nf0856: well good afternoon everybody er today's lecture's topic is tension 
structures as you can see er this term encompasses all kinds of er three-
dimensional structural forms and two-dimensional structural forms er ranging 
from suspension bridges cable nets cable trusses and fabric fabric membranes 
now all these terms will become clearer as we go through the lecture we've got 
plenty of illustrative examples to show you the lecture falls into several 
parts initially namex is going to in-, introduce er the basic principles behind 
the structural actions in tension structures i will then move on to discussing 
fabric membranes and then we conclude the lecture or first part of the lecture 
er with er pneumatic membrane structures er in the second part of the lecture 
we're going to show you a video on tension structures which will reinforce some 
of the concepts ideas presented in the first part of the lecture and then 
finally 
we're going to move on to a workshop where we we're going to be experimenting 
with er tensegrities and what else er reciprocal frames 
nm0857: reciprocal frame structures yeah 
nf0856: er and so on so it's going to be an action packed afternoon [laugh] 
okay i hope you're going to enjoy it now over to namex 
nm0857: right well as er namex has said i'm going to introduce some of the 
basic principles er of tensile structures and one of the really basic 
principles is the fact that they are tensile structures and you can demonstrate 
their efficiency by something as simple as a strip of paper which er will carry 
quite a reasonable load in tension but you try and 
invert this structure so that it's carrying this load in compression turn it 
the other way up and of course it won't even support its own weight so that's 
the first lesson to learn that tensile structures are highly efficient because 
they they don't buckle er i'm sure you all know about buckling behaviour of 
structures and the majority of materials are actually reasonably strong in 
tension therefore er you can use most materials as er for tension structures er 
the second thing we're going to look at is the er behaviour of horizontal 
tension structures and er the simplest form of that is just a structure hanging 
under its own weight and here i've got a a chain er which is hanging under its 
own weight and as you can see it forms a curve and this curve where it's er 
just acting under its own er self-weight is known as a catenary curve the load 
is not quite uniform along 
the structure as a a metre of span at the end is er contains a greater length 
of cable than er a metre in the middle if we then put some load on the 
structure you see that er in fact it's now changed shape and er a point load in 
the centre forms approximately a V-shape structure if we then put er an 
additional load on the structure we see that it's changed shape again and er 
forming a trapezoidal shape and er in the handout you can see that er i've 
given you the different shapes that er a cable actually takes up er depending 
on the loading er the top there we have er the catenary under self-weight of 
the cable and as i said er the weight of the cable actually at the ends is 
greater per 
metre of span than it is in the middle here er if you take a a uniformly 
distributed load on the the cable or chain then it takes up a parabolic form er 
if you have a load that's zero in the centre and maximum at the ends then you 
get an n-, an elliptical er form of the cable or chain er point load gives you 
a triangle and that varies depending on the position of the load er trapezoidal 
where you have two loads and er the more loads you add you get er a polygonal 
sh-, shape so that's er the second leshon lesson to learn about er this type of 
structure they they are er they change shape as according to the load as the 
load changes the shape of the structure changes and these are known as 
funicular structures one thing that we we need to look at er for tension 
structures they can't just act on their own in tension they have to be 
restrained in some way and er we can look at various er retr-, restraining 
systems and again 
you've got these in the handout er the most obvious one the most commonly used 
one is to have c-, cables supported on some mast structures and then to tie 
this structure back er to a foundation in the ground with er another tension 
element so you have a continuous cable round er this acts is acting in 
compression the rest is in tension and then you need some form of of anchorage 
at the bottom an alternative way of er restraining this type of structure is to 
er have some form of buttressing system er where you have inclined supports and 
er this diagram shows a massive buttressing system where the self-weight of the 
buttress is causing an overturning moment and that tensions up the cable 
maintains it in position so the cable's pulling here creating a moment in this 
direction and the supporting structure the eccentric self-weight creates a 
moment in the other direction and the third type of system is to actually have 
