# Statics

## ðŸŸ¦Â  Welcome!

If you're on this page, you probably aspire to be an engineer one day! That's awesome! I'm thrilled to be a small part of your journey.

The fundamentals of Statics are based in mathematics. For this reason, this course can be taught in a very theoretical and abstract manner. Some professors prefer to teach it this way.

I am a visual/spatial thinker and prefer to teach this course with practical examples. This is why I have given my materials the title of Seeing Structures.Â

My 2D and 3D visualizations have been designed to help you bridge the abstraction of engineering theory with the practicality and purpose of real-world engineering practice. They also help scaffold spatial analysis skills and provide an example that you can emulate in order to develop your own ability to communicate graphically.

Please rest assured that despite my tendency to explain complex ideas with pictures, this is not a "watered-down" Statics course. It has simply been designed in a way that is intuitive, fast to learn, and student-centered. At least, that has been my intent.Â

Note that work on this site began in Summer 2023 and is currently in progress. Please be patient, it will take me a few years of revision to polish these materials so that they are the best they can possibly be!

## ðŸŸ¦Â  What is Statics?

To put it simply, Statics is the study of rigid bodies or assemblies of bodies (structures) that are stationary. They are not in motion; they are in static equilibrium.

Statics is the bridge between the theory you learned in Physics and the upper-level engineering courses shown in the diagram below.

## ðŸŸ¦Â  A Preliminary Example

To begin our journey, let's pretend that someone has locked us in a room full of random objects and asked us to create something that was both sculptural and symmetric.Â

No glue, tape, or other connectors were provided, so we built the sculpture by stacking objects on top of each other. Here is the design we came up with:

(You can ignore the note about constructing a free body diagram; we will do that later.)

Our structure is not in motion. It doesn't have a tendency to translate (move) up, nor down, nor east, south, north, or west. It also doesn't have a tendency to rotate or pivot. Intuitively, we observe that this structure is in static equilibrium.

All of a sudden, a large dog runs into the room! The dog runs forward, slams into one of the tables, and then runs away. Because of the impact force transferred from the dog to the table (which affects the books, which in turn affects the planks, which in turn jostles the beam), the bowling ball begins to roll and hits the floor. Obviously, the motion of the bowling ball is a dynamics problem: the bowling ball translates and rotates due to the force the dog applied into the system.

In Statics, we will only study systems in static equilibrium. You won't have to deal with any unruly dogs until you take Dynamics.

In Mechanics of Materials (sometimes called Solid Mechanics, Mechanics of Solids, or Mechanics of Deformable Bodies), you will study the internal workings of the bodies, as well as the way they change shape when loaded with force. For instance, the beam depicted above would slightly sag and curve under the weight of the bowling ball.Â

In Statics, we limit our study to what we will call rigid bodies. This means that we will not concern ourselves with how bodies deform (change shape) when forces are applied.

## ðŸŸ¦Â  How to navigate the Seeing Structures interactive models

By the way, that last image is a screenshot from an interactive model that you can access at this link. In fact, the screenshot above is actually a hyperlink to the same place. Please take a moment to learn how to use these models. We need to think in 3D in this class (visual-spatial thinking). The models will help you develop that important skill. We will have to switch back and forth between the reality of 3D and the practicality of 2D drawings. This particular model has both 3D and 2D views programmed in. Make sure that you are able to access the pre-programmed views:

Step 1: Click the link and allow time for the model to load.

Step 2: Click the "expand" arrow at the right side of the screen.

Step 3: Clicking "views" and navigating from each named view to the next. Depending on the complexity of the model and your internet speed, these may take a few seconds to load and display.

the expand arrow
the views button

## ðŸŸ¦Â  How does Statics link to my future studies?

Consider the image below. Student (a) is studying Statics. They have balanced an object on their index finger. The system is in static equilibrium as shown.Â

Student (b) is studying Mechanics of Materials. The system is still in static equilibrium, but this student is focusing on the curved shape of the deformed geometry, as the block sags (slightly) under its own weight.Â

Student (c) is studying Dynamics. They attempted to support the block off-center, but as this system is not in static equilibrium, the block falls to the ground. This student may be studying the position, velocity, and rotation of the block as a function of time. (Alternatively, perhaps this student is still working on mastering Statics.)

## ðŸŸ¦Â  Is Statics important to my major?

You may be majoring in a field in which Statics is incredibly important (e.g. Civil Engineering, Mechanical Engineering, and closely related fields). The fundamentals you'll learn in this course will be a critical foundation that will allow you to succeed in your upper-level courses.

But perhaps you don't fall into that category. Perhaps you're enrolled in a program that requires you to take Statics as a breadth topic (e.g. Environmental Engineering, Electrical Engineering, Chemical Engineering, etc.).Â

If you fall into that latter category, please don't discount this course. I have found that most students truly enjoy learning this material, regardless of their chosen major. In addition to Statics, here's what you'll get out of the course: better focus on being detail-oriented, increased sensitivity to units and signs, the useful notational tool called engineering notation, better engineering problem-solving skills, and an improved ability to communicate with graphics.