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GATE 2016 CE (CE1) – Question 47

Steel Structures · Plastic analysis of beams and portal frames · 2 marks · Multiple choice

A propped cantilever of span L carries a vertical concentrated load at the mid-span. If the plastic moment capacity of the section is Mp, the magnitude of the collapse load is

  1. $8M_p/L$
  2. $6M_p/L$
  3. $4M_p/L$
  4. $2M_p/L$

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Show answer and explanation

Correct answer: (B) $6M_p/L$

Explanation

A collapse mechanism forms plastic hinges at the fixed support and at the midspan load. For a load-point displacement Δ, the fixed-end rotation is2Δ/L and the relative rotation at the interior hinge is4Δ/L. Equating external work PΔ to Mp(2Δ/L+4Δ/L) gives **P=6Mp/L, B**.