Question

The beam of an overall depth 250 mm and length 13 m is used in a building subjected to two different thermal environment. Temperature at top and bottom surface of the beam is ${36}^{\circ }$ and ${72}^{\circ }C,\alpha =1.5\times {10}^{-5}$ per $C^{\circ }$ The vertical deflection of the beam (in m) at its span is

• A. 45.63

Answer 1

The correct option is A 45.63

$m=\frac{x}{2}$
$\Rightarrow 1.\Delta =\int m.\frac{\alpha \Delta T.dx}{D}$
$=2{\int }_0^{6.5}\left(\frac{x}{2}\right)\left(\frac{1.5\times {10}^{-5}\times 36\times dx}{0.25}\right)$
$=\frac{1.5\times {10}^{-5}\times 36}{0.25}\frac{(6.5{)}^2}{2}m$
$=0.04563m=45.63mm$