GATE 2018 CE (CE2) – Question 50
A prismatic propped cantilever of span L and plastic moment capacity $M_p$ carries a concentrated load at midspan. If collapse load is $\alpha M_p/L$, then α is ______.
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Correct answer: 6.0 to 6.0
Explanation
The collapse mechanism has plastic hinges at the fixed end and midspan. For a midspan drop δ, each half rotates $2\delta/L$, and relative rotation at the middle is $4\delta/L$. Internal work is $M_p(2\delta/L+4\delta/L)=6M_p\delta/L$. Equating to external work gives $W=6M_p/L$, hence α = 6.