Solved Examples for Method of Joints for Truss Analysis

The theoretical basis of the method of joints for truss analysis has already been discussed in this article '3 methods for truss analysis'. " 2 examples will be presented in this this article to clarify those concepts further.

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 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.

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 1-6.

Figure. 2

Solution:

We free the joints V and IV by passing imaginary cuts through the bars, and we assume that the members 1-6 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

These articles might also be useful:
☞Analysis of 2D Truss Structure in SAP 2000

☞3 Methods for Truss Analysis

☞Statically determinate trusses