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<?xml version="1.0"?>

<!DOCTYPE TEI.2 SYSTEM "base.dtd">




<title>Tension structures</title></titleStmt>

<publicationStmt><distributor>BASE and Oxford Text Archive</distributor>


<availability><p>The British Academic Spoken English (BASE) corpus was developed at the

Universities of Warwick and Reading, under the directorship of Hilary Nesi

(Centre for English Language Teacher Education, Warwick) and Paul Thompson

(Department of Applied Linguistics, Reading), with funding from BALEAP,

EURALEX, the British Academy and the Arts and Humanities Research Board. The

original recordings are held at the Universities of Warwick and Reading, and

at the Oxford Text Archive and may be consulted by bona fide researchers

upon written application to any of the holding bodies.

The BASE corpus is freely available to researchers who agree to the

following conditions:</p>

<p>1. The recordings and transcriptions should not be modified in any


<p>2. The recordings and transcriptions should be used for research purposes

only; they should not be reproduced in teaching materials</p>

<p>3. The recordings and transcriptions should not be reproduced in full for

a wider audience/readership, although researchers are free to quote short

passages of text (up to 200 running words from any given speech event)</p>

<p>4. The corpus developers should be informed of all presentations or

publications arising from analysis of the corpus</p><p>

Researchers should acknowledge their use of the corpus using the following

form of words:

The recordings and transcriptions used in this study come from the British

Academic Spoken English (BASE) corpus, which was developed at the

Universities of Warwick and Reading under the directorship of Hilary Nesi

(Warwick) and Paul Thompson (Reading). Corpus development was assisted by

funding from the Universities of Warwick and Reading, BALEAP, EURALEX, the

British Academy and the Arts and Humanities Research Board. </p></availability>




<recording dur="00:54:21" n="6939">


<respStmt><name>BASE team</name>



<langUsage><language id="en">English</language>



<person id="nf0856" role="main speaker" n="n" sex="f"><p>nf0856, main speaker, non-student, female</p></person>

<person id="nm0857" role="main speaker" n="n" sex="m"><p>nm0857, main speaker, non-student, male</p></person>

<personGrp id="ss" role="audience" size="s"><p>ss, audience, small group </p></personGrp>

<personGrp id="sl" role="all" size="s"><p>sl, all, small group</p></personGrp>

<personGrp role="speakers" size="4"><p>number of speakers: 4</p></personGrp>





<item n="speechevent">Lecture</item>

<item n="acaddept">Engineering</item>

<item n="acaddiv">ps</item>

<item n="partlevel">UG</item>

<item n="module">unknown</item>




<u who="nf0856"><kinesic desc="overhead projector is on showing transparency" iterated="n"/> well good afternoon everybody <pause dur="0.6"/> # today's lecture's topic <pause dur="0.2"/> is tension structures as you can see <pause dur="0.8"/> # this term encompasses all kinds of # <pause dur="0.2"/> three-dimensional structural forms and two-dimensional structural forms <pause dur="0.7"/> # ranging from suspension bridges <pause dur="0.4"/> cable nets cable trusses <pause dur="0.6"/> and <pause dur="0.2"/> fabric fabric membranes <pause dur="0.4"/> now all these terms will become clearer as we go <pause dur="0.2"/> through the lecture <pause dur="0.3"/> we've got plenty of illustrative examples to show you <pause dur="1.1"/> the lecture falls into several parts <pause dur="1.1"/> initially <pause dur="0.3"/> <gap reason="name" extent="1 word"/> is going to <trunc>in</trunc> introduce # <pause dur="0.3"/> the basic principles behind the structural actions <pause dur="0.5"/> in tension structures <pause dur="0.9"/> i will then move on to discussing <pause dur="0.6"/> fabric membranes <pause dur="1.0"/> and then we conclude the lecture or first part of the lecture <pause dur="0.3"/> # with # <pause dur="0.2"/> pneumatic membrane structures <pause dur="1.3"/> # in the second part of the lecture we're going to show you a video <pause dur="0.5"/> on tension structures <pause dur="0.3"/> which will reinforce some of the concepts ideas presented in the first part of the lecture <pause dur="0.7"/> and then finally

we're going to move on to a workshop where <pause dur="0.4"/> we we're going to be experimenting with # <pause dur="0.2"/> tensegrities <pause dur="0.9"/> and what else # <pause dur="0.5"/> reciprocal frames </u><u who="nm0857" trans="overlap"> reciprocal frame structures yeah </u><pause dur="0.5"/> <u who="nf0856" trans="pause"> # and so on so it's going to be an action packed <pause dur="0.2"/> afternoon <vocal desc="laugh" iterated="n"/> okay i hope <pause dur="0.7"/> you're going to enjoy it <pause dur="0.2"/> now over to <gap reason="name" extent="1 word"/> </u><gap reason="break in recording" extent="uncertain"/> <u who="nm0857" trans="pause"> right well as # <gap reason="name" extent="1 word"/> has said i'm going to introduce some of the basic principles <pause dur="0.3"/> # <pause dur="0.2"/> of tensile structures <pause dur="0.5"/> and one of the <pause dur="1.0"/> really basic principles is <pause dur="1.2"/> the fact that they are tensile structures <pause dur="0.5"/> and you can demonstrate their efficiency <pause dur="0.5"/><kinesic desc="holds up strip of paper with weight attached" iterated="n"/> by something as simple as a strip of <pause dur="0.3"/> paper <pause dur="0.6"/> which # <pause dur="0.9"/> will carry quite a reasonable load <pause dur="0.3"/> in tension <pause dur="0.5"/> but you try and

invert this structure so that it's carrying this load in compression <pause dur="0.4"/> turn it the other way up <pause dur="0.3"/><kinesic desc="turns strip of paper with weight attached the other way up" iterated="n"/> and of course <pause dur="0.3"/> it won't even support its own weight <pause dur="0.4"/> so <pause dur="0.7"/> that's the first <pause dur="0.3"/> lesson to learn that tensile structures are highly efficient <pause dur="0.4"/> because they they don't buckle <pause dur="0.8"/> # i'm sure you all know about buckling behaviour of structures <pause dur="1.6"/> and the majority of materials are actually reasonably strong in tension therefore <pause dur="0.7"/> # you can use most materials <pause dur="0.3"/> as # for tension structures <pause dur="1.5"/> # <pause dur="0.3"/> the <pause dur="2.2"/><kinesic desc="holds up metal chain" iterated="n"/> second thing we're going to look at is the <pause dur="0.8"/> # behaviour of <pause dur="0.9"/> horizontal <pause dur="1.0"/> tension structures <pause dur="0.5"/> and # the simplest form of that is just a structure hanging under its own weight <pause dur="0.5"/> and here i've got a <pause dur="0.5"/> a chain <pause dur="0.7"/> # which <pause dur="0.8"/> is hanging under its own weight <pause dur="0.4"/> and as you can see it forms a curve <pause dur="0.6"/> and this curve where it's # just acting under its own <pause dur="0.4"/> # self-weight <pause dur="0.3"/> is known as a catenary curve <pause dur="0.5"/> the load is not quite uniform along

the structure as <pause dur="0.5"/> a a metre of span at the end <pause dur="1.0"/> is # <pause dur="0.2"/> contains a greater length of cable <pause dur="0.4"/> than # a metre <pause dur="0.2"/> in the middle <pause dur="4.7"/><event desc="attaches weight to metal chain" iterated="n"/><kinesic desc="holds up metal chain with weight attached" iterated="n"/> if we then put some load on the structure <pause dur="0.2"/> you see that # <pause dur="0.2"/> in fact <pause dur="0.3"/> it's now changed <pause dur="0.2"/> shape <pause dur="0.7"/> and # a point load in the centre <pause dur="0.2"/> forms <pause dur="0.2"/> approximately a V-shape <pause dur="0.6"/> structure <pause dur="3.0"/> if we then put # <pause dur="0.2"/> an additional load <pause dur="0.9"/><event desc="attaches weight to metal chain" iterated="n"/> on the structure <pause dur="1.4"/><kinesic desc="holds up metal chain with weight attached" iterated="n"/> we see that it's <pause dur="0.9"/> changed shape again <pause dur="0.8"/> and # <pause dur="2.6"/> forming <pause dur="1.8"/> a trapezoidal <pause dur="0.2"/> shape <pause dur="1.0"/> and # <pause dur="0.2"/> <kinesic desc="puts on transparency" iterated="n"/> in the handout you can see <pause dur="0.4"/> that # i've given you the different shapes that # <pause dur="0.2"/> a cable actually takes up <pause dur="0.7"/> # depending on the loading <pause dur="0.5"/> # the top <kinesic desc="indicates point on screen" iterated="n"/> there we have # the catenary under self-weight of the cable <pause dur="0.5"/> and as i said # the weight of the cable actually at the ends is <pause dur="0.2"/> greater per

metre of span <pause dur="0.3"/> than it is in the middle <kinesic desc="indicates point on screen" iterated="n"/> here <pause dur="0.5"/> # <pause dur="0.2"/> if you take a a uniformly distributed load <pause dur="0.7"/> on <pause dur="0.3"/> the <pause dur="0.2"/> the cable or chain <pause dur="0.4"/> then it takes up a parabolic form <pause dur="0.8"/> # if you have a load that's zero in the centre and maximum at the ends then you get an <trunc>n</trunc> <pause dur="0.3"/> an elliptical <pause dur="0.7"/> # <pause dur="0.5"/> form of the cable or chain <pause dur="0.7"/> # point load gives you a triangle <pause dur="0.2"/> and that varies depending on the position <pause dur="0.4"/> of the load <pause dur="0.6"/> # trapezoidal where you have two loads <pause dur="0.4"/> and # <pause dur="0.3"/> the more loads you add <pause dur="0.2"/> you get # <pause dur="0.2"/> a polygonal <trunc>sh</trunc> <pause dur="0.4"/> shape <pause dur="0.6"/> so <pause dur="1.1"/> that's # the second leshon lesson to learn about # this type of structure <pause dur="0.5"/> they <pause dur="0.3"/> they are # <pause dur="1.0"/> they change shape <pause dur="0.3"/> as according to the load as the load changes <pause dur="0.4"/> the shape of the structure changes <pause dur="1.7"/> and these are known as funicular <pause dur="0.2"/> structures <pause dur="8.8"/> <event desc="takes off transparency" iterated="n"/> one thing that we we need to look at # <pause dur="1.3"/> for tension structures they <pause dur="0.2"/> can't just act <pause dur="0.4"/> on their own in tension they have to be restrained in some way <pause dur="1.1"/><kinesic desc="puts on transparency" iterated="n"/> and # we can look at various # <pause dur="0.3"/> <trunc>retr</trunc> restraining systems <pause dur="0.2"/> and again

