GATE CE 2025 Set 2 — Question 38
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Structural Engineering → Indeterminate Analysis & Influence Lines → Analysis of Beams
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Question
The figure shows a propped cantilever with uniform flexural rigidity (in N.m) and subjected to a moment (in N.m). Consider forces and displacements in the upward direction as positive.Find the upward reaction at the propped support B (in N) when this support settles by , given in metres.
Correct answer
(C) (3M)/(2L) - (3EIΔ)/(L³)
Solution
1.Deflection due to Moment : A clockwise moment at the free end of a cantilever causes a downward deflection . In the upward-positive convention, .
2.Deflection due to Reaction : An upward reaction at the prop causes an upward deflection .
3.Compatibility Condition: The net upward displacement at B must equal the settlement .
4.Solving for :
Thus, the correct option is (C).Continue learning with Success Tracker
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