Engineering T ; of; USEFUL DATA ON REINFORCED CONCRETE BUILDINGS FOR THE DESIGNER AND ESTIMATOR BY THE ENGINEERING STAFF OF THE CORRUGATED BAR COMPANY, INC. UNIVERSITY OF CAUFOR1 PARTMENT OF CIVIL PRICE, $2St- SECOND EDITION CORRUGATED BAR COMPANY, INC. BUFFALO, N. Y. 1919 [I Engineering Copyright, 1920 By CORRUGATED BAR COMPANY, INC. BUFFALO, N. Y. PREFACE FOR more than 25 years we have been engaged in the design and development of reinforced concrete construction. During this period we have had occasion to publish technical data from time to time of interest to the engineer, the architect and the contractor. As a result of these publications we find there is a growing demand for a compilation of data relating to the design of reinforced concrete buildings. A number of comprehensive treatises have been published to meet this demand, but they deal generally with method and theory of design rather than with quantitative results. It is not intended, nor is it expected, that this handbook can take the place of any of the excellent textbooks on concrete design or replace the services of the designing engineer. It is hoped that it will supplement the works of reference and as far as possible eliminate the manual labor involved in the repeated application of formulas and diagrams to the determination of the dimensions of a structure. It is the further aim of the book to give under one cover all of the data needed by the busy engineer or estimator in meeting the every- day problems in concrete building design, or briefly to place in his hands designing information that in a measure parallels the familiar handbook of the structural steel manufacturer. Until such time as a national building code may be adopted, there will be recognized the impossibility of preparing a thoroughly satisfactory set of reinforced concrete standards so that we have of necessity confined ourselves to stress combinations most widely accepted and within these limits to give a satisfactory range of working values, values that give the "answer," without further resort to calculation, when the conditions of the problem are known. Several of the more comprehensive publications on reinforced con- crete contain some excellent diagrams that greatly facilitate the designer's work. A few of these diagrams have been incorporated in the present volume and due acknowledgment for their use is hereby made to the work of Messrs. Turneaure & Maurer entitled "Principles of Reinforced Concrete Construction" and to "Reinforced Concrete Construction," by George A. Hool, S. B., Professor of Structural Engineering, University of Wisconsin. Further acknowledgment is also made to those members of our organization who so ably assisted in the compilation of the data and to their efforts is due what measure of success may attend the publication of this volume. CORRUGATED BAR COMPANY, INC. Buffalo, N. Y., March 15, 1919. 785274 FORMULAS FOR REINFORCED CONCEETTE DESIGIST It is recognized by all authorities on the -design of reinforced concrete structures, that the common theory of flexure does not apply for wide ranges of stress. For stresses in excess of those commonly used in design the relation between stress and deformation is not uniform and this divergence becomes more pronounced as the stress increases. Under these conditions the parabola is the curve which most nearly expresses the relation between stress and deformation and is the relation which should be used in the discussion of experimental or test data to obtain accuracy of results. In the design of structures, however, the stresses used are low, a condition for which it can safely be assumed that the deformation of any compression fibre in a beam is proportional to its distance from the neutral axis. The error in this assumption is small and is on the side of safety. The formulas which follow are for working loads and assume a straight line varia- tion of stress to deformation of concrete in compression. Tension in the concrete is neglected. * STANDARD NOTATION (a) Rectangular Beams. The following notation is recommended: f a = tensile unit stress in steel. /c =compressive unit stress in concrete. E a = modulus of elasticity of steel. EC = modulus of elasticity of concrete. M = moment of resistance, or bending moment in general. A a = steel area. 6 = 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 =T-J- (b) T-Beams. b = width of flange. b f = width of stem. t thickness of flange. (c) 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. * From: Transactions of Am. Soc. of C. E. Vol. LXXXI, December, 1917. CORRUGATED BAR COMPANY, INC C" = total compressive stress in steel. d' = depch to center of eompressive steel. z = depth to resultant of C and C'. (d) Shear, Bond and Web Reinforcement. V = total shear. V = total shear producing stress in reinforcement. v = shearing unit stress. u = bond stress per unit area of bar. o = circumference or perimeter of bar. 2o=sum of the perimeters of all bars. T a = total stress in single reinforcing member. s = Horizontal spacing of reinforcing members. (e) Columns. A = total net area. A = area of longitudinal steel. AC =area of concrete. P = total safe load. (a) Rectangular Beams. Position of neutral axis, Arm of resisting couple, FORMULAS k = -V2pn+ (pn) z pn. (D (2) [For / B = 15,000 to 16,000 and / = 600 to 650, j may be taken at ~ o Fiber stresses, M M /8 A.jd 2M _2pf a Jc jkbd* k (3) (4) USEFUL DATA Steel ratio, for balanced reinforcement, 1 1 (5) (6) T-Beams. FIG. 2. Case I. When the neutral axis lies in the flange, use the formulas for rectan- gular beams. Case II. When the neutral axis lies in the stem. The following formulas neglect the compression in the stem. Position of neutral axis, ft* 2nA a +2bt Position of resultant compression, Arm of resisting couple, Fiber stresses, 2kd-t 3 jd=dz. f -JL h A a jd Mkd bt(kd-\t)jd fs k n l-k (6) (7) (8) (9) (10) (For approximate results the formulas for rectangular beams may be used.) The following formulas take into account the compression in the stem; they are recommended where the flange is small compared with the stem: Position of neutral axis, j2 \ (b-b')t* (nA a +(b-b')t\* nA a +(b-b')t. b' r \ b' ) b' Position of resultant compression, (12) t(2kd-t)b+(kd-t)* b' 7 CORRUGATED BAR COMPANY, INC. Arm of resisting couple, Fiber stresses, / = /.= M A B jd 2Mkd [(2kd-i)bt+(kd-t)*b']jd (c) Beams Reinforced for Compression. FIG. 3. Position of neutral axis, ')* -n(p+p'} Position of resultant compression, Arm of resisting couple, Fiber stresses, /c=- QM M A-k nfe ~ Shear, Bond, and Web Reinforcement. For rectangular beams, (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) USEFUL DATA (For approximate results j may be taken at ) The stresses in web reinforcement may be estimated by means of the following formulas: Vertical web reinforcement, V'a T -=i (24 > Bars bent up at angles between 20 and 45 deg. with the horizontal and web members inclined at 45 deg., In the text of the report it is recommended that two-thirds of the external vertical shear (total shear) at any section be taken as the amount of total shear producing stress in the web reinforcement. V therefore equals two-thirds of V. The same formulas apply to beams reinforced for compression as regards shear and bond stress for tensile steel. For T-Beams, v =Vjd (26) w =- (27) [For approximate results j may be taken at ^ ] o (e) Columns. Total safe load, P=/cUc+nyl 8 ) =f c A(l+(n-l)p] (28) Unit stresses, (29) /s=n/ c (30) CORRUGATED BAR COMPANY, INC. EXPLANATION OF THE USE OF DESIGNING DIAGRAMS Rectangular beams or slabs, reinforced for tension only, may readily be designed by the aid of Diagram 1, page 16. This diagram assumes a value for E of 2,000,000 or n = 15, which is recommended for the design of beams and slabs. Example 1. Given a beam having a span of 24 ft. simply supported, to carry a load of 4,000 Ib. per ft. including estimated dead load; / c = 650, f a = 16,000, E = 2,000,000, n = 15. Determine size of beam required. u _ (4,000)(24)(24) =288j(x)0 ft lb =3>456000 in , b o On Diagram 1, page 16, find the intersection of curves for / 8 = 16.000 and / c = 650 and read K= ^ =107.5 and p=0.77%=0.0077 M_ 3,456,000 A - A OA- * M 3,456,000 Assuming 6=24 in, d = ^ = \ (24)(1Q75) =36.6 ^=^=(0.0077X24X36.6) =6.76 sq. in. It will be noted that by selecting a value for either 6 or d the problem may be com- pletely solved. This selection may be governed by the relative cost of steel and con- crete or may be limited by clearance. Care should always be taken to ascertain if the section selected to resist bending moment is satisfactory in shear. In the example: V 48,000 = TT- T = - 7=r - = 62.5 lb. per sq. m. (24) (36.6) It will be noted that j has been taken as 3* which is sufficiently close when used in o calculations for bond and shear stresses. The result indicates web reinforcement would be required, for a limit of 40 lb. per sq. in. shear on the concrete. Example 2. Given a beam of 20 ft. span having fixed ends and carrying a total load of 1,000 lb. per ft; 6 = 10 in., d=18 in, A a = 2. 20 sq. in. and n = 15. Find/ 6 , /<., j and k. M = 400,000 fed 2 (10) (18) (18) 10 USEFUL DATA On Diagram 1 find the intersection of K=123.5 and p=1.22 and read / 8 = 11,900, fe = 650. On the upper portion of the diagram for p = 1 . 22 find j = . 846 and k = . 452. T-Beams. In the design and investigation of T-beams Diagrams 2, 3 and 4, pages 17, 18 and 19 will be found useful. These diagrams apply only when the neutral axis falls below the under side of the flange of the T-beam. When the neutral axis falls above, the diagrams for rectangular beams apply. Diagram 2 can be used only when the area of steel is such that/ 8 is 16,000 and Dia- gram 3 when / B is 18,000. From these diagrams, for any assumed value of d and for fixed values of M , t and b, we may obtain .; for determining the steel area required and also the value of / c . If / c is fixed, knowing M and t, we may find the value of b or d, by assuming one of them, and obtain the corresponding steel area. It should be borne in mind that b must not exceed code or specification limits. Diagram 4 gives values of k and j for T-beams and is useful in checking steel and concrete stresses, the dimensions and reinforcement being known. Example 1. Given a T-beam having a span of 24 feet, freely supported, to carry a total load of 2,000 Ib. per foot, *=5 in., 6 = 30 in., / = 1 6,000, / c = 650, n = 15, t? = 120. 4> =24,000 Assuming a width of stem of 10 in. we find from shear considerations, V 24000 =22.85 m. t From Diagram 2 trace upward from the value of - =0.219 to intersection with the a curve f or / c = 650 and read ^ =92.0. Substituting for M and d the values given above we find 1,728,000 _ (6) (22. 85) (22.85) 6 = 35. 8 in. This exceeds the fixed dimension of 30 in. for 6 so that it becomes necessary to assume a new value for d. Try d = 26 in. then j =0.192 a and from Diagram 2 6 = 29. 7 in. This value is sufficiently close so as to require no further revision. To find the area of steel required first obtain j from the right-hand side of Diagram 2 by tracing upward from / c = 650 to intersection of r-^ = 86.0 and read ; = 0.913 11 CORRUGATED BAR COMPANY, INC. M 1,728,000 then A s = j^ = ( o.913) (26) (16,000) = 4 ' 55 Sq ' 11L Example 2. Given a T-beam of 20 ft. span, ends freely supported, < = 4 in., d = 2Q in., 6 = 30 in., ^4==4.0 sq. in. Find the total load per foot this beam will carry when n= 15 and/B and/ are not to exceed 16,000 and 650 pounds per square inch, respectively, JL1-02 d 20 On the left of Diagram 4 from the intersection of ^=0.2 and p = 0.667% read k = . 40 and on the right from the intersection of p = . 667% and k = . 40 read j = . 912 M e = A a f e jd =(4.0) (16,000) (0.912) (20) = 1,167,360 in. Ib. = 650 (l - (2)(Q 4 0)(20) ) (30) (4) (0.912) (20) = 1,067,040 in. Ib. The resisting moment of the concrete, being less than that of the steel, will govern the carrying capacity of the beam. Equating the external moment (M = - wl z ) in o inch pounds to the resisting moment of the concrete and solving for w we find 8M (8) (1,067,040) = I2T* ~ (12) (20) (20) == Beams Reinforced for Compression. It is sometimes desirable or necessary to place reinforcement in the compression side of a beam in order to maintain the con- crete stress within safe limits. Continuous beams of T section are frequently deficient in concrete area at the supports, where due to the reversal of moment, the stem is in compression. When the stress in the concrete at this point exceeds that specified, the straight bars in the bottom of the beam may be carried through the support and utilized as compressive reinforcement. A continuous T-beam has the following dimensions: t = 6 in., 6 = 30 in., d = 34 in., b'= 14 in. The negative moment is 2,400,000 in. Ib. It will be assumed that the working stress in the concrete at the center of the beam is 650 pounds per square inch which may be increased 15% at the support, in accordance with recommendations of the Joint Committee, so that the value at this point is 747 pounds per square inch, steel stress 16,000 pounds per square inch. Determine the amount of compression steel required. In the top for tension, 2,400,000 (16,000) (I) (34) Vv = 5.04 sq. m. M_ 2.400.000 bd* (14) (34) (34) ~ Entering Diagram 1 with #=148, we find, f or / 8 = 16,000, that f c = 805. The reduc- 12 USEFUL DATA tion of/c to 747 will then be ^-= = 7.2%. Entering Diagram 5, on the left margin, with 7.2 and moving to the right to the "concrete curve," thence downward, the amount of compressive steel to effect the reduction in / c is found to be 0.20% or (14) (34) (0.002) =0.95 sq. in. Combined Bending and Direct Stress. In the design of columns, arch rings, etc., the resultant of the external forces does not always coincide with the center of gravity of the cross section of the member. In such cases consideration must be given to the combined action of bending and direct stress. For reinforced concrete members the general formula for extreme fibre stress where compression exists over the entire section, is w My W= Total direct load. p = Percentage of reinforcement = -~ y = Distance from center of gravity of section to extreme fibre. 7 C = Moment of inertia of concrete section about the gravity axis I B = Moment of inertia of steel area about the gravity axis. The other symbols are as given in the standard notation, pages 5 and 6. It is in the case of rectangular sections with symmetrical reinforcement, that we most frequently meet with problems involving bending and direct stress and Dia- grams 6, 7, 8a and 8b, will be found to greatly facilitate the solution of such problems. In the case of a homogeneous material no tension exists on the cross section when the resultant falls within the middle third. For a concrete section reinforced with steel bars the conditions are altered somewhat and the resultant may fall slightly outside the middle third without producing tension on the section. In those cases where com- pression exists over the whole section Diagram 6 may be employed, but where there is tension over part of the section Diagrams 7 and 8a or 8b should be used. Case I. No Tension on the Cross Section. Consider a column 18 inches square, reinforced with 4-1 in. square bars, carrying a load of 150,000 Ib. concen- trated 1 in. from the center of the column. Find the maximum unit stress in the concrete. Percentage of reinforcement, p = -r- 8 = QQ\ Qg) = 1 23% The eccentricity z = 1 in. and y=Yg = 0.0555 Entering Diagram 6 with j = . 0555, tracing vertically to p = 1 . 23% and then to the left margin find K'= 1 .09, a factor by which the average unit stress must be multi- plied to find the maximum unit stress. 505 Ib. per sq. in. 13 CORRUGATED BAR COMPANY, INC. To obtain the minimum concrete unit stress we know that the minimum is as much below the average as the maximum is above. In this example the average concrete unit stress is f , w . - ' / 1KWyl \ = 394 Ib. per sq. in. Thus the minimum unit stress is ^J ~r 394- (505-394) =283 pounds per square inch. Case II. Tension on the Cross-Section. Suppose the column of Case I had an applied moment of 800,000 in. Ib. in addition to an axial load of 100,000 Ib. Then M 800,000 * = JF = T6o66o = T-H- -" 4 As before po=1.23% entering Diagram 7 with ~ = 0.444, tracing vertically to p =1.23%, then to the left margin, k =0.60. Now entering Diagram 8a with this value of k and tracing to p = 1 . 23%, the value of F is found to be 0. 139. Then M 800,000 Max ''= w- (0.139) (18) (18) (18) = 987 P0unds per Sq ' m ' This resulting fibre stress is larger than is usually permitted and would necessitate a redesign of the column section in order to reduce the stress to the limit allowable. 14 USEFUL DATA W ^ ^ AilCO I PP 'OOP" Pr^QO ^PPP'" 33<^ PPP COPt^OS O T-I T-I os O X . . TH PPP ooo Tt< CO CO T-I ^5 p coco p ppp 1 " 1 (^ V^ U T J > co Sod ooo 000 ^^(MOS ddd^ co co ob T-I Tt< t* O CO ^O GO C^l odd 00 CO CO OS t s - . P CO GO CN PPP 1 ^ ,r:S?8^ ;ScoSo| ddd :S 000 000 iO OS CO OS GO T-H POP CO"* OS OO P iO CO P CO CO CO CO ppp 1 " 1 000 ,igm SJoS^ ppp T-I ii P (N i ^^ "* C^l CO ddd 50 If 1 10 O ^^ CO CO CO O ^f OOP ^ -H CO (N O (M O ' OO t^ <^ iO I s ** CO CO ^000 S OCOOUI odd' ooo ooo 15 CORRUGATED BAR COMPANY, INC. Percentage of Reinforcement 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.0 IlllllllillUJIIIIII IhlillllllllllllllLilllll II I Mil II II Mill I I 'I 0.0 0.8 50 40 0.5% 1.0% Percentage of Reinforcement DIAGRAM 1 Coefficients of resistance K and values of j and k for rectangular beams. 16 USEFUL DATA ~hs . S .22 17 CORRUGATED BAR COMPANY, INC. S I S 8 8 od 18 USEFUL DATA 19 CORRUGATED BAR COMPANY, INC. Percentage of Compressive Steel 0.5% 1% 1.5% 0.5% 1% 1.5% Percentage of Compressive Steel DIAGRAM 5 Compressive reinforcement of beams. 20 USEFUL DATA Values of ^ 0.10 0.12 0.14 0.16 0.18 0.20 0.22 2.00 1.90 0.90 0.90 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 Values of ^ DIAGRAM 6 Bending and direct stress. Values of K', a factor by which the average stress is multiplied to obtain the maximum fibre stress. 21 CORRUGATED BAR COMPANY, INC. Values of 0.17 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 1.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.2 0.1 0.2 0.1 DIAGRAM 7 Bending and direct stress. Values of k, the ratio of distance of neutral axis from extreme fibre to total thickness or depth, f, when d' = T 22 USEFUL DATA Values of k 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 O.I 0.17 0.16 0.15 ft*, gravity axis, v .[. R, N 3, |*/r*J w r>4-^- x< i ! _. ^,{. ,'R ~ ~^>L^ r-^J rC- ' flij X / / y M / ' II Kr kt~ i I "2 <^^ ^f^ > f 1 /Ml U - d-- ~i* i "S ^" x x 5 lo i< - ' -/- /ill f2 1 ^^ ^^ 35 / ^ y i \j \ i / 1 >< ^ ^ fllCr** / ' ^I/lM ' *.'**' **'**' ' 2 ^ / > / / 1 1 ~**'' x x "^ ^' x j Z i 5 > '/['Ml 0,14 0.13 x ^--X^-.-^^--.--.-^ '^"1 ^ /' I / i , / X x 1 * x.-*" 51 " oi ^ j 1 M / /I / -^ ^H^f ' [/ f /I ,' ,' ft, g 0.12 0.11 0.10 0.09 0.08 0.07 0.06 H - J \~ ;x**~~ -^=-"^ "" ; -=-=- = - - ^ / / ^/ / / _.-" ^ . ^ aS^^ / / ~T 1 7 __,.- 7p-- U-J / / ^ s ' "^ ii5t_ xi^ 1 / j J / sf x - -. ^' ^ / ll / / ^' ^"^ - "^-s.^ y r-WJ / 7 S ^*-- L_ . ^: ^ : ^ n._.__ i= --SaSil ' j M -^ ^L ? * ^ ^ = - : ---^^----^^; ---7 7~TI , ' V '*> ^o \l\ \ / , -" - = -- ^'^^ ^^^ y E&I ,. X / - ^ 1 ^^.,__ :^_ ! ^ "~M1 S "^ v, ^ ^ y y ^ ^ / -^bfe ^f? -^^ ^^~"in i T 71 =1 12 5 \ ^--^y - 3 " a: \j\ 5 f^ M "S ^^ I I 5 -^ FW* ^* \ /| I Sk ^ V ^ v^ ,' J S * / = ensi oJ ' ^ kt' ^ /-d ^ - n -'c'jt 1 ^ s^ v^ J Case II s J/J ^ ^ ^ , s\ \ _. 1 1 0.17 o.i6 0.15 S 0.12-5 o.io 0.08 0.07 0.06 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Values of k DIAGRAM 8a Bending and direct stress. M Values of coefficient F in formula for obtaining extreme fibre stress / c = "r 23 CORRUGATED BAR COMPANY, INC. c 0.32 0.30 0.28 0.26 0.24 B* o 8 0.22 1 0.20 0.18 0.16 0.14 Values of k .9 0.8 0.7 0.6 0.5 0.4 03 0.5 0.32 0.30 0.28 0.26 0.24 t ' "3 0.22 g 1 0.20 0.18 0.16 0.14 0.12 n=15 f c = - r-^+TS M W -2k) / / / / f f / / 1 / 1 1 , n ( !> / / " / * / / 1 / 1 7 / h 7 1 i / / / f 1 / 1 y / / / 1 / i i 1 / / < / / / / / f / 1 y I ll ll / ll // / / / . ? / , / I / / y 1 li / / 7 // / 7 ^ I ^ / / / 1 / 1 1 / 1 f I i / i\ / / r / ( ^ / / / * > 1 / 7 1 1 ' / j^ ^ / / / / / f / / 1 7 I / / / / / / \* ^/ / / ' / / 1 1 / ; / I f /i / n / / / / / / $ ^/ / / / / /^ V 1 1 1 i / / t / / / / / < t / 9|S 7 I / / 1 f / / 7 / ^ / ^ ' / / / / J / / ' < */\$ / / / 1 7 / 1 2 / i / x / x ^ * x ,1 / / ^ / / <-\ f / / 1 i / j / f _/ / / / / X / y / / x / / l b / fa t f / / ' * l / / 7 / / / / , / / ' x X / / / X / x 7 x / / / t / 7 / / ^ / / ) / f I / / A , / / / / x X x / / / ' / / / v ^ / / / / 1 / i / /I / , / x x / x ^ x , X / / , r / / / \ '/ / 1 f / / / / / / X / / / x X ^ x X X ' / / / I 'f j / / f / / / / / / x X x x X x / / X X T ' / / / / W y ^ / 1 / J i / 1 f t X , / x x x x ' ^ x x x x ^ . / / / ' & / / i x X / x x x x x x x x x) x x / / / / / '^ / / / / / x x x x x x J x X ^ x ' ^ x x x , / / / ' p / t t i 1 x X ' x x x x x x x X' x x x x X ' / ? / ' ^ / 1 2 x x x x ' x x X x ' r x ^ x x ' x x . x X / / / / ^ T x x x ^ x x 2 x ^ x x - ^ x X x XI '^ x X x / / 7 OB' s/ x x x ^ / - Cx x xl x 1 -1 x x X X X x 7 9* ' / x x ^> x x1 x "^ X" x ? x>l X ' x -- 5 ^ ^ , x x x s 2 / x x x x X X J x x x X X x ,*- ^ ^ I * X ^ X x x x x X x x X " x x x x X X X ^^ ^ ^ ^ ' ^ ^' x -- *** ^ / x ^i xj x ^ ^ , * ^ r"i ^-* ^ ** ^*- ^^- ^ ^ ^. x- ^ ^ " X X X x x ^ X ^ ^ -^ -^* ^ *** "^ ^-* , .^^ j f O $ t3 d- ! 1 frf }(*? X -" .^* ^^ < . ^-^ .--' - .> X ^ X x ^ > .-* ' , -* - . \[\ ^J .'Jc neutral axis ' X ^ ^ X *" ^*- ^^ - ^ ' ^, ^ ^^ Case II Tension over part of Section u &Ur 1 ^ J ^^ E K -fct * 0.12 0. Va 9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 Values of fc DIAGRAM 8b Bending and direct stress. tlues of coefficient F in formula for obtaining extreme fibre stress f c =^r- 1 W when d'= < 24 USEFUL DATA 1.0 0.9 "S n 0.8 ^ 0.7 0.6 0.5 L.O l 1 1.2 1.3 1 4 1 5 1 6 I. 1 ! ] .8 19 2.0 2.1 0.0 B ^^- * f *--'* ~ ** ' ^x QJ ^' ^/ ^ ^^ / ^ n j 7 ^/ / / f) o / / / j~ f 2 I 3 1 . 2 1 i ~w .-.tr^r. -'4f 1 1 i! ~i ~j i ; i (- ! ; / - - 4 1 1 y / I --0.5 ^ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 Ratio -^1- DlAGRAM 9 Curve showing distribution of load for rectangular slabs supported at the four edges. 25 CORRUGATED BAR COMPANY, INC. GENERAL FORMULAS FOR BEAMS REACTIONS, BENDING MOMENTS, SHEARS AND DEFLECTIONS CAUSED BY VARIOUS APPLIED LOADS The classes of beam loading given on the following pages cover the majority of cases occurring in reinforced concrete design. The formulas may be applied to a beam of any material, although it should be noted that those for deflection and maximum safe load require modification for use in connection with reinforced concrete beams. In the application of deflection and maximum load formulas to reinforced concrete beams account must be taken of the fact that the moment of inertia of the section and the modulus of elasticity of the material enters into the computations, thereby introducing elements of uncertainty that do not exist in the case of homogeneous beams, at least not within the limits of working stresses. Bearing this fact in mind it will be necessary to make certain assumptions before applying these formulas. These assumptions may be stated briefly as follows: 1. The moment of inertia is considered substantially uniform throughout the length of the beam, and shall be taken as that of the section of the beam at the center of the span. 2. The section shall be considered intact from top of beam to center of steel. 3. The modulus of elasticity of the concrete shall be taken as the average or secant modulus up to the working compressive stress. For such a beam the moment of inertia of a section is the moment of inertia of the concrete about the neutral axis plus n times the moment of inertia of the steel about the same axis, or -fc> for rectangular beams. -fc) 2 for T-beams The value of the modulus of elasticity to use in the deflection formula is that of the concrete, or It is recommended, from the consideration of test data, that 8 or 10 be used for n to secure fair agreement between computed and measured deflection. A more com- plete discussion of the subject of deflection of reinforced concrete beams will be found in "Principles of Reinforced Concrete Construction" by Turneaure and Maurer. The formulas, pages 28 to 37 inclusive, pertain to superimposed loads only, the weight of the beam itself being neglected. This fact should not be overlooked when applying the formulas in practice. The maximum safe load formulas apply only to homogeneous beams. To obtain the maximum safe load for a reinforced concrete beam, equate the maximum external bending moment, including the bending moment of the weight of the beam, to the internal resisting moment of the section and solve for w m . 26 USEFUL DATA NOTATION. The following notation has been adopted in the formulas: P, p = Concentrated loads in pounds. w = Superimposed load in pounds per unit length of beam or slab. W = Superimposed load supported by beam or slab in pounds. I = Length of beam in feet. L Length of beam in inches. RI, RI = Reactions at supports of beam, in pounds. V x = Total transverse shear in pounds, at distance x. V m Total maximum transverse shear in pounds. M m = Maximum positive external bending moment in foot-pounds. M' m = Maximum negative external bending moment in foot-pounds. x = Distance in feet to point of zero shear, or to M m . w m = Maximum safe load in pounds per unit length of beam or slab for load distribution indicated in each case. P m = Maximum safe concentrated load in pounds. / = Working unit-stress in flexure, in pounds per square inch. (This does not apply to reinforced concrete beams.) / = Moment of inertia of cross-section in inches 4 . S = Section modulus of cross-section in inches 3 . (Thic does not apply to reinforced concrete beams.) D = Maximum deflection in inches. y = Distance in feet to point of maximum deflection D. NOTE: When substituting numerical values in formulas all quantities must be expressed in the same units. For example in formulas for deflection E and / are usually expressed in terms of inches, therefore w must be taken as pounds per linear inch and L in inches. j DIVERSITY OF CALIFORNIA &TMENT OF CIVIL ENGINES*; IG BERKELEY. CALlr OHNIA 27 CORRUGATED BAR COMPANY, INC. 1. Cantilever Beam. Concentrated load. ! Jfj L x =P(x-a) m = P(Z-a) Moment Diagram D =^-_(2L3-3aL 2 +a3) (Right end) f Vm\ Sh4r Diagram D& = P (L-a)* (At load P) 6tiil 2. Cantilever Beam. Uniformly distributed load, Km Moment Diagram ; Shear Diagram It = w=wl=V m 7 TL =WX b*! ^-f-f Pm = 6T 2 " 3. Cantilever Beam. Load increasing uniformly to fixed end. ,w Moment Diagram _ wl 2 _ W( 21 wx* 61 Shear Diagram ^ ~~ or\j?j 28 USEFUL, DATA 4. Cantilever Beam. Load increasing uniformly to free end. a, -ip-=f-r. F, -f (a-,) Moment Diagram L/'"x 4/ 2 Shear Diagram n 11 wL* = 120 17 5. Beam Supported at Ends. Concentrated load near one end. t<- a -** & . Pb Pbx Moment Diagram ZEIL Shear Diagram y = - -\/36(/+a) a < b and ?/ on same --* F x =Ri PI for x between loads. .Moment F m = Maximum Reaction. Diagram _ L _ /O ! I I JW I I (W\ ! ^* = Pi T (J-z)+P 2 -7- for z between loads. 1rulli1lllltmlK! * * M m = Greater of Jl/i and M 2 8. Beam Supported at Ends. Two equal unsymmetrical concentrated loads. 6* p IP R< =^(l-a-\-b) F x =Ri P for # between loads. F m = Maximum Reaction Moment p Diagram M* = -j (al ax-}-bx) for x between loads. |p Shear Diagram ' -iy x lf m = Greater of Mi and 3/2 P = 126?i-i,+a) (wben '' >a) 9. Beams Supported at Ends. Two equal symmetrical concentrated loads. Fx =0 for x between loads. MX. =M m =Pa for x between loads. RA \ L j. P - ^ m 12o Moment j) = Diagram 2 -4a 2 ) At center. Shear Diagram Q* Whena=- f.-5 23 648 / 30 USEFUL DATA 10. Beam Supported at Ends. Three unequal unsymmetrical concentrated loads. *-a r *"~ 6 r - Le | M 6 2 a 3 - ------- -; IP. Jft Moment |K Diagram 2Pb _ _ 2Pa ~T K2 ~~T V m = Greater Reaction Mt^jSPb-Pfa-ad M m = Greatest of Mi M* and Ms = M Z if Pi < Ri when (Pi+P 2 )>Ri = M 3 if P 3 > Rz 11. Beam Supported at Ends. Three equal concentrated loads placed as shown. K ..l.. -.X- Jf .J...