you've got these <pause dur="0.4"/> in the handout <pause dur="0.6"/> # the most obvious <pause dur="1.4"/> one the most commonly used one <pause dur="0.2"/> is to have <pause dur="0.4"/> <trunc>c</trunc> cables supported on <pause dur="0.6"/> some mast <pause dur="0.2"/> structures <pause dur="1.2"/> and then to tie this structure back <pause dur="0.6"/> # to a foundation in the ground <pause dur="0.4"/> with # another <pause dur="0.2"/> tension element so you have <pause dur="0.3"/> a continuous cable round <pause dur="0.6"/> # this acts <pause dur="0.2"/> is acting in compression the rest is in tension <pause dur="0.5"/> and then you need some form of <pause dur="0.2"/> of anchorage <pause dur="0.2"/> at the bottom <pause dur="3.0"/> an alternative way of # restraining <pause dur="0.2"/><kinesic desc="indicates point on screen" iterated="n"/> this type of structure is to # <pause dur="0.5"/> have some form of buttressing system <pause dur="0.7"/> # where you have inclined supports <pause dur="0.5"/> and # <kinesic desc="indicates point on screen" iterated="n"/> this diagram shows <pause dur="0.2"/> a massive <pause dur="0.3"/> buttressing system <pause dur="0.3"/> where the self-weight of the buttress <pause dur="0.4"/> is causing an overturning moment <pause dur="0.4"/> and that <pause dur="0.6"/> tensions up the cable <pause dur="0.3"/> maintains it in position <pause dur="0.3"/> so the cable's pulling <kinesic desc="indicates point on screen" iterated="n"/> here <pause dur="0.2"/> creating a moment in <kinesic desc="indicates point on screen" iterated="n"/> this direction <pause dur="0.5"/> and the <pause dur="0.8"/> supporting structure <pause dur="1.2"/> the <pause dur="0.4"/> eccentric self-weight <pause dur="0.2"/> creates a moment in the other direction <pause dur="3.9"/> and the third type of system is to actually have a <pause dur="0.2"/> some <pause dur="0.2"/> closed ring <pause dur="0.2"/> round your tension structure <pause dur="0.4"/> so in

<kinesic desc="indicates point on screen" iterated="n"/> this case here we've got # <pause dur="0.6"/> a series of cables simply <trunc>sp</trunc> <pause dur="0.3"/> spanning <pause dur="0.3"/> # a space here <kinesic desc="indicates point on screen" iterated="n"/><pause dur="0.5"/> and # these connect to a a rigid beam round the outside <pause dur="0.7"/> # # which would be in bending <pause dur="0.3"/> and then <pause dur="0.6"/> the force from <kinesic desc="indicates point on screen" iterated="n"/> this side is carried in compression across to <pause dur="0.2"/> the other side so you actually form a <pause dur="0.3"/> a closed circuit <pause dur="2.5"/> so that's # <pause dur="0.9"/> <event desc="takes off transparency" iterated="n"/> three ways of retaining the structure <pause dur="3.7"/> # these are all lightweight structures <pause dur="0.3"/> and therefore <pause dur="0.7"/> # <pause dur="0.8"/> a major problem is to <pause dur="0.6"/> # <pause dur="0.8"/> restrain <pause dur="0.3"/> the structure <pause dur="0.2"/> when you have wind loading <pause dur="0.4"/> # as you know <pause dur="1.0"/> or i hope you know <pause dur="0.5"/> by now <pause dur="0.2"/> # on <pause dur="0.3"/> structures that are fairly flat <pause dur="0.4"/> # you tend to get # <pause dur="0.5"/> suction <pause dur="0.3"/> wind forces <pause dur="0.4"/> and therefore <pause dur="0.5"/> # <pause dur="0.3"/> although the dead loads <pause dur="0.2"/> of the structure are acting downwards under gravity <pause dur="0.4"/> the wind loads are trying to lift the structure up <pause dur="0.2"/> and a cable <pause dur="0.7"/> is very resistant <pause dur="0.2"/> when the <pause dur="0.4"/> loads are down <pause dur="0.2"/> but it doesn't have <pause dur="0.4"/> much resistance when you're trying to <pause dur="0.7"/> resist suction forces the structure <kinesic desc="puts on transparency" iterated="n"/> will deform a lot <pause dur="0.8"/> so # <pause dur="0.2"/> there

are various ways of # <pause dur="2.6"/> restraining <pause dur="0.6"/> # the wind uplift forces <pause dur="0.5"/> the <pause dur="0.9"/> obvious one <pause dur="0.7"/> is to increase the self-weight of the structure <pause dur="1.1"/> over the span so you <trunc>in</trunc> <pause dur="0.2"/> increase the dead weight <pause dur="0.4"/> # which to me is completely opposed to the idea of having a tension lightweight structure <pause dur="0.4"/> if you then put a lot of load on it to <pause dur="0.2"/> to stop it from <pause dur="0.5"/> moving about in the wind <pause dur="0.6"/> so although that works and is used sometimes it's <pause dur="0.2"/> to me not the ideal solution <pause dur="2.7"/> another way of restraining which is slightly better is to actually put some <pause dur="0.4"/> # <pause dur="1.1"/> inverted arch or shell structure <pause dur="0.5"/> # around the cable <pause dur="0.4"/> and that again is <pause dur="1.4"/> a relatively heavyweight structure <pause dur="0.4"/> and # to me is not a <pause dur="0.2"/> particularly good solution although it's lighter than the first one where you're just using dead load <pause dur="0.3"/> you are are actually using a <pause dur="0.5"/> a <kinesic desc="indicates point on screen" iterated="n"/> structure here to to resist the uplift forces <pause dur="2.5"/> # the third way is # to actually have <pause dur="1.0"/> an opposing cable so <pause dur="0.3"/> you have a hanging cable <pause dur="0.5"/> and then you have <pause dur="0.4"/> # <pause dur="1.3"/> another cable which is curved in the opposite

direction <pause dur="0.4"/> and between those in <kinesic desc="indicates point on screen" iterated="n"/> this case you have some struts <pause dur="0.5"/> # there are various ways you can do this you could actually have <pause dur="0.3"/> a cable which runs <pause dur="1.2"/> on another profile <kinesic desc="indicates point on screen" iterated="n"/> down here <pause dur="0.2"/> and have struts in the middle and ties at the ends <pause dur="0.3"/> so there are various combinations or permutations of this but this is <pause dur="0.2"/> forming what's known as a cable truss <pause dur="0.2"/> system <pause dur="0.4"/> and there you are actually having a lightweight <pause dur="0.2"/> # structure <pause dur="1.5"/> this is in one plane <pause dur="0.4"/> but # <pause dur="0.6"/> also you have problems you need to restrain the structure in the other direction <pause dur="0.3"/> so a fourth <pause dur="0.2"/> solution <pause dur="0.2"/> which # <pause dur="0.5"/> is probably <pause dur="1.0"/> # <pause dur="0.5"/> the best <pause dur="0.3"/> is to actually have some transverse cables <pause dur="0.4"/> so you've got <pause dur="0.4"/> one set of cables hanging in one direction <pause dur="0.4"/> then in the other direction <pause dur="0.5"/><kinesic desc="indicates point on screen" iterated="n"/> these cables that ran <pause dur="0.6"/> in the planar truss across the top here <pause dur="0.4"/> are running across your structure <pause dur="0.4"/> so you have a system <pause dur="0.8"/> in one direction hanging <pause dur="0.2"/> and in the opposite direction <pause dur="0.4"/> these cables are <pause dur="0.7"/> inverted <pause dur="0.2"/> and they are <pause dur="0.6"/> actually prestressed <pause dur="0.2"/> against each other <pause dur="1.7"/> so that's the the various sort

of stabilizing systems <event desc="takes off transparency" iterated="n"/> to resist <pause dur="0.6"/> wind <pause dur="0.2"/> uplift <pause dur="2.6"/> right so # <pause dur="0.7"/> that's the sort of theory and # <pause dur="0.7"/> now i'll go on and show you some <pause dur="0.5"/> slides # which demonstrate these types of structures </u><gap reason="break in recording" extent="uncertain"/> <u who="nm0857" trans="pause"><kinesic desc="projector is on showing slide" iterated="n"/> # starting <pause dur="0.2"/> with a <pause dur="1.7"/> an early <pause dur="0.6"/> form of tension structure <pause dur="0.6"/> # a sailing <pause dur="0.2"/> sailing boat of course demonstrates <pause dur="0.4"/> # <pause dur="0.7"/> two or three different types of tension structure the stays <pause dur="0.5"/> # the mast <pause dur="0.4"/> and # the membranes the sails <pause dur="1.0"/> very simple membrane structures <pause dur="0.4"/> and these would use # <pause dur="1.2"/> cellulose fibre <pause dur="0.7"/> <trunc>e</trunc> elements <pause dur="0.4"/> # as the tension elements <pause dur="6.1"/> <kinesic desc="changes slide" iterated="n"/> of course # suspension bridges were also made using # <pause dur="1.0"/> ropes <pause dur="0.7"/> and # rattan <pause dur="0.2"/> binds and so on <pause dur="0.5"/> # to make simple tension <pause dur="0.2"/> # <pause dur="0.3"/> suspension <pause dur="0.3"/> bridges <pause dur="1.1"/> but the <pause dur="1.0"/> the earliest long span bridges <pause dur="0.4"/> were made using wrought iron <pause dur="0.6"/> and # this is the Menai Suspension Bridge <pause dur="0.2"/> across to the Island of Anglesey <pause dur="0.4"/> in Wales <pause dur="0.6"/> # <pause dur="0.2"/> designed by Thomas Telford # finished in eighteen-twenty-six <pause dur="0.4"/> using

