Question

An inclined load of 30 kN acts at angle ${30}^{\circ }$ on a cantilever beam as shown. The maximum bending stress developed anywere in beam will be;

• A. 45 MPa
• B. 77.94 MPa
• C. 122.94 MPa
• D. None of these

Answer 1

The correct option is C 122.94 MPa


${\sigma }_{max}=\frac{M_{x}y}{I_x}+\frac{M_{y}x}{I_y}$
Hence, $x=y=100mm$
$l_x=l_y=\frac{(200{)}^4}{12}m{m}^4$
Maximum moment will occur at A
$M_x=P\cos {30}^{\circ }\times 4=30\times 4\times \frac{\sqrt{3}}{2}=103.92kN-m$
$M_y=P\sin {30}^{\circ }\times 4=60kN-m$
${\sigma }_{max}=\frac{100}{\frac{(200{)}^4}{12}}(103.92+60)\times {10}^6=122.94MPa$