GATE CE 2025 Set 1 — Question 29
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Structural Engineering → Indeterminate Analysis & Influence Lines → Analysis of Frames
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Question
Consider the frame shown in the figure under the loading of couples at the joints B and G. Considering only the effects of flexural deformations, which of the following statements is/are true:
Correct answer
(B) Shear force is zero in the member CD; (C) There is no rotation in the joint C
Solution
The frame and the loading are symmetric about the vertical axis passing through member CD.
1.Symmetry Analysis:
- Due to symmetry, the rotation at joint C must be zero (). Thus, statement (C) is true.
- For a symmetric structure under symmetric loading, there is no horizontal sway ().
- Member CD is fixed at D and connected to joint C. Since , , , and , the member CD undergoes no flexural deformation. Therefore, the bending moments and the shear force . Thus, statement (B) is true.
- At joint B, the equilibrium equation is .
- (since )
- Substituting into the equilibrium equation: .
- The bending moment in BC at end C is . Since , statement (D) is false.
- The shear force in member BC is .
- By symmetry, the shear force in member CG is also . Both act downwards on joint C. The axial force in member CD is the sum of these shears: . Thus, statement (A) is false.
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