64 REINFORCED CONCRETE CONSTRUCTION 



T' T, and, if b i? used to denote the breadth of beam, the stress 

 per unit area 



_T'-T (1) 



bx 



The forces acting on this portion of the beam must be in equilib- 

 rium, hence the couples must balance. Thus, 

 Vx = (T'-T)id 





(2) 



Substituting in equation (1), we have 



,'-*- 



~bjd 



The value of / for working loads varies within narrow limits 

 and v will change but slightly if the different values of / are 



FIG. 31. 



inserted in equation (2). The average value of / for beams in 

 ordinary construction is 7/8. Using this value, equation (2) 

 reduces to 



v = S - (3) 



It is clear that the shearing stress is the same at all points 

 between the neutral axis and the steel; above the neutral axis 

 the shear follows the parabolic law as in the plain concrete beam. 

 Fig. 31 represents the distribution of shearing stress (both 

 horizontally and vertically) on a vertical cross-section where 

 the bending moment is not a maximum. 



It is quite as satisfactory for purposes of comparison to use the 

 average value of the shearing stress, or 



_1 (4) 



bd 



