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GATE 2021 CE (CE2) – Question 38

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

A simply supported prismatic steel beam of span L has a point load P at L/3 from the left. Which statement compares collapse plastic moments from static and kinematic methods?

the source diagram and labels are reproduced in the attached image.
  1. $M_{p,static}>2PL/9=M_{p,kinematic}$
  2. $M_{p,static}=2PL/9\ne M_{p,kinematic}$
  3. $M_{p,static}=2PL/9=M_{p,kinematic}$
  4. $M_{p,static}<2PL/9=M_{p,kinematic}$

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Correct answer: (C) $M_{p,static}=2PL/9=M_{p,kinematic}$

Explanation

Reactions are 2P/3 and P/3, giving maximum moment $(2P/3)(L/3)=2PL/9$. A plastic hinge at the load produces the exact collapse mechanism; equating external and internal work yields the same value. Both bounds coincide: **C**.