### Plane and Space Trusses

4.1 Assumptions for Analysis of Trusses 4.2 Arrangement of Members of Plane Trusses-Internal Stability 4.3 Equations of Condition for Plane Trusses 4.4 Static Determinacy, Indeterminacy, and Instability of Plane Trusses 4.5 Analysis of Plane Trusses by the Method of Joints 4.5.1 Plane Trusses by the Method of Joints Problems and solutions 4.6 Analysis of Plane Trusses by the Method of

### Space Trusses

Space trusses, because of their shape, arrangement of members, or applied loading, cannot be subdivided into plane trusses for the purposes of analysis and must, therefore, be analyzed as three-dimensional structures subjected to three-dimensional force systems. As stated in Section 4.1, to simplify the analysis of space trusses, it is assumed that the truss members are connected at their ends

### Complex Trusses

Trusses that can be classified neither as simple trusses nor as compound trusses are referred to as complex trusses. Two examples of complex trusses are shown in Fig. 4.27. From an analytical viewpoint, the main di¤erence between simple or compound trusses and complex trusses stems from the fact that the methods of joints and sections, as described previously, cannot be

### Compound Trusses Problems and Solutions

Example 4.10 Determine the force in each member of the compound truss shown in Fig. 4.25(a). Solution Static Determinacy The truss has 11 members and 7 joints and is supported by 3 reactions. Since m þ r ¼ 2j and the reactions and the members of the truss are properly arranged, it is statically determinate. The slopes of the inclined

### Analysis of Compound Trusses

Although the method of joints and the method of sections described in the preceding sections can be used individually for the analysis of compound trusses, the analysis of such trusses can sometimes be expedited by using a combination of the two methods. For some types of compound trusses, the sequential analysis of joints breaks down when a joint with two

### Plane Trusses by the Method of Sections Problems and Solutions

Example 4.7 Determine the forces in members CD;DG, and GH of the truss shown in Fig. 4.22(a) by the method of sections. Solution Section aa As shown in Fig. 4.22(a), a section aa is passed through the three members of interest, CD;DG, and GH, cutting the truss into two portions, ACGE and DHI. To avoid the calculation of support reactions,

### Analysis of Plane Trusses by the Method of Sections

The method of joints, presented in the preceding section, proves to be very efficient when forces in all the members of a truss are to be determined. However, if the forces in only certain members of a truss are desired, the method of joints may not prove to be ancient, because it may involve calculation of forces in several other

### Plane Trusses by the Method of Joints Problems and solutions

Example 4.3 Identify all zero-force members in the Fink roof truss subjected to an unbalanced snow load, as shown in Fig. 4.18. Solution It can be seen from the figure that at joint B, three members, AB;BC, and BJ, are connected, of which AB and BC are collinear and BJ is not. Since no external loads are applied at joint