Question

Consider a propped cantilever beam ABC under two loads of magnitude P each as shown in the figure below. Flexural rigidity of the beam is EI



The rotation at $B$ is

• A. $\frac{5PLa}{16EI}$ (clockwise)
• B. $\frac{5PLa}{16EI}$ (anticlockwise)
• C. $\frac{59PLa}{16EI}$ (clockwise)
• D. $\frac{59PLa}{16EI}$ (anticlockwise)

Answer 1

The correct option is A $\frac{5PLa}{16EI}$ (clockwise)



Rotation at B in clockwise direction
${\theta }_B=\frac{ML}{EI}-\frac{\left(\frac{9Pa}{8L}\right)L^2}{2EI}-\frac{\frac{9Pa}{8}L}{EI}$
$=\frac{2PaL}{EI}-\frac{9PaL}{16EI}-\frac{9PaL}{8EI}$
$=\frac{5}{16}\frac{PaL}{EI}$

Another Approach:
Using Moment Area Method



support $A$ is fixed so
${\theta }_A=0$
${\theta }_B-{\theta }_A=$ Area of $\frac{M}{EI}$ diagram between $A$ and $B$
$=\frac{1}{2}[\frac{9Pa}{4EI}+\frac{9Pa}{8EI}]-\frac{2PaL}{EI}$
${\theta }_B=-\frac{5}{16}\frac{PLa}{EI}$
$\Rightarrow {\theta }_B=\frac{5}{16}\frac{PLa}{EI}$ (clockwise)