Welcome to the video lecture series of the

course on Strength of Materials. Well, I am

S.K.Bhattacharyya from the department of civil engineering at IIT Kharagpur. If you further

want to contact me on this particular e-mail address which is [email protected] Now, the

course on Strength of Materials is designed in such a way that it covers basic aspects

of the first course on the Strength of Materials. It is expected to cover the entire course

in 40 lessons which is of 1-hour duration module. And it is expected that the whole course is

covered in 10 modules. . In Module 1 we expect to complete the analysis

of stress and will have six lessons including the

lesson which we will be discussing today where we will be introducing the concept of stress. Module 2 will have around eight lessons, which

will be on the analysis of strain. Module 3 is the application of stress and

strain, which is on thin-walled pressure vessels and will

have three lessons. Module 4 is on torsion and will have four

lessons Module 5 is on bending of beams, which will

also have four lessons. .. Module 6 is on stresses in beams, which will

have also four lessons. Module 7 is on deflection of beams and will

have four lessons. Module 8 is on combined stresses and will

have three lessons. Module 9 is on stability of columns and will

have two lessons and Module 10 is on springs and will have two

lessons. So thereby, in these ten modules, we expect

to cover around 40 lessons in which the entire aspect

or the basic aspect of strength of material is going to be covered. . .Now this particular course on the engineering

mechanics, as we know, basically has three fundamental areas and they are;

The Statics The Dynamics and

The Mechanics of material. Now it is expected that you have already gone

through aspects of statics and dynamics. You have

noticed probably that statics and dynamics mainly concentrate on the study of external

effects on rigid bodies. We do not worry about the deformation of the

body, or deformation of the bodies is neglected. Whereas in mechanics of materials, we deal

with the study of bodies, which are subjected to externally applied loads. We look into the aspects of the internal effects

of the loads, which are acting externally and the deformation

characteristics of the structural member. So in

mechanics of materials, we are interested in these two aspects, internal effects of

the externally applied load and the deformations that are

caused within the body because of the externally applied load. And in fact, of these both, the aspects deformation

of the load and deformation play an important role while designing a member. . In fact we look into what we mean by design. When we try to arrive at a particular size

of the member, we need to know how much it deforms

and what is the effect of external load on that

member internally and these aspects are dealt in the particular subject, which we call mechanics

of the material. .. Now mechanics of material: in fact, when you

look into this, you will find they are called by

different names; they are called strength of materials or mechanics of deformable bodies

or mechanics of solids. Now whatever the name we may call the subject

as, basically, they contain the same information or they will give you

similar information, whether it is mechanics of

material or strength of materials or mechanics of deformable bodies or mechanics of solids;

they mean the same thing. Now here we have termed it as strength of

materials. . Now it is interesting that all branches of

engineering deal with some kind of physical systems. And these physical systems are composed of

the individual parts. When we look into different .systems from different engineering disciplines,

we will find that these physical systems are composed of different elements. And each individual element, when connected

together, gives the whole system. Now these systems of the individual units

are to be defined or assigned a definite physical size, and these elements

are fabricated from some materials. And we need to

know the characteristics of these materials or behavior of these materials. This helps to know the

whole structure of the system or whole physical system that are made of different elements

and can help us to understand whether they can

stand the external load. This is the objective of this

particular subject, wherein we look into what these elements are, what are the different

kinds of forces they are subjected to, and what is

the behavior of these elements against these external

loads. Now, if we talk about a building structure,

which you must have noticed in several places this

particular building structure is made of some kind of materials and also this particular

building structure is made of some individual elements

and all these elements, when combined together, they give this building a structural form. Now it is expected that this building structure

should perform some of the functions for which it

has been built or it has been designed. Now the

functions this particular structure is subjected to, different kinds of loadings, and these

loadings could be generated from the environmental

aspect such as for the effect of wind on the structure

or this particular structure may be subjected to earthquake forces. Now apart from these loadings,

