GATE ME 2026 Set 1 — Question 49
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Strength of Materials → Beams & Columns → Bending & Shear Stresses
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Question
A simply supported beam is subjected to an external point load as shown in the figure below. The beam has a rectangular cross-section of . A is a pin support and B is a roller support. The shear stress developed at point C, lying on the neutral axis of the beam, is . Neglecting the mass of the beam, the magnitude of the applied load is _______ kN (rounded off to 1 decimal place).
Correct answer
2.9 to 3.1
Solution
1.Calculate Reactions:
Let the total length of the beam be .The load is applied at from support A.
Taking moments about A: .
From vertical equilibrium: .
2.Determine Shear Force at C:
Point C is located from support A. The shear force at any point between A and the load is constant and equal to .Therefore, .
3.Calculate Shear Stress at Neutral Axis:
For a rectangular cross-section, the maximum shear stress occurs at the neutral axis and is given by:Given and cross-sectional area .
4.Solve for P:
The magnitude of the applied load is .Continue learning with Success Tracker
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