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One way of determining the sense of the force in a truss member is to visualize the probable deformed shape of the structure as it world develop if the member considered were imagined to be removed. The nature of force in the member can then be predicted on the basis of an analysis of its role in preventing the deformation visualized.
Consider the diagonals shown in truss A in Figure 4-2(a). If the diagonals were imagined removed, the assembly would dramatically deform, as illustrated in Figure 4-2(b), since it is a non triangulated configuration. In order for the diagonals too keep the type of deformation shown from occurring, it is evident that the left and right diagonals must prevent points B-F and points B-D,
(a) Basic truss assemblies
(b) The senses of the forces in the diagonals can be determined by first imagining them to be removed and then ascertaining their role in preventing the probable type of truss deformation that would occur. Thus, a diagonal placed between B and F in truss A would have to be in tension because its role is to prevent B and D from drawing apart in the manner indicated.
(c) Final force distribution in trusses:
C, compression: T, tension
(d) A "cable" or "arch" analogy can also be used to determine the senses of the forces in different members. In the truss to the left, member FBD is imagined to be a "cable" and is obviously in tension. Other members serve roles related to maintaining the equilibrium of this basic "cable" configuration.
Figure 4-2 Forces in truss members : the senses of the forces in some simple truss configurations can be determined through intuitive approaches . More complex trusses require quantitative approaches.
(a) Basic cable" unit: the diagonal members are obviously in tension
(b) A simple truss configuration can be formed by placing a horizontal member between the ends of the cable. The horizontal member is in compression since it resists the inwardly directed cable thrusts.
(c) The same configuration can be raised vertically by end compression members.
(d) A more complex truss form can be generated by imaging the entire assembly shown in (c) to be carried by another cable member. Another horizontal compression element is then needed to resist the cable thrusts.
(e) The same process can be repeated to form even more complex trusses. Note that the forces in the vertical and diagonal members increase away from the middle of the truss since increased portions of the external loading are carried. Member sizes could be designed to increase accordingly.
(f) The total force present in the upper chord is greatest at mid span, where the "inpidual" top chords are actually combined into one member. Chord forces decrease toward either end of the truss. The same is true for the lower tension chord.
FIGURE 4-3 Cable analogy in truss analysis: many complex truss forms can be imagined to be composed of a series of simpler basic cable units. If the directions of the diagonals were all reversed, an arch analogy could be used to analyze the structure. This analogy approach, however, is useful for only a few limited truss forms.
respectively, from drawing apart. Consequently diagonals placed between these points would be pulled upon. Hence, tension forces would develop in the diagonal members. The diagonals shown in truss B in Figure 4-2 must be in a state of compression since their function is to keep points A-E and C-E from drawing closer together. With respect to member BE in both trusses, it is fairly easy to imagine what would happen to points B and E if member BE were removed. In truss A, points B and E would have a tendency to draw together, hence compressive forces develop in any member placed between these two points. In truss B, however, removal of member BE leads to no change in the gross shape of the structure (since it remains a stable triangulated configuration), hence the member serves no direct role for this loading. It is a zero-force member. Note that members AF FE, ED, and DC in truss B could also be removed without altering the basic stability of the remainder of the configuration, and hence are also zero-force members. This is obviously not true for the same members in truss A. Final forces in both truss A and truss B are illustrated in Figure 4-2(c).