^-J.-^ I 4 K I- 4 fr I * M = Pl M m 2 P _ fS ^ m ~Ql Shear Diagram D = 19 PU ^ ^^ oo4 // 12. Beam Supported at Ends. Uniform load partially distributed. D agram Shear Diagram *, ...ruiMiii.-? 2 31 CORRUGATED BAR COMPANY, INC. 13. Beam Supported at Ends. Uniform load partially discontinuous. 21 Rz Moment y = Greater Reaction Diagram Shear Diagram ^ = j_ a _ 6+ *1 (when 6>a) .-------^> i^g 14. Beam Supported at Ends. Uniformly distributed load. Moment Diagram wl 2 Wl Shear Diagram Z) = 3/ 2 334 15. Beam Supported at Ends. Load increasing uniformly to center. Moment Shear Diagram wl* ,. Diagram M m = 32 USEFUL DATA 16. Beam Supported at Ends. Load decreasing uniformly to center. 17. Beam Supported at Ends. Load increasing uniformly to one end. x =0.5774/ a J = 1.3/S x Shear Diagram 2/ = . 519 Z D =0.00652 ^ 18. Beam Fixed at Ends. Load increasing uniformly to center. wl = '=! 32 33 CORRUGATED BAR COMPANY, INC. 19. Beam Fixed at Ends. Load decreasing uniformly to center. id 4 JT.-Jf.- g 20. Beam Supported at Ends. Uniformly distributed load plus load increasing uniformly to one end. TT-^ Moment D agram Shear Diagram Approx. between . 50 / and . 58 / 21. Beam Fixed at One End, Supported at Other. Concentrated load. , . fe-P(z-a) For x >a Diagram x\ = p Shear Diagram M ' m = 0/2 (^ 2 ~ a3 ) "* PL 3 _ j* 2 when y = a= . 414Z, D = . 0098 -^~ 34 USEFUL DATA 22. Beam Fixed at One End, Supported at Other. Load increasing uniformly IV Rl k i- to fixed end. To 10 ,__Moment y = ^ _^ I iV>>w rUnornrv, JQ <^ ^ X- "To Shear rjiagram M m = . 03 wl* x' =0.775/ 23. Beam Fixed at One End, Supported at Other. Uniformly distributed load. Tt & f fpi ! 3 ^ ! L^t-J *-- x >i ly=0.4215I>| -z ->, Moment Diagram wx T 9 Shear Diagram x' = ^- I y ='0.4215Z D = 24. Beam Fixed at Ends. Load increasing uniformly to one end. = 7i/ 20 ft = T^TT Moment Diagram _ 1 " 20 ~ 21 Afm! : I Shear Diagram 3wlx wP wx 3 20 30 6/ M m =0.0215w;/ 2 35 CORRUGATED BAR COMPANY, INC. 25. Beam Fixed at Ends. Uniformly distributed load. Moment Diagram M * = *"* wl 2 Shear Diagram ,. 2 24 x = 2 l D - 384 El 26. Beam Fixed at Ends. Concentrated load at center. u~4-~* 1 I p :i T Rz x =pa; - between ft and \Moment Diagram 1 / 3 2 P ( 4 -fij Shear Diagram Tfc Z) = 192 27. Beam Fixed at Ends. Concentrated load. h =P -a) 2 (2o+0 ^C 1 i ,:$* a; >> -4_/ F x = 7?i between R\ and P ^Moment Diagram F Xj = jRa between P and /? 2 3/x =^iX+M' m between RI and P = - P a(Z-a) 2 Shear Dis USEFUL DATA 28. Beams Supported at Ends. Concentrated moving loads. Case 1 /-N *L_ Max. V when x=o Max. M when x= - :fli = P :^(atP) Case 2 4 K -X Max. F when x = Max. M when x = (2J - a) y(2/-a) = (2/-a) When a exceeds 0.586/, use Case 1 for M m . CaseS j<- Max. V when x=a Max. M when x = >= | (3*-4a) j J When a exceeds 0.45J, use Case 2 for M m . - -i Max. V when z=o F m = Ri = *. , F -*T^ -^ a Max. M whenx= - I Z ^-p I M m =^P ^ "____ l J Maximum moment may occur under one load only. Case 5 r a ->t a -*- a *i MaX * V Whe X=a QQQGv^ Max. If when x= j(2/-a) , ^F > 2 4/ When a exceeds 0.268/, use Case 3 for M m . Z - ^i Max. V when x=a * ^ j /zf~ "t 2 Max. M when x= - + ^ ^ x >-j * t^. z >j JT _ g 2 ^P p Maximum moment may occur for I two loads only. See Case 2. Max. V when x=b. If - > ^ use Case 6. Ca^r 1 ^-''-^-- a -^-^ 2p P jR ^.._ x ->i T 2 Max. M when x = i (21- a) I M m = "^ (2/-a) I -p6 Maximum moment may occur as for Case 6. 37 CORRUGATED BAR COMPANY, INC. MOMENTS AND SHEARS FOR CONTINUOUS BEAMS The moment factors commonly specified for continuous beams assume equal spans and uniform loads. While these factors are within safe limits for the usual conditions met with in building design, cases arise where it is advisable to investigate the actual moments and shears produced, through inequality of span and load, by the theorem of three moments. This theorem may be employed in problems involving either uniform or concentrated loads or combinations of the two, but a full discussion of the theory involved would be out of place in a book of this character and, therefore, only a brief statement cov- ering its application will be given. In the formulas and diagrams which follow it is assumed that the moment of inertia is constant throughout the length of the beam and that the supports retain their same relative position after the beam is loaded as before. UNIFORM LOAD For uniform load the theorem is expressed by the formula, Mi w FIG. 4 The equation as written applies to the moments at the supports in span li and h; by increasing all the subscripts by one it will apply to spans 1 2 and h and so on for as many spans as there are in the structure. It will thus be seen that there may be ob- tained as many equations as there are unknown moments, assuming that the moments at the first and last support are zero or their values are known. Having obtained the moments at the supports, the shears and moments at any other section of the beam may be found by the following equations. Consider for example, spans h and / 2 in Fig. 4. v = M 2 Mi w^i li h 2 z . a ~ 2 The reaction at any support (R i} Rz, etc.) will be equal to the shear on its right plus that on its left with the sign reversed. USEFUL DATA The distance to the point of zero shear, provided the shear changes sign in the span, is Xi = - for span l\ Wi Xz = for span It The bending moment at this point, M = Mi+ViXi l ^- for span li M=M 2 +Vzx 2 - for span /, If the sign of this moment is plus, it is the maximum positive moment. If the sign is minus, it is the minimum negative moment and indicates that no positive moment exists at any point of the span. By changing the subscripts as previously mentioned the formulas may be applied to any span. CONCENTRATED LOADS For concentrated loads the theorem is expressed by the formula, . r t*i* $ 2 k * '4 *--* n ^ r i t t i Xl y I * 2 ' ' n i 5F 2 ------* 535- / -4 F4 --- ir -T FIG. 5 Applied to spans h and h, Fig. 5, the formula would be written as follows: The shears will then be: Knowing the moments at the supports, the shears and moments at any section may be obtained as in the case of continuous beams with uniformly distributed loads. Careful attention must be paid to the use of the proper algebraic signs in the fore- going equations. Equal Spans. Uniform load over all spans: Diagram 10, page 45, gives moment coefficients of wl 2 at critical sections of continuous beams of from two to 39 CORRUGATED BAR COMPANY, INC. seven spans and Diagram 11 gives shear coefficients of wl at supports for the same case. Example. For a beam of three spans the negative moment at the first interior support is . IQwl 2 . The shear at the end of the middle span is TTJW/ and at the inner support of the end span it is TQ W ^- Equal Concentrated Loads on All Spans: Diagram 12, page 46, shows three cases of loading. (1) Loads at middle points. (2) Loads at third points. (3) Loads at middle and quarter points. The full irregular line is the moment curve and the broken line represents the shear line for each case of loading. The ordinates to the moment line are coefficients of PI and the ordinates to the shear line are coefficients of P. The numerical coefficients are given at critical sections. Example: At the central span of a five-span girder loaded at the third points, the negative moment at the adjacent support is 0.211 PI; the positive moment at either of the loads is 0. 122PZ and the reaction at the adjacent support is 1.93P. The moments and shears of any uniform load should be combined with those of the concentrated loads on the girder. Partial Uniform Load: Diagrams 13, 14, 15 and 16, pages 47 and 48, for two and three span beams, give moment and shear coefficients that are maximum for the indicated positions of the uniform load; the ends of the beams being either free or fixed. Unequal Spans. Uniform Load: In the design of schools, hospitals, hotels public buildings, garages and shop buildings, the layout usually involves continuous beams of unequal span. The application of the three moment theorem in such cases can best be illustrated by means of problems. M2 \W2 MS Wz Mj-0 fe ------------ ... ......... ...zdb-^-4i _______ ,,.,, ........... 4 Bl #2 3 #4 Live load per foot of span = 800 Ibs. Dead ........ " =1000 " FIG. 6 Problem I. Assume a beam of three unequal spans as shown in Fig. 6, carrying a live load of 800 pounds per linear foot and a dead load of 1,000 pounds per linear foot. Find the critical moments, shears and reactions, the ends being assumed simply supported. Casel l h .-. __>!< i 2 ~~ >|-. / 3 --- Live Load on All Spans. The ends being simply supported Mi = M 4 = Q. The moments Mt and M at the intermediate supports can now be found. 40 USEFUL DATA From page 38, Substituting numerical values in these two equations: 7MM-10M. = - (1 - 8 4 ) (25)3 - (1 ' 80 4 ) (10) = -7.481.250 ..... (1) = -4.050.000 ..... (2) Multiplying equation (1) by 6 and subtracting equation (2) 41(W 2 = -40,837,500 M 2 = -99,604 ft. Ib. and we find M 3 = -50,899 ft. Ib. Substituting in Eq. (2) M s = -50,899 ft. Ib. From page 38, Vl = (-99,604) (1.800) (25) = - 25 -- ' -- 2 - = F' a = Fx- Wi= 18,516- (1,800) (25) (-50.899)-(-99,604) , (1,800) (10) = ^ - - F' 3 =F 2 -W2=13,870-(1,800) (10) T , Mi M 3 . Wsk R, =F 2 +F' 2 =13,870+26,484=40,3541b. R 3 =73+^3=20,545+4,130=24,675 Ib. R, =F' 4 = 15,455 Ibs. Distance from left support to point of zero shear, FI 18,516 ,~ f^. = -26,484 Ib. = -4,130 Ib. -15,455 Ib. = 7.71 ft. for span 41 CORRUGATED BAR COMPANY, INC. Moment at point x it M = = (18,516) (10.29) - ( 1 ' 80 )( 1Q - 29 ) 2 = +95,243 ft. Ib. This is the maximum positive moment in span /i for this condition of loading. Moment at point x^, ,, ,, . T7 M = M 2 + V z x t = ( -99,604) +(13,870) (7.71) - t 1 ' 800 ) (7.71) 2 = _46,166 ft. Ib. 2 This is the minimum negative moment in span 4 and indicates that no positive mo- ment exists in the span for this condition of loading, a point that is worthy of notice, as quite commonly this span is designed for positive moment only. Moment at point a? 3 , = (-50,899) +(20,545) (11.41) - (1>8 ) ^ 11 - 41)2 = +66.350 ft. Ib. If the beam is subjected to partial loading larger moments, shears and reactions may be obtained than in Case 1. The maximum values for this problem are given in the following cases when the live load is placed as shown. Case 2 Max. M, = - 103,506 ft. Ib. Max. F' 2 = - 26,640 Ib. Max. F 2 = + 16,992 Ib. Max. R 2 =+ 43,632 Ib. --- .t CaseS Max. M 3 =- 58,521ft. Ib. Max. F' 3 =- 9,465 Ib. Max. F 3 =+ 20,926 Ib. Max. R 3 = + 30,391 Ib. t PliMM I h J^~ Max. positive moment in span /i= + 97,300 ft. Ib. Case 4 Max. positive moment in span Z 3 = + 67,300 ft. Ib. Max. F! = + 18,614 Ib. Max. F' 4 =- 15,606 Ib. , Max. Ri = + 18,614 Ib. Max. R<=+ 15,606 Ib. Case 4 also gives the position of live load for maximum negative moment at the center of span Z 2 . 42 USEFUL DATA Problem II. Assume a beam having a long central span and two shorter end spans of equal length, as shown in Fig. 7, carrying a live load of 2,500 pounds per linear foot and a dead load of 2,200 pounds per linear foot. To find the critical moments, shears and reactions, assuming the ends simply supported. \w\ 1 M S IX v'\v z , vAv 3 , [* j I=20 '- ^ 1 2 =40'- >|* Ji=20'- Live load per ft. of span = 2500 Ib. Dead -2200 " FlG. 7 The solution of this problem involves the same procedure as that carried out in detail for Problem I, Case 1, and, therefore, the results only are tabulated below for the various cases of critical loading. Case 1 ll I miiiiiiiiiimiiimmiii . Case 2 M z = M 3 =- 528,750 ft. Ib. Positive moment at point Xi = + 44,978 ft. Ib. Positive moment at point a? 2 = +411,250 ft. Ib. F!= +20,562 Ibs. F' 2 = -73,438 Ibs. F 2 = +94,000 Ib. Rt= 20,562 Ibs. fl 2 = 167,438 Ib. Max. M 2 =- 544,375 ft. Ib. Max. F' 2 =- 74,219 Ib. Max. F 2 =+ 95,562 Ib. ^ Max. Jk = +169,781 Ib. = - 2,094 Ib. 12 NOTE. This loading gives negative reaction, Case 3 Max. positive moment in j.____i r !<-. 1 2 ^____.j r -_._>! gpan ^+442,500 ft. Ib. NOTE. This loading gives negative reactions Ri and R 4 = 2,875 Ib. Case 4 - 1 1 T _;, ^If. ; ^ ' Max. positive moment in span Zi= +116,294 ft. Ib. Max. F! = +33,063 Ib. Max. JRi = +33,063 Ib. 43 CORRUGATED BAR COMPANY, INC. The condition of simply supported ends assumed in Problems I and II is that which occurs when the beam frames into a brick wall. If, however, the ends frame into a column or girder, the moment at the end support will not equal zero, but will have a value depending upon the degree of fixity. This may be as large as ^ where small beams frame into heavy columns. For ordinary conditions the Joint Committee recommends a value of rr^- 16 We will now take Problem II, Case 1, and substitute for MI, a value -ry- and for 72 3/4, -T7T- and note the effect on the various moments and shears. 16 -117,500 ft. ,b. , From symmetry Mz=Ms Inserting numerical values, (-117,500) 160M 2 = (-9,400,000-75,200,000)+2,350,000 (-84,600,000+2,350,000) , 140fi o ff 1K 514,063 ft. Ib. Fi = (-514,063) -(-117,500) + (4,700) (20) 20 2 F' 2 = 27,172- (4,700) (20) = -66,828 Ib. Fj = (-514,063)-(-514,063) } (4,700) (40) & = 27,172 Ib. Rz = 94,000+66,828 = 160,828 Ib. _ 27,172 _ Xl """ Moment at x lt M = (-117,500) + (27,172) (5.78) - (4>700) ^ ' 78)2 = -38,955ft. Ib. 94,000 =20ft ' Moment at x 2 ,M = (-514,063) +(94,000) (20)- > 2 = + 425,937 ft. Ib. It will be noted that for Problem II, Case 1, with the ends partially restrained, negative moment exists throughout span l\. 44 USEFUL DATA DIAGRAM 10 Moment coefficients of w/ 2 for continuous beams of equal spans supported at the ends and uniformly loaded. 12 ots 615^ sTo 1 2 3 17 |15 13J13 28 28~ 23 [16 23|20 18T19 197*18 20J23 15|~0 38 38 38 38 38 38 63t56 49f61 53^53 6lf9 55^63 o 104 104 104 104 104 104 75s6 660 142 142 142 142 142 142 142 142 DIAGRAM 11 Shear coefficients of wl for continuous beams of equal spans supported at the ends and uniformly loaded. 45 CORRUGATED BAR COMPANY, INC. ^qf^ ] I <-. .31!^ 7 .69; p . .31 Loads at Middle Points 32]fiSLmrifl^ .73; ..^ptM* ,244 " - Loads at Third Points U^ 394 1.60 Loads at Middle and Quarter Points DIAGRAM 12 Moment coefficient of PI and shear coefficient of P for continuous beams of equal spans supported at the ends and loaded as indicated. 46 USEFUL DATA w pounds per foot --, Ri \\ 1^.10 Moment and Shear Diagram Supported Ends ,.054 wl2 .021 wJ2 Moment and Shear Diagram Fixed Ends DIAGRAM 13 Moment and shear coefficients for continuous beams of two equal spans with uniformly distributed load on one span only. w pounds per foot., w pounds per foot -, TWl ,059 w*2 Moment and Shear Diagram Supported Ends ! .028 wl 2 ITTTrK --r jj.m wl^ Rl r Moment and Shear Diagram Fixed Ends DIAGRAM 14 Moment and shear coefficients for continuous beams of three equal spans with uniformly distributed load on two end spans only. 47 CORRUGATED BAR COMPANY, INC. w pounds per foot , Moment and Shear Diagram Supported Ends Moment and Shear Diagram Fixed Ends DIAGRAM 15 Moment and shear coefficients for continuous beams of three equal spans with uniformly distributed load on center span only. . w pounds per foot^ ^ r :078 wl2 "BI ,'039^2 Moment and Shear Diagram Supported Ends .022 wZ 2., Moment and Shear Diagram Fixed Ends DIAGRAM 16 Moment and shear coefficients for continuous beams of three equal spans with uniformly distributed load on center and one end span only. 48 USEFUL DATA CONTENTS OF STORAGE WAREHOUSES Material Weights per Cubic Foot of Space, Pounds Height of Pile, Feet Weights per Square Foot of Floor, Pounds Recom- mended Live Loads, Pounds per Square Foot GROCERIES, WINES, LIQUORS, ETC. Beans, in bags 40 8 320 Canned Goods, in cases 58 6 348 Coffee, Roasted, in bags .... 33 8 264 Coffee, Green, in bags 39 8 312 Dates, in cases 55 6 330 Figs, in cases . . ... 74 5 370 Flour, in barrels 40 5 200 Molasses, in barrels 48 5 240 250 to 300 Rice, in bags 58 6 348 Sal Soda, in barrels 46 5 230 Salt, in bags 70 5 350 __~ - Soap Powder, in cases 38 8 304 >pr Starch, in barrels ... 25 6 150 Sugar, in barrels 43 5 215 Sugar, in cases 51 6 306 Tea, in chests 25 8 200 Wines and Liquors, in barrels . . 38 6 228 DRY GOODS, COTTON, WOOL, ETC. Burlap, in bales 43 6 258 Coir Yarn, in bales 33 8 264 Cotton, in bales, compressed . . 18 8 144 Cotton Bleached Goods, in cases . 28 8 224 Cotton Flannel, in cases .... 12 8 96 Cotton Sheeting, in cases .... 23 8 184 Cotton Yarn, in cases 25 8 200 Excelsior, compressed . ... 19 8 152 Hemp, Italian, compressed . . . 22 8 176 Hemp, Manila, compressed . . . 30 8 240 200 to 250 Jute, compressed . . . 41 8 328 Linen Damask, in cases 50 5 250 Linen Goods, in cases .... 30 8 240 Linen Towels, in cases 40 6 240 Sisal, compressed 21 8 168 Tow, compressed 29 8 232 Wool, in bales, compressed . . . 48 Wool, in bales, not compressed 13 8 104 Wool, Worsted, in cases .... 27 8 216 49 CORRUGATED BAR COMPANY, INC. CONTENTS OF STORAGE WAREHOUSES Material Weights per Cubic Foot of Space, Pounds Height of Pile, Feet Weights per Square Foot of Floor, Pounds Recom- mended Live Loads, Pounds per Square Foot BUILDING MATERIALS Cement, Natural 59 6 354 300 to 400 Cement, Portland 73 6 438 Lime and Plaster 53 5 265 HARDWARE, ETC. Door Checks 4^ Hinges TTtJ 64 Locks, in cases, packed 31 Sash Fasteners 48 Screws . . ... 101 Sheet Tin, in boxes 278 2 556 300 to 400 Wire Cables, on reels 425 Wire, Insulated Copper, in coils . 63 5 315 Wire, Galvanized Iron, in coils 74 43^ 333 Wire, Magnet, on spools .... 75 6 450 DRUGS, PAINTS, OIL, ETC. Alum, Pearl, in barrels 33 6 198 Bleaching Powder, in hogsheads 31 3$i 102 Blue Vitriol, in barrels 45 5 226 Glycerine in cases en Q-J2 Linseed Oil, in barrels 36 _ 6 216 Linseed Oil, in iron drums . . . 45 4 180 Logwood Extract, in boxes . . . 70 5 350 Rosin, in barrels 48 ft 288 200 to 300 Shellac, Gum 38 \J ft, ^-fOO 228 &\J\J L(J O\J\J Soda Ash, in hogsheads 62 2% 167 Soda, Caustic, in iron drums . . . 88 31^ 294 Soda, Silicate, in barrels .... 53 6 318 Sulphuric Acid 60 1% 100 White Lead Paste, in cans . . . 174 31^ 610 White Lead, dry 86 4M 408 Red Lead and Litharge, dry . . . 132 3% 495 MISCELLANEOUS Glass and Chinaware, in crates 40 8 320 Hides and Leather, in bales . . . 20 8 160 Hides, in bundles 37 8 296 Paper, Newspaper and Strawboards 35 6 210 300 Paper, Writing and Calendered 60 6 360 Rope, in coils 32 6 192 50 USEFUL DATA BUILDING CODE REQUIREMENTS FOR LIVE LOAD Structure Baltimore ! 1 | 1 '" 1 Milwaukee i Apartments 60 50 70 40 40 50 30 50 Public Rooms and Halls .... 100 100 Assembly Halls 100 100 100 125 125 Fxd. Seat Auditoriums 75 100 50 Mov. Seat Auditoriums 125 80 Churches 100 100 125 KO Dance Halls . . 200 100 150 100 Drill Rooms 200 100 Theaters 100 100 100 125 50 Theater Balconies Theater Stairways 80 Dwellings 60 50 40 40 40 50 30 50 Hospitals 70 KA K/) QA K.f) Hotels 60 70 50 40 75 30 50 First Floors . . 100 Corridors Office Rooms 50 Manufacturing Light Manufacturing Mercantile 175 125 125 125 2^0 120 100 100 150 100 200 100 100 100 Retail Stores 125 125 120 100 100 100 100 100 Heavy Storehouses 250 2^)0 1^0 200 "Warehouses 2^0 1 ^0 ICA 900 Offices 75 100 70 50 50 7*. 40 75 First Floor IK/) 100 1 W on 100 Corridors Public Buildings Schools Class Rooms Assembly Rooms 75 60 IOK. 100 7K 100 60 100 40 60 100 Corridors ... .... fiO Stairways fiO Sidewalks . 200 QflO QAA 1^0 300 Stables, Carriage Houses, Garages . . Stairways General 100 70 120 100 100 75 on 85 80 fio 85 Fire Escapes . ........ 7O R 00 f s Slope Under 20 40 Aft OK OK Oft on Cft Over 20 (Hor. Proj.) tjO Wind Pressures QA OA 20 90 OA on 51 CORRUGATED BAR COMPANY, INC. BUILDING CODE REQUIREMENTS FOR LIVE LOAD Structure New Orleans 1 1 Philadelphia Pittsburgh St. Louis 1 Seattle Washington Apartments 40 40 ,50 60 40 50 Public Rooms and Halls 70 75 Assembly Halls . .... 100 100 150 100 Fxd. Seat Auditoriums 75 75 Mov. Seat Auditoriums 125 100 Churches 75 75 Dance Halls 150 100 Drill Rooms 150 950 Theaters 100 75 75 Theater Balconies Theater Stairways 100 Dwellings 40 40 40 70 50 60 40 50 Hospitals 40 50 60 50 Hotels 40 40 50 60 40 50 First Floors 100 75 Corridors 1?5 100 75 Office Rooms 75 Manufacturing 150 ?00 150 ?50 Light Manufacturing 1?5 1 9 100 1?5 195 Mercantile ?00 150 Retail Stores 1?5 1?0 1?0 150 195 195* 110 Heavy Storehouses 150 250 150 Warehouses . . . ?00 150 900 150 ?50 150 Offices 70 60 60 60 60 50 75 First Floor 100 195 Corridors 100 110 Public Buildings 135 100 100 110 Schools Class Rooms . 60 75 75 75 75 50 75 Assembly Rooms T>5 75 Corridors 195 100 Stairways Sidewalks . . 300 300 150 Stables, Carriage Houses, Garages . . Stairways, General 70 100 75 75 100 Fire Escapes .... . 70 100 Roofs Slope under 20 30 40 30 50 30 30 40 95 Over 20 (Hor. Proj.) 30 90 40 95 ^^ind Pressures 30 30 30 90 30 USEFUL DATA WEIGHTS OF MATERIAL Substance Weight, Pounds per Cubic Foot Substance Weight, Pounds per Cubic Foot ASHLAR MASONRY Granite, syenite, gneiss . . . Limestone, marble 165 160 EARTH, ETC., EXCAVATED. (CONTINUED) Earth, dry, loose 76 Sandstone, bluestone .... MORTAR RUBBLE MASONRY Granite, syenite, gneiss . . . Limestone, marble Sandstone, bluestone .... 140 155 150 130 Earth, dry, packed Earth, moist, loose Earth, moist, packed . . . Earth, mud, flowing .... Earth, mud, packed .... Riprap, limestone 95 78 96 108 115 80-115 DRY RUBBLE MASONRY Granite, syenite, gneiss . . . Limestone, marble Sandstone, bluestone .... BRICK MASONRY Pressed brick . . 130 125 110 140 Riprap, sandstone Riprap, shale Sand, gravel, dry, loose . . . Sand, gravel, dry, packed . . Sand, gravel, dry, wet . . . EXCAVATION IN WATER 90 105 90-105 100-120 118-120 Common brick 120 Sand or gravel 60 Soft brick 100 Sand or gravel and clay . . 65 Clay 80 CONCRETE MASONRY River mud 90 Cement, stone, sand .... 144 Soil 70 Cement, slag, etc 130 Stone riprap 65 Cement, cinder, etc VARIOUS BUILDING MATERIALS Ashes, cinders . . 100 40-45 MINERALS Asbestos 153 Cement, Portland, loose . . 90 ICQ Barytes Basalt 281 184 Lime gypsum loose 53-64 Bauxite 159 JVIortar set 103 Borax 109 Slags, bank slag . . 67-72 Chalk 137 Slags bank screenings 98-117 Clay, marl 137 Qfi Dolomite 181 Slags, slag sand 49-55 Feldspar, orthoclase .... 159 Gneiss serpentine .... 159 EARTH, ETC., EXCAVATED Granite syenite 175 Clay, dry 63 Greenstone, trap 187 Clay, damp, plastic .... 110 Gypsum, alabaster 159 Clay and gravel, dry 100 Hornblende 187 53 CORRUGATED BAR COMPANY, INC. WEIGHTS OF MATERIAL Substance Weight, Pounds per Cubic Foot Substance Weight, Pounds per Cubic Foot MINERALS CONTINUED Limestone, marble .... 165 COAL, PILED CONTINUED Coal, peat turf 9fl_9A M^agnesite 187 Coal charcoal 6\J-&\) 1fL-1 A Phosphate rock, apatite . . . Porphyry 200 172 Coal, coke IU 14 23-32 Pumice, natural 40 Quartz, flint Sandstone, bluestone .... Shale slate 165 147 175 Soapstone talc 169 METALS, ALLOYS, ORES STONE, QUARRIED, PILED Qfi Aluminum, cast-hammered . Aluminum, bronze Brass, cast-rolled 165 481 534 Limestone, marble, quartz . Sandstone 95 82 Bronze, 7.9 to 14% Sn . . . Copper, cast-rolled 509 556 Shale 92 Copper, ore pyrites 262 Greenstone, hornblende . . . BITUMINOUS SUBSTANCES 107 Gold, cast-hammered .... Iron, cast, pig Iron, wrought 1205 450 485 Asphaltum 81 Iron, steel 490 Coal anthracite Q7 Iron, speigel-eisen . . . 468 Coal, bituminous Coal lignite 84 78 Iron, ferro-silicon Iron, ore, hematite . . . 437 325 Coal, peat, turf, dry .... 47 Iron, ore limonite 237 Coal, charcoal, pine .... Coal, charcoal, oak 23 33 Iron, ore magnetite .... Iron, slag 315 172 Coal coke 75 Lead . . 710 Graphite Lead ore galena 465 Paraffine 56 Manganese 475 Petroleum 54 Manganese ore, pyrolusite 259 Petroleum refined 50 Mercury 849 Petroleum benzine 46 Nickel 565 Petroleum gasoline Pitch 42 69 Nickel monel metal .... Platinum, cast-hammered 556 1330 Tar, bituminous COAL AND COKE, PILED Coal anthracite 75 47-58 Silver, cast-hammered . . . Tin, cast-hammered .... Tin, ore, cassiterite Zinc, cast-rolled 656 459 418 440 Coal bituminous lignite 50-54 Zinc ore blende 253 54 USEFUL DATA WEIGHTS OF MATERIAL Substance Weight, Pounds per Cubic Foot Substance Weight, Pounds per Cubic Foot VARIOUS SOLIDS Cereal, oats, bulk 32 TIMBER CONTINUED Maple, hard .... 43 Cereal, barley, bulk .... 39 Maple, white 33 Cereal, corn, rye, bulk . . . 48 Oak, chestnut 54 Cereal, wheat, bulk .... Hay and Straw, bales . . . 48 20 Oak, live Oak, red, black 59 41 Cotton, Flax, Hemp .... 93 Oak, white 46 Fats Flour, loose 58 28 Pine, Oregon Pine, red .... 32 30 Flour, pressed Glass, common . . 47 156 Pine, white Pine yellow long-leaf 26 44 Glass, plate or crown .... Glass, crystal 161 184 Pine, yellow, short-leaf . . . Poplar 38 30 Leather Paper Potatoes, piled 59 58 42 Redwood, California .... Spruce, white, black . . . Walnut, black 26 27 38 Rubber, caoutchouc .... Rubber, goods 59 94 Walnut, white Moisture Contents* 26 Salt, granulated, piled . . . Saltpeter 48 67 Seasoned timber 15 to 20% Green timber up to 50% Starch 96 Sulphur 125 Wool . . . 82 VARIOUS LIQUIDS Alcohol, 100% 49 Acids, muriatic 40% .... Acids, nitric 91% Acids, sulphuric 87% .... Lye, Soda, 66% 75 94 112 106 TIMBER, U. S. SEASONED Oils, vegetable . 58 Ash, white-red 40 K7 Cedar, white-red Chestnut 22 41 Water, 4C, max. density . . Water 100C 62.428 59 830 Cypress . . 30 \Vn tfr i Iffi Elm, White Fir, Douglas spruce .... 45 32 Water, snow, fresh fallen . . Water, sea water 8 64 Fir, eastern Hemlock 25 29 Hickory ... 49 GASES, Ara = l Locust 46 Air 0C 760 mm 0807 55 CORRUGATED BAR COMPANY, INC. WEIGHTS OF BUILDING MATERIALS Kind Weight in Ib. per sq. ft. FLOORS %" Maple finish floor and %" Spruce under floor on 2" x 4" sleepers, 16" centers, with 2" dry cinder concrete filling Cinder concrete filling per inch of thickness 18 7 12 18 21 23 5 10 6 5H 16 9^ 12 20 6 Asphalt mastic flooring 1H" thick 3" creosoted wood blocks on J^" mortar base Solid flat tile on 1" 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 }4" thick Sheathing I" thick Yellow Pine 2" Book Tile 3" Book Tile . . Kind WEIGHT IN LB. PER SQ. FT. Unplastered One Side Plastered Both Sides Plastered WALLS 9" 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" Brick Wall . 18" Brick Wall 22" Brick Wall 26" Brick Wall 4" Brick 4" Tile Backing 4" Brick, 8" Tile Backing 9" Brick 4" Tile Backing 8" Tile 12" Tile PARTITIONS 3" Clay Tile 4" Clay Tile 6" Clay Tile 8" Clay Tile 10" Clay Tile 3" Gypsum Block 4" Gypsum Block 6" Gypsum Block 2" Solid Plaster 4" Solid Plaster 4" Hollow Plaster . MASONRY Kind Weight in Ib. per cu. ft. Kind Weight in Ib. per cu. ft. Concrete, cinder 110 Mortar rubble, sandstone . . . 130 Concrete, stone 140 to 150 Mortar rubble, limestone . . . 150 Concrete, reinforced stone . . Brick masonry, soft 150 100 Mortar rubble, granite .... Ashlar sandstone 155 140 Brick masonry, common . . . 125 Ashlar limestone 160 Brick masonry, pressed .... 