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Section 6.4 Method of Sections

The Method of Sections is a more targeted process than the Method of Joints, which is used to solve for the unknown forces within a limited number of members in a truss. The method involves cutting the truss into individual sections and analyzing each section as a separate rigid body. The advantage of the Method of Sections is that the only internal member forces exposed are those which you have cut through, the remaining internal forces are not exposed and thus ignored.

Using the Method of Sections.

First, determine if a truss can be modeled as a simple truss (see Identifying Simple Trusses above).

Identify and eliminate all zero-force members. The eliminate of zero-force members is not required but can minimize your computations, see Zero-Force Members above.

Next, take out your imaginary chain saw and evaluate various section cuts through the entire truss. These cuts should include some (or all) of the members you are asked to solve for.

Note that every cut member exposes the internal axial force which exists in that member. Hence if you cut three members, you’ll have three new unknowns to solve for. Exposing four (or more) members is not advised as you only have three equilibrium equations to solve for the exposed axial force unknown values.

Technically, the cut does not need to be a straight line, but often it is.

Figure 6.4.1.
  1. Solve for reactions (if needed). If your section free-body diagram will include reaction forces, go back to your full section free-body diagram and solve for the reactions you will need on your section free-body diagram.
  2. Draw your section free-body diagram:
  3. Always draw known forces in their known direction and value (whether external, reaction, or interaction) and make sure to include any applied and reaction force which are also applied to the portion of your truss remaining.
  4. Draw unknown forces in assumed directions and uniquely label them. A common practice for trusses is to assume that all unknown forces are in tension (or pulling away from the free-body diagram of the pin) and label them based on the member they represent (like \(F_{AB}\)).
  5. Write out and solve the force equilibrium equations for your section free-body diagram. If you assumed that all forces were tensile earlier, remember that negative answers indicate compressive forces in the members.
  6. If you have not solved for the required members with one section cut, then add a Method of Joints step or another Method of Sections step. Recall that is is possible to mix and match methods when necessary.