Project ForgeStrength of Materials
Bending of Beams
GATE 2012
Easy
A cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of the beam cross section about the neutral axis is I and the Young's modulus is E. The magnitude of the maximum deflection is
- ML²/(2EI)
- BML²/EI
- C2ML²/EI
- D4ML²/EI
Explanation
For a cantilever of length L loaded by a pure end moment M, the maximum deflection (at the free end) is δ=ML²/(2EI), a standard result obtained by double-integrating EI(d²y/dx²)=M with the fixed-end boundary conditions y(0)=y′(0)=0.
Source: GATE ME 2012 (Booklet Code A) (2012)
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.