a some closed ring round your tension structure so in 
this case here we've got er a series of cables simply sp-, spanning er a space 
here and er these connect to a a rigid beam round the outside er er which would 
be in bending and then the force from this side is carried in compression 
across to the other side so you actually form a a closed circuit so that's er 
three ways of retaining the structure er these are all lightweight structures 
and therefore er a major problem is to er restrain the structure when you have 
wind loading er as you know or i hope you know by now er on structures that are 
fairly flat er you tend to get er suction wind forces and therefore er although 
the dead loads of the structure are acting downwards under gravity the wind 
loads are trying to lift the structure up and a cable is very resistant when 
the loads are down but it doesn't have much resistance when you're trying to 
resist suction forces the structure will deform a lot so er there 
are various ways of er restraining er the wind uplift forces the obvious one is 
to increase the self-weight of the structure over the span so you in-, increase 
the dead weight er which to me is completely opposed to the idea of having a 
tension lightweight structure if you then put a lot of load on it to to stop it 
from moving about in the wind so although that works and is used sometimes it's 
to me not the ideal solution another way of restraining which is slightly 
better is to actually put some er inverted arch or shell structure er around 
the cable and that again is a relatively heavyweight structure and er to me is 
not a particularly good solution although it's lighter than the first one where 
you're just using dead load you are are actually using a a structure here to to 
resist the uplift forces er the third way is er to actually have an opposing 
cable so you have a hanging cable and then you have er another cable which is 
curved in the opposite 
direction and between those in this case you have some struts er there are 
various ways you can do this you could actually have a cable which runs on 
another profile down here and have struts in the middle and ties at the ends so 
there are various combinations or permutations of this but this is forming 
what's known as a cable truss system and there you are actually having a 
lightweight er structure this is in one plane but er also you have problems you 
need to restrain the structure in the other direction so a fourth solution 
which er is probably er the best is to actually have some transverse cables so 
you've got one set of cables hanging in one direction then in the other 
direction these cables that ran in the planar truss across the top here are 
running across your structure so you have a system in one direction hanging and 
in the opposite direction these cables are inverted and they are actually 
prestressed against each other so that's the the various sort 
of stabilizing systems to resist wind uplift right so er that's the sort of 
theory and er now i'll go on and show you some slides er which demonstrate 
these types of structures 
nm0857: er starting with a an early form of tension structure er a sailing 
sailing boat of course demonstrates er two or three different types of tension 
structure the stays er the mast and er the membranes the sails very simple 
membrane structures and these would use er cellulose fibre e-, elements er as 
the tension elements of course er suspension bridges were also made using er 
ropes and er rattan binds and so on er to make simple tension er suspension 
bridges but the the earliest long span bridges were made using wrought iron and 
er this is the Menai Suspension Bridge across to the Island of Anglesey in 
Wales er designed by Thomas Telford er finished in eighteen-twenty-six using 
wrought iron which was sort of the new strong tensile material and er it would 
actually work to the limit of the of the material eighty-eight er newtons per 
square millimetre as the tensile strength and this is hanging in a sort of 
somewhere between the parabolic and er catenary curve er with er more modern 
materials high strength steel once steel was developed in the eighteen-fifties 
then er various processes produced er high strength steel wires and Roebling 
the er North American engineer er made some very elegant er suspension bridges 
including one over Niagara Falls this is Brooklyn Bridge in er New York and you 
can see the suspension cables and also some cable stays er as er modern 
materials and design methods have improved we can see now this is the Severn 
Bridge which is one of the longest spans in the world although the Japanese 
have now got er a bridge which is almost two kilometres 
long er you can see the the size of the tension elements have gone down er over 
the years as material strengths have improved as an example of the of the 
buttress system this is er Dulles Airport in Washington where er you can see 
these inclined columns are actually sort of tilted away from the roof span 
