Chapter 3, Problem 47P

In Prob. 3–46, h → 0 as x → 0, which cannot occur. If the maximum shear stress τ_max due to direct shear is to be constant in this region, show that the depth h at location x is given by

$h=\frac{3}{2}\frac{Fc}{lb{\tau }_{\max }}0\le x\le \frac{3}{8}\frac{Fc{\sigma }_{\max }}{lb{\tau }_{\max }^2}$