Mechanical Engineering Exam > Mechanical Engineering Videos > Strength of Materials (SOM) > Thin Cylinder & Spherical Shells
Thin Cylinder & Spherical Shells Video Lecture | Strength of Materials (SOM) - Mechanical Engineering
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FAQs on Thin Cylinder & Spherical Shells Video Lecture - Strength of Materials (SOM) - Mechanical Engineering
| 1. What is a thin cylinder? |  |
Ans. A thin cylinder is a three-dimensional object with circular bases and straight sides that are very thin compared to the radius of the cylinder. It is commonly used in engineering and physics to represent objects like pipes or tubes.
| 2. How is the volume of a thin cylinder calculated? | |
Ans. The volume of a thin cylinder can be calculated by multiplying the area of the base (which is a circle) by the height of the cylinder. The formula for the volume of a thin cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder.
| 3. What are spherical shells? | |
Ans. Spherical shells are hollow three-dimensional objects that consist of two concentric spheres with different radii. They are commonly used in physics and mathematics to represent objects like hollow balls or shells.
| 4. How is the surface area of a spherical shell calculated? | |
Ans. The surface area of a spherical shell can be calculated by subtracting the surface area of the smaller sphere (inner surface) from the surface area of the larger sphere (outer surface). The formula for the surface area of a spherical shell is A = 4π(R^2 - r^2), where R is the radius of the outer sphere and r is the radius of the inner sphere.
| 5. What are the applications of thin cylinders and spherical shells? | |
Ans. Thin cylinders and spherical shells have various applications in engineering and physics. Thin cylinders are used in the design of pressure vessels, such as gas cylinders and hydraulic cylinders. Spherical shells are used in architecture for designing domes and in physics for modeling celestial bodies like planets or stars.
Text Transcript from Video
Let us take a new chapter in som the
name of the chapter is
as we can see here the name of the
chapter is Thin Cylinders and Spherical
shells now what is Thin cylinder Thin
cylinders are devices which are used in
engineering applications these are also
called as pressure vessels when we talk
about thin cylinders their definition is
thin cylinders are that cylinders in
which the thickness is xx part of
diameter or even less as I have written
here the definition of thin cylinders
thin cylinders are that cylinders in
which the thickness is 28 part of
diameter or even less it means if I
consider small T as the thickness of the
cylinder and D is the diameter of
cylinder so here we have the diameter
thickness should be it should be less
than the twentieth part of diameter that
is if you divide the diameter of
cylinder into twentieth part thickness
should be even less than that so here I
have the relation that thickness upon
diameter it should be less than one upon
20 where I can say small T is the
thickness of cylinder
it will be in mmm and small D is the
diameter here I can say internal
diameter because pressure vessels we are
more interested in their internal
diameters so here we have internal
diameter and it is also in terms of mm
so here it is very much clear from the
definition that thin cylinders are that
cylinders in which the thickness is xx
part of diameter or even less so
thickness should be less than diameter
divided by 20 therefore I have a
relation that if T by D is less than 1
by 20 that kind of cylinders are termed
as thin cylinders otherwise we would be
calling them as thick cylinders that is
if the thickness to diameter ratio is
greater by or it is greater than 1 by 20
so here is the definition of thin
cylinders now we would be seeing the
applications of thin cylinders now thin
cylinders are used in various
engineering applications like we can say
pressure cookers IC engines then boilers
in which the steam is produced so they
are such kind of objects they are
example of thin cylinders and as we have
seen by the relation in thin cylinders
the thickness is very less compared to
the diameter or here I can say internal
diameter
so here is an important point that thin
cylinders are those in which the
thickness is very small compared to the
internal diameter next thin cylinders
are used in LPG cylinders then boilers
are also example of thin cylinders then
we have IC engines that is internal
combustion engines etc so these are some
of the examples of you can we can say
ten cylinders that is the engineering
applications next as we know thin
cylinders they are operating or they are
having inside them pressurized fluid it
can be air gas steam water mixture of
air and fuel etcetera so thin cylinders
are subjected to internal pressure and
because of this pressure what will be
happening that stresses are developed
inside the sand cylinder so internal
pressure gives rise to internal stresses
so there are some kind of stresses which
are developed in that thin cylinders
that stresses we would be seeing just
now next here we can say since the
thickness is very small then the chances
of failures would be more because
failure takes place at that location
where area is minimum so we can say that
the thickness should be
