Question

A cantilever of constant depth carries a uniformly distributed load on the whole span. To make the maximum stress at all sections the same, the breadth of the section at a distance x from the free end should proportional to

• A. x
• B. $\sqrt{x}$
• C. $x^2$
• D. $x^3$

Answer 1

The correct option is C $x^2$

At a distance x from free end

$M_x=\frac{W{x}^2}{2}$

$and,Z_x=\frac{b_x{d}^2}{6}$

Maximum bending stress,

$f=\frac{M_x}{Z_x}$

$\therefore b_x=\frac{3w{x}^2}{f{d}^2}$

The breadth is proportional to $x^2$.