MOS

Welcome to the course, mechanics of solids.

So, as I told you in the introduction, that this course is very very fundamental and very

very conceptual and this is the basic course if you are doing civil engineering, mechanical

aerospace and so on.

So, if you do this kind of engineering basically this course will be the bread and butter.

So, everyday day to day life you have to use this course.

So, I mean for getting the idea of your actual engineering say materials or structures or

whatever you are considering in your studies, basically mechanics of solid will be the backbone

for that particular concept.

Well.

So, what is the objective?

So, objective of this course is this course is to serve as an introduction to mechanics

of deformable solid bodies.

The primary course objective is to equip the students with the tools necessary to solve

mechanics problems, which involves first static analysis of a component to find the internal

actions, forces and moments.

Second, determine stresses strains and deformation due to internal actions and third compare

them with known acceptable values ok So, this requires the familiarity with the

vocabulary of the subject skill of drawing free body diagrams.

So, free body diagram is a very important, say concept which will be discussed later

on when we will be progressing in this particular course.

So, you will see that without this free body diagram concept, it is very difficult to understand

the the mechanical system or the mechanics of a particular body.

So, and the understanding of the material behaviour under loads, so, it is expected

to improve your engineering design skills.

So, this is a grading policy, as I told you in the introduction slide that is, for homework

40 percent weightage is there and time to time your homework will be given, homework

assignment and for the final examination 60 percent weightage is there.

This is the brief course outline.

So, we will cover this, these things in this particular course, equilibrium of forces.

So, it includes force vectors, moment of force, resultants of coplanar forces system, free

body diagrams, equations of equilibrium, friction and frictional force on flat belts, method

of joints and sections for pin, jointed trusses, frames and machines.

Next is deformable bodies under axial load.

It includes uniaxial loading and elastic deformation, statically determinate and indeterminate problems

force method of analysis.

Next is state of stress.

It includes concept of stress.

Normal and shear stress, equilibrium of differential element, plane stress, stress on any arbitrary

plane that is nothing but the stress transformation.

Mohr’s circle, principal stresses and maximum in-plane shear stresses, absolute maximum

shear stress.

Next is state of strain.

It includes analysis of deformation and strain components plane strain and its transformation

Mohr’s circle and strain rosettes.

Next is, stress strain relationship and failure theories.

So, it includes tensile test and stress strain curve, elastic stress strain relationships,

thermal strains, generalized hooks law for plane stress problem, relation between elastic

moduli, criteria of initial yielding, distortional strain energy, von mises and tresca yield

theories.

Next is bending.

Say it includes bending moments and shear force.

Bending deformations, bending stresses normal as well as transverse.

Built up, that is composite members, deflection due to bending by double integrations and

method of superposition, statically indeterminate beams.

Next is torsion.

So, under this we will cover torsional deformation of circular shafts.

So, we will be restricting ourselves only to the circular shafts.

So, we will not be considering any rectangular or any other shape of shafts.

Torsional stress and angular twist, statically indeterminate torque loaded members.

Then coming to combined stresses, it includes thin walled pressure vessels stress caused

by combined axial flexural and torsional loadings.

Next is energy methods, it includes elastic strain energy, axial flexure and torsional,

complementary energy and castiglianos theorem.

Then finally, we will talk about stability.

So, it includes stability of equilibrium, elastic instability and buckling, column buckling

and Euler load.

So, this is the brief course outline.

Now we will look at the course plan how the course will move; however, this plan is very

very tentative.

Ok.

So, we will cover all the things, but it is, it is not necessary that we will stick to

the exact course plan, because it depends on how we will cover the course in the coming

weeks.

Ok.

So, this is a kind of tentative plan.

Ok

So, in first week we will cover, we will try to cover free body diagram with examples on

modelling of typical supports and joints, conditions for equilibrium in 3D and 2D friction

limiting and non limiting cases.

In week 2 we will try to cover force displacement relationship and geometric compatibility for

small deformations with illustrations through simple problems on axially loaded members

and thin walled pressure vessels.

In week 3 we will try to cover concept of stress at a point, plane stress case, transformations

of stresses at a point, principal stresses and Mohr’s circle.

In week 4, displacement field, concept of strain at a point, plane strain case, transformation

of strain at a point, principal strains and Mohr’s circle and finally, strain rosette.

