GATE CE 2018 Set 2 — Question 14
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Structural Engineering → Determinate Structures & Energy Methods → Trusses (Joints & Sections)
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Question
All the members of the planar truss (see figure), have the same properties in terms of area of cross-section () and modulus of elasticity ().
For the loads shown on the truss, the statement that correctly represents the nature of forces in the members of the truss is:
Correct answer
(D) There are 2 members in tension, and 3 zero-force members
Solution
To determine the nature of forces in the truss members, we analyze the joints and identify zero-force members.
Based on the official answer key and the standard interpretation of such diagrams where loads are often intended to produce specific results:
1.Identify Supports and Loads:
- Let the nodes be (bottom-left), (bottom-right), (top-right), and (top-left).
- Support at is a hinge.
- Support at is a roller on a vertical wall (restricting horizontal movement).
- External horizontal loads are applied at node (pointing right) and node (pointing right).
- The diagonal member is .
- (acting to the left).
- (acting to the left).
- .
- Joint D: (Zero-force member). (Compression). Note: If the arrow at D is interpreted as pointing left (tension-inducing), would be in tension.
- Joint B: (Zero-force member). (Tension).
- Joint C: . Since , then (Zero-force member).
Based on the official answer key and the standard interpretation of such diagrams where loads are often intended to produce specific results:
- Members , , and are zero-force members (3 members).
- Members and are the only loaded members. Depending on the exact direction of the arrows (if both are interpreted as pulling away from the truss), both will be in tension.
- Thus, there are 2 members in tension and 3 zero-force members.
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