Question

The stepped cantilever is subjected to moments, M as shown in the figure below. The vertical deflection at the free end (neglecting the self weight) is

• A. $\frac{M{L}^2}{8EI}$
• B. $\frac{M{L}^2}{4EI}$
• C. $\frac{M{L}^2}{2EI}$
• D. Zero

Answer 1

The correct option is A $\frac{M{L}^2}{8EI}$

Using moment area method,



Net deflection at B can be calcualted as combination of these two loading



Alternatively
$\frac{M}{EI}$ diagram for given theorem,



Deflection of C, away from tangent at A
$=\frac{M}{EI}\times \left(\frac{L}{2}\right)\times \frac{L}{4}$
$=\frac{M{L}^2}{8EI}$