Lec-2 Strength of Materials


Good morning. This is Dr. S. P. Harsha faculty
of Mechanical and Industrial Engineering Department, IIT Roorkee. I am going to present today the
basic course of Engineering Science, that is The Strength of Material in which the first
lecture is the introduction lecture in which I am you know present the key features of
the strength of material like what are the forces, what kind of forces are being applied
in the solid mechanics like if there is a pulling kind of thing or the compression is
there or if there is no uniaxial-biaxial forces and then, how these forces have been set up
within the solid bodies. Due to these forces, what are the internal resistances in the solid
object through which there are you know like the stresses are there, the strains are there,
the deformations are there. So, all these issues I represent here in this first lecture.
This course is basically developed under the National Program on Technological Enhanced
Learning. So, as you see you know like this course comes
under Engineering science because in that there are lots of applications. So, we can
you know like usually subdivide these engineering sciences into various category, and the first
category is solid mechanics in which there are solid objects which are interacting to
each other. So, we need to analyze those solid objects using the mechanics concept.
So, in that there are you see you know like the two main branches. One is the statics
in which the static forces are being set up in the solid bodies, and the forces are there
due to interaction. So, the other branch of the solid mechanics is the dynamic which the
dynamic forces are there in which the forces are being you know like the time varying component.
So, when the objects are in the moving part, we know that the dynamic forces are then dominating
in those conditions. So, the solid mechanics is basically dealing with the solid objects
which are interacting. Then, the second subdivision is there under
the engineering science part is the fluid mechanics. In fluid mechanics, basically we
are you know like dealing with how the fluids are interacting to each other, and what are
the molecules in these fluid mechanics. They are interacting, that is what you see there
are various forces which we can say that cohesive forces are there, or the combined forces are
there due to which the fluids are being confined to in the main object. That is what you see
you know like here, there are various categories in the fluid mechanics also like if the fluid
is very tiny or thin. Then, we can say that you know the laminar flow is going on when
there is no dynamics in the fluid particles, or the second category we can say there is
a turbulence in which there are hectic motion, or we can say truly non-linear dynamic motions
are their of the fluid particles. So, there is the interaction or we can say there is
intermediate portion in between those laminar as well as the turbulence parts.
So, these two you know like the subdivisions of the engineering science is basically dealing
with the different domain. One is the solid as well as another one is the fluid, and the
third one is the heat transfer. So, heat transfer can take place into you know like either the
solid as well as in the fluid. So, that is why you see we are categorizing this heat
transfer into three main categories. One is you know like the main mode is there, that
is the conduction mode which is highly molecular phenomena like if you see you know like if
you have the different temperatures all across the solid, then there is a heat transfer right
from one end to another end through conduction. So, this is a purely molecular phenomenon.
Second we have the convection which is different than the first one because in that there is
a interaction between the solid as well as the fluid, and the convection takes place,
and the third is there is the radiation which you know like is the macroscopic phenomena
in which the radiations are there which is emitting from an object, and there are you
see you know like the different laws are there to analyze those things. Then, the final which
is an important division of an engineering science, that is the properties of material
in which you see know like we are generally categorizing the material into various categories,
but broadly speaking there are two main categories under this that is the ductile material as
well as that is the brittle material. In the ductile material, again there is you
know like that the ductility is the property. So, in that we are assuming that if a material
is ductile, then it is pretty easy to extend or it is pretty easy to just pull those materials,
but if we have a brittle material, then it does not have that kind of property. So, what
we are doing in that we are it is because you know like the brittle materials are good
in the compressive stress, the compress strength. So, they are good you know like the harder
material. So, based on what properties are there we are always applying you know like
the material towards application. So, this you know like if you are dealing
with the individual subdivision of the engineering sciences. Then we will find that it is not
like we cannot fully analyze all the structures using the individual you know like concept
of these mechanics, either solid mechanics, fluid mechanics or the heat transfer in which
the temperature phenomena’s are there or the properties of material in which you see
there are various properties like the stiffness is there like the damping is there, like hardness
is there, toughness is there, the impact is there. So, these are the properties you know
like which always gives you the basic information which material is applicable to what kind
of application. Although you see there are you know close
link in between them in terms of the physical principles, and that is why you see we are
using these basics. These are we can say are the four basic pillars of the engineering
sciences, and you see if you want to make any kind of building, we need to know that
what these interactions are there in between these four properties, or we can say subdivisions
of the engineering sciences. So, that is why we are saying that you know like we need to
put the basic link based on the physical principles involved and that is the nature.
Nature is always saying that you see you need to maintain that what the physical setup is
there in between these objects. And then you see we can go for the variety of the methods
of the analysis which are employed for all these things, and that is the basic study
of the engineering sciences, but here you see you know like as far as this course is
concerned or main focuses on solid mechanics that actually how these solid objects are
being set up, how these forces are being well set up within those objects. Then, if we are
going towards introduction as I told you that is as for the subject is concerned. The solid mechanics as a subject may be defined
as a branch of applied mechanics, because again you see you know like what we are doing
here is in the applied mechanics we can go for solid as well as fluid mechanics. But
here it is the basic branch of the applied mechanics, solid mechanics in which we are
dealing with the behavior of solid bodies as I told you earlier subjected to variety
of loads. If there is a pulling, then we can say, technically
we can say it is a tensile pulling, or the tensile load is there. If there is a compression,
then we can see the compressive loading is there, but these two loads you see you know
like comes under the main category known as the uniaxial loading because you see if the
load application is there, always you see you know like load can be defined by the variety
of things like you see if you are saying that it is a force, then force is nothing, but
the mass into acceleration, but the key feature in the force is what is the point of application.
