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GATE 2021 CE (CE2) – Question 17

Structural Analysis · Statically indeterminate structures: force and displacement methods · 1 mark · Multiple choice

A rigid bar of mass m is supported by three identical massless columns of length L, each fixed against end rotation. Each column has lateral deflection $\delta=PL^3/(12EI)$. Find horizontal natural angular frequency.

the source diagram and labels are reproduced in the attached image.
  1. $6\sqrt{EI/(mL^3)}$
  2. $L^{-1}\sqrt{2EI/m}$
  3. $2\sqrt{6EI/(mL^3)}$
  4. $2L^{-1}\sqrt{EI/m}$

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Correct answer: (A) $6\sqrt{EI/(mL^3)}$

Explanation

One column has lateral stiffness $P/\delta=12EI/L^3$. The three columns act in parallel, so total stiffness is 36EI/L³. The SDOF angular frequency is $\sqrt{k/m}=\mathbf{6\sqrt{EI/(mL^3)}}$, **A**. The column masses are neglected as specified.