Question

A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment ,M, as shown in the figure. The deflection of the beam at $x=\frac{L}{2}$ is

• A. $\frac{M{L}^2}{16EI}$
• B. $\frac{M{L}^2}{4EI}$
• C. $\frac{M{L}^2}{2EI}$
• D. $\frac{M{L}^2}{8EI}$

Answer 1

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

$Y_C-Y_A={\left(\frac{A\overline{X}}{EI}\right)}_{AC}$
$Y_C-0=\frac{1}{EI}[\frac{-ML}{2}\times \frac{L}{4}]$
$Y_C=\frac{M{L}^2}{8EI}$ (downward)