Truss Analysis MCQ with answer and solution

Concept

Identifying zero-force members at unloaded joints

Formula

ΣF_\perp = 0 -> F₃ = 0

Step-by-step solution

1. Consider a joint where three members meet with no applied load or support reaction. 2. If two of the members are collinear along an axis, they balance each other along that line. 3. Projecting equilibrium along the axis perpendicular to the collinear members yields F₃ × sin(θ) = 0. 4. Since the third member is not collinear (sin(θ) ≠ 0), its internal force F₃ must equal zero. Answer: C

Explanation

By standard equilibrium inspection rules, if three members meet at an unloaded joint where two members are collinear, resolving forces perpendicular to the collinear line reveals that the third non-collinear member must carry zero force.

Why the other options are wrong

A) Two non-collinear members at an unloaded joint identifies TWO zero-force members, not a single one. B) At a loaded joint with collinear members, forces balance the external load. D) Perpendicular orientation alone does not ensure zero force without joint equilibrium.

Shortcut

3 members at unloaded joint + 2 collinear = 3rd member is zero-force.

Common mistake

Overlooking that external loads or support reactions at the joint invalidate the zero-force condition.