wrought iron <pause dur="0.2"/> which was <pause dur="0.3"/> sort of the new strong tensile material <pause dur="0.8"/> and # <pause dur="0.3"/> it would actually work to the limit of the of the material <pause dur="0.7"/> eighty-eight # newtons per square millimetre <pause dur="0.3"/> as the tensile strength <pause dur="1.9"/> and this is hanging <pause dur="0.4"/> in <pause dur="1.7"/> a sort of <pause dur="1.2"/> somewhere between the parabolic and # catenary curve <pause dur="3.1"/> <kinesic desc="changes slide" iterated="n"/> # with # more modern materials high strength steel once steel was developed in the eighteen-fifties <pause dur="0.4"/> then <pause dur="0.4"/> # various processes produced # high strength steel wires <pause dur="0.5"/> and Roebling <pause dur="0.2"/> the # <pause dur="0.3"/> North American engineer <pause dur="0.5"/> # <pause dur="0.9"/> made some <pause dur="1.2"/> very elegant <pause dur="0.3"/> # <pause dur="1.1"/> suspension bridges including one over Niagara Falls this is Brooklyn Bridge in # <pause dur="0.5"/> New York <pause dur="0.2"/> and you can see the suspension cables and also some cable stays <pause dur="3.3"/> <kinesic desc="changes slide" iterated="n"/> # <pause dur="0.2"/> as <pause dur="0.4"/> # modern materials and design methods have improved <pause dur="0.4"/> we can see now this is <pause dur="0.2"/> the Severn Bridge which is one of the <pause dur="0.4"/> longest spans in the world although the Japanese have now got # <pause dur="1.4"/> a bridge which is almost two kilometres

long <pause dur="1.1"/> # you can see the <pause dur="0.2"/> the size of the tension elements have gone down <pause dur="0.7"/> # over the years <pause dur="1.2"/> as material strengths have improved <pause dur="3.3"/> <kinesic desc="changes slide" iterated="n"/> as an example of the of the buttress <pause dur="0.2"/> system this is # <pause dur="0.2"/> Dulles Airport <pause dur="0.3"/> in Washington <pause dur="0.7"/> where <pause dur="0.5"/> # <pause dur="0.2"/> you can see these inclined <pause dur="0.5"/> columns <pause dur="0.4"/> are actually sort of tilted away from <pause dur="0.4"/> the roof <pause dur="0.9"/> span <pause dur="0.5"/> which is cables running between these columns <pause dur="0.3"/> and then <pause dur="0.5"/> to stabilize it it does actually use the inverted <pause dur="0.2"/> shell <pause dur="0.6"/> type structure <pause dur="0.4"/> so you have <pause dur="0.2"/> a system of cables enclosed by <pause dur="0.6"/> # reinforced concrete <pause dur="5.8"/><kinesic desc="changes slide" iterated="n"/> # one of the <pause dur="0.3"/> earliest # <pause dur="2.1"/> enclosed ring type systems was the <pause dur="1.1"/> Raleigh <pause dur="0.2"/> arena <pause dur="1.4"/> where you have <pause dur="0.2"/> a system of <pause dur="1.1"/> cables running in <kinesic desc="indicates point on slide" iterated="n"/> this direction <pause dur="0.2"/> and another system of cables running in a in the other <trunc>dir</trunc> <pause dur="0.2"/> opposing direction <pause dur="0.5"/> and that is actually enclosed <pause dur="0.2"/> within this ring <pause dur="1.0"/> of two inclined arches <pause dur="1.0"/> which are <pause dur="0.2"/> self-stressing because the weight of the arch is trying to pull the structure <pause dur="1.7"/><kinesic desc="indicates point on slide" iterated="n"/> this is tending to fall down in <kinesic desc="indicates point on slide" iterated="n"/> this direction tensioning the

# the cables <pause dur="0.9"/> crossing the <trunc>str</trunc> <pause dur="1.7"/> <kinesic desc="changes slide" iterated="n"/> across the span <pause dur="3.7"/> taking the idea of the cable truss into # three dimensions <pause dur="0.3"/> # the simplest <pause dur="0.4"/> a simple structure is # <pause dur="0.5"/> the bicycle wheel type structure <pause dur="0.4"/> where you have <pause dur="0.3"/> a <trunc>n</trunc> a node in the centre where all the cable trusses meet <pause dur="0.3"/> and you have a ring beam <pause dur="0.3"/> which is in compression <pause dur="0.4"/> and this is exactly the same as a bicycle wheel <pause dur="0.5"/> # <pause dur="0.7"/> the bike that you ride <pause dur="0.5"/> # <pause dur="0.4"/> you have <pause dur="0.4"/> a similar sort of system <pause dur="0.5"/> a compression ring round the outside <pause dur="0.5"/> and the hub in the middle <pause dur="0.3"/> and you are actually <pause dur="0.4"/> riding on tension <pause dur="1.1"/> when <kinesic desc="changes slide" iterated="n"/> you ride a bicycle <pause dur="1.4"/> # this is an example in Tunisia <pause dur="0.3"/> of # one of these bicycle <pause dur="0.7"/> wheel type roofs <pause dur="3.4"/> <kinesic desc="changes slide" iterated="n"/> # other <pause dur="1.8"/> tension type structures you can have # straight <pause dur="0.2"/> # cable stays <pause dur="0.3"/> and these are used for bridges and for buildings <pause dur="0.3"/> this is the <pause dur="0.3"/> Inmos factory <pause dur="0.3"/> in # south Wales <pause dur="0.4"/> and you can see this is almost like an inverted tree

type structure <pause dur="0.4"/> with all of these in direct tension <pause dur="0.2"/> and then the compression structure <pause dur="0.3"/> supporting that in the centre <pause dur="3.5"/> <kinesic desc="changes slide" iterated="n"/> or the Renault parts distribution factory <pause dur="0.8"/> in Swindon <pause dur="0.5"/> # architect # <pause dur="0.2"/> Norman Foster <pause dur="0.9"/> and # <pause dur="0.3"/> quite <pause dur="0.5"/> well known among <pause dur="0.2"/> in the architectural world for the <pause dur="0.2"/> bright yellow structure <pause dur="0.5"/> the high-tech <trunc>s</trunc> <pause dur="0.3"/> style <pause dur="0.8"/> # <pause dur="0.3"/> this again is cable-stayed <pause dur="0.5"/> in three dimensions <pause dur="0.5"/> the the sort of cable trusses <kinesic desc="changes slide" iterated="n"/> work across <pause dur="0.6"/> and in three directions <pause dur="1.6"/> # <pause dur="0.2"/> the Fleetguard <trunc>f</trunc> # Factory <pause dur="0.4"/> in Quimper <pause dur="0.3"/> in # <pause dur="0.5"/> France <pause dur="2.0"/> # a Richard Rogers # project <pause dur="0.8"/> # <pause dur="0.5"/> this again is # cable-stayed <pause dur="0.5"/> and has cables that run <pause dur="0.3"/> in # <pause dur="0.5"/> hanging and <pause dur="0.2"/> in the inverted direction <pause dur="0.4"/> to resist wind forces on the roof <pause dur="3.9"/> <kinesic desc="changes slide" iterated="n"/> and # this slide also shows that you need some restraining <trunc>s</trunc> <pause dur="0.2"/> system <pause dur="0.2"/> for horizontal wind forces <pause dur="1.0"/> in this type of structure <pause dur="4.1"/> <kinesic desc="changes slide" iterated="n"/> another form of # three-dimensional <pause dur="0.4"/> # <pause dur="0.4"/>

tensile structure is the cable dome <pause dur="0.6"/> and this shows the principle <pause dur="0.2"/> of # the cable dome developed by # David Geiger <pause dur="0.7"/> and used <pause dur="0.2"/> for some of the Olympic # structures in Seoul <pause dur="2.2"/> and # here <pause dur="0.6"/> shows the cross section <pause dur="0.7"/> the structure's originally hanging <pause dur="0.2"/> and then you tension up <kinesic desc="indicates point on slide" iterated="n"/> these cables on the outside <pause dur="0.4"/> that lifts up this <pause dur="0.2"/> ring of struts <pause dur="0.5"/> # this is in three dimensions <pause dur="1.0"/> # <pause dur="0.7"/> and then you <trunc>taesio</trunc> tension up the next cable lifts up this ring of struts and so on until you end up with a dome shape <pause dur="0.8"/> # <pause dur="1.6"/> <kinesic desc="changes slide" iterated="n"/> in three dimensions <pause dur="0.2"/> this # <pause dur="0.3"/> i think i've showed you before <pause dur="0.2"/> in one of the earlier lectures <pause dur="0.4"/> the # <pause dur="0.3"/> Atlanta <pause dur="0.9"/> <trunc>sor</trunc> Georgia Dome in Atlanta <pause dur="0.2"/> which # was used for the <pause dur="0.8"/> # <pause dur="1.3"/> last Olympic Games <pause dur="0.5"/> and # here <pause dur="0.5"/> a similar sort of cable <pause dur="2.2"/> <kinesic desc="changes slide" iterated="n"/> cable dome was used <pause dur="0.6"/> and this is the inside <pause dur="0.2"/> you can see the the struts and the <pause dur="0.4"/> inclined cables and the rings of cables </u><gap reason="break in recording" extent="uncertain"/> <u who="nf0856" trans="pause"> <gap reason="name" extent="1 word"/>

