Chapter 1 Introduction to Statics
Engineering Statics is the gateway into engineering mechanics, which is the application of Newtonian physics to design and analyze objects, systems, and structures with respect to motion, deformation, and failure. In addition to learning the subject itself, you will also develop skills in the art and practice of problem solving and mathematical modeling, skills that will benefit you throughout your engineering career.
The subject is called “statics” because it is concerned with particles and rigid bodies that are in equilibrium, and these will usually be stationary, i.e. static.
The chapters in this book are:
- Introduction to Statics— an overview of statics and an introduction to units and problem solving.
- Forces and Other Vectors— basic principles and mathematical operations on force and position vectors.
- Equilibrium of Particles— an introduction to equilibrium and problem solving.
- Moments and Static Equivalence— the rotational tendency of forces, and simplification of force systems.
- Rigid Body Equilibrium— balance of forces and moments for single rigid bodies.
- Equilibrium of Structures— balance of forces and moments on interconnected systems of rigid bodies.
- Centroids and Centers of Gravity— an important geometric property of shapes and rigid bodies.
- Internal Forces— forces and moments within beams and other rigid bodies.
- Friction— equilibrium of bodies subject to friction.
- Moments of Inertia— an important property of geometric shapes used in many applications.
Your statics course may not cover all of these topics, or may move through them in a different order.
Below are two examples of the types of problems you’ll learn to solve in statics. Notice that each can be described with a picture and problem statement, a free-body diagram, and equations of equilibrium.
Equilibrium of a particle: A \(\lb{140}\) person walks across a slackline stretched between two trees. If angles \(\alpha\) and \(\theta\) are known, find the tension in each end of the slackline.
![A woman walking across a slackline stretched between two trees. Her arms are outstretched for balance.](external/images/slackline.png)
Person’s point of contact to slackline:
\begin{gather*}
\Sigma F_x = 0\\
-T_1 \cos \alpha + T_2 \cos \theta = 0\\
\\
\Sigma F_y = 0\\
T_1 \sin \alpha +T_2 \sin \theta -W = 0
\end{gather*}
Equilibrium of a rigid body: Given the interaction forces at point \(C\) on the upper arm of the excavator, find the internal axial force, shear force, and bending moment at point \(D\text{.}\)
![A backhoe with a boom which is connected to the car body and cab. A boom cylinder is connected to the boom and cab to actuate (move) the boom. At the end of the boom, the stick (arm) is connected, the end of which is the bucket. The arm cylinder connects the boom arm to the stick arm to change the angle between the two.](external/images/crane01.png)
Section cut FBD:
\begin{gather*}
\Sigma F_x = 0\\
-C_x + F_x - V_x - N_x = 0\\
\\
\Sigma F_y = 0\\
-C_y - F_y - V_y + N_y = 0\\
\\
\Sigma M_D = 0\\
+(d_y)C_x + (d_x)C_y - M_D = 0
\end{gather*}
The knowledge and skills gained in Statics will be used in your other engineering courses, in particular in Dynamics, Mechanics of Solids (also called Strength or Mechanics of Materials), and in Fluid Mechanics. Statics will be a foundation of your engineering career.
![A schematic showing the relationship between subjects take by engineers. Calculus and Physics are the foundation to be able to learn engineering statics. The "Engineering Mechanics Trilogy" is encircled, and the relationships described between the three subjects - statics, dynamics, and solids. Statics is depicted as "no movement". Dynamics is depicted as "Hold on. Everything is moving." Solids is depicted as "it’s what inside that counts". After learning statics, you will move to Solids (mechanics of materials) by learning about shear and moment, frames, and virtual work. Also from the fundamentals of statics you will move to Dynamics, where you will learn more about friction and machines. A common thread between all three subjects is includes equilibrium, moment of inertia, and centroids. Additional content that you’ll add to your Statics knowledge in Solids includes: stress and strain, material properties, and torsion. Additional content you’ll add to your Statics knowledge in Dynamics is the concept that the sum of the forces is equal to mass multiplied by acceleration and that this is NOT equal to zero, as it is in Statics. You will also learn about motion and accelerations.](external/images/mindmap.png)