# Concepts from Timoshenko Book of Mechanics

#### pamichel

Hi everyone,

I just thought that it might be useful for everyone if we go through the concepts from the book of mechanics by Mr. Timoshenko. Its a great book. Some people from this forum advised me to refer this book for mechanics. I find it very useful. But I would like to write about the concepts I find interesting in the book. It will of course help me to review my knowledge, in turn it might help amateurs also. Not to mention, everyone (no matter how much knowledgeable he is) needs to revise his concepts. There would not be a better way to do so through this thread. Please note that this is a discussion thing and ANYONE is invited to discuss/comment/critic in this thread. I would try to update this thread as I read the book. As people in this forum are active, I am sure I will receive good cooperation from them. The thing is due to my work, I will be able to update only wtice or thrice a week.

Regards,
Pami.

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#### PerennialII

Gold Member
.... Haven't taken a look at that classic in a while, I'm in .

Staff Emeritus
Gold Member
Best of luck !

#### pamichel

CONCURRENT FORCES IN A PLANE” is the name of the first chapter, which is appropriate. The other cases may be parallel forces in a plane; non-conconcurrent and non-parallel forces in a plane; all types of forces in space. These becomes the consequent chapters in the book. The advance is logical. Obviosuly these chapters are pacakaged in one part; Part 1 of the book, named Statics.

No points for guessing the first defination we come across is that of statics. Just thinking regarding the litteral meaning of the word, we get – state of bodies at rest or that of not in motion. Common sense will tell us that bodies at rest are those bodies that have achieved equilibrium after they have been acted by external forces. In this way the author states (rather logically as we derived), that statics deals with the conditions of equilibrium of bodies acted upon by forces.

One thing important to be noted here that in the Statics part of the book, the author will exclusively deal with equilibrium of bodies. He will invariably discuss with us the prevalent methods to find out the system of forces, identify them and analyse to reach the ultimate condition of that body – equlibrium. The author will discuss the ‘tricks of trade’ on how to evolve a method of thinking by which we can easily analyse the equlibrium condition of a body. I need not say, the key word in Statics is equilibrium.

The other key words we will come across in statics part are force and bodies. What kind of bodies are we here dealing with? Rigid Bodies . At this point of time, we cannot directly jump to complex situations – so we simplify the work by analysing the rigid bodies – those which do not deform at all! The author then moves on to define – strength of materials – That part of study which deals with internal deformation of a body – in other words non- rigid bodies. At this point all we want to know is about the force. How to analyse a force, how to represent a force, how equlibrium is achieved by forces. Yes, force is he next key word of statics. What will happen to the body? This question will be answered in Strength of materials. We need not worry about that now.

Key words : Equilibrium, force and rigid bodies.

Always remember this – Only three things are required to define a force.
1. Magnitude of that force. (100lb; 300lb; whatever)
2. Point of application of that force.
3. Its direction.

Suspend a ball to a string. What you will find is that due to gravity the ball if pulling the string down. Here string – rigid body and force – gravity. Magnitude of force? Obviously weight of the ball. Point of application of force? All over the ball or string. But for convinience (rememeber our aim here is to analyse force and equilibrium) we assume that this force to be concentrated at one single point; at such a point where the effect of it on equilibrium is not changed as in real situation. No doubt the point of application of force thus becomes a defining factor. (In case of our example of string and ball –the force of gravity is assumed to be concentrated at a point which is called centre of gravity of the ball. Whats centre of gravity? Tune in to Chapter : Parallel forces in space. Logically it is the resultant of all the forces acting all over the ball. The resultant force is acting along a point – centre of gravity (CG). Different bodies obviously will have different CG’s. It depends on size and shape of the body.

The last thing required to define the force is its direction or line of action. The reason is obvious. In ball-string example the direction of force is – vertically downward. Now remember we want to analyse this force. We have defined it. But for analysing we need to represent this force. How? Vector. Vector is straight line segment with arrow. Length of this line will indicate the magnitude of our force; arrow tells direction of force; and origin of the line segment will tell the point of application of the force. No doubt vector represents the force in all sense.

#### Pyrrhus

Homework Helper
Nice, but the title is misleading, you never wrote about concurrent forces in a plane! , This is basicly your Intro to any book of Mechanics for engineers (Statics, Dynamic, Material, etc...).

In my opinion when you mention Rigid bodies, which are the types of system in Statics, you should also mention the principle of transmisibility (traslation), which refers to moving a force vector along its line of action. Focus on the laws and principles for rigid bodies in statics, mention them and what they state. Also about center of gravity, the gravity field is an important factor, not just only the size and shape of the body, also if the body is homogeneous (uniform density).

So far, it was a good read. There are a lot of subjetc to cover, maybe when you exhaust the systems solved by Statics, i can talk a little about the ones not solved by statics, hyper static systems of degrees 1 and above.

Oh and are you going to cover some vector algebra? classical mechanics range of applicability?

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