If the point of application is same like if I am pulling from both the side, this force
is known as the load that is the tensile loading. That means the pulling is there. If in uniaxial
even loading if I am saying that this is the compression which is also acting on the same
axis, we can say it is compressive kind of loading.
So, these two, either the tensile as well as the compressive comes under the uniaxial
loading, but if it is a biaxial loading means you see you know like on the plane like this
x and y, if the load is there, then we cannot say it is uniaxial loading. So, loading can
be of uniaxial. As I discussed, it can be of biaxial or triaxial, but we need to know
that actually if these loadings or the forces are being there. They have to be you know
like satisfy the static as well as the dynamic conditions of the object and then, all we
can say that the object is under equilibrium position. So, there are as I told you the
variety of various types of loadings. So, if it is a uniaxial, then tensile as well
as the compressive loading is there. If it is biaxial, then it is shear loading. If object
is stationary or if objective is moving, then we can say it is a kind of torsional loading
like the shaft is moving, and both the side if the forces are there, the reacting or couples
are there or the forces are there, you see we can say this kind of torsional loading
is there. This is usually subdivided into further twisting which is the basic thing.
You see first is the mechanics of the rigid bodies, or we can say it is simple mechanics
in which the statics and the dynamics is there. Second is the mechanics of deformable bodies.
That means you see you know like one side we are saying that this is the rigid body
in which there is a minimum chance of the deformation. Since, the solid objects are
there, they are interacting, but they are so rigid that there is no deformation and
if there is no deformation, then there is no excitation, but if on the other side if
you are saying that the deformable objects are there like you see you know like most
of the objects, they are deformable based on what the stiffness is there within this
object. This is a unique property of the deformation
and then, you see we need to you know that actually how much deformation is there. It
is a temporary deformation or the permanent deformation. So, all these kind of analysis
which is being studied under the mechanics of the deformable bodies, first you see that
under the introduction of this mechanics of deformable solids, which is also a part of
or we can say the category of the applied mechanics is known by several names like strength
of materials, mechanics of materials, and in that you see again we are dealing with
actually if there is a deformable body, then whether it is a temporary deformation. Then,
you see you know like under the temporary deformation, there are varieties of laws like
there is this modulus of Young’s elasticity where the force is you know like proportional
to the deformation, or there are other models of elasticities.
So, we are dealing with many things and many of the limits like yield limit is there, proportional
limit is there under the deformable bodies, but if it is a permanent deformation, then
there is a kind of cracks are there or the spells are there on the object. Then, we need
to know that actually how much the stress or the force concentrations are there within
those permanent deformations. So, this a different branch of the applied mechanics in which we
are dealing with the deformable part, and that is why you see you know like in all those
strength of materials or the mechanics of materials, you are basically dealing with
the stress stain and the deformation, but if we are dealing with the other part that
is mechanics of the rigid bodies which is primarily concerned with the statics and the
dynamic behavior static, and dynamic behavior under external force is of the engineering
components and system which are treated as the infinitely strong and un-deformable.
That is what you see you know like if you are saying that the stiffness is too hard,
we say if the body is so stiff that even if we apply the load, it cannot be deformable
and then, it is pretty hard to analyze because you see the forces are there and they are
interacting. We can set up those forces, but we cannot analyze using the stress strain
or the deformation concept. So, this is a different part of the applied mechanics and
then, you see primarily we are here with the forces motion associated with the particles
as well as the rigid bodies in which there is a stress strain as well as the deformation
occurs. So, here you see as I told you that mechanics
of solid, it is a branch in which there is kind of deformable bodies are there. So, mechanics
of deformable solid is more concerned with the internal forces and associated changes
in the geometry of the components involved because of the interaction of these objects.
So, here you see of particular importance as you know like we are discussing with the
geometric changes because if there is an impact, you will always find that there is a kind
of noise. Why these noises are there? It is because of the deformation.
So, how these deformations are being set up whether these deformations are permanent or
temporary, these kinds of analysis which we are going to deal in this kind of subject
of a particular importance which we need to give on the properties of material. What are
the properties which we are using is either the ductile as well as brittle material, the
strength of which will always determine, always gives you the information whether the component
will fail by breaking in the service means how long it can bear those forces or we can
say whether these forces, what are the forces which are applying to those things, whether
it can sustain those forces or not are up to what you see all those designs basically
you know like use this kind of basic information and the stiffness. This is the basic property
as I told you for the deformable object, a stiffness of which will determine whether
the amount is deformable. They will suffer whatever you see the deformation object is
there whether it is acceptable or not acceptable. So, in that if you see, therefore the subject
of mechanics of material or the strength of material is basically central to the whole
activity of the engineering design because in engineering design, basically whatever
the drawing is supplied to us, we need to know that you see whether those objects or
the dimensions are sustainable to the load application or not. In that what you see in
that engineering design, we always apply that what the material properties are there or
what kind of loads are being applied, or whether you see this material can observe those kind
of energies or the impacts or the load, or it can be safely operated or not.
So, this kind of you see you know like the interaction of the information, we are always
using for the mechanics of material and for the basic of the engineering design. Usually
the objective you know like objectives in the analysis, any kind of analysis, the dynamic
as well as the static analysis will be determination of the stresses, the internal resistances
like the strains. That is how we see deformations are there and the deflection produced by these
loads. These are three key terms in the mechanics
of solid which we need to see that what kind of stresses are being set up within the object,
what strains are there and how deflections have been taken place by these load application.
And in that what you see that theoretical as well as the experimental analysis always
gives the key information whether whatever the analysis which you have done is real to
the nature, or which is applicable to the real nature or not, and that is what you see
