Calculate the Force in Each Member of an Asymmetric Truss Using Method of Joints

A static force problem that appears in both physics and engineering courses.

An asymmetrical truss which is uneven from one side to the other is loaded off center and supported by a pin and a roller. Solve for the reaction forces on the truss as well as the force in each beam or member of the truss. Then determine whether each beam is in tension or compression.

The challenging aspect of this truss is solving for the reaction forces by the supports holding up the truss. The sum of all torque around any point on an object in equilibrium is zero. So looking at torques produced first around the pin we can determine the force by the roller, then by looking around the roller we can determine the force by the pin.

After determining the support forces we can then apply the method of joints to each joint on the truss to solve for the forces in each beam or member of the truss. This is done by effectively looking at each joint as a 2D free body diagram and working out all of the forces so that the sum of all forces in both the horizontal and vertical axes work out to be zero.

Trusses are a fundamental part of the study of static structures and static equilibrium. Truss Analysis comes up in most courses that deal with statics. This includes introductory physics courses such as high school physics, AP Physics 1, AP Physics C Mechanics. As well as introductory engineering courses such as PLTW Principles of Engineering (POE).

This problem also serves as the foundation for more advanced statics engineering courses that appear at a college level in fields such as civil engineering.