What scenario leads to a zero-force member when three members frame into a truss joint?

A zero-force member in a truss can be identified using certain criteria related to the arrangement of the members at a joint. In the scenario where two members are aligned and there are no external forces acting at that joint, the third member, which is not aligned with the other two, will be a zero-force member. This is because, with no external load applied and two members acting in the same direction (collinear), there is no requirement for force to be transmitted through the third member.

In a truss analysis, if a joint has only two non-collinear members and no external load or support applied directly at the joint, the third member does not need to carry any force, thus making it a zero-force member. Understanding this concept helps engineers in simplifying the analysis of truss systems by identifying members that do not contribute to the overall structural integrity under specific loading conditions.