Method of Joints. Method of Joints. Method of Joints. Method of Joints. Method of Joints. Method of Joints. CIVL 3121 Trusses - Method of Joints 1/5

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1 IVL 3121 Trusses - 1/5 If a truss is in equilibrium, then each of its joints must be in equilibrium. The method of joints consists of satisfying the equilibrium equations for forces acting on each joint. Recall, that the line of action of a force acting on a joint is determined by the geometry of the truss member. The line of action is formed by connecting the two ends of each member with a straight line. x y Since direction of the force is known, the remaining unknown is the magnitude of the force. Joint Joint Verticals Upper chord members Tension orce Joint Joint iagonals Lower chord members ompression orce gusset plate weld Upper chord in compression Idealized joint members connected by a frictionless pin Lower chord in tension This is a Pratt truss

2 IVL 3121 Trusses - 2/5 Upper chord in compression 1. If possible, determine the support reactions Lower chord in tension 2. raw the free body diagram for each joint. In general, assume all the force member reactions are tension (this is not a rule, however, it is helpful in keeping track of tension and compression members). This is a Howe truss 3. Write the equations of equilibrium for each joint, x y 4. If possible, begin solving the equilibrium equations at a joint where only two unknown reactions exist. Work your way from joint to joint, selecting the new joint using the criterion of two unknown reactions. 5. Solve the joint equations of equilibrium simultaneously, typically using a computer or an advanced calculator. xample - onsider the following truss xample - onsider the following truss irst, determine the support reactions for the truss irst, determine the support reactions for the truss M () () y y = x y y y y = - x y y x x x = - y y

3 IVL 3121 Trusses - 3/5 The equations of equilibrium for Joint The equations of equilibrium for Joint x = x cos 45 = lb. y = The forces in the truss can be summarized as: = (T) = 77.2 lb. () = (T) Problem etermine the force in each member of the truss Problem etermine the force in each member of the truss 4 ft ft. 4 ft. Problem etermine the force in each member of the truss Truss analysis may be simplified by determining members with no loading or zero-force. These members may provide stability or be useful if the loading changes. Zero-force members may be determined by inspection of the joints

4 IVL 3121 Trusses - 4/5 ase 1: If two members are connected at a joint and there is no external force applied to the joint y 1 y sin 1 1 = ase 2: If three members are connected at a joint and there is no external force applied to the joint and two of the members are colinear y 1 x 1cos 2 2 = x x y sin 1 1 = etermine the force in each member of the truss shown etermine the force in each member of the truss shown Using ase 2 and Using ase 1 and Using ase 1 and etermine the force in each member of the truss shown The remaining non-zero forces can be found using the method of joints The equations of equilibrium for Joint 4 4 x 5 5 = y 5 5 = lb. = lb. ()

5 IVL 3121 Trusses - 5/5 nd of Trusses - Part 2 ny questions?