Question

A cantilever carries a uniformly distributed total load W over its whole length and a concentrated upwards load W at its free end, The net vertical deflection at the free end is

• A. Zero
• B. $\frac{5}{24}.\frac{W{I}^3}{EI}downwards$
• C. $\frac{5}{48}.\frac{W{I}^3}{EI}upwards$
• D. $\frac{5}{48}.\frac{W{I}^3}{EI}upwards$

Answer 1

The correct option is C $\frac{5}{48}.\frac{W{I}^3}{EI}upwards$



The vertical deflection at end B due to point load W is given by

${\Delta }_{B_1}=\frac{W{I}^3}{3EI}\left(upwards\right)$


The vertical deflection at end B due to total load W over its whole length is

${\Delta }_{B_2}=\frac{W{I}^3}{8EI}\left(download\right)$

$\therefore {\Delta }_{net}={\Delta }_{B_1}-{\Delta }_{B_2}=\frac{W{I}^3}{3EI}-\frac{W{I}^3}{8EI}$

$=\frac{5}{24}\frac{W{I}^3}{EI}\left(upwards\right)$