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Frames and Trusses Example

Easy DifficultyFE Statics

Identify zero-force members in a simple truss using joint equilibrium and geometry.

Concept

In a truss, members are two-force members (force along the member). At a joint, equilibrium requires \sum F_{x} = 0 and \sum F_{y} = 0 . A zero-force member carries no load; it can often be identified by inspection: e.g. if two members meet at a joint with no external load and are not collinear, then the third member (if any) at that joint may be zero-force; or if two members are collinear and no external load, the third is zero-force. \sum F_{x} = 0, \sum F_{y} = 0 at each joint If 2 members at a joint and no external load, both are zero-force (or equal)

In a planar truss, joint C has three members: CA (horizontal to the left), CB (vertical down), and CD (horizontal to the right). No external load acts at C. Find: Which member(s), if any, are zero-force? (Assume CA and CD are collinear along the horizontal.)

Joint C: members CA, CB, CD; CA and CD collinear (horizontal); CB vertical No external load at C

Resolve forces at C. If CA and CD are collinear (same line of action) and CB is perpendicular to them, then \sum F_{y} = 0 gives force in CB = 0 (since CA and CD have no y-component). So member CB is zero-force. \sum F_{x} = 0, \sum F_{y} = 0 at each joint

Member CB is a zero-force member. Members CA and CD can carry axial force (equal and opposite if no other loads at C) to satisfy \sum F_{x} = 0 .

Truss: 2-force members; joint equilibrium \sum F = 0