Introduction – Strength of Materials

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. .

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100 thoughts on “Introduction – Strength of Materials

  1. 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 .

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

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

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

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

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

  7. 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?

  8. 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

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

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