which are expected to come on this building from the environmental or the surrounding

environment, it is also subjected to some kind of loads. For example, its own weight of the element:

there could be loads where human being will be

moving around and there could be loads, which are arising because of some operation of the

equipment inside the building. So these building structures as a whole and

the individual components, combining which we have formed

this whole structure, they are subjected to these

external loads. Now, we will have to know or we will have

to find out what are the effects of these external

loads on the building structure as a whole and in the individual units, in parts, what

are the effects of these loads? Now it may so happen that the flow of the

building on which the people are moving, if it deforms excessively then

there is a possibility that it may not be in a usable

form and as a result it may not be in a serviceable condition. So we will have to know whether

elements within this whole structure, whether they can withstand the external load of which

we just talked about, whether it can perform

that it does not have excessible [excessive?] deformation, whether the whole structure is

stable in its form because of such environmental loading or huge loading or wind loading or

earthquake. Whether the whole structure is in a stable

position or not? Now these are the answers we would like to

found out. And the area which

covers this is nothing but the Strength of Materials. .. Other than the building structure, there is

another interesting structure that is the bridge structure,

which is bridging the gap between the two sides or two ends of the river. Now as we have seen in

the case of the building structure we have loading from the environment, which we have

said from the wind or the earthquake. Now this particular structure, apart from

those loading, will be subjected to the loads because of the movement

of the water. The supporting structure, which is

holding this bridge, will have the loads because of the movement of water. So that is an

additional load coming on this structure; also there will be vehicular movement on this

particular supporting structure that also imparts particular

load on this structural form, and as you can see

the ones re-structured should withstand these loads without undergoing the excessive

deformation. Or the strength of the re-structure should

be such that it can withstand these external loads. Also, as you can see, this particular structure

is composed of different elements. So individually

these elements should be in a position to withstand all these loads. So again what I would like to

emphasize is that structures, when we consider they are fabricated or constructed out of

individual elements and combined together. So each individual element will be subjected

to some kind of forces which we will see as we

progress in the course and those members should be

in a position to withstand those forces safely without causing any failure of those elements. If

any individual element fails that may lead to the failure of the whole structure. .. Now let us look into the other areas of the

subject. For example, the spacecraft structure. These

are also subjected to different kinds of environmental loading apart from the loading which will

be generated for the movement of the spacecraft. And their structural body is made up of some

material, which should withstand the forces that it is subjected to and also one of the

requirements of these spacecraft is that the materials, which we use for the whole structure

of the body, should be lighter in nature. Now if we have to adhere to this particular

condition, that means we need to look into the

particular type of material, which can withstand safely the forces that will be generated in

this particular structural form. At the same time it should not contribute

too much weight to the structural form. And in one word, the whole structure should

be stable; it should be strong to withstand the external forces and also it

should not have excessive deformation in different positions. .. We look into this particular mechanical equipment,

which is used for testing purposes. Now this

mechanical equipment has several parts when the loads are applied for testing. . Now these

individual parts are to be assigned size in such a way that they do not undergo excessive

loading or in other words that the load distribution

should be such that the parts sizes should be such that

they can withstand the load which is coming when it is raised. So you can see whether building

structure or bridge structure or you talk about spacecrafts or you talk about the mechanical

components; even the electronic engineer when they use printed circuit boards wherein the

chips are mounted. The boards are to be strong enough to withstand

any environmental loading that is coming on that. It should be positioned properly, the support. It should not fail. Therefore, you see any physical system used

by any engineering discipline they are, they should

be such that they can withstand the external load coming on such structural form. So our

objective is to analyze these individual parts with which all these structural forms are

used. Structural forms, in general, could be building

structure, it could be bridge structure, it could be

spacecrafts or it could be mechanical components. So any of these structures, when they are

built with these individual components, now these

individual components are to be analyzed and see

that they satisfy the strength requirements, they satisfy the deformation requirements,

and they satisfy the stability requirements. This is what we look for in this particular

