Question

A square section as shown in the figure below is subjected to bending moment M.

What is the maximum bending stress?

• A. ${\sigma }_{bc}={\sigma }_{bt}=\frac{12M}{h^3}$
• B. ${\sigma }_{bc}={\sigma }_{bt}=\frac{6M}{h^3}$
• C. ${\sigma }_{bc}={\sigma }_{bt}=\frac{9M}{2h^3}$
• D. ${\sigma }_{bc}={\sigma }_{bt}=\frac{9M}{h^3}$

Answer 1

The correct option is B ${\sigma }_{bc}={\sigma }_{bt}=\frac{6M}{h^3}$

From theory of pure bending

$\frac{M}{I}=\frac{f}{y}$

$\Rightarrow f_{max}=\frac{M}{I}\times y_{max}$

$\Rightarrow {\sigma }_{bc}={\sigma }_{bt}=\frac{M\times 12}{h\times h^3}\times \frac{h}{2}$

$\Rightarrow {\sigma }_{bc}={\sigma }_{bt}=\frac{6M}{h^3}$