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

  • question_answer A plane stressed clement is subjected to the state of stress given by \[{{\sigma }_{x}}={{\tau }_{xy}}=10\,\text{kgf/c}{{\text{m}}^{\text{2}}}\] and \[{{\sigma }_{x}}=0.\] Maximum shear stress in the element is equal to:

    A) \[50\sqrt{3}\,\text{kgf}\,\,\text{c}{{\text{m}}^{\text{2}}}\]        

    B) \[100\,\text{kgf/c}{{\text{m}}^{\text{2}}}\]

    C) \[50\sqrt{5}\,\text{kgf/c}{{\text{m}}^{\text{2}}}\]        

    D) \[150\,\text{kgf/c}{{\text{m}}^{\text{2}}}\]

    Correct Answer: C

    Solution :

    \[{{\tau }_{\max }}=\frac{1}{2}\sqrt{{{({{\sigma }_{x}}-{{\sigma }_{y}})}^{2}}+4{{\tau }^{2}}_{xy}}\] \[=\frac{1}{2}\sqrt{{{(100-0)}^{2}}+4\times {{100}^{2}}}\] \[=50\sqrt{5}\,\,\text{kgf/c}{{\text{m}}^{\text{2}}}\]

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