GATE CE 2017 Set 2 — Question 32
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Structural Engineering → Stress, Strain & Beams → SFD & BMD
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Question
Consider the three prismatic beams with the clamped supports , , and as shown in the figures.
Given that the modulus of elasticity, is ; and the moment of inertia, is , the correct comparison of the magnitudes of the shear force and the bending moment developed at the supports is
Correct answer
(C) S_P < S_Q S_R; M_P = M_Q = M_R
Solution
Calculate Shear Force () and Bending Moment () at the support for each beam:Beam P:
Beam Q:
Beam R:
(only a concentrated moment is applied)
Comparison:
Shear forces: . This satisfies .
Bending moments: .Therefore, option (C) is correct.
Beam Q:
Beam R:
(only a concentrated moment is applied)
Comparison:
Shear forces: . This satisfies .
Bending moments: .Therefore, option (C) is correct.
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