Home › Previous year questions › GATE 2020 PI › Question 39GATE 2020 PI – Question 39 General Engineering · Applied Mechanics · 2 marks · Multiple choice
A simply supported beam of length L carries uniform transverse load W N/m. Its rectangular section has width b and depth t. Find the maximum bending-stress magnitude.
$3WL^2/(4bt^2)$ $4WL^2/(3bt^2)$ $2WL^2/(3bt^2)$ $3WL^2/(2bt^2)$ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (A) $3WL^2/(4bt^2)$
Explanation Maximum moment is WL²/8 at midspan. The rectangular-section modulus is I/c=(bt³/12)/(t/2)=bt²/6. Therefore σmax=M/Z=(WL²/8)(6/bt²)=3WL²/(4bt²), A.
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