introduced the general principles # <pause dur="0.4"/> of tension structures but concentrating on non-fabric <pause dur="0.6"/> # <pause dur="0.4"/> tension structures <pause dur="0.4"/> what i'll be talking about are fabric membranes tension membranes and by fabric i understand <pause dur="0.5"/> both the <pause dur="0.2"/> material membranes <pause dur="0.6"/> and cable nets <pause dur="0.3"/> as well <pause dur="1.4"/> # if i can have the first slide now <pause dur="3.6"/> <kinesic desc="changes slide" iterated="n"/> # in general fabric <pause dur="1.9"/> fabric membranes offer limitless possibilities <pause dur="0.3"/> to create large <pause dur="0.5"/> unobstructive # <pause dur="0.8"/> unobstructed areas <vocal desc="clears throat" iterated="n"/> to provide shelter from rain snow wind <pause dur="0.7"/> # <pause dur="0.3"/> here we see # <pause dur="0.7"/> a beach residence a beach palace in Saudi Arabia built in # <pause dur="0.7"/> i think nineteen-ninety <pause dur="0.4"/> the <pause dur="0.4"/> and designed by a German firm Sonderkonstruktionen und Leichtbau <pause dur="0.5"/> # <pause dur="0.2"/> for short S-L <pause dur="1.0"/> # if you look at the <pause dur="0.3"/> view inside <pause dur="1.1"/> <kinesic desc="changes slide" iterated="n"/> # you can see lovely curvatures developing <pause dur="0.5"/> but also what we see here <pause dur="1.0"/> are <pause dur="0.4"/> the lines of the cutting pattern <pause dur="0.6"/> this is something that i will # discuss later <pause dur="0.7"/> 'cause it's

one <pause dur="0.2"/> thing to derive a shape of the membrane another one <vocal desc="clears throat" iterated="n"/> <pause dur="0.2"/> is to actually build it out of strips of fabric <pause dur="0.5"/> as you can see here <pause dur="2.2"/> # <pause dur="0.4"/> <kinesic desc="changes slide" iterated="n"/> another example <pause dur="0.8"/> it's a convertible roof for an open-air <trunc>thea</trunc><pause dur="0.3"/> air theatre in # <pause dur="0.3"/> Luxembourg <pause dur="0.6"/> # it's a hanging fabric structure in unopened state <pause dur="0.6"/> and here <kinesic desc="changes slide" iterated="n"/> you'll see it in <pause dur="0.4"/> open state <pause dur="1.2"/> # again it was designed <pause dur="0.2"/> # by S-L and consultant i think Frei Otto from Stuttgart <pause dur="1.5"/> # that was a a <pause dur="0.8"/> an earlier structure nineteen-eighty-eight <pause dur="1.4"/> <kinesic desc="changes slide" iterated="n"/><vocal desc="clears throat" iterated="n"/> <pause dur="1.2"/> these are convertible umbrellas for a mosque in Medina in Saudi Arabia again designed by S-L <pause dur="0.4"/> you see these umbrellas <kinesic desc="indicates point on slide" iterated="n"/> here in a semi-open state <pause dur="1.1"/> # <pause dur="0.5"/><kinesic desc="changes slide" iterated="n"/> and then in fully open state <pause dur="1.3"/> the fabric used <pause dur="0.4"/> # was woven Teflon <pause dur="0.3"/> # it's the most expensive fabric you can have <pause dur="1.1"/> # <pause dur="0.7"/> and it was coated <pause dur="0.6"/> # with

tetrafluoride <pause dur="0.3"/> coating to protect it from <pause dur="0.4"/> # <pause dur="0.4"/> sun degradation <pause dur="1.1"/> # <pause dur="0.9"/> the posts are air-conditioned <pause dur="0.6"/> they <trunc>pro</trunc> produce air conditioning <pause dur="0.4"/> # during the summer and during winter <pause dur="0.6"/> as well wouldn't it be lovely to have something like that in the middle of <gap reason="name" extent="1 word"/> over Lady Godiva <pause dur="0.7"/> what a difference it would make <vocal desc="laughter" n="sl" iterated="y" dur="1"/> <pause dur="1.0"/> but one umbrella costs somewhere around one-million pounds because it's got gold and precious stones there as well <pause dur="0.9"/> # the reason why these structures are <pause dur="0.5"/> seen <pause dur="0.5"/> # in countries such as Saudi Arabia is because of the # the religion there and the belief in purity of form <pause dur="3.0"/> <kinesic desc="changes slide" iterated="n"/> # closer to home <pause dur="0.3"/> # this is from <pause dur="0.8"/> <gap reason="name" extent="1 word"/>'s town <pause dur="0.3"/> i don't know if you want to be associated with Nottingham but this is Inland Revenue in Nottingham <pause dur="0.7"/> a membrane structure the fabric used there is # <pause dur="0.4"/> P-V-C coated polyester <pause dur="1.8"/> # <pause dur="2.9"/> the structure doesn't look particularly lightweight what creates a an

image of of it being # light is that <pause dur="0.3"/> all the steel elements <pause dur="0.2"/> the the <pause dur="0.3"/> the masts <pause dur="0.4"/> and the structure inside <pause dur="0.4"/> # were painted white <pause dur="0.3"/> but there's a lot of steel in the structure <pause dur="0.6"/> and it does not <pause dur="0.3"/> actually <kinesic desc="changes slide" iterated="n"/> look lightweight <pause dur="0.5"/> now here you see some detail <pause dur="1.7"/> # between the fabric panels # and again the <pause dur="0.7"/> the seams <pause dur="0.6"/> # cutting pattern seams which are not very attractive to <pause dur="0.4"/> <kinesic desc="changes slide" iterated="n"/> to the eye <pause dur="1.2"/> construction detail <pause dur="0.2"/><kinesic desc="indicates point on slide" iterated="n"/> these are often very very important to prevent structure from deterioration you can see the end detail here <kinesic desc="indicates point on slide" iterated="n"/><pause dur="0.3"/> and another one <pause dur="1.6"/> <kinesic desc="changes slide" iterated="n"/> which shows a a sort of uniform distribution of <pause dur="0.2"/> # stresses along the edge of the <pause dur="0.2"/> the membrane <pause dur="3.3"/> <kinesic desc="changes slide" iterated="n"/> and <pause dur="0.3"/> moving on to # <pause dur="1.6"/> cable nets now <pause dur="0.2"/> # this is an example of a aviary in Munich <pause dur="0.6"/> except it's not really a cable structure <pause dur="0.2"/> # <pause dur="0.8"/> it's a mesh <pause dur="0.8"/> # made of # <pause dur="1.1"/> wires it's a it's a wire mesh <pause dur="0.6"/> stretched

over <pause dur="0.9"/> over <pause dur="0.2"/> some metal posts which are actually stabilized by means of # cable stays <pause dur="0.8"/> <kinesic desc="changes slide" iterated="n"/> and you can see <pause dur="0.4"/> # a construction process here <pause dur="1.7"/> # <pause dur="2.2"/> but the problems that these structure present are similar to those <pause dur="0.4"/> that fabric membranes # <pause dur="0.3"/> present for designers that is <pause dur="0.3"/> # finding the shape and finding the cutting pattern <pause dur="0.3"/> for the complete structure <pause dur="3.2"/> <kinesic desc="changes slide" iterated="n"/> now <vocal desc="clears throat" iterated="n"/> <pause dur="0.5"/> going to a more classical example of membrane structures here we see <pause dur="0.4"/> # Munich Olympic Complex <pause dur="0.4"/> # the stadium <pause dur="0.8"/> which sort of <pause dur="0.3"/> resembles the shape of a caterpillar if if if you think it does resemble a caterpillar the designers # <pause dur="0.3"/> would be delighted because it's supposed to resemble natural structures <pause dur="0.4"/> a swimming pool <pause dur="0.2"/> and a sports' stadium <pause dur="1.0"/> # it isn't really a fabric <pause dur="0.2"/> membrane <kinesic desc="changes slide" iterated="n"/> it's a cable <pause dur="0.7"/> # roof <pause dur="0.2"/> membrane can <trunc>s</trunc> <pause dur="0.3"/> perhaps see a better <pause dur="0.2"/> picture of it here <pause dur="0.5"/> # <pause dur="1.5"/> <kinesic desc="changes slide" iterated="n"/>

it's a <trunc>s</trunc> it's a a grid of cables <pause dur="0.4"/> # overlaid with acrylic <pause dur="0.5"/> panels <trunc>translu</trunc> # acrylic cladding <pause dur="0.7"/> there's a <kinesic desc="changes slide" iterated="n"/> better slide of it here <pause dur="0.3"/> as you can see <pause dur="2.8"/> # <pause dur="1.9"/> Munich Olympic Complex marked a departure from <pause dur="0.2"/> # <pause dur="1.3"/> <kinesic desc="changes slide" iterated="n"/> physical modelling of this structure up until then up <trunc>un</trunc> until <pause dur="0.2"/> nineteen-<pause dur="0.5"/>seventy-two <pause dur="0.5"/> # <pause dur="1.1"/> tension membranes were designed with help of a physical model you can see a physical model <pause dur="0.4"/><kinesic desc="indicates point on slide" iterated="n"/> here <pause dur="0.7"/> for the # the Munich # <pause dur="0.3"/> Olympic Stadium <pause dur="0.7"/> and then measurements were taken sort of painstaking <pause dur="0.2"/> # <pause dur="0.2"/> care <pause dur="0.6"/> and then the dimensions of the structure would be scaled up <pause dur="0.7"/> but that of course <kinesic desc="changes slide" iterated="n"/> created errors <pause dur="1.6"/> # <pause dur="0.6"/> what we see here <pause dur="0.2"/> is an earlier structure <pause dur="0.5"/> it's Montreal <pause dur="0.7"/> # <pause dur="0.3"/> it was German # pavilion for the Expo sixty-seven in Montreal it's a <pause dur="0.2"/> cable net and fabric structure <pause dur="0.5"/> # designed by <pause dur="0.6"/> # Frei Otto and his team from the Institute of <trunc>s</trunc> of Lightweight Structures in Stuttgart <pause dur="1.5"/> # <pause dur="1.6"/> this structure

