tor end spans. W7.2 (ra) The moment over supports shall not be less than the formula -^- and the sum of OO the moments over one support and at the center of the span shall be taken not less than the WL* formula -TO-- In which above formula " TF" is the load per lineal foot and "L" the length of the span. (n) For square or rectangular slabs, the distribution of the loads in the two directions, shall be inversely as the cubes of the two dimensions. (o) Exposed metal of any kind will not be considered a factor in the strength of any part of any concrete structure, and the plaster finish applied over the metal shall not be deemed sufficient protection unless applied of sufficient thickness and so secured as to meet the approval of the Commissioner of Buildings. (p) Shrinkage and thermal stresses shall be provided for by introduction of steel. Limiting Width of Flange in "T" Beams. (a) In the calculation of ribs, a portion of the floor slab may be assumed as acting in flexure in combination with the rib. The width of the slab so acting in flexure is to be governed by the shearing resistance between rib and slab, but limited to a width equal to one-third of the span length of the ribs between sup- ports and also limited to a width of three-quarters of the distance from center to center between ribs. (6) No part of the slab shall be considered as a portion of the rib, unless the slab and rib are cast at the same time. (c) Where reinforced concrete girders support reinforced concrete beams, the portion of floor slab acting as flange to the girder must be reinforced with rods near the top, at right angles to the girder, to enable it to transmit local loads directly to the girder and not through the beams. Reinforced Concrete Columns Limit of Length Per cent of Reinforcement Bending Moment in Columns Tying Vertical Rods. (a) Reinforced concrete may be used for 271 columns in which the concrete shall not be leaner than a 1:2:4 mixture and in which the ratio of length to least side or diameter does not exceed twelve, but in no case shall the cross section of the column be less than 64 sq. in. Longitudinal reinforcing rods must be tied together to effectively resist outward flexure at intervals of not more than twelve times least diameter of rod and not more than 18 in. When compression rods are not required, reinforcing rods shall be used, equivalent to not less than one-half of 1 per cent (0.005) of the cross sectional area of the column; provided, however, that the total sectional area of the reinforcing steel shall not be less than 1 sq. in., and that no rod or bar be of smaller diameter or least dimensions than /^-in. The area of rein- forcing compression rods shall be limited to 3 per cent of cross sectional area of the column. Vertical reinforcing rods shall extend upward or downward into the column, above or below, lapping the reinforcement above or below enough to develop the stress in rod by the allowable unit for adhesion. When beams or girders are made monolithic with or rigidly attached to reinforced concrete columns, the latter shall be designed to resist a bending moment equal to the greatest possible unbalanced moment in the beams or girders at the columns, in addition to the direct loads for which the columns are designed. (6) When the reinforcement consists of vertical bars and spiral hooping, the concrete may be stressed to one-fourth of its ultimate strength as given on page 270, provided, that the amount of vertical reinforcement be not less than the amount of the spiral reinforcement, nor greater than 8 per cent of the area within the hooping; that the percentage of spiral hooping be not less than one-half of 1 per cent nor greater than 1.5 per cent; that the pitch of the spiral hooping be uniform and not greater than one-tenth of the diameter of the column, nor greater than 3 in.; that the spiral be secured to the verticals at every intersection in such a manner as to insure the maintaining of its form and position, that the verticals be spaced so that their distance apart, measured on the circumference be not greater than 9 in., nor one-eighth the circumference of the column within the hooping. In such columns, the action of the hooping may be assumed to increase the resistance of the concrete equivalent to two and one-half times the amount of the spiral hooping figured as vertical reinforcement. No part of the concrete outside of the hooping shall be considered as a part of the effective column section. Structural Steel Columns. When the vertical reinforcement consists of a structural steel column of box shape, with lattice or batten plates of such a form as to permit its being filled with concrete, the concrete may be stressed to one-fourth of its ultimate strength as given in table on page 270, provided that no shape of less than 1 sq. in. section be used and that the spacing of the lacing or battens