which is cables running between these columns and then to stabilize it it does 
actually use the inverted shell type structure so you have a system of cables 
enclosed by er reinforced concrete er one of the earliest er enclosed ring type 
systems was the Raleigh arena where you have a system of cables running in this 
direction and another system of cables running in a in the other dir-, opposing 
direction and that is actually enclosed within this ring of two inclined arches 
which are self-stressing because the weight of the arch is trying to pull the 
structure this is tending to fall down in this direction tensioning the 
er the cables crossing the str-, across the span taking the idea of the cable 
truss into er three dimensions er the simplest a simple structure is er the 
bicycle wheel type structure where you have a n-, a node in the centre where 
all the cable trusses meet and you have a ring beam which is in compression and 
this is exactly the same as a bicycle wheel er the bike that you ride er you 
have a similar sort of system a compression ring round the outside and the hub 
in the middle and you are actually riding on tension when you ride a bicycle er 
this is an example in Tunisia of er one of these bicycle wheel type roofs er 
other tension type structures you can have er straight er cable stays and these 
are used for bridges and for buildings this is the Inmos factory in er south 
Wales and you can see this is almost like an inverted tree 
type structure with all of these in direct tension and then the compression 
structure supporting that in the centre or the Renault parts distribution 
factory in Swindon er architect er Norman Foster and er quite well known among 
in the architectural world for the bright yellow structure the high-tech s-, 
style er this again is cable-stayed in three dimensions the the sort of cable 
trusses work across and in three directions er the Fleetguard f-, er Factory in 
Quimper in er France er a Richard Rogers er project er this again is er cable-
stayed and has cables that run in er hanging and in the inverted direction to 
resist wind forces on the roof and er this slide also shows that you need some 
restraining s-, system for horizontal wind forces in this type of structure 
another form of er three-dimensional er 
tensile structure is the cable dome and this shows the principle of er the 
cable dome developed by er David Geiger and used for some of the Olympic er 
structures in Seoul and er here shows the cross section the structure's 
originally hanging and then you tension up these cables on the outside that 
lifts up this ring of struts er this is in three dimensions er and then you 
taesio-, tension up the next cable lifts up this ring of struts and so on until 
you end up with a dome shape er in three dimensions this er i think i've showed 
you before in one of the earlier lectures the er Atlanta sor-, Georgia Dome in 
Atlanta which er was used for the er last Olympic Games and er here a similar 
sort of cable cable dome was used and this is the inside you can see the the 
struts and the inclined cables and the rings of cables 
nf0856: namex 
introduced the general principles er of tension structures but concentrating on 
non-fabric er tension structures what i'll be talking about are fabric 
membranes tension membranes and by fabric i understand both the material 
membranes and cable nets as well er if i can have the first slide now er in 
general fabric fabric membranes offer limitless possibilities to create large 
unobstructive er unobstructed areas to provide shelter from rain snow wind er 
here we see er a beach residence a beach palace in Saudi Arabia built in er i 
think nineteen-ninety the and designed by a German firm Sonderkonstruktionen 
und Leichtbau er for short S-L er if you look at the view inside er you can see 
lovely curvatures developing but also what we see here are the lines of the 
cutting pattern this is something that i will er discuss later 'cause it's 
one thing to derive a shape of the membrane another one is to actually build it 
out of strips of fabric as you can see here er another example it's a 
convertible roof for an open-air thea-, air theatre in er Luxembourg er it's a 
hanging fabric structure in unopened state and here you'll see it in open state 
er again it was designed er by S-L and consultant i think Frei Otto from 
Stuttgart er that was a a an earlier structure nineteen-eighty-eight these are 
convertible umbrellas for a mosque in Medina in Saudi Arabia again designed by 
S-L you see these umbrellas here in a semi-open state er and then in fully open 
state the fabric used er was woven Teflon er it's the most expensive fabric you 
can have er and it was coated er with 
tetrafluoride coating to protect it from er sun degradation er the posts are 
air-conditioned they pro-, produce air conditioning er during the summer and 
during winter as well wouldn't it be lovely to have something like that in the 
middle of namex over Lady Godiva what a difference it would make [laughter] but 