you know like we are doing both kind of analysis here. Now, the stress is the key feature as
I told you that we need to now define what you mean by the stress. Let us introduce the
concept of stress. As we know that the main problem of engineering
mechanics of material is the investigation of the internal resistance of body because
you see you know like if we apply the load, always body will react by the third law of
the this Newton that the reaction you know like action reaction is there. So, as you
apply any kind of load, whether it is a uniaxial, biaxial or triaxial load, always a kind of
resistance will take place. So, whether you see you know like this kind of resistances
can be well setup within the object or not. So, as we can say that the internal resistance
of body, or we can say the nature of forces which are being set up within the body can
balance or not. If it cannot balance, then body will break, but if it can balance, whatever
the applied forces are there and internal forces if they can well set up within those
object due to the external application, we can say that the body is well established
under the application of load because load is always you see as I told you that force
can be you know like defined by two ways. One by magnitude that is mass into acceleration.
That is nothing, but the load and by the point of application how these forces are acting
on an object and accordingly, the resistance forces are coming and we are saying that the
intensity of the internal resistance is the stress. Either internal resistances per unit
area, that is the intensity and that is external applied load as I told you forces are always
termed as the loads. Now, you see these external applied forces,
which are the key generation of this stress can be due to many of the reasons. First,
the basic reason is due to service conditions, the objects are under the cyclic loading or
the tensile loading or like you see you know like as we are going towards any of the machine.
If you are analyzing, we will find that the bearings are there, gears are there, the shafts
are there. They are always under the different kinds of loads, and accordingly we are considering
we want to design the bearing. We want to design the shaft. If you want to
design the gears, or if you want to design any of static part of the machine, we are
always you know like clearly observe that how these forces are being set up or due to
the environment in which the component works, whether it is on the normal temperature condition
or severe temperature conditions. Because of these things you see the thermal expansions
are there, or we can say later on that thermal stresses are there, or you see through I know
like other reasons for the applied forces are through the contact with other members.
And that is why you see the contact mechanics are there, and we are you know like here concerning
about that how deformations are being taken place due to this interaction.
Then you see due to the fluid pressure that you see if rho g h if you are saying that
rho is the density g is you know like the gravitational acceleration, and height up
to how much you know like height, these fluid pressures are being accelerating on an object,
and you know like in that even the g is there. That is the gravitational acceleration or
the inertia forces. Due to inertia forces also, you see there is one of the basic reason
that the stresses are you know inducing in an object. So, now you see you know like if you come
to the main point that these internal forces give rise to a concept of the stress. Therefore,
we can say that you know like the stress is nothing, but the internal forces, the internal
intensity of the forces like internal force per unit area, and if you see this figure,
in this figure as we have used the rectangular bar in which there is an axial pulling and
since, it is a uniaxial pulling, we can see that this is the P P or F. This is tensile
for which the extension is there, and if you want to analyze those things, then first we
need to see whether this object is under stable condition or not.
If it is under stable condition, that means, whatever these forces or axial pulling are
there, they are well set up within those objects. That means, you see whatever the internal
resistances are there within this object, they are well set up and these internal resistances
are basically due to this external, this excitation force that is P or F which is there in terms
of the Newton, and always we are concerning about these forces because of where the part
of application of these forces are, and that is why we are saying that these are the tensile
pulling like here you see from both end, this the tensile pulling. So, if you want to analyze those things, first
we need to make the cross section and that is why you see you know like in this, then
this diagram we are shown here that there are two main parts and on both of the sides,
both of the end sides here, the P external excitation force is there and due to this
externally applied load. We have seen that if you cut those thing at both ends through
this XX line, these internal resistances are there.
So, each portion of these rectangular bars, either on the left or right side is in equilibrium
under the action of these applied loads, the tensile load I should say and the internal
forces are always acting at the XX section just opposite to the applied load, and that
is why you see we can say that this is well established or equilibrium region. If you are talking about the analysis of the
stress or strain within those things, we can say that the stress is defined by the force
intensity or the internal resistance force is per unit area. And hence, we use the symbol
sigma just to represent the stress, that is P by A, where A is the cross-sectional area
here which is the rectangular area is there because the rectangular bar we have used in
the previous case. So, here we are using an assumption that the
total force of the total load carried out by these rectangular bar is uniformly distributed
all across the area, because if the load is non-inform, that definitely you see you know
like the deformation or whatever the internal resistances are non-uniform. And then, we
cannot say that this object is in equilibrium position, but the stress distribution which
we can say that you see you know if the area is different at different regions. The stress
distribution is obviously different from uniform, or may be local regions of high stress regions
are there known as the stress concentration. So, if there is any abrupt change in an object,
we can say that the stress concentration is more and we need to design carefully for those
kinds of regions. So, if we are talking about the normal stress, then there is no problem
because this is uniformly distributed because of the uniform force distribution in an object. If the force carried out by a component is
not uniformly distributed as I discussed during that stress concentration over the cross sectional
area. We must consider the small segment or a small area delta A which carries a small
load delta P, or we can say the total load P, and that is why we can define the small
segment of deformation that you see the small stress is there. That del F by del A or we
can set particular stress. Generally you know like it holds true only when a point, or we
can say you know like for small region, or we can say the infinite decimal region that
the sigma is nothing, but the limit of delta A tends to be 0 del F by del A.
So, generally what we are doing here is, if we found that abrupt changes are there within
the object, or we can say object is not uniformly rectangular or any shape defined shape, what
we are doing here is, we are simply categorizing this object into various categories and then,
some of those things because you see we define stresses for a small segment as we have seen
