Question

A timber beam is 100 mm wide and 150 mm deep. The beam is simply supported and carries a central concentrated load W. If the maximum stress in shear is $2N/m{m}^2$, what would be the corresponding load W on the beam?

• A. 20 kN
• B. 30 kN
• C. 40 kN
• D. 25 kN

Answer 1

The correct option is C 40 kN

In case of rectangular beam, we have

$q_{max}=1.5q_{avg}$

$\Rightarrow q_{max}=1.5\times \frac{S}{bd}$

But maximum shear force at any section of the beam with a central concentrated load W is $\frac{W}{2}$

$\therefore q_{max}=1.5\times \frac{W}{2\times 100\times 150}$

$\Rightarrow W=\frac{2\times 2\times 15000}{1.5\times {10}^3}kN$

$\Rightarrow W=40kN$