REENFORCED CONCRETE 

 whence, by solving for the unit stresses p c and p t 



161 



or, solving one of these two relations for A, say the first, we have 



(SJf/. /-x 

 =-J - (1+ Vn). 



For ordinary concrete % may be taken as 25. Also, using a factor 

 of safety of 8, the working stress p c becomes p c = 300 lb./in. 2 Substi- 

 tuting these numerical values in the above, the formula for the depth 

 of the beam in terms of the external moment takes the simple form 



FIG. 109 



h = 



4 



h being expressed in inches, and M in 

 inch-pounds per inch of width of beam. 

 For a reenforced concrete beam the 

 tensile strength of the concrete may be 

 neglected. Let E c and E 8 denote the moduli of elasticity for con- 



7? 



crete and steel respectively, and let -~ = n. Then, if x denotes the 



distance of the neutral axis from the top fiber (Fig. 109), the 

 assumptions in this case are expressed by the relations 



*- = E , and = E t , 



s s h x 

 whence 



or, solving for x, 



Now if A denotes the area of steel reenforcement per unit width of 

 beam, then 



and consequently, since R c = R s , 



. Ps E c Ps h ~ X 



