Method of Sections

It sometimes is needed to calculate the value of a force that is not on the side of the structure, then it might be easier to use the Method of Sections. This is a method to calculate member forces by making a virtual cut somewhere in the structure and then introducing member forces. It is used that every smaller section of the structure also needs to be in equilibrium.

Figure 1. A virtual cut in a truss structure to expose new forces

Figure 2. The free body diagram for the part obtained from the virtual cut, with the pivot point P being the middle of the structure

Example

Let's say $T_1$ at point 1 is needed to be calculated with the length of the members being $l = 1$ and the angles inside the triangle equal to $α = 60°$. First, a virtual cut is made as seen in Figure 1. In figure 5 the free body diagram of this section is shown.

A straightforward way of calculating $T_1$ in this case is by using the 3rd equilibrium equation involving moments. If point P is used as a pivot, there only is 1 unknown apparent in the moment equation. Since $T_2$ and $T_3$ don't have any effects on the moment around P.

Since $T_1$ is less than 0, this member is in compression.

Now is shown how to calculate forces in a truss structure by using the Method of Sections. Most things about truss structures are explained. In the next article is explained how to easily find a zero force member in truss structures.