About thin shells

This is about science produced by the California Institute of Technology

and originally broadcast by station KPP C. Pasadena Calif.

The programs are made available to the station by national educational radio.

This program is about thin shelves with host Dr. Robert McGregor

and his guest Dr. Charles Babcock assistant professor of aeronautics.

Here now is Dr. McGregor.

I think it would be helpful Chuck if we began with an explanation of what you mean

by a thin shell.

Well I didn't feel basically any type of

structure which is very thin. One direction as compared to

the other direction is like a piece of paper for example which is very thin to the thickness as compared

to say its length or its wit or you might take a 10

candidate our example because a tin can is a structure which is you know is very thin

as compared to which other dimensions and you know the twist diameter or to its length Yeah

about a bill in the Senate. Yeah it didn't show structure too because it's very thin and One

Direction is compared to the other. And basically the description the shell

describes the type of the analysis as you might do on this type.

Structure and that's a technical term. Yeah right right. It describes

a certain discipline in the analysis of structures.

And so when you say thin shell somebody knows it you know you're talking about a certain set of

assumptions made in some type of analysis.

So there's a certain characteristic. Aspect of a piece of

structure which identifies it within shallows and to which you can apply then

certain mathematical methods and right here is exactly to analyzing its behavior right

where things show is important to us.

Well you know all types of structures from

what you might describe as civil engineering structures ones like water

tanks is a good example.

You know they were driving through the Midwest and see large water tanks. These

are basically sand shell structures. You have rows of

buildings which can be constructed as thin shell structures and of course they play

a very important role in aerospace structures. For

example airplanes missiles boosters and spacecraft. Are

largely all constructed then shell structures and so in that sense

they are very important as a major structural component

of butchers and space craft missiles so there's a whole family of

structures that we call things shells which have utility in our society

and all kinds of applications for things that we see in the field.

And to all the way to a very complicated and complex things like

missiles and aircraft. How long of space

rather than shells been an important structural technique it

is something that the human race is used for an extended period hundreds of years so it's a

new concept probably of a day in the order of 100 years or

100 years.

Right.

The analysis of thin shelves has started well.

Roughly it's a hundred fifty years ago. In fact it's rather interesting. One of

the first analysis that was done on thin shelves was essentially to

determine the tones of a bell. This was done as I think banking

on the early 1900s. They decided it would be a better way to build

bells if they could figure out ahead of time how they should how they should design it

such that they could see the right tones.

And so this is really the beginning of shelf theory which actually occurred

considerably before the formal mathematical take needs which we now

have available is that the first experience in recorded history.

Well I don't as far as I know yes and there probably are. Our other one's

back about 18 20 something this time somebody said Down decided he ought

to find a better way to design a bell.

And so this was really what you might consider at the beginning of shell

analysis. Oh they were rather sick but still it was it from the

analysis standpoint was really a shallow analysis as you would call it.

Oh I think though and I want you to many other experiences that we've had that.

Ideas have been in use and concepts have been in use long before we attempted to

formalize them by mathematical analysis or attempt

to understand the basic characteristics.

Well that's true yes. Cranston's the

early aqueducts of the Romans were arch structures you know an arch is

really sort of a basic concept show on the words one dimensional shell.

That's right. Yeah right it's a wonder what we call one dimensional shell

would you. You've soon found out there was a lot easer to support a certain amount.

If you if you built a structure in the form of an arch rather than just

putting the structure between two points in a straight line and just suspending it like a rock like a

bean.

Right what we call a bean which is essentially a straight arch You know it's and it's a lot easier to

support it if you make it like an arch and of course this was long before people really

understood.

Concepts of arches and shells and so forth but through experience you

saw a show in a sense isn't an arch or as arch would have a particular kind

of loading but also in the way but we call it in technical terms a two

dimensional. Configuration residents aligned at the surface. That's right.

Right and argue that our church has essentially one dimension from one

morning to the other whereas a shelf he would describe as going say on a piece of

paper from one corner to another and down the edge so that we have two dimensions as compared to the one

dimensional structure.

When you mentioned that among the characteristics which identify a

shell the fin Shao is the ratio of the thickness to a characteristic dimensions that

like the radius if there is a curvature and M there are other factors for

example or the living conditions essential to the consideration.

Well yes in a sense they are in other words the

characteristic dimension.

As I said was something like the thickness of the shell as compared to the other dimensions or raise the curvature

and so forth. In addition you would have to look at the loading and other words

you would look at say how I had it at a sensitive characteristic dimension of the

loading also. In other words if you had a loading which consisted of

a point load then an arch with a with a very well right here on

unload over a very small area then the assumptions made begin to break down a little bit

because of the of the character of the loading. But generally most physical

loads are spread out over an area which is large enough that you don't get into much

trouble such as a wind load. I went a good way to write a pressure loader

so for in fact you avoid putting point loads on shells.