140 Ashlar granite 165 56 USEFUL. DATA FLOORS AND ROOFS WITH EXPLANATION OF TABLES Types. The selection of the best type of floor and roof construction depends upon the spans, loads to be carried, character of the building and local conditions. Build- ings readily divide themselves into two general groups, those primarily for the housing of people, and those for warehousing and industrial purposes. In structures of the first group, comprising office and public buildings, schools, hospitals, hotels, apartments, dwellings and garages the majority of the spans are long and the loads light (40 to 125 pounds per square foot). Such conditions require a greater depth of slab, to avoid undue deflection, than would be demanded for strength alone, and the problem is usually solved through the use of a concrete ribbed floor employing clay or composition tile, metal or wood forms of whatever depth may be necessary. In the case of clay or composition tile they always remain a part of the permanent floor and may be said to represent the best type of form or filler for con- crete ribbed slabs; they add stiffness and strength to the construction and in no way detract from its fireproof ness. To reduce the cost, however, metal forms are frequently used and may be of either the removable or permanent type. Permanent metal forms are of light gauge steel sheets, stiffened transversely by corrugations, to enable them to withstand the loads and impacts of service; they add nothing to the struc- tural efficiency of the floor and, in fact, may damage the concrete through expansion of the exposed metal in case of fire. For this reason, if metal forms are used, those of a removable type would seem the proper selection. For buildings in the warehouse and industrial group the loads usually vary from 125 to 500 pounds per square foot. Where the panels are square, or approximately so, the flat slab type of floor presents the utmost advantages structurally and economically. If, however, the ratio of length of short to long side of panel exceeds 1 :1M a beam and girder floor with solid concrete slabs should generally be used. Treatment. All beams, including the ribs in concrete ribbed slabs, may be classed under one of two types rectangular or T-section. In rectangular beams, the con- crete above the neutral axis within the limits of the width of the beam must resist the total compressive stress (assisted in special cases by additional steel in the com- pression area); whereas, in the T-section beam the flange, when built monolithically with the web, materially increases the compressive resistance of the beam and con- sequently its carrying capacity. The tables of safe loads for ribbed slabs, continuous or partially continuous, are based on a length of span equal to the distance center to center of supports, with the condition that the tile or form, as the case may be, shall extend to within not less than twelve inches of the center of support as indicated by the illustrations at the head of the tables. The critical section for bending is usually at this point and as the ratio between the bending moment here and at the center of span varies with each change of span, it would be uneconomical to maintain a constant steel area for each fixed depth of slab on all spans. In these tables the proper steel area for each depth and span length is given. Load and Moment Conditions. The carrying capacity of beams and slabs is dependent upon the condition of fixity at the supports and the stresses allowed in the 57 CORRUGATED BAR COMPANY, INC. steel and concrete. The safe load tables, pages 61 to 106 inclusive, have been prepared rtyt/2 7/1/2 on the basis of two different stress combinations and for moments of -g-, JQ and wl* TTr* The governing conditions are stated in the heading of each table. It is important to note that in the case of ribbed slabs or of T-beams continuous over supports, that the critical compressive stress usually occurs at the supports where the flange is in tension and the stem of the beam is in compression, thereby resolving the problem into that of a beam of rectangular section. However, as only a short section of the beam is under maximum compression at this point it is considered entirely permissible to employ a higher unit stress in the concrete here than at the center of span. This feature has been carefully considered in preparing the tables for continuous or semi-continuous ribbed slabs and T-beams and the maximum fibre stress in the concrete at supports has been held to a value not exceeding 15% greater than the fibre stress noted in the table. This is in accordance with the recommendations of the Joint Committee on Concrete and Reinforced Concrete. In the case of T-beams continuous over supports the straight bars in the bottom of the beam are considered to act as compressive reinforcement and should be carried past the face of the support a sufficient distance to develop their stress in bond. Shear. After selecting from the tables the proper slab or beam to be used for any particular load, special attention should be given to the shear reinforcement required. For the solid concrete slabs the loads given produce shears of less than forty pounds per square inch on the area bjd. For the concrete ribbed slabs loads to the left of the heavy stepped line produce shears in excess of ninety pounds per square inch on bjd and vertical stirrups should be used in addition to the bent up bars in the ribs. In the case of the beam tables, to satisfy the majority of code requirements, stirrups will have to be provided. Particular attention is called to the fact that all loads to the left of the heavy stepped line produce shears in excess of 120 pounds per square inch on bjd. Fireproofing. In preparing the tables the depth of fireproofing under the rein- forcement was taken at % i n - f r solid and ribbed slabs and 1% m - f r beams. As the fireproofing determines the effective depth for any given slab or beam it will be nec- essary to increase or reduce the table load should a change be made in the amount of fireproofing. This may be effected by multiplying the sum of the superimposed and dead loads of the table by the square of the ratio of the new effective depth to the given effective depth. This gives the new total load from which should be deducted the dead load in order to obtain the new superimposed load. The following examples illustrate the use of the tables: Solid Concrete Slabs. Given a floor layout consisting of solid concrete slabs, continuous over beams spaced 12'-0" in the clear. The floor to carry a live load of 150 pounds per square foot, a wood finish on sleepers embedded in 2 inches of cinder concrete and a plastered ceiling; the finish and plaster weighing together 25 pounds per square foot, giving a total superimposed load of 175 pounds per square foot. The stress in the steel not to exceed 16,000 pounds per square inch and in the concrete 650 pounds per square inch. 58 USEFUL DATA The table on page 63 for slabs continuous over supports and based on the specified unit stresses shows that a 6^-inch slab reinforced with Y% round bars, 7^ inches on centers, will carry 178 pounds per square foot. Concrete Ribbed Slabs Clay Tile Fillers: Given a floor of 22'-0" span, non- continuous. This floor is to carry a live load of 70 pounds per square foot, a wood floor on cinder concrete fill and a plastered ceiling; the finish and plaster weighing together 27 pounds per square foot, thus giving a total superimposed load of 97 pounds per square foot. Steel stress 16,000 pounds per square inch and concrete 650 pounds per square inch. The table on page 67 for non-continuous slabs shows that a 10"+2^" slab with 1.15 square inches of steel in each rib will carry 106 pounds per square foot and a 12"+2" slab with 1.04 square inches of steel will carry 112 pounds per square foot. If the 10" +2W slab is selected the area of steel called for in the table may be reduced in the ratio of actual total load per square foot to the total carrying capacity per square foot or, New steel area = (1.15) L -j =1.10 sq. in. per rib. This area may be secured by using 1*4" rounds and \ l /% rounds in alternate ribs or 2-%" squares in each rib. If the 12"-|-2"slab is used the table area of 1.04 square inches may be similarly reduced to 0.96 square inch and a \Y% round bar placed in each rib. Concrete Ribbed Slabs Steel or Wood Forms. Consider a floor slab of 21 '-0" span continuous on one end only. The floor is to carry a live load of 80 pounds per square foot, a wood floor on cinder concrete fill weighing 18 pounds per square foot and a ceiling of plaster on metal lath weighing 10 pounds per square foot, giving a total superimposed load of 108 pounds per square foot. The table on page 74 gives for a 12"+3" slab reinforced with 1.30 square inches of steel in each rib a carrying capacity of 122 pounds per square foot. As this is in excess of the requirements the table area of steel may be reduced as in the previous example arid an area of 1.20 square inches used. This area is secured by using 2- J^" round bars in each rib. Tee-Beams, Continuous over supports. Determine size and reinforcement of a beam in a floor construction assuming the span to be 22 feet, the superimposed load 200 pounds per square foot, the floor slab 4}/" thick and the distance center to center of beams as 7'-0". The beam is continuous over supports and the unit stresses employed are to be as follows: / 8 , 16,000; / c , 650; and v, 120. Haunches are not to be used at the ends of the beams. This represents the type of beam usually encountered in building construction commonly referred to as a T-beam, but due to the continuity at supports its capacity must necessarily be rated on the section of the web of the beam rather than upon the T-section at center of span. From the data given the total load per square foot of floor, including the Weight of the slab, is found to be 256 pounds per square foot, or 1,792 pounds per linear foot of beam. By referring to the table on page 98 it will be found that a 10" x 26" beam reinforced with 4-1" round bars will carry, exclusive of the weight of beam, 1,927 pounds, which from a practical standpoint fulfills the conditions of the problem. 59 CORRUGATED BAR COMPANY, INC. If it is required to maintain a minimum depth of beam it will be found that a 14" x 22" beam, reinforced with 6-%* round bars will carry the load. It will be noted, however, that the shallower beam requires more steel and concrete. To determine the number of stirrups required for the 10" x 26" beam, find the end shear. (2,062) (^ = 113 Ib. per sq. in. (0(10) (23) From the table on page 107 for an end shear of 120 pounds per square inch a 10-inch beam of 22 foot span requires 20-%* round stirrups, and for an end shear of 100 pounds per square inch, 14-%* round stirrups. As the actual end shear is 113 pounds per square inch, by interpolation, 18-%" round stirrups will be sufficient. In the tables which follow the endeavor has been made to give a fairly wide range of values from which to make the desired selection of size of member and reinforcement required, so that knowing the load and span the designer may enter the tables and choose the beam or slab which best meets the needs of his particular case, much as he would select a beam from a safe load table in a structural steel hand- book. 60 USEFUL DATA 383 goo S - ,* o c **~> *^ p jj 'bs^ y J3d qIS jo o CO ^ co l> O OO O CO 00 i-H ^ o co oo o CM co GOO5COCOCO-H i ii-HOOOCO'CiOCO co ^o oo c^ co I~H T (OT ICO CO CO ^^ CO OO CO CO 00 CO O OO O CD T 1 CO CD CO i"H t^* CD CO TH CO CO iO O CO CO i-H C<) CO "* CD l^. Oi 61 CORRUGATED BAR COMPANY, INC. SO sr! 2 'OS qIS jo T-H 1C * O CO Oi O5 CO Tfri to t> 00 O - O5 O !> Oi r- 1 CO IO i i IN COOC.Oi' I Oi O^ 00 GO CO CO^OI^-OCO cOr-iCOO5.OiCOl>.T-( I-HI li li-H 1^ OOT-HT- i COOOi Tti ^fl>-T iiOC^i I COCOO^OCO 00 loo CO i i O TH O^ t^* 1-1 T- I - lO rH CO OO rH rH CO l> OS C$ CO T t i I rH i I CSI C^J S ca rH rH rH - T* OO 00 CO rH 1> 22!i^!?22^S ir * ) '^ cs;|00 CO CO OS CM CO CO CO rH tO rH > CO >O 00 C^ CO H rH T-H T-l CO TH CO Tjn 00 T O OS CO 00 Tf< rH rH T-H C^ CO rH t^. O5 OO (M Oi 00 O >O Tf T-H (M CO ^T 1 Ss tO CO CO rH rH OS t>- t>- rH rH C3 CO U O 00 l>- CO OS 00 \M\^\cq\oo\oo\oo\oo\oo\-|(\,j(\,ji rH\ r1\ rH\ U5\ IO\ U5\ IO\ kO\ OT\ PS\ C<9\ IO tO CO rH l> ^ O OO 00 OS O CO W O rH Solid Concrete Slabs ?? CORRUGATED BAR COMPANY, INC. rT bs~ Q'BIS Oi . CO U5 CO OO O "3 t^ O CO ss s ^ ss cOCSOSCNiOOOcO co^oi>ococoos *OOO'-i'i-HiOOi-'Ti-Ht~ T-H ^H -rH CNJ CO CO os oo co o^ os ^fl>i (tOi^ r- ii ^CN t^ co co *-H oo T lOSCOiO^T TjHrfitOCOl> i (i (lOl-^CO COCOOiCOOi cOOOl^-CO OOl^iOiO U3 ^ T-I CN O\ CO\ iH\ rH\ i-H\ i-i\ IO\ IO\ \ U5\ P5\ l^^OcOCNOSiOT-Ht^T^QCOCNOS^O CO < ^OiOCOCOl>OOOOOSOO' ii iCN USEFUL DATA S oc L x qIS jo t>- O5 rt* i i O ^H Oi CO to CO 00 O - Oi rH CO CO OO T 4 Tt* t^ t>* iO.COQi>. OOfMOCDiOt i COI>i HiOi lOS rH ^H s ! C^l O5 ^O O^ CO ' iO-O0i 'CO* IT li-H COO>O(MOCpO5Oi (N CO d ^f T 1 i-H i I CO CO C^ CO l> i i C^ CO - IO O to OO -^ T-I (N CO Tjn CO t'-COOSOOt-'COOOOOt^COOOOOOt^t'- Solid Concrete Slabs 65 CORRUGATED BAR COMPANY, INC. CTJ r 4* S & I-H OO C-COCO "tft>O5OCOlOOOCO S CO-^COOS O jocogb^cftoopcoir 1 - i I T-H T-H T-H 1-H (M OOOOCOl>.i iiOOi i i TH T-I C i i l> IO 53 95 la iO t^ CO CO CO CO CO O 00 CO CO t O 1 I 1 I T I CO CO Oi CO 00 O 00 3 rHt^oo^cocoooT-j IO rH Oi t>- CO C CO rH TH (N CO % 8 g ^ ol i-H (N - CO 00 oooot>.coosoooot>j>. 66 USEFUL DATA -S co" , S cq 10 rfi o CO "^ CO *O CO S rH CO M< t^- Tt< >O Tj< CO s S? 3 & S S o 1 IO IN CO ^ CO 00 CO O5 00 II S 5 S S S 8 S 1 Z I 0^ iO ^O CI> C^ *O O^ CO *O CO O^ ^H O^ C^ s % e O l>- O CD O CO i-H ^ s s i 3 cr t/} s s s s a s g o i-H g K c -fe = Sis 1 i 2 c GO O5 CO CO CS 00 T~< CO i (l 6- O 2 2 1 COOt^-GOt^-T-HCOC^T-H CO CO O 1 CO *-O O 1 "^ ~^ I s * ,-H r-( ,-H C^ C^ (M -C s ^COQCCOOC'^'-^ ,_H i-H rH ^D C^ "^ "^ T < 00 C^ CO OO 3 rH > CiT-HCOCOiOi-HtNOOi (lOCO C*^ ^t 1 l> i 1 * OO CO CO C"J O^ ^ CO T-H T ( C^ C^ CO CO CO ^t 1 to H S sg iPsslia5 1 w co COr iO lOCOCOcO OOO IO !> C^ !> t^* CO t > * CO O5 C5 T IT (C^COCO^t 1 TfICO cxi i I C< CO Tfl Tt^ iO t> rH ooooo^co *O CO 1 s * OO O5 i C \^l \^ N^l \^ ^i(N(NCNi(N01 ^ 3 ^ t^. to 05 '"" ci "* o' ^ <=i ?ooo?>or'i-ir*^O^' i(M ci 6 ci ci'~ l ci 1 ~ H ci'~ 1 o CO ^ CO ^ t>* co (N oo * oo ij oo 05 ^ O ^ -I *- C) ^" O " C> t^^fM^-^^iO 00 ^ CO rf 8 CO ^ CO ^ o c '~ l c 2SS ^ CO > l> O ^ ^ to *H ^ o ^- 10 ^* oo So O^ Oi ^b co oo oo (N (N o o 68 DATA O i 1 ~ BHS I n -| ^ co^ o O O O O k'/It9*Sgg'! ooooo d d o o d c> o d d d d o^o d o o o 8 . 22 8 o o ' ' c> d d o ^ o *, fc *. 6 8 TH C, rH o 1 I d TH O C^ ? t^ ^ ^t* - 55 eo ci e CO CO C, QG C* oo oo (N Clay Tile Ribbed Slabs 69 Clay Tile Ribbed Slabs CORRUGATED BAR COMPANY, INC. 35S a -4 -4 p g -|) M II I * !J ii ^l iO >0 Eg 3 5 IO CO CO O 05 CO O CO co 55 g 8 8 So CO 3 S S SCO O5 (N C^ "^ Oi CO 00 OO CO i""l rHCOt^OOOOCOO5 OiOCOt>-OOO5O5O OOOOOOOi-H rH t^. 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Oi >O T~< >O >H CO Ti ^ 10 ^ ^ CO >^ CO ^ co ^ t ; CO O) to (M . OS CO r-4 O CO CO i I , I CO rjn lO I-H iO CM OS CM t^. tO I> GO 82 co i i co co ^ to o co ^H rH i-H O CO %%3 t*** OS i-H CO ^-H CO t^ T)H OS Oi to l>- os to os t> OS i I O CO O GO CO (M 10 CO CO to CM i I tO CO tO CO CM 1 I b- b- ?5 O CO to to i i b- CO OS i I CO O to tO OS i-l CO rrH CO CO S S 8 S 2 to i ( OS to CO CO "5 to CO tO CO t^ (M GO (M CO O GO CO O O t^ "O O CO ^ ^^^^ \oo lO\ - CO COOtOOS - OO OS O i-H tO t>- T* 1 I Tfl 1 I t>. CO t >COOOOS COt^OSO i-H i-H !** OS CO CO OS i"H OS CO t^-* !> OO *H CO ^O CO 1C O CO ^COt^OO T-I t O 00 CO CO i CO co oo o i i iO to C^ CO 00 CO 00^^ CO o r-~ t~ oo COOO'* ' (M O 00 O iO l-H CO TH CO Tf i I l> OS i I CO i CO *O I 1 I 1 1 1> >!> 00 O5 CO i-H O - CO CO tO OS CO *O OS CO i ^^ CO t*" ' 00 00 !M OO (M CO I rH (N (M i CO T-l Tfi I .i.j Rectan- gular Beams CO IO CO rH t-- CM rH CO CO CO ^ Tt< Oi CM 00 t- CM CM CO to rH 1 I tO b- O rH QO 1 I 1 I IO 00 rH rH CM Tfi -* CM Oi tO (M O CO CO CO CO OO CM O t^ O rH to oo oo O rJH CO ^ 00 OO CO * rH CO CM Tt< rH CO CO CM CO 00 rH rH rH rH CM rH rH CO 00 00 rH 00 rH rH 00 10 CO rH IO * O 00 rH CO rH CO C5 Oi b r^ O tO O CO t~ O S CD CO CO - l>- CM to oo -^ rH O tO t>. CM to ^3 22^5 *g | 000 rH CO !> T)H t^ t^ CO ^ T^ 8 \N r-(\ rHrH(N rH \00 \rj* NflO \00 \HI \r(( i\ co\ >\ >o\ w\ eo\ rH(N(M(M COt^O OOO COCOS tOOO COOOO OOO- to CO ) t^m CO CO i to CO GO Oi i I CO OO COI-O O CO CO O CO CO t^- CO iO CO CO O^> O^ CO O OO CO rt< O -^ CO CO T-H t^ O CO t^ to CO CO OO O O CO t-i |> CO to i GO O5 i CO iO i GO 1-1 . IO O5 i -GO 1-HTt* CO CO Oi Oi(M T-I 00 t^ (M oo o ill tO (M iO CO O5 T-H r(H O s O5 O nj S3 r" QO oo p p !> (M O - CM iO CO CO OS TJ4 CO CO 00 2 CM CM 10 CO t>- os CO TJ4 iO CO O CO !> CM OO OO CM !> t> O T-H CM CM ^H T-H CM CO T-H 00 I> I- t- t> OS T-H QO OS OS r OS Tt< t^ 00 T-H CM O t- t Tt< CM CO co co o CO ^ CO O T-H iO CO l~ CO o to CO T I 00 CM CM to ^f CO CM T-H CO fri OS CO l^ CO t^ 00 CO OS OS CO a Oj CO CO 00 r-i >O O t^ 4 iO 00 OS O C> C<\ CO CO >O rt* CO b- CO CO ^H i i i i - OO (M CO IO ^ 1 I OS T-I CM CO CM s? T-H IO ""Sf . OS t^ O CP T^ ^ CO b- CM OO CM O \,f \00 \00 \J}( \00 co\ t\ \ eo\ \ \00 \00 \H< \r|< t^\ C\ eo\ co\ T_| ,-1 CM i-H T-H CM T-H rHCMCMCM i-tCM COCO COOOO OOOCM OOOCM OOOCM^ OOOC^^ i I T IT I T IT I T-Hl-Hi-H i It I i-H 83 Rectan- gular Beams CORRUGATED BAR COMPANY, INC. --?-* ^ . .iSi 1 i ! ; \ -4 S3 CQ -HI 1 - f4 ' 1 i 1 I | j a ^ 1 C3 '^ J 1 'LA s -H W x ^1 / 3 ! i _.^* f: - a t- CO CO 00 O >O 00 05 10 00 t- TH 10 CO 10 00 00 TH 00 OS CO IO 00 CO OO IO is r-* *# co t- rH O> CO CO C N CO ^ TH ooeooo cooioo t-COOt- COTfCOCO OSCOOrH COIO'*'* THCOCOCO COCOCO-<1 O IO O O t> T* t*- CD IO CO ^ U5 10 O e$8 ^ SIO O IO TH CO ^ CO CO O 00 CO t- o <* t- CO IO t- Tjt IO IO rf 00 CO Sco t> 10 O 10 oj 10 10 oo CO CO 1< Tf III CO CO CO CO t~ TH OS 00 IO TH TH N CO Tt kO ill SCOTHTH THTJ.OCO SJS^S t-t-TH rHOt-CO COCOCOOO SOI CO TH t~LOt-Tj< OTjIOSiH 10 t- 00 tOCOOOTH OOSiHTj* COTHC1N THCJCJN THCJNN r-l j| I CO rH CO CO rH CO CO CO rH CO CO CO rH CO CO N CO CO CO TH 84 USEFUL DATA Rectan- gular Beams o o . 00 ( r N ft ---?-' 1 Qi /) o', I w 1' m i 1 i : j l.-t, C^ C^l ^^ CO "^ CO t* O i^ CO to CO 00 - CO to to CO to < - 10 i-nto^ i COOOOSC. 22 z2 r 1 P 2 O5 CO !> 4 s * IN* ^H CO CO i-H "f C^OC^CO O T-I iO ^ CO "t 1> 1 I OS r-i ^H CO IO 10 00 iO >O O O vO 00 OO OS OO Tfl 1> ^ T-H O C^J O (MO (N CO i i t^- CO O OS CO to CO t^ \M \00 FH\ io\ l-Hi-l O O 00 CO O to OO COOOO OOO(N OOOlM CO 85 Rectan- gular Beams CORRUGATED BAR COMPANY, INC. mm <= 4^^^ till". CQ 's 1 1 W a lH :J/ 2 tc - : 4 I \ I ^H IO Oi OO CQ "^ ^^ T-H !> l> T-H ^H 10 CO "^ t^ CO Oi CO CO t^ OO *O t^- 00 Oi CO t>* CO I-H t^(M O Oi i-H I SIS! T-H 1 I 1 I T (lOOit^- I>-T I I CO O i-H T-H 00 i Oi OO **! O3 C^ I T I CO Oi i-H TJH O C^ i O CS Oi 1 00 CO i~^ ^i O5 :^; 8: IC^COCO O CO CO Oi CO CO Oi CO O ' T-H T-H T-H T-H TH i-H i-H C\ 00 O C I i-^ t>- OO O 1C *O T i CO O O ' OS CM CO Q CO CM CN iO CM OO O i I CO t^ ' ) t^ OO *^ C^l OO OS ' CO t^ *C CO Oi CO O O QO CO O CM O CO OO CO t^ 10 1^ oo co oo o i ;2^5 i(M i 00 -^ l> >OOO Ci< i-t OO !> CO O O O O5 -H O CO i CO- i I (M OO Tj< i CM co * o co oo t^ eot^ o 10 IO iO >-O >O !>. CO CO OS CQ CM O I-H (N CNJ CO C iO O iO C^J (M 00 1O Oi !> ^ iO CO -noca o O OS co ^ co l> C 1 T t 10 oo ^H *O CO I s * O^ tO O5 lO t>* 00 CO t>- t> o t oo i i O^ CO OS 'O *-H O5 O^ O^ 4 s * CO iH *O t^* I-H - 10 CO \rJ( W\ t>\ io\ eo\ eo\ COOOO OOO(M OOO- rH OS 00 ^f Tt< COO i-t t>- OO . (M rH(M(M CO t>. rH IO OS C^^^^ CO (M O OO (M O i co os 10 o T-H r>. i > '3 1 1 c o g T3 0> 1 o o o t> CD CO 00 O l-H CD 00 *O 00 OO 00 i-H rH OS CO O l-H 05 00 OS OS rH iO C^ CO b- O 00 O C3 rH rH oo 3 rH [^ CO t. 00 rH rH CO t- 1-1 00 O> in CD O ^g I ( rH rH rH rH l-H 3 O 05 O t^ t*^ 00 00 CO O CO CO iO CO 00 t^* O5 St>- O O 00 T}H rH iO O . (N CO r-l iH rH (N l-H (M (N S CD iO OS rH 1 S 1 1 (N >O l^ iO CO l> (M (N CO rH rH 10 CO 00 i 1 rH rH t>- IO O O CO I-H CO t^* CD ^ CO CO C^ C^ C^ C^l CO CO || iO CO iO O * Tt O OS CO 1^ 00 iO O5 CO C^ CSI C^ CO C^l CO ^ a ! I ^ 1 rH | rH rH rH ^\ ^ fc i-H rH rH rH rH rH (M CD iO CO CO O k J CO 00 00 O g^ ' 1, is E ted, CO C<1 00 - i-H . CN O O - rH rH * OJ O CN O CN Tj< rH i-H So 1 t- eo 10 eo * CN t- OB c* J t* OJ O CN O CD O CN T!< CO to s S 1 g rH rH rH rH t> O t>- rH CN CO O CO rH CN 10 CN CN CO Q? ^H tO GO rH rH CO eo co OJ CO OJ CO tO CN rH CO O CO CO OJ rH rH rH rH rH rH 1 1 I S i rH rH rH rH CN rH CN eo CO rH rH O CN CO 2 S S S CM 00 cxi OJ rH CO b- 2-* OJ CO CO rH CO tO CO CO O CN O JO tO l^ r* Oi CO G& CN CO 00 OS 1> OS O I-H |> OO b- O 'b-CO OSIO 00 Tt C CO b CO OS b CO OO Tf i ( OS i ii>ooo oo i co >o c-i^ob- 1 b- i I CO i-t CO i I >0 t-H olS !>. i-HOS r-KN OlO T-H cob- os o it b 'b- COb- 0- COt^ O 1 I t-H i I i-H i-H >-Hi IC^ b- O' * b- 1 HO *' i CO i i > i OS i I IO O5 i i c^ O CO b CO i T-H iO OS CO CO i T- ( CO CO . T^ Q O I CO Tp^ 00 O T-H O5 COCOOiCO OJCOtO OS t^"* 00 I ^ T I O O i CO * ^2 ^2 CO CO tO to , T-H CO CO CO CO C- T-H T-HO Ttf TtJOOt-Ti! CO 1 i-HT-HrH(M T-H (N CO CO l>- CO OO CO COCO ^ CO CO to ~~ OO CO Oi t^ CO O CO CO *? I-H t>. to to CO I-H CO CO CO COCOCO-* i to CO C< I O5 T-H Of ICO^ t^ O ^P ^^ CO CO O^ ^O IH OO (M l^ (N T-H(N I rH O< i CO CO 00 i t IO Oi i CO 00 O5 00 JO pi ^i OO t^* i t>. Oi i I i rH T I rH O t^ ^rH oStO CO * CO 00 00 t> C<) (N O ^ rHrH rHrHi-HC^ rHCQOICO CiCOt^ i iO CO ' O t i i O OS i (N CO Qflpi-H -^ I I I I rH rH rH C^ COOOOfN COOOOIN TTco CD CO t> CO I CO CO Tt< O Tfl COCO rH !> OO Ol CO CO i I CO rH t^ CO-^ OO - CDTt^i-H>O OS CO t> i ( i ^-t^H^HCQ r-M(N COOO C^O OSCO^OO ^OcOb CO ^O OS OS CO CO "^ OO OS O-l ^O CO C^ i-d-t?5(N i-ic^cqeo c^c^co i i O O ^ CI O C<> !>. i I C<1 ' O Tfi CO OS CO i . T-H 1000' IO O5 ^ 1-1 (N O^ i i t^ co oo o T OO ^*" i iO O "^ i T-H C^ (M i CO O *O iO ill I CO CO l>- co O CO CO ( \ VPO ^ T-H t-\ -f-C^CO J2SS "S + CO(NCO -fCOCNCO " (N O C^ Tt* CO USEFUL DATA Tee .-, . ....... :::: 1 ^ 1 0. 9 | I ---4 I 1 1 ' t pj ^ E T*" i! E I! CO tN SCO O5 t^ 00 b. rH T} IO IO 00 O - co kO co CO OS rH 00 00 O ^* CO CO O O 00 rH - O Ol CO 10 00 04 rH 01 t^ 00 IN 00 (M t- o o rH (N CO CO CO O eococo OOO CNO CO lO 100 USEFUL DATA Tee Beams f** HB j J i -~-l li ^ I s, I UJ f 1 ft A.J 2 y ! ---\ ' 1 ! ' ' ; S ^' .1 I" We Sect 00 O OS t^ oo o S 1 1 OS CO t>-fHO IOCOCOCO cocoeo ^cococc CO OS w OSCOOO OOOSt^CD COCOCOCO TjlCOCOCO 101 Tee Beams CORRUGATED BAR COMPANY, INC. 8 1 *-. 1 CO CO CO Tt< CO M g s 1 i-H II 00 eo 1, 2 1 I Sco 00 CO O l-H i-H t- eo be l-H T-H T-H 1 1 g CO eo .S O 00 CO i O5 o I-H i-H us eo H- 1 T? 2 i 1 O 00 I CO 1 T i-H CO CO rj< i 1 i-H CO co CO 00 i-H l-H g CO eo S O> CO 1 I 1 S 1 CO !> CO CO rH i-H 1 O CO O CO T-l CO 5 eo 1 1 S 1 1 1 % 1 i 1 l-H 1 g CO CO S k 1 1 CO 8 CO CO 22 % CO CO* s I * co Oi i i H CO I 2 CO t"< rH 00 CO CO CO s | 05 i-H T-H CO 1 o CO TH CO CO CO CO 0) CO CO 1 1 00 00 OO CO CO CO 10 CO 10 -^ CO CO CO CO o I o 10 CO CO I-H CO CO CO | 1 1 T-l T-H s $ S X < M El 1 CO Tj< CO CO i-H CO rf E b o PH I 1 \QO I 1 I 1 T-H i-H I-H I-H 1 CO TJH co co -* |* 'E c i < CO O O O O5 CO ^O * CO COCO r^COCOCO O GO CO CO ^t* co co co co COi-it^cOCD OOOCOCOCO lOT^cococo co <* * T}< rj< f\ II c Tt- CO O O C. *O OO O5 T-H CO ^^ *O t s 8 - GO i i rjncOOO T-H t co oo 11 in rH O5(M Tfl> ' i ^f i i (N I CO $Z3 O I> CD Tt< rH i 1 r- 1 C^ CO Ofl t^. 1-1 b- CO t> O5 C^ ,-H rH IOCO T- 1 t>- CO l>- ^ !>. i I Tf* l-H T-H (M (N t^ CD i CO CO i lOt^i O5 CO CO CO T I 1-H lO 'Tfl co 1-1^ oo CO O^ JO t> CO C^ i i lO i i Oi O T-H CO CO Oi i-H rH O i I TfH O CO 00 Tt< O5 O5CO lOt^ COOOO- Tf I t CO < i-H O OO OO r-< !> CO GO T-H O^ 1 CO '^ TH CO ^^ 10 CO 000 CO ^* OO T"H " iO O C^ iO COOO Oi I-H 1 1- O I CO rH O^ CO CO < T^ (M (Mi CO -^ . 1C C^ r- 1 O-r - 10 oo o co I-H OO Tt ^ 1-1 > ift O O O i I "^ t> ^O CO C*l C^ OS C^ ' ll-HCO OOl-HlOOS CO i II i I rH i I T-H l-H rH i I TJH IO C^ t> i-H i-H i-H rH O O v^^ T -I i i CO O \ r\\PO I i-H l-H t-X 1 " 1 QOO \00 \00 VflO \W \00 SflO NOO \00 \00 ri\ ri\ ri\ \ e-K c^s eoX c^\ ri\ cj\ 1 1 1 1 1 1 1 1 1 1 OO(N(NTj< T}-OCOrt qis ^< Oi ^5 C^ ^D O5 CO ^O C^ CO CO 0005'-tWfi5t^p'-H C i ((MCOiOOOO OOOOO5O505OO'-il>OOOOO5OSOO' i^-H .2 OOOOOOOOOJOSOOO'H'-" 81 111 Flat Slabs CORRUGATED BAR COMPANY, INC. wr fe o 5 3-^r-l' U-Q jo:*ii< ft] jo }Ti3iaA\. ~ g" 1 ^ 1 *o T-H OO !>. -^ i-H i i 00 O rH^CN i i 00 O i il> ^ co co co co a OOOOOOOCiOi-Hi-ifNCOCO CO CO CO CO t^* !> OO QO COCOC000000000000505CT) .S OCOOOCOO5OCOC5 *j lOtO^OCOCOCOt^fr^t^ 112 USEFUL DATA Flat Slabs PH 02 ^ S S II 1 O CT> 2 .a O C/2 jo *q3 qis CCS 8 Q\ TH\ CO\ \M \Tf rH\ ^H\ \P* rH\ OSO5OT I \N rH\ \ l-K COOOOOOOOOOOOOOOiOO eo eo eo eo CO CD CD CD t> l> !> 113 CORRUGATED BAR COMPANY, INC. COLUMN TABLES Concrete columns are usually reinforced either with vertical bars tied together at intervals by steel hoops or with vertical bars and spiral hooping. These two general types of column are referred to in the tables, pages 115 to 132, as "Tied Columns" and "Spiral Columns." These tables give safe loads in thousands of pounds for columns to meet the requirements of the New York or Chicago building codes, or the Final Report of the Joint Committee on Concrete and Reinforced Concrete. In New York City the code recognizes but two concrete mixes for columns, viz., 1: 2: 4 and 1: l/^: 3, while Chicago and the Joint Committee permit, in addition to these two, a 1 : 1 : 2 mix. Where it is desired to hold the column size to a minimum the advantage of the richer mix is apparent. In the matter of percentages of vertical and spiral reinforcement it will be recog- nized that it is not practicable to give all possible combinations that could be worked out but there is a sufficient range in each table to satisfactorily cover most require- ments. Consider, for example, the spiral columns based on New York code require- ments, pages 122 to 124. For each column there is given five different percentages of vertical steel and three different percentages of spiral reinforcement for each mix, thus yielding fifteen load variations for one size of column. Similarly for the balance of the column tables. The following formulas express the requirements for safe column load for each of the three codes used: TIED COLUMNS New York P = Af c [I + (n - 1) p] Chicago P = Af c [1 + (n - 1) p] Joint Committee P = Af [1 + (n - 1) p] SPIRAL COLUMNS New York P = f c (A - pA) + nf c pA + 2f B p' A Chicago P = Af c (1 + 2.5 np'} [1 + (n - 1) p] Joint Committee P = Af c [1 + (n - 1) p] In the above formulas the values of / c and n are noted in the tables. In each case p represents the percentage of vertical steel and p' the percentage of spiral. The value of f a in the New York formula is taken at 20,000 pounds per square inch. 114 USEFUL DATA Square Tied Columns Column '" Size""" SQUARE TIED COLUMNS SAFE AXIAL LOADS IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS Ratio of Length of Column to its Side, limited to 15 Column Size Core Size ROUND BAR TIES ROUND BAR VERTICALS 1:2:4 Concrete /c = 500 Ib. per sq. in. n=15 1: IK: 3 Concrete fo = 600 Ib. per sq. in. n=12 Size Spacing in. in. in. in. No. Size 34 5 4 % 35 41 34 7 4 Yi 38 44 12 8 34 9 4 *yk 41 46 M 11 12 4 4 X 44 49 50 54 34 5 4 H 44 52 34 7 4 3^ 46 54 13 9 34 9 4 % 49 57 34 11 4 % 53 60 i^ 12 4 % 57 64 M 12 4 l 62 69 34 7 4 y^ 55 65 \,' 9 4 % 59 68 14 10 34 11 4 % 62 72 34 12 4 y& 67 76 \/ 12 4 i 72 81 34 12 4 1H 78 86 34 7 4 3^ 66 78 34 9 4 JHt 69 81 15 11 34 11 4 M 73 84 j9 12 4 Ji 77 88 i^ 12 4 1 82 93 34 12 6 1 93 104 K 7 4 K 77 92 34 11 4 M 84 98 16 12 i^ 12 4 % 89 102 34 12 4 1 94 107 34 12 4 IK 100 113 M 12 6 IK 114 126 K 9 4 ^ 93 110 34 11 4 M 97 113 17 13 \/ 12 4 Jll 101 117 34 12 6 % 110 125 34 12 6 1 117 133 34 12 8 1 128 143 34 9 4 N 107 126 34 12 4 TxC 115 134 18 14 34 12 4 1 120 139 34 12 6 J^ 123 142 34 12 6 IK 140 158 34 12 8 IK 154 171 34 9 4 % 121 143 34 12 4 K 129 151 19 15 M 12 6 % 138 159 34 12 6 1 145 166 34 12 8 1 156 176 34 12 8 IK 168 188 115 Square Tied Columns Column CORRUGATED BAR COMPANY, INC. Size '*.; SQUARE TIED COLUMNS SAFE AXIAL LOADS IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS Ratio of Length of Column to its Side, limited to 15 Column Size Core Size ROUND BAR TIES ROUND BAR VERTICALS 1: 2:4 Concrete /c = 500 Ib. per sq. in. n = 15 1:1K:3 Concrete /c = 600 Ib. per sq. in. n = 12 Size Spacing in. in. in. in. No. Size ^ 11 4 % 140 165 is 12 4 1 150 174 20 16 y 12 6 153 177 M 12 8 K 162 185 \/ 12 8 IK 184 206 1 A 12 10 IK 197 219 y 11 4 M 157 185 y 12 4 l 166 194 21 17 \/ 12 6 l 177 204 Yi 12 8 1 188 215 Yi 12 8 IK 200 226 y 12 12 IK 228 252 y* 11 4 M 174 206 12 6 T/ 187 218 22 18 y 12 6 1 195 226 M 12 8 I 206 236 M 12 8 \Y^ 231 259 M 12 12 IK 245 273 M 9 6 % 193 229 M 12 6 K 206 240 23 19 M 12 6 IK 222 256 M 12 10 l 235 268 M 12 10 250 282 M 12 12 IK 284 314 M 11 6 M 219 258 M 12 6 l 233 271 24 20 M 12 6 242 279 y 12 10 l 255 292 M 12 12 IK 284 319 M 12 16 IK 311 345 M 11 6 M 239 282 i/ 12 6 l 254 296 25 21 M 12 8 i 265 306 B 12 12 l 286 327 12 14 IK 318 356 M 12 18 IK 346 383 K 9 8 7^ 259 307 M 12 8 276 322 26 22 12 10 1 297 342 J2 12 12 1 308 353 M 12 14 340 382 M 12 18 IK 367 409 y 9 10 y 286 338 YL 12 10 K 307 357 27 23 M 12 10 l 320 369 M 12 14 l 341 390 \/ 12 16 IK 376 422 M 12 20 IK 404 449 116 USEFUL DATA Square Column Tied Columns Size * oyUArvl^ llr^JJ CUljUJyiiNb ' '.<" fc*-.l>.'