Method of Joints

Method of joints

The method of joints is a method to calculate internal member forces, by isolating a joint, as seen in figure 1 and 2, and introducing forces that act on the joint, after which the equilibrium equations can be used to calculate the unknown forces.

Figure 1. A free body diagram of a small truss structure

Figure 2. The free body diagram for the most left point, A, of the truss structure from Figure 1

Example

Let's say that we want to calculate $T_1$ and $T_2$ with the angle α of the triangle being 60° in terms of the weight $W$. We can easily do that using the equilibrium equations and the method of joints. We first formulate the equilibrium equations for this particular case:

We know have 2 equations and 2 unknowns, so we can solve for both unknowns:

Thus $T_1 = -0.58W$ and $T_2 = 0.29W$, where $T_1$ is in compression since its value is less than 0 and $T_2$ is in tension since its value is more than 0.

Now is shown how to calculate forces in a truss by hand using the Method of Joints. See the next article to learn how to calculate these forces by using the Method of Sections.