in this del F by del A. So, you know like we can again sum up those thing by summing
of this limit of delta A 1, delta A 2 and delta 3 and so on, and then accordingly we
can get the total stress after the whole object. Now, you see if you are going for the unit
of the stress because stress is nothing, but the intensity of the internal resistances.
The basic units in the S I system is Newton per meter square, or we can say the Pascal
well known scientist which gave the concept of the pressure and pressure was also you
see the force per unit area. So, it has the same meaning you know like it is the internal
resistances, or we can say internal resistance of the force or we can say it is internal
intensity of forces. That is why we can define those things by Newton per meter square, or
Pascal or if you go for higher side of these things, then it is kilo Pascal that is 1000
Pascal or giga Pascal, that is 100-1000 mega Pascal, 100-1000 Pascal or giga Pascal, that
is 10 to the power 9 Pascal or sometimes it is pretty common to use the Newton per millimeter
square that is also you know equals to mega Pascal. So, while you know like this is pretty
common, this unit is there in India or in particular i should say Asia or European countries,
but U. S. you see United States of America, they are using this pound per square inch
that is Psi, that is the FPS unit. Now, you see you know like this was the basic
concept of the stresses. I am sure talking about the types of stresses. There are two
basic types of stresses. One is the normal stress and one is the shear stress. Normal
stress means as I told you when the uniaxial loading is there, because of the uniaxial
loading, what are the internal resistance per unit area that always comes out from the
normal stress component. That is why you see we are categorizing normal stress component
by either pulling or the compression because they are with the uniaxial part.
Second basic stress is shear stress. If they are not the uniaxial, if they have some sort
of eccentricity or these stresses are there for a plane, where X and Y planes are there.
That means, here or here you see you know like these stresses are being coming through
the forces. We are always saying that it is shear stress. So, normal stress is an axial
stress, shear stress is a plane stress. Other stresses are the derived stresses from these
two like you see you know if you are talking about the normal stress, then as I told you
there are two components of that. By pulling the tensile, stresses are there and by compression,
the compressive stresses are there. Shear stresses also has two components like
one is if it is stationary object, and you see the twisting is there, then the shear
stresses are there because it is along the plane or if you see we have the torsional
stresses. That means if the object is moving, we have the torsional stresses. Another combination
of these stresses is that we have the bending stresses. We have due to you see whenever
the object is there in the bending stresses, we have both kind of things, the tensile as
well as the compression because both the stresses are coming simultaneously at different points
of the bending. Then, we have you know like another that is the thermal stresses. Thermal
stresses are always coming which is not the part of that, but it is always coming due
to the temperature variation, and it is being set up you know like just to make a component
equilibrium under the different temperature environment.
So, these are you know like the derived stresses I should say, and some of the basic stresses
are there like the normal as well as the shear stresses just like as I told the torsional
stresses which is encountered in the twisting of a shaft which is also a basic form of the
shear stresses. So, now come to the main part that you know
like how these stresses are there, and how we can define those things of first, the basic
stress is the normal stress. We have defined the stress as force per unit area that is
the internal intensity of the resistances. If the stresses are normal to the area concerned
like you see here, if you see this is sigma 1 and see this is sigma 1 towards this area,
and this is sigma 1 towards that area. So, if the stress is acting normal to the area
concerned, so this is my effective area and the stress is acting towards the normal to
that. That means, there you see if a stress is acting and this is my plane you see or
this is the area of concerned. I should say this is the normal stress, and the normal
stress is always defined by a Greek letter sigma as I told you. So, always we need to
see that what the point of application of the force or the stress is. Internal stress
is there, internal intensity of the resistance is there. If it is normal, then we can say
or if it is perpendicular at the area concerned, we can say this is normal stress. So, this is also as I told you like known
as the uniaxial state of stress because they are acting at the uniaxial because of the
stress acts only in one direction, either the tensile or the compression. However, a
state you know like whatever you see this kind of state which rarely exists in this
object. So, what we are doing here is always going for the biaxial or the triaxial state
of the stress to define all those stress which are being set up within the component. So,
a state of stress is where either two mutual perpendicular stresses are there in the biaxial,
or three mutual perpendicular normal stresses are being set up in the object. So, we define by this figure like this is
the above figure is the biaxial state of stress in which two forms of the stresses are there.
In the x axis, you see this normal stress is there. It is always lying along this line
and in the y axis also, this is always along this line. This normal stress component is
there. So, sigma 1 and sigma 2 are the biaxial state. The biaxial state of stress is there.
The two forms are there and the second one is the triaxial state of stress which is you
see you know like the sigma 1, sigma 2 or sigma 3 is there. So, if you are considering
all three axes, sigma 1 or this sigma 2 or sigma 3, all these stresses are being well
set up in this object and we can analyze accordingly. So, uniaxial, biaxial or triaxial, this is
always you see. Now, if you want to define the real state of stress, always we need to
go to that which will give you the real true value of the stresses in those objects. Now,
you see come to the normal stress component. In the normal stress components, it can be
either as I told you pulling or it can be compression. So, if it is pulling like you
see in this figure, if this is a rectangular bar and if it is pulling from both the ends
and since, you see you know like this is the normal stress component is there, uniaxial
part is there. So, if it is pulling, we can say that the tensile stresses are being set
up within this object. That means, if it is pulling the internal resistances are set up
that they will resist this kind of pulling. So, that is why we can say whatever the stresses
are being induced in this object due to the application of this force, tensile force,
these stresses are known as the tensile stresses. Simultaneously, we can say that if the compression
is there, this is also you see the uniaxial state of stress is there. So, if you are saying
that actually these forces are being well set up within those things, we can say the
internal resistances are. So, you know like opposite to this kind of compression and they
will always towards the opposite to these actions of these forces. We can say these
are the compressive stresses. In these two, you know like the forms of the normal stresses
like the tensile stress and the compressive stress.
As we have discussed that these stresses are normal parallel to these planes. So, now,
our effective planes are we can say the matter of concern is this plane, where these forces