-AO.C)""(i: '< : : fci'JMJ SAFE AXIAL LOADS IN THOUSANDS OF POUNDS . !t&$#i *, ;' . - ;,':>, S NEW YORK CITY BUILDING CODE REQUIREMENTS Ratio of Length of Column to its Side, limited to 15 Column Size Core Size ROUND BAR TIES ROUND BAR VERTICALS 1: 2:4 Concrete /c = 500 Ib. per sq. in. n = 15 1: 1J^:3 Concrete /c = 6001b. persq.in. n = 12 Size Spacing in. in. in. in. No. Size X 9 10 Ys 310 366 12 10 % 330 385 28 24 % 12 12 1 354 408 14 12 14 1 365 418 M 12 18 l/^ 413 463 H 12 22 l^i 441 490 8 9 12 H 338 399 12 12 8 363 423 29 25 M 12 12 i 378 437 /4 12 14 jix 410 467 M 12 18 IL/J 438 493 H 12 20 1M 484 537 J 9 12 H 364 430 M 12 12 8 388 453 30 26 M 12 12 i 404 468 M 12 14 i^ 435 497 M 12 20 477 537 H 12 22 i>l 527 584 M 9 12 % 390 462 J4 12 14 T/ 424 493 31 27 M 12 14 1 441 510 M 12 16 476 542 i^ 12 22 l^i 518 582 8 12 24 1M 571 632 \/ 9 14 y* 422 499 M 12 14 v% 451 526 32 28 M 12 14 i 469 543 M 12 16 1^6 503 575 /4 12 24 ILZ 559 628 H 12 26 1M 615 680 M 9 14 H 450 533 M 12 14 Txj 479 560 33 29 /4 12 16 1 508 587 i^ 12 18 545 623 /4 12 24 1H 587 662 12 28 1M 660 731 j^ 9 16 5^ 484 572 M 12 16 T 518 604 34 30 M 12 18 1 549 633 M 12 18 575 658 /i 12 24 \\/ 656 734 H 12 30 1M 707 782 M 9 16 K 515 609 Ji 12 16 548 640 35 31 Ji 12 18 i 579 670 M 12 20 iH 619 707 M 12 24 IM 686 771 M 12 32 iM 755 835 117 Square CORRUGATED BAR COMPANY, INC. Tied < Column Size l^ SQUARE TIED COLUMNS .< l:'-:^ ^ *>'^ :!'' ,; " | 1$ SAFE AXIAL LOADS IN THOUSANDS OF POUNDS $ CHICAGO BUILDING CODE REQUIREMENTS . Ratio of Length of Column to its Side, limited to 12 Column Size Core Size ROUND BAR TIES ROUND BAR VERTICALS 1:2:4 2,000 Ib.Concrete /c = 400 Ib. per sq. in. n = 15 1:1^:3 2,400 Ib.Concrete / c = 4801b. per sq. in. n = 12 1: 1:2 2,900 Ib.Concrete /c = 580 Ib. per sq. in. n = 10 Size Spacing in. in. in. in. No. Size 11 8 8 7 9 4 4 8 32 35 37 40 44 46 J4 7 4 % 39 45 53 12 9 H 9 4 % 42 48 56 Yi 10 4 Ft 46 52 60 % 7 4 % 47 54 64 13 10 a 9 10 4 4 8 50 53 57 61 67 71 H 12 4 i 8 58 65 74 % 7 4 2i 55 65 77 14 11 B 9 10 4 4 K 58 62 67 71 79 83 >i 12 4 1 66 75 87 M 7 ^ 64 76 90 14 9 8^ 68 78 93 15 12 M 10 Ji 71 82 96 L 12 1 75 86 100 M 13 1H 80 90 104 y 7 Y 74 88 104 M 9 % 77 90 107 16 13 Ji 10 V* 81 94 111 1^ 10 6 % 88 100 117 M 12 6 1 94 106 123 M 7 4 % 85 101 120 10 4 V* 92 107 126 17 14 M 12 4 \ 96 111 130 /4 10 6 % 99 113 133 X 13 6 l*i 112 125 145 H 7 4 y* 97 114 137 L/ 10 4 TX 104 121 143 18 15 M 10 6 % 110 127 149 ix 12 6 i 116 133 155 M 12 8 i 125 141 163 , 9 4 M 112 132 158 A 12 4 i 120 139 165 19 16 ^ 10 6 123 142 167 JL 10 8 7^ 129 148 174 ft 13 8 1H 147 165 190 A 9 4 2 126 148 177 12 4 1 133 155 184 20 17 A 12 6 1 142 164 192 A 12 8 1 151 172 200 A 13 8 IH: 160 181 209 A 9 4 M 139 165 197 A 10 6 % 150 174 207 21 18 A 12 6 1 156 179 213 A 12 8 l 165 189 221 A 15 8 itf 185 207 239 118 USEFUL DATA Square Column r Columns !' Size SQUARE TIED COLUMNS Hi ._-. i^ SAFE AXIAL LOADS IN THOUSANDS OF POUNDS o' o i giU CHICAGO BUILDING CODE REQUIREMENTS i ],,, Ratio of Length of Column to its Side, limited to 12 /Jf Column Size Core Size ROUND BAB TIES rlOUND BAR VERTICALS 1:2:4 2,000 Ib.Concrete /c = 4001b. per sq. in. n = 15 1:1^:3 2,400 Ib.Concrete /c = 4801b. per sq. in. n = 12 1:1:2 2,900 Ib.Concrete / c = 580 Ib. per sq. in. n = 10 Size Spacing in. in. in. in. No. Size A 7 6 7^ 155 183 219 JL 10 6 165 192 228 22 19 JL 13 6 IK 178 205 241 JL 12 10 1 188 215 250 A 13 10 IK 200 226 261 A 9 6 H 175 206 246 A 12 6 l 186 217 257 23 20 A 13 6 IK 193 223 263 A 12 10 l 204 233 273 A 13 12 IK 227 255 294 A 9 6 H 191 226 270 A 12 6 l 203 237 280 24 21 A 12 8 1 212 245 289 A 12 12 l 229 261 305 A 13 14 IK 254 285 328 A 7 8 % 207 245 294 A 10 8 % 221 258 306 25 22 A 12 10 l 238 274 322 A 12 12 l 246 282 330 A 13 14 IK 272 306 353 % 7 10 KX 229 270 323 % 10 10 K 245 286 338 26 23 % 12 10 1 256 296 348 % 12 14 1 273 312 364 % 13 16 IK 301 338 390 Y 7 10 % 248 293 350 % 10 10 T/' 264 308 365 27 24 % 12 12 1 283 326 383 Y* 12 14 1 292 335 392 y 13 18 IK 330 371 427 % 7 12 !N 271 320 382 % 10 12 7X 291 338 400 28 25 y 12 12 1 303 350 412 % 13 14 IK 328 374 435 H 13 18 IK 350 395 456 y 7 12 % 291 344 411 y% 10 12 T/^ 311 362 430 29 26 y% 12 12 \ 323 374 441 y* 13 14 1 V 348 398 465 y 13 20 IK 382 429 495 y 7 12 Y 312 370 442 % 10 14 1/0 339 394 467 30 27 y% 12 14 1 353 408 480 % 13 16 IK 381 434 506 H 13 22 IK 414 465 537 y% 7 14 6 A 338 399 477 y% 10 14 K 361 421 499 31 28 y% 12 14 l 375 434 512 y& 13 16 IK 403 460 538 H 13 24 IK 447 502 579 119 Square Tied Columns CORRUGATED BAR COMPANY, INC. Column "" Size"" :*: &-j>;i>-.t>.?:.a : *..*&: * SQUARE TIED COLUMNS SAFE AXIAL LOADS IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS Ratio of Unsupported Length of Column to its Side, limited to 15 Column Size Core Size ROUND BAR TIES ROUND BAR VERTICALS 1:2:4 2,000 Ib.Concrete /c = 4501b. per sq. in. n = 15 1:1K:3 2,500 Ib.Concrete /c = 562.5 Ib. per sq. in. n = 12 1:1:2 3,000 Ib.Concrete /c = 6751b. per sq. in. n = 10 Size Spacing in. in. in. in. No. Size K 8 4 K 34 41 48 12 8 8 10 4 37 44 51 12 4 % 40 47 54 1 A 12 4 y% 44 51 58 \i 8 4 K 41 50 59 is 10 4 44 53 62 13 9 \^ 12 4 M 48 56 65 M 12 4 T/^ 52 60 69 8 12 4 1 56 65 74 V A 10 4 % 53 64 75 \ 12 4 % 56 67 78 14 10 M 12 % 60 71 82 i^ 12 1 65 76 87 8 12 IK 70 81 92 y\ 10 M 62 76 89 \y 12 8^ 66 79 92 15 11 M 12 % 70 83 96 1^ 12 1 74 87 101 M 12 1 84 97 110 u 76 92 108 H 80 96 112 16 12 M 12 i 85 100 116 IK 90 106 121 102 118 133 % 87 106 125 % 91 110 129 17 13 1 A 12 6 % 99 117 136 6 i 106 124 143 8 i 116 134 152 4 H 103 125 147 4 i 108 130 151 18 14 K 12 6 H 111 133 154 6 IK 126 147 169 8 IK 138 159 181 4 H 116 141 166 6 H 124 149 174 19 15 A 12 6 i 131 156 181 8 i 141 165 190 8 IK 151 176 200 4 l 135 163 192 6 138 166 195 20 16 A 12 8 K 145 174 202 8 IK 165 193 221 10 IK 178 205 233 4 1 150 182 214 6 160 192 224 21 17 A 12 8 i 170 201 233 8 IK 180 212 243 12 IK 205 236 268 120 USEFUL DATA Square Tied Columns Column Size ..I SQUARE TIED COLUMNS SAFE AXIAL LOADS IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS Ratio of Unsupported Length of Column to its Side, limited to 15 Column Size Core Size ROUND BAR TIES ROUND BAR VERTICALS 1:2:4 2,000 Ib.Concrete / c = 4501b. per sq. in. n = 15 2,500 Ib.Concrete /c = 562.5 Ib. per sq. in. n = 12 1:1:2 3,000 Ib.Concrete /c = 6751b. per sq in. n=>10 Size Spacing in. in. in. in. No. Size 6 V* 169 204 241 6 1 175 211 247 22 18 A 12 8 8 12 k 185 208 221 221 243 256 257 278 291 g t/ 185 225 266 g \V 200 240 280 23 19 A 12 10 10 12 IB 219 225 255 252 265 294 291 304 333 g i 210 254 299 24 20 A 12 6 10 12 r 218 230 255 262 274 299 306 318 343 16 ij| 280 324 367 g 1 228 277 326 g i 238 287 336 25 21 A 12 12 14 i 258 286 306 334 355 382 18 iij 311 359 406 g i/ 248 302 356 10 /% 267 321 374 26 22 H 12 12 14 i 277 306 331 358 384 411 18 iy s 331 383 435 10 7 / 276 335 393 27 23 % 12 10 14 16 1 1 288 307 338 346 366 396 405 424 454 20 1M 363 421 478 10 V* 297 361 425 12 / 8 319 382 446 28 24 % 12 14 18 i 328 372 392 434 456 497 22 ijj 397 459 521 12 _, 327 396 466 12 i 341 410 479 29 25 % 12 14 18 369 394 438 462 506 531 20 1M 436 503 571 12 i/ 350 425 500 12 1 364 438 514 30 26 K 12 14 20 392 429 466 503 541 577 22 1M 474 547 620 14 V* 381 462 543 14 1 397 478 559 31 27 H 12 16 22 24 1*1 428 466 514 508 545 593 588 625 671 121 Spiral Columns CORRUGATED BAR COMPANY, INC. Column _ "'Diameter' " * j. * .x^-o. *7..<7.-*tx " rv SPIRAL COLUMNS SAFE AXIAL LOADS IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODE REQUIREMENTS Ratio of Length of Column to its Side or Diameter, limited to 15. Column Core ROUND BAR 1:2:4 Concrete 1:1^:3 Concrete Diam. Diam. VERTICALS / c = 5001b. persq. in. /c = 600 Ib. per sq. in. in. in. No. Size 71 = 15 n = 12 4 M 100 124 154 111 135 165 16 12 4 % 104 128 158 115 139 169 4 % 109 133 162 119 143 173 4 i 114 138 168 124 148 178 7 74 122 146 175 131 155 185 M"-iM"p y&"$-\y*"p 4 % 120 148 182 132 160 195 17 13 4 % 124 152 187 136 165 199 5 l 135 163 197 146 175 209 8 % 141 169 204 152 180 215 5 134 168 208 149 183 &"$-2y & "p 223 5 % 139 173 213 154 188 228 18 14 1 y^ 145 179 219 159 193 233 6 1 157 191 231 170 204 244 8 1 168 202 242 181 214 255 6 ' 216 255 151 199 238 168 19 15 6 6 Z % 157 164 204 211 244 251 174 180 221 227 261 267 7 1 177 224 264 192 240 279 9 1 188 235 275 203 250 290 7 &"-2^"p 219 279 330 21 17 8 8 H 204 213 264 273 316 325 226 234 286 294 337 346 8 1 224 284 335 244 304 356 11 1 240 300 352 259 319 371 8 ^ 219 A"4>-2M"p 283 347 243 307 371 22 9 % 229 294 358 253 317 382 9 y~ 239 304 368 263 327 391 10 1 256 321 385 279 343 407 12 1 267 332 396 289 353 417 8 * 255 321 381 1 282 348 408 23 19 10 % 261 327 387 288 353 414 10 % 272 338 398 298 364 424 11 1 291 357 417 316 381 441 11 IK 307 373 433 331 397 457 NOTE Size and pitch of spiral wire is given at head of each group of loads for eacn size column. 122 USEFUL DATA Spiral Columns SPIRAL COLUMNS SAFE AXIAL LOADS IN THOUSANDS OF POUNDS NEW YORK CITY BUILDING CODK REQUIREMENTS Ratio of Length of Column to its Side or Diameter, limited to 15. Column Core ROUND BAR 1:2:4 Concrete 1:1H:3 Concrete Diam. Diam. VERTICALS /o = 500 Ib. per sq. in. / = 6001b. persq. in. in. in. No. Size n = 15 n = 12 8 - 275 344 419 305 374 449 24 20 10 10 y 281 292 350 361 426 437 311 321 380 390 455 466 12 I 316 385 461 344 413 488 12 1H 333 403 478 360 429 505 8 ^ 302 378 464 335 &"4>-2K"p 411 H"-iM"p 591 00 10 V% 376 467 562 415 507 601 11 1 394 486 581 433 524 619 13 1H 424 516 611 461 552 647 16 1H 445 537 631 481 572 667 10 % 395 496 606 438 ^"4>-2^"p 540 650 28 24 10 12 l l 419 430 520 531 630 641 461 471 562 572 673 683 14 15 1% 461 493 563 594 673 '704 501 531 602 632 713 742 10 7 /s 439 550 653 485 597 699 on 25 10 1 452 564 666 497 609 712 12 1 463 575 677 508 620 722 15 501 613 715 544 656 758 16 1M 534 646 748 575 687 789 10 467 ^"4>-2M"p 581 l A"$-Wp 518 632 H"-l/^"p 1204 qq 35 15 1H 786 955 1140 876 1045 1230 16 819 988 1173 907 1077 1261 24 1M 887 1056 1241 972 1141 1326 31 18 948 1117 1302 1029 1198 1383 NOTE Size and pitch of spiral wire is given at head of each group of loads for each size column. 124 USEFUL DATA Spiral Columns - 8 I L-. g e grr 1 ESS |ss l*m ro jd a 2 ** ^-Ngoooo *p* ^ & ID *? ia <> rH rf OtDt-00 g 3fat9 rH OrH O) CO 10 || S X 1 ? S i ?ass8 ^ O t* U5 ^}* 1C ^-NO^O A, r?SotSS 1 B Hs HS $ 1 SSSi ^oot>co ^ 05t-(MO S-S HS ? 1 ^-50 CO CO TC *P* ^J-CO C^ t- rH ?SSr3S T* e J 5 rH ^ b, \* "\ SO CO N CO ^ rH O rH OJ CO % ^-rH 0050^000 ^ ^p, ^oot--*.o column HS < ? 1 1, 2- ^rlS* ^ t- O5O05D rH useooo o ^ co rH 050(N^f oads for eacl S Is ^ rH OrHCgcO 5 * t- D > 00 rH rH rH (N CO -* 50 ft, ^OOOOUirH rH COTftCOO ft, \flO >OOOOt~COrH rH O t-OO O C rH 050rH(M "^oo ia icio oo rH O rH CJ CO ^f ?, ^co 100 -t rH COCO WO ?*S3S3 ? * HS HS 1 S 1 II 1 w ^ ^ ^ ^ a I 1L oooooooo 00 00 CO 00 oooooooooo 00000505 ooooooo of spiral v II' (M 1 CO S rH 2 1 ' s t- rH oo 05 1 125 Spiral Columns CORRUGATED BAR COMPANY. INC. I & I O M S 8*1? 02 a % s a n =3 5 . g .S o * . fe "5 O " O O 5ig I e ^ e- 10100 - 10COOO- A cgegwoo 2 TH os o o v-H /-s -} M ^* ^0- "^ooe-'S'f ^oso-( CO t- 1 ec 10 .rH N M IN (N \ 10 TH T * os 1-1 eg eo in .1-1 eg eg eg eg X ^ x oo 10 1- c 4-Scgcgs " N -* o eg oo oo "7 1 eg co rf CD oo ^.cg eg eg eg eg N t- 10 03 00 ^.t- oo as eg 1 s eg eg eg co N eg * -0-co co co co co t-iot-co we- os co cococot cg^socD A.O5 eg co i e, ^^l O CO 00 10 }< IO CD OO rH .0. eg eg eg eg co * t- oo o j-t m . ,-t eg eg eg X oooocgeg - -- 1 eg eg eg eg oooocgcg eg Do>co .IOCD t-O rj< eg eg eg coco . eg eg eg co co U5VOO coioooeg .0. COCOCOrf 1 n eg 10 o e-os coe- eg eg cococo X CD co CD io-j< |WN -CO CD eg 1-1 eg 'i-iegcocDosi'T'coiot-oicg >.cg cgcgcgcg ^A.cgegcgcgco oooocgco ooooco-^" 126 USEFUL DATA Spiral Columns 6 .S I Sis =2 l U3 S $s SR R c ~ N o oo ^OS C 1- oi oo t- ^.00 CO CO T)< Tf OJOOCOlO 10 -O Cvl Ct- O O5 t- > o co <*< oo .03 eo cc eo - < 00 Tj< < 10 t- ^-1 <* Tl< -^HO U5 I-H c t- &S A ^< Tj* 1 t- 1- 10 U500(M < n< rf 10 R O Tf oo >-H 127 Spiral Columns CORRUGATED BAR COMPANY, INC. Cfl a | < o -a , 5 ^ 9 ft^ ii i E ft S ^, Ot-r^^ S5S? ;oo r-i in N co Nt*4^veitt} ^B l 00 t- N 00 OS A -^ t^- i-H t ^-* ?*"0 50 t- t- 00 WMCOIO' ft S ^! SR ja, NOJ^^WOO A o ^j< t-cooo f^CO CO CO t- t- , ^is oo NOJ 10 ooco^ 10 oo 10 OOOOOi \ ooooo ->-i ca "5 o 10 oo ^HCOOJ m .io co co co t- OOW^Hirt t^t-0004 m tnoom 128 USEFUL DATA s i I g | | Q I! i i S K S CC 8 ^ 3 f t-00 .t- t> t- 00 rf OOOSOS rj. CO OS < 'p OS C -l 00 C t-oooo T i- ^ (N <> -l 00 CD ^.t-t-ooooos 10 -^< eo * 01 eo i-< oo S OS H rH - T CpOO5 C^J O iX> ^.00 00 OS ooeoiot> r i-iooo !?;-oo oo co oo eo Cjl Tf t> rH 00 IO --t~ t- 00 00 OS -0 1> eo t- IH X zz Sj r^-NOs Tft- M^HTl 724 835 945 131 Spiral Columns CORRUGATED BAR COMPANY, INC. SPIRAL COLUMNS SAFE AXIAL LOADS IN THOUSANDS OF POUNDS JOINT COMMITTEE RECOMMENDATIONS Ratio of Unsupported Length of Column to its Core Diameter, limited to 10 Column Diam- eter Core Diam- eter ROUND SPIRAL WIRE ROUND BAR VERTICALS 1:2:4 2,000 Ib. Concrete / c = 697.5 Ib. per sq. in. n = 15 1:1K:3 2,500 Ib. Concrete / c = 8721b.per sq. in. n = 12 1:1:2 3,000 Ib.Concrete / = 1,046 Ib. per sq. in. n = lO Size Pitch in. in. in. in. No. Size 12 y s 564 685 807 14 i 601 722 843 34 30 H 2y 2 15 IK 638 759 880 18 IK 708 828 947 23 IM 769 887 1005 13 H 603 733 863 15 1 641 771 900 35 31 M &A 15 IK 672 801 930 18 IK 742 870 997 25 IX 826 952 1078 14 % 643 782 920 15 i 676 814 952 36 32 y* &A 16 IK 716 854 991 20 1M 800 937 1073 26 1M 873 1008 1142 14 M 679 826 974 15 IK 742 889 1035 37 33 H 2M 16 1M 788 934 1080 21 Ik 851 996 1140 28 IK 932 1075 1219 14 1 740 897 1053 15 IK 779 935 1090 38 34 H 2M 16 1M 825 980 1135 22 IK 897 1051 1203 29 1M 981 1133 1285 14 1 778 945 1110 15 IK 817 982 1146 39 35 y* 2 l /s 16 1M 863 1028 1192 24 IM 958 1122 1283 31 IM 1043 1205 1365 14 i 817 993 1168 16 IK 865 1040 1215 40 36 Hi 2 1 A 17 IM 914 1087 1262 25 1M 1010 1182 1353 33 1M 1106 1276 1446 14 1 857 1043 1228 16 IK 905 1090 1274 41 37 M 2 18 IM 965 1149 1333 26 IM 1061 1243 1425 35 IM 1169 1349 1528 15 i 906 1102 1298 17 IK 956 1151 1345 42 38 H 2 19 IM 1019 1212 1406 28 IM 1126 1318 1509 37 IM 1234 1424 1613 132 'U8-%"0bars, 9-3 each way USEFUL DATA FOOTING TABLES The purpose of a footing is to distribute the column load uniformly over the soil so that unequal settlements may be avoided. To accomplish this one of three general types of foundation may be used: (a) square spread footings; (b) combined spread footings; (c) spread footings supported by piles. Tables covering these three types are given on pages 136 to 142. In special cases there may be employed cantilever footings or a raft foundation extending over the entire lot area. To cover these in tabular form, however, would be difficult. In the table for square column foot- ings the method of design outlined in Bulletin 67, University of Illinois, has been followed and its application is illustrated in the following problem. Problem Given a column load of 500,000 pounds. Design a square spread footing, reinforced in two directions, for an allowable soil pressure of 6,000 pounds per square foot; diameter of column 25 inches; punching shear not to exceed 120 pounds per square inch; bond stress limited to 100 pounds per square inch; / 8 = 16,000 and/ c = 650. Approximating the weight of the footing at 400 pounds per square foot, the net soil reaction will be 6,000 400 = 5,600 pounds per square foot. The area of the footing will be, 500,- 000-^5,600 = 90.4 sq. ft. and we will use a footing 9' 6" x 9' 6". FIG. 9 The effective depth of footing is found by dividing the column load, less the net soil reaction directly under the column area, by the perimeter of the column multiplied by the unit punching shear, or Eff. depth = 500,000-19,000 =51 in. (25) (3. 14) (120) To the effective depth should be added 3 inches of concrete for the protection of the metal, giving a total depth of footing of 4' 6". The area of steel, in one direction, to resist the moment of the net soil reaction about the edge BC of the cap, is (2. 71) (5,600) (1.53) (12) ~] (33) (16,000) 4.10 sq. in. This area is equivalent to 14 %" round bars. As it is required to maintain the bond stress at 100 pounds per square inch 133 CORRUGATED BAR COMPANY, INC. (assuming the use of deformed bars), the number of bars selected for moment consider- ations may not be sufficient to accomplish this. In this case the unit bond stress, . (14) (1.965) (33) = 130 lb. per sq. in. The allowable bond stress is exceeded and it will be necessary, therefore, to increase the number of */%' round bars required for moment in the ratio 130/100; or a total of 18-^g" round bars will be needed in each direction at a uniform spacing of 6 inches. The quantities of material required by this design are: Concrete 233 cu. ft., steel 36-%" round bars 9' 3" long. The combined spread footing is employed in those cases where the footings under wall columns are not permitted to extend beyond the building line; this necessitates extending the footing under the wall column to the adjacent interior column and mak- ing it of such dimensions that its center of area coincides with the center of gravity of the column loads that bear upon it. The footing thus becomes a distributing beam, uniformly loaded by the upward reaction of the soil, and is reinforced accordingly in the upper face longitudinally between columns, and in the lower face transversely under each column. The designs given in the tables on pages 136 to 139 cover a fairly wide range of con- ditions and as will be noted it is only required to know the loads and the distance center to center of the columns to obtain a complete solution of the problem. Results are all given in terms of the distance I in feet center to center of columns. Where con- ditions depart from what might be called the average, the results given in the tables will be slightly in error but not sufficiently so to disturb the safety or economy of the design. Example Given a 24-inch square wall column carrying a load PI, of 350,000 pounds and a 26-inch diameter interior column carrying a load P 2 , of 450,000 pounds, or Py =1.3. The columns are spaced 18 feet on centers and the allowable soil pressure is 6,000 pounds per square foot. The sum of the loads is 800,000 pounds and the distance c is one foot. Entering the table on page 138 with Pi+P 2 = 800,000 we find opposite the ratio P *L =1.3; the following dimensions and steel areas: L = 1 . 13J+2c = (1 . 13) (18) + (2) (1) = 22 . 34 ft. H =( h =3. 6-^=3. 6-^=0. 60ft. D O A a =27.3sq. in. 2,465 2,465 . 1,895 1,895 _ or A\= -j- =Qgiy = 5.85 sq. in. 134 USEFUL DATA The disposition of the reinforcing steel is indicated in the cuts at the head of the table. Where soil conditions are of such a nature that spread footings cannot be used, resort must be had to piles of either wood or concrete. If the piles are cut off below the low water line, wooden piles may be used, but if exposed to alternate wet and dry conditions wood is subject to rot and concrete piles should be employed. The tables of pile caps given on pages 141 and 142 are designed for concrete piles having an assumed carrying capacity of 30 tons per pile. The style and reinforcement of cap and num- ber of concrete piles required are determined from the tables, when the column load is known. Designs for concrete piles of the pre-cast type are given in the table on page 143. Except under the most adverse conditions as regards surface and sub-soil, a load of 30 tons per pile may be safely used and if the piles are driven to rock a 50% increase in load should be permissible. The amount of reinforcement used is considered a minimum consistent with successful handling of the pile from the casting yard to its place in the work. 135 Combined Footings CORRUGATED BAR COMPANY, INC. 0> V O fl 1 ^ si I a| Jjlllll II II QQ ^H t*^ CO !> ^^ *O ' ' !> "^ 00 CO 00 Oi t^* ' 1 ^O C2 O^ OS 00 ^^ CO ~co o o jo o P T2 T; 2 rJ i> a.a^a.a* 1 Tfi Tt< oo oo oo COOOOO M O5 O5 C< T i ICO I CO - I co I o CO I CO I CO 00 ICO ICO I I CO O5 CO CO 8888 8888 88888888 oooo oooo oooo oooo oooo oooo O5 O5 36 OO O5 O5 OO OO O5 O5 00 OO O5 O5 OO 00 O5 35 00 O5 O5 00 OO OOOO 00000000 OOOO 00000000 'O i-i . COCOiO 1-1 ico I IcO CO -ico Ico I I 05 - 00 rZSSSSS 12 TJI CO CO CO *^ :33 ICO ICO * ICO 00 "Mco I p 10 8888 8888 8888 8888 8888 8888 dodo dodo dodo dodo dodo dodo ++-f--f- ~{~~{~~l~4~ ~i~~l~~f"4~ ~f~H~H~~h ~H~l~~f~H~ ~^~^^'^' osot3638 os ol 3o 36 osos3636 osos3636 osos3635 ososooo^ oooo oooo oooo oooo oooo oooo i-HiOOCO O^OOS^ 1 t^C-O t^ CO CO iO O5 OO t>- t>- O O O5 OS 00 t^( - t>- < co, ^8: CO^H< OS OS ' : S' CO (N ! B 137 Combined Footings CORRUGATED BAR COMPANY, INC. tl ! - |1 1 3| I So: ; "7? H 5 i 3 a8 CO CO ^^ i^ Os C^ T^ CO OS t> CO lO CO C^ OS l>- i-l rH l I ^H CO CO C^ (M t^ CO 1O CO CO -^ CO CO CO CO CO Tt< * ^ Tt ^^S'S? ^^SS ?2K^ G^S5SS COC^ C^ ?5 S CO GO CN> CO CO r- l CO - os co 00 I> I>- O -H O O5 OS OS >O i -o + OSCOCOO *O i ( t^ rJH OOOO CM (M rH rH co t^ ^D o^ oo 1 s * ^D o^ co t^ ^^ o^ co 1 s * ^^ 05 co t^* ^D os co 1 s * ^D Oi CO t> 139 CORRUGATED BAR COMPANY, INC. 1* n SQUARE COLUMN FOOTINGS i i 1 X, Unit Stresses / 8 , 16,000 |*T=fc==B^S=JL- .___.____. 4! /c. 650 t r L Soil Value Column Load Minimum Column Diameter h b Reinforcement Round Bars Each Way We pt Steel Volume of Concrete ft. in. Ib. per sq. ft. in lOOOlb. in. ft. in. ft. in. No. Size Ib. cu. ft. 5 4000 96 13 7 i 10 14 H 88.8 23.7 5 6000 145 16 8 2 3 16 Yn 100.3 29.3 5 8000 194 18 10 2 7 15 y* 94.1 38.8 5 6 4000 116 14 8 2 1 14 y? 97.0 33.3 5 6 6000 175 17 10 2 6 15 Y, 104.0 44.4 5 6 8000 234 19 11 2 10 16 y* 110.9 51.6 6 4000 137 15 9 2 3 14 v* 106.3 44.5 6 6000 207 18 11 2 9 16 121.4 58.2 6 8000 278 20 1 2 11 18 I A 136.6 65.2 6 6 4000 161 16 9 2 4 17 y 140.3 51.6 6 6 6000 242 19 1 2 10 17 y% 140.3 73.2 6 6 8000 324 21 1 2 3 4 17 y% 140.3 91.5 7 4000 186 17 10 2 6 17 Y 151.5 66.2 7 6000 280 20 1 1 3 1 18 y? 160.4 92.3 7 8000 375 23 1 3 3 7 19 1 A 169.3 113.6 7 6 4000 212 18 11 2 9 18 1 A 172.3 84.3 7 6 6000 322 22 1 1 3 3 20 1 A 191.4 105.2 7 6 8000 429 24 1 4 3 9 20 = 1001b. EARTH SURCHARGED M7=1001b. WATER w = 62.51b. 0.2948wfc H = 0.1474wfc 2 M = 0.5896w;fc 3 0.7034wfc H 0.35llwh z M = 1.4068w;/i 3 P wh # = O.Sph M = 4Hh ft. Ib. Ib. in. Ib. Ib. Ib. in. Ib. Ib. Ib. in. Ib. IT 29 15 59 70 35 141 63 31 125 2 59 59 472 141 141 1,125 125 125 1,000 3 88 132 1,592 211 317 3,798 188 281 3,375 4 118 236 3,773 281 563 9,003 250 500 8,000 5 147 368 7,370 352 879 17,584 313 781 15,625 6 177 531 12,735 422 1,266 30,385 375 1,125 27,000 7 206 721 20,223 492 1,723 48,251 438 1,531 42,875 8 236 944 30,187 563 2,251 72,025 500 2,000 64,000 9 265 1,193 42,982 633 2,849 102,551 563 2,531 91,125 10 295 1,475 58,960 703 3,517 140,673 625 3,125 125,000 11 324 1;782 78,476 774 4,255 187,236 688 3,781 166,375 12 354 2,124 101,883 844 5,064 243,084 750 4,500 216,000 13 383 2,490 129,535 914 5,943 309,060 813 5,281 274,625 14 413 2,891 161,786 985 6,893 386,008 875 6,125 343,000 15 442 3,315 198,990 1,055 7,913 474,773 938 7,031 421,875 16 472 3,776 241,500 ,125 9,003 576,199 1,000 8,000 512,000 17 501 4,259 289,670 ,196 10,164 691,129 1,063 9,031 614,125 18 531 4,779 343,855 ,266 11,395 820,408 1,125 10,125 729,000 19 560 5,320 404,407 ,336 12,696 964,879 1,188 11,281 857,375 20 590 5,900 471,680 ,407 14,067 1,125,388 1,250 12,500 1,000,000 21 619 6,500 546,029 ,477 15,509 1,302,777 1,313 13,781 1,157,625 22 649 7,139 627,806 ,547 17,021 1,497,891 1,375 15,125 1,331,000 23 678 7,797 717,366 ,618 18,604 1,711,574 ,438 16,531 1,520,875 24 708 8,496 815,063 ,688 20,257 1,944,670 ,500 18,000 1,728,000 25 737 9,213 921,250 ,758 21,980 2,198,023 ,563 19,531 1,953,125 26 766 9,958 1,036,280 ,829 23,774 2,472,479 ,625 21,125 2,197,000 27 796 10,746 1,160,509 ,899 25,638 2,768,876 ,688 22,781 2,460,375 28 825 11,550 1,294,290 ,969 27,572 3,088,064 1,750 24,500 2,744,000 29 855 12,398 1,437,975 2,040 29,577 3,430,885 1,813 26,281 3,048,625 30 884 13,260 1,591,920 2,110 31,652 3,798,184 1,875 28,1,25 3,375,000 31 914 14,167 1,756,477 2,180 33,797 4,190,803 1,938 30,031 3,723,875 32 943 15,088 1,932,001 2,251 36,012 4,609,588 2,000 32,000 4,096,000 33 973 16,045 2,118,846 2,321 38,298 5,055,382 2,063 34,031 4,492,125 34 1,002 17,034 2,317,364 2,391 40,655 5,529,030 2,125 36,125 4,913,000 35 1,032 18,060 2,527,910 2,462 43,081 6,031,375 2,188 38,281 5,359,375 Angle of repose = 33 144 USEFUL DATA Retaining 'Walls -jit T *S^"%^s 4 \ 1 I- 1- h- CANTILEVER RETAINING WALLS J , 4 4- + -f-4--t 4 H--I t 44- SURFACE OF EARTH HORIZONTAL '-. L 4--f-4--f f-H- 1? 4 \ 1 I 1 I- 4--4 t 4--4--4- Angle of repose, 33. , I . JS&N 4 1- HT+TtT-f ^H^fefT+T+T^ Weight of earth 100 Ib. per cu. ft. r*-0-* L > ? \ tl^S|I f s = 16,000 Ib. per sq. in. f *E(\ 11^ , _ ;_^ ? E^ ^^l [ II 1 1 1 1 1 j c ooU ID. per sq. in. L ^ty~ i i i ; i i i i i n = 15 Section Elevation CONCRETE Height of WallH a b c. Soil Pressure at Toe Soil Pressure at Heel Concrete per ft. Length of Wall ft. ft. in. ft. in. ft. in. Ib. per sq. ft. Ib. per sq. ft. cu. ft. 7 1 1 1 10 1460 90 10.41 8 1 1 1 1 2 1 1470 270 12.35 9 1 1 1 2 2 9 1770 130 14.04 10 1 2 1 4 2 10 2000 60 16.14 11 1 2 1 6 3 2 2100 90 17.65 12 1 3 1 8 3 7 2210 160 20.37 13 1 4 1 8 4 2480 120 23.10 14 1 4 2 1 4 3 2400 240 24.95 15 1 5 2 1 4 7 2680 200 27.79 16 1 5 2 2 4 11 2870 170 29.45 17 1 6 2 3 5 3 3060 160 32.65 18 1 7 2 4 5 7 3280 140 36.00 19 1 7 2 6 6 1 3350 230 38.25 20 1 8 2 8 6 6 3430 310 42.13 REINFORCEMENT Bars in all Cases of Round Section M BAH8 10' 6" 11' 9" 12' 9" 14' 3" 15' 3" 16' 3" 17' 6" 18' 6" 19' 6" 20' 6" 21' 6" 22' 6" JV BARS O BARS y* 3' 9" 4' 3" 4' 9" 5' 0" 5' 3" 6' 3" 6' 6" 6' 6" 7' 3" 7' 3" 8' 0" 8' 3" 8' 9" 9' 0" y* OQ.S 12 12 12 10 11 11 10 2' 3" 2' 3" 2' 6" 2' 9" 3' 3" 3' 3" 4' 0" 4' 0" 4' 3" 4' 3" 4' 3" 5' 0" 5' 0" P BARS y* u 3' 0" 3' 3" 4' 3" 4' 6" 4' 9" 5' 6" 6' 6" 6' 9" T 6" T 9" 8' 0" 8' 6" 9' 3" 9' 9" L BARS 6 A 14.4 15.7 21.3 26.2 32.3 41.8 63.4 75.4 88.9 105.2 122.2 139.8 174.7 192.9 Hooks are required at lower end of M and AT bars for walls over 11' 0* In height. 145 Retaining Walls CORRUGATED BAR COMPANY, INC. CANTILEVER RETAINING WALLS SURFACE OF EARTH SURCHARGED Angle of repose, 33. Weight of earth 100 Ib. per cu. ft. / 8 = 16,000 Ib. persq. in. / c = 650 Ib. per sq. in. n=15 x CONCRETE Height of Walltf a 6 c Soil Pressure at Toe Soil Pressure at Heel Concrete per ft. Length of Wall ft. ft. in. ft. in. ft. in. Ib. per sq. ft. Ib. per sq. ft. cu. ft. 7 1 1 4 2 8 2230 270 11.55 8 1 1 1 A 1 6 3 7^ 2370 510 14.79 9 1 3 1 8 4 1 2700 540 18.12 10 1 4^ 1 10 4 6^ 3020 580 21.61 11 1 6 2 4 8 3300 640 24.90 12 1 7 1 A 2 3 5 1^ 3730 550 29.12 13 1 9 2 5 5 7 4060 580 33.50 14 1 10^ 2 8 5 9^ 4340 620 37.90 15 2 2 10 6 2 4770 550 42.75 16 2 1H 3 6 5^ 5170 510 47.70 17 2 3 3 2 6 11 5490 550 53.28 18 2 4^ 3 4 7 2K 5930 470 58.85 19 2 6 3 8 7 6 6090 550 65.05 20 2 7H 4 7 8H 6330 630 71.30 REINFORCEMENT Bars in all Cases of Round Section M BARS H 18 8' 6" 9' 9" 10' 9" 12' 6" 14 17 13 16 19^ 13' 6" 9" 9" 0" 18' 0"! 3"! 18 20' 3" iy 8 BARS IS i_s 14 17 13 16 18 4' 0" 4' 6" 5' 6' 0" 7' 6 7' 9 8' 6 9' 0" 9' 6 0"! 18 llO' 6" iy s 16KH' 18 |22' 6"1M 18 |ll' 16^23' 9*1] BARS H 0"iy s 18 16J 18 *|18 ft-lH 5' 6" 5' 9" 6' 3" 6' 6" 6' 9" 7'0 7' 6" V 9" 8' 3" 8' 6" O BARS P BARS 8J^10' 8 7^10' 0" 6" L BARS H fl 18.9 24.5 33.8 43.3 49.5 61.9 85.0 100.3 122.4 139.2 164.0 185.8 215.7 241.0 Hooks are required at lower end of M, N and Q bars for walls over 9' 0" in height. 146 USEFUL DATA Founda- tion FOUNDATIONS BEARING CAPACITY OF SOILS Soil SAFE BEARING POWER IN TONS PER SQUARE FOOT Minimum Maximum Rock, the hardest, in thick layers in native bed . . . Rock equal to best ashlar masonry . ... 200 25 15 5 6 4 1 8 4 2 0.5 30 20 10 8 6 2 10 6 4 1 Rock equal to best brick masonry Rock equal to poor brick masonry Clay in thick beds always dry Clay in thick beds, moderately dry .... Clay, soft Gravel and coarse sand, well cemented Sand dry compact and well cemented Sand, clean dry Quicksand, alluvial soils, etc. .... COEFFICIENTS AND ANGLES OF FRICTION Materials in Contact Coefficient Angle of Friction Masonry upon masonry 0.65 33 00' IVIasonry upon wood with grain 60 31 00' Masonry upon wood, across grain 50 26 40' Masonry on dry clay .... 50 26 40' Masonry on wet clay 33 18 20' Masonry on sand 40 21 50' Masonry on gravel 0.60 31 00' From "A Treatise on Masonry Construction," by Prof. Ira O. Baker. 