Question

A rectangular beam of width 100 mm is subjected to a maximum shear force of 60 kN. The corresponding maximum shear stress in the cross-section is $4N/m{m}^2$. The depth of the beam should be

• A. 200 mm
• B. 150 mm
• C. 100 mm
• D. 225 mm

Answer 1

The correct option is D 225 mm

For a rectangular beam

${\tau }_{max}=\frac{3}{2}\times {\tau }_{avg}$

$\Rightarrow {\tau }_{max}=\frac{3}{2}\times \frac{P}{bd}$

$\Rightarrow 4=\frac{3}{2}\times \frac{60\times {10}^3}{100\times d}$

$\Rightarrow d=225mm$