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

- $6\sqrt{\frac{EI}{mL^{3}}}\text{rad/s}$

- $\frac{1}{L}\sqrt{\frac{2EI}{m}}\text{rad/s}$

- $6\sqrt{\frac{6EI}{mL^{3}}}\text{rad/s}$

- $\frac{2}{L}\sqrt{\frac{EI}{m}}\text{rad/s}$

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