164 REINFORCED CONCRETE CONSTRUCTION 



of the diameters by their distances from the neutral axis. Since 

 the compressive steel will generally be nearer the neutral axis 

 than the tensile steel, it follows that, if the compression bars are 

 no larger in diameter than the tension bars, the bond stress per 

 square inch will always be less than that of the tension bars and 

 the above formula need not be used. 



The formula derived above may be used in any special case in 

 designing, but generally it will be sufficient to consider simply 

 the compressive stress in the steel and provide a sufficient length 

 from this point to the end of the bar to transmit this stress. The 

 working strength of the steel in compression cannot be reached 

 without exceeding the compressive strength of the concrete in 

 which it is embedded. Consequently, in common design it will 

 be satisfactory to provide a lap beyond the center of support 

 sufficient to take care of compressive stress in the steel equal to 

 the maximum as determined by the concrete. 



Illustrative Problem. A continuous T-beam, uniformly loaded, has a 

 bending moment at the center of each span of 358,000 in.-lb. Negative 

 bending moment at the supports and the positive bending moment at the 



wl 2 

 center of span are figured by the formula 10 . The tensile steel at the 



\.i 



center of span consists of four 3/4-in. round rods, b' = 9 in. d = 15.5 in. 

 Design the supports using working stresses recommended by the Joint 

 Committee. 



At the supports the flange of the T-beam, being in tension, is negligible 

 and the T-beam changes into a rectangular beam with steel in top and 

 bottom. Two of the tensile rods on each side of the supports will be bent 

 up and made to lap over the top of the supports, while the other two rods 

 on each side will be continued straight and lapped over supports at the 

 bottom of beam. It will be assumed that the steel at the center of span 

 has already been chosen so that this may be done. 



The ratios of steel in tension and compression are the same, and are 

 respectively: 



(4) (0.4418) 

 P=P "-" 



With these values of p and p', and n = 15, also assuming , =0.1 (this value 



is assumed simply to make it easier for the student to check up the com- 

 putations in practice, the correct ratio should be taken) we obtain the 

 following from equations (3), (5), (7), and (9), of Art. 62: L = 0.291, 

 K = 0.01 15, and L' = 0.0266 



Maximum pressure in concrete is 



57 lb ' per square inch> by formula (4) 



