Stability and Determinacy of Trusses MCQ with answer and solution

Concept

For a plane truss, Ds = m + r − 2j. If Ds > 0, the truss is statically indeterminate.

Formula

D_s = m + r − 2j

Step-by-step solution

1. The degree of static indeterminacy is D_s = m + r − 2j. 2. Given m + r > 2j, so D_s > 0. 3. There are more unknowns than equilibrium equations. 4. So the frame is stable and statically indeterminate.

Explanation

The unknowns are the member forces (m) plus the reactions (r). Each joint gives 2 equations, so there are 2j equations. When there are more unknowns than equations, the frame is statically indeterminate, and it is taken as stable.

Why the other options are wrong

A: Determinate needs m + r = 2j. C: Unstable is the case when m + r < 2j. D: It is incomplete, because it does not say the frame is indeterminate.

Shortcut

= determinate, > indeterminate, < unstable.

Common mistake

Choosing only 'Stable' and forgetting that the frame is also indeterminate.