GATE CE 2022 Set 1 — Question 51
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Structural Engineering → Indeterminate Analysis & Influence Lines → Analysis of Frames
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Question
Consider the linearly elastic plane frame shown in the figure. Members , and are welded together at joint . Joints , and are fixed supports. A counter-clockwise moment is applied at joint . Consider flexural rigidity for each member and neglect axial deformations.
If the magnitude (absolute value) of the support moment at is , the magnitude (absolute value) of the applied moment (in kN-m) to maintain static equilibrium is ___________. (round off to the nearest integer)
Correct answer
57 to 63
Solution
1.Determine Member Lengths:
- Length of () = (vertical).
- Length of () = .
- Length of () = .
Since all members are fixed at their far ends and have the same and length :
3.Distribution Factor (DF):
The distribution factor for member at joint is:4.Moment Distribution:
When moment is applied at joint , the moment distributed to member at end is:5.Carry-over Moment:
The moment carried over to the fixed support is half of the moment at end :6.Solve for :
Given :Applied moment .
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