be not greater than the least width of the columns. Curtain Walls in Skeleton Construction Buildings. Buildings having a complete skeleton construction of steel or of reinforced concrete construction, or a combination of both, may have exterior walls of reinforced concrete 8 in. thick; provided, however, that such walls shall support only their own weight and that such walls shall have steel reinforcement of not less -than three-tenths of 1 per cent in each direction, vertically and horizontally, the rods spaced not more than 12-in. centers and wired to each other at each intersection. All bars shall be lapped for a length sufficient to develop their full stress for the allowable unit stress for adhesion. Additional bars shall be set around open- ings, the verticals wired to the nearest horizontal bars, and the horizontal bars at top and bottom of openings shall be wired to the nearest vertical bars. The steel rods shall be combined with the concrete and placed where the combination will develop the greatest strength, and the rods shall be staggered or placed and secured so as to resist a pressure of 30 Ib. per square foot, either from the exterior or from the interior on each and every square foot of each wall panel. Flat Slabs* 1. Definitions. Flat slabs as understood by this ruling are reinforced concrete slabs, supported directly on reinforced columns with or without plates or capitals at the top, the whole construction being hingeless and monolithic without any visible beams or girders. The construction may be such as to admit the use of hollow panels in the ceiling or smooth ceiling with depressed panels in the floor. 2. The column capital shall be defined as the gradual flaring out of the top of the column without any marked offset. 3. The drop panel shall be defined as a square or rectangular depression around the column capital extending below the slab adjacent to it. 4. The panel length shall be defined as the distance c. to c. of columns of the side of a square panel, or the average distance c. to c. of columns of the long and short sides of a rectangular panel. 5. Columns. The least dimension of any concrete column shall be not less than one- twelfth the panel length, nor one-twelfth the clear height of the column. * Went into effect Mar. 1, 1918. 272 6. Slab Thickness. The minimum total thickness of the slab in inches shall be deter- mined by the formula: t = W /44( = square root of W divided by 44), where t = total thickness of slab in inches, W = total live-load and dead-load in pounds on the panel, measured c. to c. of columns. 7. In no case shall the thickness be less than >^ 2 of the panel length (L/32) for floors, nor VIQ of the panel length (Z//40) for roofs (L being the distance c. to c. of columns). 8. In no case shall the thickness of slab be less than 6 in. for floors or roofs. 9. Column Capital. When used the diameter of the column capital shall be measured where its vertical thickness is at least 1)^ in. and shall be at least 0.225 of the panel length. The slope of the column capital shall nowhere make an angle with the vertical of more than 45 deg. Special attention shall be given to the design of the column capital in con- sidering eccentric loads, and the effect of wind upon the structure. 10. Drop Panel. When used, the drop panel shall be square or circular for square panels and rectangular or elliptical for oblong panels. 11. The length of the drop shall not be less than one-third of the panel length (Z//3) if square, and not less than one-third of the long or short side of the panel respectively, if rectangular. 12. The depth of the drop panel shall be determined by computing it as a beam, using the negative moment over the column capital specified elsewhere in this ruling. 13. In no case, however, shall the dimensions of the drop panel be less than required for punching shear along its perimeter, using the allowable unit shearing stresses specified below. 14. Shearing Stresses. The allowable unit punching shear on the perimeter of the column capital shall be ^oo f the ultimate compressive strength of the concrete as given on page 270. The allowable unit shear on the perimeter of the drop panel shall be 0.03 of the ultimate compressive strength of the concrete. In computing shearing stress for the purpose of determining the resistance to diagonal tension the method specified by the ordinance shall be used. 15. Panel Strips. For the purpose of establishing the bending moments and the resisting moments of a square panel, the panel shall be divided into strips known as strip A and strip B. Strip A shall include the reinforcement and slab in a width extending from the center line of the columns for a distance each side of this center line equal to one- quarter of the panel length. Strip B shall include the reinforcement and slab in the half width remaining in the center of the panel. At right angles to these strips, the panel shall lie divided into similar strips A and B, having the same widths and relations to the center line of the columns as the above strips. These strips shall be for designing purposes only, and are not intended as the boundary lines of any bands of steel used. 16. These strips shall apply to the system of reinforcement in which the reinforcing bars are placed parallel and at right angles to the center line of the columns, hereinafter known as the two-way system, and also to the system of reinforcement in which the reinforcing bars are placed parallel, at right angles to and diagonal to the center line of the columns hereinafter known as the four-way system. 