In week 5, we will discussion of experimental results on 1D material behaviour concepts

of elasticity, plasticity, strain hardening failure, which will cover fracture as well

as yielding idealization of 1D stress strain curve generalized hooks law, with and without

thermal strains for isotropic materials, complete equations of elasticity.

Though we are talking about plasticity, but plasticity will be recovered I mean nominally

because we will mainly concentrate on the elastic analysis and elastic equilibrium.

So, when we will be talking about the failure criterion all, so little bit of plasticity

will be required, so, that will be covered depending on the requirement.

Then in week 6, we will cover force analysis.

That is, axial force, shear force, bending moment and twisting moment diagrams of slender

members.

Then week 7, we will try to cover torsion of circular shafts and thin walled tubes,

plastic analysis and rectangular shafts not to be discussed.

So, please try to understand, so we will it is, it is beyond the scope.

So, we are excluding this part from the syllabus.

Ok So, a moment in week 8, we will cover moment

curvature relationship for pure bending of beams with symmetric cross section, bending

stress, shear stress, shear center and plastic analysis not to be discussed.

In week 9, we will cover cases of combined stresses, concept of strain energy, yield

criteria.

We think we will try to cover deflection due to bending, integration of the moment curvature

relationship for simple boundary conditions and method of superposition.

In week 11, we will we will look at strain energy and complementary strain energy for

simple structural elements.

Those under axial load shear force bending moment and torsion.

Castiglianos theorem, for deflection analysis and in turn indeterminate problems.

In week 12 we will talk about concept of elastic instability, introduction to column buckling,

Euler’s formula, post buckling behaviour not to be discussed.

So, this is, this is the brief course plan so; however, we may or may not stick to the

actual course plan, because it depends how we will move in the course.

So however, we will cover these things whatever we are talking about at this moment we will

cover all the things, but not exactly in the in this sequence.

Ok.

Sometimes we will, we will jump from one one part to another part and then we will come

back again something like that, but all the things will be covered in this particular

course.

So, these are the reference books.

So, we will look at different books and we will try to pick up the concept from different

books.

So, first one is Crandall, Dahl, Lardner and Siva Kumar, 2012.

The name of the book is an introduction of the mechanics of solids, third edition, Tata

McGraw Hill.

The second one is shames engineering mechanics statics and dynamics, fourth edition prentice

hall of India.

Then Meriam and Krieg 2004 the name of the book is engineering mechanics statics, fifth

edition, John Wiley and Sons.

Then next is Popov, 1998 the name of the book is engineering mechanics of solids, Pearson.

So, these are the books, we will be, we will be covering, we will be, will be looking at

these at this different books for our course.

Now there are few announcements regarding the homework.

Because the homework will be given on the regular basis, and you have to solve those

homework and you have to submit the homework assignment.

The homework problems will be assigned regularly to help you deepen understanding of the course

material covered.

You are strongly advised to attempt them.

They will be graded and solution will be posted on the course website.

Please remember the reason you are asked to do homework, which is, so that you can learn

to reason and solve these types of problems yourself.

Late submission will not be graded.

Ok.

Well, so with this brief introduction now we can we can exactly start our course.

So, first we will talk about these things, as we have planned tentatively.

First one is free body diagram with examples on modelling of typical supports and joints,

conditions for equilibrium in 3D and 2D friction: limiting and non limiting cases.

So, let us go to the board because this course is very very fundamental.

So, I, I prefer to do the whole course on the blackboard, so that you can also observe

as I move on.

So, now what is mechanics?

basically we are talking about so much mechanics of solids mechanics, I mean some time you

will be coming across the mechanics of fluids and all those things what do we do you mean

by mechanics right.

So, mechanics is nothing, but, but the science of forces and motions.

Ok.

So, mechanics is nothing, but the science of forces and motions.

So, any any material in the, I mean any solid material you are considering in the in the

universe.

So, that material if you are applying, some external forces as well as moments on that

particular material or the particular say body system, and if you are expecting some

movements, ok or the motions then that physics whatever you are getting from that whole system

to understand that physics basically you need to know mechanics.

So, this is by and large is the definition of mechanics.

Now, what do you mean by applied mechanics.

So, applied mechanics, is the science

of applying the principles of mechanics to systems of practical interest in order

to first understand their behaviour

and second to develop rational.

And the second is, to develop rational rules for their design.

Ok.

So, this is your applied mechanics.

So, basically the mechanics as I told you to understand how the forces will behave and

how the forces will cause some motion.

Ok.

