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

  • question_answer A simply supported beam carrying a concentrated load W at mid-span deflects by \[{{\delta }_{1}}\] under the lode. If the same beam carries the load W such that it is distributed uniformly over entire length and undergoes a deflection \[{{\delta }_{2}}\] at the mid span. The ratio, \[{{\delta }_{1}}:{{\delta }_{2}}\] is:

    A) 2 : 1                             

    B) \[\sqrt{2}:1\]     

    C) 1.6 : 1              

    D) 1 : 2

    Correct Answer: C

    Solution :

    \[{{\delta }_{1}}=\frac{W{{l}^{3}}}{48\,EI}\] \[{{\delta }_{1}}=\frac{5}{348}\,\,\frac{w{{L}^{4}}}{EI}=\frac{5}{348}\,\,\frac{W{{L}^{3}}}{EI}\] \[{{\delta }_{1}}:{{\delta }_{2}}::\frac{1}{48}:\frac{5}{348}\] \[::1:\frac{5}{8}::1.6:1\]

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