147 CORRUGATED BAR COMPANY, INC. !N gSSSSSSSgSSSSlgSg&SSg OO OO OO O d dd OO O rH O rH r-J t-J 5 1O t- rH to O CO - COCO 00 i i COCO COO5 OiQO Tt^O OO T-II-H do do do do do do dr-i ^ ^ r-J i-J i 1> COO (MO5 tOtO TI-<*; O5OO O'* Tt^iO OOl O i-Hi-H t^oo OO5 coco rH(M oiio O OOO OCO COCO COO 1 :r 00 S t^O5 COO OO^O CO>O (MO OOO i IT-H OO COr-i OO r-lrH O5OO COO5 CO'* OO OOO CIO ^ Tt< OO rH(M (MCO T^ O COOO O>r-l r-t 10 Tt^Oi OOCO 3 I n &< X t- w .s OOO OOCO "-"O O5CO r-lO COCO COO C5(M COO OrH rH(M CO"* T^cO t>- OS O5- COr-l lO(M Ot^ OOO OrH rH(M CO^t IOCO t^OS OCO COt^ t^-rH rHCO B ctf OO OO OO OO OO 1-HrH rHrH rH(M (M CO OSCO tOCO rHrH (M(M COO COI> OOrH (MO OO O5O -*rH OO OO OO OO Oi-J r-ir-J rH(M rH(M (MCO X 1O 11-* T^rH COtO t>-tO COCO rHt- rHOO 1>CO OOrH l-tl-H (MCO "*1O COOO O(M COCO l>rH rHl>. CO 1 * do dd do do dr-J r-Ji-J THo ** ooo oo-* io>o rHrH (MCO -*CO t* OS OCO '*00 OO"* COO OSI> OO OO OO OO r-JrH r-Jr-i r-J(M (MCO (MCO s ^* COt- O51- OOS OCO CO'* "*CO (MCO co OO OO OO rHrH rHrH (M 0.4305 0.1453 0.4901 i Mft 0.4900 0.1886 0.6363 American Steel & Wire Co. Gauges. STANDARD SPACERS SPIRAL WIRE T-SECTION SPACERS Diam. in. Height ft. Gauge Practical Equiv. Size Wt. per ft. for two Spacers 9 to 15 ItolS 3 M*4> 1 x 1 x Y % 1.60 16 to 30 1 to 20 3 X"* iMxlMx^ 2.00 9 to 15 1 to 15 A"4> IMxl^xK 2.00 16 to 30 1 to 20 &" l^xlMx^ 2.96 9 to 15 1 to 15 4 yt* lMxlMx^-3 2.00 16 to 30 1 to 20 I y** iMxiMx^ 2.96 9 to 30 1 to 20 A> l^xl^x^ 3.60 9 to 30 Ito20 i 1 A"$ l^xl^x-A 3.60 NOTE. For spirals over 30 inches in diameter use twice the num- ber of spacers specified for spirals under 30 inches in diameter. 156 USEFUL DATA COLUMNS AREAS, PERIMETERS, WEIGHTS, VOLUMES AND MOMENTS OF INERTIA NOTE Moments of Inertia calculated about Axis A-A Column "Sections ,._.. ^^ A < A-C ~L d r i >. / Area Peri- Weight Volume Moment Area Peri- Weight Volume Moment meter per ft. per ft. of Inertia meter per ft. per ft. of Inertia in. sq. in. in. Ib. cu. ft. in.4 sq. in. in. Ib. cu. ft. in.4 12 113.1 37.70 117.8 0.78 1018 119.3 39.76 124.3 0.83 1136 13 132.7 40.84 138.2 0.92 1402 140.0 43.08 145.8 0.97 1565 14 153.9 43.98 160.3 .07 1886 162.4 46.39 169.2 1.12 2105 15 176.7 47.12 184.1 .22 2485 186.4 49.70 194.2 1.29 2775 16 201.1 50.27 209.5 .40 3217 212.1 53.02 220.9 1.47 3591 17 227.0 53.41 236.5 .57 4100 239.4 56.33 249.4 1.66 4577 18 254.5 56.55 265.1 .77 5153 268.4 59.65 279.6 1.86 5753 19 283.5 59.69 295.3 .97 6397 299.1 62.99 311.6 2.08 7142 20 314.2 62.83 327.3 2.18 7854 331.4 66.27 345.2 2.30 8768 21 346.4 65.97 360.8 2.40 9547 365.3 69.59 380.5 2.53 10658 22 380.1 69.12 395.9 2.64 11499 401.0 72.90 417.7 2.78 12837 23 415.5 72.26 432.8 2.88 13737 438.2 76.21 456.5 3.04 15335 24 452.4 75.40 471.2 3.14 16286 477.2 79.53 497.1 3.31 18181 25 490.9 78.54 511.4 3.41 19175 517.8 82.84 539.4 3.59 21406 26 530.9 81.68 553.0 3.69 22432 560.0 86.16 583.3 3.89 25042 27 572.6 84.82 596.5 3.97 26087 603.9 89.47 629.1 4.19 29123 28 615.8 87.96 641.5 4.27 30172 649.5 92.78 676.6 4.51 33683 29 660.5 91.11 688.0 4.59 34719 696.7 96.10 725.7 4.84 38759 30 706.9 94.25 736.3 4.91 39761 745.6 99.41 776.7 5.17 44388 31 754.8 97.39 786.2 5.24 45333 796.1 102.72 829.3 5.52 50609 32 804.2 100.53 837.7 5.58 51472 848.3 106.04 883.6 5.89 57462 33 855.3 103.67 890.9 5.94 58214 902.2 109.35 939.8 6.26 64988 34 907.9 106.81 945.7 6.30 65597 957.7 112.66 997.6 6.64 73231 35 962.1 109.96 1002.2 6.68 73662 1014.8 115.98 1057.1 7.04 82234 36 1017.9 113.10 1060.3 7.06 82448 1073.6 119.29 1118.3 7.45 92043 37 1075.2 116.24 1120.0 7.47 91998 1134.1 122.61 1181.3 7.87 102704 38 1134.1 119.38 1181.3 7.87 102354 1196.3 125.92 1246.1 8.30 114265 39 1194.6 122.52 1244.4 8.29 113561 1260.0 129.23 1312.5 8.74 126777 40 1256.6 125.66 1308.9 8.72 125664 1325.5 132.55 1380.7 9.20 140288 157 CORRUGATED BAR COMPANY, INC. COLUMNS AREAS, PERIMETERS, WEIGHTS, VOLUMES AND MOMENTS OF INERTIA. NOTE. Moments of Inertia calculated about Axis A-A A, j * IV A & A i --- A Area Peri- meter Weight per ft. Volume per ft. Moment of Inertia Area Weight per ft. Volume per ft. Moment of Inertia in. sq. in. in. Ib. cu. ft. in.4 sq. in. Ib. cu. ft. in.4 12 144 48 150.0 1.00 1728 12.0 12.5 0.083 144 13 169 52 176.0 1.17 2380 13.0 13.5 0.090 183 14 196 56 204.2 1.36 3201 14.0 14.6 0.097 229 15 225 60 234.4 1.56 4219 15.0 15.6 0.104 281 16 256 64 266.7 1.78 5461 16.0 16.7 0.111 341 17 289 68 301.0 2.01 6960 17.0 17.7 0.118 409 18 324 72 337.5 2.25 8748 18.0 18.8 0.125 486 19 361 76 376.0 2.51 10860 19.0 19.8 0.132 572 20 400 80 416.7 2.78 13333 20.0 20.8 0.139 667 21 441 84 459.4 3.06 16207 21.0 21.9 0.146 772 22 484 88 504.2 3 36 19521 22.0 22.9 0.153 887 23 529 92 551.0 3.67 23320 23.0 24.0 0.160 1014 24 576 96 600.0 4.00 27648 24.0 25.0 0.167 1152 25 625 100 651.0 4.34 32552 25.0 26.1 0.173 1302 26 676 104 704.2 4.69 38081 26.0 27.1 0.181 1465 27 729 108 759.4 5.06 44287 27.0 28.1 0.187 1640 28 784 112 816.7 5.44 51221 28.0 29.2 0.194 1829 29 841 116 876.0 5.84 58940 29.0 30.2 0.201 2032 30 900 120 937.5 6.25 67500 30.0 31.2 0.208 2250 31 961 124 1001.0 6.67 76960 31.0 32.3 0.215 2483 32 1024 128 1066.7 7.12 87381 32.0 33.3 0.222 2731 33 1089 132 1134.4 7.56 96827 33.0 34.4 0.229 2995 34 1156 136 1204.2 8.03 111361 34.0 35.4 0.236 3275 35 1225 140 1276.0 8.50 125052 35.0 36.5 0.243 3573 36 1296 144 1350.0 9.00 139968 36.0 37.5 0.250 3880 37 1369 148 1426.0 9.50 156180 37.0 38.5 0.257 4221 38 1444 152 1504.2 10.02 173761 38.0 39.6 0.264 4573 39 1521 156 1584.4 10.57 192787 39.0 40.6 0.271 4943 40 1600 160 1666.7 11.11 213333 40.0 41.7 0.278 5333 158 USEFUL DATA Moments of Inertia Dia. <. of- > Circle MOMENT OF INERTIA OF COLUMN VERTICALS ARRANGED IN A CIRCLE EXPRESSED IN TERMS OF CONCRETE INCHES 4 7=n/ 8 Diameter of Circle n=12 n = 15 Percentage of Column Verticals Percentage of Column Verticals in. 1% 2% 3% 4% 1% 2% 3% 4% 12 244 488 732 976 305 610 915 1220 13 336 672 1008 1344 420 840 1261 1681 14 452 904 1356 1808 565 1130 1696 2261 15 596 1192 1787 2383 745 1491 2234 2979 16 771 1543 2314 3085 964 1928 2893 3857 17 983 1966 2949 3932 1229 2458 3686 4915 18 1235 2471 3706 4942 1544 3089 4633 6178 19 1534 3067 4601 6135 1917 3835 5752 7669 20 1883 3766 5649 7532 2354 4708 7062 9416 21 2289 4578 6866 9155 2861 5723 8584 11445 22 2757 5514 8271 11028 3446 6893 10339 13786 23 3293 6587 9880 13173 4117 8234 12351 16469 24 3905 7809 11714 15618 4881 9763 14644 19525 25 4597 9194 13791 18389 5747 11494 17241 22988 26 5378 10756 16134 21512 6723 13447 20170 26893 27 6254 12509 18763 25018 7819 15638 23456 31275 28 7234 14467 21701 28935 9043 18086 27129 36173 29 8324 16648 24971 33295 10406 20812 31218 41623 30 9533 19065 28598 38131 11917 23834 35751 47669 31 10869 21737 32606 43475 13587 27175 40762 54349 32 12340 24681 37021 49362 15427 30854 48282 61709 33 13957 27914 41870 55827 17448 34896 52344 69747 34 15727 31454 47181 62908 19661 39322 58983 78643 35 17660 35321 52981 70642 22078 44156 66234 88312 36 19767 39534 59301 79068 24711 49423 74134 98845 37 22057 44113 66170 88226 27574 55147 82721 110294 38 24539 49079 73618 98158 30678 61355 92033 122710 39 27226 54453 81679 108905 34036 68073 102109 136146 40 30128 60256 90384 120512 37664 75328 112992 150656 NOTE. For calculation of the moment of inertia the bars are assumed transformed into a con- tinuous cylinder having a sectional area equivalent to the sum of the area of the bars. 159 CORRUGATED BAR COMPANY, INC. A MOMENTS OF INERTIA OF BARS INCHES 4 FOR VARIOUS DISTANCES FROM AN Axis A- A Values Expressed in Nearest Whole Numbers Arm SQUARE BARS ROUND BARS in. K" %" H" Jr 1* W% 1M" fcF 6 A" %" w V 1H" 1^4 2 1 2 2 3 4 5 6 1 1 2 2 3 4 5 2J^ 2 2 4 5 6 8 10 1 2 3 4 5 6 8 3 2 4 5 7 9 12 14 2 3 4 5 7 9 11 3H 3 5 7 9 12 16 19 2 4 5 7 10 12 15 4 4 6 9 12 16 20 25 3 5 7 10 13 16 20 4^ 5 8 11 16 20 26 32 4 6 9 12 16 20 25 5 6 10 14 19 25 32 39 5 8 11 15 20 25 31 5J^ 8 12 17 23 30 38 47 6 9 13 18 24 30 37 6 9 14 20 28 36 46 56 7 11 16 22 28 36 44 6^ 11 17 24 32 42 54 66 8 13 19 25 33 42 52 7 12 19 28 38 49 62 77 10 15 22 29 39 49 60 7H 14 22 32 43 56 71 88 11 17 25 34 44 56 69 8 16 25 36 49 64 81 100 13 20 28 39 50 64 79 8J-6 18 28 41 55 72 92 113 14 22 32 43 57 72 89 9 20 32 46 62 81 103 127 16 25 36 49 64 81 100 9^ 23 35 51 69 90 114 141 18 28 40 54 71 90 111 10 25 39 66 77 100 127 156 20 31 44 60 79 99 123 IOH 28 43 62 84 110 149 172 22 34 49 66 87 110 135 11 30 47 68 93 121 153 189 24 37 53 73 95 120 149 11^ 33 52 74 101 132 168 207 26 41 58 80 104 132 162 12 36 56 81 110 144 182 225 28 44 64 87 113 143 177 13 42 66 95 129 169 214 264 33 52 75 102 133 168 208 14 49 77 110 150 196 248 306 38 60 87 118 154 195 241 15 56 88 127 172 225 285 352 44 69 99 135 177 224 276 16 64 100 144 196 256 324 400 50 79 113 154 201 255 314 17 72 113 163 221 289 366 452 57 89 128 174 227 287 355 18 81 127 182 248 324 410 506 64 99 143 195 255 322 398 19 90 141 203 276 361 457 564 71 111 160 217 284 359 443 20 100 156 225 306 400 506 625 79 123 177 241 314 398 491 21 110 172 248 338 441 558 689 87 135 195 265 346 438 541 22 121 189 272 371 484 613 756 95 148 214 291 380 481 594 23 132 206 298 405 529 670 827 104 162 234 318 416 526 649 24 144 225 324 441 576 729 900 113 177 254 346 452 573 707 25 156 244 352 479 625 791 977 123 192 276 376 491 621 767 26 169 264 380 518 676 856 1056 133 207 299 407 531 672 830 27 182 285 410 558 729 923 1139 143 224 322 438 573 725 895 28 196 306 441 600 784 992 1225 154 241 346 471 616 779 962 29 210 329 473 644 841 1065 1314 165 258 372 506 661 836 1032 30 225 352 506 689 900 1139 1406 177 276 398 541 707 895 1105 32 256 400 576 784 1024 1296 1600 201 314 452 616 804 1018 1257 34 289 452 650 885 1156 1463 1806 227 355 511 695 908 1149 1419 36 324 506 729 992 1296 1640 2025 254 398 573 779 1018 1288 1591 38 361 564 812 1106 1444 1828 2256 283 443 638 868 1134 1435 1772 40 400 625 900 1225 1600 2025 2500 314 491 707 962 1257 1590 1964 42 441 689 992 1351 1764 2233 2756 346 541 779 1061 1385 1753 2165 44 484 756 1089 1482 1936 2450 3025 380 594 855 1164 1521 1924 2376 46 529 827 1190 1620 2116 2678 3306 415 649 935 1272 1662 2103 2597 48 576 900 1296 1764 2304 2916 3600 452 707 1018 1385 1810 2290 2828 160 USEFUL DATA Beam Quantities BEAM QUANTITIES CUBIC FEET OF CONCRETE PER LINEAR FOOT OF BEAM Depth WIDTH IN INCHES in. 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 6 0.17 0.21 0.25 0.29 0.33 0.38 0.42 0.46 0.50 0.54 0.58 0.63 0.67 0.71 0.75 7 0.19 0.24 0.29 0.34 0.39 0.44 0.49 0.53 0.58 0.63 0.68 0.73 0.78 0.83 0.88 8 0.22 0.28 0.33 0.39 0.44 0.50 0.56 0.61 0.67 0.72 0.78 0.83 0.89 0.94 1.00 9 0.25 0.31 0.38 0.44 0.50 0.56 0.63 0.69 0.75 0.81 0.88 0.94 1.00 1.06 1.13 10 0.28 0.35 0.42 0.49 0.56 0.63 0.69 0.76 0.83 0.90 0.97 1.04 1.11 1.18 1.25 11 0.31 0.38 0.46 0.53 0.61 0.69 0.76 0.84 0.92 0.99 .07 1.15 1.22 .30 1.38 12 0.33 0.42 0.50 0.58 0.67 0.75 0.83 0.92 1.00 1.08 .17 1.25 1.33 .42 1.50 13 0.36 0.45 0.54 0.63 0.72 0.81 0.90 0.99 1.08 1.17 .26 1.35 1.44 .53 1.63 14 0.39 0.49 0.58 0.68 0.78 0.88 0.97 1.07 1.17 1.26 .36 1.46 1.56 .65 1.75 15 0.42 0.52 0.63 0.73 0.83 0.94 1.04 1.15 1.25 1.35 .46 1.56 1.67 .77 1.88 16 0.44 0.56 0.67 0.78 0.89 1.00 1.11 1.22 1.33 1.44 .56 1.67 1.78 1.89 2.00 17 0.47 0.59 0.71 0.83 0.94 1.06 1.18 1 30 1.42 1.54 .65 1.77 1.89 2.01 2.13 18 0.50 0.63 0.75 0.88 1.00 1.13 1.25 1.38 1.50 1.63 .75 1.88 2.00 2.13 2.25 19 0.53 0.66 0.79 0.92 1.06 1.19 1.32 1.45 1.58 1.72 .85 1.98 2.11 2.24 2.38 20 0.56 0.69 0.83 0.97 1.11 1.25 1.39 1.53 1.67 1.81 .94 2.08 2.22 2.36 2.50 21 0.58 0.73 0.88 1.02 1.17 1.31 1.46 1.60 1.75 1.90 2.04 2.19 2.33 2.48 2.63 22 0.61 0.76 0.92 1.07 1.22 1.38 1.53 1.68 1.83 1.99 2.14 2.29 2.44 2.60 2.75 23 0.64 0.80 0.96 1.12 1.28 1.44 1.60 1.76 1.92 2.08 2.24 2.40 2.56 2.72 2.88 24 0.67 0.83 1.00 1.17 1.33 1.50 1.67 1.83 2.00 2.17 2.33 2.50 2.67 2.83 3.00 25 0.69 0.87 1.04 1.22 1.39 1.56 1.74 1.91 2.08 2.26 2.43 2.60 2.78 2.95 3.13 26 0.72 0.90 1.08 1.26 1.44 1.63 1.81 1.99 2.17 2.35 2.53 2.71 2.89 3.07 3.25 27 0.75 0.94 1.13 1.31 1.50 1.69 1.88 2.06 2.25 2.44 2.63 2.81 3.00 3.19 3.38 28 0.78 0.97 1.17 1.36 1.56 1.75 1.94 2.14 2.33 2.53 2.72 2.92 3.11 3.31 3.50 29 0.81 1.01 1.21 1.41 1.61 1.81 2.01 2.22 2.42 2.62 2.82 3.02 3.22 3.42 3.62 30 0.83 1.04 1.25 1.46 1.67 1.88 2.08 2.29 2.50 2.71 2.92 3.13 3.33 3.54 3.75 31 0.86 1.08 1.29 1.51 .72 1.94 2.15 2.37 2.58 2.80 3.01 3.23 3.44 3.66 3.88 32 ! 0.89 1.11 1.33 1.56 .78 2.00 2.22 2.44 2.67 2.89 3.11 3.33 3.56 3.78 4.00 33 0.92 1.15 1.38 1.60 .83 2.06 2.29 2.52 2.75 2.98 3.21 3.44 3.67 3.90 4.13 34 0.94 1.18 1.42 1.65 .89 2.13 2.36 2.60 2.83 3.07 3.31 3.54 3.78 4.01 4.25 35 0.97 1.22 1.46 1.70 .94 2.19 2.43 2.67 2.92 3.16 3.40 3.65 3.89 4.13 4.38 36 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 37 1.03 1.28 1.54 1.80 2.06 2.31 2.57 2.83 3.08 3.34 3.60 3.85 4.11 4.37 4.63 38 1.06 1.32 1.58 1.85 2.11 2.38 2.64 2.90 3.17 3.43 3.69 3.96 4.22 4.49 4.75 39 1.08 1.35 1.63 1.90 2.17 2.44 2.71 2.98 3.25 3.52 3.79 4.06 4.33 4.60 4.88 40 1.11 1.39 1.67 1.94 2.22 2.50 2.78 3.06 3.34 3.61 3.89 4.17 4.45 4.72 5.00 41 1.14 1.42 1.71 1.99 2.28 2.56 2.85 3.13 3.42 3.70 3.99 4.27 4.55 4.84 5.12 42 1.17 1.46 1.75 2.04 2.33 2.63 2.92 3.21 3.50 3.79 4.08 4.38 4.67 4.96 5.25 43 .19 .49 1.79 2.09 2.39 2.69 2.99 3.28 3.58 3.88 4.18 4.48 4.78 5.08 5.38 44 .22 .53 1.83 2.14 2.44 2.75 3.06 3.36 3.67 3.97 4.27 4.58 4.89 5.19 5.50 45 .25 .56 1.88 2.19 2.50 2.81 3.13 3.44 3.75 4.06 4.38 4.69 5.00 5.31 5.63 46 .28 .60 1.92 2.24 2.56 2.88 3.19 3.51 3.83 4.15 4.47 4.79 5.11 5.43 5.75 47 1.31 .63 1.96 2.28 2.61 2.94 3.26 3.59 3.92 4.24 4.57 4.90 5.22 5.55 5.88 48 .33 .67 2.00 2.33 2.67 3.00 3.33 3.67 4.00 4.33 4.67 5.00 5.33 5.67 6 00 161 Column Head Quantities CORRUGATED BAR COMPANY, INC. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Cubic Feet of Concrete in Head when Angle is 45 1 | | I I I I | I I I I I I I I I | I I i i | ! I I I I I I 5 10 15 20 25 30 35 Cubic Feet of Concrete in Head when Angle is 30 The above diagram gives the volume of the ring of concrete forming the head. Volumes given are for octagonal heads and columns. For square heads and columns multiply the volume by 1.21 For round heads and columns multiply the volume by 0.95. DIAGRAM 17 For obtaining volume of concrete in column heads of columns supporting flat slab floors. 162 USEFUL DATA QUANTITIES OF MATERIALS FOR ONE CUBIC YARD OF RAMMED CONCRETE BASED ON A BARREL OF 3.8 CUBIC FEET The following table gives the quantities of materials required for one yard of concrete. The results given have been taken from a similar table in Concrete Plain and Reinforced by Taylor and Thompson, with the author's permission, to use this copyrighted matter. "oportions Proportions PERCENTAGES OP VOIDS IN BROKEN STONE OR GRAVEL by by 50% Broken 45% 40% 30% Parts Volumes Stone Screened Average Gravel or Graded to Uniform size Condition Mixed Mixtures v i _ MX ; 03-0 a m - 1 a 8 I "C QJ S 9 3 5 s o o o 3 o *O g fcO M) t-502 02 OQ O 02 02 O 02 02 O 02 02 Bbl. Cu. Ft. Cu.Ft. Bbl. Cu Yd Cu.Yd Bbl. Cu-Yd. Cu.Yd. Bbl. Cu.Yd. Cu.Yd. Bbl. Cu.Yd. Cu.Yd. 1 1.5 1 3.8 5.7 3.19 0.45 0.67 3.08 0.43 0.65 2.97 0.42 0.63 2.78 0.39 0.59 2 1 3.8 7.6 2.85 0.40 0.80 2.73 0.38 0.77 2.62 0.37 0.74 2.43 0.34 0.68 2.5 3.8 9.5 2.57 0.36 0.90 2.45 0.34 0.86 2.34 0.33 0.82 2.15 0.30 0.76 3 3.8 11.4 2.34 0.33 0.99 2.22 0.31 0.94 2.12 0.30 0.90 1.93 0.27 0.82 .5 2 5.7 7.6 2.49 0.53 0.70 2.40 0.51 0.68 2.31 0.49 0.65 2.16 0.46 0.61 .5 2.5 5.7 9.5 2.27 0.48 0.80 2.18 0.46 0.77 2.09 0.44 0.74 1.94 0.41 0.68 .5 3 5.7 11.4 2.09 0.44 0.88 2.00 0.42 0.84 1.91 0.40 0.81 1.76 0.37 0.74 .5 3.5 5.7 13.3 1.94 0.41 0.96 1.84 0.39 0.91 1.76 0.37 0.87 1.61 0.34 0.79 .5 4 5.7 15.2 1.80 0.38 1.01 1.71 0.36 0.96 1.63 0.34 0.92 1.48 0.31 0.83 1.5 4.5 5.7 17.1 1.69 0.36 1.07 1.60 0.34 1.01 1.51 0.22 0.96 1.37 0.29 0.87 1.5 5 5.7 19.0 1.59 0.34 1.12 1.50 0.32 1.06 1.42 0.30 1.00 1.28 0.27 0.90 2 3 7.6 11.4 1.89 0.53 0.80 1.81 0.51 0.76 1.74 0.49 0.74 1.61 0.45 0.68 2 3.5 7.6 13.3 1.76 0.49 0.87 1.68 0.47 0.83 1.61 0.45 0.79 1.48 0.42 0.73 2 4 7.6 15.2 1.65 0.46 0.93 1.57 0.44 0.88 1.50 0.42 0.84 .38 0.39 0.78 2 4.5 7.6 17.1 1.55 0.44 0.98 1.48 0.42 0.94 1.41 0.40 0.89 .28 0.36 0.81 2 5 7.6 19.0 1.47 0.41 1.03 1.39 0.39 0.98 1.32 0.37 0.93 .20 0.34 0.84 2 5.5 7.6 20.9 1.39 0.39 1.08 1.31 0.37 1.01 1.25 0.35 0.97 .13 0.32 0.87 2 6 7.6 22.8 1.32 0.37 1.11 1.25 0.35 1.06 1.18 0.33 1.00 .06 0.30 0.89 2.5 3 9.5 11.4 1.72 0.61 0.73 1.66 0.58 0.70 1.60 0.56 0.68 .49 0.52 0.63 2.5 3.5 9.5 13.3 1.62 0.57 0.80 1.55 0.55 0.76 1.49 0.52 0.73 .38 0.49 0.68 2.5) 4 9.5 15.2 1.52 0.54 0.86 1.46 0.51 0.82 1.40 0.49 0.79 .29 0.45 0.73 2.5 4.5 9.5 17.1 1.44 0.51 0.91 1.37 0.48 0.87 1.31 0.46 0.83 .20 0.42 0.76 2.5 5 9.5 19.0 1.37 0.48 0.96 1.30 0.46 0.92 1.24 0.44 0.87 .13 0.40 0.80 2.5 5.5 1 9.5 20.9 1.30 0.46 1.01 1.23 0.43 0.95 1.17 0.41 0.91 .07 0.38 0.83 2.5 6 1 9.5 22.8 1.24 0.44 1.05 1.17 0.41 0.99 1.11 0.39 0.94 1.01 0.36 0.85 2.5 6.5 1 9 5 24 7 1 18 42 1 08 1.12 0.39 1.02 1 06 37 97 96 0.34 0.88 2.5 7 1 9.5 26.6 1.13 0.40 1.11 1.07 0.38 1.05 1.01 0.36 0.99 0.91 0.32 0.90 3 4 11.4 15.2 1.42 0.60 0.80 1.36 0.57 0.77 1.30 0.55 0.73 1.21 0.51 0.68 3 4.5 11.4 17.1 1.34 0.57 0.85 1.28 0.54 0.81 1.23 0.52 0.78 1.13 0.48 0.72 3 5 11.4 19.0 1.28 0.54 0.90 1.22 0.52 0.86 1.17 0.49 0.82 1.07 0.45 0.75 3 5.5 11.4 20.9 1.22 0.52 0.94 1.16 0.49 0.90 1.11 0.47 0.86 1.01 0.43 0.78 3 6 11.4 22.8 1.16 0.49 0.98 1.11 0.47 0.94 1.05 0.44 0.89 0.96 0.41 0.81 3 6.5 11.4 24.7 1.12 0.47 1.02 1.06 0.45 0.97 1.01 0.43 0.92 0.92 0.39 0.84 3 7 11.4 26.6 1.07 0.45 1.05 1.01 0.43 0.99 0.96 0.40 0.95 0.87 0.37 0.86 3 7.5 11.4 28.5 1.03 0.44 1.09 0.97 0.41 1.02 0.92 0.39 0.97 0.83 0.35 0.88 3 8 11.4 30.4 0.99 0.42 1.11 0.93 0.39 1.05 0.88 0.37 0.99 0.80 0.34 0.90 4 5 15.2 19.0 1.13 0.64 0.80 1.08 0.61 0.76 1.04 0.59 0.73 0.96 0.54 0.68 4 6 15.2 22.8 1.04 0.59 0.88 0.99 0.56 0.84 0.95 0.54 0.80 0.87 0.49 0.73 4 7 15.2 26.6 0.96 0.54 0.95 0.92 0.52 0.91 0.88 0.50 0.87 0.80 0.45 0.79 4 8 15.2 30.4 0.90 0.51 1.01 0.85 0.48 0.96 0.81 0.46 0.91 0.74 0.42 0.83 4 9 15.2 34.2 0.84 0.47 1.06 0.80 0.45 1.01 0.76 0.43 0.96 0.68 0.38 0.86 4 10 15.2 38.0 0.79 0.44 1.11 0.75 0.42 1.06 0.71 0.40 1.00 0.64 0.36 0.90 5 10 19.0 38.0 0.73 0.52 1.03 0.69 0.49 0.97 0.66 0.46 0.93 0.60 0.42 0.84 6 12 1 22.8 45.5 0.62 0.52 1.04 0.58 0.49 0.98 0.56 0.47 0.94 0.50 0.42 0.84 NOTE. Variations In the fineness of the sand and the compacting of the concrete may affect the qi titles by 10% in either direction. Use 45% column for average conditions and for broken stone with dnst screened out. Use 50% column for broken stone screened to uniform size Use 40% column for gravel or mixed stone and gravel. Use 30% column for scientifically graded mixtures. 163 CORRUGATED BAR COMPANY, INC. BARS One of the assumptions always made in connection with the design of reinforced concrete structures is that the steel and concrete are so intimately united by means of the bond that the two materials act together as a single new material. For many years it was insisted upon that the adhesion between concrete and plain bars was sufficient, but as the art of reinforced concrete construction developed the sufficiency of this adhesion began to be questioned and various methods were devised, such as hook- ing or splitting the ends of the bars, to prevent their slipping in the concrete. Such methods are but makeshifts at best, as bond to be effective must be continuous, and in practically all reinforced concrete designs of to-day the demand is for a deformed bar of proper design a bar that grips the concrete in a positive manner by means of projecting ribs normal to the direction of stress. The design tables appearing in this book are based on the employment of a properly designed deformed bar, and their use in connection with other types of bars is not recommended. CORRUGATED ROUNDS STANDARD SIZES SIZE IN INCHES % H *A 3 A 1 IH m Net Area in Square Inches . Weight per Foot in Pounds . Perimeter in Inches . . . 0.11 0.38 1.23 0.19 0.66 1.66 0.30 1.05 2.10 0.44 1.52 2.53 0.60 2.06 2.95 0.78 2.69 3.36 0.99 3.41 3.80 1.22 4.21 4.23 CORRUGATED SQUARES STANDARD SIZES SIZE IN INCHES y* X y 2 K H H 1 1H 1M Net Area in Square Inches . Weight per Foot in Pounds . Perimeter in Inches . . . 0.06 0.22 1.00 0.14 0.49 1.50 0.25 0.86 2.00 39 1.35 2.50 0.56 1.94 3.00 0.76 2.64 3.50 1.00 3.43 4.00 1.26 4.34 4.50 1.55 5.35 5.00 164 USEFUL DATA Specifications. Purchasers can greatly influence the prompt shipment of orders for ordinary "mill shipment" by considering, in the preparation of their specifications and material bills, the factors connected with the methods and internal organization of a steel mill. Adherence to the Manufacturers' Standard Specifications for Defornled Concrete Reinforcing Bars (see page 188), will always facilitate prompt shipment. It is, of course, possible to furnish any class of material that is within the power of the mill to roll, but where specifications are in any way special the entire order must be made from special heats. The process is one out of the ordinary routine of the mill, billets already prepared cannot be used, and delay in the filling of the order is certain. Sizes. It is necessary in the rolling of steel bars, for a mill to finish rolling all of the bars on its schedule of one particular size before changing the rolls for other sizes of bars. In mill parlance, what is known as a "rolling" extends over a period of several days and an order containing a large number of sizes might be compelled to remain in the mill until the completion of the entire rolling, so that where quick shipment is desired, the number of sizes on an order should be kept as low as possible. In addition to confining the order to as few sizes as may be consistent with the requirements, every endeavor should be made to avoid specifying bars in r^th sizes. This is an error frequently made by inexperienced designers in an effort to meet a theoretical steel area required by their calculations, and can only result in delay at the mill and increased labor and confusion in the field through the necessity of handling a multiplicity of bars of slightly varying size. Lengths. In ordinary mill practice the bars are rolled to lengths varying from 100 to 300 feet and sheared into lengths called for by the material bills as they come from the rolls. When, however, the number of lengths are very large and where there are only a small number of bars of one length, the shearing cannot be done as fast as the bars are rolled, consequently the bars must be laid to one side and sheared after the conclusion of the rolling in order that the operation of the mill may not be delayed. It is, therefore, always desirable to keep the number of lengths as low as possible where quick shipment is a necessary requirement. The lengths should always be given to the nearest inch as bars are not ordinarily sheared to a greater degree of accuracy. Where it is important that the length called for be exact, a note to this effect should be placed opposite the item on the order. Fabrication. For all reinforced concrete structures there is usually a considerable amount of fabricated reinforcement to be furnished. Sometimes this fabrication is done in the field but through the use of special machinery and methods of operation all classes of bending and other fabrication of bar reinforcement can be accomplished with greater accuracy and advantage in the shop than in the field, and in the majority of instances it is advisable for the purchaser to specify "shop fabrica- tion." Accompanying all orders for fabricated material there should be furnished in addi- tion to the list of number of pieces, size and length of- bar, a sketch of each differently fabricated piece with the dimensions plainly marked thereon. A few of the details 165 CORRUGATED BAR COMPANY, INC. most frequently encountered in practice are given below, showing in each case the detail dimensions required by the shop. 1-1 X, v inside Lap inside 166 USEFUL DATA Wire AMERICAN STEEL AND WIRE CO.'S STEEL AND IRON WIRE GAUGE AND DIFFERENT SIZES OF WIRE Diameter Inches Steel Wire Gauge Diameter Inches Area, Square Inches Pounds per Foot Feet per Pound Feet per 2,000 Lbs. H 0.500 0.19635 0.6625 1.50 3018 * 0.490 0.18857 0.6363 1.51 3023 H 0.468 0.17202 0.5804 1.72 3445 I 0.460 0.16619 0.5608 1.78 3566 ft 0.437 0.14998 0.5061 1.97 3952 * 0.430 0.14532 0.4901 2.04 4081 3 L ! 0.406 0.12946 0.4368 2.28 4578 * 0.393 . 0.12130 0.4094 2.44 4885 N 0.375 0.11044 0.3726 2.68 5367 f 0.362 0.10292 0.3473 2.87 5758 H 0.343 0.09240 0.3117 3.20 6412 I 0.331 0.08604 0.2904 3.44 6887 A 0.312 0.07645 0.2579 3.87 7755 0.307 0.07402 0.2497 4.00 8011 1 0.283 0.06290 0.2123 4.71 9420 A 0.281 0.06210 0.2092 4.78 9560 2 0.263 0.05432 0.1834 5.45 10905 M 0.250 0.04908 0.1656 6.03 12077 3 0.244 0.04675 0.1578 6.33 12674 4 0.225 0.03976 0.1342 7.45 14903 A 0.218 0.03732 0.1259 7.94 15885 5 0.207 0.03365 0.1135 8.81 17621 6 0.192 0.02895 0.0977 10.23 20471 A 0.187 0.02746 0.0926 10.79 21598 7 0.177 i 0.02460 0.0830 12.04 24096 8 0.162 0.02061 0.0696 14.36 28735 A 0.156 0.01911 0.0644 15.52 31056 9 0.148 0.01720 0.0580 17.24 34482 10 0.135 0.01431 0.0483 20.70 41408 H 0.125 0.01227 0.0414 24.15 48309 11 0.120 0.01130 0.0382 26.17 52356 12 0.105 0.00865 0.0292 34.24 68493 A 0.093 0.00679 0.0229 43.66 87336 13 0.092 0.00664 0.0224 44.64 89286 14 0.080 0.00502 0.0169 59.17 118343 15 0.072 0.00407 0.0137 72.99 145985 16 0.063 0.00311 0.0105 95.23 190476 167 CORRUGATED BAR COMPANY, INC. IICO !> I* * 168 USEFUL DATA Properti of Sections gs y 2 I I IB Q < Sis 169 CORRUGATED BAR COMPANY, INC. Sis '^ P? SI I ?? "" 170 USEFUL DATA ^ o I! I Q ounds 43 27 27 32 36 40 32 The stresses given are for green timber. For temporary structures an increase of 50% in the working stresses is permissible. *Unit stresses adopted by The Am. Ry. Eng. Asso. for railroad structures. 172 USEFUL DATA Timber WOODEN BEAMS UNIFORMLY LOADED Loads given are total loads for a beam one inch thick and for a maximum bending stress of 1,000 pounds per square inch. Span in Feet DEPTH OP BEAM IN INCHES 2 4 6 8 10 12 14 16 18 20 2 187 3 148 4 111 5 89 356 6 74 296 7 63 254 8 56 222 500 9 198 444 10 178 400 711 11 162 364 646 12 148 333 593 926 13 308 547 855 14 286 508 794 15 267 474 741 1067 16 250 444 694 1000 17 418 654 941 1281 18 395 617 889 1210 19 374 585 842 1146 20 356 556 800 1089 1422 21 529 762 1037 1354 22 505 727 990 1293 1636 23 483 696 947 1237 1565 24 463 667 907 1185 1500 1852 25 640 871 1138 1440 1778 SQUARE WOODEN COLUMNS Loads given are in thousands of pounds for a working stress parallel to the grain of 1,000 pounds per square inch. p=i,ooo(i- yL Height of Column SIDE OP SQUARE IN INCHES 4 6 8 10 12 14 16 18 20 24 5 12.0 27.0 48.0 75.0 108.0 147.0 192.0 243.0 300.0 432.0 6 11.2 27.0 48.0 75.0 108.0 147.0 192.0 243.0 300.0 432.0 7 10.4 27.0 48.0 75.0 108.0 147.0 192.0 243.0 300.0 432.0 8 9.6 26.4 48.0 75.0 108.0 147.0 192.0 243.0 300.0 432.0 9 8.8 25.2 48.0 75.0 108.0 147.0 192.0 243.0 300.0 432.0 10 8.0 24.0 48.0 75.0 108.0 147.0 192.0 243.0 300.0 432.0 11 22.8 46.4 75.0 108.0 147.0 192.0 243.0 300.0 432.0 12 21.6 44.8 75.0 108.0 147.0 192.0 243.0 300.0 432.0 14 19.2 41.6 72.0 108.0 147.0 192.0 243.0 300.0 432.0 16 38.4 68.0 105.6 147.0 192.0 243.0 300.0 432.0 18 35.2 64.0 100.8 145.6 192.0 243.0 300.0 432.0 20 32.0 60.0 96.0 140.0 192.0 243.0 300.0 432.0 To obtain the carrying capacity of beams or columns where the unit stress pounds per square inch, increase or decrease the table loads proportionately. unit stress is other than 1,000 173 CORRUGATED BAR COMPANY, INC. AREAS OF CIRCULAR SEGMENTS FOR RATIOS OF RISE AND CHORD Area = CxR x Coefficient A Coeffi- cient R C A Coeffi- cient R C A Coeffi- cient R C A Coeffi- cient R C 1 0.6667 0.0022 46 0.6722 0.1017 91 0.6895 0.2097 136 0.7239 0.3373 2 0.6667 . 0044 47 0.6724 . 1040 92 0.6901 0.2122 137 0.7249 0.3404 3 0.6667 . 0066 48 0.6727 . 1063 93 0.6906 0.2148 138 0.7260 0.3436 4 0.6667 0.0087 49 0.6729 0.1086 94 0.6912 0.2174 139 . 7270 0.3469 5 0.6667 0.0109 50 0.6732 0.1109 95 0.6918 0.2200 140 0.7281 0.3501 6 0.6667 0.0131 51 0.6734 0.1131 96 0.6924 . 2226 141 . 7292 0.3534 7 0.6668 0.0153 52 . 6737 0.1154 97 0.6930 0.2252 142 . 7303 0.3567 8 0.6668 0.0175 53 0.6740 0.1177 98 0.6936 0.2279 143 0.7314 0.3600 9 0.6669 0.0197 54 0.6743 . 1200 99 0.6942 0.2305 144 0.7325 0.3633 10 0.6670 0.0218 55 0.6746 . 1224 100 0.6948 0.2332 145 0.7336 0.3666 11 . 6670 0.0240 56 0.6749 0.1247 101 0.6954 0.2358 146 0.7348 0.3700 12 0.6671 . 0262 57 0.6752 0.1270 102 0.6961 0.2385 147 0.7360 . 3734 13 0.6672 . 0284 58 0.6755 0.1293 103 0.6967 0.2412 148 0.7372 . 