Question

Consider a square-shaped area ABCD on the ground with this centre at M as shown in the figure. Four concentrated vertical loads of P = 5000 kN are applied on this area, one at each corner.


The vertical stress increment (in kPa up to one decimal place) due to these loads according to the Boussinesq's equation at a point 5m right below M is

• A. 190.84

Answer 1

The correct option is A 190.84
Due to one corner load

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

$r=\sqrt{2^2+2^2}=2\sqrt{2}m$

z = 5 m

P = 5000 kN

${\sigma }_z=\frac{3\times 5000}{2\pi \times 5^2}{\left[\frac{1}{1+{\left(\frac{2\sqrt{2}}{5}\right)}^2}\right]}^{5/2}$

$=47.709kN/m^2$

So due to four load vertical stress

$=4{\sigma }_z$

$=4\times 47.709$

$=190.84kN/m^2$