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Zero force member for truss

In a truss system, some members are not carrying any force. This called zero-force member. This member may added to increase truss stability. Identifying these members will simplify the process of analyzing truss. the determination of zero force member can be done by inspecting of truss joints, and there are two cases

  • if we check the joint c for truss shown in figure 1, this joint has no external load, and two members are connected to this joint at a right angle. if we sum force in y-direction Σfy=0, we get FCD=0, similarly in x-direction FCB=0. For joint A, no external load applied to this joint. If we sum forces in y-direction Σfy=0, we get FAB=0. Similarly, in x-direction FAE=0.

Figure 1

  Figure 1-a 

Figure 1-b

  • A quick look at this truss. We can notice joint c and joint d with no external load. Inspecting joint C will be a bit difficult because 4 members are connected to joint c. Starting with joint D. member DF is perpendicular to member DE and CD. if we sum the forces in the y-direction. As showing in figure 2-a. We will get FDF=0. For joint F, axial force on member FD=0, therefore if we sum the force in the y-direction, the force component of member FD will be zero. As a result, the force in member FC equals zero because there are no other forces in the y-direction. For joint C there is one zero force member CF, other members we can't determine if it is zero force or no. 

In summary for a truss joint with two non-collinear(not at the same line) members only with no external force. Those members are zero force member as in joint c for truss in figure 1. for a joint with three members only. Given that two collinear members. The third member will be zero force member as shown for joint d for the truss in figure 2. identifying zero force member will save the time and effort required to analyze a given truss. Also, it will simplify the analysis by eliminating zero force members.
Figure 2

                     Figure 2-a                                                                   Figure 2-b


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