Question

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

• A. $\frac{M{L}^2}{2EI}$
• B. $\frac{M{L}^2}{EI}$
• C. $\frac{2M{L}^2}{EI}$
• D. $\frac{4M{L}^2}{EI}$

Answer 1

The correct option is A $\frac{M{L}^2}{2EI}$

Deflection
$=\frac{1}{EI}\left(MomentofareaofBMD\right)$
$=\frac{1}{EI}\times M\times L\times \frac{L}{2}=\frac{M{L}^2}{2EI}$