Basic knowledge of Statics (Summary) - part I

This note is just summary from my notebook of engineering statics. It is not included all about the statics but it can be enough to remind some people who are majored in engineering. Even students studied about the statics but it is easy to forget about what you and I studied in the University. Therefore, I decided to take a note to remind not only myself about what I learned but also for you who is reading this post. Please kindly note that this is just brief summary of statics. If you want to know more details, just check out your text book or visit book store to learn more about statics. Then let me start and hope you enjoy about this.

Someone explained about the definition of engineers in comparison with scientists.
"The scientist describes what is. The engineer creates what never was."
Like this, engineers are not having an effort to find out "why it comes", but have a capability to make new things by collecting some of information and knowledge what you learn or what the people know. This is the reason why the engineering keep developing and should know about the basic engineerings.

As same as other statics engineering books, this note will show as follows;

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I. Force (part I)
II. Particle Equilibrium (part I)
III. Moments (part I)
IV. Equilibrium Equations and Equibalent Systems (part II)
V. Equilibrium of Rigid Bodies (part II)
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I. Force

Let's start about the Force.
What is the Force? There are various explanation of what is Force. But here, I would make a note the Force is 'Any interaction which tends to change the motion of an object'. In other words, "Push" or "Pull" on a body.
Easy to understand about the Force, people use two method : Scalar and Vector.
Scalar is a quantity that can multiply vectors in the context of vector spaces. Simply, it has no associated direction.
Vector has magnitude and direction.

   i) Scalar

• A quantity that can multiply vectors in the context of vector spaces
• A quantity that is independent of specific class of coordinate systems

   ii) Vector

• An element of the real coordinate space

II. Particle Equilibrium

From the Statics, Particle Equilibrium is a balance of forces on a particle. Thus, the net force is zero condition and the acceleration is also 0m/s2. People says this is from Newton's 1st Law of Motion. However, the equilibrium does not mean the particle is at rest condition.

To remind you about Newton's 1st Law of Motion, here is a short note for your reference.

Newton's 1st Law of Motion

• When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.
• A particle originally at rest, or moving in a straight line with constant velocity, will remain in that state when not subjected to an unbalanced force.

III. Moments

The moment of force acting is often called Torque. It is tendency of a Force to cause rotation about a point or axis of vector coordinate. In other words, it can be calculated involving a distance and a Force. For the calculation, it can be expressed by Varignon's Theorem which is called the principle of Moments.

Varignon's Theorem

• The moment of any force is equal to the algebraic sum of the moments of the components of that force.

 cf )

Here is a sample practice by using above theorem.
This is the way to find out the moment from O point. Bold letters are the vector scale.

Sol )

mO = rOA × F

rOA = 2 𝑖 + 3 𝑗

    AF = 4 𝑖 - 3 𝑗

    |AF| = 5

    eAF = AF / |AF|

          = 0.8 𝑖 - 0.6 𝑗

    F = |F| eAF 

       = 20 ( 0.8 𝑖 - 0.6 𝑗 )

       = 16 𝑖 - 12 𝑗 

    mO = rOA × F

          = ( 2 𝑖 + 3 𝑗 ) × ( 16 𝑖 - 12 𝑗 )

          = - 72 𝑘 in∙lb

          = 72 in∙lb ↩

We can calculate the moment not only at the center of the body but also any other point on a line or Axis. The equation is as below. This is called a moment of a force about a Line/Axis.

Mp = r × F
P : any point on line/axis
û : the vector in the direction of the Line/Axis


As we have seen above the Particle Equilibrium, we can also think about the equilibrium of moment. It is called a Moment of a Couple. This has a tendency of a pair of forces to cause rotation of a body. With regards to this couple moment, it has also connection with force of a couple. We can simply think about this force of a couple has equal in magnitude with opposite directions of the force. In addition, the force of couple is acting along with parallel line of actions. Below picture can help your understanding about the equivalent force system as well as moment of a couple.