Trusses are support members that are joined together at the ends. The function of a truss is to transmit loads to a support joint. In this section, we will analyze a simplified version of planar trusses called simple trusses, which consist of two-force members connected by frictionless joints/pins.

- All loading is applied at the joints.
- The weight of the truss is negligible.

Because of these assumptions, all trusses are *two force members*, with the forces on the truss acting along the axis of the member.

A two force member is a rigid body that has two forces (no moments) acting on it in two locations, say \(A\) and \(B\). Equilibrium of the two-force member implies

- \(|F_A| = |F_B|\)
- \( \vec{F_A} \) and \( \vec{F_B} \) act along the same line of action.

- Two noncolinear members share a pin with no support or external forces (Zero force member example, left)
- Two colinear forces with a third noncolinear force on a pin (zero force member example, right)

These rules will help us simplify trusses and solve for the internal forces in the desired members.

Drawing free-body diagrams on trusses is simple. As mentioned in the beginning, we will choose the entire truss as our system and draw the free-body diagram to determine the reaction forces on pinned/roller joints. Note we will need more equations and free-body diagrams on individual truss members to fully determine the reaction forces. See statics reference pages on how that is done. The following is a diagram showcasing eliminating zero-force members as well as the free-body diagram on the truss.

Stage: 0

- Draw a free-body diagram for the entire truss and solve for the external reaction forces and moments at the supports
- Draw a free-body diagram of a joint with at least 1 known force and at most two unknown forces
- Use the equations of equilibrium for the joint to solve for the unknown forces
- Repeat steps 2 and 3 to find the forces in the trusses you are interested in.

*Note:* Remember that truss members that are in compression "push back" on the pin joints, and truss members that are in tension "pull" on the pin joints.