GATE CE 2019 Set 2 — Question 30
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Structural Engineering → Indeterminate Analysis & Influence Lines → Indeterminate Structures
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Question
The degree of static indeterminacy of the plane frame as shown in the figure is _______ 
Correct answer
15 to 15
Solution
To find the degree of static indeterminacy () of the given plane frame, we can use the formula:
Where is the number of external reaction components.
Where is the number of closed loops and is the number of internal releases.
1.External Indeterminacy ():
Where is the number of external reaction components.
- Fixed support at the left: 3 reactions
- Hinged support in the middle: 2 reactions
- Hinged support at the right: 2 reactions
2.Internal Indeterminacy ():
For a plane frame, Where is the number of closed loops and is the number of internal releases.
- Number of closed loops (): The frame has 2 bays and 2 stories above the ground beam, forming 4 closed loops.
- Internal releases (): There is one internal hinge provided on a member. A hinge on a member in a 2D frame releases 1 constraint (moment).
3.Total Static Indeterminacy ():
Alternatively, using the general formula:- Members () = 12
- Joints () = 9
- = 7
- = 1
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