Question

A line load of infinite length has an intensity q per unit length. What is the vertical stress ${\sigma }_z$ at a depth z below the earth at the centre of the load?

• A. ${\sigma }_z=\frac{2qz}{\pi }$
• B. ${\sigma }_z=\frac{2q}{\pi z}$
• C. ${\sigma }_z=\frac{2q{z}^2}{\pi }$
• D. ${\sigma }_z=\frac{2q}{\pi z^2}$

Answer 1

The correct option is B ${\sigma }_z=\frac{2q}{\pi z}$

Vertical stress at a point P due to a line load of intensity q/unit length.
$\therefore {\sigma }_z=\frac{2q}{\pi z}{\left[\frac{1}{(1+(x/z{)}^2)}\right]}^2$
where,
x = distance of point from centre line of load
z = depth of point below the centre of load