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Structural analysis (method of joints)


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Structural analysis (method of joints)

  1. 1. STRUCTURAL ANALYSISSimple TrussA truss is a structure composed of slender members joined together t their end points. The memberscommonly used in construction consist of wooded struts or metal bars. The joint connection are usuallyformed by bolting or welding the ends of the members to a common plate, called a gusset plate, (Figure1) or by simply passing a large bolt or pin through each member (Figure 2).Assumptions for DesignTo design both the members and the connections of a truss, it is first necessary to determine the forcedeveloped in each member when the truss is subjected to a given loading. In this regard, two importantassumptions will be made: (1) All loadings are applied at the joints. In most situations, such as for bridge and roof trusses, this assumption is true. Frequently in the force analysis the weight of the member is neglected since the forces supported by the members are usually large in comparison to their weight. (2) The members are joined together by smooth pins. In cases where bolted or welded joint connections are used, this assumption is satisfactory provided the center lines of joining members are concurrent.Two methods used for truss analysis a. Methods of joints b. Methods of sectionsTHE METHOD OF JOINTSIn order to analyze or design a truss, we must obtain the force in each of its members. If we were toconsider a free-body diagram of the entire truss, then the forces in the members would be internalforces, and they could not be obtained from an equilibrium analysis. Instead, if we consider theequilibrium of a joint of the truss then a member force becomes an external force on the joint’s free-body diagram, and the equations of equilibrium can be applied to obtain its magnitude. This forms thebasis for the method of joints.
  2. 2. Example 1:Determine the force in members GE, GC and BC of the truss shown in the figure. Indicate whether themembers are in tension or compression.SOLUTION:
  3. 3. ____________________________________________________
  4. 4. __________________________Example 2:Determine the force in members in BF, BG and AB, and state if the members are in tension orcompression.
  5. 5. SOLUTION:
  6. 6. Hence, reactions at A and G;