Question

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

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

Answer 1

The correct option is C $x^2$

$Maximumstress,\sigma =\frac{M}{Z}=constant$

$\therefore M\propto Z$

Let the section be of constant depth 'd'


BM at a section x from free end,

$M=\frac{w{x}^2}{2}$

$\frac{w{x}^2}{2}\propto \frac{b{d}^2}{6}$
(where b is width at 'x' distance)

$\therefore b\propto x^2$