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

  • question_answer Hoop stress and longitudinal stress in a boiler shell under internal pressure are \[100\,\text{MN/}{{\text{m}}^{\text{2}}}\] and \[50\,MN/{{m}^{2}}\] respectively. Young's modulus of elasticity and Poisson's ratio of the shell material are \[200\,\text{GN/}{{\text{m}}^{\text{2}}}\] and 0.3 respectively. The hoop strain in boiler shell is:

    A) \[0.425\times {{10}^{-\,3}}\]                

    B) \[0.5\times {{10}^{-\,3}}\]

    C) \[0.585\times {{10}^{-\,3}}\]                

    D) \[0.75\times {{10}^{-\,3}}\]

    Correct Answer: A

    Solution :

    \[{{\sigma }_{\theta }}=100\,\text{MN/}{{\text{m}}^{\text{2}}}\text{,}\] \[{{\sigma }_{t}}=50\,G\text{N/}{{\text{m}}^{\text{2}}}\text{,}\] \[E=200\,M\text{N/}{{\text{m}}^{\text{2}}}\text{,}\] \[v\text{ }=\text{ }0.3\] \[{{E}_{\theta }}=\frac{1}{E}[{{\sigma }_{\theta }}-v{{\sigma }_{1}}]\] \[=\frac{1}{200\times {{10}^{3}}}[100-0.3\times 50]\] \[=42.5\times {{10}^{-\,5}}\]or\[0.425\times {{10}^{-\,3}}\]

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