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4-2 GENERAL PRINCIPLES
4-2-1 Triangulation
A truss is an assemblage of inpidual linear elements arranged in a triangle or combination of triangles to form a rigid framework that cannot be deformed by the application of external forces without deformation of one or more of its members. The inpidual elements are typically assumed to be joined at their intersections with pinned connections (see Sections 2-4-1 and 3-3-2).Members are customarily arranged so that all loads and reactions occur only at these intersections.
The primary principle underlying the use of the truss as a load-carrying structure is that arranging elements into a triangular configuration results in a stable shape. Consider the two protected structures shown in Figure 4-l(b) and (c). Application of a load to the structure shown in Figure 4-l(b) will cause the massive deformation indicated. This is an unstable structure ,which forms a collapse mechanism under external loading. A structure of this type may be deformed without a change in length of any inpidual member. The triangulated configuration of members shown in Figure 4-l(c) clearly could not deform or collapse in a similar manner. This configuration is thus stable. Any deformations that occur in this stable structure are relatively minor and are associated with small changes in member length caused by forces generated in the members by the external load. Similarly, the angle formed between any two members remains relatively unchanged under load in a stable configuration of this type. This is in marked contrast to the large angle changes which occur between members in an unstable configuration of elements [see Figure 4-l(b)]. The external force causes forces to be developed in members of the stable triangulated structure. As will be explained in detail in Section 4-3-2, the forces developed are either purely tensile or purely compressive. Bending is neither present nor can it be developed as long as external loads are applied at nodal points.
Since a basic triangle of members is a stable form, it follows that any structure made of an assembly of triangulated members is also a rigid, stable structure. This idea is the principle underlying the viability and usefulness of the truss in building, since larger rigid forms of any geometry can be created by the aggregation of smaller triangular units. Again, the effect of external loads is to produce a state of either_pure tension or compression in the inpidual members of the assembly. For common trusses with vertically acting loads, compressive forces are usually developed in upper chord members and tensile forces in lower chord members. Either type of force may develop in an interstitial member, although there is often an alternating pattern of tensile and compressive forces present.
It is extremely important that trusses be loaded only with concentrated loads that act at joints for truss members to develop only tensile or compressive members. If loads are applied directly onto truss members themselves, bending stresses will also develop in the loaded members in addition to the basic tensile or compressive stresses already present, with the consequence that member design is greatly complicated and the overall efficiency of the truss is reduced.
4-2-2 Member Forces: Qualitative Analyses
As discussed in following sections, the nature of the forces in the members of any truss can be determined through application of the basic equations of equilibrium. For some simple truss configurations , however , the basic sense (tension, compression, zero) of the forces in many members can be determined by less involved techniques which may prove useful in visualizing how certain trusses carry external loads.