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The Arup Journal THE ARUP JOURNAL OCTOBER 1980 Vol. 15 No. 3 October 1980 Contents Published by Ove Arup Partnership THEARUP 13 Fitzroy Street. London, Wl P 680 Ed nor : Peter Haggett Art Editor : Desmond Wyeth FSIA D JOURNAL Assistan t Editor : David Brown Lightweight structures : 2 Introduction, by P. Rice A brief history of 6 cable and membrane roofs, by B. Forster Air-supported structures : 11 fire and smoke hazards, by M . Law Coated fabrics 14 for lightweight structures, by A . Read and T. O' Brien Form finding, control 19 and modification for tension structures, by A. Day Form definition for the 21 Bridge of Don exhibition and sports centre, Aberdeen, by A. Day Environmental considerations 22 of lightweight structures, by J . Campbell Front cover: Photo reproduced by courtesy of Heather Angel MSc FR PS Back cover : Mecca Conference Centre (Photo : Buro Gutbrod/ Frei Otto) conditions and the method of manufacture through experience the vital relationship Lightweight are wholly inter-related. between stiffness, geometry or curvature and For engineers the philosophical base which the stability of the surface under changing structures: underpins this study of lightweight structures loads. One other important characteristic is has been a barrier to developing a mathe­ that the surface is free of bending stiffness. Introduction matical understanding of their behaviour. For a fabric or tension net this is self-evident, At the time these structures were being but the consequence of this obvious charac­ Peter Rice developed, computer techniques were teristic is that the surface stiffness depends emerging based upon the finite element and upon the prestress and the two-way curvature Lightweight structures is a broad. if rather stiffness method of analysis. This is a static at any point. The modelling is used to hel p inappropriate, name for a group of surface system of analysis which assumes that generate surfaces which have a balanced structures made from fabrics or tension or deflections are small and can be ignored when relationship between curvature in one direc­ compression nets. The structures are light­ calculating structural equilibrium. One of the tion and curvature in the other and between weight because the nets or fabric are the principal characteristics of lightweight struc­ curvature at different parts of the surface. lightest available materials with adequate tures is that this premise is not true. Indeed The prestress compensates for the lack of structural properties to span in two directions. they change their geometry in response to bending stiffness and helps eliminate flutter. Tents and nets have, of course, been in each new load application. Consequently In order to be more precise in the discussions existence for a long time. Recently, however, many devices were developed to mimic this on lightweight structures. the structural forms stimulated by the early work of Frei Otto and characteristic and they were grafted onto the are classified into five main types : others, a new understanding and vocabulary standard stiffness analysis programs. Recently, Tents, prestressed tents and prestressed cable of possible shapes has emerged. Originally as Alistair Day explains in another paper, networks the research attempted to define the factors direct dynamic techniques have been Air-supported structures developed which model accurately the way which made for efficient structural forms. