# Method of Sections to Solve a Truss

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This Demonstration solves a truss using the method of sections, which involves "cutting" along several selected members and taking the sum of the forces, forces and moment about a point.

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Contributed by: Rachael L. Baumann (September 2017)

Additional contributions by: John L. Falconer

(University of Colorado Boulder, Department of Chemical and Biological Engineering)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The method of sections is used to calculate the forces in each member of the truss. This is done by making a "cut" along three selected members. First, calculate the reactions at the supports. Taking the sum of the moments at the left support:

.

Next do a force balance of the forces:

,

where and are the reaction forces, and and are the point load forces in the negative direction.

Begin solving for the forces of the members by making cuts. The order of the balances listed here is the order in which they should be solved. Force balances are done assuming we can figure out which members are under tension and which are under compression. A labeled truss is shown in Figure 1.

Cut 1, to the right of joint :

,

.

Cut 2, to the right of joints and :

,

,

.

Cut 3, to the right of joints and :

,

,

.

Cut 4, to the right of joints and :

,

,

.

Cut 5, to the right of joints and :

,

,

.

Cut 6, to the right of joints and :

,

.

Note that all the vertical members are zero members, which means they exert a force of 0 kN and are neither a tension nor a compression force; instead they are at rest.

Figure 1.

Reference

[1] SkyCiv Cloud Engineering Software. "Tutorial to Solve Truss by Method of Sections." (Aug 18, 2017) skyciv.com/tutorials/tutorial-to-solve-truss-by-method-of-sections.

## Permanent Citation