Question

The flexural rigidity ($EI$) of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load $P$ and bending moment $PL/2$ are applied at the free end of the beam then the value of the slope at the free end is

• A. $\frac{1}{2}\frac{P{L}^2}{EI}$
• B. $\frac{P{L}^2}{EI}$
• C. $\frac{3}{2}\frac{P{L}^2}{EI}$
• D. $\frac{5}{2}\frac{P{L}^2}{EI}$

Answer 1

The correct option is B $\frac{P{L}^2}{EI}$

${\theta }_1=\frac{P{L}^2}{2EI}$
${\theta }_2=\frac{ML}{EI}=\frac{P{L}^2}{2EI}$
By superposition,
$\theta ={\theta }_1+{\theta }_2=\frac{P{L}^2}{EI}$