Question

A cantilever beam with flexural rigidity of 200 $N{m}^2$ is loaded as shown in the figure. The deflection (in mm) at the tip of the beam is _________

• A. 0.26042

Answer 1

The correct option is A 0.26042
$EI=200N{m}^2$
$y_C=y_B+{\theta }_B(L-a)$
$y_B=\frac{P{a}^3}{3EI}=\frac{500\times {\left\{\frac{50}{1000}\right\}}^3}{3\times 200}$
= $1.04167\times {10}^{-4}m$
${\theta }_B=\frac{P{a}^2}{2EI}=\frac{500\times {\left\{\frac{50}{1000}\right\}}^2}{2\times 200}$
= $3.125\times {10}^{-3}rad$
$y_C=y_B+{\theta }_B(L-a)$
= [$1.04167\times {10}^{-4}$]
$+[3.125\times {10}^{-3}\times \frac{50}{1000}]$
$=2.6042\times {10}^{-4}m=0.26042mm$