Method of Joints | Analysis of Simple Trusses

Method of Joints
The free-body diagram of any joint is a concurrent force system in which the summation of moment will be of no help. Recall that only two equilibrium equations can be written

$\Sigma F_x = 0$   and   $\Sigma F_y = 0$


This means that to solve completely for the forces acting on a joint, we must select a joint with no more than two unknown forces involved. This can be started by selecting a joint acted on by only two members. We can assume any unknown member to be either tension or compression. If negative value is obtained, this means that the force is opposite in action to that of the assumed direction. Once the forces in one joint are determined, their effects on adjacent joints are known. We then continue solving on successive joints until all members have been found.