strong enough to resist internal
pressure that is the thin cylinders
should be of sufficient thickness so as
to avoid any failure due to internal
pressure developed next they should be
non corrosive non-toxic and should not
react chemically with the fluids that is
the thin cylinders they should be non
corrosive non-toxic and should not react
chemically with the fluids so these are
some important points which we have seen
regarding the thin cylinders the first
one was in thin cylinders the thickness
is very less compared to the internal
diameter next point thin cylinders are
used in LPG cylinders boilers IC engines
etcetera next they are subjected to
internal pressure internal pressure
gives rise to internal stresses the
thickness should be strong enough to
resist internal pressure at last they
should be non corrosive non toxic and
should not react chemically with the
fluids so here were selling some
important points regarding thin
cylinders now let us start with the
stresses acting on thin cylinders the
next rating is
the stresses acting on thin cylinders
basically there are two kinds of
stresses which are acting on thin
cylinders I will write it here there are
two major stresses acting on thin
cylinders the first one is called as
circumferential or it is also called as
hope stress second one is called as
longitudinal stress so these are the
basic two kinds of stresses and you can
say they are major stresses apart from
there there would even be thermal
stresses developed but here we are not
interested in thermal stress we are more
interested in the stress like
circumferential long and longitudinal
which changes the dimension of that thin
cylinder or you can say which will break
that thin cylinder so let us start first
with the circumferential or hoop stress
for circumferential or hoop stress first
let me give you the diagram that how
this cylinder would be breaking and we
would be getting the stresses here so
let me illustrate this with a diagram
suppose we consider a thin cylinder
whose thickness is small compared to its
internal diameter now this cylinder
would be filled with some kind of fluid
or here I can say it will be pressurized
fluid so this kind of thin cylinder
which we have here once it is filled
with a pressurized fluid so how this
cylinder would be behaving or how the
stress would be acting on this I can
illustrate this with the help of a
diagram for y'all it would be in such a
way
the cylinder would be breaking in such a
way that here we have the bottom half in
next there would be the top half
so now as we can see from these diagrams
that if there is circumferential stress
it would be breaking this thin cylinder
into two halves radially that is while
the pressure is developed that internal
pressure will be acting perpendicular to
the circumference and it will be
breaking the cylinder into two halves as
I have shown you all the cylinder would
be in such form and here some internal
pressure of the fluid would be acting
that is at these internal surfaces and
even here now if I consider small L as
the length of the thin cylinder if we
can say that the diameter of this thin
cylinder is small D small D is the
diameter the thickness of this cylinder
will be small T so here I can say that
for such kind of thin cylinder as we
know the relation thickness upon
diameter should be less than 1 by 20 and
the hoop stress is that stress which
breaks the cylinder into two halves
circumferentially like this the cylinder
would be breaking into this form top and
bottom and here I will say that hoop
stress it would be denoted by Sigma H
and it would be given by PD upon 2 T
so this formula we have to remember if
you want to calculate how much is the
hoop stress in the thin cylinder where
the small P is the pressure or internal
pressure of this fluid D is the diameter
internal diameter we can say of the thin
cylinder small T is the thickness of
thin cylinder so if we know all these
parameters we can get the value of hoop
stress and hoop stress is also called as
circumferential stress which breaks the
cylinder into two parts next let us see
what is longitudinal stress
now let us see what happens to a
cylinder if there is internal pressure
and longitudinal stress is developed
if we have pressurized fluid here and I
can say that L is the length of this
thin cylinder so because of the pressure
developed what will happen that this
cylinder it will be elongated internally
like an internal tensile force will be
acting because of the pressurized fluid
and because of this internal tensile
force there are chances of the cylinder
to elongate and break into two parts
so as we can see here because of the
internal pressure developed there are
chances of this cylinder to elongate and
fail that is it would be subjected to
tension and then the cylinder would be
breaking into two half so the stress
which is developed which causes the
failure in this manner along the length
that is called as longitudinal stress
and longitudinal stress is denoted by
the formula Sigma suffix L is equal to
VD upon 40 where I can say that small P
is the internal pressure D is the
diameter or mostly it is the internal
diameter of the cylinder like I can mark
small D here T is the thickness of this
thin cylinder small D so from this if I
know internal pressure internal diameter
