GATE ME 2022 Set 2 — Question 26
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Engineering Mechanics → Statics → Free-Body Diagrams & Equilibrium
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Question
A square plate is supported in four different ways (configurations (P) to (S) as shown in the figure). A couple moment is applied on the plate. Assume all the members to be rigid and mass-less, and all joints to be frictionless. All support links of the plate are identical.The square plate can remain in equilibrium in its initial state for which one or more of the following support configurations?
Correct answer
(B) Configuration (Q); (C) Configuration (R); (D) Configuration (S)
Solution
For a rigid body to be in equilibrium under an applied couple , the support reactions must be able to produce an equal and opposite resisting couple. The support links are two-force members, so the reaction force at each support must act along the axis of the link.
1.Configuration (P): All four links are parallel. A system of parallel links cannot resist a moment in the plane of the plate because any small rotation would not be resisted by the links (they would simply rotate together like a parallelogram linkage). Thus, it is kinematically unstable for an applied moment in its plane.
2.Configuration (Q): The links are not all parallel. They are arranged such that they can provide reaction forces with components that create a counter-moment to .
3.Configuration (R): The links are arranged in a way that they can provide a resisting couple. Specifically, the horizontal and vertical links can provide the necessary force components to balance the applied moment.
4.Configuration (S): The inclined links are arranged such that their lines of action do not meet at a single point and are not all parallel, allowing them to resist the applied couple .
Therefore, configurations (Q), (R), and (S) can maintain equilibrium.Continue learning with Success Tracker
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