# Background knowledge¶

In this page we will go through introductory bending theory, as typically covered in an introductory statics course. We will start by a quick overview of the required knowledge, and then derive our analysis from basic principles.

Our starting point will be the fact that for a body to be at rest, the **vector sum** of all external forces \(\mathbf{F_i}\) and moments \(\mathbf{M_i}\) acting on it must be zero.

Furthermore, for a system to be at rest, each of its components need to be at rest.
This means that Eq. (1) must be satisfied **for each** component in our system.

Note that \(\mathbf{F_{1C}} = \mathbf{-F_{2C}}\), according to the *action and reaction principle*.
If you are still not 100% comfortable with the action and reaction principle, you should review that before proceeding.
As a self-test, the concept presented in this educational video should be completely obvious to you.

So far, we have only thought about reaction forces as applied *externally* to one or more rigid bodies.
In other words, each rigid body has been considered to be fully contained in a single subsystem.
However, Eq. (1) can tell us much more than that if we lift that restriction.
This equation applies to every arbitrary subset of a body, and not only to full bodies.
We are going to exploit this to a larger extent in the next section.