Stability and Determinacy of Trusses MCQ with answer and solution

Concept

Perfect truss definition and static determinacy

Formula

m = 2j - 3 (plane) or m = 3j - 6 (space)

Step-by-step solution

1. By classical definition, a perfect truss is an internally stable pin-jointed framework that is statically determinate. 2. For a 3D space truss with j joints, the condition for determinacy is m = 3j - 6. 3. For j = 5 joints: m = 3(5) - 6 = 15 - 6 = 9 members. 4. The given truss possesses exactly 9 members and 5 joints, fulfilling the determinacy criterion. 5. Therefore, the truss is statically determinate. Answer: A

Explanation

In structural mechanics, a perfect truss is defined as a stable framework that has just the requisite number of members to maintain its shape under loading without redundant internal constraints, making it statically determinate. For a 3D space truss with j = 5 joints, m = 3j - 6 = 3(5) - 6 = 9 members, which is statically determinate.

Why the other options are wrong

B) Indeterminate requires redundant members (m > 3j - 6). C) Mechanism requires insufficient members (m < 3j - 6). D) Partially constrained refers to external support boundary conditions.

Shortcut

Perfect truss = Just enough members to prevent collapse without redundancy = Statically determinate.

Common mistake

Confusing plane truss criteria (m = 2j - 3 = 7) with 3D space truss criteria (m = 3j - 6 = 9).