Case 1: Pin-Pin
The pin supports restrain movement of member B and resist ALL the forces acting on adjacent members. Therefore, member B is a zero force member.
Case 2: Two Member Joint
Members A and D are two non-parallel members connected at joint 2, which has no applied force or support reaction. Therefore, BOTH members A and D are zero force members.
With the elimination of member D, joint 4 is only shared between two members: C and E. Since there is a force parallel to member E, the other non-parallel member, C, is a zero force member.
Case 3: Three Member Joint
Does not apply.
Simplified Truss
Knowing that the internal forces in members A, B, C, D, and E are zero, we can eliminate them from the picture to simplify truss analysis. As shown below, we only need to find the internal force of member E, which is conveniently the same as the force applied to it at joint 4.
StructNotes 