Concept of Thin Cylinder – Thin Cylindrical and Spherical Shells – Strength of Materials


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

64 Replies to “Concept of Thin Cylinder – Thin Cylindrical and Spherical Shells – Strength of Materials”

  1. greeting sir!!!
    The hoop tension must be resisted by a) steel only b) partly by concrete partly by steel c)concrete only d )all

  2. sir your lectures r really very effective for me n all of us ..so I want u to plz give us a lecture on THICK CYLINDER topic

  3. Thank you sir for the videos of yours. U deserve more videos. And I shared these videos for my friends too

  4. Sir explain is very good you have take class on thick cylinder we are waiting for it explain. Steps by steps

  5. sir your are teaching is very useful for me sir kindly explain me how to design vacuum vessel internal presser is 3bar and extrenal pressure 1bar material is ss304L
    design as per ASME standard 8

  6. Hello Friends,

    Watch Complete Video Series of Subject Strength of Materials only on Ekeeda Application.

    Use Coupon Code "NEWUSER" and access any one Subject free for 3 days!

    Download Ekeeda Application and take advantage of this offer.

    Android:- https://play.google.com/store/apps/details?id=student.ekeeda.com.ekeeda_student&hl=en

    iOS:- https://itunes.apple.com/tt/app/ekeeda/id1442131224

  7. Sir I think you should first learn then teach others you teach just basic things no good concepts neither good problems nothing. You are spoiling the carrier of thousands of individuals in the name of gate. Gate asks much better questions

Leave a Reply

Your email address will not be published. Required fields are marked *