Question

The vertical stress at depth, z directly below the point load P is (k is a constant)

• A. $k\frac{P}{z}$
• B. $k\frac{P}{z^3}$
• C. $k\frac{P}{z^2}$
• D. $k\frac{P}{\sqrt{z}}$

Answer 1

The correct option is C $k\frac{P}{z^2}$

As per Boussinesq Equation

${\sigma }_z=\frac{3}{2\pi }.\frac{P}{z^2}{\left[\frac{1}{1+{\left(\frac{r}{z}\right)}^2}\right]}^{5/2}$

$=K.\frac{P}{z^2}$

where, K = Boussinesq's influence factor

${\sigma }_z=\frac{3}{2\pi }{\left[\frac{1}{1+{\left(\frac{r}{z}\right)}^2}\right]}^{5/2}$