GATE CE 2022 Set 2 — Question 51
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Question
The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams and are connected with the help of the vertical linear spring with spring constant . The fixed supports are provided at and . It is given that flexural rigidity , , and . Force is applied at the center of beam such that the force in the spring becomes zero.
The magnitude of force (in kN) is ________. (round off to the nearest integer)
Correct answer
620 to 660
Solution
If the force in the spring is zero, the beams and act independently as cantilevers, and the vertical deflections at points and must be equal ().
The deflection at the free end is the sum of the deflection at the center and the additional deflection due to the slope at the center:
1.Deflection at for beam :
Beam is a cantilever of length with a point load at the free end . The flexural rigidity is .2.Deflection at for beam :
Beam is a cantilever of length fixed at , with a point load at its center (distance from ). The flexural rigidity is .The deflection at the free end is the sum of the deflection at the center and the additional deflection due to the slope at the center:
3.Equating deflections:
Given :The magnitude of force is 640 kN.Continue learning with Success Tracker
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