Question

A cantilever beam is shown in the figure. The moment to be applied at free end for zero vertical deflection at the point is

• A. $9kN-m$ clockwise
• B. $9kN-m$ anti-clockwise
• C. $12kN-m$ clockwise
• D. $12kN-m$ anti-clockwise

Answer 1

The correct option is C $12kN-m$ clockwise


Deflection due to $9kN$ will be


Moment should be applied as shown:

Deflection due to applied moment will be:


Writing deflection compatibility equation at free end for deflection to be zero:
${\delta }_1={\delta }_2$
$\frac{9\times 2^3}{3EI}=\frac{M\times 2^2}{2EI}$
$M=\frac{9\times 2\times 2}{3}$
$M=12kN-m$ (clockwise)