subject of strength of material. .. As we have discussed, appropriate sizing is

necessary for these parts to safely withstand the

imposed forces and at an optimal cost. Though we are not going to talk much about

the cost aspect of it, but when you talk about the

strong design we are concerned with both the safety and

cost. When we say safety, we mean that the elements

should be assigned the sizes in such a way that it can withstand any external loads. And these external loads could arise from

any of such conditions as we discussed. And many a time, it so happens that we give

larger size for a particular element and thereby, we satisfy

the strength or the deformation of the requirement. But

it may so happen that a smaller size of that could easily withstand that force without

causing much of harm in terms of strength or deformation. Naturally then, the smaller size will be more

economical than the larger size, which we can go

for though both are safe in terms of strength, size and deformation. Hence what we need to do is

not only that we should look into these strength, stability and deformation characteristics,

but we should look into the cost aspect also when

we look into the proper design. That is the job of the

designer. Well, for the time being, we will not look

into the cost aspect of it but we will be more

concerned with the aspect of strength, we will be more concerned with the aspect of

deformation and the aspect with the stability. And that is what we will be looking into in

this particular course. .. Hence, it is essential to study the behavior

of material from the strength and deformation point of

view, as well as the characterization of different kinds of forces, which cause different types

of stresses in the material. In fact, in a few minutes, we will look into

what really means by stress. So we are concerned about the strength, the

deformation and of course we would like to look into

the effects of different kinds of forces that this particular member will be subjected to,

that can cause different kinds of stresses in the material. . Now the subject, which deals with the analytical

deformation of the strength, the deformation characteristics which you call as stiffness

and stability of different members, is normally .designated as the Strength of Materials. I emphasize that we like to look into these

three aspects: one is strength another is stiffness, which

is nothing but the deformation characteristics of the

members and the stability of different elements, which we look into in this particular course

and which are the combination of these three. That means characterization of the strength,

the deformation, the stiffness and the stability. All we look into in this particular course,

which we normally call as Strength of Materials. . So now we are in fact in Strength of Materials,

we are interested in these three characteristics: first one is strength, another is stiffness

and another is stability and these are called as three Ss of

strength of material. So we are concerned with the three Ss: parameter

strength, stiffness and stability. .. Well now, having looked into this background

of strength of material, we look into the historical

background of this particular course. In fact the Strength of Materials is quite

an old subject. In

the earlier part of the seventeenth century in fact Galileo, Leonardo-Da-Vinci tried to

give rational meaning of these aspects of structural

members. Prior to that, in fact, people used to use

these concepts, which were based on the experience and mainly based on the rule of the thumbs. But Galileo started giving explanation in

a more rational way about the different aspects of the

forces in the words in terms of tension, in terms of compression, and of course they or

Galileo emphasized more on the experimental side of

these elemental characteristics. In fact, Strength of Materials in that sense

is a fascinating blend of both the experiment and

theoretical aspects. In fact, Leonard Euler in 1744 gave his theory

on the column buckling. Now

he had explained how you arrive at critical buckling load for a column member. But since he

didn’t have any experimental evidence, in fact, it took almost 100 years to establish

or reestablish this particular theory of Euler’s. Still today, we talk about the Euler’s column

buckling aspect. In fact in the earlier stages we had lot of

theoretical explanation we had experimental evidences but subsequently the

French investigators like, to name a few, Cauchy,

Nervier, Poisson, Coulomb, St. Venant and several others. They had devoted their attention to

these areas: theoretical development of strength of material aspect or the mechanics material

of the aspect, based on which, we find that this

particular subject, where it stands today, is based on

their research investigations. And several theories came up based on their

research findings. .. With this background what we expect from this

particular course is that once this particular course is completed that means once somebody

goes through all these lecture lessons of ten

modules, it is expected that one should be in a position to understand the classification

of different kinds of forces that structural

components are subjected to. Now, when we say

structural components the structural component we talk in a generalized term, it is not that

