Engineering Statics: Open and Interactive

When analyzing structures we are dealing with multi-body systems and need to recall Newton’s 3rd Law, “For every action, there is an equal and opposite reaction.”

This law applies to multi-body systems wherever one body connects to another. At any interaction point, forces are transferred from one body to the interacting body as equal and opposite action-reaction pairs. These forces cancel out and are invisible when the structure is intact. Only when we cut through a member or joint in the isolation step of creating a free-body diagram, do we expose the interaction forces. When drawing free-body diagrams of the components of structures, it is critically important to represent these action-reaction pairs consistently. You may assume either direction for one, but the other must be equal and opposite.

For example, look at the members and joints in the truss below. Diagram (a) shows the truss members held together by pins at \(A\text{,}\) \(B\text{,}\) and \(C\text{.}\) The forces holding the parts together cancel and are not shown. In the ‘exploded’ view (b), the parts have been separated and the action-reaction pairs are exposed. Member \(AB\) is in tension, and the forces acting on it, also called \(AB\text{,}\) oppose each other and tend to stretch the member. These stretching forces are accompanied by equal and opposite forces, also called \(AB\) acting on pins \(A\) and \(B\text{.}\) Tensile forces \(BC\) and compressive forces \(CA\) behave similarly.