Project ForgeStrength of Materials
Bending of Beams
GATE 2017
Easy
A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is
- P²L³/6EI
- BP²L³/3EI
- CPL³/3EI
- DPL³/6EI
Explanation
Bending moment at distance x from the free end: M(x)=Px. Strain energy U = ∫₀ᴸ M²/(2EI) dx = ∫₀ᴸ P²x²/(2EI) dx = P²L³/(6EI).
Source: GATE ME 2017 Session 2 (ME-2) (2017)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.