GATE CE 2017 Set 2 — Question 42
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Structural Engineering → Indeterminate Analysis & Influence Lines → Analysis of Frames
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Question
Consider the portal frame shown in the figure and assume the modulus of elasticity, and the moment of inertia, for all the members of the frame.
The rotation (in degrees, up to one decimal place) at the rigid joint would be __________
Correct answer
0.9 to 1.1
Solution
First, calculate the flexural rigidity in consistent units (kN and m):
The moment at joint is caused by the loads on the cantilever segment :
Joint is connected to members and , both of which are fixed at their far ends ( and ) and have lengths of .
The rotational stiffness of a member fixed at the far end is .
Total stiffness at joint : The rotation in radians is:
Convert radians to degrees:
Rounding to one decimal place, the rotation is .
The moment at joint is caused by the loads on the cantilever segment :
Joint is connected to members and , both of which are fixed at their far ends ( and ) and have lengths of .
The rotational stiffness of a member fixed at the far end is .
Total stiffness at joint : The rotation in radians is:
Convert radians to degrees:
Rounding to one decimal place, the rotation is .
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