and thickness of the sin thin cylinder I
can get the value of longitudinal stress
it will be in terms of Newton per mm
square now as we have seen hoop stress
or circumferential stress it was PD upon
2 D longitudinal stress is PD upon 4 T
in other words we can say that the hoop
stress is equal to twice of longitudinal
stress this formula we have to remember
hoop stress which also will also be
Newton per mm square so here we have
circumferential stress that is the
stress which causes the cylinder to
break circumferentially into two halves
the top and bottom like I have shown you
all previously that the cylinder would
be breaking into two half
this is circumferential stress where
hoop stress is it is given by PD upon 2
T next we have the longitudinal stress
which breaks the cylinder along its
length value is PD upon 4 T and as we
can see hoop stress is double that then
that of the longitude
so these concepts we have to remember
regarding the thin cylinder
name of the chapter is
as we can see here the name of the
chapter is Thin Cylinders and Spherical
shells now what is Thin cylinder Thin
cylinders are devices which are used in
engineering applications these are also
called as pressure vessels when we talk
about thin cylinders their definition is
thin cylinders are that cylinders in
which the thickness is xx part of
diameter or even less as I have written
here the definition of thin cylinders
thin cylinders are that cylinders in
which the thickness is 28 part of
diameter or even less it means if I
consider small T as the thickness of the
cylinder and D is the diameter of
cylinder so here we have the diameter
thickness should be it should be less
than the twentieth part of diameter that
is if you divide the diameter of
cylinder into twentieth part thickness
should be even less than that so here I
have the relation that thickness upon
diameter it should be less than one upon
20 where I can say small T is the
thickness of cylinder
it will be in mmm and small D is the
diameter here I can say internal
diameter because pressure vessels we are
more interested in their internal
diameters so here we have internal
diameter and it is also in terms of mm
so here it is very much clear from the
definition that thin cylinders are that
cylinders in which the thickness is xx
part of diameter or even less so
thickness should be less than diameter
divided by 20 therefore I have a
relation that if T by D is less than 1
by 20 that kind of cylinders are termed
as thin cylinders otherwise we would be
calling them as thick cylinders that is
if the thickness to diameter ratio is
greater by or it is greater than 1 by 20
so here is the definition of thin
cylinders now we would be seeing the
applications of thin cylinders now thin
cylinders are used in various
engineering applications like we can say
pressure cookers IC engines then boilers
in which the steam is produced so they
are such kind of objects they are
example of thin cylinders and as we have
seen by the relation in thin cylinders
the thickness is very less compared to
the diameter or here I can say internal
diameter
so here is an important point that thin
cylinders are those in which the
thickness is very small compared to the
internal diameter next thin cylinders
are used in LPG cylinders then boilers
are also example of thin cylinders then
we have IC engines that is internal
combustion engines etc so these are some
of the examples of you can we can say
ten cylinders that is the engineering
applications next as we know thin
cylinders they are operating or they are
having inside them pressurized fluid it
can be air gas steam water mixture of
air and fuel etcetera so thin cylinders
are subjected to internal pressure and
because of this pressure what will be
happening that stresses are developed
inside the sand cylinder so internal
pressure gives rise to internal stresses
so there are some kind of stresses which
are developed in that thin cylinders
that stresses we would be seeing just
now next here we can say since the
thickness is very small then the chances
of failures would be more because
failure takes place at that location
where area is minimum so we can say that
the thickness should be
strong enough to resist internal
pressure that is the thin cylinders
should be of sufficient thickness so as
to avoid any failure due to internal
pressure developed next they should be
non corrosive non-toxic and should not
react chemically with the fluids that is
the thin cylinders they should be non
corrosive non-toxic and should not react
chemically with the fluids so these are
some important points which we have seen
regarding the thin cylinders the first
one was in thin cylinders the thickness
is very less compared to the internal
diameter next point thin cylinders are
used in LPG cylinders boilers IC engines
etcetera next they are subjected to
internal pressure internal pressure
gives rise to internal stresses the
thickness should be strong enough to
resist internal pressure at last they
should be non corrosive non toxic and
should not react chemically with the
fluids so here were selling some
important points regarding thin
cylinders now let us start with the
stresses acting on thin cylinders the
next rating is
the stresses acting on thin cylinders
basically there are two kinds of
