1. The problem is to understand and apply the method of joints to analyze trusses. 2. The method of joints involves isolating each joint in a truss and applying the equilibrium equations: $$\sum F_x = 0 \quad \text{and} \quad \sum F_y = 0$$ These equations state that the sum of all horizontal and vertical forces at a joint must be zero for the structure to be in equilibrium. 3. Important rules: - Forces in members are either tension (pulling away from the joint) or compression (pushing toward the joint). - Start analyzing joints where there are at most two unknown forces. 4. Steps to solve: - Draw a free-body diagram of the joint. - Resolve forces into horizontal and vertical components. - Apply equilibrium equations to solve for unknown forces. 5. Example: Suppose a joint has two members and an external load. Set up equations: $$\sum F_x = 0: F_{member1,x} + F_{member2,x} + F_{external,x} = 0$$ $$\sum F_y = 0: F_{member1,y} + F_{member2,y} + F_{external,y} = 0$$ 6. Solve these simultaneous equations to find the forces in the members. This method is repeated joint by joint until all member forces are found.