was totally designed using <kinesic desc="changes slide" iterated="n"/> fabric models and # <pause dur="0.3"/> soap film models you can see another view of the same structure here <pause dur="0.9"/> # <pause dur="0.6"/> <trunc>w</trunc> <pause dur="0.7"/> what is of interest are these eye loops <kinesic desc="indicates point on slide" iterated="n"/> here <pause dur="0.2"/> and they are <pause dur="0.8"/> there <pause dur="0.2"/> purely to distribute <pause dur="0.2"/> the stresses because <trunc>alou</trunc> <pause dur="0.3"/> around the masts we've got concentration of stresses and this is to do <pause dur="0.4"/> to to dissipate the stresses <pause dur="2.0"/> <kinesic desc="changes slide" iterated="n"/> # this is a construction of the actual net <pause dur="2.8"/> <kinesic desc="changes slide" iterated="n"/> # a physical model <pause dur="0.7"/> with an eye loop which also serves as a window <pause dur="2.3"/> <kinesic desc="changes slide" iterated="n"/> and a soap film model <pause dur="0.5"/> i shall talk about soap film models a little bit more <pause dur="0.2"/> later on <pause dur="0.5"/> because soap films are <pause dur="0.5"/> a means of <pause dur="0.2"/> # deriving the shape deriving the form <pause dur="0.4"/> the way in which <kinesic desc="indicates point on slide" iterated="n"/> this eye loop has been formed <vocal desc="clears throat" iterated="n"/> was by placing a string on a soap film <pause dur="1.8"/> and then drawing the # the soap film up <pause dur="0.7"/> as

far it could go to to derive the shape <pause dur="5.5"/> <kinesic desc="changes slide" iterated="n"/> # this is a a fabric model in fact # <pause dur="0.2"/> the earlier if i go back <kinesic desc="changes slide" iterated="n"/> the earlier structure <pause dur="1.3"/> is a prototype for the Institute of # <pause dur="0.4"/> <trunc>e</trunc> <pause dur="0.3"/> Lightweight Structures in Stuttgart which was a part of the # <pause dur="0.8"/> # the complex for Montreal <pause dur="0.4"/> and the structure was actually transported <pause dur="0.3"/> # <pause dur="0.3"/> on the university campus it is now <pause dur="0.5"/> preserved as a historical building <pause dur="0.3"/> if you ever visit University of Stuttgart it really is worth a visit <pause dur="0.2"/> going <pause dur="0.5"/> to look at the structure from outside and inside as well <pause dur="1.0"/> # <pause dur="1.2"/> <kinesic desc="changes slide" iterated="n"/> okay and that's <pause dur="0.5"/> the shape was derived with the <kinesic desc="changes slide" iterated="n"/> help of a soap film model <pause dur="1.0"/><kinesic desc="changes slide" iterated="n"/> here we've got a fabric model <pause dur="0.4"/> with some instrumentation some load input on it to take some measurements of how it would deflect <pause dur="0.4"/> <kinesic desc="changes slide" iterated="n"/> under loading <pause dur="0.7"/> and a cable net model <pause dur="0.5"/> as well <pause dur="2.8"/>

<kinesic desc="changes slide" iterated="n"/> and the cutting pattern model <pause dur="6.5"/> there are various possibilities in which you can <pause dur="0.3"/> cut fabric <pause dur="0.5"/> to get # the required form <pause dur="0.6"/> but this really # is an area of <kinesic desc="changes slide" iterated="n"/> intensive research <pause dur="2.0"/> now <pause dur="1.0"/> i've already touched upon the subject of # modelling # <pause dur="0.2"/> indicating that one can # use fabric models and soap film models to derive <trunc>sh</trunc> the shape of tension membranes <pause dur="0.3"/> but of course <pause dur="0.4"/> nowadays what we tend to do is to model these shapes using computer <pause dur="1.1"/> # <pause dur="0.8"/> so <pause dur="1.1"/> here is a computational model of a a fabric membrane <pause dur="1.4"/> <kinesic desc="changes slide" iterated="n"/> and <pause dur="0.2"/> the same structure modelled using a soap film and using fabric <pause dur="1.6"/> okay <pause dur="3.5"/> the problem with # <pause dur="0.7"/> <kinesic desc="changes slide" iterated="n"/> computational modelling is that <pause dur="0.4"/> tension membranes are geometrical non-linear structures they <pause dur="0.6"/> # <pause dur="0.8"/> deflect a lot under given loading <pause dur="0.8"/> so <pause dur="0.6"/> compared to the traditional sort of rigid <trunc>s</trunc> # structural forms <pause dur="0.3"/> in which the displacement of

the structure corresponds to the amount of loading <pause dur="0.4"/> # <pause dur="0.2"/> this relationship is actually <pause dur="0.3"/> # <pause dur="0.7"/> not valid for tension structures we cannot describe # the behaviour <pause dur="0.4"/> # by <kinesic desc="indicates point on slide" iterated="n"/> this equation stiffness matrix multiplied by displacement <pause dur="0.2"/> equals load <pause dur="0.4"/> and from from that relationship <trunc>ship</trunc> therefore we can <trunc>d</trunc> calculate displacements and we solve the structure for loads and for displacements <pause dur="0.7"/> 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 <pause dur="0.2"/> applied load P <pause dur="0.5"/> but <pause dur="0.2"/> something <pause dur="0.4"/> P <pause dur="0.2"/> with a tilde <pause dur="0.9"/> and then what we have to do then <pause dur="0.4"/> is to calculate the difference <trunc>be</trunc> between P and P-delta <pause dur="0.5"/> P <pause dur="0.2"/> P-tilde <pause dur="0.5"/> to get an increment in displacement and we have to keep accumulating this <trunc>i</trunc> <pause dur="0.2"/> increments <pause dur="0.6"/> and substituting <pause dur="0.5"/> to this equation until we actually satisfy this equation so it's <pause dur="0.8"/> the modelling is done <pause dur="0.3"/> in an iterative process and

on your handout <pause dur="0.4"/> there is a full explanation of with what is actually going on as far as <pause dur="0.4"/> # mathematical modelling or computational modelling is <pause dur="0.4"/> concerned <pause dur="0.9"/> to show you # a stages of numerical modelling i've got a little example <pause dur="0.2"/> # to show you next <pause dur="0.2"/> <kinesic desc="changes slide" iterated="n"/> # <pause dur="0.5"/> if we were to model a membrane such as you see here <pause dur="1.2"/> # on plan <pause dur="1.8"/> # what we would do <kinesic desc="changes slide" iterated="n"/> we would # <pause dur="1.7"/> if we've got a powerful computer program <pause dur="0.5"/> as a first guess we would say <pause dur="0.6"/> we want to stretch a membrane between <kinesic desc="indicates point on slide" iterated="n"/> these boundaries <pause dur="0.4"/> and it has to reach this <pause dur="0.2"/> this boundary circle <kinesic desc="indicates point on slide" iterated="n"/> here <pause dur="0.3"/> so initially we we say it's flat except for the last roof elements <pause dur="0.4"/> and if we iterate <pause dur="1.1"/> # <pause dur="0.9"/> and start refining the shape until we get <pause dur="0.6"/> an equilibrium <pause dur="0.5"/> <kinesic desc="changes slide" iterated="n"/> then we get <pause dur="0.9"/> # <pause dur="2.0"/> <kinesic desc="changes slide" iterated="n"/> the actual this is a plan view of the shape we <trunc>s</trunc> we get a <pause dur="0.4"/> elements which are distorting on on plan kind of spider <pause dur="0.2"/>

spider's web <pause dur="0.5"/> initially if i look back <pause dur="1.0"/> <kinesic desc="changes slide" iterated="n"/> you see these lines were straight <pause dur="1.5"/> what we end up <pause dur="1.6"/> <kinesic desc="changes slide" iterated="n"/> is something like that <pause dur="1.6"/> <kinesic desc="changes slide" iterated="n"/> and the final structure <pause dur="1.3"/><kinesic desc="changes slide" iterated="n"/> looks like that <pause dur="2.9"/> so that creates <pause dur="0.4"/> problems keeping the line the lines of the # <pause dur="1.4"/> # of the elements straight because <pause dur="0.7"/> ideally we should <pause dur="0.2"/> we would like to use those form as cutting pattern lines as seam lines but it is not always <pause dur="0.4"/> # <pause dur="0.3"/> possible </u><gap reason="break in recording" extent="uncertain"/> <u who="nf0856" trans="pause"> there is no denying that lightweight tension membranes are very popular structures particularly amongst architects <pause dur="1.0"/> because <pause dur="0.4"/> they can convey a very dramatic expression <pause dur="0.2"/> you can create very exciting shapes <pause dur="0.6"/> # <pause dur="0.4"/> utilizing fabric in tension <pause dur="0.9"/> but also <pause dur="0.4"/> # they have a great potential <pause dur="0.3"/> for <pause dur="0.5"/> carrying loads efficiently <pause dur="3.3"/> this brings us to the point of what constitutes <pause dur="0.3"/> an efficient structure <pause dur="1.5"/> and <pause dur="0.3"/> <kinesic desc="changes transparency" iterated="y" dur="6"/>

to follow a quotation from <pause dur="1.0"/> i forget who the author of this book is one of the # recently published book on <pause dur="0.6"/> # <pause dur="0.8"/> structural architecture <pause dur="2.2"/> or structural art <pause dur="1.0"/> # <pause dur="0.6"/> the message that comes across is this <reading>for an efficient structure use tension <pause dur="0.2"/> rather than compression <pause dur="1.0"/> and either in preference to bending</reading> <pause dur="1.2"/> ironically what we teach you here <pause dur="0.7"/> is nothing but bending bending bending bending of beams bending of columns bending of slats <pause dur="0.7"/> okay <pause dur="0.3"/> so this course has been put on to <pause dur="0.8"/> # <pause dur="0.3"/> <kinesic desc="changes transparency" iterated="y" dur="11"/> take you away from this <pause dur="0.2"/> a little bit <pause dur="5.7"/> now <vocal desc="clears throat" iterated="n"/> <pause dur="0.3"/> we need to consider the difference the basic differences between tension membranes and conventional structures so if we were to summarize <pause dur="0.5"/> the main features of tension membranes <pause dur="0.4"/> the first point that has to be made is that <pause dur="0.4"/> the shape of a tension membrane has to be found <pause dur="0.7"/> # <pause dur="0.4"/> there is no mathematical function that will describe the surface this is the problem <pause dur="0.5"/> so you

