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

  • question_answer Circumferential and longitudinal strains in cylindrical boiler under internal steam pressure, are \[{{\varepsilon }_{1}}\] and \[{{\varepsilon }_{2}}\] respectively. Change in volume of the boiler cylinder per unit volume will be:

    A) \[{{\varepsilon }_{1}}+2{{\varepsilon }_{2}}\]               

    B) \[{{\varepsilon }_{1}}+{{\varepsilon }_{2}}^{2}\]

    C) \[2{{\varepsilon }_{1}}+{{\varepsilon }_{2}}\]               

    D) \[{{\varepsilon }_{1}}^{2}+{{\varepsilon }_{2}}\]

    Correct Answer: C

    Solution :

    \[{{\varepsilon }_{\theta }}=\frac{1}{E}({{\varepsilon }_{\theta }}-v{{\sigma }_{1}})={{\varepsilon }_{1}}\] \[{{\varepsilon }_{2}}=\frac{1}{E}({{\sigma }_{1}}-v{{\sigma }_{\theta }})={{\varepsilon }_{2}}\] \[V=\pi dl\] \[InV=In\,\pi +2\,In\,d+In\,l\] \[\frac{\delta \,V}{V}=2\frac{\delta d}{d}+\frac{\delta l}{l}\] \[{{\varepsilon }_{0}}=2{{\varepsilon }_{1}}+{{\varepsilon }_{2}}\]

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