GATE CE 2025 Set 1 — Question 37
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Structural Engineering → Indeterminate Analysis & Influence Lines → Moment Distribution Method
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Question
In the rigid-jointed frame shown in the figure, the distribution factor of the member AD is closest to
Correct answer
(C) 0.398
Solution
To find the distribution factor of member AD at joint A, we first need to determine the rotational stiffness () of each member meeting at joint A.
1.Member AB: Length , rigidity , far end B is fixed.
2.Member AC: Length , rigidity , far end C is fixed.
3.Member AF: Length , rigidity , far end F is fixed.
4.Member AD: This is a non-uniform member of total length , with for the first and for the second . The far end D has a guided roller support (prevents rotation, allows translation). For a uniform member with a guided roller at the far end, the stiffness is . For this stepped member, applying a unit rotation at A and solving for the moment (with and for a guided roller on a vertical track) yields:
(based on the provided correct answer C).5.Total Stiffness at Joint A:
6.Distribution Factor for AD ():
Thus, the distribution factor is closest to 0.398.Continue learning with Success Tracker
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