By the way you design if you are going to put a point load on so you had something you want to hang on the edge of the

shell instead of suspending it by a very small point you put up there

and reinforcement down something that sort of distributes to bits a load right. And this is just to

distribute the load over a larger area so that you don't exceed the maximum strength.

The material even in the case of a distributed load does it make any difference in the

case of a shell such as a tin can where the load is from outside such as the

pressure from the outside or pressure from the inside.

Oh yeah very very definitely. The problem did you get into the same say it said

take a long thin wire. For instance if you take a

long thin wire and you pull on it you know it will carry a great deal of load has great potential.

That's right right right. But if you take the same long wiring you stated between two people and you start

pushing right and you realize it can't take very much load. Yes so you come

into another phenomena then which is not only the load bearing which which deals with

the load carrying capacity of the the structure and this is called really buckling.

What a monster. Intention. You may be able to carry a great number of what a

great deal of load but if you just reverse the sign of the load or reverse the magnet to the direction direction that

right then you find that you enter a new phenomenon which is called buckling

and this is another this is another field of analysis both in Shell analysis and

other in other structures that you have to take into account when looking at a structure.

So in the case of shell structures and shell structures an important aspect of the loading is

that so-called phenomenon of blocking which will determine what its characteristics would be in terms of

design and the strength has today. Now you mentioned that in our

contemporary scene there are many applications and examples of thin shell structures.

We just speak a little further on this. Sure.

Well I mentioned before things like water tanks and things like rusty structures

and in addition you have coarse an airplane is basically

a thin shell structure. It's largely a pressure vessel or a pressure

container. Because it is pressurized Minas I was also

subjected to other loads that from the air and so

forth I'm just a dead weight of the structure and so it's a thin shell structure things

like the boosters of the Apollo boosters and so forth

are largely pressurized. Then shell structures are a great big tank.

Yeah they're just big tin cans all stuck together in one fashion or another and so they

fall very nicely into the dense shell structure category.

Before we get into not care how about some examples which are perhaps

more near at hand. You mention pipes and conduits and

mention of water tanks now water tank for example is a thin shell with an internal pressure right into the

hydrostatic pressure of the water or whatever fluid is contained within it. Are there

other examples in civil engineering about such things as

a case on set of structures that are used I think things of this sort where

they're subjected to external pressure.

That's again a tank as an attack right in the pressure from the OP from the outside causing it the

claps inward right.

Other structures like the.

Domes on observatories. I think one of the polymer observatory is a

quite thin structure quite thin.

Shell and it's subjected extra loads both from snow I think it's designed for a

certain amount of snow they can carry on enough of it which exerts an external pressure on it. When

the wind loads right in its own weight and its own weight you know which is a very from

Sylvan hearing standpoint may be more to put on the load just the weight of the structure itself.

You mentioned a moment when you realize of course that the such structures have been used for a long

time and you indicated that back from the time of the Romans when arches were first developed

it was the phenomena of buckling one that was that would cope with the Only in

recent times and understood or is it something that the people would satisfactory.

Well you know actually the way we talk about buckling in a sense a day

you wouldn't have and he and I structure there was a more of a problem

of the Keystone falling out her right yeah already essentially

a slipping of the masonry structure of the buckling that we talk

about today is more concerned with metallic structures or plastic

structures and things of this sort and so it from it.

It isn't the same type of phenomenon as you had in the early So there's I don't know if

continuity of the material I duck till it hit I had you put a structure together like an Irish

unit can not only take a compression load which when the pieces rub together but

they you can push line with no force right when you put it together and you can pull them apart with no

force at all. So there must be a continuity of the material and certain ductile in material in order

for it to buckle or pop in and out yet I'd say unbuckling the way we talk about it. Yeah generally

today.

Yes that's true but the other type of failure was another mode of

failure which just sort of thinking the allies too. But it's a different type of failure.

Well some of them I was so shit that I'm buckling phenomenon with the structures

associated with aircraft and missiles and structures of that

type. Is a something which has been encountered before in our civil engineering practice

and buildings and and bridges and foundations and so on. Where

are the dimensions and characteristics of the structures. So

much different that buckling is not an important consideration.

Well it is in a number of cases it is an important consideration

but the face a little different problem in a structure which sits on the ground and one that

flies and one that structure its on the ground.

Your weight is not your overall important factor and I would You can

take a structure and add a little bit more material to it and beef it up without any

great consequence. On the other than the cost of additional material. But when you get

into a flight vehicle an airplane our spacecraft.

Then your weight is of course is a very premium consideration you must consider its

prime importance and then when you start cutting

down weight then you get into the area where you have to be much more concerned about bucking the sort

of the question of thinness done becomes a paramount consideration time so

that as you go to from ground structures to air structures aircraft

application that the question of thinness becomes exceedingly important a buckling bucking

phenomenon therefore becomes more crucial consideration in the design.

