GATE CE 2018 Set 2 — Question 50
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Structural Engineering → Connections & Plastic Analysis → Plastic Analysis (Beams)
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Question
A prismatic propped cantilever beam of span and plastic moment capacity is subjected to a concentrated load at its mid-span. If the collapse load of the beam is , the value of is ______
Correct answer
6 to 6
Solution
For a propped cantilever beam with a concentrated load at mid-span, the collapse mechanism involves the formation of plastic hinges at the fixed support and under the point load.
Let be the rotation at the fixed support. By geometry, the rotation under the load is and the rotation at the prop is .
Internal work done, .
External work done, .
Equating internal and external work:
.
Given , we find .
Let be the rotation at the fixed support. By geometry, the rotation under the load is and the rotation at the prop is .
Internal work done, .
External work done, .
Equating internal and external work:
.
Given , we find .
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