one umbrella costs somewhere around one-million pounds because it's got gold 
and precious stones there as well er the reason why these structures are seen 
er in countries such as Saudi Arabia is because of the er the religion there 
and the belief in purity of form er closer to home er this is from namex's town 
i don't know if you want to be associated with Nottingham but this is Inland 
Revenue in Nottingham a membrane structure the fabric used there is er P-V-C 
coated polyester er the structure doesn't look particularly lightweight what 
creates a an 
image of of it being er light is that all the steel elements the the the masts 
and the structure inside er were painted white but there's a lot of steel in 
the structure and it does not actually look lightweight now here you see some 
detail er between the fabric panels er and again the the seams er cutting 
pattern seams which are not very attractive to to the eye construction detail 
these are often very very important to prevent structure from deterioration you 
can see the end detail here and another one which shows a a sort of uniform 
distribution of er stresses along the edge of the the membrane and moving on to 
er cable nets now er this is an example of a aviary in Munich except it's not 
really a cable structure er it's a mesh er made of er wires it's a it's a wire 
mesh stretched 
over over some metal posts which are actually stabilized by means of er cable 
stays and you can see er a construction process here er but the problems that 
these structure present are similar to those that fabric membranes er present 
for designers that is er finding the shape and finding the cutting pattern for 
the complete structure now going to a more classical example of membrane 
structures here we see er Munich Olympic Complex er the stadium which sort of 
resembles the shape of a caterpillar if if if you think it does resemble a 
caterpillar the designers er would be delighted because it's supposed to 
resemble natural structures a swimming pool and a sports' stadium er it isn't 
really a fabric membrane it's a cable er roof membrane can s-, perhaps see a 
better picture of it here er 
it's a s-, it's a a grid of cables er overlaid with acrylic panels translu-, er 
acrylic cladding there's a better slide of it here as you can see er Munich 
Olympic Complex marked a departure from er physical modelling of this structure 
up until then up un-, until nineteen- seventy-two er tension membranes were 
designed with help of a physical model you can see a physical model here for 
the er the Munich er Olympic Stadium and then measurements were taken sort of 
painstaking er care and then the dimensions of the structure would be scaled up 
but that of course created errors er what we see here is an earlier structure 
it's Montreal er it was German er pavilion for the Expo sixty-seven in Montreal 
it's a cable net and fabric structure er designed by er Frei Otto and his team 
from the Institute of s-, of Lightweight Structures in Stuttgart er this 
structure 
was totally designed using fabric models and er soap film models you can see 
another view of the same structure here er w-, what is of interest are these 
eye loops here and they are there purely to distribute the stresses because 
alou-, around the masts we've got concentration of stresses and this is to do 
to to dissipate the stresses er this is a construction of the actual net er a 
physical model with an eye loop which also serves as a window and a soap film 
model i shall talk about soap film models a little bit more later on because 
soap films are a means of er deriving the shape deriving the form the way in 
which this eye loop has been formed was by placing a string on a soap film and 
then drawing the er the soap film up as 
far it could go to to derive the shape er this is a a fabric model in fact er 
the earlier if i go back the earlier structure is a prototype for the Institute 
of er e-, Lightweight Structures in Stuttgart which was a part of the er er the 
complex for Montreal and the structure was actually transported er on the 
university campus it is now preserved as a historical building if you ever 
visit University of Stuttgart it really is worth a visit going to look at the 
structure from outside and inside as well er okay and that's the shape was 
derived with the help of a soap film model here we've got a fabric model with 
some instrumentation some load input on it to take some measurements of how it 
would deflect under loading and a cable net model as well 
and the cutting pattern model there are various possibilities in which you can 
cut fabric to get er the required form but this really er is an area of 
intensive research now i've already touched upon the subject of er modelling er 
indicating that one can er use fabric models and soap film models to derive sh-,
the shape of tension membranes but of course nowadays what we tend to do is to 
model these shapes using computer er so here is a computational model of a a 
fabric membrane and the same structure modelled using a soap film and using 
