Analysis of Trusses by the Method of Joints: Dismember the truss and create a freebodydiagram for each member and pin. The two forces exerted on each member areequal, have the same line of action, andopposite sense.RB. Forces exerted by a member on the pins orjoints at its ends are directed along the memberand equal and opposite.. Conditions of equilibrium on the pins provide2n equations for 2n unknowns. For a simpletruss.2n=m+3.MaysolveformmemberBforces and 3 reaction forces at the supports.BB.Conditionsforequilibriumforthe entiretrussprovide 3 additional equations which are notindependent of the pin equations.6
Analysis of Trusses by the Method of Joints • Dismember the truss and create a freebody diagram for each member and pin. • The two forces exerted on each member are equal, have the same line of action, and opposite sense. • Forces exerted by a member on the pins or joints at its ends are directed along the member and equal and opposite. • Conditions of equilibrium on the pins provide 2n equations for 2n unknowns. For a simple truss, 2n = m + 3. May solve for m member forces and 3 reaction forces at the supports. • Conditions for equilibrium for the entire truss provide 3 additional equations which are not independent of the pin equations. 6
Zero-force Members.Forces in opposite members intersecting inFAB1two straight lines at a joint are equal.FAC: The forces in two opposite members areFAEequal when a load is aligned with a thirdmember. The third member forceis equalFADCto the load (including zero load)FAC.Theforces intwo members connected at ajoint are equal if the members are alignedand zero otherwise.: Recognition of joints under special loadingconditions simplifies a truss analysis25kN150kNF25kNHREGC20kN7
Zero-force Members • Forces in opposite members intersecting in two straight lines at a joint are equal. • The forces in two opposite members are equal when a load is aligned with a third member. The third member force is equal to the load (including zero load). • The forces in two members connected at a joint are equal if the members are aligned and zero otherwise. • Recognition of joints under special loading conditions simplifies a truss analysis. 7
Sample ProblemSOLUTION:1000lb20001b. Based on a free-body diagram of the-12 ft-12ft-entire truss, solve the 3 equilibriumBACequations for the reactions at E and C8 ft+. Joint A is subjected to only two unknownDEmemberforces.Determinethesefromthejoint equilibrium requirements-12ft6ft6 ft:In succession,determineunknownmember forces at joints D, B, and E fromjoint equilibrium requirements.Using the method of joints, determinethe force in each member of the truss.: All member forces and support reactionsare known at joint C. However, the jointequilibrium requirements may be appliedtochecktheresults.8
Sample Problem Using the method of joints, determine the force in each member of the truss. SOLUTION: • Based on a free-body diagram of the entire truss, solve the 3 equilibrium equations for the reactions at E and C. • Joint A is subjected to only two unknown member forces. Determine these from the joint equilibrium requirements. • In succession, determine unknown member forces at joints D, B, and E from joint equilibrium requirements. • All member forces and support reactions are known at joint C. However, the joint equilibrium requirements may be applied to check the results. 8