3768 14 0.6672 . 0306 59 0.6758 0.1316 104 0.6974 0.2439 149 0.7384 0.3802 15 0.6673 0.0328 60 0.6761 . 1340 105 . 6980 0.2466 150 . 7396 0.3837 16 . 6674 0.0350 61 0.6764 0.1363 106 0.6987 0.2493 151 0.7408 0.3872 17 0.6674 0.0372 62 0.6768 . 1387 107 . 6994 0.2520 152 0.7421 0.3901 18 0.6675 . 0394 63 0.6771 0.1410 108 0.7001 0.2548 153 . 7434 0.3946 19 0.6676 0.0416 64 0.6775 . 1434 109 0.7008 0.2575 154 0.7447 0.3977 20 0.6677 . 0437 65 . 6779 0.1457 110 0.7015 0.2603 155 0.7460 0.4013 21 0.6678 . 0459 66 0.6782 . 1481 111 0.7022 0.2631 156 0.7473 0.4049 22 . 6679 . 0481 67 0.6786 0.1505 112 0.7030 0.2659 157 0.7486 0.4085 23 0.6680 0.0504 68 0.6790 0.1529 113 . 7037 0.2687 158 0.7500 0.4122 24 0.6681 0.0526 69 0.6794 0.1553 114 0.7045 0.2715 159 0.7514 0.4159 25 0.6682 0.0548 70 0.6797 0.1577 115 0.7052 0.2743 160 0.7528 0.4196 26 0.6684 0.0570 71 0.6801 0.1601 116 0.7060 0.2772 161 0.7542 . 4233 27 0.6685 0.0592 72 0.6805 0.1625 117 0.7068 0.2800 162 0.7557 0.4270 28 0.6687 0.0614 73 0.6809 0.1649 118 0.7076 0.2829 163 0.7571 0.4308 29 0.6688 0.0636 74 0.6814 0.1673 119 0.7084 0.2858 164 0.7586 0.4346 30 0.6690 0.0658 75 0.6818 0.1697 120 0.7092 0.2887 165 0.7601 0.4385 31 0.6691 0.0681 76 . 6822 0.1722 121 0.7100 0.2916 166 0.7616 . 4424 32 0.6693 0.0703 77 0.6826 0.1746 122 0.7109 0.2945 167 0.7632 0.4463 33 0.6694 0.0725 78 0.6831 0.1771 123 0.7117 0.2975 168 0.7648 0.4502 34 0.6696 0.0747 79 0.6835 0.1795 124 0.7126 0.3004 169 0.7664 0.4542 35 0.6698 0.0770 80 . 6840 0.1820 125 0.7134 0.3034 170 0.7680 0.4582 36 0.6700 0.0792 81 0.6844 0.1845 126 0.7143 0.3064 171 0.7696 0.4622 37 . 6702 0.0814 82 . 6849 . 1869 127 0.7152 0.3094 172 0.7712 0.4663 38 0.6704 . 0837 83 0.6854 0.1894 128 0.7161 0.3124 173 0.7729 0.4704 39 0.6706 0.0859 84 0.6859 0.1919 129 0.7170 0.3155 174 0.7746 0.4745 40 0.6708 0.0882 85 0.6864 . 1944 130 0.7180 0.3185 175 0.7763 0.4787 41 0.6710 0.0904 86 0.6869 0.1970 131 0.7189 0.3216 176 0.7781 0.4828 42 0.6712 . 0927 87 0.6874 0.1995 132 0.7199 0.3247 177 0.7799 0.4871 43 0.6714 0.0949 88 0.6879 . 2020 133 0.7209 0.3278 178 0.7817 0.4914 44 0.6717 0.0972 89 0.6884 0.2046 134 0.7219, . 3309 179 0.7835 0.4957 45 0.6719 0.0995 90 6890 0.2071 135 0.7229 0.3341 180 0.7854 0.5000 174 USEFUL DATA 2 i i Si I 'a & O2 C cq 1 e|-o e o 1 -1 e 175 CORRUGATED BAR COMPANY, INC. NATURAL TRIGONOMETRIC FUNCTIONS SINES 0' 10' 20' 30' 40' 50' 60' 0.00000 0.00291 0.00582 0.00873 0.01164 0.01454 0.01745 89 1 0.01745 0.02036 0.02327 0.02618 0.02908 0.03199 0.03490 88 2 0.03490 0.03781 0.04071 0.04362 0.04653 0.04943 0.05234 87 3 0.05234 0.05524 0.05814 0.06105 0.06395 0.06685 0.06976 86 4 0.06976 0.07266 0.07556 0.07846 0.08136 0.08426 0.08716 85 5 0.08716 0.09005 0.09295 0.09585 0.09874 0.10164 0.10453 84 6 0.10453 0.10742 0.11031 0.11320 0.11609 0.11898 0.12187 83 7 0.12187 0.12476 0.12764 0.13053 0.13341 0.13629 0.13917 82 8 0.13917 0.14205 0.14493 0.14781 0.15069 0.15356 0.15643 81 9 0.15643 0.15931 0.16218 0.16505 0.16792 0.17078 0.17365 80 10 0.17365 0.17651 0.17937 0.18224 0.18509 0.18795 0.19081 79 11 0.19081 0.19366 0.19652 0.19937 0.20222 0.20507 0.20791 78 12 0.20791 0.21076 0.21360 0.21644 0.21928 0.22212 0.22495 77 13 0.22495 0.22778 0.23062 0.23345 0.23627 0.23910 0.24192 76 14 0.24192 0.24474 0.24756 0.25038 0.25320 0.25601 0.25882 75 15 0.25882 0.26163 0.26443 0.26724 0.27004 0.27284 0.27564 74 16 0.27564 0.27843 0.28123 0.28402 0.28680 0.28959 0.29237 73 17 0.29237 0.29515 0.29793 0.30071 0.30348 0.30625 0.30902 72 18 0.30902 0.31178 0.31454 0.31730 0.32006 0.32282 0.32557 71 19 0.32557 0.32832 0.33106 0.33381 0.33655 0.33929 0.34202 70 20 0.34202 0.34475 0.34748 0.35021 0.35293 0.35565 0.35837 69 21 0.35837 0.36108 0.36379 0.36650 0.36921 0.37191 0.37461 68 22 0.37461 0.37730 0.37999 0.38268 0.38537 0.38805 0.39073 67 23 0.39073 0.39341 0.39608 0.39875 0.40142 0.40408 0.40674 66 24 0.40674 0.40939 0.41204 0.41469 0.41734 0.41998 0.42262 65 25 0.42262 0.42525 0.42788 0.43051 0.43313 0.43575 0.43837 64 26 0.43837 0.44098 0.44359 0.44620 0.44880 0.45140 0.45399 63 27 0.45399 0.45658 0.45917 0.46175 0.46433 0.46690 0.46947 62 28 0.46947 0.47204 0.47460 0.47716 0.47971 0.48226 0.48481 61 29 0.48481 0.48735 0.48989 0.49242 0.49495 0.49748 0.50000 60 30 0.50000 0.50252 0.50503 0.50754 0.51004 0.51254 0.51504 59 31 0.51504 0.51753 0.52002 0.52250 0.52498 0.52745 0.52992 58 32 0.52992 0.53238 0.53484 0.53730 0.53975 0.54220 0.54464 57 33 0.54464 0.54708 0.54951 0.55194 0.55436 0.55678 0.55919 56 34 0.55919 0.56160 0.56401 0.56641 0.56880 0.57119 0.57358 55 35 0.57358 0.57596 0.57833 0.58070 0.58307 0.58543 0.58779 54 36 0.58779 0.59014 0.59248 0.59482 0.59716 0.59949 0.60182 53 37 0.60182 0.60414 0.60645 0.60876 0.61107 0.61337 0.61566 52 38 0.61566 0.61795 0.62024 0.62251 0.62479 0.62706 0.62932 51 39 0.62932 0.63158 0.63383 0.63608 0.63832 0.64056 0.64279 50 40 0.64279 0.64501 0.64723 0.64945 0.65166 0.65386 0.65606 49 41 0.65606 0.65825 0.66044 0.66262 0.66480 0.66697 0.66913 48 42 0.66913 0.67129 0.67344 0.67559 0.67773 0.67987 0.68200 47 43 0.68200 0.68412 0.68624 0.68835 0.69046 0.69256 0.69466 46 44 0.69466 0.69675 0.69883 0.70091 0.70298 0.70505 0.70711 45 60' 50' 40' 30' 20' 10' 0' COSINES 176 USEFUL DATA NATURAL TRIGONOMETRIC FUNCTIONS COSINES 0' 10' 20' 30' 40' 50' | 60' 1.00000 1.00000 0.99998 0.99996 0.99993 0.99989 0.99985 89 1 0.99985 0.99979 0.99973 0.99966 0.99958 0.99949 0.99939 88 2 0.99939 0.99929 0.99917 0.99905 0.99892 0.99878 0.99863 87 3 0.99863 0.99847 0.99831 0.99813 0.99795 0.99776 0.99756 86 4 0.99756 0.99736 0.99714 0.99692 0.99668 0.99644 0.99619 85 5 0.99619 0.99594 0.99567 0.99540 0.99511 0.99482 0.99452 84 6 0.99452 0.99421 0.99390 0.99357 0.99324 0.99290 0.99255 83 7 0.99255 0.99219 0.99182 0.99144 0.99106 0.99067 0.99027 82 8 0.99027 0.98986 0.98944 0.98902 0.98858 0.98814 0.98769 81 9 0.98769 0.98723 0.98676 0.98629 0.98580 0.98531 0.98481 80 10 0.98481 0.98430 0.98378 0.98325 0.98272 0.98218 0.98163 79 11 0.98163 0.98107 0.98050 0.97992 0.97934 0.97875 0.97815 78 12 0.97815 0.97754 0.97692 0.97630 0.97566 0.97502 0.97437 77 13 0.97437 0.97371 0.97304 0.97237 0.97169 0.97100 0.97030 76 14 0.97030 0.96959 0.96887 0.96815 0.96742 0.96667 0.96593 75 15 0.96593 0.96517 0.96440 0.96363 0.96285 0.96206 0.96126 74 16 0.96126 0.96046 0.95964 0.95882 0.95799 0.95715 0.95630 73 17 0.95630 0.95545 0.95459 0.95372 0.95284 0.95195 0.95106 72 18 0.95106 0.95015 0.94924 0.94832 0.94740 0.94646 0.94552 71 19 0.94552 0.94457 0.94361 0.94264 0.94167 0.94068 0.93969 70 20 0.93969 0.93869 0.93769 0.93667 0.93565 0.93462 0.93358 69 21 0.93358 0.93253 0.93148 0.93042 0.92935 0.92827 0.92718 68 22 0.92718 0.92609 0.92499 0.92388 0.92276 0.92164 0.92050 67 23 0.92050 0.91936 0.91822 0.91706 0.91590 0.91472 0.91355 66 24 0.91355 0.91236 0.91116 0.90996 0.90875 0.90753 0.90631 65 25 0.90631 0.90507 0.90383 0.90259 0.90133 0.90007 0.89879 64 26 0.89879 0.89752 0.89623 0.89493 0.89363 0.89232 0.89101 63 27 0.89101 0.88968 0.88835 0.88701 0.88566 0.88431 0.88295 62 28 0.88295 0.88158 0.88020 0.87882 0.87743 0.87603 0.87462 61 29 0.87462 0.87321 0.87178 0.87036 0.86892 0.86748 0.86603 60 30 0.86603 0.86457 0.86310 0.86163 0.86015 0.85866 0.85717 59 31 0.85717 0.85567 0.85416 0.85264 0.85112 0.84959 0.84805 58 32 0.84805 0.84650 0.84495 0.84339 0.84182 0.84025 0.83867 57 33 0.83867 0.83708 0.83549 0.83389 0.83228 0.83066 0.82904 56 34 0,82904 0.82741 0.82577 0.82413 0.82248 0.82082 0.81915 55 35 0.81915 0.81748 0.81580 0.81412 0.81242 0.81072 0.80902 54 36 0.80902 0.80730 0.80558 0.80386 0.80212 0.80038 0.79864 53 37 0.79864 0.79688 0.79512 0.79335 0.79158 0.78980 0.78801 52 38 0.78801 0.78622 0.78442 0.78261 0.78079 0.77897 0.77715 51 39 0.77715 0.77531 0.77347 0.77162 0.76977 0.76791 0.76604 50 40 0.76604 0.76417 0.76229 0.76041 0.75851 0.75661 0.75471 49 41 0.75471 0.75280 0.75088 0.74896 0.74703 0.74509 0.74314 48 42 0.74314 0.74120 0.73924 0.73728 0.73531 0.73333 0.73135 47 43 0.73135 0.72937 0.72737 0.72537 0.72337 0.72136 0.71934 46 44 0.71934 0.71732 0.71529 0.71325 0.71121 0.70916 0.70711 45 60' 50' 40' 30' 20' 10' 0' SINES 177 CORRUGATED BAR COMPANY, INC. NATURAL TRIGONOMETRIC FUNCTIONS J. AJNliHiNia 0' 10' 20' 30' 40' 50' 60' 0.00000 0.00291 0.00582 0.00873 0.01164 0.01455 0.01746 89 1 0.01746 0.02036 0.02328 0.02619 0.02910 0.03201 0.03492 88 2 0.03492 0.03783 0.04075 0.04366 0.04658 0.04949 0.05241 87 3 0.05241 0.05533 0.05824 0.06116 0.06408 0.06700 0.06993 86 4 0.06993 0.07285 0.07578 0.07870 0.08163 0.08456 0.08749 85 5 0.08749 0.09042 0.09335 0.09629 0.09923 0.10216 0.10510 84 6 0.10510 0.10805 0.11099 0.11394 0.11688 0.11983 0.12278 83 7 0.12278 0.12574 0.12869 0.13165 0.13461 0.13758 0.14054 82 8 0.14054 0.14351 0.14648 0.14945 0.15243 0.15540 0.15838 81 9 0.15838 0.16137 0.16435 0.16734 0.17033 0.17333 0.17633 80 10 0.17633 0.17933 0.18233 0.18534 0.18835 0.19136 0.19438 79 11 0.19438 0.19740 0.20042 0.20345 0.20648 0.20952 0.21256 78 12 0.21256 0.21560 0.21864 0.22169 0.22475 0.22781 0.23087 77 13 0.23087 0.23393 0.23700 0.24008 0.24316 0.24624 0.24933 76 14 0.24933 0.25242 0.25552 0.25862 0.26172 0.26483 0.26795 75 15 0.26795 0.27107 0.27419 0.27732 0.28046 0.28360 0.28675 74 16 0.28675 0.28990 0.29315 0.29621 0.29938 0.30255 0.30573 73 17 0.30573 0.30891 0.31210 0.31530 0.31850 0.32171 0.32492 72 18 0.32492 0.32814 0.33136 0.33460 0.33783 0.34108 0.34433 71 19 0.34433 0.34758 0.35085 0.35412 0.35740 0.36068 0.36397 70 20 0.36397 0.36727 0.37057 0.37388 0.37720 0.38053 0.38386 69 21 0.38386 0.38721 0.39055 0.39391 0.39727 0.40065 0.40403 68 22 0.40403 0.40741 0.41081 0.41421 0.41763 0.42105 0.42447 67 23 0.42447 0.42791 0.43136 0.43481 0.43828 0.44175 0.44523 66 24 0.44523 0.44872 0.45222 0.45573 0.45924 0.46277 0.46631 65 25 0.46631 0.46985 0.47341 0.47698 0.48055 0.48414 0.48773 64 26 0.48773 0.49134 0.49495 0.49858 0.50222 0.50587 0.50953 63 27 0.50953 0.51320 0.51688 0.52057 0.52427 0.52798 0.53171 62 28 0.53171 0.53545 0.53920 0.54296 0.54674 0.55051 0.55431 61 29 0.55431 0.55812 0.56194 0.56577 0.56962 0.57348 0.57735 60 30 0.57735 0.58124 0.58513 0.58905 0.59297 0.59691 0.60086 59 31 0.60086 0.60483 0.60881 0.61280 0.61681 0.62083 0.62487 58 32 0.62487 0.62892 0.63299 0.63707 0.64117 0.64528 0.64941 57 33 0.64941 0.65355 0.65771 0.66189 0.66608 0.67028 0.67451 56 34 0.67451 0.67875 0.68301 0.68728 0.69157 0.69588 0.70021 55 35 0.70021 0.70455 0.70891 0.71329 0.71769 0.72211 0.72654 54 36 0.72654 0.73100 0.73547 0.73996 0.74447 0.74900 0.75355 53 37 0.75355 0.75812 0.76272 0.76733 0.77196 0.77661 0.78129 52 38 0.78129 0.78598 0.79070 0.79544 0.80020 0.80498 0.80978 51 39 0.80978 0.81461 0.81946 0.82434 0.82923 0.83415 0.83910 50 40 0.83910 0.84407 0.84906 0.85408 0.85912 0.86419 0.86929 49 41 0.86929 0.87441 0.87955 0.88473 0.88992 0.89515 0.90040 48 42 0.90040 0.90569 0.91099 0.91633 0.92170 0.92709 0.93252 47 43 0.93252 0.93797 0.94345 0.94896 0.95451 0.96008 0.96569 46 44 0.96569 0.97133 0.97700 0.98270 0.98843 0.99420 1.00000 45 60' 50' 40' 30' 20' 10' 0' COTANGENTS 178 USEFUL DATA NATURAL TRIGONOMETRIC FUNCTIONS C OTANGENTS 0' 10 7 20' 30' 40' 50' 60' 00 343.77371 171.88540 114.58865 85.93979 68.75009 57.28996 89 1 57.28996 49.10388 42.96408 38.18846 34.36777 31.24158 28.63625 88 2 28.63625 26.43160 24.54176 22.90377 21.47040 20.20555 19.08114 87 3 19.08114 18.07498 17.16934 16.34986 15.60478 14.92442 14.30067 86 4 14.30067 14.72674 13.19688 12.70621 12.25051 11.82617 11.43005 85 5 11.43005 11.05943 10.71191 10.38540 10.07803 9.78817 9.51436 84 6 9.51436 9.25530 9.00983 8.77689 8.55555 8.34496 8.14435 83 7 8.14435 7.95302 7.77035 7.59575 7.42871 7.26873 7.11537 82 8 7.11537 6.96823 6.82694 6.69116 6.56055 6.43484 6.31375 81 9 6.31375 6.19703 6.08444 5.97576 5.87080 5.76937 5.67128 80 10 5.67128 5.57638 5.48451 5.39552 5.30928 5.22566 5.14455 79 11 5.14455 5.06584 4.98940 4.91516 4.84300 4.77286 4.70463 78 12 4.70463 4.63825 4.57363 4.51071 4.44942 3.38969 4.33148 77 13 4.33148 4.27471 4.21933 4.16530 4.11256 4.06107 4.01078 76 14 4.01078 3.96165 3.91364 3.86671 3.82083 3.77595 3.73205 75 15 3.73205 3.68900 3.64705 3.60588 3.56557 3.52609 3.48741 74 16 3.48741 3.44951 3.41236 3.37594 3.34023 3.30521 3.27085 73 17 3.27085 3.23714 3.20406 3.17159 3.13972 3.10842 3.07778 72 18 3.07768 3.04749 3.01783 2.98869 2.96004 2.93189 2.90421 71 19 2.90421 2.87700 2.85023 2.82391 2.79802 2.77254 2.74748 70 20 2.74748 2.72281 2.69853 2.67462 2.65109 2.62791 2.60509 69 21 2.60509 2.58261 2.56046 2.53865 2.51715 2.49597 2.47509 68 22 2.47509 2.45451 2.43422 2.41421 2.39449 2.37504 2.35585 67 23 2.35585 2.33693 2.31826 2.29984 2.28167 2.26374 2.24604 66 24 2.24604 2.22857 2.21132 2.19430 2.17749 2.16090 2.14451 65 25 2.14451 2.12832 2.11233 2.09654 2.08094 2.06553 2:05030 64 26 2.05030 2.03526 2.02039 2.00569 .99116 .97680 .96261 63 27 1.96261 .94858 1.93470 1.92098 .90741 .89400 .88073 62 28 1.88073 .86760 1.85462 1.84177 .2907 .81649 .80405 61 29 1.80405 .79174 1.77955 1.76749 .75556 .74375 .73205 60 30 1.73205 .72047 1.70901 1.69766 .68643 .67530 .66428 59 31 1.66428 .65337 1.64256 1.63185 .62125 .61074 .60033 58 32 1.60033 .59002 1.57981 1.56969 .55966 .54972 1.53987 57 33 1.53987 1.53010 1.52043 1.51084 .50133 .49190 1.48256 56 34 1.48250 1.47330 1.46411 1.45501 .44598 1.43703 1.42815 55 35 1.42815 1.41934 1.41061 1.40195 .39336 1.38484 1.37638 54 36 1.37638 1.36800 1.35968 1.35142 .34323 1.33511 1.32704 53 37 1.32704 1.31904 1.31110 1.30323 .29541 1.28764 1.27994 52 38 1.27994 1.27230 1.26471 1.25717 .24969 .24227 1.23490 51 39 1.23490 1.22758 1.22031 1.21310 .20593 .19882 1.19175 50 40 1.19175 1.18474 1 . 17777 1.17085 . 16398 .15715 1 . 15037 49 41 1.15037 1.14363 1 . 13694 1.13029 . 12369 .11713 1.11061 48 42 1.11061 1 . 10414 1.09770 1.09131 .08496 .07864 1.07237 47 43 1.07237 1.06613 1.05994 1.05378 1.04766 .04158 1.03553 46 44 1.03553 1.02952 1.02355 1.01761 .01170 .00583 1.00000 45 60' 50' 40' 30' 20' 10' 0' TANGENTS 179 CORRUGATED BAR COMPANY, INC. NATURAL TRIGONOMETRIC FUNCTIONS SECANTS 0' 10' 20' 30' | 40' 50' 60' 1.00000 .00000 1.00002 .00004 1.00007 1.00011 1.00015 89 1 1.00015 .00021 .00027 .00034 1.00042 1.00051 1.00061 88 2 1.00061 .00072 .00083 .00095 1.00108 1.00122 1.00137 87 3 1.00137 .00153 .00169 .00187 1.00205 1.00224 1.00244 86 4 1.00244 .00265 .00287 .00309 1.00333 1.00357 1.00382 85 5 1.00382 .00408 .00435 .00463 1.00491 1.00521 1.00551 84 6 1.00551 .00582 .00614 .00647 1.00681 1.00715 1.00751 83 7 1.00751 .00787 .00825 .00863 1.00902 1.00942 1.00983 82 8 1.00983 .01024 .01067 .01111 1.01155 1.01200 1.01247 81 9 1.01247 .01294 .01342 .01391 1.01440 1.01491 1.01543 80 10 1.01543 .01595 .01649 .01703 1.01758 1.01815 1.01872 79 11 1.01872 .01930 .01989 .02049 1.02110 1.02171 1.02234 78 12 1.02234 .02298 .02362 .02428 1.02494 1.02562 1.02630 77 13 1.02630 1.02700 .02770 .02842 1.02914 1.02987 1.03061 76 14 1.03061 1.03137 .03213 .03290 1.03368 1.03447 1.03528 75 15 1.03528 1.03609 1.03691 .03774 1.03858 1.03944 1.04030 74 16 1.04030 .04117 1.04206 .04295 1.04385 1.04477 1.04569 73 17 1.04569 .04663 1.04757 .04853 1.04950 1.05047 1.05146 72 18 1.05146 .05246 .05347 .05449 1.05552 1.05657 .05762 71 19 1.05762 .05869 .05976 .06085 1.06195 1.06306 .06418 70 20 1.06418 .06531 .06645 1.06761 1.06878 1.06995 .07115 69 21 1.07115 .07235 .07356 1.07479 1.07602 1.07727 .07853 68 22 1.07853 .07981 .08109 1.08239 1.08370 1.08503 .08636 67 23 1.08636 .08771 .08907 1.09044 1.09183 1.09323 .09464 66 24 1.09464 .09605 .09750 1.09895 1 . 10041 1 . 10189 .10338 65 25 1.10338 1.10488 .10640 1.10793 1.10947 1.11103 .11260 64 26 1.11260 1.11419 .11579 1.11740 1.11903 1.12067 .12233 63 27 1.12233 1 . 12400 .12568 1.12738 1.12910 1.13083 .13257 62 28 1.13257 1 . 13433 43610 1.13789 1 . 13970 1.14152 . 14335 61 29 1.14335 1 . 14521 . 14707 1.14896 1.15085 1 . 15277 .15470 60 30 1 . 15470 1.15665 . 15861 1 . 16059 1 . 16259 1.16460 .16663 59 31 1.16663 1.16868 .17075 1.17283 1 . 17493 1.17704 .17918 58 32 1.17918 1 . 18133 .18350 1 . 18569 1.18790 1.19012 . 19236 57 33 1 . 19236 1 . 19463 .19691 1.19920 1.20152 1.20386 .20622 56 34 1.20622 1.20859 .21099 1.21341 1.21584 1.21830 .22077 55 35 1.22077 .22327 .22579 1.22833 1.23089 1.23347 .23607 54 36 1.23607 .23869 .24134 1.24400 1.24669 1.24940 .25214 53 37 1.25214 .25489 .25767 1.26047 1.26330 1.26615 .26902 52 38 1.26902 .27191 .27483 1.27778 1.28075 1.28374 .28676 51 39 1.28676 .28980 .29287 1.29597 1.29909 1.30223 .30541 50 40 1.30541 .30861 1.31183 1.31509 1.31837 1.32168 .32501 49 41 1.32501 .32838 1.33177 1.33519 1.33864 1.34212 .34563 48 42 1.34563 .34917 1.35274 1.35634 1.35997 1.36363 1.36733 47 43 1.36733 .37105 1.37481 1.37860 1.38242 1.38628 1.39016 46 44 1.39016 .39409 1.39804 1.40203 1.40606 1.41012 1.41421 45 60' 50' 40' 30' 20' 10' 0' COSECANTS 180 USEFUL DATA NATURAL TRIGONOMETRIC FUNCTIONS COSECANTS 0' 10 20' 30' 40' 50' 60' X 343.77516 171.88831 114.59301 85.94561 68.75736 57.29869 89 1 57.29869 49.11406 42.97571 38.20155 34.38232 31.25758 28.65371 88 2 28.65371 26.45051 24.56212 22.92559 21.49368 20.23028 19.10732 87 3 19.10732 18.10262 17.19843 16.38041 15.63679 14.95788 14.33559 86 4 14.33559 13.76312 13.23472 12.74550 12.29125 11.86837 11.47371 85 5 11.47371 11.10455 10.75849 10.43343 10.12752 9.83912 9.56677 84 6 9.56677 9.30917 9.06515 8.83367 8.61379 8.40466 8.20551 83 7 8.20551 8.01565 7.83443 7.66130 7.49571 7.33719 7.18530 82 8 7.18530 7.03962 6.89979 6.76547 6.63633 6.51208 6.39245 81 9 6.39245 6.27719 6.16607 6.05886 5.95536 5.85539 5.75877 80 10 5.75877 5.66533 5.57493 5.48740 5.40263 5.32049 5.24084 79 11 5.24084 5.16359 5.08863 5.01585 4.94517 4.87649 4.80973 78 12 4.80973 4.74482 4.68167 4.62023 4.56041 4.50216 4.44541 77 13 4.44541 4.39012 4.33622 4.28366 4.23239 4.18238 4.13357 76 14 4.13357 4.08591 4.03938 3.99393 3.94952 3.90613 3.86370 75 15 3.86370 3.82223 3.78166 3.74198 3.70315 3.66515 3.62796 74 16 3.62796 3.59154 3.55587 3.52094 3.48671 3.45317 3.42030 73 17 3.42030 3.38808 3.35649 3.32551 3.29512 3.26531 3.23607 72 18 3.23607 3.20737 3.17920 3.15155 3.12440 3.09774 3.07155 71 19 3.07155 3.04584 3.02057 2.99574 2.97135 2.94737 2.92380 70 20 2.92380 2.90063 2.87785 2.85545 2.83342 2.81175 2.79043 69 21 2.79043 2.76945 2.74881 2.72850 2.70851 2.68884 2.66947 68 22 2.66947 2.65040 2.63162 2.61313 2.59491 2.57698 2.55930 67 23 2.55930 2.54190 2.52474 2.50784 2.49119 2.47477 2.45959 66 24 2.45859 2.44264 2.42692 2.41142 2.39614 2.38107 2.36620 65 25 2.36620 2.35154 2.33708 2.32282 2.30875 2.29487 2.28117 64 26 2.28117 2.26766 2.25432 2.24116 2.22817 2.21535 2.20269 63 27 2.20269 2.19019 2.17786 2.16568 2.15366 2.14178 2.13005 62 28 2.13005 2.11847 2.10704 2.09574 2.08458 2.07356 2.06267 61 29 2.06267 2.05191 2.04128 2.03077 2.02039 2.01014 2.00000 60 30 2.00000 1.98998 1.98008 1.97029 .96062 1.95106 1.94160 59 31 .94160 1.93226 1.92302 1.91388 .90485 1.89591 .88709 58 32 .88708 1.87834 1.86970 1.86116 .85271 1.84435 .83608 57 33 .83608 1.82790 1.81981 1.81180 .80388 1.79604 .78829 56 34 .78829 1.78062 1.77303 1.76552 .75808 1.75073 .74345 55 35 .74345 1.73624 1.72911 1.72205 .71506 1.70815 .70130 54 36 .70130 1.69454 1.68782 1.68117 .67460 1.66809 .66164 53 37 .66164 1.65526 1.64894 1.64268 .63648 1.63035 .62427 52 38 .62427 1.61825 1.61229 1.60639 .60054 .59475 .58902 51 39 .58902 1.58333 1.57771 1.57213 .56661 .56114 .55572 50 40 1.55572 1.55036 1.54504 1.53977 1.53455 .52938 .52425 49 41 1.52425 1.51918 1.51415 1.50916 1.50422 .49933 .49448 48 42 1.49448 1.48967 1.48491 1.48019 1.47551 .47087 .46628 47 43 1.46628 1.46173 1.45721 1.45274 1.44831 .44391 .43856 46 44 1.43956 1.43524 1.43096 1.42672 1.42251 .41835 .41421 45 60' 50' 40' 30' 20' 10' 0' SECANTS 181 CORRUGATED BAR COMPANY, INC. FUNCTIONS OF NUMBERS 1 TO 49 XTrt xi,,i_ - Square Cube 1,000 x No. = E HAMETER .NO. Square Cube Root Root Logarithm Reciprocal Circum. Area l 1 i 1.0000 1.0000 0.00000 1000.000 3.142 0/7854 2 4 8 1.4142 1.2599 0.30103 500.000 6.283 3.1416 3 9 27 1.7321 1.4422 0.47712 333.333 9.425 7.0686 4 16 64 2.0000 1.5874 0.60206 250.000 12.566 12.5664 5 25 125 2.2361 1.7100 0.69897 200.000 15.708 19.6350 6 36 216 2.4495 1.8171 0.77815 166.667 18.850 28.2743 7 49 343 2.6458 1.9129 0.84510 142.857 21.991 38.4845 8 64 512 2.8284 2.0000 0.90309 125.000 25.133 50.2655 9 81 729 3.0000 2.0801 0.95424 111.111 28.274 63.6173 10 100 1000 3.1623 2.1544 1.00000 100.000 31.416 78.5398 11 121 1331 3.3166 2.2240 1.04139 90.9091 34.558 95.0332 12 144 1728 3.4641 2.2894 1.07918 83.3333 37.699 113.097 13 169 2197 3.6056 2.3513 1.11394 76.9231 40.841 132.732 14 196 2744 3.7417 2.4101 . 14613 71.4286 43.982 153.938 15 225 3375 3.8730 2.4662 .17609 66.6667 47.124 176.715 16 256 4096 4.0000 2.5198 .20412 62.5000 50.265 201.062 17 289 4913 4.1231 2.5713 .23045 58.8235 53.407 226.980 18 324 5832 4.2426 2.6207 .25527 55.5556 56.549 254.469 19 361 6859 4.3589 2.6684 .27875 52.6316 59.690 283.529 20 400 8000 4.4721 2.7144 .30103 50.0000 62.832 314.159 21 441 9261 4.5826 2.7589 .32222 47.6190 65.973 346.361 22 484 10648 4.6904 2.8020 .34242 45.4545 69.115 380.133 23 529 12167 4.7958 2.8439 .36173 43.4783 72.257 415.476 24 576 13824 4.8990 2.8845 .38021 41.6667 75.398 452.389 25 625 15625 5.0000 2.9240 1.39794 40.0000 78.540 490.874 26 676 17576 5.0990 2.9625 1.41497 38.4615 81 . 681 530.929 27 729 19683 5.1962 3.0000 1.43136 37.0370 84.823 572.555 28 784 21952 5.2915 3.0366 1.44716 35.7143 87.965 615.752 29 841 24389 5.3852 3.0723 1.46240 34.4828 91 . 106 660.520 30 900 27000 5.4772 3.1072 1.47712 33.3333 94.248 706.858 31 961 29791 5.5678 3.1414 1.49136 32.2581 97.389 754.768 32 1024 32768 5.6569 3.1748 1.50515 31.2500 100.531 804.248 33 1089 35937 5.7446 3.2075 1.51851 30.3030 103.673 855.299 34 1156 39304 5.8310 3.2396 1.53148 29.4118 106.814 907.920 35 1225 42875 5.9161 3.2711 1.54407 28.5714 109.956 962.113 36 1296 46656 6.0000 3.3019 1.55630 27.7778 113.097 1017.88 37 1369 50653 6.0828 3.3322 1.56820 27.0270 116.239 1075.21 38 1444 54872 6.1644 3.3620 .57978 26.3158 119.381 1134.11 39 1521 59319 6.2450 3.3912 .59106 25.6410 122.522 1194.59 40 1600 64000 6.3246 3.4200 .60206 25.0000 125.66 1256.64 41 1681 68921 6.4031 3.4482 .61278 24.3902 128.81 1320.25 42 1764 74088 6.4807 3.4760 .62325 23.8095 131.95 1385.44 43 1849 79507 6.5574 3.5034 .63347 23.2558 135.09 1452.20 44 1936 85184 6.6332 3.5303 .64345 22.7273 138.23 1520.53 45 2025 91125 6.7082 3.5569 .65321 22.2222 141.37 1590.43 46 2116 97336 6.7823 3.5830 1.66276 21.7391 144.51 1661.90 47 2209 103823 6.8557 3.6088 1.67210 21 . 2766 147.65 1734.04 48 2304 110592 6.9282 3.6342 1.68124 20.8333 150.80 1809.56 49 2401 117649 7.0000 3.6593 1.69020 20.4082 153.94 1885.74 182 USEFUL DATA FUNCTIONS OF NUMBERS 50 TO 99 Square Cube 1,000 X No. = D AMETER No. Square Cube Root Root Logarithm Reciprocal Circum. Area 50 2500 125000 7.0711 3.6840 .69897 20.0000 157.08 1963.50 51 2601 132651 7.1414 3.7084 .70757 19.6078 160.22 2042.82 52 2704 140608 7.2111 3.7325 .71600 19.2308 163.36 2123.72 53 2809 148877 7.2801 3.7563 .72428 18.8679 166.50 2206.18 54 2916 157464 7.3485 3.7798 .73239 18.5185 169.65 2290.22 55 3025 166375 7.4162 3.8030 .74036 18.1818 172.79 2375.83 56 3136 175616 7.4833 3.8259 .74819 17.8571 175.93 2463.01 57 3249 185193 7.5498 3.8485 .75587 17.5439 179.07 2551.76 58 3364 195112 7.6158 3.8708 .76343 17.2414 182.21 2642.08 59 3481 205379 7.6811 3.8930 .77085 16.9492 185.35 2733.97 60 3600 216000 7.7460 3.9149 .77815 16.6667 188.50 2827.43 61 3721 226981 7.8102 3.9365 .78533 16.3934 191.64 2922.47 62 3844 238328 7.8740 3.9579 .79239 16.1290 194.78 3019.07 63 3969 250047 7.9373 3.9791 .79934 15.8730 197.92 3117.25 64 4096 262144 8.0000 4.0000 1.80618 15.6250 201.06 3216.99 65 4225 274625 8.0623 4.0207 1.81291 15.3846 204.20 3318.31 66 4356 287496 8.1240 4.0412 1.81954 15.1515 207.35 3421 . 19 67 4489 300763 8.1854 4.0615 1.82607 14.9254 210.49 3525.65 68 4624 314432 8.2462 4.0817 1.83251 14.7059 213.63 3631.68 69 4761 328509 8.3066 4.1016 1.83885 14.4928 216.77 3739.28 70 4900 343000 8.3666 4.1213 1.84510 14.2857 219.91 3848.45 71 5041 357911 8.4261 4.1408 1.85126 14.0845 223.05 3959.19 72 5184 373248 8.4853 4.1602 1.85733 13.8889 226.19 4071.50 73 5329 389017 8.5440 4.1793 1.86332 13.6986 229.34 4185.39 74 5476 405224 8.6023 4.1983 1.86923 13.5135 232.48 4300.84 75 5625 421875 8.6603 4.2172 1.87506 13.3333 235.62 4417.86 76 5776 438976 8.7178 4.2358 1.88081 13.1579 238.76 4536.46 77 5929 456533 8.7750 4.2543 1.88649 12.9870 241.90 4656.63 78 6084 474552 8.8318 4.2727 1.89209 12.8205 245.04 4778.36 79 6241 493039 8.8882 4.2908 1.89763 12.6582 248.19 4901.67 80 6400 512000 8.9443 4.3089 1.90309 12.5000 251.33 5026.55 81 6561 531441 9.0000 4.3267 1.90849 12.3457 254.47 5153.00 82 6724 551368 9.0554 4.3445 1.91381 12.1951 257.61 5281.02 83 6889 571787 9.1104 4.3621 1.91908 12.0482 260.75 5410.61 84 7056 592704 9.1652 4.3795 1.92428 11.9048 263.89 5541.77 85 7225 614125 9.2195 4.3968 1.92942 11.7647 267.04 5674.50 86 7396 636056 9.2736 4.4140 1.93450 11.6279 270.18 5808.80 87 7569 658503 9.3274 4.4310 1.93952 11.4943 273.32 5944.68 88 7744 681472 9.3808 4.4480 1.94448 11.3636 276.46 6082.12 89 7921 704969 9.4340 4.4647 1.94939 11.2360 279.60 6221.14 90 8100 729000 9.4868 4.4814 .95424 11.1111 282.74 6361.73 91 8281 753571 9.5394 4.4979 .95904 10.9890 285.88 6503.88 92 8464 778688 9.5917 4.5144 .96379 10.8696 289.03 6647.61 93 8649 804357 9.6437 4.5307 .96848 10.7527 292.17 6792.91 94 8836 830584 9.6954 4.5468 .97313 10.6383 295.31 6939.78 95 9025 857375 9.7468 4.5629 .97772 10.5263 298.45 7088.22 96 9216 884736 9.7980 4.5789 .98227 10.4167 301.59 7238.23 97 9409 912673 9.8489 4.5947 1.98677 10.3093 304.73 7389.81 98 9604 941192 9.8995 4.6104 1.99123 10.2041 307.88 7542.96 99 9801 970299 9.9499 4.6261 1.99564 10.1010 311.02 7697.69 183 CORRUGATED BAR COMPANY, INC. DECIMALS OF AN INCH FOR EACH Fractions Decimals Fractions Decimals 64ths 32nds leths 8ths 64ths 32nds 16ths 8ths A 0.015625 H 0.515625 A 0.03125 H 0.53125 A 0.046875 If 0.546875 A 0.0625 A 0.5625 A 0.078125 H 0.578125 A 0.09375 H 0.59375 g 0.109375 If 0.609375 v% 0.125 N 0.625 _*_ 0.140625 I* 0.640625 A 0.15625 H 0.65625 _ii_ 0.171875 g _H_ 0.671875 0.6875 A 0.1875 H 0.203125 if 0.703125 A 0.21875 M 0.71875 0.234375 H '0.734375 X 0.25 M 0.75 H 0.265625 H 0.765625 4 0.28125 If 0.78125 H 0.296875 -H 0.796875 A 0.3125 H 0.8125 g 0.328125 0.828125 H 0.34375 H 0.84375 tt 0.359375 M 0.859375 */8 0.375 K 0.875 g 0.390625 H 0.890625 H 0.40625 H 0.90625 H 0.421875 M 0.921875 A 0.4375 M 0.9375 0.453125 ti 0.953125 tt 0.46875 0.96875 H 0.484375 If 0.984375 y 2 0.5 1 1.00 184 USEFUL DATA DECIMALS OF A FOOT FOR EACH OF AN INCH In. 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10" 11" 0.0000 . 0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.7500 0.8333 0.9167 A 0.0026 0.0859 0.1693 0.2526 0.3359 0.4193 0.5026 0.5859 0.6693 0.7526 0.8359 0.9193 A 0.0052 0.0885 0.1719 0.2552 0.3385 0.4219 0.5052 0.5885 0.6719 0.7552 0.8385 0.9219 ft 0.0078 0.0911 0.1745 0.2578 0.3411 0.4245 0.5078 0.5911 . 6745 0.7578 0.8411 0.9245 K 0.0104 0.0937 0.1771 0.2604 0.3437 0.4271 0.5104 0.5937 0.6771 0.7604 0.8437 0.9271 A 0.0130 0.0964 0.1797 0.2630 0.3464 0.4297 0.5130 0.5964 0.6797 0.7630 0.8464 0.9297 A 0.0156 0.0990 0.1823 0.2656 0.3490 0.4323 0.5156 0.5990 0.6823 0.7656 0.8490 0.9323 A 0.0182 0.1016 0.1849 0.2682 0.3516 0.4349 0.5182 0.6016 . 6849 0.7682 0.8516 0.9349 U 0.0208 0.1042 0.1875 0.2708 0.3542 0.4375 0.5208 0.6042 0.6875 0.7708 0.8542 0.9375 ft 0.0234 0.1068 0.1901 0.2734 0.3568 0.4401 0.5234 0.6068 0.6901 0.7734 0.8568 0.9401 A 0.0260 0.1094 0.1927 0.2760 0.3594 0.4427 0.5260 0.6094 0.6927 0.7760 0.8594 0.9427 H 0.0286 0.1120 0.1953 0.2786 0.3620 0.4453 0.5286 0.6120 0.6953 0.7786 0.8620 0.9453 H 0.0312 0.1146 0.1979 0.2812 0.3646 0.4479 0.5312 0.6146 0.6979 0.7812 0.8646 0.9479 H 0.0339 0.1172 0.2005 0.2839 0.3672 0.4505 0.5339 0.6172 0.7005 0.7839 0.8672 0.9505 A . 0365 0.1198 0.2031 0.2865 0.3698 0.4531 0.5365 0.6198 0.7031 0.7865 0.8698 0.9531 if 0.0391 0,. 1224 0.2057 0.2891 0.3724 0.4557 0.5391 0.6224 0.7057 0.7891 0.8724 0.9557 H 0.0417 0.1250 0.2083 0.2917 0.3750 0.4583 0.5417 0.6250 0.7083 0.7917 0.8750 0.9583 H 0.0443 0.1276 0.2109 0.2943 0.3776 0.4609 . 