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Railways NTPC (Technical Ability) Engineering Mechanics and Strength of Materials Question Bank Strength of Materials

  • question_answer
     A Long slender bar having uniform rectangular cross- action \['B\times H'\] is acted upon by an axial compressive force. The sides B and H are paralled to x-and y-axes respectively. The ends of the bar are fixed such that they behave as pinpointed when the bar buckles in a plane normal to x-axis, and they behave as built-in when the bar buckles in a plane normal to y-axis. If load capacity in either mode of buckling is same, then the value of \[\frac{H}{B}\] will be B:

    A) 2                                 

    B) 4

    C) 8                                 

    D) 16

    Correct Answer: A

    Solution :

    \[{{P}_{x}}=\frac{{{\pi }^{2}}E{{I}_{x}}}{{{L}^{2}}}=\frac{{{\pi }^{2}}EB{{H}^{3}}}{12{{L}^{2}}}\] \[{{P}_{y}}=\frac{4{{\pi }^{2}}E{{I}_{y}}}{{{L}^{2}}}=\frac{4{{\pi }^{2}}EB{{H}^{3}}}{12{{L}^{2}}}\] For \[{{P}_{x}}={{P}_{y}}\] \[\frac{{{\pi }^{2}}EB{{H}^{3}}}{12{{L}^{2}}}=\frac{4{{\pi }^{2}}EB{{H}^{3}}}{12{{L}^{2}}}\] Or  \[{{H}^{2}}=4{{B}^{2}}\] \[\frac{H}{B}=2\]


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