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

  • question_answer According to the maximum shear stress theory failure, permissible twisting moment in a circular shaft is T. The permissible twisting moment in the same shaft as per the maximum principal stress 6 theory of failure will be                       

    A) T/2                              

    B) T          

    C) \[\sqrt{2T}\]                  

    D) 2T        

    Correct Answer: D

    Solution :

    According to the maximum shear stress theory, \[{{\tau }_{\max }}=\frac{{{\sigma }_{1}}-{{\sigma }_{2}}}{2}={{\tau }_{y}}=\frac{{{\sigma }_{y}}}{2}\] \[\frac{16T}{\pi {{d}^{3}}}=\frac{{{\sigma }_{y}}}{2}\]      \[\therefore \,\,\,\,\,\,\,\,{{\sigma }_{y}}=\frac{32T}{r{{d}^{3}}}\] According to maximum principal stress theory, \[{{\sigma }_{1}}={{\sigma }_{y}}\frac{32T}{r{{d}^{3}}}=2\left( \frac{16T}{\pi {{d}^{3}}} \right)\] Hence, permissible torque = 2T

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