Method of Sections

The power of the Method of Sections lies in its ability to find forces in members located in the middle of a complex truss without first having to solve for the forces in all the preceding members, as required by the Method of Joints. The key is to choose a section cut that passes through no more than three members whose forces are unknown. This is because there are only three independent static equilibrium equations available for a 2D rigid body.

Once the section is cut, one of the two resulting pieces of the truss is chosen for analysis. All external forces (loads and support reactions) acting on that piece are shown, along with the unknown internal forces of the cut members. These internal forces are typically assumed to be in tension (pulling on the joint). A negative result in the calculation simply indicates that the member is actually in compression (pushing on the joint). The moment equilibrium equation, \(\Sigma M_A=0\), is particularly powerful. By summing moments about a point where two of the three unknown forces intersect, the third unknown force can often be solved for with a single equation.