GATE CE 2026 Set 2 — Question 50
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Structural Engineering → Stress, Strain & Beams → Axial Deformation
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Question
Linearly elastic, homogeneous, uniform bars BCD and FG shown in the figure have fixed supports at B and G, respectively. For both the bars, axial rigidity is . A gap of exists between D and F prior to application of any load (i.e. ). Small deformation and infinitesimal strain assumptions are valid for the given bars.
(Figure not to scale)The magnitude of the horizontal reaction (in kN) at B after application of the axial force of at C is ______ (rounded off to the nearest integer).
Correct answer
16 to 16
Solution
1.Check if the gap closes:
Assuming no contact at D, the displacement of point D () is due to the elongation of segment BC caused by force . Segment CD carries no force in this case.Since the free displacement of D () is greater than the initial gap (), the bars will come into contact.
2.Statically Indeterminate Analysis:
Let be the compressive contact force developed between D and F. This force acts to the left on bar BCD and to the right on bar FG.- Displacement of D () to the right:
- Displacement of F () to the right (compressing bar FG against support G):
- Compatibility condition (the bars meet at the gap):
3.Calculate Reaction at B:
From the equilibrium of bar BCD, the horizontal reaction at B () must balance the applied force and the contact force :The magnitude of the horizontal reaction at B is .
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