5443 0.6276 0.7109 0.7943 0.8776 0.9609 A 0.0469 0.1302 0.2135 0.2969 0.3802 0.4635 0.5469 0.6302 0.7135 0.7969 0.8802 0.9635 H 0.0495 0.1328 0.2161 0.2995 0.3828 0.4661 0.5495 0.6328 0.7161 0.7995 0.8828 0.9661 H 0.0521 0.1354 0.2188 0.3021 0.3854 0.4688 0.5521 0.6354 0.7188 0.8021 0.8854 0.9688 H 0.0547 0.1380 0.2214 0.3047 0.3880 0.4714 0.5547 0.6380 0.7214 0.8047 0.8880 0.9714 H 0.0573 0.1406 0.2240 0.3073 0.3906 0.4740 0.5573 0.6406 0.7240 . 8073 0.8906 0.9740 B 0.0599 . 1432 0.2266 0.3099 0.3932 0.4766 0.5599 0.6432 0.7266 0.8099 0.8932 0.9766 X 0.0625 0.1458 0.2292 0.3125 0.3958 0.4792 . 5625 0.6458 0.7292 0.8125 0.8958 0.9792 II 0.0651 0.1484 0.2318 0.3151 0.3984 0.4818 0.5651 0.6484 0.7318 0.8151 0.8984 0.9818 if . 0677 0.1510 0.2344 0.3177 0.4010 0.4844 0.5677 0.6510 0.7344 0.8177 0.9010 0.9844 & 0.0703 0.1536 0.2370 0.3203 0.4036 0.4870 0.5703 0.6536 0.7370 . 8203 0.9036 0.9870 W 0.0729 0.1562 0.2396 . 3229 0.4062 0.4896 0.5729 0.6562 0.7396 0.8229 0.9062 0.9896 ft 0.0755 0.1589 0.2422 0.3255 0.4089 0.4922 0.5755 0.6589 0.7422 0.8255 0.9089 0.9922 H 0.0781 0.1615 0.2448 0.3281 0.4115 0.4948 0.5781 0.6615 0.7448 0.8281 0.9115 0.9948 H . 0807 0.1641 0.2474 0.3307 0.4141 0.4974 0.5807 0.6641 0.7474 0.8307 0.9141 0.9974 i 1.0000 185 CORRUGATED BAR COMPANY, INC. AMERICAN SOCIETY FOR TESTING MATERIALS PHILADELPHIA, PA., U. S. A. AFFILIATED WITH THE INTERNATIONAL ASSOCIATION FOR TESTING MATERIALS STANDARD SPECIFICATIONS FOR PORTLAND CEMENT ADOPTED, 1904; REVISED, 1908, 1909, 1916, 1918 STANDARD. Portland cement is the product obtained by finely pulverizing clinker produced by calcining to incipient fusion, an intimate and properly proportioned mixture of argillaceous and calcareous materials, with no additions subsequent to calcination excepting water and calcined or uncalcined gypsum. I. CHEMICAL PROPERTIES Chemical Limits. The following limits shall not be exceeded: Loss on ignition, per cent 4 . 00 Insoluble residue, per cent . 85 Sulf uric anhydride (SO 3 ), per cent 2.00 Magnesia (MgO), per cent 5.00 II. PHYSICAL PROPERTIES Specific Gravity. The specific gravity of cement shall be not less than 3.10 (3.07 for white Portland cement). Should the test of cement as received fall below this requirement a second test may be made upon an ignited sample. The specific gravity test will not be made unless specifically ordered. Fineness. The residue on a standard No. 200 sieve shall not exceed 22 per cent by weight. Soundness. A pat of neat cement shall remain firm and hard, and show no signs of distortion, cracking, checking, or disintegration in the steam test for soundness. Time of Setting. The cement shall not develop initial set in less than 45 minutes when the Vicat needle is used, or 60 minutes when the Gillmore needle is used. Final set shall be attained within 10 hours. Tensile Strength. The average tensile strength in pounds per square inch of not less than three standard mortar briquettes composed of one part cement and three parts standard sand, by weight, shall be equal to or higher than the following: Age at Test Days Storage of Briquettes Tensile Strength Ib. per sq. in. 7 28 Iday 1 day in moist air, 6 days in water in moist air, 27 days in water 200 300 The average tensile strength of standard mortar at 28 days shall be higher than the strength at 7 days. III. PACKAGES, MARKING AND STORAGE Packages and Marking. The cement shall be delivered in suitable bags or barrels with the brand and name of the manufacturer plainly marked thereon, unless shipped in bulk. A bag shall contain 94 Ib. net. A barrel shall contain 376 Ib. net. 186 USEFUL DATA Storage. The cement shall be stored in such a manner as to permit easy access for proper inspection and identification of each shipment, and in a suitable weather- tight building which will protect the cement from dampness. IV. INSPECTION Inspection. Every facility shall be provided the purchaser for careful sampling and inspection at either the mill or at the site of the work, as may be specified by the purchaser. At least 10 days from the time of sampling shall be allowed for the com- pletion of the 7-day test, and at least 31 days shall be allowed for the completion of the 28-day test. The cement shall be tested in accordance with the methods herein- after prescribed. The 28-day test shall be waived only when specifically so ordered. V. REJECTION Rejection. The cement may be rejected if it fails to meet any of the requirements of these specifications. Cement shall not be rejected on account of failure to meet the fineness requirement if upon retest after drying at 100 degrees C. for one hour it meets this requirement. Cement failing to meet the test for soundness in steam may be accepted if it passes a retest using a new sample at any time within 28 days thereafter. Packages varying more than 5 per cent from the specified weight may be rejected; and if the average weight of packages in any shipment, as shown by weighing 50 packages taken at random, is less than that specified, the entire shipment may be rejected. 187 CORRUGATED BAR COMPANY, INC. MANUFACTURERS' STANDARD SPECIFICATIONS FOR DEFORMED CONCRETE REINFORCEMENT BARS ROLLED FROM BILLETS REVISED APRIL 21, 1914 Manufacture. Steel may be made by either the open-hearth or Bessemer process. Bars shall be rolled from standard new billets. Chemical and Physical Properties. The chemical and physical properties shall conform to the following limits: Properties Considered Structural Grade Intermediate Grade Hard Grade PHOSPHORUS, maximum, Bessemer . . 0.10 0.06 55-70,000 33,000 1,250,000 0.10 0.06 70-85,000 40,000 1,125,000 0.10 0.06 80,000 min. 50,000 1,000,000 Open-hearth Ultimate tensile strength, Ib. per sq. in. . Yield point, minimum, Ib. per sq. in. . . Elongation, per cent in 8-in., minimum COLD BEND WITHOUT FRACTURE: Bars under %-in. in diameter or thickness Bars %-in. in diameter or thickness and over Tens. Str. 180 d. = lt 180d. = 2/. Tens. Str. 180d = 3/. 90d. = 3*. Tens. Str. 180d=4*. 90d. = 4*. The intermediate and hard grades will be used only when specified. Chemical Determinations. In order to determine if the material conforms to the chemical limitations prescribed in the preceding tables, analysis shall be made by the manufacturer from a test ingot taken at the time of the pouring of each melt or blow of steel, and a correct copy of such analysis shall be furnished to the engineer or his inspector. Yield Point. For the purposes of these specifications, the yield point shall be determined by careful observation of the drop of the beam of the testing machine, or by other equally accurate method. Form of Specimens. Tensile and bending test specimens may be cut from the bars as rolled, but tensile and bending test specimens of deformed bars may be planed or turned for a length of at least nine inches if deemed necessary by the manufacturer in order to obtain uniform cross-section. Number of Tests, (a) At least one tensile and one bending test shall be made from each melt of open-hearth steel rolled, and from each blow or lot of ten tons of Bessemer steel rolled. In case bars differing ^g-inch and more in diameter or thick- ness are rolled from one melt or blow, a test shall be made from the thickest and thinnest material rolled. Should either of these test specimens develop flaws, or should the tensile test specimen break outside of the middle third of its gauged length, it may be discarded and another test specimen substituted therefor. In case a tensile test specimen does not meet the specifications, an additional test may be made. (6) The bending test may be made by pressure or by light blows. 188 USEFUL DATA Modifications in Elongation for Thin and Thick Material. For bars less than 3^-inch and more than %-inch nominal diameter or thickness, the following modifi- cations shall be made in the requirements for elongation: (a) For each increase of J's-mch in diameter or thickness above %-inch, a deduc- tion of 1 shall be made from the specified percentage of elongation. (6) For each decrease of j^-inch in diameter or thickness below y^-inch, a deduc- tion of 1 shall be made from the specified percentage of elongation. Finish. Material must be free from injurious seams, flaws or cracks, and have a workmanlike finish. Variation in Weight. Bars for reinforcement are subject to rejection if the actual weight of any lot varies more than 5 per cent over or under the theoretical weight of that lot. NOTE: The chemical and physical properties are given for three different grades of steel. In using the specification care should be taken to indicate clearly the grade desired. 189 CORRUGATED BAR COMPANY, INC. GENERAL SPECIFICATIONS FOR MATERIALS AND LABOR USED IN REINFORCED CONCRETE CONSTRUCTION MATERIALS Cement. The cement used for reinforced concrete construction shall be Portland cement which shall meet the requirements of the specifications and methods of tests last adopted by the American Society for Testing Materials. Aggregates, (a) Fine. Fine aggregates shall consist of uniformly graded sand or screenings by particles not exceeding J^-inch in diameter; not more than 30 per cent by weight shall pass a sieve having 50 meshes per linear inch. Particles shall be hard and clean; shall be free from coatings and soluble substances; shall contain no vegetable loam or other organic matter; and shall yield a 1 :3 mortar of a strength at the age of seven days of not less than 70 per cent of that of 1 :3 mortar of the same consistency and made with the same cement and standard Ottawa sand. (6) Coarse. Coarse aggregates shall consist of gravel or crushed stone which is retained on a screen having 3<-inch diameter holes and shall be graded from the smallest to the largest particles. The maximum size of particles shall be determined from the following table: Nature of work Maximum Sizes in Inches Light slabs or partitions using mesh or expanded metal . . 3/ Flat Slab Floors, Beams and Slabs, Girders, Columns, Re- taining Walls, Footings and other moderately heavy work % Heavy work 1% Size and quality of stone for rubble concrete shall meet the approval of the Engineer. All coarse aggregates shall be clean, hard, durable, free from coatings and all delete- rious matter. Water. The water used in mixing concrete shall be free from oil, acid, alkali or organic matter. Concrete shall not be mixed with sea water. Metal Reinforcement. Bars used as reinforcement in reinforced concrete work shall be manufactured from new billet-steel and shall satisfy the specifications known as the Manufacturers' Standard Specifications for Billet-Steel Concrete Reinforcement Bars. All bars other than spiral wire shall be an approved deformed bar having a positive mechanical bond with the concrete equal to that of the Corrugated Bar, manufactured by the Corrugated Bar Company, Inc., Buffalo, N. Y. FORMS Character. Forms for reinforced concrete construction shall be substantial and unyielding, and shall conform to the design of the structure. They shall have a smooth surface in contact with the concrete, which shall be free from adhering material or from other defects which shall mar the finished surface. They shall be sufficiently tight to prevent the leakage of mortar. The forms shall be so made that all interior angles caused by the junction of slabs and beams or other members shall be chamfered one inch. All exterior angles shall be made square. Oiling and Inspection. Before placing the concrete in the forms, all debris in the space to be occupied by the concrete shall be removed. Handholes shall be pro- vided at the base of the forms of all columns to render this space accessible for cleaning. 190 USEFUL DATA The forms shall be thoroughly oiled (thin mineral oil) before the concrete is placed; or the sin-face shall be thoroughly wetted (excepting in freezing weather). PLACING OF REINFORCEMENT All reinforcement shall be placed in accordance with the plans furnished by the Engineer. All loose rust or scale, all adhering material, and all oil or other substance which will tend to destroy bonding between the concrete and the reinforcement shall be removed before pouring begins. MIXING OF CONCRETE Mixing shall be done in a batch machine mixer of a type which will insure uniform distribution of the materials throughout the mass, and shall continue for the minimum time of one and one-half minutes after all ingredients are assembled in the mixer. For mixers of two or more cubic yards capacity the minimum time of mixing shall be two minutes. The drum of the machine shall be operated at a uniform speed of 200 feet per minute. Unit of Measure. Measurements of fine and coarse aggregates and of cement, shall be by loose volume. The unit of measure shall be a bag of cement containing 94 pounds net, which should be considered the equivalent of one cubic foot. Proportioning. The fine and coarse aggregates shall be so proportioned with the cement as to secure the ultimate compressive strength, in twenty-eight days, upon which the design of the structure was based. The following table is recommended as the maximum ultimate compressive strength of different mixtures of concrete at twenty-eight days: TABLE OF COMPRESSIVE STRENGTHS OF DIFFERENT MIXTURES OF CONCRETE (In Pounds per Square Inch) Aggregate 1:3* 1:4H* 1:6* 1:7H* 1:9* Granite, trap rock Gravel, hard limestone and hard sandstone . . . Soft limestone and sandstone 3300 3000 2200 2800 2500 1800 2200 2000 1500 1800 1600 1200 1400 1300 1000 Cinders 800 700 600 500 400 Consistency. The materials shall be mixed wet enough to produce a concrete of such consistency as will flow sluggishly into the forms and about the metal reinforce- ment, and which at the same time can be conveyed from the mixer to the forms with- out separation of the coarse aggregate from the mortar. A properly mixed concrete is one which thoroughly sustains or supports the coarser aggregate throughout the mass and which when dumped from a barrel or buggy neither breaks nor flows readily over the edge. Retempering. The remixing of mortar or concrete that has partly set shall not be permitted. *The proportions here given are on the basis of separately measured aggregates. For instance; a 1:6 mixture refers to a mixture based on one part of cement and six parts of aggregates which were measured before being combined. A standard 1 :2:4 mix, therefore, falls in the above class of 1:6 mix. 191 CORRUGATED BAR COMPANY, INC. Conveying and Placing. After the mixing of the concrete has been completed, it shall be conveyed as rapidly as possible to the place of deposit. No concrete shall be placed which has partly set. Where concrete is conveyed by spouting, the plant shall be of such size and design as to insure a practically continuous flow in the spout. The angle of the spout shall be. such as to allow the concrete to flow without a separa- tion of the ingredients. The spout shall be thoroughly cleaned by flushing before and after each run. Where it is impossible to deliver the concrete at the place of deposit without separation of the ingredients, the concrete shall be discharged upon a mixing board where it shall be mixed by turning until of uniform consistency before placing in the forms. The concrete shall be deposited in the forms in such a manner as will permit the most thorough compacting obtained by working with a straight shovel or slicing tool kept moving up and down until all the ingredients are in their proper place. Light horizontal reinforcement shall be raised from the bottom forms to allow the flow of the concrete under it. Where chairs are used, or where heavy reinforcement is definitely wired in place, the mass shall be thoroughly worked to insure contact of the mortar with the lower face of the reinforcing material. Before concrete is placed upon previously poured concrete, care shall be taken to remove all debris from the concrete surface. All laitance shall be removed and the surface shall be thoroughly wetted and slushed with mortar consisting of one part Portland cement and two parts fine aggregate. When it is necessary to stop pouring at a place where pouring will be resumed at a later date, all necessary grooves for joining future work shall be made before the con- crete has set. Construction Joints. Construction joints in columns shall be located at the base of the bell or flare occurring immediately below the floor slab in flat slab construction. In beam and girder construction the joint in the columns shall be located at the base of the lowest intersecting member at each floor. Vertical joints formed by bulkheads which it may be necessary to construct in slab or beams shall be made at the center of the span of such slab or beam. In girders into which intersecting members are framed at the center of the span, the bulkhead shall be located within the middle third of the length of the span of such girder. On large beams or girders these bulkheads shall be placed inclined upward toward the nearest column. Horizontal joints in large girders or other massive units shall be properly keyed by notching. Lintel beams, whether above or below the slab, shall be poured monolithically with the slab. No construction joints shall be allowed in footings, the pouring to be continued until the whole footing is completed to the base of the column. All other joints in pouring shall be made only upon the approval of the Engineer. Placing Concrete in Freezing Weather. No concrete shall be mixed or placed at a freezing temperature unless special precautions are taken to prevent the use of materials covered with ice crystals or containing frost, and to prevent the concrete from freezing before it has set and sufficiently hardened. The material used shall be warmed well above the freezing point and the space of 192 USEFUL DATA the structure in which pouring is taking place shall be maintained at a temperature well above the freezing point. Aggregates and water used shall not be heated to more than 70 degrees. The use of salt to lower the freezing point shall not be permitted. Placing Concrete Under Water. Concrete may be placed only in still water, with the use of a tremie properly designed and operated. Concrete shall be mixed with more water than is ordinarily permissible so that it will flow readily through the tremie. Coarse aggregate used in concrete thus placed shall not be more than one inch in diameter. In case the flow of concrete is interrupted, or in case it is necessary to provide a construction joint, care shall be taken to remove all laitance before proceeding with the work. Protection of Exposed Surfaces. The surfaces of concrete exposed to prema- ture drying shall be covered and kept wet for a period of at least seven days after pouring. REMOVAL OF FORMS Fornis shall not be removed from the concrete until it is sufficiently hard to permit of this being done with safety. In weather of a temperature above 60 degrees, the minimum time after pouring for the removal of forms shall be as follows: Wall forms and forms for the sides of beams 2 days Column forms and forms under slabs of span less than 4 feet . 4 days Slabs of span between supported girders or shoring between 4 and 10 feet 6 days Supports or shoring shall be maintained under horizontal members a minimum time after pouring in accordance with the following table: Beams, Girders and Flat Slabs in ordinary building construction . 3 weeks Spans over 30 feet At least 1 month Under all floors upon which building materials are being placed during construc- tion, the supports or posts shall be left at least two weeks longer than specified in the above schedules. In weather of a temperature below 60 degrees, the forms and supports shall be left in place a longer period, depending upon the weather encountered. Especial care shall be taken in the removal of forms from any concrete that may have become frozen. Where it is likely that the concrete might have frozen, it may be tested by placing a piece of the concrete in warm water or upon a stove, after which, if the concrete is properly set, it shall not show any deterioration due to such treatment. A similar test may be made directly upon the structure by submitting it to the flame of a blow torch, which treatment will not produce any melting, if the concrete is properly set. If the concrete has frozen, the forms shall not be removed from it until it has had sufficient time to thoroughly thaw and set in warm weather. 193 CORRUGATED BAR COMPANY, INC. RECOMMENDATIONS ON DESIGN AND WORKING STRESSES IN REINFORCED CON- CRETE CONSTRUCTION. (From the Final Report of the Joint Committee on Concrete and Reinforced Concrete, July 1, 1916) 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 pro- portioned 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 struc- tures, 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 con- traction. 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 advanta- geous 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 latter 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 mono- lithically with the beam, the span may be measured from the section where the com- bined 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. 194 USEFUL, DATA 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 degrees 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. 3. The modulus of elasticity of concrete in compression is constant within the usual limits of working stresses. The distribution of compressive stress in beams 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 compression 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 controlling factors in design. 195 CORRUGATED BAR COMPANY, INC. 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 pro- portion of the live and dead load equal to that given by the formula r = r 0.5, where o 1 = length and b breadth of slab. The 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 given design, the probable distribution should 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-pr- for both dead and live loads, where w represents the load per linear unit and I the span length. (6) For beams the bending moment at center and at support for interior spans wl 2 , w I 2 should be taken at -y^ and for end spans it should be taken at -y^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 restrained, the bending moment both at the central support and near the middle of wl 2 the span should be taken at (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 196 USEFUL DATA may be taken; for small beams running into heavy columns this should be increased, wt 2 but not to exceed ^ iZi 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 cantilever 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 founda- tions should be provided; for unequal settlements are liable to produce unsightly, if not dangerous 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 considerably 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 supplying the necessary strength. But it should be recognized that even with a de- formed 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. 197 CORRUGATED BAR COMPANY, INC. 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 reinforce- ment 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 even in this case at the beginning of loading the diagonal tension developed is taken principally by the concrete, the deformations which are developed in the concrete permitting but little stress to be taken by the web rein- forcement. 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 rein- forcement. 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, and 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 horizontal 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 reinforce- ment. 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. 198 USEFUL DATA 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 compression 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 of 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 extend- ing 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 condsidered 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, suffi- cient 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 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 durability 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. 199 CORRUGATED BAR COMPANY, INC. 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 nega- tive moment exists, as is the case near the supports in a continuous beam, web rein- forcement 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 strengthened against diagonal tension failure by so arranging and proportioning the horizontal reinforcement that the unit stresses at points of large shear shall be rela- tively low. It does not seem feasible to make a complete analysis of the action of web rein- forcement, 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 rein- forcement 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 com- paring 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 unsupported 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 enclos- ing the structrual shapes. Columns may be reinforced by longitudinal bars; by bands, hoops, or spirals, to- gether with longitudinal bars; or by structural forms which are sufficiently rigid to 200 USEFUL DATA 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 deformation 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 construction. Generally, for high percentages of steel, the concrete will develop relatively low unit stresses, and caution should be used in placing depend- ence 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 % inch in diameter 12 inches apart, nor more than 16 diameters of the longitudinal bar: the unit stress recommended 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 Section (c) 6, page 195. 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 sufficient 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 one 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 201 CORRUGATED BAR COMPANY, INC. 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 pro- vided to take this tension. Reinforcing for Shrinkage and Temperature Stresses. When areas of con- crete 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 cracks 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 dis- tance 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 resis- tance per unit of surface area. To be most effective, therefore, reinforcement (in amount generally not less than one-third of one per cent of the gross area) of a form which will 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 rein- forcing 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 connections. 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 construction which is now extensively used and which has recognized advan- tages 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 reinforcement. The conditions attending deposition and placing of concrete are favorable to 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. USEFUL DATA (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 1% 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 bot- tom 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 dimension 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 condi- tions 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 recommended, 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 corresponding side of the panel as measured 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 203 CORRUGATED BAR COMPANY, INC. 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. 0=Sum of live load and dead load in pounds per square foot. Then, for a slab without dropped panels, minimum t=Q.Q24L\/w+l% for a slab with dropped panels, minimum t=Q.Q2L\/ r w-}-l; for a dropped panel whose width is four-tenths of the panel length, minimum <=0.03 In no case should the slab thickness be made less than six inches, nor should the thickness of a floor slab be made less than one-thirty-second of the panel length, nor the thickness 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 rf Column-Head Section Mid-Section Column-Head Position of resultant of shear on quarter peripheries of two column capitals. Center of Gravity of load on half panel. tion Outer Section Inner Secti n !