GATE Civil Engineering
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A single story building model is shown in the figure. The rigid bar of mass ‘$\text{m}$’ is supported by three massless elastic columns whose ends are fixed against rotation. For each of the columns, the applied lateral force $\text{(P)}$ and corresponding moment $\text{(M)}$ are also shown in the figure. The lateral deflection $\left ( \delta \right )$ of the bar is given by  $\delta =\frac{PL^{3}}{12EI}$, where $\text{L}$ is the effective length of the column, $\text{E}$ is the Young's modulus of elasticity and $\text{I}$ is the area moment of inertia of the column cross-section with respect to its neutral axis.

For the lateral deflection profile of the columns as shown in the figure, the natural frequency of the system for horizontal oscillation is

  1. $6\sqrt{\frac{EI}{mL^{3}}}\text{rad/s}$
  1. $\frac{1}{L}\sqrt{\frac{2EI}{m}}\text{rad/s}$
  1. $6\sqrt{\frac{6EI}{mL^{3}}}\text{rad/s}$
  1. $\frac{2}{L}\sqrt{\frac{EI}{m}}\text{rad/s}$
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