• # 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) 4C) 8                                 D) 16

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