SLABS, CROSS-BEAMS, AND GIRDERS 151 



48. (a) Design a center span slab to carry a live load of 250 Ib. per square 

 foot. Slab is to span 8 ft. and is to be fully continuous, with the one- 

 way type of reinforcement, (b) Design section of continuous cross- 

 beams with span of 12 ft. Take b f = 8 in. 



49. In a square panel, 14 ft. X 14 ft., of the two-way type of reinforcement, 

 what thickness of slab and what size and spacing of tension rods will 

 be required to carry a live load of 400 Ib. per square foot; slab is to be 

 in a center span and fully continuous? 



50. A center span floor panel is to be 12 ft. X 14.4 ft., and the slab is to 

 be fully continuous and reinforced in both directions. Design such 

 a slab to carry a live load of 400 Ib. per square foot. 



51. Design the center cross-section of the 12-ft. supporting beams for the 

 floor slab in the preceding problem. The beam receives its load from 

 two floor panels. Consider the depth of beam (d) fixed at 18 in. 

 (total depth 20 in.) and use four plain round rods. 



52. The flange of a T-beam is 20 in. wide, and 5 in. thick. The beam is 

 to sustain a bending moment of 550,000 in.-lb. What amount of steel 

 is necessary? Take d=2Q in. 



60. Economical Proportions of T-Beams. When a floor-slab 

 forms the flange of a T-beam, it is possible to determine eco- 

 nomical proportions for the stem. 



Consider a portion of a rectangular beam one unit in length. 

 Let c = cost of concrete per unit volume; r = ratio of cost of 

 steel to cost of concrete per unit volume; C = cost of beam per 

 unit length; d' = depth of beam below slab. Then 



/.w+i/a&j 



using the approximate formula (b) of the preceding article. 

 When d' is fixed by the head room available, the cost will be a 

 minimum when b f is made as small as possible, and its value will 

 then be determined by the shearing stress or by the space 

 required for the rods. The expression also shows that the cost 

 will decrease with increased values of / and that with a fixed 

 value of b'd' the cost decreases with increase in depth. If the 

 value of b' is assumed as fixed, then there is a definite value of d 

 which will give minimum cost. By calculus the following 

 expression has been deduced from the preceding equation and 

 will give the value of d for minimum cost when the value of b' is 

 fixed: 



11 



