Question

A steel beam of hollow square section of 50 mm outer side and 40 mm inner side is simply supported on a span of 4 m. The maximum concentrated load that the beam can carry at the middle of span if bending stress is not to exceed 120 N/mm${}^2$ (in N) is

• A. 1860
• B. 4785
• C. 1476
• D. 3684

Answer 1

The correct option is C 1476

Let W be the maximum concentrated load.

$\therefore$ Maximum bending moment,

$M=\frac{WL}{4}=\frac{W\times 4}{4}=W\times 1000N-mm$

$y=\frac{50}{2}=25mm$

$I=\frac{{50}^4}{12}-\frac{{40}^4}{12}=307500m{m}^4$

$Z=\frac{I}{y}=\frac{307500}{25}=12300m{m}^3$

$Now,\sigma =\frac{My}{I}$

$\Rightarrow M=\frac{\sigma I}{y}=\sigma Z$

$\Rightarrow W\times 1000=120\times 12300$

$\Rightarrow W=1476N$