fabric okay the problem with er computational modelling is that tension 
membranes are geometrical non-linear structures they er deflect a lot under 
given loading so compared to the traditional sort of rigid s-, er structural 
forms in which the displacement of 
the structure corresponds to the amount of loading er this relationship is 
actually er not valid for tension structures we cannot describe er the 
behaviour er by this equation stiffness matrix multiplied by displacement 
equals load and from from that relationship ship-, therefore we can d-, 
calculate displacements and we solve the structure for loads and for 
displacements if we did that with a tension membrane what we would what we 
would find we calculate the displacements we feed those displacements back to 
the original equation and we find we get a different right-hand side not equal 
to the load applied load P but something P with a tilde and then what we have 
to do then is to calculate the difference be-, between P and P-delta P P-tilde 
to get an increment in displacement and we have to keep accumulating this i-, 
increments and substituting to this equation until we actually satisfy this 
equation so it's the modelling is done in an iterative process and 
on your handout there is a full explanation of with what is actually going on 
as far as er mathematical modelling or computational modelling is concerned to 
show you er a stages of numerical modelling i've got a little example er to 
show you next er if we were to model a membrane such as you see here er on plan 
er what we would do we would er if we've got a powerful computer program as a 
first guess we would say we want to stretch a membrane between these boundaries 
and it has to reach this this boundary circle here so initially we we say it's 
flat except for the last roof elements and if we iterate er and start refining 
the shape until we get an equilibrium then we get er the actual this is a plan 
view of the shape we s-, we get a elements which are distorting on on plan kind 
of spider 
spider's web initially if i look back you see these lines were straight what we 
end up is something like that and the final structure looks like that so that 
creates problems keeping the line the lines of the er er of the elements 
straight because ideally we should we would like to use those form as cutting 
pattern lines as seam lines but it is not always er possible 
nf0856: there is no denying that lightweight tension membranes are very popular 
structures particularly amongst architects because they can convey a very 
dramatic expression you can create very exciting shapes er utilizing fabric in 
tension but also er they have a great potential for carrying loads efficiently 
this brings us to the point of what constitutes an efficient structure and 
to follow a quotation from i forget who the author of this book is one of the 
er recently published book on er structural architecture or structural art er 
the message that comes across is this for an efficient structure use tension 
rather than compression and either in preference to bending ironically what we 
teach you here is nothing but bending bending bending bending of beams bending 
of columns bending of slats okay so this course has been put on to er take you 
away from this a little bit now we need to consider the difference the basic 
differences between tension membranes and conventional structures so if we were 
to summarize the main features of tension membranes the first point that has to 
be made is that the shape of a tension membrane has to be found er there is no 
mathematical function that will describe the surface this is the problem so you 
have to resolve into some kind of form finding before you start er the 
structure can increase its stresses under say wind loading given even tenfold 
so initial surface tensions have to be low the structure undergoes very large 
displacements which leads to geometrical non-linearity which has to be modelled 
in modelled on computer er as an iterative process of satisfying proven 
equations and finally because the the design process is so complex the analysis 
form er the analysis part forms a very significant cost er part of the whole 
cost of the of the design unlike for conventional structures when er the 
designer's fees are are very low compared to all the other er costs and these 
costs are attributed mainly to the fact that we have a three stage design 
procedure which involves form finding patterning and static analysis now i only 
touched upon form finding which means finding a three-dimensional shape under 
tension patterning is the stage where you try to construct the membrane from 
finite strips of fabric and in they come about two to three metres wide and 
then final s-, finally static analysis we have to see how the shape is going to 
behave under wind loading er or snow loading and if the deflections are 
excessive or if flat areas will develop then you go back to form finding 
refining your form again how do we go about form finding the first stage well 
