GATE CE 2014 Set 1 — Question 18
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Structural Engineering → Connections & Plastic Analysis → Plastic Analysis (Beams)
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Question
The ultimate collapse load () in terms of plastic moment by kinematic approach for a propped cantilever of length with acting at its mid-span as shown in the figure, would be
Correct answer
(C) P = (6Mₚ)/(L)
Solution
Using the Principle of Virtual Work for the collapse mechanism:
1.Plastic hinges form at the fixed support (X) and under the point load ().
2.Let the virtual displacement under the load be .
3.Rotation at the fixed support X is .
4.Rotation at the hinge under the load is . Since the other end Y is a simple support, . Thus, the total rotation at hinge is .
5.Internal Work .
6.External Work .
7.Equating .
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