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GATE 2017 ME (ME2) – Question 19

Mechanics of Materials · Shear force and bending moment diagrams · 1 mark · Multiple choice

A cantilever of length L and flexural rigidity EI carries a free-end load P. Its bending strain energy, neglecting transverse shear, is ______.

  1. $P^2L^3/(6EI)$
  2. $P^2L^3/(3EI)$
  3. $PL^3/(3EI)$
  4. $PL^3/(6EI)$

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Show answer and explanation

Correct answer: (A) $P^2L^3/(6EI)$

Explanation

At distance x from the free end, bending moment magnitude is Px. Integrating bending energy gives U=∫₀ᴸ(Px)²/(2EI) dx=P²L³/(6EI). Thus **A**. The same result follows from U=Pδ/2 with tip deflection δ=PL³/(3EI).