Which condition defines two non-collinear members as zero-force members?

When considering the conditions under which two non-collinear members are identified as zero-force members in a structural framework, the scenario where there are no external forces or reactions acting on the joint is indeed a defining characteristic. In this context, if a joint has two non-collinear members connected to it and there are no external loads or support reactions applied at that joint, those members will not carry any load; hence, they are classified as zero-force members.

This principle is grounded in the equilibrium of structures. For a joint to remain in equilibrium, the sum of forces must equal zero. If there are no external influences, the only forces present are those transmitted through the members connected to the joint. Consequently, both members must be zero-force members because no load can be equilibrated through them.

Other potential conditions such as requiring both members to carry equal loads, being internal to the frame, or utilizing a scenario involving bending at the joint do not necessarily dictate the status of zero-force members. These conditions may apply to different contexts of structural behavior but do not establish the same clear criteria as the absence of external forces. Thus, the first condition provides the clearest and most fundamental reason for classifying the two non-collinear members as zero-force members.