Perfect truss (perfect frame) criterion A planar framed structure (truss) is perfect if the number of its members m is _____ (2j − 3), where j is the number of joints.

Introduction / Context:In planar truss analysis, a “perfect” (or statically determinate and stable) truss has just enough members to maintain shape without redundancy. The classical relation is m = 2j − 3.

Given Data / Assumptions:

• Planar pin-jointed truss.
• No internal mechanisms; joints are ideal pins; members carry only axial force.
• External reactions provide overall stability.

Concept / Approach:The formula m = 2j − 3 comes from counting equations of equilibrium and unknowns for a planar pin-jointed truss with adequate external restraints. If m is less than this number, the frame is deficient (mechanism). If m exceeds, it is redundant (indeterminate by statics alone).

Step-by-Step Solution:

Verification / Alternative check:Example: A simple triangle truss has j = 3, m = 3. Formula gives m = 2*3 − 3 = 3, which fits the base case.

Why Other Options Are Wrong:

• Less than: Mechanism — insufficient members to prevent distortion.
• Greater than: Redundant — indeterminate using only statics.
• Either (b) or (c): Contradicts the exact equality needed for a perfect truss.

Common Pitfalls:Applying the formula to space trusses (different relation), or to frames with non-pinned joints and bending members where the count changes.

Final Answer:equal to