That's right now it is of course important and other structures too. Like I can

mention the Palmers over time but not generally. It

becomes a more critical problem and you know they likely structures that

so.

Problem to get into in the buckling business could you talk about this

a little further you mentioned this in connection with the wire where you would push at the

end of the wires and cause the wire to collapse. Haha was

this phenomenon experienced actually.

What do we mean by buckling.

Well I need a real good example of buckling with the ordinary oil can. Which if

often they would you take. You take it well can you

press on the bottom of it and you press a certain a certain amount of force and you find

other things snaps inward. And this is basically a buckling phenomena. What

happens is you reach a certain load on the end of the 10

can where the structure becomes unstable. Of course you release the load you find out of

snaps back out. And yes so you haven't really done any damage to material

itself. You haven't permanently deformed as friends there is no primer defamation material

itself. And therefore you can distinguish the buckling failure from

say material failure material failure you'd see if you put it to her I would come back

out again.

I would still be distorted or permanently deformed right

or fracture even right. But the buckling failure at least at the

failure point may not be a cause permanent Reformation. But unfortunately you find

out that in a lot of structures if you want to reach this point where it

snaps then you find out that if it continues on going and then you

end up with the whole structure.

Now in the case of the tank can you compress at the end and cause that the pop

inward which presumably goes to a configuration of

structural configuration which is more adaptable or more supportive of the

load that you apply. Well I doubt refers to reversing the direction of load right.

Well I always kind of look at it like the following if I take the tin can and I start

putting a weight on the end of it. Then it reaches a certain point where the tin

cans. Look you're awfully heavy. I would rather go someplace else

and so it therefore adopts itself to a configuration that's easier for it to get into

to accommodate to accommodate the modern load you put on. Yes but unfortunately you find out

that when it does do this you find out that it also undergoes perma defamation.

An exceedingly enlarged flexions and I and he did I would have a failing

structure.

I want some other examples chock of things shows how

about that. The question of roof some buildings which you mention mention other than the domes of

observatories. Do have examples here.

And well I think there are some and particularly with the advent of the

pre-stressed concrete you find out that the defect misses that you

need are becoming smaller. Pre stressing and therefore these become

thinner and thinner and then they no longer.

There were not only addition just a failure of the material itself but a failure due to

the way it has been used in the wood geometry of the structure and you get

into buckling failures in that sense also what do you mean by a pre-stressed

concrete.

Well this is a country where you are concrete in general has a

reinforcing rods and it gets a raw deal raw generates was take the

tensile loads on it and what's done is that you take these these rods and you pull

them and you pull them to begin with. Well the concrete is set in one of concrete just setting right

you pull them then you point to concrete around him and he and I go on hands so it initially

need the steel rods are in tension and the concrete is in compression

and. Because when the load is applied right then but if the thing is a

concrete only take a very small tensile load Yes it and so therefore you like to put it initially in

compression so when you load it that you don't ever reach the place where the concrete breaks

which is intentional so you pre-stressed it and which mean that you cannot

get by with intersections of concrete and intersections and

meaning you and I both starting to approach this thin shell right business and I think you're beginning to

buckling problems also is that literal in that you get into bucking problems when you talk

about a large concrete pre-stressed concrete dome over a building. Well this is one

of the considerations you have to take into account when designing. Yes I don't know of any

particular stock for sale you know going anyways near that and yeah right there you are right just nothing

of the sort but is is just one design considerations that you take any

problem.

Oh how about no in the case of aircraft you said that then shows and

use throughout and this means that if used rises and when the right tail

surfaces and so fire. It was a peculiar looking geometries

that evidently doesn't make very much difference.

But yes right now it's all important that phrase basically. The as I

said the show basically is a mathematical or something

and of course a more difficult geometry get into the more difficult the

analysis.

Yes. Just one of the. Problems you get into is a complicated

geometry but basically fuselages over the fuselages that really it

took Yeah this line to go very thin shelled too bright and the tube is subjected to a

bending bending and so there are a meter Torii Hunter and the

wing is more like in simplification would be long like that like a very

flat and slender box. Right right they have a basically a block structure and

wing surface are there ways in which their characteristic

ways in which the structures buckle.

Yeah you can notice buckling. Great number

of structures in particular in the subsonic are the low speed aircraft.

You can notice that you I have buckled Sometimes you'll see buckled panels

and wing services are and if you slide surface McCourt's as normal as they're

designed that way.

