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GATE 2016 CE (CE2) – Question 48

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

A fixed-end beam has two segments of length L with plastic capacities $2M_p$ and $M_p$, as shown. A concentrated load P acts at $2L/3$ from the left support. Its minimum collapse load is ______.

Diagram for GATE 2016 CE (CE2) question 48
  1. $7.5M_p/L$
  2. $5.0M_p/L$
  3. $4.5M_p/L$
  4. $2.5M_p/L$

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Show answer and explanation

Correct answer: (A) $7.5M_p/L$

Explanation

Use hinges at the left fixed end(2Mp), the weak side of the step at x=L(Mp), and the right fixed end(Mp). For step displacement δ, end rotations areδ/L and the interior relative rotation2δ/L. Internal work is(2+2+1)Mpδ/L=5Mpδ/L. Load-point displacement is(2/3)δ, giving **P=7.5Mp/L, A**; the load-point hinge mechanism gives the higher8.25Mp/L.