10/8/08 7:29 PM4/2. Plane Trusses (Reading content)Page 1 of 5http://edugen.wiley.com/edugen/shared/resource/view_resource.uni?id=rsd15908014/2 Plane TrussesA framework composed of members joined at their ends to form a rigid structure is called a truss. Bridges, roof supports,derricks, and other such structures are common examples of trusses. Structural members commonly used are I-beams,channels, angles, bars, and special shapes which are fastened together at their ends by welding, riveted connections, orlarge bolts or pins. When the members of the truss lie essentially in a single plane, the truss is called a plane truss.For bridges and similar structures, plane trusses are commonly utilized in pairs with one truss assembly placed on eachside of the structure. A section of a typical bridge structure is shown in Fig. 4/1. The combined weight of the roadwayand vehicles is transferred to the longitudinal stringers, then to the cross beams, and finally, with the weights of thestringers and cross beams accounted for, to the upper joints of the two plane trusses which form the vertical sides of thestructure. A simplified model of the truss structure is indicated at the left side of the illustration; the forces L representthe joint loadings.Figure 4/1 Several examples of commonly used trusses which can be analyzed as plane trusses are shown in Fig. 4/2.10/8/08 7:29 PM4/2. Plane Trusses (Reading content)Page 2 of 5http://edugen.wiley.com/edugen/shared/resource/view_resource.uni?id=rsd1590801Figure 4/2 Simple TrussesThe basic element of a plane truss is the triangle. Three bars joined by pins at their ends, Fig. 4/3a, constitute a rigidframe. The term rigid is used to mean noncollapsible and also to mean that deformation of the members due to inducedinternal strains is negligible. On the other hand, four or more bars pin-jointed to form a polygon of as many sidesconstitute a nonrigid frame. We can make the nonrigid frame in Fig. 4/3b rigid, or stable, by adding a diagonal barjoining A and D or B and C and thereby forming two triangles. We can extend the structure by adding additional units oftwo end-connected bars, such as DE and CE or AF and DF, Fig. 4/3c, which are pinned to two fixed joints. In this waythe entire structure will remain rigid.10/8/08 7:29 PM4/2. Plane Trusses (Reading content)Page 3 of 5http://edugen.wiley.com/edugen/shared/resource/view_resource.uni?id=rsd1590801Figure 4/3 Structures built from a basic triangle in the manner described are known as simple trusses. When more members arepresent than are needed to prevent collapse, the truss is statically indeterminate. A statically indeterminate truss cannot beanalyzed by the equations of equilibrium alone. Additional members or supports which are not necessary for maintainingthe equilibrium configuration are called redundant.To design a truss we must first determine the forces in the various members and then select appropriate sizes andstructural shapes to withstand the forces. Several assumptions are made in the force analysis of simple trusses. First, weassume all members to be two-force members. A two-force member is one in equilibrium under the action of two forcesonly, as defined in general terms with Fig. 3/4 in Art. 3/3. Each member of a truss is normally a straight link joining thetwo points of application of force. The two forces are applied at the ends of the member and are necessarily equal,opposite, and collinear for equilibrium.10/8/08 7:29 PM4/2. Plane Trusses (Reading content)Page 4 of 5http://edugen.wiley.com/edugen/shared/resource/view_resource.uni?id=rsd1590801The member may be in tension or compression, as shown in Fig. 4/4. When we represent the equilibrium of a portion ofa two-force member, the tension T or compression C acting on the cut section is the same for all sections. We assumehere that the weight of the member is small compared with the force it supports. If it is not, or if we must account forthe small effect of the weight, we can replace the weight W of the member by two forces, each W/2 if the member isuniform, with one force acting at each end of the member. These forces, in effect, are treated as loads externally appliedto the pin connections. Accounting for the weight of a member in this way gives the correct result for the averagetension or compression along the member but will not account for the effect of bending of the member.Figure 4/4 Truss Connections and SupportsWhen welded or riveted connections are used to join structural members, we may usually assume that the connection is apin joint if the centerlines of the members are concurrent at the joint as in Fig. 4/5.Figure 4/5 We also assume in the analysis of simple trusses that all external forces are applied at the pin connections. Thiscondition is satisfied in most trusses. In bridge trusses the deck is usually laid on cross beams which are supported at the10/8/08 7:29 PM4/2. Plane Trusses (Reading content)Page 5 of 5http://edugen.wiley.com/edugen/shared/resource/view_resource.uni?id=rsd1590801condition is satisfied in most trusses. In bridge trusses the deck is usually laid on cross beams which are supported at thejoints, as shown in Fig. 4/1.For large trusses, a roller, rocker, or some kind of slip joint is used at one of the supports to provide for expansion andcontraction due to temperature changes and for deformation from applied loads. Trusses and frames in which no suchprovision is made are statically indeterminate, as explained in Art. 3/3. Figure 3/1 shows examples of such joints.Two methods for the force analysis of simple trusses will be given. Each method will be explained for the simple trussshown in Fig. 4/6a. The free-body diagram of the truss as a whole is shown in Fig. 4/6b. The external reactions areusually determined first, by applying the equilibrium equations to the truss as a whole. Then the force analysis of theremainder of the truss is performed.Figure 4/6 Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.10/8/08 7:31 PM4/3. Method of Joints (Reading content)Page 1 of 19http://edugen.wiley.com/edugen/shared/resource/view_resource.uni?id=rsd15908024/3 Method of JointsThis method for finding the forces in the members of a truss consists of satisfying the conditions of equilibrium for theforces acting on the connecting pin of each joint. The method therefore deals with the equilibrium of concurrent forces,and only two independent equilibrium equations are involved.We