of any particular structure. A structure could be building structure, it

could be bridge structure or it could be structural component of any mechanical

equipment or it could be part of any spacecrafts or any structural form we talk

about; it is a part we could talk about, it is the part or

any part of the structural system as a whole. Any part when it is subjected to any kind

of force, we should be in a position to characterize these forces, in a position to find out the

effects of the forces such as structural components: the

classification of different kinds of forces that structural components are subjected to

and then the effects of different forces on such components

and their solution techniques. This is what we will

be looking into in the particular course. Subsequently, the stresses

of these forces on the members and the deformations these members

will be subjected to will be analyzed systematically. .. Hence the scope of this particular course

includes the identification of different types of forces

that the structural components will be subjected to and as we will go along in this particular

course, you will find that in different modules that we have looked into, the different types

of forces the structural components are subjected

to and how to analyze those forces or the components of the forces that the members

will be subjected to and how to compute the stresses

in the members based on the forces. Also, we will look into the systematic evaluation

of the effects of these forces on such structural

components. . .We will be confining ourselves to the materials,

which are useful for engineering applications. This is important because, we are not going

to cover the whole lot of materials because when you

talk about the materials it is quite general in nature, it covers many aspects, different

kinds of materials, but here we will be restricting

ourselves to the materials, which are useful for

engineering applications and that is what we should keep in mind. Also, the structural members

which we talk about, they do follow the laws of Newtonian mechanics and thereby the

equilibrium of forces governed by the mechanics law will be enforced. Also, it will be essential

to know the mechanical characteristics of the materials with which the member will be

fabricated. So you see here that when we talk about these

aspects, here we will be dealing with one that is

the theoretical aspect, where we will be looking into the equilibrium of forces which are acting

on the body and we try to analyze the internal forces so governing the Newton’s laws of

mechanics adopted and subsequently we will have to use the mechanical behavior of the

material with which these structural elements will

be fabricated. Now to characterize this behavior of this

material or the mechanics of that material we need to adopt some kind of experimental

investigation. So this part will have some out put from the

test results in the laboratory. So you

see that it will be combination of the theoretical aspect along with the experimental investigation. The Strength of Materials is a blend of these

two. That is, theoretical aspects on which we apply

the laws of Newtonian mechanics and we try to characterize using the behavior of the

material based on certain experimental evidence. The combinations of these two will lead us

to different theories and will lead us to the different

classification of the stresses due to the externally applied

load on structural members. . As we go along, we will find that the whole

course will be divided broadly into two parts: one is

the logical development of the concept and another one is the application of these concepts

to the practical problems. When we talk about the logical development

of the concepts, basically based on these concepts we will try to derive the

formulae that are necessary for arriving at different .kinds of stresses in the members for the

external loads. That is what we will be looking into and

the first part will be devoted for that. For any reason the initial part will be devoted

to the derivations of the theoretical background

or the concept and based on those concepts and

formulae that we arrive at, we will be looking into some application problem areas or example

problems and in those application concepts we find, we classify into two groups, one

we call the numerical problem and other the algebraic

problem. When you talk about the numerical problems,

we will be dealing with some example problems in

which we will be assigning some specific values, whereas in the case of algebraic problems,

we will try to arrive at some expressions which

are very general in nature. Now both are having its

merits. When we talk about the numerical examples,

at each type of these examples, we will be evaluating it. We can visualize it: based on the values of

the parameters we will be arriving at, we can get a feel of those parameters, physically

what they represent and what they should be and what actually we are getting. Now when we talk about algebraic problems,

there we would be discussing about the problems which could be general in nature and thereby

we will arrive at certain expressions and these

expressions can be used for solving specific problems where we will have specific numerical

value or some parameter. This is how we classify the two groups of

problems. This is what is

indicated over here that the application concept which we derived in the initial stage, these

concepts when they are applied to practical problems, they could be applied to the numerical

problem or the algebraic problem and as we go along in the course in the different modules,

