In most truss-like structures, the bars are held together by being bolted or welded to gusset plates or simply gussets (Fig. a). Since the axial forces in members at a common joint form a concurrent force system, it is permissible to idealize the truss joints as simple pin connections (Fig. b).

A designer can specify different properties for the individual members of the truss depending on the loads they carry. However, an individual truss member is typically uniform in cross-sectional shape and size and is made of a single homogeneous material.

A two-force member is one that is loaded only at two points along its length. A truss member is, therefore, a two-force member as it is loaded only at its ends and not anywhere else along its length. Equilibrium of forces and moments requires that the forces at the two ends of a truss member be of equal magnitude, collinear, and in opposite direction. If any of these conditions is violated, then equilibrium cannot be satisfied. In Fig. a the two forces are of equal magnitude and in opposite direction, but they are not collinear. This is wrong as it violates the moment equilibrium. The force diagram in Fig. b is correct as the two forces are of equal magnitude, opposite direction and collinear.

The supports keep the truss stationary. A support exerts a reaction force on the truss in any direction along which movement is restrained.

Truss members provide the "load path" between the external loads and the supports. The load path can be identified by determining the internal axial force in each truss member. For a given truss structure, the load path depends on the locations and directions of the external forces as well as the support condition.

The easiest way to distinguish a stable truss is to remember the triangular building block. A truss that violates this rule will be unstable.

The number one reason for having redundant members is safety. One must think of what happens to the truss if a member were to fail. In a statically determinate truss, failure in one member equals failure of the whole truss. Therefore, redundant members are introduced in an effort to design a damage tolerant structure.

As for the second part of the question, we would need to use additional equations besides those of equilibrium to analyze such trusses. The additional equations come from compatibility requirements at the joints, and is a subject addressed in the Mechanics of Materials course.

The easiest way to deal with this problem is to draw a preliminary free-body diagram with all the member forces shown in tension. Then solve for the desired member forces using the equations of equilibrium. If the solution gives a negative value for an internal force, then its true direction is opposite to that shown in the free body diagram, which in this case would mean the member is in compression as opposed to tension. Once the magnitudes and directions of all internal forces are determined, then the correct free body diagram can be drawn.

For a planar or a 2-D truss, we only have two equilibrium equations to analyze a joint. Therefore, we must select a joint with no more than two unknown forces acting on it.