Determine the forces in all bars of the truss. Hint: If you have trouble computing bar for...

Determine the forces in all bars of the truss. Hint: If you have trouble computing bar forces, review K truss analysis in Example 4.6.

Example 4.6:

Using the method of sections, compute the forces in bars BC and JC of the K truss in Figure 4.17a:

Figure 4.17: (a) K truss; (b) free body to the left of section 1-1 used to evaluate F_BC; (c) free body used to compute F_JC; (d) bar forces.

Solution

Since any vertical section passing through the panel of a K truss cuts four bars, it is not possible to compute bar forces by the method of sections because the number of unknowns exceeds the number of equations of statics. Since no moment center exists through which three of the bar forces pass, not even a partial solution is possible using a standard vertical section. As we illustrate in this example, it is possible to analyze a K truss by using two sections in sequence, the first of which is a special section curving around an interior joint.

To compute the force in bar BC, we pass section 1-1 through the truss in Figure 4.17a. The free body to the left of the section is shown in Figure 4.17b. Summing moments about the bottom joint G gives

To compute F_JC, we pass section 2-2 through the panel and consider again the free body to the left (Figure 4.17c). Since the force in bar BC has been evaluated, the three unknown bar forces can be determined by the equations of statics. Use a moment center at F. Extend the force in bar JC to point C and break into rectangular components.

NOTE. The K truss can also be analyzed by the method of joints by starting from an outside joint such as A or H. The results of this analysis are shown in Figure 4.17d. The K bracing is typically used in deep trusses to reduce the length of the diagonal members. As you can see from the results in Figure 4.17d, the shear in a panel divides equally between the top and bottom diagonals. One diagonal carries compression, and the other carries tension.