GATE CE 2016 Set 1 — Question 16
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Structural Engineering → Determinate Structures & Energy Methods → Equilibrium Equations
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Question
Consider the plane truss with load as shown in the figure. Let the horizontal and vertical reactions at the joint B be and , respectively and be the vertical reaction at the joint C.Which one of the following sets gives the correct values of , and ?
Correct answer
(A) V_B = 0; H_B = 0; V_C = P
Solution
Step 1: Identify the support reactions. Joint B is a pin support, which has two reaction components: (horizontal) and (vertical). Joint C is a roller support, which has one vertical reaction component: .Step 2: Determine the geometry. The truss is composed of equilateral triangles with side length .
- The horizontal distance from B to D is , and from D to C is . Thus, the total span .
- The horizontal distance from B to G can be calculated by summing the horizontal projections of the members: .
- Since and , the load at joint G acts directly above the support at C.
- Sum of horizontal forces: (as there are no other horizontal forces).
- Sum of moments about joint B: .
- Sum of vertical forces: .
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