**Section 5
CVGS Bridge Project
Theoretical Background Material**

**Equilibrium of Rigid Bodies**

The notes in this section refer to the material in Appendix A.

Equations 4.5, 4.6, and 4.7 refer to the equations of equilibrium for a two-dimensional structure. These are used in sample problem 4.2 on a simple truss that will be supported like the one in this project (fixed at B in two directions, fixed at A in one direction). See Figure 4.1 in Appendix A also.

Ignore Section 4.5 since you want to stay away from statically indeterminate reactions (more unknowns than equations to solve for them).

**Analysis of Structures**

The bridge will be of a simple truss design (see Section 6.3). A truss is defined in Section 6.2 and, in our case, the members are assumed to be pinned together even though they will be welded (glued) together. Several typical trusses are shown in Figure 6.5. Remember, simple trusses should only be used and the following equation will help you determine if the structure is a simple truss:

m = 2n - 3

m = number of members (Popsicle sticks)

n = number of glue joints

Section 6.4 explains how the forces in each member are calculated. Sample problem 6.1 determines the force in each member of a simple truss using the method of joints calculations described in Section 6.4.

Other methods can be used to calculate member forces, such as:

Maxwell Diagrams Section 6.7

Method of Sections Section 6.8

Section 6.9 deals with combining simple trusses into one compound truss. These compound trusses (Figure 6.17 a,b) are statically determinate and the equation m = 2n - 3 holds. Compound trusses shown in Figure 6.18 are over-rigid and are statically indeterminate. Do not use these types of trusses.

Sample problems 6.3 and 6.4 use the method of sections to calculate forces in members.