Question

A cantilever beam of span 'L' is subjected to a downward load of 800 kN uniformly distributed over its length and a concentrated upward load P at its free end. For vertical diplacement to be zero at the free end,the value of P is :

• A. $300kN$
• B. $500kN$
• C. $800kN$
• D. $1000kN$

Answer 1

The correct option is A $300kN$



$\frac{w{l}^4}{8EI}=\frac{P{l}^3}{3EI}$ (Compatibility condition for $\delta =0$ at free end$)$
$\frac{\left(Wl\right)\left(l^3\right)}{8EI}=\frac{P{l}^3}{3EI}$

$\frac{800}{8}=\frac{P}{3}$

$P=\frac{800\times 3}{8}=300kN$