have to resolve into some kind of form finding before you start <pause dur="2.0"/> # <pause dur="0.8"/> the structure can increase its stresses under say wind loading given even tenfold so initial <pause dur="0.2"/> surface tensions have to be low <pause dur="1.4"/> the structure undergoes very large displacements which leads to geometrical non-linearity which has to be modelled in <pause dur="0.4"/> modelled on computer <pause dur="0.4"/> # as an iterative process <pause dur="0.2"/> of satisfying proven equations <pause dur="0.9"/> and finally because the <pause dur="0.2"/> the design process is so complex <pause dur="0.4"/> the analysis form <pause dur="0.4"/> # the analysis part forms a very significant cost <pause dur="0.4"/> # <pause dur="0.5"/> part of the whole <pause dur="0.2"/> cost of the of the design <pause dur="0.4"/> unlike for conventional structures when <pause dur="0.3"/> # <pause dur="0.2"/> the designer's fees are are very low compared to all the other <pause dur="0.3"/> # costs <pause dur="1.9"/> and these costs <pause dur="0.4"/> <kinesic desc="changes transparency" iterated="y" dur="5"/> are attributed mainly to <pause dur="0.8"/> the fact that we have a three stage design procedure <pause dur="0.5"/> which involves form finding <pause dur="0.5"/> patterning and static analysis <pause dur="0.4"/> now i only touched upon form finding which means finding a three-dimensional shape under

tension <pause dur="0.7"/> patterning <pause dur="0.9"/> is the stage where you try to construct the membrane <pause dur="0.3"/> from finite strips of fabric and in <gap reason="inaudible" extent="1 sec"/> they come about <pause dur="0.2"/> two to three metres wide <pause dur="1.5"/> and then final <trunc>s</trunc> finally static analysis <pause dur="0.3"/> we have to see how the shape is going to behave under wind loading <pause dur="0.4"/> # <pause dur="0.5"/> or snow loading <pause dur="0.5"/> and if the deflections are excessive or if flat areas will develop then you go back to form finding refining your form <pause dur="0.3"/> again <pause dur="6.8"/> <kinesic desc="changes transparency" iterated="y" dur="8"/> how do we go about form finding the first stage well <pause dur="1.0"/> we can resort to # resort to construction of physical models <pause dur="0.8"/> or we can use <pause dur="0.7"/> # computational model <trunc>n</trunc> models as far as physical models are concerned there is a a variety of them here <pause dur="0.5"/> these these were made <pause dur="0.8"/> by your predecessors as you can see <pause dur="1.2"/> and each one of them <pause dur="0.8"/> # has been arrived as <pause dur="0.9"/> as a result of sort of iterative process of refining the boundaries rethinking <pause dur="0.5"/> the the the the function and so on <pause dur="0.3"/> there are more models that we can show you <pause dur="0.4"/> # later on <pause dur="0.4"/>

# <pause dur="0.2"/> as well <pause dur="1.5"/> so that's physical modelling <pause dur="0.5"/> # <pause dur="0.6"/> soap films are a very good # material to use as well except that # <pause dur="1.1"/> in order to take measurements you have to be <pause dur="0.4"/> # using specialist equipment for taking photographs of soap film models <pause dur="0.6"/> # but they certainly can be used to verify your <pause dur="0.2"/> computational modelling </u><gap reason="break in recording" extent="uncertain"/> <u who="nf0856" trans="pause"> i've put this slide here because very often engineers <pause dur="0.6"/> are unsure what form finding means we're so used to <pause dur="0.5"/> dealing with rigid forms where we dictate the shape <pause dur="0.4"/> we know what the building is going to look like <pause dur="0.4"/> but unfortunately with membrane structures you have to find the shape <pause dur="0.5"/> the structure will adopt its own shape <pause dur="0.6"/> it <pause dur="0.3"/> the shape cannot be dictated by the designer <pause dur="0.7"/> # the only thing that can be dictated are the boundaries of the structure <pause dur="0.4"/> and to a <trunc>s</trunc> to a <trunc>s</trunc> to some extent you can alter the shape <pause dur="0.2"/> of the surface by differentially <pause dur="0.3"/> prestressing #

membrane between the boundaries <pause dur="2.0"/> now <pause dur="0.5"/> <kinesic desc="changes transparency" iterated="y" dur="4"/> if we concentrate just on computer based form finding <pause dur="0.9"/> what <pause dur="1.8"/> what does it mean what does form what can form finding computer based form finding <trunc>produ</trunc> <pause dur="0.3"/> produce <pause dur="0.4"/> there are numerous computer programs now developed and in use all over the world <pause dur="1.2"/> and they can do the following <pause dur="0.3"/> they can either find an optimal shape for you <pause dur="1.4"/> i will <trunc>s</trunc> <pause dur="0.2"/> <trunc>de</trunc> <pause dur="0.2"/> i'll <pause dur="0.2"/> # describe what i mean by optimal shape in a moment <pause dur="0.8"/> they can find <pause dur="0.2"/> a shape which is in static equilibrium <pause dur="0.2"/> but not necessarily an optimum shape <pause dur="1.3"/> or <kinesic desc="indicates point on screen" iterated="n"/> this is the worst case <pause dur="0.3"/> they can find a shape for you <pause dur="0.4"/> which only approximates the state of equilibrium <pause dur="0.7"/> and i've i've come across case cases like that <pause dur="0.5"/><kinesic desc="indicates point on screen" iterated="n"/> this last case correspond to the situation where <pause dur="1.0"/> # <pause dur="0.9"/> there are certain inherent assumptions in the computer program <pause dur="0.4"/> # which <pause dur="0.2"/> # first of all <pause dur="0.9"/> # <pause dur="1.6"/> don't # allow the computer algorithm to work very well so at the end of the iterative procedure you don't get <pause dur="0.3"/> get

a convergence <pause dur="0.3"/> sometimes lack of # <pause dur="0.2"/> experience of the analyst come comes into it <pause dur="0.8"/> # <pause dur="0.8"/> and i've come across comments from # for example Australian engineers who said well <pause dur="0.4"/> we do our analysis we put the wind load on the structure <pause dur="0.3"/> if the program doesn't converge we just forget about it <pause dur="1.5"/> okay <pause dur="0.9"/> # <pause dur="1.0"/> an optimal shape of a tension membrane is a shape <pause dur="0.6"/> such that it <trunc>usem</trunc> uses a minimal amount of material <pause dur="0.9"/> # <pause dur="1.9"/> and this can only be achieved <pause dur="0.5"/> if you have <pause dur="0.9"/> a minimum surface area <pause dur="1.0"/> a minimum surface area corresponds to what's known a minimal surface <pause dur="0.8"/> and the only structure that can reproduce <trunc>minim</trunc> <pause dur="0.4"/> minimal surfaces are soap film surfaces <pause dur="0.8"/> so soap films are very good analogues for <pause dur="0.5"/> # <pause dur="1.3"/> finding shape of membranes <pause dur="2.0"/> <kinesic desc="changes transparency" iterated="y" dur="3"/> however <pause dur="0.2"/> there's quite a lot of controversy associated with soap soap film analogy and # <pause dur="0.5"/> i think <gap reason="name" extent="1 word"/> witnessed some exchanges at conferences between me and various other engineers about <trunc>wer</trunc> <pause dur="0.2"/>

about this # <pause dur="0.6"/> problem <pause dur="0.5"/> because it is claimed that soap films <pause dur="0.4"/> are optimized only for one load case which is <pause dur="0.3"/> its own surface tension <pause dur="0.8"/> but to counteract these the these arguments <pause dur="0.6"/> one can see <pause dur="0.7"/> that the the initial surface tension in a structure this is before you apply snow load and wind load <pause dur="0.2"/> is the only permanent load acting on the structure all the other loads are temporary <pause dur="0.3"/> so it makes sense to optimize for that load <pause dur="0.3"/> load case so really there's no case made <pause dur="0.6"/> # <pause dur="0.6"/> there </u><gap reason="break in recording" extent="uncertain"/> <u who="nf0856" trans="pause"><kinesic desc="overhead projector is on showing transparency" iterated="n"/> if i were to summarize # <pause dur="1.1"/> what is actually going on in the field of # the design of tension membranes <pause dur="0.6"/> i would say that there is still a lot of research needed i've got my research student here <gap reason="name" extent="2 words"/> who's working with me <pause dur="0.7"/> on # <pause dur="0.5"/> computer modelling of tension membranes but applied to <pause dur="0.3"/> automotive industry <pause dur="0.6"/> # convertible car hoods <pause dur="1.4"/> and the factors that need to be considered are are first of all cost and durability because <pause dur="0.4"/> still despite their attractiveness tension membranes are not <pause dur="0.6"/> # <pause dur="0.2"/>

competitive against conventional roofing forms <pause dur="0.8"/> # <pause dur="0.7"/> the <pause dur="0.7"/> design process can take <pause dur="1.7"/> deriving the shape on the computer is not too difficult but cutting patterns <pause dur="0.2"/> yes they create a problem it can take <pause dur="0.3"/> up to two days to <pause dur="0.2"/> to to actually <pause dur="0.3"/> come up with <pause dur="0.2"/> a reasonable cutting pattern and even then the designers are not sure whether they should cut the fabric this way or that way <pause dur="0.4"/> what would <pause dur="0.2"/> give # a optimum use of the material <pause dur="0.6"/> # <pause dur="0.5"/> while at the same time would reproduce # <pause dur="0.5"/> you # <pause dur="0.8"/> the the <trunc>surf</trunc> the surface the form found surface <pause dur="0.7"/> because <pause dur="0.2"/> one final point i would like to make is that even if we did <pause dur="0.3"/> reproduce the soap film surface on computer accurately <pause dur="0.4"/> not everybody's capable of doing that but even if we did <pause dur="0.6"/> the second problem is we have to flatten this surface <pause dur="0.7"/> in order to get a cutting pattern <pause dur="2.2"/> and <pause dur="0.2"/> minimal surfaces soap film surfaces are non-developable surfaces so inevitably there will be <trunc>d</trunc> <pause dur="0.2"/> errors involved and distortions involved and how you minimize <pause dur="0.2"/> these errors <pause dur="0.4"/> # <pause dur="0.2"/> is a problem <pause dur="0.8"/> and as

