6.3: Method of Joints
The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which assumes that the truss members are connected by frictionless pins. The forces at each joint can be determined by considering the equilibrium of the forces acting on that joint.
Since plane truss members are in the same plane, each joint is subjected to a coplanar and concurrent force system. To apply the method of joints, the first step is to identify all the joints in the truss and label them. Next, isolate and draw a free-body diagram of each joint, showing all the forces acting on that joint.
The pull and push forces exerted on the joint in the truss are known as tensile and compressive forces, respectively. The unknown member forces on the joint are always assumed to be in tension. To solve for the unknown forces, the forces acting on that joint in the horizontal and vertical directions are added, and the principle of equilibrium is applied. This principle states that the sum of all the forces in the horizontal and vertical directions must equal zero. By solving for the unknown forces, the forces on all members of the truss can be determined.
The method of joints is a powerful and effective technique for analyzing forces in structural trusses. By breaking down the truss into isolated joints and solving for the forces at each joint, structural engineers can ensure that their structures are safe and durable.
