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Railways NTPC (Technical Ability) Engineering Mechanics and Strength of Materials Question Bank Engineering Mechanics

  • question_answer
    A circular solid shaft is subjected to a bending moment of 400 kN.m and a twisting moment of 300 kN.m. On the basis of the maximum principal stress theory, the direct stress is \[\sigma \] and according to the maximum shear stress theory, the shear stress is t The ratio \[\sigma /t\] is:

    A) \[\frac{1}{5}\]                          

    B) \[\frac{3}{4}\]

    C) \[\frac{9}{5}\]                          

    D) \[\frac{11}{6}\]

    Correct Answer: C

    Solution :

    \[{{M}_{e}}=\frac{1}{2}\left[ M+\sqrt{{{M}^{2}}+{{T}^{2}}} \right]\] \[=\frac{1}{2}\left[ 400+\sqrt{{{400}^{2}}+{{300}^{2}}} \right]\] =450 k.N.m \[{{\sigma }_{b}}=\frac{32M}{\pi {{d}^{3}}}=\frac{32}{\pi {{d}^{3}}}\times 450\] \[{{T}_{e}}=\sqrt{{{M}^{2}}+{{T}^{2}}}=500\,\,kN.m\] \[\tau =\frac{16T}{\pi {{d}^{3}}}=\frac{16}{\pi {{d}^{3}}}\times 500\] \[\frac{{{\sigma }_{b}}}{\tau }=\frac{2\times 450}{500}=\frac{9}{5}=1.8\]


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