or the stresses are just perpendicular or normal to the stress, these things. So, always
we need to be very careful that while we are observing or analyzing those forces, we need
to be very careful that how these applications are there, where they are applying whether
this here, this one or towards that direction or what is our you know like the plane of
concern. So, either in the tensile or in the compressive,
always we need to be careful that actually what the plane of action is, or what is the
matter of the area of concern. So, you know like these are two basic forms of the normal
stresses, but if we derive those things, then again we will find that one of the derived
stresses is there, that is known as the bearing stress.
Bearing stress is nothing you see you know like when one object, when two composite parts
is there means two different objects are pressing against each other. It is referred to bearing
stresses like you see two surfaces are meeting to each other, and there is a well set up
you know like forces are there in between the portion. So, these two objects, they are
in fact you know like we can say these are the compressive stresses, but if we see the
plane of area, then we will find this in this figure. This is the plane of area or the matter
of concern is there, where the stresses are just normal that these are the compressive
forces which are acting. So, if we take the object or the soil, any
of you see this is the basic phenomena is there in these soil mechanics. So, always
what we are doing here is this object is always trying to press within the soil, and these
bearing stresses are well set up within this contact region. So, this is our contact region
and these forces are there from the normal stresses. So, that is why we can say the bearing
stresses are nothing, but one of the form of this normal stresses, and since the compression
is there, so we can say that the compressive stresses are there.
So, if you want to analyze this kind of object, always we need to be careful that actually
how these forces are being set up, and how these stresses are distributing among this
contact area. So, that is what you see you know like if any eccentricity is there, or
any irregularity is there in this object, then we need to see that actually how this
stress concentrations are being taken place at different parts, and how this internal
resistances are there within this, either object or the soil because this is the contact
region of the soil and here, you see this bearing stresses are forming all around this
object. So, this is one form of the bearing stresses, and this is the derived stress of
the compressed stress one from, and then you see another part of one part was there the
normal stress component, and the second part is there that is the normal shear stress. So, let us consider now a situation where
the cross-sectional area of a block, of a particular block of material is subject to
a distribution of forces, which are parallel. Now, you see this is not normal, whatever
the forces, which is not normal to this area concerned. Now, if they are parallel means
you see this is object, and the forces are applied parallel to this area of concern.
Then, you see you know like this is we cannot say the normal stress component is there and
then, we can say that these kind of you know like forces which are parallel to the normal
axis always gives you a different kind of resistances or the area of concern.
Whatever the internal resistances are coming due to these parallel forces are always different
than the perpendicular forces, and such forces are always associated with the shearing of
the material because they are not uniaxial. They are at the different axis due to the
eccentricity and since, you see they are running parallely to the object. That means you see
these forces are different at different layers of an object. So, always you see we need to
be careful that actually how these you know like the forces are being set up, and that
is why we are saying that always it create the shearing to these different layers of
these particular objects. So, these forces are associated with that
shearing of material and always refer to the shear forces. So, shear forces you see you
know like always create some sort of shearing to the different layers of an object, and
the resulting force intensity. That means, the resulting shear force per unit effective
area is known as the shear stress. So, you see this is the another form of the shear
stress in which the forces are parallel. So, here we can see this. We have this object
since you see these are here the forces are not coming perpendicularly. They are just
parallel to these surfaces. So, we have this effective surface here, and these forces acted
parallely towards that, and now this is our area of concern where these forces are going.
So, always within this object, we have shear stresses which are being set up within this
object, and that is why you see here we are saying that these shear stresses are always
plane stresses, because they are always towards this particular you know like those planes
means here you see you know like we need to concern this particular plane because they
are all along this one. So, that is why you see you know like we need
to analyze those things that actually how these shear stresses are being setup in these
things, whether this is a uniform structure than the shear stresses, or all along uniform
along this particular plane. And if any eccentricity or if any non-irregularity is there in the
shape or the geometry of the object, then we have to be very careful because these are
the weakest area of the object, and we need to be very careful and that is why you see
accordingly we are taking the factor of safety for these kind of stresses. So, shear stresses are more I should say you
know like the dangers because you see they are running parallel to the layers of an object.
Then, you see you know like if we define these shear stresses, then the resulting force,
shear force intensity which is known as the shear stress is the mean shear stress which
is equal to this P by A P is the internal force resistance. This resistance force is
divided by the effective area, and it is always denoted by tau. So, P is a total force as
I told shear force I should say and area is the effective area under which these forces
are being acting. So, as we know that the particular stress
generally occurs you know like part only at a point. Therefore, we can say you know like
shear stress at a particular point is limit you know the tau which is limits del A tends
to 0 del F by del A. So, this is you know like the small segment of force divided by
the small area. So, generally you see this equation is valid where you see you know like
if we found that irregularities are more, and we are you know like segregating or we
are separating those individual components because you see if there strong region is
there, weakest region is there. So, what we are doing here? We know that whatever
the force distribution is there within this object is different. Then, we are careful
in the strong region how much force distribution is there. For the weakest region how much
you know like force distribution is there, and what is the area. This is the matter of
area concerned. So, accordingly what we are doing here if you are saying that if you have
an object which has you know like if you are categorizing an object in six different steps,
what we are doing here is, we are always calculating tau 1, tau 2, tau 3, tau 4, tau 5, tau 6,
and in all these tau, always we are assuming that whatever the area of concern is there,
they are always to that particular effective area.
So, that is what you see this approach is known as the infinite decimal part because
you see any of the engineering sciences we are doing like you see thermodynamics, basically
whatever those you know like the process are there like this isochoric process, isobaric
