Question

A cantilever beam of span ${}^{\prime }{L}^{\prime }$ is loaded with a concentrated load ${}^{\prime }{P}^{\prime }$ at the free end. Deflection of the beam at the free end is

• A. $\frac{P{L}^3}{48EI}$
• B. $\frac{5P{L}^3}{384EI}$
• C. $\frac{P{L}^3}{3EI}$
• D. $\frac{P{L}^3}{6EI}$

Answer 1

The correct option is C $\frac{P{L}^3}{3EI}$


We know that, ${\delta }_{freeend}=\frac{P{L}^3}{3EI}$
This can be proved by conjugate beam method as follows


Deflection in real beam $=$ bending moment in conjugate beam
${\delta }_A=B{M}_A$ in conjugage beam
$\Rightarrow {\delta }_A=\frac{1}{2}\times \frac{PL}{EI}\times L\times \frac{2L}{3}$
${\delta }_A=\frac{P{L}^3}{3EI}$