Question

A cantilever beam of constant depth carries a uniformly distributed load on the whole span. To make the maximum stress at all section the same, the ratio of width of beam at midspan and quarter span from the support will be ?

• A. 4/9
• B. 15/36
• C. 9/4
• D. 36/15

Answer 1

The correct option is A 4/9


Let's auume, at $x=l/2,b_x=b_1$

At $x=\frac{3l}{4},b_x=b_2$

Since maximum stress at all section is equal

$\sigma =\frac{M_x}{z_x}$

$M_x=\sigma z_x$

$\frac{w{x}^2}{2}=\sigma \frac{b_x{d}^2}{6}$

So, $b_x\propto x^2$

$\frac{b_1}{b_2}=\frac{(l/2{)}^2}{{\left(\frac{3l}{4}\right)}^2}=\frac{l^2\times 16}{4\times 9l^2}=\frac{4}{9}$