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

  • question_answer If the principal stresses corresponding to a two-dimensional state of stress are \[{{\sigma }_{1}}\] and \[{{\sigma }_{2}}.\]  If \[{{\sigma }_{1}}\] is greater than \[{{\sigma }_{2}}\] and both are tensile, then which one of the following would be the correct criterion for failure by yielding, according to the maximum shear stress criterion?

    A) \[({{\sigma }_{1}}+{{\sigma }_{2}})/2=\pm \,{{\sigma }_{yp}}/2\]

    B) \[{{\sigma }_{1}}/2=\pm \,{{\sigma }_{yp}}/2\]

    C) \[{{\sigma }_{2}}/2=\pm \,{{\sigma }_{yp}}/2\]

    D) \[{{\sigma }_{1}}=\pm \,{{\sigma }_{yp}}\]

    Correct Answer: A

    Solution :

    According to maximum shear stress theory \[\frac{{{\sigma }_{1}}+{{\sigma }_{2}}}{2}=\frac{{{\sigma }_{yp}}}{2}\]

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