17. Any other system of reinforcement in which the reinforcing bars are placed in cir- cular, concentric rings and radial bars, or systems with steel rods arranged in any manner whatsoever, shall comply with the requirements of either the two-way or the four-way . system herein specified. 18. Bending Moment Coefficients, Interior Panel, Two-way System. In panels where standard drops and column capitals are used as above specified, the negative bending moment, taken at a cross-section of each strip A at the edge of the column capital or over it, shall be taken as TTL/30. 19. The positive bending moment taken at a cross-section of each strip A midway between column centers shall be taken as WL/60. 20. The positive bending moment taken at a cross-section of each strip B in the middle of the panel shall be taken as WL/12Q. 21. The negative bending moment taken at a cross-section of each strip B on the center line of the columns shall be taken as WL/12Q. 22. In the formulas hereinabove given W = total live- and dead-load on the whole panel in pounds, L = panel length, c. to c. of columns. 23. Bending Moment Coefficients, Interior Panel, Four-way System. In panels where standard drops and column capitals are used as above specified, the negative bending moment, taken at a cross-section of each strip A at the edge of column capital or over it, shall be taken as WL/30. 24. The positive bending moment, taken at a cross-section of each strip A, midway between column centers, shall be taken as WL/8O. 25. The positive bending moment, taken at a cross-section of each strip B, taken in the middle of the panel, shall be taken as TFL/120. 26. The negative bending moment, taken at a cross-section of each strip B on the center line of the columns, shall be taken as JFL/120. 273 27. Bending Moment Coefficients, Wall Panels. Where wall panels with standard drops and capitals are carried by columns and girders built in walls, as in skeleton con- struction, the same coefficients shall be used as for an interior panel, except as follows: The positive bending moments on strips A and B midway between wall and first line of columns shall be increased 25 per cent. 28. Where wall panels are carried on new brick walls, these shall be laid in Portland cement mortar and shall be stiffened with pilasters as follows: If a 16-in. wall is used, it shall have a 4-in. pilaster. If a 12-in. wall is used, it shall have an 8-in. pilaster. The length of pilasters shall be not less than the diameter of the column, nor less than one-eighth of the distance between pilasters. The pilasters shall be located opposite the columns as nearly as practicable, and shall be corbeled out 4 in. at the top, starting at the level of the base of the column capital. Not less than 8-in. bearing shall be provided for the slab, the full length of wall. The coefficients of bending moments required for these panels shall be the same as those for the interior panels except as provided herewith: The positive bending moments on strips A and B midway between the wall and first line of columns shall be increased 50 per cent. 29. Where wall panels are supported on old brick walls, there shall be columns with standard drops and capitals built against the wall, which shall be tied to the same in an approved manner, and at least an 8-in. bearing provided for the slab, the full length. Where this is impracticable, there shall be built a beam on the underside of slab adjacent to the wall between columns, strong enough to carry 25 per cent of the panel load. The coefficients of bending moments for the two cases of slab support herein described shall be the same as those specified in Sect. 27 and Sect. 28 for skeleton and wall bearing condition, respectively. 30. Nothing specified above shall be construed as applying to a case of slabs merely resting on walls or ledges, without any condition of restraint. These shall be figured as in ordinary beam-and-girder construction specified in the ordinances. 