GATE CE 2015 Set 2 — Question 40
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Structural Engineering → Energy Methods & Vibrations → Equilibrium Equations
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Question
In a system, two connected rigid bars and are of identical length, with pin supports at and . The bars are interconnected at by a frictionless hinge. The rotation of the hinge is restrained by a rotational spring of stiffness, . The system initially assumes a straight line configuration, . Assuming both the bars as weightless, the rotation at supports, and , due to a transverse load, applied at is:
Correct answer
(A) (PL)/(4k)
Solution
Let the rotation at supports and be . Due to symmetry, the rotation at both supports is the same. When the transverse load is applied at , the bars and rotate by an angle . The relative rotation at the hinge is the sum of the rotations of the two bars, which is . The restoring moment in the rotational spring at the hinge is given by:
Now, consider the equilibrium of bar . Due to symmetry, the vertical reaction at support is . Taking moments about support for bar :
where is the internal vertical force at . From overall equilibrium, .
Thus, the rotation at supports and is .
Now, consider the equilibrium of bar . Due to symmetry, the vertical reaction at support is . Taking moments about support for bar :
where is the internal vertical force at . From overall equilibrium, .
Thus, the rotation at supports and is .
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