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 reaction at $C$ is

• A. $\frac{9Pa}{16L}$ (upwards)
• B. $\frac{9Pa}{16L}$ (downwards)
• C. $\frac{9Pa}{8L}$ (upwards)
• D. $\frac{9Pa}{8L}$ (downwards)

Answer 1

The correct option is C $\frac{9Pa}{8L}$ (upwards)



Deflection at C due to reaction at $C={\delta }_d$
Deflection at C due to moment at $B=d_{c_2}$
${\delta }_{c_2}=\frac{\left(2Pa\right)(L{)}^2}{2EI}+\frac{\left(2Pa\right)\left(L\right)}{EI}\times L$
$=\frac{3\left(2Pa\right)L^2}{2EI}(\downarrow )$
${\delta }_{c_1}=\frac{R_c(2l{)}^3}{3EI}=\frac{8R_c{l}^3}{3EI}(\uparrow )$
From compatibility condition
${\delta }_{c_2}={\delta }_{c_1}$
$\frac{3}{2}.\frac{2Pa{L}^2}{EI}=\frac{R_{c}8L^3}{3EI}$
$R_c=\frac{9Pa}{8L}$ (upward)