GATE CE 2024 Set 1 — Question 33
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Structural Engineering → Indeterminate Analysis & Influence Lines → Indeterminate Structures
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Question
The plane frame shown in the figure has fixed support at joint A, hinge support at joint F, and roller support at joint I. In the figure, A to I indicate joints of the frame.
If the axial deformations are neglected, the degree of kinematic indeterminacy is ________ (in integer).
Correct answer
9 to 9
Solution
The degree of kinematic indeterminacy () for a plane frame, when axial deformations are neglected, is calculated as:
Where:
Therefore, the degree of kinematic indeterminacy is 9.
Where:
- is the number of joints.
- is the number of support reactions.
- is the number of members (assuming they are inextensible).
1.Number of joints (): A, B, C, D, E, F, G, H, I. Total .
2.Number of support reactions ():
- Fixed support at A: 3 reactions ()
- Hinge support at F: 2 reactions ()
- Roller support at I: 1 reaction ()
3.Number of members (): AB, BC, CD, DE, EF, FG, GH, HI, BE, EH, CF, DG. Total .
Substituting the values into the formula:Therefore, the degree of kinematic indeterminacy is 9.
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