GATE CE 2021 Set 2 — Question 39
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Structural Engineering → Indeterminate Analysis & Influence Lines → Analysis of Frames
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Question
A frame EFG is shown in the figure. All members are prismatic and have equal flexural rigidity. The member FG carries a uniformly distributed load per unit length. Axial deformation of any member is neglected.
Considering the joint F being rigid, the support reaction at G is
Correct answer
(C) 0.482 wL
Solution
Using the slope-deflection method and considering sway (since G is a roller and the frame is unsymmetrical):
.
1.Stiffnesses: , (since G is a roller).
2.Sway condition: Horizontal reaction at E must be zero () because and there are no horizontal loads. This implies .
3.Slope-deflection equations with sway :
.
4.Joint equilibrium at F:
5.Moment at F in FG:
6.Vertical reaction at G: for member FG:
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