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Â This is module two of Mechanics of Materials part two.

Â Today's learning outcomes are to define the qualifications for

Â a structure to be treated as a thin-walled pressure vessel.

Â Give some examples of thin-walled pressure vessels, and

Â then determine a method that we'll use for analyzing thin-walled pressure vessels.

Â This is where we left off last class

Â as far as the way that the way that we have for a general analysis approach.

Â And so, we're taking an engineering structure, in this case we're taking this

Â gas storage tank, which we're going to model as a thin-walled pressure vessel.

Â We're going to look at the external loads applied to that structure.

Â In this case the external loads will be pressure inside the vessel due to

Â the liquid or gas, and that's going to generate internal forces in moments

Â which will in turn cause stresses and strains.

Â And we'll be able to use that information to determine the structural performance

Â of our engineering structure.

Â And so, thin wall pressure vessels, let's look at a section cut.

Â So, here I've taken a cut and here is the cross section.

Â If I look at a side view, we're going to say that thin walled is defined

Â as when the ratio of the wall thickness to the diameter of the vessel is so

Â small that the distribution of normal stress in the cut

Â surface is essentially uniform throughout the thickness of the shell.

Â And that's not precisely true, because there's a pressure on the inside.

Â So stress is actually maximum on the inside surface and

Â minimum on the outside surface, where we have a free surface or no stress.

Â But we're going to assume model it such that the distribution

Â is essentially uniform.

Â 1:52

And so, because we have a thin-walled pressure vessel,

Â that means that the outside diameter and

Â the inside diameter are not going to be that much different.

Â And so I'm just going to call them the diameter and I'll give it the symbol D.

Â And if D, the diameter over the thickness of the outside of the shell,

Â our vessel is greater than or equal to 20,

Â we're going to define that as a thin-walled pressure vessel.

Â So here are some examples of thin-walled pressure vessels.

Â They may be boilers, gas storage tanks,

Â perhaps pipelines, even blimps, could be spray cans.

Â All of these are good examples of what could

Â be defined as thin wall pressure vessels.

Â So now we need to look at the analysis techniques we're going to use.

Â And I want you to recall back to the first course in this four part series of

Â mechanics materials, and I'm going to ask you what should we use plane stress or

Â plane strain in analyzing these thin-walled pressure vessels?

Â You're going to have to use your engineering judgement and modeling, and

Â this is a very important step in the engineering process.

Â And you're going to have to be aware of the assumptions you make.

Â I often say that engineering is as much an art as it is a science.

Â And the art part is taking a real world engineering structure and

Â figuring out how we're going to model analyze and potentially even design.

Â 3:23

So as a review, let's go back and look at what we talked about as far as

Â plane stress in the first course of this series.

Â Plane stress said that there was no stress in the Z directions.

Â So, we only have stress in the plane or in the X Y plane.

Â And all three, all real world situations, all structures are three dimensional but

Â we can make the plane stress assumption to simplify the analysis

Â without significantly effecting the results that we get.

Â And we said that a common example of plane stress might be used

Â in the analysis of thin plates, such as the skin panels on aircraft wings.

Â 4:00

Also as a review, we talked about plane strain.

Â Plane strain is when we have no strains in the z-direction.

Â But there can be stresses in the z-direction.

Â And so this is structures where we have a large relative dimension in

Â the z-direction with restraints to prevent strain in the z-direction.

Â And so some examples I gave for my first course were dams,

Â retaining walls, tunnels, bars, tubes, compressed by forces

Â normal to their cross-sections, so they were not allowed to extend.

Â So knowing this review of plane stress and plane strain,

Â what do you think we'll use to analyze?

Â Which of those would be best to analyze thin-walled pressure vessels?

Â 4:45

And what you should come up with is two dimensional or plane stress.

Â And the reason for that is, if we look at a pressure vessel, on the outside surface,

Â if we call the perpendicular to the outside surface,

Â or the normal to the outside surface as being the z-direction,

Â there are no stresses on that outside surface.

Â And it's a thin plate, similar to or a thin engineering structure.

Â Similar to what we would see in the skin panels of aircraft.

Â Maybe a little thicker.

Â But again no stresses in the z-direction gives us a plane stress condition.

Â And so that's the method that we're going to use as we move along and

Â analyze and design thin walled pressure vessels.

Â And I'll see you next time.

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Â