The truss shown in Fig. 1 is loaded by an external force F. Determine the forces at the supports and in the members of the truss.

 The truss shown in Fig. 1 is loaded by an external force F. Determine the forces at the supports and in the members of the truss.

Figure. 1

Solution:

Fig.  represents a simple truss that is completely constrained against motion. Therefore, it is statically determinate. The members of the truss are numbered in the free-body diagram of the complete truss (Fig. 1b). Zero-force members are identified by inspection and marked with zeroes: member 4 (according to Rule 2), the members 5 and 9 (Rule 3) and the members 10 and 13 (Rule 1). To further reduce the number of unknown forces, we compute the support forces by applying the equilibrium conditions to the whole truss.

Fig. 1c shows the free-body diagrams of the joints. As previously stated, we assume that every member is subjected to tension. Accordingly, all of the corresponding arrows point away from the joints. Zero-force members are omitted in the free-body diagrams. Therefore, joint VII need not be considered. Applying the equilibrium conditions to each joint yields

These are 11 equations for the 8 unknown forces in the members and the 3 forces at the supports. Since the support forces have been computed in advance and are already known, the analysis is simplified, and three equations may be used as a check on the correctness of the results. Using the geometrical relations

It is useful to present the results in dimensionless form in a table, including negative signs:

The negative values for the members 1, 2, 6, 7 and 11 indicate that these members are under compression.