process, isentropic process, all these processes are you know like if we are going realistic,
then we cannot approach really, because that real nature is always against those things.
They are not reversible phenomena if it is a real process, but always we assume that
these processes really occur in the nature and they are reversible.
So, what you are doing here? We are always taking the small segment and within this small
segment, we assume that these processes are correctly applied whatever you see. So, similar
concept we apply here that whatever the small region is there within this small region,
we assume that whatever the force application is there and divided by whatever, this effective
area is there. If we sum up those things by integrating all those small segments, we assume
that this stress distribution is uniform, and because of this stress irrespective of
whether it is normal stress or it is shear stress; we assume that this stress is well
set up. If you sum up those things, it will give you the average normal as well as the
average shear stress component. Therefore, you know like we are always applying
that if it is delta F by delta A. For a small segment, it always limit A tends to delta
A tends to 0, and this will give you small shear stress component for a segment, and
if you sum up those things, then you will get the full stress component. So, that is why as we discussed that actually
this shear stress is always denoted by Greek symbol tau just like you see in the normal
stress component. It is always either irrespective of that this tensile stress or the compress
stress which is always being denoted by the sigma part. So, it is used to denote the shear
stress. However, it must be borne in mind that the stress, the resulting stress of these
things, any point in a body is basically resolved into two components because you know like
as we discussed that there are two main components of the stress, normal as well as the shear
and sigma as well as tau. So, how these stress components are being
acted? It acts separately as well as combinedly. How the interaction is there of these? You
see it is normal as well as this parallel stresses. I should say parallel because of
you know like the parallel forces are there in shear. So, how you know like there the
interaction is there of these forces and how the molecules of the matter you know they
are affected by the interaction of these stresses. This is really a matter of concern to analyze
under the mechanics of material, and that is why you see you know like these two, if
we want to analyze any material, then we need to resolve these two stresses.
One is the sigma; one is the tau for normal stress as well as the shear stress. One is
perpendicular of the normal stress, and other one is parallel to the area of concern as
it is clearly defined in the following figure. So, you see if you see this figure, in the
previous figure, then you will find that you see here that always the normal stress as
I have shown you that the normal stress component, this is the matter of area concern and this
perpendicular is there. If this is my matter of area of concern, then the forces are being
parallel to these things and that is why these stresses are being formed. The single shear stress takes place on the
single plane and the shear area is always cross-sectional of the rivet. So, if you are
talking about any rivet joint, always the rivet joints are being designed on the basis
of shear stress and that is how shearing is taking place, and wherever you see the shear
because you see if these rivets, they are always you see two sheets are there and they
are always combining two sheets. So, if you are pulling you see you know like the force
application is there on these two saps, you know like these two parts are different. One
is on the top up and one is on the bottom plate.
So, now the point of application of this force is acted at two different axes. So, definitely
you see if you want to combine those plates, if we are putting the rivet, then always there
is a shearing area towards those connection points. And that is why you see you know like
if you want to analyze the strength of the rivet, then always we need to design based
on the shear stress whereas, the double shear takes place in the case butt joint. So, if
we are having the butt joint, then you see the double shearing is there. That means you
see the butt joints are always acted, so that you see the area of the matter of concern
is twice than the rivets, and the shear stress is twice than the cross- sectional area of
the rivet because you see it is applied at two different points. If you see this figure, then we can clearly
differentiate those things that you see now the shear failure of the rivet. So, now, you
see here in this is our area of matter, this is our plane and this area, the top of that,
and this is our area of this matter of concern. So, here you see now these if it is parallel,
so this is the parallel part. So, what we have? We have tau that is the shear stress,
and this is normal which is the perpendicular part. So, we have the sigma, so normal stress.
So, if we want to find out that how much, what is the strength of these rivets, what
we need to resolve these components like one is the parallel, one is the perpendicular,
so what is the resultant force is there and you see by resolving those things in this,
the resultant force sr cos theta or sin theta. We can get the effective solution that actually
how much you know like those individual as well as the combined stresses are being setup,
or combined forces are being set up within this region. Once you know these things by
resolving in x and y direction, you can get effective solution that actually how these,
either shear stress or the normal stress are effectively concerned to the design of these
kind of structures. So, as we discussed in that, that shear stresses
are always dominating in these kinds of structures, where the rivet as well as the butt joints
are there. So, if we are talking about the butt joint in which we have these two, this
is one plate, this is another plate, you see these two plates are there in which the force
is acting. So, what we did here is, we simply combined these plates by these butt joints.
So, now if we apply this axial pulling here, you know like this is the shearing area because
it will just try to pullout, but this will try to make the cohesiveness here.
So, here this is the effective area, where shear stresses are always dominating and you
see now we are saying that the two butt joints, if two butt joints mean you see here that
we have two different plates. One is this total plate which is being combined you know
like by both of the butt joints, these two plates you see bottom and top which is always
confined, which is always binded by these butt joints, but we have these you know like
the separate plates. So, if you apply those things here, this region is the effective
region where shear stresses are being set up.
Now, if you go to another point that is you see the lap joint. In lap joint, it is pretty
straight and this is the perfect example of the shear stress because you see here the
line of action if you see here, this is my line of action for this force. As I told you
the force is nothing, but the point of line of action. So, here you see this is the point
where the line of action of force is there. Here the line of action of force is here.
So, if I now combine those things, the nature of this force will try to tend this one towards
this direction. The nature of force of this P will try to tend towards this direction.
So, we have a clockwise region motion is there, but this lap joint will try to you know like
put the resistance towards this clockwise motion or I should say actually the line of
action. So, you see here at these portions, where