we can resort to er resort to construction of physical models or we can use er 
computational model n-, models as far as physical models are concerned there is 
a a variety of them here these these were made by your predecessors as you can 
see and each one of them er has been arrived as as a result of sort of 
iterative process of refining the boundaries rethinking the the the the 
function and so on there are more models that we can show you er later on 
er as well so that's physical modelling er soap films are a very good er 
material to use as well except that er in order to take measurements you have 
to be er using specialist equipment for taking photographs of soap film models 
er but they certainly can be used to verify your computational modelling 
nf0856: i've put this slide here because very often engineers are unsure what 
form finding means we're so used to dealing with rigid forms where we dictate 
the shape we know what the building is going to look like but unfortunately 
with membrane structures you have to find the shape the structure will adopt 
its own shape it the shape cannot be dictated by the designer er the only thing 
that can be dictated are the boundaries of the structure and to a s-, to a s-, 
to some extent you can alter the shape of the surface by differentially 
prestressing er 
membrane between the boundaries now if we concentrate just on computer based 
form finding what what does it mean what does form what can form finding 
computer based form finding produ-, produce there are numerous computer 
programs now developed and in use all over the world and they can do the 
following they can either find an optimal shape for you i will s-, de-, i'll er 
describe what i mean by optimal shape in a moment they can find a shape which 
is in static equilibrium but not necessarily an optimum shape or this is the 
worst case they can find a shape for you which only approximates the state of 
equilibrium and i've i've come across case cases like that this last case 
correspond to the situation where er there are certain inherent assumptions in 
the computer program er which er first of all er don't er allow the computer 
algorithm to work very well so at the end of the iterative procedure you don't 
get get 
a convergence sometimes lack of er experience of the analyst come comes into it 
er and i've come across comments from er for example Australian engineers who 
said well we do our analysis we put the wind load on the structure if the 
program doesn't converge we just forget about it okay er an optimal shape of a 
tension membrane is a shape such that it usem-, uses a minimal amount of 
material er and this can only be achieved if you have a minimum surface area a 
minimum surface area corresponds to what's known a minimal surface and the only 
structure that can reproduce minim-, minimal surfaces are soap film surfaces so 
soap films are very good analogues for er finding shape of membranes however 
there's quite a lot of controversy associated with soap soap film analogy and 
er i think namex witnessed some exchanges at conferences between me and various 
other engineers about wer-, 
about this er problem because it is claimed that soap films are optimized only 
for one load case which is its own surface tension but to counteract these the 
these arguments one can see that the the initial surface tension in a structure 
this is before you apply snow load and wind load is the only permanent load 
acting on the structure all the other loads are temporary so it makes sense to 
optimize for that load load case so really there's no case made er there 
nf0856: if i were to summarize er what is actually going on in the field of er 
the design of tension membranes i would say that there is still a lot of 
research needed i've got my research student here namex who's working with me 
on er computer modelling of tension membranes but applied to automotive 
industry er convertible car hoods and the factors that need to be considered 
are are first of all cost and durability because still despite their 
attractiveness tension membranes are not er 
competitive against conventional roofing forms er the design process can take 
deriving the shape on the computer is not too difficult but cutting patterns 
yes they create a problem it can take up to two days to to to actually come up 
with a reasonable cutting pattern and even then the designers are not sure 
whether they should cut the fabric this way or that way what would give er a 
optimum use of the material er while at the same time would reproduce er you er 
the the surf-, the surface the form found surface because one final point i 
would like to make is that even if we did reproduce the soap film surface on 
computer accurately not everybody's capable of doing that but even if we did 
the second problem is we have to flatten this surface in order to get a cutting 
pattern and minimal surfaces soap film surfaces are non-developable surfaces so 
inevitably there will be d-, errors involved and distortions involved and how 
