I. Truss Analysis by Method of joints

1. If a truss is in equilibrium, then each of its joints must also be in equilibrium.
   
2. The method of joints consists of satisfying the equilibrium conditions for the forces exerted on the pin at each joint of the truss.
   
3. Truss members are all straight two-force members lying in the same plane.
   
4. The force system acting at each pin is coplanar and concurrent (intersecting)
   
5. Rotational or moment equilibrium is automatically satisfied at the joint, only need to satisfy ∑ Fx = 0, ∑ Fy = 0
   Draw the free-body diagram of a joint having at least one known force and at most two unknown forces (may need to first determine external reactions at the truss supports)
   
6. Establish the sense of the unknown forces
   
7. Always assume the unknown member forces acting on the joints free-body diagram to be in tension (pulling on the pin)
   
8. Assume what is believed to be the correct sense of an unknown member force
   
9. In both cases a negative value indicates that the sense chosen must be reversed
   
10. Orient the x and y axes such that the forces can be easily resolved into their x and y components
    
11. Apply ∑ Fx = 0 and ∑ Fy = 0 and solve for the unknown member forces and verify their correct sense
    
12. Continue to analyze each of the other joints, choosing ones having at most two unknowns and at least one known force
    
13. Members in compression push on the joint and members in tension pull on the joint
    
14. Mechanics of Materials and building codes are used to size the members once the forces are known