SLABS, CROSS-BEAMS, AND GIRDERS 153 



between t and d. (See Art. 59 for suitable proportions.) The 



value of -= is then known and k and / can be determined from 

 d 



Eqs. (1), (4), and (5). The area of steel and the breadth of 

 flange are then found from Eq. (7) . 



(Note. When making approximate computations for shear 

 or bond stress along the horizontal tension rods, an average value 

 of / = 7/8 may be assumed, as for rectangular beams.) 



Illustrative Problem. A T-beam in a floor system is subjected to a 

 maximum shear of 19,000 Ib. and a maximum moment of 722,000 in.-lb. 

 Determine the economical depth of beam. Use working stresses recom- 

 mended by Joint Committee. Assume the ratio of unit cost of steel to 

 cost of concrete = 70. Thickness of floor slab is 3 3/4 in. 



Cross-section of web as determined by shear b'd= ' = 181 sq. in. 



% luo 



From formula of Art. 60, for 



6' = Sin. d = 21. 7 in. . 

 b'= 9 in. d = 20. 6 in. 

 b' = 10 in. d = 19.7in. 



If the object is to obtain suitable proportions, either of the last two 

 breadths with corresponding depths may be selected but, for convenience 

 in placing steel, the breadth of 10 in. and depth of 19.7 in. will most likely 

 give the best design. 



Illustrative Problem. Design a T-beam with span of 40 ft. Assume 

 dead load = 1400 Ib. per foot. Live load = 3000 Ib. per foot. The 

 beam is to be simp'y supported at the ends and the flange is to be pro- 

 portioned as well as the web; that is, the flange does not form a part of 

 a floor system already determined. Use working stresses recommended 

 by the Joint Committee. 



This problem comes under Case (3) in the design of T-beams and the 

 method previously suggested will be followed. 



The total bending moment, 



M _ (4400) (40).(12) = 10 , 56 o,000in.-lb. 



The maximum shear 



V = (4400) (20)= 88,000 Ib. 

 The required net web area 



,,, 88,000 

 = b'd = ' = 838 sq. in. 



This area can be supplied by a web 



6' = 16 in. d = 53in. 

 6' = 17 in. d = 50in. 

 V = 18 in. rf = 47in. 

 fe' = 19in. d = 44in. 

 6' =20 in. d = 42in. 



