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GATE 2021 ME (ME2) – Question 41

Mechanics of Materials · Energy methods · 2 marks · Multiple choice

A plane frame PQR (fixed at P and free at R) is shown in the figure. Both members (PQ and QR) have length, L, and flexural rigidity, $EI$. Neglecting the effect of axial stress and transverse shear, the horizontal deflection at free end, R, is

L-shaped frame fixed at P, horizontal PQ and downward QR each length L; force F acts rightward at free end R. See the attached source image.
  1. $5FL^3/(3EI)$
  2. $4FL^3/(3EI)$
  3. $2FL^3/(3EI)$
  4. $FL^3/(3EI)$

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Show answer and explanation

Correct answer: (B) $4FL^3/(3EI)$

Explanation

In PQ the bending moment is constant FL, while along QR it varies linearly from zero at R to FL at Q. The strain energy is $U=[F^2L^3+F^2L^3/3]/(2EI)$.

Castigliano gives $\delta_R=\partial U/\partial F=4FL^3/(3EI)$. **Answer: B**.