Zero-Force Member

A truss member that experiences no stress under loading conditions is called a zero-force member.

For a truss joint with two non-collinear members and no external load or support reaction, both members must be zero-force members.

A free-body diagram is drawn for this joint. The sum of the forces along the vertical direction equals zero, making force along BA zero. Using the equilibrium equation along the horizontal direction gives force along BC as zero.

For a joint with three members, including two collinear members, the third member is a zero-force member, provided no external load or support reaction is applied at this joint.

Again, drawing a free-body diagram and applying the static equilibrium conditions, proves that the force along CA is zero.

Consider a truss with a roller and pin support and an external load at joint E.

The joints with three members, including two collinear members, are identified. The zero-force condition at these joints implies FG, EH and FD are zero-force members.

However,  ED cannot be a zero-force member because of the external load.