we have taken different examples and different

areas, which satisfy the requirements of different engineering disciplines. Those structural components can be used for

characterizing the behavior of those individual elements. So they can be used according to the need

of any structural system. . When we talk about the numerical problems

or the algebraic problems, we talk about the units

and the basic units which are used. We use the international system of units in

this particular course. And the basic units for these in the international

system are .Metre is for length. Let us call this length as L. Kilogram the

abbreviated form is kg that is for mass M and Time we use second abbreviated

form as s for time, which we can call this time as

T. Based on these basic units L, M and T, we arrive at certain derived units. . Now when you talk about the units for the

area; Area as we know is the product of two linear

parameters. So let us call L, which is in meters, multiplied

by L is in meter and there by we will get the unit of area m square. Now when we talk about the unit for velocity,

which is distance by time so L by T and if we substitute the units

for these basic parameters we get m by s. Now if we

talk about the units for acceleration, which is rate of change of velocity, it is L by

T square and thereby gives the unit as m by s square. Now once you know the acceleration, then based

on Force P this is equal to Mass, the basic unit

of which is kg times the acceleration, as you have seen in the units, which is m by

s square. So

this gives us the unit kg m by s square. This unit kg m by s square we normally designate

as Newton(N). And the abbreviated form of the Newton is

N. So when you talk about the unit of

force, it is N. Now for higher values we use kilo Newton,

which is 10 to the power 3 Newton, we define in mega Newton, which is 10 to the

power 6 Newton. .. Also many a time, we use parameters as we

have seen Force, which we define in Newton, it

could be in kilo Newton or mega Newton, which is 10 to the power 3 Newton or 10 to the power

6 Newton. And we define another parameter, which we

call as stress in few minutes. This unit

for stress or the stress we define as the force per unit area. So as we have defined, the unit of

force is Newton and area is m square. So the unit for stress we call N by m square

and this is called as Pascal, Pa. When one Newton of force is acting on one

square meter of area, in fact this amount comes

small, where Newton load is very small when compared to meter square area is very large,

many a times this stress we represent in terms

of mega Pascal or kilo Pascals. Now when we talk of

kilo Pascals, we have designated as kilo Newton, the kilo Pascal is 10 to the power 3Pa and

mega Pascal is 10 to the power 6Pa. Many a time, instead of defining area in meters,

we define in terms of millimeters (mm), the stress in N

by mm square, and this equals 10 to the power 6

Newton per meter square(10 to the power 6). As we have seen Newton per meter square is

Pascal. So this is 10 to the power 6Pa. Now 10 to the power 6Pa is nothing but one

mega Pascal. So we can say that one mega Pascal is equal

to one Newton per millimeter square. Also many a

time we use the unit Gigapascal it is 10 to the power 9. So 10 to the power 9 into N by mm

square. So the stresses can be represented as either

Pascals or kilo Pascals or mega Pascals or Gigapascal. As you can see, based on these units that

we use in international system that your length in

meter, the mass in kg and the time in second and based on those basic units, we can arrive

at the derived units and we look into these in this

particular course. We will be more concerned with

the units of the stresses, which is Pascal, and thereby at many a place you will come

across kilo Pascal, mega Pascal or the Gigapascal for

the units of the stresses. .. Having known the units, let us look into the

aspects of the forces that the body or the member is

subjected to. Now we come across a term which is called

a body force; now the body force is basically associated with the units, the volume

of the body, and thereby it is basically a distributed system, that is, the force which

is distributed over the entire volume of the body. Or

in that sense the gravitational force or the inertial force or the magnetic force – these

are the forces which we term as body forces. Now, though it is distributed over the volume,

when we try to analyze the forcing system, the body force

we apply assuming that it is at the centre of the

gravity of the body. So when we analyze a particular structural

component, the body force we apply at the centre of the gravity of the

body. Basically these are the forces: the gravitational

force, the inertia force or the magnetic force are generally termed as body force. .. Now, having known the body force, we are interested

