GATE CE 2021 Set 2 — Question 17
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Structural Engineering → Energy Methods & Vibrations → Natural Frequency
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Question
A single story building model is shown in the figure. The rigid bar of mass '' is supported by three massless elastic columns whose ends are fixed against rotation. For each of the columns, the applied lateral force () and corresponding lateral deflection () are also shown in the figure. The lateral deflection () of the bar is given by , where is the effective length of the column, is the Young's modulus of elasticity and is the area moment of inertia of the column cross-section with respect to its neutral axis.
📷 Figure: Building model and lateral deflection profile
For the lateral deflection profile of the columns as shown in the figure, the natural frequency of the system for horizontal oscillation isCorrect answer
(A) 6 √((EI)/(mL³)) rad/s
Solution
The stiffness of a single column fixed at both ends is given by . Since there are three identical columns supporting the rigid bar in parallel, the total lateral stiffness of the system is . The natural frequency of the system is calculated as .
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