far as durability's concerned one should avoid at <pause dur="0.7"/> any cost <pause dur="0.2"/> differential prestressing of fabric but unfortunately <pause dur="0.2"/> this is what the designers do these days <pause dur="0.4"/> if the shape doesn't look right <pause dur="0.6"/> # <pause dur="0.9"/> because the boundaries were ill chosen <pause dur="0.2"/> they tend to <pause dur="0.3"/> prestress the fabric in one direction more than in the other <pause dur="0.2"/> 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 <pause dur="0.4"/> are futile <pause dur="0.6"/> # and differential prestressing of fabrics will <pause dur="0.4"/> lead to fatigue of fibres as well <pause dur="0.2"/> those which are stressed more are going to <pause dur="0.5"/> # not not going to last as as long <pause dur="1.1"/> that is all i can say <pause dur="0.6"/> # <pause dur="0.5"/> what i haven't talked about is # pneumatic membranes <pause dur="0.2"/> <trunc>everyth</trunc> everything i've said so far relates to <pause dur="0.8"/> surface stressed membranes <pause dur="0.4"/> where they are stressed by means of tension <pause dur="0.3"/> applied to the boundary <pause dur="1.5"/> # <pause dur="0.9"/> but another category of structures <pause dur="0.5"/> # <pause dur="0.9"/> that i use <pause dur="0.9"/> # are so-called pneumatic structures and i think <gap reason="name" extent="1 word"/>

<gap reason="name" extent="1 word"/> would like to <pause dur="0.2"/> show you a few slides about those <pause dur="0.3"/> they are stressed differently <pause dur="0.4"/> they're not stressed at the boundary they're stressed by air pressure inside them </u><gap reason="break in recording" extent="uncertain"/> <u who="nm0857" trans="pause"><kinesic desc="projector is on showing slide" iterated="n"/> # <pause dur="1.4"/> yes as <gap reason="name" extent="1 word"/>'s <pause dur="0.3"/> just said the # <pause dur="2.4"/> membrane structures are <pause dur="0.3"/> do have to be pretensioned in some way <pause dur="0.5"/> and the difference with inflated structures is this pretension <pause dur="0.3"/> is actually applied <pause dur="0.4"/> by <pause dur="0.6"/> # an air pressure <pause dur="0.2"/> within somewhere within the structure <pause dur="0.6"/> so here's an example just to show what you can do with inflated structures <pause dur="0.5"/> # <pause dur="0.6"/> you may just spot there's something like a <pause dur="1.8"/> a hoover motor down here blowing this <pause dur="0.4"/> # dinosaur up <pause dur="2.7"/> so you can see the sort of thing that you can do with <kinesic desc="changes slide" iterated="n"/> # <pause dur="0.2"/> inflated structures <pause dur="2.8"/> # <pause dur="0.2"/> we've all <pause dur="0.5"/> # come across inflated structures # blown up balloons for parties even a simple <pause dur="0.8"/> # <pause dur="1.0"/> bag foil bag you can just blow that up with air pressure <pause dur="0.4"/> but if you have the wrong shape of structure <pause dur="0.4"/>

then in fact you get these wrinkles which if you're having a permanent structure <pause dur="0.2"/> you don't really want <pause dur="0.4"/> these these are undesirable <pause dur="0.4"/> # make the structure <pause dur="0.2"/> a bit more flexible the surface of the structure more flexible <pause dur="2.6"/> and of course we # <pause dur="1.3"/> <kinesic desc="changes slide" iterated="n"/> every time we use # road transport <pause dur="0.6"/> # <pause dur="0.2"/> we ride on inflatable structures the tyres of cars and bicycles <pause dur="0.5"/> are <pause dur="0.7"/> load supporting inflated structures <pause dur="2.2"/> # the forms of inflatable structures can be modelled <pause dur="0.4"/> # using soap <pause dur="0.2"/> # soap films <pause dur="0.3"/> and this is # <pause dur="0.4"/> these are <pause dur="0.2"/> a slide of # some of the experiments done by Frei Otto <pause dur="0.8"/> # <pause dur="0.3"/> in the nineteen-sixties <pause dur="0.5"/> # <pause dur="0.2"/> showing how <pause dur="0.2"/> you can combine <pause dur="0.3"/> soap bubble shapes and these could be used potentially <pause dur="0.6"/> for inflated structures <pause dur="3.3"/> <kinesic desc="changes slide" iterated="n"/> right if i can switch to the # <pause dur="1.1"/> overhead now </u><gap reason="break in recording" extent="uncertain"/> <u who="nm0857" trans="pause"> # <pause dur="2.9"/> # there are various <event desc="turns on overhead projector" iterated="n"/> # types of <pause dur="0.4"/> # <pause dur="0.2"/> air inflated structures <pause dur="0.6"/> <kinesic desc="puts on transparency" iterated="n"/> and i don't have

any fancy computer <pause dur="0.2"/> generated pictures <pause dur="0.5"/> # these are freehand sketches <pause dur="0.9"/> # <pause dur="0.7"/> the simplest one is just <pause dur="1.0"/> a single skin structure <pause dur="0.5"/> with <pause dur="0.8"/> # air pressure inside and that's <pause dur="0.2"/> what's known as an air supported <pause dur="0.4"/> structure <pause dur="5.4"/> <kinesic desc="reveals covered part of transparency" iterated="n"/> then <pause dur="4.2"/> the the next type is an air inflated structure where you have a double skin <pause dur="0.5"/> and # generally this requires <pause dur="0.2"/> a higher pressure <pause dur="0.5"/> of air <pause dur="0.6"/> in between the two skins <pause dur="0.5"/> and that that forms an <pause dur="0.2"/> encloses the space then with a double skin <pause dur="0.3"/><kinesic desc="indicates point on screen" iterated="n"/> in this case the air pressure is inside the structure <pause dur="0.7"/> inside the complete volume in <kinesic desc="indicates point on screen" iterated="n"/> this second case the air pressure is on the inside <pause dur="0.5"/> in between those two walls <pause dur="2.3"/> they're the two basic types of structure <pause dur="0.2"/> then there are variations <kinesic desc="changes transparency" iterated="y" dur="4"/> on that hybrids <pause dur="0.5"/> # <pause dur="3.8"/> you can combine <pause dur="0.4"/> # high pressure tubes <pause dur="0.9"/> inflated tubes <pause dur="0.5"/> and # in this case <kinesic desc="indicates point on screen" iterated="n"/> here evacuate a double skinned membrane in between the <pause dur="0.2"/> high pressure tubes <pause dur="0.5"/> # to form

an enclosed space <pause dur="2.9"/> # the basic # <pause dur="1.2"/> air supported volume <pause dur="0.2"/> can be restrained <pause dur="0.4"/> and reinforced by # <pause dur="0.4"/> cables <pause dur="0.3"/> set within the structure so you get this sort of <pause dur="0.5"/> chrysalis type <pause dur="0.2"/> form <pause dur="0.9"/> # <pause dur="1.1"/> quite organic looking structure <pause dur="6.9"/> <kinesic desc="changes transparency" iterated="y" dur="5"/> # an alternative form is to have # <pause dur="0.3"/> very similar to the <pause dur="0.6"/> previous one here <pause dur="0.3"/> is just to have # <pause dur="0.5"/> high pressure tubes and a simple membrane <pause dur="0.2"/> unpressurized in between the two <pause dur="2.1"/> and a final <pause dur="0.4"/> hybrid type form <pause dur="0.5"/> # is to have an air supported structure but then to actually stiffen the walls <pause dur="0.3"/> by having those inflated <pause dur="0.3"/> so in this case it's a <pause dur="0.4"/> # sort of hemispherical structure <pause dur="0.3"/> you've got air pressure inside to maintain it <pause dur="0.2"/> and then <kinesic desc="indicates point on screen" iterated="n"/> these <pause dur="0.6"/> are double skins <pause dur="0.3"/> and # they're inflated with pressure <pause dur="0.2"/> as well <pause dur="0.7"/> # <pause dur="1.9"/> so <pause dur="0.9"/> a combination of # support air support and # <pause dur="0.2"/> air inflation <pause dur="0.3"/> various types of structure <pause dur="0.7"/> right if i could go back to the slides i'll show you a few examples <pause dur="0.8"/> <event desc="turns off overhead projector" iterated="n"/> of # <pause dur="1.0"/> those

structures <pause dur="4.3"/> this is # <pause dur="2.0"/> and the majority of them are actually yeah inflated structures this is an air inflated structure <pause dur="1.1"/> the <pause dur="0.2"/> German pavilion at the Expo nineteen-<pause dur="0.3"/>ninety-two in Seville <pause dur="0.7"/> where <pause dur="0.4"/> the <pause dur="0.6"/> there were two <pause dur="0.5"/> # steel rings <pause dur="0.7"/> and # a double skin membrane <pause dur="0.9"/> # <pause dur="0.4"/> spanning between those two rings and then that <pause dur="0.2"/> the <pause dur="0.3"/> the space between <pause dur="0.5"/> with two membranes was inflated with air <pause dur="0.3"/> and that formed <pause dur="0.6"/> # this sort of <unclear>taurus</unclear> type <pause dur="0.3"/> structure <pause dur="0.4"/> which was then suspended with another tensile structure <pause dur="0.6"/> # <pause dur="0.2"/> from the mast in the centre here <kinesic desc="indicates point on screen" iterated="n"/><pause dur="0.5"/> and with the stabilizing cables <pause dur="0.3"/> to hold it in position <pause dur="0.5"/> so it does actually demonstrate <pause dur="0.8"/> a couple of # <pause dur="0.9"/><kinesic desc="changes slide" iterated="n"/> tensile type structures <pause dur="1.2"/> then in the United States # there are various <pause dur="0.5"/> # <pause dur="0.9"/> air <pause dur="0.9"/> supported structures used for large stadiums <pause dur="1.2"/> and # <pause dur="0.2"/> in these the air pressure is actually inside <pause dur="1.2"/> the whole stadium <pause dur="0.4"/> and # <pause dur="0.4"/> to stop it going into a ballooning into a huge <pause dur="0.3"/> roof <pause dur="0.4"/> there are restraining cables <pause dur="0.5"/> # to hold the structure down <pause dur="0.3"/> and minimize the volume that has to be inflated <pause dur="1.2"/> <kinesic desc="changes slide" iterated="n"/>

