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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:

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 is in each end of the slackline.

A woman  walking across a slackline stretched between two trees. Her arms are outstretched for balance.
A standard unit circle is used to describe the angles of vectors in all problems in this text. "Down" is used to indicate that the force acts towards the ground (toward the gravitational center of the earth, or 270 degrees on the unit circle), and "up" is used to indicate that a force acts at 180 degrees from "down" (90 degrees on a unit circle). Similarly, right indicates that the force acts towards zero degrees on the unit circle, and left indicates that a force acts towards 180 degrees on a unit circle.

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.

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_x + 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.
Figure 1.0.1. Map of how Statics builds upon the prerequisites of Calculus and Physics and then informs the later courses of Mechanics of Solids and Dynamics.