# Trusses

A **truss** is an engineering structure that is made
entirely of **two force members**. In addition, statically
determinate trusses (trusses that can be analyzed completely using the
equilibrium equations), must be **independently rigid**.
This means that if the truss was separated from its connection points,
no one part would be able to move independently with respect to the rest
of the truss.

Trusses can be broken down further into **plane trusses**
and **space trusses**. A plane truss is a truss where all
members lie in a single plane. This means that plane trusses can
essentially be treated as two dimensional systems. Space trusses on the
other hand have members that are not limited to a single plane. This
means that space trusses need to be analyzed as a three dimensional
system.

## Analyzing Trusses

When we talk about analyzing a truss, we are usually looking to identify not only the external forces acting on the truss structure, but also the forces acting on each member internally in the truss. Because each member of the truss is a two force member, we simply need to identify the magnitude of the force on each member, and determine if each member is in tension or compression.

To determine these unknowns, we have two methods available: the
**method of joints**, and the **method of sections**.
Both will give the same results, but each through a different process.

The method of joints focuses on the joints, or the connection points where the members come together. We assume we have a pin at each of these points that we model as a particle, we draw out the free body diagram for each pin, and then write out the equilibrium equations for each pin. This will result in a large number of equilibrium equations that we can use to solve for a large number of unknown forces.

The method of sections involves pretending to spilt the truss into two or more different sections and them analyzing each section as a separate extended body in equilibrium. In this method we determine the appropriate sections, draw out free body diagrams for each section, and then write out the equilibrium equations for each section.

The method of joints is usually the easiest and fastest method for solving for all the unknown forces in a truss. The method of sections on the other hand is better suited to targeting and solving for the forces in just a few members without having to solve for all the unknowns. In addition, these methods can be combined if needed to best suit the goals of the problem solver.