* \l--~ -* ....... \l Outer FIG. 10 FIG. 11 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 two column capitals (see Fig. 10), 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 (6) 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 ihe column), the stresses considered are the components which act parallel to the normal stresses on the straight portion of the section. An- alysis shows that, for a uniformly distributed load, and round columns, and square 204 USEFUL DATA 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; l\ =one side of the oblong panel measured from center to center of columns; /2 = 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. M y = numerical sum of positive moment and negative moment in the other direction. (See paper and closure, Statical Limitations upon the Steel Requirement in Rein- forced Concrete Flat Slab Floors, by John R. Nichols, Jun. Am. Soc. C. E., Transac- tions Am. Soc. C. E. Vol. LXXVII.) For oblong panels, the equations for the numerical sums of the positive moment and the negative moment at the two sections named become, Where Af x = is the numerical sum of the positive moment and the negative moment for the sections parallel to the dimensions lz, and M y is the numerical sum of the positive moment and the negative moment for the sections parallel to the dimensions l\. 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 distri- bution is not known definitely, it will be necessary to make an empirical apportion- ment 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 large breadth 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 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 co-efficients somewhat less than those given in a preceding paragraph as derived by analysis is warranted, the calculations of resisting moment and stresses in concrete 205 CORRUGATED BAR COMPANY, INC. and reinforcement being made according to the assumptions specified m this report and no change being made in the values of the working stresses ordinarily used. Ac- cordingly, 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. 11), will be called the inner section, and that portion in the two outer quarters of the width of the panel (GH and IJ, Fig. 11) 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. 11) will be called the mid-section, and the two remaining portions (ABC and DEF, Fig. 11), 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 posi- tive moment for a section in the middle of a panel extending across its width be taken as wl 1 1 TT- I Of this moment, at least 25 per cent should be provided for in the 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 jer 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. (g) Negative Moment. For a square interior panel, it is recommended that the negative moment for a section which 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 altogether forming the projected width of the panel) be taken as w>Z IZ 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 sec- tions 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 ^zwlz 1 l\ 77- 1 on a section parallel to the dimension 1 / 2c\ 2 / 2 , and wlAh =- 1 on a section parallel to dimension Z T ; and that the negative 1 / 2c\ 2 moment be taken as r-= wlz I h r- 1 on a section at the edge of the panel correspond- 206 USEFUL DATA ing to the dimension Z 2 , and rrzwli I k ^ 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. (i) Wall Panels. The co-efficient 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 co-efficient of positive moment at the section hah* way 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 concentrated load should be provided for in the design of the slab. The co-efficient of negative moments at the wall to take bending in the direction perpendicular to the wall line may be determined by the conditions of re- straint 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. (j) Reinforcement In the calculation of moments all the reinforcing bars which cross the section under consideration and which fulfill the requirements given under paragraph (/) of this chapter 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. 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 co-efficient of one-fourth should be used instead of one-fifth. (t) 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 207 CORRUGATED BAR COMPANY, INC. 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. (m) 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 determining 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= ' for slabs with dropped panels, where W is the sum of the dead and live load on a panel, b 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 assumption of a uniform distribution over the section of the slab around the peri- phery 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 slab. 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 co-efficients, apportionments, and thicknesses recom- mended are for slabs which have several rows of panels in each direction, and in which the size of the panels is approximately the same. For structures having a width of one, 208 USEFUL DATA 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 mo- ment to be taken by a column will depend upon the relative stiffness of columns and slab, and computations 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 proportioning 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 percentages 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 f made and stored under laboratory conditions. In the absence of definite knowledge in advance of construc- tion 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 accord- ance with the recommendations of this report. Although occasional tests may show higher results than those here given, the Com- mittee 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 1:3* 1:4H* 1:6* 1:7H* 1:9* Granite, trap rock 3300 2800 2200 1800 1400 Gravel, hard limestone and hard sandstone . . . 3000 2500 2000 1600 1300 Soft limestone and sandstone . . 2200 1800 1500 1200 1000 Cinders 800 700 600 500 400 NOTE. For variations in the moduli of elasticity see section on "Working Stresses." Bearing. When compression is applied to a surface of concrete of 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. t See Consistency, page 191 *See foot note, page 191. 209 CORRUGATED BAR COMPANY, INC. Axial Compression. For concentric compression on a plain concrete pier, the length of which 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 pre- ceding 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 22 (see page 8) are recom- mended : (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 hori- zontally not more than one-half the depth of the beam; or for beams in which longi- tudinal 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 rein- forcing 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 at- tached 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 longi- tudinal 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 Formula 24 or 25 (see page 9). The effect of longitudinal 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 198) 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 43^ per cent of the compressive strength of the concrete over the effective cross-section of the beam (Formula 22). The limit of tensile stress in the bent up portion of the bar calculated by Formula 25, 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 210 USEFUL, DATA 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 24 or 25 (see page 9). 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 compu- tations 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, and (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. 211 CORRUGATED BAR COMPANY, INC. SUBJECT INDEX PAGES AMERICAN Society for Testing Materials, cement specifications 186-187 AREAS Circles 182-183 Circular segments 174 Column sections 157-158 Corrugated Bars 164 Reinforcement for slabs 148 Triangles 175 Various sections 168-171 Wire .. ; ... 167 BARS Moments of inertia 160 Reinforcing 164^166 Specifications 188-189 BEAMS Continuous, moments and shears 38-48 Continuous, moment factors 196-197 Quantities of concrete 161 Rectangular, designing diagrams, explanation 10 Rectangular, diagrams for values of j, k and K 16 Rectangular, formulas 6 Rectangular, standard notation Rectangular, tables of safe loads 79-90 Rectangular, table of values of p, k, j and K Reinforced for compression, designing diagrams, explanation . . . 12-13 Reinforced for compression, diagram 20 Reinforced for compression, formulas 8 Reinforced for compression, standard notation 5 Span of 194-195 Stirrup reinforcement, table 107 Tee, continuous, explanation of tables 59-60 Tee, designing diagrams, explanation Tee, diagrams for values of K and j 17-18 Tee, diagrams for values of k and j Tee, dimensions 195 Tee, formulas Tee, standard notation 5 Tee, tables of safe loads 91-106 Wooden 173 BENDING and direct stress, combined 13-14 and direct stress, combined, diagrams 21-24 BOND Formulas Standard notation 6 Strength 197-198 BRACKETS 194-195 BUILDING code requirements for live loads 51-52 BUILDING materials weights of 56 CAPS for reinforced concrete piles 141-142 CEMENT specifications 186-187 CIRCLES Areas and circumferences 182-183 CIRCULAR segments Areas CIRCUMFERENCES of circles 182-183 COLUMN Heads, diagram for volume of concrete in Sections, areas, perimeters, etc 157-158 Spirals, pitch and percentage 150 Spirals, standard wire and spacers 156 Spirals, weight per foot 151-155 Verticals, moments of inertia 159-160 212 USEFUL DATA PAGES COLUMNS Bending moments 209 Designing diagrams, explanation 13-14 Formulas Joint Committee recommendations 200-202 Length 195 Spiral, tables of safe loads 122-132 Square tied, tables of safe loads 115-121 Standard notation 6 Tables, explanation Vertical steel for various percentages of core area 149 Wooden 173 COMPRESSIVE reinforcement of beams, diagram 20 CONCRETE General specifications 190-193 Massive , . 194 Quantities of materials 163 CONSTRUCTION General specifications 190-193 Recommendations on design and working stresses, Joint Committee 194-211 CoRR-Plate floors Explanation 108-109 Tables 110-113 CORRUGATED Bars 164 CUBES and cube roots of numbers 182-183 DECIMALS of a foot 185 of an inch 184 DEFLECTION General formulas 26-37 DESIGN Final report of Joint Committee 194-211 DESIGNING diagrams Explanation 10-14 DIAGRAM Compressive reinforcement of beams 20 Distribution of load for rectangular slabs 25 Values of K, j and k for rectangular beams and slabs 16 Values of k and j for tee beams 19 Values of K' for combined bending and direct stress 21 Values of k for combined bending and direct stress 22 Volume of concrete in column heads 162 DIAGRAMS Designing, explanation 10-14 Moment and shear coefficients for continuous beams, equal spans 45-48 Values of F for combined bending and direct stress 23-24 Values of K and j for tee beams 17-18 DIAGONAL tension and shear 198-200 DISTRIBUTION of load for rectangular slabs, diagram 25 EARTH pressures 144 F Diagram for values of, for combined bending and direct stress .... 23-24 FIREPROOFING Explanation of slab and beam tables 58 FLAT SLAB Explanation of 108-109 Column heads, diagram for volume of concrete in 162 Joint Committee recommendations 202-209 Floors, tables 110-113 FLOORS and roofs Explanation of tables 57-60 FOOTINGS Combined column, tables 136-139 Explanation of tables 133-135 For reinforced concrete piles 141-142 Square column, table 140 FORMULAS For columns For properties of sections 168-171 For reactions, bending moments, shears and deflections ... 26-37 For reinforced concrete design 5-9 For trigonometric solution of triangles 175 213 CORRUGATED BAR COMPANY, INC. PAGES FOUNDATIONS Bearing capacity of soils 147 FRACTIONS and equivalent decimals 184 FRICTION Coefficients and angles 147 FUNCTIONS Natural trigonometric 176-181 of numbers 182-183 GYRATION Radius of, various sections 168-171 INERTIA Moments of, bars 166 Moments of, column sections 157-158 Moments of, column verticals 159 Moments of, various sections 168-171 j Diagram for values in rectangular beams and slabs 16 j Diagram for values in tee beams 17-19 j Table of values for rectangular beams and slabs 15 JOINT Committee Final report on design and working stresses 194-211 K Diagram for values of, rectangular beams and slabs 16 Diagram for values of, tee beams. 17-18 Table of values, rectangular beams and slabs 15 k Diagram for values of, combined bending and direct stress 22 Diagram for values of, rectangular beams 16 Diagram for values of, tee beams 19 Table of values of, rectangular beams and slabs 15 K' Diagram for values of, combined bending and direct stress 21 LOAD Building code requirements 51-52 Distribution of, for rectangular slabs 25 LOADS Dead and live 194 Safe, for flat slab floors 110-113 Safe, for rectangular beams 79-90 Safe, for spiral columns 122-132 Safe, for square tied columns 115-121 Safe, superimposed for clay tile ribbed slabs 67-72 Safe, superimposed for ribbed slabs 73-78 Safe, superimposed for solid concrete slabs 61-66 Safe, for tee beams 91-106 In warehouses 49-50 For wooden beams and columns 173 LOGARITHMS of numbers 182-183 MANUFACTURERS' standard specifications for deformed bars 188-189 MATERIALS Building, weight of Quantities for concrete 163 Weights of 53-55 MODULUS Section, various sections 168-171 MOMENTS Bending, continuous beams 38-48 Bending, general formulas for 28-37 Of inertia, bars .160 Of inertia, column sections 157-158 Of inertia, column verticals 159 Of inertia, various sections 168-171 Theorem of three 38-44 p Table of values of, rectangular beams and slabs PERIMETERS Column sections 157-158 PILE caps 141-142 PILES Reinforced concrete 143 PRESSURES Earth and water 144 PROPERTIES of sections 168-171 RADIUS of gyration of various sections 168-171 REACTIONS General formulas for 28-37 RECIPROCALS of numbers 182-183 214 USEFUL DATA PAGES REINFORCEMENT Corrugated Bars 164-166 RETAINING walls Cantilever 145-146 RIBBED slabs Clay tile, safe load tables 67-72 Explanation of tables for 59 Steel or wood forms, safe load tables 73-78 ROOFS Floors and, explanation of tables 57-60 SECTION modulus Various sections 168-171 SECTIONS Properties of 168-171 SEGMENTS Area of circular 174 SHEAR for continuous beams 38-48 SHEAR Diagonal tension and 198-200 Explanation of slab and beam tables 58 Formulas for General formula for 28-37 Standard notation for 6 SHRINKAGE Reinforcing for 202 SLAB Area of reinforcement per foot width 148 Flat, Joint Committee recommendation 202-209 SLABS Clay tile ribbed, explanation of tables 59 Clay tile ribbed, tables of safe loads 67-72 Continuous, moment factors 196-197 Distribution of load for rectangular 25 Flat, explanation of 108-109 Flat, tables 110-113 Ribbed, explanation of tables 59 Ribbed, table of safe loads 73-78 Solid concrete, explanation of tables 58-59 Solid concrete, tables of safe loads 61-66 Supported on four sides SOIL values Combined column footings 136-139 Square column footings SOILS Bearing capacity of SPACERS Column spiral, tee section SPACING of slab bars for steel areas per foot width 148 SPAN of beams 194-195 SPECIFICATIONS for deformed bars 188-189 for Portland cement 186-187 general, for reinforced concrete 190-193 SPIRALS Column, pitch and percentage Column, standard wire and spacers Column, weight per foot height 151-155 SQUARES and square roots of numbers 182-183 STIRRUP reinforcement for uniformly loaded beams 107 STRESS Combined bending and direct Combined bending and direct, diagrams 21-24 STRESSES Joint Committee recommendations 194-211 Temperature and shrinkage 202 Timber 172 Working, Joint Committee 209-211 TABLES American Steel and Wire Company's gauges Area of reinforcement per foot width of slab Areas of circular segments Bearing capacity of soils Caps for reinforced concrete piles 141-142 Cantilever retaining walls 145-146 Column spiral weights 151-155 Column vertical steel 149 215 CORRUGATED BAR COMPANY, INC. TABLES Combined column footings 136-139 Corrugated Bars 164 Decimals of a foot 185 Decimals of an inch 184 Earth and water pressures 144 Flat slab floors 110-113 Functions of numbers 182-183 Moments of inertia of bars 160 Moments of inertia of column verticals 159 Natural trigonometric functions 176-181 Properties of column sections 157-158 Properties of sections 168-171 Quantities of materials for concrete 163 Reinforced concrete piles 143 Safe loads, clay tile ribbed slabs 67-72 Safe loads, rectangular beams 79-90 Safe loads, ribbed slabs, steel or wood forms 73-78 Safe loads, solid concrete slabs 61-66 Safe loads, tee beams 91-106 Spiral columns, safe loads 122-132 Spiral wire and spacers 156 Spirals, pitch and percentage 150 Square column footings 140 Square tied columns, safe loads 115-121 Stirrup reinforcement for uniformly loaded beams 107 Timber 172-173 Trigonometric solution of triangles 175 Values of p, k, j and K 15 Volume of concrete in beams 161 TEMPERATURE Reinforcing for 202 THEOREM of three moments 38-44 TIMBER Tables 172-173 TRIANGLES Trigonometric solution of 175 TRIGONOMETRIC Natural, functions 176-181 Solution of triangles VOLUMES Column sections 157-158 Of concrete in beams 161 Of concrete in column heads 162 WALLS Cantilever retaining 145-146 WAREHOUSES Table of weight of contents 49-50 WATER pressure 144 WEB reinforcement Formulas for 8-9 Standard notation for For uniformly loaded beams 107 WEIGHTS of building materials 56 Column sections 157-158 Column spirals 151-155 Corrugated Bars 164 Of materials 53-55 Of timber 172 WIRE American Steel and Wire Company's gauges 167 Column spiral WOODEN beams and columns , 173 216 RICE LEADERS OF THE WORLD ASSOCIATION ANNOUNCES THE ELECTION To MEMBERSHIP OF THE CORRUGATED BAR COMPANY, INC. 8Y INVITATION MEMBER OF NEW YORK. U.S. A. THIS Association is a cooperative organization composed solely of concerns which adhere to the highest standards in the conduct of their business. These are the QUALIFICATIONS FOR MEMBERSHIP HONOR: A recognized reputation for fair and honorable business dealings. QUALITY: An honest product, of quality truthfully repre- sented. STRENGTH : A responsible and substantial financial standing. SERVICE: A recognized reputation for conducting business in prompt and efficient manner. Membership in the Association is an evidence of the distinctive position which the Corrugated Bar Company, Inc. holds as a Specialist in Concrete Reinforcement and Design. It testifies as to the quality of this company's products and ser- vice, and the character of the directing officials. It is a further assurance that these products are made by a con- cern worthy of utmost confidence, as only manufacturers of the highest standing in name, product and policy are privileged to display the Association Emblem. CORRUGATED BARS THE question of using plain or deformed bars for reinforced concrete construction has been answered in the United States where the volume of such construction is probably greater than in all the rest of the world. Fifteen years ago about 80% of the reinforcement used was plain bars, to-day 80% is deformed bars. Nearly all building codes, architects' and engineers' specifications and committee recommendations of technical societies allow larger working values for the bond stress of deformed than for plain bars. A review of available test data on bond shows clearly that American practice is on a very sound basis. Diagram 1 is the average resulting from the tabulation and analysis of the thousands of bond tests made by recognized authorities in the United States and Europe on both plain CORRUGATED ROUNDS and Corrugated Bars. The variation in the case of plain bars, from a very low value for a minimum to a maximum value which approximates only the average of Corrugated Bars, is due entirely to the fact that the bond of a plain bar is a function of accidental surface condition. A smooth bar has a very low bond value; a rusty, pitted, rough bar may have a high value. An important difference in behavior between plain and Corrugated Bars is shown in Diagram 2. This diagram is a composite of load slip curves taken from University of Illinois tests where conditions were practically identical, and illustrates clearly that plain bars reach a maximum bond value at about 0.01 inch slip and then decrease while Corrugated Bars have much higher bond at the same slip and increase in resistance until a final value several times that of plain bars is reached. It is not good engineering practice to leave the bond the most important function of the reinforcement to chance, while all the other physical properties of the material are required to conform to rigid specifi- cations within narrow limits. To realize the highest efficiency of bond value, a deformed bar of proper CORRUGATED SQUARES design is required; merely roughening the surface of a bar by haphazard projections may actually decrease its bond value. The twisted bar, for example, for years considered a standard deformed bar, has been found on careful examination to have lower bond resistance than a plain bar. The conditions governing the design of a satisfactory deformed bar are clearly stated in Bulletin No. 71, University of Illinois, Engineering Experiment Station, as follows: "In a deformed bar of good design the projections should present bearing faces as nearly as possible at right angles to the axis of the bar. The areas of the projections should be such as to preserve the proper ratio between the bearing stress against the concrete ahead of the projections and the shearing stress over the surrounding en- velope." Of all the deformed bars on the market the Corrugated Bar is the only one that substantially fulfills these requirements. 1100 1000 100 1100 1000 Summary-for Beam Tests Summary for Pull Out Tests Note:-; Tests included cover plain, bars-from " to IY H diam. and Corrugated Bars from. V* n to \ Yx diam. All embedments 8? Age 60 to 70 days Mixrl:-2:4. Key to Diagram Minimum Value Average Value Maximum. Value 100 DIAGRAM 1 01 ..02 .03 .04 .05 Slip m.inches DIAGRAM 2 CORR-MESH CORR-MESH is a ribbed expanded metal a one-piece product, made from a high-grade of rolled sheet steel. The ribs provide strength and stiffness to the sheets which give firm support to concrete and plaster both during construction and after. The metal between the ribs is expanded into a diamond mesh. !*3>Vcenter to center of ribs-*i 13" center to center of outside ribs- %* RIB CORR-MESH For walls and partitions, %" Rib Corr-Mesh is plastered both sides with cement mortar, forming a monolithic wall of great strength. The ribs do away with extra studding a saving in material and labor cost. For walls and floors, J4" Rib Corr-Mesh acts as form work. It supports the wet concrete; no deck centering is required. APPLICATION OF %" RIB CORR-MESH FOUNDRIES AND LIGHT MANUFACTURING PLANTS: Replaces cor- rugated iron and wood siding. Corr-Mesh is the ideal method of con- struction for roofs, floors, partitions and exterior walls. RAILROADS: Handsome, permanent, fireproof stations, sheds and wayside buildings in stucco at low cost. AMUSEMENT PARK BUILDINGS : Corr-Mesh makes possible the only low cost construction on which insurance can be obtained. CORR-MESH CENTER TO CENTER OF RIBS 18 CENTER TO CENTER OF OUTSIDE RIBS %6" RIB CORR-MESH For ceilings, 5 /ie" Rib Corr-Mesh is used extensively, where it greatly reduces the material required in the supporting framework, and cuts down the cost of erection. For stucco construction it eliminates furring strips and makes a strong and permanent reinforcement for the plaster covering. APPLICATION OF 5 /io" RIB CORR-MESH RESIDENCES: Stucco walls are handsome, permanent and fire- resisting. Old wooden houses may be transformed at small cost into attractive residences of greatly increased value. GARAGES, STABLES AND OUTBUILDINGS of stucco construction with 6 /io" Rib Corr-Mesh are low in cost, permanent, and free from repair expense. FENCES which present an artistic and substantial appearance are constructed with Corr-Mesh. CORRUGATED BAR COMPANY, INC. BUFFALO, N. Y. FABRICATED REINFORCEMENT READY TO PLACE IN THE FORMS READY TO PLACE CORK-BAR UNITS SHOP fabricated reinforcement marks a turning point in reinforced concrete construction. It is only a question of time when the practice of organizing a fab- rication crew, for each job, with local inexperienced common labor, must give way to well-established shop practice, in which hand labor is replaced by machine production. Shop fabrication secures accuracy, thereby eliminat- ing one important factor of uncertainty in construc- tion. It secures economy and facilitates supervision and inspection. It saves storage and working space at the building site, often a matter of great importance, and by decreasing the amount of labor in the field removes some of the uncertainty and annoyance connected with the handling of labor. Reinforcement should not only be fabricated in the shop, but assembled into units, as far as practicable, properly marked and made ready to place directly in the forms. For beam reinforcement the Corr-Bar Unit is an ideal example of shop fabricated reinforcement. Instead of depending upon the skill of the individual workman to fabricate and assemble twenty to thirty pieces and place them properly in the forms, one unit is made in the shop by machine operators under the direction of an organi- zation especially trained to do this work. The unit is inspected and marked and so equipped with supporting devices as to insure its proper place in the structure. CIVI ENGINEERING SERVICE DEPARTMENT THE Corrugated Bar Company, Inc., since its inception, more than twenty-five years ago, has been primarily an engineering organiza- tion. It has been a pioneer in the field of reinforced concrete not only in the development of scientifically correct reinforcing materials and systems of construction, but through investigation and presenta- tion of rational methods of design. Under the direction of its engineers elaborate and painstaking research and test programs have been carried out, earning for the company an enviable reputation and standing in professional circles. The engineering department has developed under highly competi- tive conditions, making it of necessity efficient and economical in the execution of its designs and it is safe to say that for variety and wealth of experience it is unsurpassed by any organization of its kind. As a result of its experience it has been called upon frequently to act in a consulting capacity on numerous reinforced concrete structures in the United States and many foreign countries. The constantly increasing demand for this class of service resulted in the organization of an Engineering Service Department. The service rendered by this department divorced entirely from the company's products is available to architects and engineers on a fee basis and consists of: 1. A study of conditions and selection of a type of construction best suited to the purpose of the building. 2. Preliminary and comparative sketches, estimates and cost data as a basis of negotiation between the architect or engineer and his client. 3. Preparation of detail plans and specifications including placing diagrams, fab- rication details and bar lists. By the use of this Service the owner obtains a low bid on the con- struction best suited to his building and it guarantees full patent pro- tection on any materials or construction involved in the plans supplied. CORRUGATED BAR COMPANY, INC. MUTUAL LIFE BUILDING BUFFALO, N. Y. DISTRICT OFFICES NEW YORK, N. Y. Whitehall Building, 17 Battery Place CHICAGO, ILL. Great Northern Building, 20 W. Jackson Street PHILADELPHIA, PA. Transportation Building, 26 S. Fifteenth Street BOSTON, MASS. 27 School Street ST. Louis, Mo. Boatmen's Bank Building DETROIT, MICH. Penobscot Building MILWAUKEE, Wis. Wells Building KANSAS CITY, Mo. Waldheim Building ST. PAUL, MINN. Pioneer Building ATLANTA, GA. Grant Building SYRACUSE, N. Y. Union Building HOUSTON, TEXAS 700 N. San Jacinto Street MUTTHEWS-NORTHRL'P CALIFORNIA PARTMENT OF CIVIL ENQ!NSi . CALR OK UNIVERSITY OF CALIFORNIA OF CIVIL ENGINES, Zi -^>iiA UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. f954^) LD 21-100m-9 1 '48(B399sl6)476 YB 24131 785274 Cb Eng* Library UNIVERSITY OF CALIFORNIA LIBRARY