Question

In the cantilever shown below, a moment and a point load is applied as shown in the figure. The upward deflection observed at free end is given by $\beta \left(\frac{P{L}^3}{EI}\right)$, then the value of $\beta$ is

• A. 1.17

Answer 1

The correct option is A 1.17
$\text{Deflection due to point load (P) at free end}=\frac{P(2L{)}^3}{3EI}(\uparrow )=\frac{8P{L}^3}{3EI}(\uparrow )$

Deflection due to moment (PL) at free end $=\frac{\left(PL\right)L^2}{2EI}+\frac{\left(PL\right)LL}{EI}=\frac{P{L}^3}{2EL}+\frac{P{L}^3}{EI}=\frac{3P{L}^3}{2EI}(\downarrow )$

$\text{Net upward deflection}=-\frac{3P{L}^3}{2EI}+\frac{8P{L}^3}{3EI}=\frac{-9+16P{L}^3}{6EL}=\frac{7P{L}^3}{6EI}$

$\Rightarrow \beta =1.17$