External and Internal Forces. Method of Sections

External forces act on a body from other bodies or physical fields. Within a loaded body, its parts interact with one another; this interaction is represented by internal forces.

Method of sections

To expose the internal interaction, the body is conceptually cut at the location of interest. Either side may then be removed — left or right — and the action of the removed part on the retained part is replaced by internal force and moment resultants at the cut.

Both choices describe the same internal interaction. Correct equilibrium equations therefore give consistent results whether the left or right portion is analyzed.

Internal resultants of a member

In a general spatial case, the resultant force and moment at a cross-section are resolved into components. Common notation includes axial force $N$, shear forces $Q$, torque $T$, and bending moments $M$. Which components are nonzero depends on the loading.

Using the method

After isolating a portion of the member, its internal resultants are found from equilibrium. These resultants are then used to determine stresses. For example, under centric axial tension or compression the primary internal resultant is $N$.

Physical meaning

An internal resultant represents the integrated effect of stresses over the entire cross-section. Stress describes how that interaction is distributed locally over the section.