31. Bending Moment Coefficients, Wall and Interior Columns. Wall columns in skeleton construction shall be designed to resist a bending moment of TFL/60 at floors and TFL/30 at roof. The amount ot steel required for this moment shall be independent of that required to carry the direct load. It shall be placed as near the surfaces of the column as practicable on the tension sides, and the rods shall be con- tinuous in crossing from one side to another. The length of rods below the base of the capital and above the floor line shall be sufficient to develop their strength through bond, but not less than 40 diameters, nor less than one-third the clear height between the floor line and the base of the column capital. 32. The interior columns must be analyzed for the worst condition of unbalanced loading. It is the intention of this ruling to cover ordinary cases of eccentric loads on the columns by the requirement of Sect. 5. W T here the minimum size of column therein specified is found insufficient, however, the effect of the resulting bending moment shall be properly divided between the adjoining slab and the columns above and below according to best principles of engineering, and the columns enlarged sufficiently to carry the load safely. 33. Bending Moment Coefficients, Panels Without Drops, or Capitals, or Both. In square panels where no column capital or no depressions are used, the sum total of positive and negative bending moments shall be equal to that computed by the following formula: B.M. = (TFL/8)(1.53 - 4k + 4.18A; 3 ) where B.M . = numerical sum of positive and negative bending moments, regardless of algebraic signs. W = total live- and dead-load on the whole panel. L = length of side of a square panel, c. to c. of columns. k = ratio of the radius of the column or column capital to panel length, L. This total bending moment shall be divided between the positive and the negative moments in the same proportion as in the typical square panels for two-way or four-way systems specified above for interior and wall panels respectively. 34. Point of Inflection. For the purpose of making the calculations of the bending moment at the sections away from the column capital, the point of inflection shall be considered as being one-quarter the distance c. to c. of columns, both crosswise and diagonally, from the center of the column. 35. Tensile Stress in Steel and Compressive Stress in Concrete. The tensile stress in steel and the compressive stress in the concrete to resist the bending moment shall be calculated on the basis of the reinforcement and slab in the width included in a given strip, and according to the assumptions and requirements given in the first three articles on 274 page 270. The steel shall be considered as being concentrated at the center of gravity of all the bands of steel in a given strip. 36. For the four-way system of reinforcement the amount of steel to resist the negative bending moment over the support in each strip A shall be taken as the sum of the areas of steel in one cross band and one diagonal band. The amount of steel to resist the positive bending moment of each strip B shall be considered as the area of the steel in a diagonal band. The amount of steel to resist the positive bending moment in each strip A shall be considered as the area of the steel in a cross band, and the amount of steel to resist the negative moment in each strip B shall be the steel included in the width of strip B. 37. For the two-way system of reinforcement the amount of steel to resist the bending moment in any strip shall be considered as the area of steel included in the width of the strip. 38. In both systems of reinforcement the compressive stress in the concrete in any strip shall be calculated by taking the area of steel considered for each strip and applying it in a beam formula based on the principles given in the article on "Design for Slabs, Beams and Girders" on page 270. 39. Where drop panels are used, the width of beam assumed to resist the compressive stresses over the column capital shall be the width of the drop. 40. The width of beam, where no drop panels are used, shall be the width of steel bands. Where this is found insufficient, the area shall be increased by introducing compression steel in the bottom of slab. 41. Rectangular Panels. When the length of panel in either two-way or four-way system does not exceed the breadth by more than 5 per cent, all computations shall be based on a square panel whose side equals the mean of the length and breadth, and the steel equally distributed among the strips according to the coefficients above specified. 42. In no rectangular panel shall the length exceed the breadth by more than one-third of the latter. 43. Rectangular Panels, Four-way System. In the four-way system of reinforcement, where length exceeds breadth by more than 5 per cent, the amount of steel required in strip A, long direction, both positive and negative, shall be the same as that required for the same strip in a square panel whose length is equal to the long side of the rectangular panel. 