you minimize these errors er is a problem and as 
far as durability's concerned one should avoid at any cost differential 
prestressing of fabric but unfortunately this is what the designers do these 
days if the shape doesn't look right er because the boundaries were ill chosen 
they tend to prestress the fabric in one direction more than in the other to 
control the shape and the result of that is that the structure with time will 
creep anyway will try to adopt the minimum energy form anyway so such attempts 
are are futile er and differential prestressing of fabrics will lead to fatigue 
of fibres as well those which are stressed more are going to er not not going 
to last as as long that is all i can say er what i haven't talked about is er 
pneumatic membranes everyth-, everything i've said so far relates to surface 
stressed membranes where they are stressed by means of tension applied to the 
boundary er but another category of structures er that i use er are so-called 
pneumatic structures and i think namex 
namex would like to show you a few slides about those they are stressed 
differently they're not stressed at the boundary they're stressed by air 
pressure inside them 
nm0857: er yes as namex's just said the er membrane structures are do have to 
be pretensioned in some way and the difference with inflated structures is this 
pretension is actually applied by er an air pressure within somewhere within 
the structure so here's an example just to show what you can do with inflated 
structures er you may just spot there's something like a a hoover motor down 
here blowing this er dinosaur up so you can see the sort of thing that you can 
do with er inflated structures er we've all er come across inflated structures 
er blown up balloons for parties even a simple er bag foil bag you can just 
blow that up with air pressure but if you have the wrong shape of structure 
then in fact you get these wrinkles which if you're having a permanent 
structure you don't really want these these are undesirable er make the 
structure a bit more flexible the surface of the structure more flexible and of 
course we er every time we use er road transport er we ride on inflatable 
structures the tyres of cars and bicycles are load supporting inflated 
structures er the forms of inflatable structures can be modelled er using soap 
er soap films and this is er these are a slide of er some of the experiments 
done by Frei Otto er in the nineteen-sixties er showing how you can combine 
soap bubble shapes and these could be used potentially for inflated structures 
right if i can switch to the er overhead now 
nm0857: er er there are various er types of er air inflated structures and i 
don't have 
any fancy computer generated pictures er these are freehand sketches er the 
simplest one is just a single skin structure with er air pressure inside and 
that's what's known as an air supported structure then the the next type is an 
air inflated structure where you have a double skin and er generally this 
requires a higher pressure of air in between the two skins and that that forms 
an encloses the space then with a double skin in this case the air pressure is 
inside the structure inside the complete volume in this second case the air 
pressure is on the inside in between those two walls they're the two basic 
types of structure then there are variations on that hybrids er you can combine 
er high pressure tubes inflated tubes and er in this case here evacuate a 
double skinned membrane in between the high pressure tubes er to form 
an enclosed space er the basic er air supported volume can be restrained and 
reinforced by er cables set within the structure so you get this sort of 
chrysalis type form er quite organic looking structure er an alternative form 
is to have er very similar to the previous one here is just to have er high 
pressure tubes and a simple membrane unpressurized in between the two and a 
final hybrid type form er is to have an air supported structure but then to 
actually stiffen the walls by having those inflated so in this case it's a er 
sort of hemispherical structure you've got air pressure inside to maintain it 
and then these are double skins and er they're inflated with pressure as well 
er so a combination of er support air support and er air inflation various 
types of structure right if i could go back to the slides i'll show you a few 
examples of er those 
structures this is er and the majority of them are actually yeah inflated 
structures this is an air inflated structure the German pavilion at the Expo 
nineteen- ninety-two in Seville where the there were two er steel rings and er 
a double skin membrane er spanning between those two rings and then that the 
the space between with two membranes was inflated with air and that formed er 
this sort of taurus type structure which was then suspended with another 
tensile structure er from the mast in the centre here and with the stabilizing 
cables to hold it in position so it does actually demonstrate a couple of er 