to know the kind of surface forces. This is

another kind of force which acts on the body, that is, the surface force. From the name itself you

can make out these forces act on the surface of the body. We call these the area elements of the

body. Now these forces on the surface, supposing

this is the structural body, we have two kinds of support. The body is supported at these points and

subjected to the forces at these points. Now

these forces, which we call as concentrated load at these points, act on these particular

surfaces of the body; this particular force is acting

and it is over a small area and thereby the force

concentration at that particular point. That particular force we call as concentrated

force. It could

be distributed over like in some area, in this particular case if you look into that,

it is distributed and this we call as distributed force system. The body on the surface could be subjected

to either a concentrated force or a distributed force. Now when these surface forces act on the boundary,

we call that as surface traction. So please keep in mind the surface forces

could be a concentrated force or a distributed force. When this forcing system acts on the boundary,

we call that as surface traction. .. Now, having known the body force and the surface

force, another aspect that we would be dealing with quite frequently would be the

internal force. Now to know the internal force, we

will have to look into one aspect, which we call as a free body diagram. Now let us consider a

body which is supported at these two points, and subjected to these loads P 1 and P 2 . And

these we call as external loads. So the external loads are acting on this particular

body. Now since this

particular body is in equilibrium, under the actions of these external loads, there will

be some amount of reactive forces generated at these

support points. So, if we remove these supports from this

body, and represent the body in this form where P 1

and P 2 are the forces acting on the body, which we call as active force and because

of these active forces on the body there are reactive

forces, which are R 1 and R 2 . Now these active forces

of P 1 and P 2 and reactive forces of R 1 and R 2 are keeping this body in equilibrium. Hence when

we consider or represent body with the external loads, in fact these reactive forces are also

external loads, but when we represent the whole body, when we free or we make them free

from these supports, and represent them using the

active force and the reactive force, this particular

diagram we call as free body diagram. So this is the free body diagram of the structure

as a whole. That means, we have freed this structure from

its supporting constraints and applied the reactive forces over there. Now if I like to cut this particular body

through a line and divide and break it into two halves, then if this particular

structure is cut through the line divided into two

halves, then what do you get? .. Then we get a form, something like this, wherein

you see this particular half of the body is subjected to these external loads, P 1 and

P 2 . Since the whole body is in equilibrium, the parts of

the body should also be in equilibrium. So when we make a cut in the body and separate

it out into two halves, as you can see internally

there are forces which will be generated, which are

called S 1 , S 2 and S 3 . And the other half will also have the reactive forces, and these

forces will be equal and opposite in nature because in

static form they are in equilibrium condition. Now these forces, which are generated internally

to equilibrium these loads, we call these forces

as internal forces. And these diagrams also are called as free

body diagrams. So as you can see

free that to obtain a free body diagram, we can remove the reactive constraints and make

the body from the support and thereby we draw

all the external loads acting on that. That is also a

free body diagram or we cut the body and make different parts and on that we show the external

force and the internal force and that is also a free body diagram. Now this free body diagram

gives us the idea of the internal forces. .. Now in mechanics of materials or Strength

of Materials, what we are concerned with is this

internal forces or the intensity of the forces that are acting. Now as you have seen these internal

forces equilibrate the external forces and keep the body in equilibrium. Hence what we are

interested to find out is the intensity of these forces and how they keep the body in

equilibrium and thereby reduce the deformation of the

whole structure. Now if we look into this particular

body, wherein we have taken a cut and this cut, if you take the normal to this cut, this

directs along the x axis. On these we have a small force ΔP acting

on a small area, which is ΔA. Now it is customary to

decompose this force into two directions: one is perpendicular to the direction and

another one is along the plane of the cross section. Now if we do that, if we decompose this load

perpendicular section, which is Δ P x because it is the

direction of x and further in the plane the load in the

section can be decomposed into two directions, one is ΔP y and another is ∆Pz . Now since

