Example 1
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. 1a represents a simple truss that is completely constrained against motion. Therefore, it is statically determinate. The members of the truss are numbered in the freebody diagram of the complete truss (Fig. 1b). Zeroforce 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 freebody 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. Zeroforce members are omitted in the freebody 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.
Example 2
Fig. 2 shows a spatial truss loaded by two external forces F at the joints IV and V. Compute the forces in the members 16.

Solution:
We free the joints V and IV by passing imaginary cuts through the bars, and we assume that the members 16 are in tension. The vector equations of equilibrium for these joints are given by
We free the joints V and IV by passing imaginary cuts through the bars, and we assume that the members 16 are in tension. The vector equations of equilibrium for these joints are given by
The initially unknown unit vectors can be determined from the vectors connecting adjacent joints, e.g., for e_{(V/VI)} we obtain
Similarly, the other unit vectors are
Introducing these into the two vector equations we get the six scalar equations
Their solution yields the forces
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