tensile type structures then in the United States er there are various er air 
supported structures used for large stadiums and er in these the air pressure 
is actually inside the whole stadium and er to stop it going into a ballooning 
into a huge roof there are restraining cables er to hold the structure down and 
minimize the volume that has to be inflated 
er problems occur with these these type of structures where you can get sort of 
strange bulges and er with er ice and snow the valleys fill up and you can 
actually have rupture of the membrane due to overloading er if you the valleys 
fill with ponds er you might recognize this person in the middle here er this 
is er an air system of air inflated structures that were er assembled at the 
University of Nottingham for a conference last year by students from Stuttgart 
er i think i've shown you just a single slide of this before er these are 
actually salami skins salami sausage skins er to demonstrate er how you can 
actually produce er quite large air inflated structures er these were actually 
ten metres high er this is the basic material and er this is how crude the 
assembly method was just er tying off the ends of the s-, sausage tubes 
er this gives you some idea of the scale of the structures er and the air 
inflation is sufficient for them to be rigid er self-supporting columns ten 
metres high er and and to resist er light breezes as lateral loading er this se-
, shows what happens with the tubes when they go into bending er because er as 
we were saying bending actually is a less efficient way of carrying loading but 
if you want curved-shaped forms you might actually have some bending in your 
structure and you might notice how this actually forms er what er i was talking 
about in one of the earlier lectures natural structures the er structure of er 
cane er where you have the nodes at er points up the er up a tubular structure 
and that actually tends to reinforce it and the same happens naturally in these 
tubes under pressure er this also is an air inflated sorry an air supported 
structure er which was erected at the University of 
Nottingham er last Monday er by er er an artist who works solely with inflated 
er s-, air supported structures er and it will be going on tour er in Germany 
er as a promotional er exhibit for er er a tour company holiday tour company er 
it's er over a thousand square metres of structure and er air supported made 
out of er coloured er P-V-C fabric and er the cutting patterns here w-, earlier 
namex was talking about cutting patterns were actually just derived by eye and 
by using books on welding practice [laugh] how to cut tubes to join them 
together so no computer programs were used in this at all [laugh] purely 
guesswork and er simple geometry mathematics er and as a result of that you can 
see there are actually wrinkles in the structure in certain places and one 
thing about er 
inflated structures under pressure the er there is a relationship between the 
pressure in the structure and the radius of the curvature and the tensile er 
stress in the surface and er generally the tighter the radius er to maintain 
the same tension in the surface you er actually need more pressure so where 
there is actually a tighter radius here you can see it's not quite so inflated 
as the rest of the structure here where the cutting pattern has been derived 
quite well and there is a bigger radius of curvature the the structure is 
actually quite well er inflated er just to show you how little you need to er 
support a structure of this size er about six of these er fans were were 
installed to blow air warm air in fact this was actually heating the air er as 
it was a very cold day last Monday er blowing air into the into the volume 
which took about an hour to inflate er 
another problem of course with er air supported structures is holding them down 
and er in this case as it was a temporary structure it's actually held down 
with these bags full of water er which are attached to the structure on the 
outside 
nf0856: and designed by Nowitzki i think in the fifties and it's a self-
stressing er structure er you can see it doesn't have very heavy anchors of 
foundation because it works on the principle we could demonstrate of two people 
sort of leaning like that okay so you don't require very heavy foundation level 
anchor so that's a very interesting saddle shape structure 
nf0856: so far as the membrane structure's concerned it's a very poor example 
er because the boundaries for the membrane are not very well chosen as a result 
we get a very flat surface so the student obviously did not exploit the 
possibilities that exist er when one experiments with boundaries as far as low 
and high points are concerned er which can alter the surface er geometry 
dramatically so it's not a very good example in fact 
nf0856: inclined posts i suppose namex what else can we say about it should i 
go and get 
nm0857: 
nf0856: the other model but it will take about ten minutes [laugh]