GATE CE 2020 Set 1 — Question 51
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Structural Engineering → Stress, Strain & Beams → Axial Deformation
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Question
A rigid, uniform, weightless, horizontal bar is connected to three vertical members P, Q and R as shown in the figure (not drawn to the scale). All three members have identical axial stiffness of . The lower ends of bars P and R rest on a rigid horizontal surface. When NO load is applied, a gap of exists between the lower end of the bar Q and the rigid horizontal surface. When a vertical load is placed on the horizontal bar in the downward direction, the bar still remains horizontal and gets displaced by in the vertically downward direction.
The magnitude of the load (in kN, round off to the nearest integer), is ___________.
Correct answer
129 to 131
Solution
Given:
Axial stiffness
Vertical displacement
Gap for member Q Since the bar remains horizontal, all members displace by downwards.
Displacement of P and R:
Force in P and R: Member Q starts taking load only after the gap is closed.
Effective displacement of Q:
Force in Q: Total load .
Axial stiffness
Vertical displacement
Gap for member Q Since the bar remains horizontal, all members displace by downwards.
Displacement of P and R:
Force in P and R: Member Q starts taking load only after the gap is closed.
Effective displacement of Q:
Force in Q: Total load .
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