Mathematics is the language of engineers. Engineering problems are often solved by applying mathematical principles to solve a problem. In this blog post, we will apply mathematics to determine the force in each member of a truss. This blog post will be broken into two parts: determining whether or not members are in tension or compression and finding the magnitude of forces for all members that are in tension or compression. Part One: Determining Whether or Not Members Are in Tension or Compression The first thing that we need to do is determine whether the members of the truss are under tension or compression. To do this, we will apply Hooke’s law and Newton’ third law. We’ll start by taking a look at an example truss as shown below and then applying these concepts to our problem. In the following figure, $$F$$ represents all points where forces were applied; while $$\mathbf{x}$$ represent nodes on which no force was applied (elements). The unknowns for this system are represented by $${{\bf x}}$$, with equations given between curly brackets ({ }). This equation