we are interested in the intensity of the force over

this area, so ∆P and ∆A give us the intensity and that

∆P we call as stress. So stress basically equals

. Now we have taken the components along x, y

∆A and z directions, and mind that we have taken

a cut, the perpendicular to that is matching with

∆Py ∆Px

the x direction. Now this –

– we call this as the stress in the x direction τ x ,

is the ∆A

∆A ∆Pz

in the z direction. Now on a limiting scale, when we talk

stress in the y direction and the ∆A

about the stress, at a point when this ∆A tends to zero this τ x , τ y and τ z give

us the stress at a particular point. .. Now the way we have given these designations,

if you look into τ it is the term of stress, the

first subscript defines the plane, as I said, for a body we have taken a cut, the normal

drawn to the plane, directs towards the axis x. This we call as x plane. This particular we call it as stress. Now τ xx indicates that it is the stress

in x plane and directed towards x and τ xy indicates that the

stress in x plane is directed towards y, and τ xz indicates the τ in x plane directed

towards the z. Now, when we have the plane and direction

coinciding or if this is the direction of the normal to

the plane and this is also directed towards this, this we call as the normal stress. We denote this

generally with σ x . Sigma x defines that this particular stress is normal to the plane

and this normal stress could be tensile or compressive

in nature. When the pull, when this particular force

is perpendicular to the plane and it tries to pull the body, we call that as tensile

and when it pushes the body we call that as a compressive

stress. We will look into more aspects in later

lessons. Also the stresses, which are acting in the

plane of the act, we call that as shear stress. .. So stresses, multiplied by the respective

areas, on which they act, give us the forces and at

section, the vector sum of these forces is known as the stress resultant. Basically, in the problem

of Strength of Materials, we are interested to evaluate this stress resultant and from

those stress resultants, we compute the values of the stresses

of a body, which are subjected to different kinds

of loads. . Now in this example we are interested to draw

the free body diagram for this. Now this is the

part which is subjected to a tensile pull. Now if you would like to draw the free body

diagram of the whole part then, the free body diagram

will be like this: that it is acting on by this force .which is passing through the centre of gravity

of this member, so the reactive force will also be

P. Or if we take a cut somewhere, it will be a small part of the body and that also

will be in equilibrium under action of these loads. This is free body of α the part of the structural

form. . Also, if you like to draw the free body diagram

for this structural form, which are bars subjected to this load P, now as we have done, make

these structures free from the support and thereby get

the reactive forces, they could be in this form or we can take a cut in this particular

structural form and thereby you get the reactive forces,

the active forces and the member forces. This is the

free body diagram of this particular part. And this is how we make the elements free

and take a cut, which give us the free body diagram of

the structure. .. Hence to summarize in this particular lesson,

we have included the general idea about the scope

of the subject, we have discussed the typical application areas where strength of material

can be applied. What is the scope of this particular subject? What are the disciplines where we come

across the different problems based on the strength of the material formulae, where based

on what we can get the solutions for such problems? Then concept of different forces also we have

looked into: the concept of free body diagram and thereby the concept of stress. . These are the questions for you. What are the units of the Force and Stress? .What is the definition of normal stress? What is meant by free body diagram? What are the axioms on which the behavior

of the deformable member subjected to forces depend? Now look into these questions. If you go through this lesson, you should

be in a position to answer these questions. We will be discussing about the answers of these questions in

the next session. .

amy duff ????

chk d audio man

i hate str of english

I'm swat from AAIT in Ethiopia N I must say that Ya & da whole IIT are in deed da gift from God. Coz I've been attendin' surveying and maths and they saved me from gettin' dismissed. tnx N God bless U .

Have a nice topic Related to my course 🙂

thanx prf.gooood skilll

i gel refresh my mind

please check the audio…..

m studyin civil engineering ..help me .. i find it tough 🙁

Indians are always loyal and honest to their work and life.

nice lecture.

