• # question_answer A simply supported beam of rectangular section 4 cm by 6 cm carries a mid-span concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is$\delta$. If the beam is now supported with the 4cm side parallel to line of action of loading, the deflection under the load will be: A) 0.44 $\delta$               B) 0.67 $\delta$C) 1.5 $\delta$                 D) 2.25 $\delta$

Correct Answer: D

Solution :

Mid-span deflection of a simply supported beam carrying concentrated load at the centre, $\delta =\frac{W{{L}^{3}}}{48El}$ $\delta \propto \frac{1}{l}$ $\frac{{{\delta }_{2}}}{{{\delta }_{_{1}}}}=\frac{{{I}_{1}}}{{{I}_{2}}}$ $\frac{{{\delta }_{2}}}{{{\delta }_{_{1}}}}=\frac{\left( \frac{4\times {{6}^{2}}}{12} \right)}{\left( \frac{6\times {{4}^{2}}}{12} \right)}={{\left( \frac{6}{4} \right)}^{2}}$ ${{\delta }_{2}}=2.25\delta$

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