So, that is nothing, but that physics is basically your mechanics, as you have seen from your

10 plus 2 also in tenth standard also.

So, that is called the mechanics part of physics.

Now, what do you mean by applied mechanics?

So, applied mechanics is the science of applying the principles of mechanics.

So, mechanics cannot go beyond some principles.

So, you have some principles, some rules of the game.

So, you cannot violate that.

So, applied mechanics is a science of applying the principles of mechanics, to systems of

practical interest, in order to understand their behaviour ok and the second one is to

develop rational rules for their design.

Ok.

So, these are 2 fundamental things ok.

So, now what is the principle of mechanics?

Now coming to the principle of mechanics, so what are the different things we need to

know to understand the mechanics of a system?

Ok.

First one as I told you, first one is force and the second one is motion ok, so force

and motion.

So these 2 things basic I mean if you consider any system ok and if the system is under some

force it will try to impart or try to show some motion, ok so these 2 things - one is

your cause another one is your effect something like that.

So, these 2 things we will we will collectively ok talking about the mechanics of the problem.

So, these are 2 things which you need to know to analyse any system any mechanical system

ok, for which for which actually you, you are, you want to get the solution.

So, now this motion if you talk about.

Ok.

So, this motion, it involves this motion involves geometry and time.

So, if you talk about the motion.

So, it it includes 2 things.

One thing is geometry and another thing is time ok.

So now, so, 2 different types of movements you generally expect, suppose here I am applying

some force in some system ok I will expect 2 different types of movements.

One, one is that the whole system is moving that is the displacement of the translation;

that means overall change in the position.

And another kind of movement we can expect that is the deformation; that means, the body

is not moving from or it is not changing the position, rather you are getting the deformation

right, to something like that if you if you talk about this paper.

So, if I want to experience some movement from this paper ok.

So, either it can change the position from this position to this position, this is another

one movement without any deformation or I can get this kind of movement that is, means;

that means, deformation is happening ok reduction in diameter or a larger in diameter or whatever.

So, these 2 things will conceal will constitute the movement.

So, you can have only one; that means, the body is moving from one position to another

position without any deformation.

So, that thing is called a rigid body movement, there is no deformation, the body is completely

considered as a rigid body.

Or you can have the deformation only; that means, the body is not moving.

Suppose if I am putting the force here the body is not moving, but rather maybe some

deformation is happening.

So, that kind of movement you can have or you can have both the things together: body

is changing the position as well as it is expressing the deformation.

So, these 2 things will will constitute the movement.

Now, if you want to analyse any mechanical system.

So, what are the things or what are the steps are involved in that analysis.

So if you want to analyse, analysis of mechanical system.

So, if you want to analyse any mechanical system.

Any whatever mechanical system we are talking about or we are we are seeing in day to day

life like your, if you want to analyse any building structure, if you want to a analyse

any bridge structure, if you want to analyse any machine equipments or any any, any kind

of machines, if you want to analyse the aircraft.

So, any mechanical system if you analyse, so this is this is as a whole you can you

can analyse a particular say a particular component of the aircraft, particular component

on the machine.

So, everything is a mechanical system.

So, if you want to analyse a mechanical system.

So, basically what are the steps involved there?

Study of forces the study of forces; that means, you want to, you want to know that

what are the forces, what are the externally applied forces are applied on the body, on

the system.

So, that is very very important.

First you you try to analyse or first first you try to get the information about the cause;

that means, what are the things are applied externally on the body.

So, that start study of forces, then, next one is study of motion and deformation.

Ok.

So, next stage will include the study of motion and deformation.

So, this is the cause because of these force you may expect some motion, as I told you

may express some motion or deformation in the system ok.

So, that you analyse and then the third one, third step is application of laws relating

the forces to the motion and deformation.

Ok.

So, this is your third step.

So, in the third step what we are looking at, we are looking at the application of laws,

I told you that mechanics cannot go beyond or cannot break any laws.

So, there are some laws and those laws are valid or those laws are important to analyse

any system ok.

So, application of laws relating the forces ok to the motion and deformation, so you study

in the first step you study forces the second step you study the motion or deformation;

that means, in one step you are you are observing where the cause, in the second step you are

observing the effect, and then you try to correlate or try to get a relation between

the cause and the effect right.

So, I will stop here today.

So, we will continue in the next class, I mean what exactly we will try to cover in

this particular course to analyse any mechanical system.

Thank you very much.