Making Section Cuts

Recall, for all plane truss structures, the following three conditions are assumed:

1. All members are in the same plane.
2. All loading is at the joints.
3. All joints are pinned (free rotation).

These conditions require all member forces to act in the direction of the member, and there are no moment loads in the truss members (assuming straight members).

In the previous Method of Joints, each joint was independently analyzed which resulted in numerous joint calculations. If only one member force is desired it does not make sense to solve for many joints. The Method of Sections is an alternative method to solve for interior member forces that is simpler than the Method of Joints.

In the Method of Sections, the truss is cut into two sections. The removed section is replace with unknown member forces acting in the direction of the cut member. They can be pointing in either direction, but generally, they are drawn away from the section to represent tension.

The unknown member forces at the section cut can be solved using the equilibrium equations, ΣF_x = 0, ΣF_y = 0, and ΣM = 0.

Since there are only three equilibrium equations, the truss section cut should be located where there are only three unknown member forces.

It was previously stated that all external loads on a truss must be at the joints. If there is load at a location that is not a joint, the load needs to be split and applied to the nearest joints.

Distributing the mid-span load to the adjacent joints is only an approximate solution so that the structure can be analyzed as a truss. If there is large mid-span loads, the structure should be analyzed as a frame with possible bending moments in the members. Frame analysis is beyond this course and is not addressed in statics courses.