44. The amount of steel, strip A, short direction, positive and negative, shall be the same as that required for the same strip in a square panel, whose length is equal to the short side of the rectangular panel. 45. The amount of steel in strip B, positive and negative, shall be the same as that required for similar strip in a square panel whose length is equal to the mean of the long and the short side of the rectangular panel. 46. In no case shall the amount of steel in the short side be less than two-thirds of that required for the long side. 47. Rectangular Panels, Two-way System. In the two-way system of reinforcement the amount of steel required for the positive and the negative moment of each strip A shall be determined in the same manner as indicated for the four-way system above. 48. The amount of steel in strip B, positive and negative, running in short direction, shall be equal to that required for the same strip in a square panel whose length equals the long side of the rectangular panel. 49. The amount of steel in strip B, long direction, positive and negative, shall be equal to that required for the same strip in a square panel, whose length equals the short side of the rectangular panel. 50. In no case shall the amount of steel in strip B, long direction, be less than two-thirds of that in the short direction. 51. Walls and Openings. Girders and beams shall be constructed under walls, around openings and to carry concentrated loads. 52. Spandrel Beams. The spandrel beams or girders shall, in addition to their own weight and the weight of the spandrel wall, be assumed to carry 20 per cent of the wall panel load uniformly distributed upon them. 53. Placing of Steel. In order that the slab bars shall be maintained in the position shown in the design during the work of pouring the slab, spacers and supports shall be provided satisfactory to the Commissioner of Buildings. All bars shall be secured in place at intersections by wire or other metal fastenings. In no case shall the spacing of the bars exceed 9 in. The steel to resist the negative moment in each strip B shall extend one- quarter of the panel length beyond the center line of the columns in both directions. 54. Splices in bars may be made wherever convenient, but preferably at points of minimum stress. The length of splice beyond the center point, in each direction, shall not be less than 40 diameters of the bars, nor less than 2 ft. The splicing of adjacent bars shall be avoided as far as possible. 55. Slab bars which are lapped over the column, the sectional area of both being in- cluded in the calculations for negative moment, shall extend not less than 0.25 of the panel length for cross bands and 0.35 of the panel length for diagonal bands, beyond the column center. 275 56. Computations. Complete computations of interior and wall panels and such other portions of the building as may be required by the Commissioner of Buildings shall be left in the office of the Commissioner of Buildings when plans are presented for approval. 57. Test of Workmanship. The Commissioner of Buildings or his representative may choose any two adjacent panels in the building for the purpose of ascertaining the character of workmanship. The test shall not be made sooner than the time required for the cement to set thoroughly, nor less than 6 weeks after the concrete had been poured. 58. All deflections under test load shall be taken at the center of the slab, and shall be measured from the normal unloaded position of the slab. The two panels selected shall be uniformly loaded over their entire area with a load equal to the dead-load plus twice the live-load, thus obtaining twice the total design load. The load shall remain in place not less than 24 hr. If the total deflection in the center of the panel under the test load does not exceed 3^ o f the panel length, the slab may be placarded to carry the full design live- load. If it exceeds this amount of deflection, and recovers not less than 80 per cent of the total deflection within 7 days after the load is removed, the slab may be placarded to carry the full design live-load. If the deflection exceeds the allowable amount above specified, and the recovery is less than 80 per cent in 7 days after the removal of the test load, other tests shall be made on the same or other panels, the results of which will determine the amount of live-load the slabs will be permitted to carry. 59. General. The design and the execution of the work shall conform to the general provisions and the spirit of the Chicago Building Ordinances in points not covered by this Ruling and to the best engineering practice in general. 276 r.N OK IS DUE ON THE LAST DA 1 STAMPED BELOW AN INITIAL FINE OP 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. .... APR 24 1941 ADD H 4 4rt4) Arn 11 1942 APR 18 1943 APR -Jr, * 1&1943 jefAj *^