GATE CE 2023 Set 1 — Question 26
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Structural Engineering → Determinate Structures & Energy Methods → Determinate Structures
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Question
Consider the following three structures:
Which of the following statements is/are TRUE?
| Structure | Description |
|---|---|
| Structure I | Beam with hinge support at A, roller at C, guided roller at E, and internal hinges at B and D |
| Structure II | Pin-jointed truss, with hinge support at A, and rollers at B and D |
| Structure III | Pin-jointed truss, with hinge support at A and roller at C |
Correct answer
(A) Structure I is unstable; (B) Structure II is unstable; (C) Structure III is unstable
Solution
To determine the stability of each structure, we analyze them individually:
1.Structure I: This is a beam with internal hinges at and . The segment is supported by a hinge at and a roller at . However, there is an internal hinge at . Since , , and are collinear, this segment forms a mechanism (it can 'fold' at ). Therefore, Structure I is unstable.
2.Structure II: This is a pin-jointed truss with a hinge at and rollers at and . The rollers at and are on vertical walls, meaning their reactions are horizontal. The line of action of the reaction at (vertical line ) passes through . The line of action of the reaction at (horizontal line ) also passes through . Since all external reactions (except those at ) pass through the hinge at , they provide no resistance to a moment about . The structure can rotate freely about , making it a mechanism. Therefore, Structure II is unstable.
3.Structure III: This is a pin-jointed truss consisting of two panels. The left panel () is a rectangle with four joints and four members but no diagonal member. For a truss panel to be stable, it must be triangulated (). For this panel, and , so . The panel can undergo shear deformation as a mechanism. Therefore, Structure III is unstable.
Since all three structures are unstable, options (A), (B), and (C) are correct.Continue learning with Success Tracker
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