Shear Stresses in R.C.C. beam (Reinforced cement concrete beam), Stress Based Approach (Elastic Theory), IS Code Approach
SHEAR STRESSES IN R.C.C. BEAMS
Stress Based Approach (Elastic Theory)
R.C.C. is a composite materials so the exact shear distribution as per elastic theory is very complex. It is shown in Fig. 5.2(b)
by the hatched portion of the curve.It is parabolic in the compression zone with zero at the top and maximum at the neutral axis. The value of shear-stress is constant in the tensile zone and is equal to the maximum shear-stress (q) because the concrete, below the neutral axis (tensile zone) is assumed to be cracked and neglected. The maximum value of shear stress (q) as per elastic theory is given by
\[q=\frac{V}{bjd}\]
where V = shear force at the section
b and d = dimensions of the section
j = Lever arm depth factor
IS Code Approach
As per IS code 456:2000 the stress based approach does not represent the true behaviour of the R.C.C. beam in shear. Hence, the equation for shear stress i.e.,\[ q=\frac{V}{bjd}\] has been simplified. IS code recommends the use of nominal shear stress\[ (\tau _{y})\] for R.C.C. beams. The nominal shear stress\[ (\tau_{v})\] or average shear stress distribution is shown in Fig. 5.2(b) and is given by
\[\tau_{v}=\frac{V}{bd}\]