stresses which are acting on thin
cylinders I will write it here there are
two major stresses acting on thin
cylinders the first one is called as
circumferential or it is also called as
hope stress second one is called as
longitudinal stress so these are the
basic two kinds of stresses and you can
say they are major stresses apart from
there there would even be thermal
stresses developed but here we are not
interested in thermal stress we are more
interested in the stress like
circumferential long and longitudinal
which changes the dimension of that thin
cylinder or you can say which will break
that thin cylinder so let us start first
with the circumferential or hoop stress
for circumferential or hoop stress first
let me give you the diagram that how
this cylinder would be breaking and we
would be getting the stresses here so
let me illustrate this with a diagram
suppose we consider a thin cylinder
whose thickness is small compared to its
internal diameter now this cylinder
would be filled with some kind of fluid
or here I can say it will be pressurized
fluid so this kind of thin cylinder
which we have here once it is filled
with a pressurized fluid so how this
cylinder would be behaving or how the
stress would be acting on this I can
illustrate this with the help of a
diagram for y'all it would be in such a
way
the cylinder would be breaking in such a
way that here we have the bottom half in
next there would be the top half
so now as we can see from these diagrams
that if there is circumferential stress
it would be breaking this thin cylinder
into two halves radially that is while
the pressure is developed that internal
pressure will be acting perpendicular to
the circumference and it will be
breaking the cylinder into two halves as
I have shown you all the cylinder would
be in such form and here some internal
pressure of the fluid would be acting
that is at these internal surfaces and
even here now if I consider small L as
the length of the thin cylinder if we
can say that the diameter of this thin
cylinder is small D small D is the
diameter the thickness of this cylinder
will be small T so here I can say that
for such kind of thin cylinder as we
know the relation thickness upon
diameter should be less than 1 by 20 and
the hoop stress is that stress which
breaks the cylinder into two halves
circumferentially like this the cylinder
would be breaking into this form top and
bottom and here I will say that hoop
stress it would be denoted by Sigma H
and it would be given by PD upon 2 T
so this formula we have to remember if
you want to calculate how much is the
hoop stress in the thin cylinder where
the small P is the pressure or internal
pressure of this fluid D is the diameter
internal diameter we can say of the thin
cylinder small T is the thickness of
thin cylinder so if we know all these
parameters we can get the value of hoop
stress and hoop stress is also called as
circumferential stress which breaks the
cylinder into two parts next let us see
what is longitudinal stress
now let us see what happens to a
cylinder if there is internal pressure
and longitudinal stress is developed
if we have pressurized fluid here and I
can say that L is the length of this
thin cylinder so because of the pressure
developed what will happen that this
cylinder it will be elongated internally
like an internal tensile force will be
acting because of the pressurized fluid
and because of this internal tensile
force there are chances of the cylinder
to elongate and break into two parts
so as we can see here because of the
internal pressure developed there are
chances of this cylinder to elongate and
fail that is it would be subjected to
tension and then the cylinder would be
breaking into two half so the stress
which is developed which causes the
failure in this manner along the length
that is called as longitudinal stress
and longitudinal stress is denoted by
the formula Sigma suffix L is equal to
VD upon 40 where I can say that small P
is the internal pressure D is the
diameter or mostly it is the internal
diameter of the cylinder like I can mark
small D here T is the thickness of this
thin cylinder small D so from this if I
know internal pressure internal diameter
and thickness of the sin thin cylinder I
can get the value of longitudinal stress
it will be in terms of Newton per mm
square now as we have seen hoop stress
or circumferential stress it was PD upon
2 D longitudinal stress is PD upon 4 T
in other words we can say that the hoop
stress is equal to twice of longitudinal
stress this formula we have to remember
hoop stress which also will also be
Newton per mm square so here we have
circumferential stress that is the
stress which causes the cylinder to
break circumferentially into two halves
the top and bottom like I have shown you
all previously that the cylinder would
be breaking into two half
this is circumferential stress where
hoop stress is it is given by PD upon 2
T next we have the longitudinal stress
which breaks the cylinder along its
length value is PD upon 4 T and as we
can see hoop stress is double that then
that of the longitude
so these concepts we have to remember
regarding the thin cylinder
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Nov 21, 2024 Last updated |
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