150 REINFORCED CONCRETE CONSTRUCTION 



Supposing this beam to fall under Case I, we find 



k = \/2(0.0030)(15) + (0.0030) 2 (1 5) 2 - (0.0030) (15) = 0.258 

 / = 0.914 



Hence, fcd = (0.258) (16.0) =4.1 in., and the neutral axis is in the flange; 

 that is, the case was correctly guessed. 

 The corrected value of a s , is 



M 356,300 



= 1.53 sq. in. 



(16,000)(0.914)(16.0) 

 1 .53 



Hence, &=\/2(0.0027)(15) + (0.0027) 2 (15) 2 - (0.0027)(15) =0.247 



The stress in the concrete is then found to be 

 . 2f 8 p (2)(16,000)(0.0027) 



fc= k 0.247 ~ = 35 lb ' per Square mch 



which is satisfactory. Four 3/4-in. round rods will give the required steel 

 area. 



It is quite evident in the above problem that the compressive stress in 

 the concrete could not be a determining factor in the design, but the com- 

 putations are all given to show the student the method to be followed in 

 the design of T-beams of larger size. 



Illustrative Problem. The flange of a T-beam is 24 in. wide and 4 in. 

 thick. The beam is to sustain a bending moment of 480,000 in.-lb. What 

 depth of beam and amount of steel is necessary? 



Try d = 18 in. Approximately, yd = 16 in. Then formula (8) or formuja 

 (b), Art. 59, gives: 



M 480,000 



1 88 



Then equation (6) gives / = 0.910 and the corrected value of a, is 

 ____480,000_ 

 (16,OOOK0.9lb)(18)~ 

 Then equation (2) gives 



fa* = 5.61 in., or & = 0.312 



and shows that the beam falls under Case II, as assumed. 

 The stress in the concrete is found from equation (8) to be 



(16,000)(0.312) 

 ' c /T*\7irroio\ *85 lb. per square inch, which is permissible. 







PROBLEMS 



46. A floor slab is simply supported and reinforced in only one direction. 

 The span in the direction of the reinforcement is 8 ft., d = 4 in., and 

 1/2-in. round bars are used, placed 7 in. center to center. Determine 

 the safe load per square foot including the weight of slab. 



47. What thickness of slab and what sizes and spacing of bars will give a 

 resistance of 4900 ft.-lb. per foot of width? 



