The Joint Committee has recommended the following rules for determining flange width: In beam and slab construction an effective bond should he 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.
(b) 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-Bcams, due consideration should be given the compressive 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.
112. Shear and Bond Stresses.—Stresses clue to shear in the concrete and bond stresses between the steel and concrete in T-beams are found by the same methods that are used for rectangular beams. The shearing and diagonal tension stresses must be carried by the web of the beam, the area of flange not being considered in finding unit shear. Using the same notation as for rectangular beams and letting b' represent the width of the web of the T-beam, the formulas as applied to T-beams become: The Width of the Web (b') must be sufficient to provide proper area for carrying shear, as shown in (33), and also to allow for properly spacing the steel, as explained in Section 109. b' should not usually be taken at less than d/3, except in heavy beams where a thickness of d '4 Imy be allowable. The value of j, when not known, may be assumed as without material error, and the value of vj in (33) may be taken as of the allowable unit shear.
d he constant for any particular we place Q = ply , Q 3'rticular P` values of unit stresses and t d. Substituting in Formula (30) we obtain if = Qbtd and 31 bt = Qd or In Diagram I, values of fc and p are given in terms of various values of d j t and Q for n=15 and fs = 16,000. This diagram may he used in design of beams when these units are to be employed, or similar diagrams may easily be prepared for other values of and n.
Diagram II gives values of p and j in terms of fs, and d, 1, when n =15. This diagram may be used in reviewing a beam of known dimensions and reinforcement, or in design when values of other than that used in Diagram I are to be employed.
Examples.—The following examples illustrate the use of these diagrams and formulas in computation.
11. A T-beam has dimensions as follows: b=45 inches, inches, d=20 inches, inches. It is reinforced with ten ;-inch round steel bars. If the safe unit stresses of steel and concrete are 16,000 and 650 lb. in." respectively, what is the safe resisting moment for the beam? Solution.—Table X, A =.1118X 10=4.418 in.'-, and p= 4.415 4a X20 = .0049. From Diagram II, for p= .0049 and d 1=5, we find = 29, and j= .914. If = 650, 650 X 29 =18850. This is =138 For b'=8, d=18 or for d= 20 inches. Either of these values would give proper form to the web. The deeper beam will require less steel and may be used provided it gives suf ficient width for placing the steel, and if the stress upon the concrete is satisfactory. Assume d=20 inches. Then d/t=4 and (31) 930000 X 5 X 20 _ 310. For these values Diagram I gives f=40 and p = .0054. A = pbd = .0054X 20X 30 =3.24 and (20) in.
From Table X, for six -inch square bars, A =3.37 o = 18.0 in.
four 16-inch square bars, A=3.52 o=15.0 in. four 1-inch round bars, A =3.14 °o=12.56 in.
The four 16-inch bars could be placed in the 7-inch width of web in two rows (see Section 109). The six i-inch bars need a width of at least 7 inches and could be used in two rows by increasing the width of web by ; inch.
If d be made 21 inches, the steel needed would be A =3.09 and the four 1-inch round bars could be used in two rows in the 7-inch width. At ordinary prices, the saving in steel would more than pay for the increased amount of concrete, and this would make the cheapest beam.