Great

Great

very useful lecture 4 studants pursuing b.tech-rakesh c.b.r.i roorkee

awesome….

is it same for mechenical branch ?

its a better thing that for civil to teaching as

A terrific introduction to this subject. Thank you..

Very good lecture Sir..

The lecture is nice, but the accent is a bit too heavy for non-indian students

is this for mechanical also???????

very useful for structural engineers

best teacher ever.. with best examples…. thank u for saving life of non iitians….

Can anyone refer me similar channel like this which covers best and all topics of civil engineering lectures .Thanhks nptrlhrd.

thank u sir ..:)

Im an aerospace engineering student and I find this course very useful. Thanks!

Thank you Sir.

Very useful lecture. Concept of Stress and Strain has been explained very clearly specially when a slab is cut diagonally.Thank you sir

can you please give me the link of the next video if there is any?

i would be grateful 😀

excellent sir ….!!!

good

It was excellent sir…

Why I am not being able to hear the sound of this lecture??? Can anyone help me?

if magnetic force is body force … will it act from the centre of gravity of the body … ?

its nice

it's good, but audible when volume is increased….

excellent sir,

can we get the topic in hindi lectures

reply soon…there is a paper of my brother

sir

Any AMIE Student's Who have Completed sec A? please let me know..

G

thankuuuuuuu sir..it's just amazing……loved it ….wow……!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

thank you

the most important GOD i need Him tnx

Quality of video is not good

tanx sir very beneficial

please upload good quality video,only right side is audible.

very good

may i know email adress clearly plasea

sir I can't understand SOM any simple trick I understand SOM

please some body tell me some book which matches this lecture as wel as for practice

Thank you very much sir for sharing your knowledge….if you can please upload some videos for competitive exams for gate and ies exams…

civil engineer ranjit Yadav

There is no sound for these SOM lectures

civil engg drcs and som how to download

Thank you so much for your time and excellent explanation- Greatly appreciated-

place diploma 2du sem egg graphics -2m-scheme

pls update, its 9 yrs old

Nice

need examples for every concepts..and some diagrama and 3d diagrams

sir can you upload in hindi

plz try to provide these videos offline

is your lecture enough for SOM I mean I don't know more about it just want to start my study PLizz tell…

The video is made in 2008 , we can't complain about its clearity😅

i find this course very useful thank u very much

thanku sir

P = (2*pi*N*T) / (60 *1000) kW , N – rpm, T – Nm . And. T=9.55*10^6 * P/ n Nmm, P – kW , n – rpm Can anyone prove that above 2 equations are equal with proper steps and proof?

rama

piece r16 jntuk sylabus teaching

@12:20 This is the picture of a fighter jet, not a space craft.

not composed ,component

nyce lecture

Great sir you explained it very well

Thanks sir

Lot thanks

No audio

so boring

He said "we look into this particular course" 98726467893 times in this video

Explain problems sir., please

Thnxx sir your video very nice I like

& very use ful

good

Can anyone refer me license key?

https://unacademy.com/lesson/course-overview/5IPCAEAT/?source=Course <–check this

Hello sir I m preparation gate and I am in 3year of ME student so I want to complete SOM So i do preparation to see this video series it is way I chose right or wrong pleas reply as soon as possible

Nice lecture but video quality is very poor, please improve it

https://www.youtube.com/channel/UCe-FudRoiqzW0n5cJUGjkgA

Online civil engineering coaching

Sir these Modules cover Both SOM 1 and SOM 2 ?

Teaching is so bad

Please I would also need the calculations part.

Such a nice lecture

Please upload estimating and costing lectures

🎧🔇😦😧😩

Sir please tell us as class room classes

Sir in stress strain curve,stress is independent term,then why we are taking stress in y-axis and strain on x-axis

Aweosme sir

Will any body Suggest me Video lecture for M.tech in Structural Engineering

Nice

Perfect

Increase the quality of video

Where are other modules included?

intro to stress starts at 33:59

Can watch this series to prepare for mechanical-strength of materials (sppu) ?