GATE CE 2023 Set 2 — Question 54
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Structural Engineering → Indeterminate Analysis & Influence Lines → Analysis of Frames
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Question
For the frame shown in the figure (not to scale), all members (AB, BC, CD, GB, and CH) have the same length, and flexural rigidity, . The joints at B and C are rigid joints, and the supports A and D are fixed supports. Beams GB and CH carry uniformly distributed loads of per unit length. The magnitude of the moment reaction at A is . What is the value of (in integer)?
Correct answer
6 to 6
Solution
The cantilevers GB and CH apply external moments to joints B and C respectively.
For GB: (counter-clockwise on joint B).
For CH: (clockwise on joint C).Due to symmetry of the frame and loading, and there is no sway.
Using slope-deflection equations (clockwise positive):
(since )
Equilibrium at joint B:
Moment at A:
Comparing with , we get .
For GB: (counter-clockwise on joint B).
For CH: (clockwise on joint C).Due to symmetry of the frame and loading, and there is no sway.
Using slope-deflection equations (clockwise positive):
(since )
Equilibrium at joint B:
Moment at A:
Comparing with , we get .
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