Question

Two columns A and B are standing 5 m apart. The loads transferred from them taken as point loads of magnitude 50 t and 30 t respectively. The resultant vertical stress due to two loads on a horizontal plane 3 m below ground surface under column 'B' is in $t/m^2$.

• A. 1.69
• B. 2.85
• C. 0.95
• D. 7.45
  

Answer 1

The correct option is A 1.69


$\therefore {\sigma }_z={\sigma }_A+{\sigma }_B$

$\therefore \text{Due to load 'A':}{r}_A=5m$

${\sigma }_A=\frac{3}{\pi }\times \frac{Q_A}{Z^2}\times {\left[\frac{1}{1+{\left(\frac{r}{Z}\right)}^2}\right]}^{\frac{5}{2}}$
$=\frac{3}{2\pi }\times \frac{5}{3^2}\times {\left[\frac{1}{1+{\left(\frac{5}{3}\right)}^2}\right]}^{\frac{5}{2}}=0.096t/m^2$

Due to load 'B': $r_B=0$

$\therefore {\sigma }_B=\frac{3}{2\pi }\times \frac{Q_B}{Z^2}=\frac{3}{2\pi }\times \frac{30}{3^2}=1.591$

$\therefore {\sigma }_z=1.591+0.096=1.687\simeq 1.69t/m^2$​​​​​​