Stability and Determinacy of Trusses MCQ with answer and solution

Concept

Static Instability of Pin-Jointed Frames

Formula

m + r < 2j

Step-by-step solution

1. Count the total constraints: sum of members (m) and support reactions (r). 2. Count the total equilibrium equations available for 'j' joints: 2j. 3. Compare both values: if m + r \< 2j, the total constraints are less than the required equations, making the frame statically unstable.

Explanation

For a 2D pin-jointed frame, 2j equations are required to maintain static equilibrium across all joints. When the total number of members and reactions (m + r) is less than 2j, the frame lacks enough constraints to support loads, making it structurally unstable.

Shortcut

Remember: - Less (< 2j): Unstable / Deficient (too few members to hold up) - Equal (= 2j): Just Enough / Stable & Determinate - Greater (> 2j): Over-supported / Indeterminate

Common mistake

Students often confuse the condition for instability (m + r < 2j) with static indeterminacy (m + r > 2j) or static determinacy (m + r = 2j), or forget to include support reactions (r) in the equilibrium condition.