# <pause dur="1.1"/> problems occur with these these type of structures <pause dur="0.2"/> where you can get sort of <pause dur="0.4"/> strange bulges <pause dur="0.4"/> and # with # <pause dur="0.2"/> ice and snow the valleys fill up <pause dur="0.5"/> and you can actually have rupture of the membrane <pause dur="0.5"/> due to overloading <pause dur="0.4"/> # if you <pause dur="0.3"/> the valleys fill with ponds <pause dur="3.8"/> <kinesic desc="changes slide" iterated="n"/> # <pause dur="1.0"/> you might recognize this person in the middle <kinesic desc="indicates point on screen" iterated="n"/> here <pause dur="1.6"/> # this is # an air <pause dur="0.2"/> system of air inflated structures that were <pause dur="0.5"/> # <pause dur="0.7"/> assembled at the University of Nottingham for a conference last year by students from Stuttgart <pause dur="0.6"/> # <pause dur="0.5"/> i think i've shown you <pause dur="0.2"/> just <pause dur="0.2"/> a single slide of this before <pause dur="0.4"/> # these are actually salami skins <pause dur="0.3"/> salami sausage skins <pause dur="0.5"/> # to demonstrate <pause dur="0.4"/> # <pause dur="0.8"/> how you can actually produce <pause dur="0.5"/> # quite large air inflated structures <pause dur="0.6"/> # these were actually ten metres high <pause dur="1.7"/> <kinesic desc="changes slide" iterated="n"/> # this is the basic material <pause dur="3.1"/> <kinesic desc="changes slide" iterated="n"/> and # this is how crude the assembly method was just # <pause dur="0.3"/> tying off the ends of the <trunc>s</trunc> <pause dur="0.2"/> sausage tubes <pause dur="3.4"/> <kinesic desc="changes slide" iterated="n"/>

# this gives you some idea of the scale of the structures <pause dur="1.2"/> # <pause dur="0.3"/> and the air inflation is sufficient <pause dur="0.2"/> for them to be <pause dur="0.4"/> rigid <pause dur="0.2"/> # self-supporting columns <pause dur="0.4"/> ten metres high <pause dur="0.4"/> # and and to resist <pause dur="0.5"/> # light breezes <pause dur="0.4"/> as lateral loading <pause dur="6.3"/> <kinesic desc="changes slide" iterated="n"/> # this <trunc>se</trunc> shows what happens with the tubes when they go into bending <pause dur="0.3"/> # because <pause dur="0.3"/> # as we were saying bending actually is <pause dur="0.5"/> a less efficient way of carrying loading but if you want <pause dur="0.4"/> curved-shaped forms you might actually have some bending in your structure <pause dur="0.7"/> and you might notice how this actually forms <pause dur="0.8"/> # <pause dur="0.9"/> what # i was talking about in one of the earlier lectures natural structures the # <pause dur="1.0"/> structure of # <pause dur="0.8"/> cane <pause dur="2.0"/> # where you have the nodes at <pause dur="1.0"/> # points <pause dur="0.2"/> up the # <pause dur="1.0"/> up a tubular structure and that actually tends to reinforce it <pause dur="0.3"/> and the same happens naturally in these tubes <pause dur="1.5"/> <kinesic desc="changes slide" iterated="n"/> under pressure <pause dur="3.2"/> # this also is an air inflated <pause dur="0.9"/> sorry an air supported structure <pause dur="1.0"/> # <pause dur="0.4"/> which was erected <pause dur="0.2"/> at the University of

Nottingham <pause dur="1.1"/> # last Monday <pause dur="1.5"/> # by <pause dur="0.7"/> # <pause dur="0.5"/> # an artist who works solely with inflated <pause dur="0.9"/> # <trunc>s</trunc> <pause dur="0.9"/> air supported structures <pause dur="0.7"/> # <pause dur="1.4"/> and it will be going on tour <pause dur="0.6"/> # <pause dur="0.8"/> in Germany <pause dur="0.6"/> # as a promotional <pause dur="0.8"/> # exhibit for # # <pause dur="0.9"/> a tour company <pause dur="0.9"/> holiday tour company <pause dur="0.7"/> # it's # over a thousand square metres of structure <pause dur="0.9"/> and # <pause dur="1.2"/> air supported <pause dur="1.0"/> <kinesic desc="changes slide" iterated="n"/> made out of # coloured <pause dur="0.2"/> # P-V-C <pause dur="1.2"/> fabric <pause dur="1.6"/> and # the cutting patterns here <trunc>w</trunc> earlier <gap reason="name" extent="1 word"/> was talking about cutting patterns were actually just <pause dur="0.4"/> derived by <pause dur="0.4"/> eye <pause dur="0.7"/> and by using books on welding practice <vocal desc="laugh" iterated="n"/> <pause dur="0.8"/> how to cut tubes to join them together <pause dur="0.5"/> so no computer programs were used in this at all <pause dur="0.2"/> <vocal desc="laugh" iterated="n"/> <pause dur="0.4"/> purely guesswork and # <pause dur="0.7"/> simple geometry mathematics <pause dur="0.7"/> # <pause dur="0.9"/> and as a result of that you can see there are actually wrinkles in the structure <pause dur="2.7"/> in certain places <pause dur="5.1"/> <kinesic desc="changes slide" iterated="n"/> and one thing about # <pause dur="2.0"/>

inflated structures under pressure <pause dur="0.5"/> the <pause dur="0.5"/> # there is a relationship between the pressure in the structure <pause dur="0.9"/> and the radius of the curvature <pause dur="0.5"/> and the tensile <pause dur="0.4"/> # stress in the surface <pause dur="0.5"/> and # <pause dur="0.3"/> generally the tighter the radius # <pause dur="0.4"/> to maintain the same tension in the surface <pause dur="0.4"/> you # actually need more pressure <pause dur="0.4"/> so where <pause dur="0.2"/> there is actually a tighter radius here you can see it's not quite so inflated as the rest of the structure <pause dur="5.7"/> <kinesic desc="changes slide" iterated="n"/> here where the cutting pattern has been derived quite well <pause dur="0.2"/> and there is a bigger radius of curvature the the structure is actually quite well <pause dur="0.5"/> # <pause dur="0.4"/> inflated <pause dur="2.5"/> <kinesic desc="changes slide" iterated="n"/> # just to show you how little <pause dur="0.4"/> you need to <pause dur="0.7"/> # support <pause dur="0.6"/> a structure of this size <pause dur="0.4"/> # about six of these # <pause dur="1.8"/> fans were were installed to blow <pause dur="0.3"/> air <pause dur="0.3"/> warm air in fact this was actually heating the air <pause dur="0.5"/> # <pause dur="0.3"/> as it was a very cold day last Monday <pause dur="0.4"/> # <pause dur="0.9"/> blowing air into the <pause dur="0.9"/> into the volume <pause dur="0.3"/> which took about an hour to inflate <pause dur="1.2"/> # <pause dur="0.3"/>

another problem of course with # air supported structures is holding them down <pause dur="0.5"/> and # <pause dur="0.4"/> in this case as it was a temporary structure it's actually held down with these bags full of water <pause dur="0.8"/> # which are attached to the structure on the outside </u><gap reason="break in recording" extent="uncertain"/> <u who="nf0856" trans="pause"><kinesic desc="displays models" iterated="n"/> and designed by Nowitzki i think in the fifties <pause dur="0.6"/> and it's a self-stressing # structure <pause dur="0.6"/> # you can see it doesn't have very heavy anchors of foundation <pause dur="0.9"/> because it works on the principle we could demonstrate of two people <pause dur="0.7"/><kinesic desc="hold both hands and lean back" n="ll" iterated="n"/> sort of <pause dur="0.7"/> leaning like that <pause dur="0.7"/> okay <pause dur="1.3"/> so you don't require very heavy <pause dur="0.3"/> foundation level anchor so that's a very interesting <pause dur="0.5"/> saddle shape <pause dur="0.2"/> structure </u><gap reason="break in recording" extent="uncertain"/> <u who="nf0856" trans="pause"> so far as the membrane structure's concerned it's a very poor example <pause dur="0.5"/> # because the boundaries for the membrane are not very well chosen as a result we get a very flat <pause dur="0.5"/> surface so the student obviously did not exploit <pause dur="0.3"/> the

possibilities that exist <pause dur="0.5"/> # when one experiments with <pause dur="0.4"/> boundaries as far as low and high points are concerned <pause dur="0.5"/> # which <pause dur="0.6"/> can alter the surface # geometry dramatically <pause dur="0.4"/> so it's not a very good example in fact </u><gap reason="break in recording" extent="uncertain"/> <u who="nf0856" trans="pause"> inclined posts i suppose <gap reason="name" extent="1 word"/> what else can we say about it <pause dur="1.4"/> should i go and get </u><u who="nm0857" trans="overlap"> <gap reason="inaudible" extent="1 sec"/> </u><u who="nf0856" trans="overlap"> the other model but it will take about ten minutes <vocal desc="laugh" iterated="n"/>