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Section 6.5 Method of Sections

The method of sections is used to solve for the unknown forces within specific members of a truss without solving for them all. The method involves dividing the truss into sections by cutting through the selected members and analyzing the section as a 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.

Subsection 6.5.1 Procedure

The procedure to solve for unknown forces using the method of sections is

  1. Determine if a truss can be modeled as a simple truss.

  2. Identify and eliminate all zero-force members. Removing zero-force members is not required but may eliminate unnecessary computations.

  3. Solve for the external reactions, if necessary. Reactions will be necessary if the reaction forces act on the section of the truss you choose to solve below.

  4. Use your imaginary chain saw to cut the truss into two pieces by cutting through some or all of the members you are interested in. The cut does not need to be a straight line.

    Every cut member exposes an unknown internal force, so if you cut three members you’ll expose three unknowns. Exposing more than three members is not advised because you create more unknowns than available equilibrium equations.

  5. Select the easier of the two halves of the truss and draw its free-body diagram.

    • Include all applied and reaction forces acting on the section, and show known forces acting in their known directions.

    • Draw unknown forces in assumed directions and label them. A common practice is to assume that all unknown forces are in tension and label them based on the endpoints of the member they represent.

  6. Write out and solve the equilibrium equations for your chosen section. If you assumed that unknown forces were tensile, negative answers indicate compression.

  7. If you have not found all the required forces with one section cut, repeat the process using another imaginary cut or proceed with the method of joints if it is more convenient.

The interactive below demonstrates the method of sections. The internal forces in the truss members are exposed by cutting through the truss at three locations. The known loads are shown in red, and the unknown reactions \(F_x\text{,}\) \(A_x\) and \(A_y\text{,}\) and unknown member forces are shown in blue. All members are assumed to be in tension. In this situation, it is not necessary to find the reactions if the section to the right of the cut is selected.

Figure 6.5.1. Method of sections demonstration.