Method of joint is a structural analysis method to determine the internal forces of members in a truss. This method is derived based on the equilibrium conditions at joints. It is basically a special case of equilibrium of concurent (intersecting) forces. In this case rotational or moment equilibrium is readily satisfied at the joint. Therefore in the method of joint for plane truss there are only two equilibrium equations required:
Procedure for method of joints:
- Select a joint having at least one known force and at most two unknown forces (because we have only two equilibrium equations). If the joint is located at the support, we may need to first determine external reactions at the truss supports.
- Draw the free-body diagram (FBD) for the selected joint. Make sure that all known and unknown forces are accounted for. For the unknown forces, the direction of the forces need to be assumed. My recommendation is to always assume that the unknown forces are in tension. Negative value from the analysis means that the actual force direction is reverse and the member is in compression.
- Orient the x and y axes so that the forces can be easily resolved into their x and y components.
- Apply the equilibrium equations and solve for the unknown member forces and check the their directions.
- Continue the same process to another joint until all internal member forces in a truss structure are solved.
As you can see, the method of joints is straight forward and not difficult. You just need to be smart in selecting the sequence of joints need to be solved because the maximum unknown forces that can be solved using this method is two. Thus sometimes method of joints cannot be applied for a particular joint because it has more than two unknow forces. In this case normally we solve it by first solving its neighborhood joints.
Thus the method of joints is basically a method to determine the internal forces in the members of truss structures by satisfying the equilibrium conditions of forces at each joint of the truss.