Railways Technical Ability Engineering Mechanics and Strength of Materials Question Bank Strength of Materials

  • 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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