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This is module two of Mechanics of Materials part two.

Today's learning outcomes are to define the qualifications for

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

Give some examples of thin-walled pressure vessels, and

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

This is where we left off last class

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

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

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

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

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

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

which will in turn cause stresses and strains.

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

of our engineering structure.

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

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

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

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

small that the distribution of normal stress in the cut

surface is essentially uniform throughout the thickness of the shell.

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

So stress is actually maximum on the inside surface and

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

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

is essentially uniform.

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

that means that the outside diameter and

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

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

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

our vessel is greater than or equal to 20,

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

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

They may be boilers, gas storage tanks,

perhaps pipelines, even blimps, could be spray cans.

All of these are good examples of what could

be defined as thin wall pressure vessels.

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

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

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

plane strain in analyzing these thin-walled pressure vessels?

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

this is a very important step in the engineering process.

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

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

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

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

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

plane stress in the first course of this series.

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

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

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

we can make the plane stress assumption to simplify the analysis

without significantly effecting the results that we get.

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

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

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Also as a review, we talked about plane strain.

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

But there can be stresses in the z-direction.

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

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

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

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

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

So knowing this review of plane stress and plane strain,

what do you think we'll use to analyze?

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

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

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

if we call the perpendicular to the outside surface,

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

there are no stresses on that outside surface.

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

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

Maybe a little thicker.

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

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

analyze and design thin walled pressure vessels.

And I'll see you next time.

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