# Statics of Non-Concurrent Force Systems

Free-Body Diagram of a Rigid Body: Free-body diagrams play a crucial role in the statics of rigid bodies. A free-body diagram is a road map that enables one to identify all the unknown loads (forces and moments) prior to the formulation and solution of equilibrium equations. In this section, we provide some hints to simplify this task, and will look at some examples of free-body diagrams.

Hints in Drawing Free-Body Diagrams

1. Identify the member of interest, and separate (free, cut) it from the rest of the system at the supports and points of contact (joints) with other members.

2. Draw a simple sketch of the freed member, and show

- All the applied forces (including weight if specified) and couple moments.

- All the support reactions and contact or joint forces. Make sure the support reactions are consistent with the way the support would prevent translational or rotational movements of the member. Also keep in mind that contact or joint forces are shown whenever a member is separated from another member.

3. Replace the distributed force (if present) by its equivalent resultant force placed at the centroid of the distribution.

4. Look for two-force members in the system. If the member of interest shown in FBD is separated from a two-force member, then the corresponding contact force is along the straight line drawn between the ends of the two-force member.

Example 1

Example 2

Example 3