this contact region is there, this whole region will suffer by shear stresses. So, like you
see for the single part for either the butt joint as well as the lap joint, always stresses
are there, but if you go to the double shear like in the butt joint as we have seen, you
see you know like here these are the effective portions, where the stresses are being well
set up. These are shear stresses because as I told you these forces are there and because
of these forces, they are well parallel to this application. That means, this is my effective
area, this is contact area, these all contact areas or the effective areas and the forces
are also parallel to the effective area. That means here only shear stresses are being acting
on this parallel, these parallel forces. So, we can say if we want to resolve any of
the forces within this butt joint, we need to be very careful that actually how these
stresses are being taken place in these object first, and second you see which areas are
the concerning areas or I should say the effective areas where the shear stresses are maximum
applied. So, here first, this figure or this figure, we can clearly see that these regions,
this region or this region or this region or this region, all these four regions where
the contact points are there, the meeting surfaces are there.
These surfaces are since parallel to the applied force; these are parallel to the applied force.
Shear stresses are being well set up within these things. The internal intensity you know
like this shear forces are well setup. So, we need to be very careful that actually if
they are uniform, then you do not have to go for delta F by delta A straight way. You
see whatever the effective area is there, how much force is there, just divide the force
per unit area and you will get the shear stresses, but if you see we have the combine stresses
like you see if let us say any other application of the force is. Then we have to be very careful
that actually how these forces are being acted on these objects, and then you see whether
they are acting perpendicular to the area affected. Then, you have to concern the normal
stress if they acted just like parallel as you see in this particular figure.
Then, you need to be very careful that actually we have only the shear stresses and no need
to consider the sigma value that is the normal stress, and if you see the final figure that
is nothing, but you see again a kind of lap joint in the double part. Then, we can see
here there is a straight shifting. So, as you apply the force, there is the load or
the force in the previous figure. You can see that there is a straight shifting of these
contact regions. So, this nothing, but the pin is there. So, pin is now sheared. So,
this one was you see earlier as I told you, this one was the key feature that actually
how it can sustain or withstand the forces. So, you see if it cannot, then you see it
will go up to this feature. If it can sustain, then it has to be there within this region.
So, this will you know like define the shear loading of any feature, and that is what you
see has a good application in boiler design because you see boiler what we are doing here.
You know like lots of internal forces are coming because of the basic purpose of the
boiler is just to generate the heat. So, as heat is generated high pressure, we are generally
categorizing various types if we are talking about the high pressure boiler. That means
the highest pressure means actually more than 400 or the mega Pascal of the steam is to
be generated within those things, either the cold fire or whatever you see you know like
this steam generation is there. So, in that you see always boiler surfaces
are being by lap joint or we can say butt joint. So, in these joints because of the
internal forces, it always try to shear those different mating surfaces and that is why
these things if boiler failure is there means explosion is there. It is because of the failure
of these one of the basic reasons is because of these failures of the joints. So, these
joints may fail and you see clear shifting is there. So, in this lecture, since it was
a basic lecture, so we discussed that what the forces are. If we are talking about solid
part, then there are deformable, there are rigid bodies. In these deformable bodies as
we have discussed that actually you know like how the deformation takes place, what is the
point of application of load is. Accordingly, we can categorize the two basic forms of the
stresses like the normally stresses as well as the shear stresses. How the normally stress
can be acted, what is the point of application of force is there in the normal stress even
itself that whether it is towards the pulling side or the compression side, or it is like
the bearing stresses. So, accordingly we can categorize those things like you see we have
the tensile stress, compressive stress or we have the bearing stress while other thing
you see we have if the forces are not parallel or not perpendicular to the plane, then automatically
it is parallel to the concerned area. Then, you see we have to be very careful that actually
since it is not on the same axis, it is on the plane along the plane. So, how they are
acting? It is whether they are just tried to tend these objects to rotate those things
or not because always when they are not uniaxial, definitely they will just try to at a different
axis. That means, due to these forces, there is a chance of the object will tend to move
in any of the direction clockwise as well as anticlockwise. So, if you want to define
the sign convention of these stresses, always we need to see that how this if uniaxial form
or biaxial or triaxial in the normal stress component or the shear stresses, how will
they act on the object, and correspondingly we will define that since these two forms
of the stresses are there, one is the normal stress, one is the shear stress.
In the normal stress, there are this tensile compressive bearing or in the shear stress
and even the shear stress torsional stress. So, these are the two broad categories and
then, you see you know like there are bending stresses which are nothing, but the combination
of the compressive as well as the shear, this normal, this compressive as well as the tensile
stresses. So, these are the derived stresses, and the last one was the thermal stresses
which you know like due to the temperature variation, they are being setup. So, in that
it again depends on what the thermal coefficient of the expansion is. So, it is a property
of the material. So, in this lecture, we basically are concerned of those kinds of stresses.
So, in the next lecture, we will just try to analyze that if these two stresses are
there, then how many forms of these stresses which we need to define, all those forces
which are being set up within the object is necessary, whether these two forms are like
you see one part is sigma, one part is tau is well set up, or do we need more part like
you see in x direction or in y direction or in z direction. In all the directions if we
are pulling uniaxial pulling or the plane forces are there like you see these parallel
forces, then these two parts are or do we need more forms of the stresses. So, like
you see you know like all these issues which we are going to discuss, and if they are pulling,
then positive direction is there and if we are compressing, then the negative direction
is there. So, what is basic direction or if it just due to this shearing part, if it is
trying to tend in the clockwise or anticlockwise direction. Then what is the sign conventions,
or if we have you know like the direction of the force and the area, if both are acting
at the same place, then you see how you can define whether it is stress or shear stress.
So, all these sign conventions with the subscripts are there. We just want to define in the next chapter. Thank you.

