Question

A steel girder can bear a load of $20tons$. If the thickness of girder is double, then for the same depression it can bear a load of :

• A. 40 ton
• B. 80 ton
• C. 160 ton
• D. 5 ton

Answer 1

Answer: (C)

160 ton

Let the load on the girder be $W_1$ and the thickness be $t_1$.
Now, when the thickness is doubled, i.e. $t_2=2t_1$, the load on the girder is $W_2$.
Depression $\delta =\frac{W{l}^3}{4b{t}^{3}Y}$
Since depression is same in both cases,
${\delta }_1={\delta }_2$
$\frac{W_1}{t_1^3}=\frac{W_2}{t_2^3}$
Hence,
$W_2=160N$