Yes big theme popping in and out of this right hand is just this is a

buckling phenomenon that you have a very thin

surface and it's here you get another problem to it it basically is that

a wing surface is then service is a flat plate and flat

plates have what is known as a very large post buckling load carrying ability I would think

and buckle but they're still able to carry the load current. Parallel right and so therefore a lot of times your

design ready. Pound to buckle

you know more speedier care of course when you start reaching modern jet aircraft. Then they can

afford to have vocal services to the ER named Dragon grease from the buckle so you want to keep

that shape.

That's why you want to keep their net in shape so they for you find out they design so they don't buckle

but it's a normal design consideration.

Aircraft wings and especially very large aircraft you'll see

some buckled in the case of the more recent

application such as missiles and booster vehicles and so on.

Well then you need when you get into an area were buckling becomes quite

important and you know I was that's one consideration. Well the thing is I'm

not on missiles and boosters.

Here it is you're required to design to a very low

weight very becomes very rich and very crucial factor and these.

And therefore your go to center and center gauge structures there.

There was structures and bucking of course and become the very important

consideration what kind of loads that a booster as it must actually loads up and

there's a lot of different types about axial loads of course is a very important one just because the thrust just to the

thrust of the engines and the engines are down one end in the woods or off through the

structures they have to transmit that would in addition you have very high bending

loads. These come from the fact that when it rises to the atmosphere it's addicted to

wind shears side to side loads right beside loads and this causes would call a

bending moment tends to bend the thing a lot of his lines in an airplane like exactly same type of

thing and if we have bending loads on the structure also so on

either of these conditions you can cause some buckling thread not properly designed right. Well how do we get

around us and modern missile design a booster design. Well there are several

there are several methods one to begin with because you used internal pressurization. I

was the structure has internal pressure and is this like the pre-stressed concrete

notion. Sounds like the same type of thing right you know what you do is you carry part

of the load by the pressurization. You put the whole thing under tension and that's running like a

balloon right.

Right in fact it's a lot of people calling these large brooms because they

are just highly pressurized vehicles and support a great number I would guess by

pressure alone I know that there's already an internal tension load in the structure and then when

he had a compression load due to the axial or due to the bending that only subtracts. That's

right that's right.

Because you always have the other design conditions where it might be able to stand by itself

without any internal pressurization. Just the weight just the weight of some of the dead weight of it

or just due to ground winds while standing on a launch pad which under

load condition you have to consider.

Yes when we've heard of launchings that have been delayed because of excessive wind conditions right then I

think this is for this kind of reason that it could be from this type of reason right.

The high wind gradients that you might get into high loads.

I was able rather rather well these days to predict the

characteristics of these things shows in terms of their buckling.

Well in some sense yes and sometimes no.

The buckling had generally depended upon

taking building one of these things and then going out and putting a load on and seeing whether or

not it could take them and I would you were able to predict in advance very

accurately the load carrying ability of the structure when it was

actually buckled you actually buckled right and because it is quite a problem because

the time you design one time to build one there's a lot of their several years lag in there.

And you would like to be able to predict more accurately in advance what is

the load carrying ability. So in the past you have had to kind of go on what

available analysis there was and. Past experience with the

same type of structure and a little bit of luck with a little fudge factor right.

And the thing is that we're trying to do now is and is

trying to be able to predict in advance more accurately of accountability

how how accurate is accurate in this context.

Well you're talking about factors of two I would say so if you can predict a

factor to it the buckling capacity would be you feel it you'd be doing

well.

Well if you would like to do a lot better than showing up in some structures you can do a lot better

now and in the end some Stephon structures you find

that you're able to predict fairly accurately the load carrying ability you know that's

just in the recent in recent years.

What is it that has caused us to make these advances and is it a better theory

that's been developed in understanding the behavior of these materials are a new mathematical

techniques and what is it.

Well it's a combination of a great number of things. I would say from

the now assistant point it has been the development of better

equations which describe the film. I was people once sat down

and taken a good hard look at the at the equations that you do mathematically.

I was manic I would describe the way the material behaved exactly right so we have more

pretty precise mathematical descriptions of the physical situation.

So then once you have a more prescribed precise description of the

physical problem then you have to go by solving the equations.

And using means the more complicated equations that you write more complicated equations

and then you get into the problem of the sawing these and of course he be digital

computer.

You know I have 10 or 15 years has considerably advanced.

The complexity equations that you can handle. And so that is

helped out and in addition to not only having better different better equations but also

having. Better methods of handling equations.

Another thing which is has happened is that

the experimental techniques that are used to

to model the large structures of the laboratory in a

laboratory have been improved.

This was about science with host Dr Robert McGrath Leon and his guest Dr.

Charles Babcock join us for our next program when Dr. Albert Hibbs will lead

a discussion about geologic history in the making about

science is produced by the California Institute of Technology and is originally broadcast

by station KPCC in Pasadena California. The programs are made

available to the station by national educational radio. This is

the national educational radio network.