45 Replies to “Lec-2 Strength of Materials”

  1. Clearly, you have a very wrong perception about the faculty teaching at "prestigious institutes like IIT". Compared to others who taught us at the very same institue, I would rate him 7/10

  2. ese toh ghantta bhi samajh nahi aata hai

    jaise aap padha rahe ho ……..class record lecture upload karo is bakwas se accha hoga

  3. sir please upload high resolution video..we can not see the equations and please tell me the link where i can download study materials for this video

  4. This is the worst video ever….
    1. His english is not even english.
    2. His accent is fake.
    3. The video quality is the worst
    4. The diagrams are not visible.
    5. This video is really a QUESTION MARK on IITs!!

  5. i have seen 15 lectures of Dr S P Harsha, i dint find any problem with his communication. I agree video clarity is bad, other than that everything is upto the mark. Concentrate first other than pointing out he is bad.

  6. Sir, i would like to request nptel to upload any other faculty of mechanical(Strength of material) just like Fluid and thermodynamics classes because this paper is not so easy as if this is made just by showing slides,and giving speech.
    I am hoping for a positive response regarding this topic.

  7. worst video I have ever seen from nptel ,,useless lecture ,,same was taught in previous and now also ,,, his speaking skills are worst ,, visualisation of diagrams is pale ,, headache one gets after watching this ,, plzzz remove this professor videos ,,plzzz

  8. worst video I have ever seen from nptel ,,useless lecture ,,same was taught in previous and now also ,,, his speaking skills are worst ,, visualisation of diagrams is pale ,, headache one gets after watching this ,, plzzz remove this professor videos ,,plzzz

  9. Funny accent..can't you speak natural English…you are making easy things difficult to understand with your accent!!!

  10. Learn nothing more than
    "You see"
    " You see like "
    "You Know like the "

    Full lecture is all about these sentences,sad to see such quality if possible please take off these playlists and make new one.

  11. Sir you have a very bad accent. Either speak in hindi or try to improve your english accent so students can understand better.

  12. Hey guys…due to poor video quality diagrams are not clearly visual..those who r facing this problem i advice u guys to refer this ppt available at their official website for diagram purpose http://www.nptel.ac.in/courses/Webcourse-contents/IIT-ROORKEE/strength%20of%20materials/homepage.htm thank you i hope this will help

  13. If you remove "you know like the" from the lecture then the lecture reduces to you know like 27 minutes from you know like 55 minutes…

  14. the details expected from iit professor are not present. its like he is some bad coaching tutor…..

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