GATE CE 2019 Set 2 — Question 47
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Structural Engineering → Indeterminate Analysis & Influence Lines → Stiffness Method
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Question
A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are and .
For the externally applied moment of at node F, the rotation (in degrees, round off to 3 decimals) observed in the rotational spring at node H is ___________
Correct answer
0.005 to 0.007
Solution
1.Analyze the frame segment by segment. Node G is an internal hinge, so the moment at G is zero ().
2.For segment FG, the applied moment at F is . The shear force required for equilibrium is . This force acts downwards at F and upwards at G.
3.This shear force is transferred to segment GH at node G. Thus, a vertical force of acts upwards at G for segment GH.
4.For segment GH to be in equilibrium, the moment at H must balance the moment caused by the force at G: (clockwise).
5.The rotational spring at H resists this moment: .
6..
7.Convert the rotation from radians to degrees: .
8.Rounding to 3 decimal places, the rotation is .
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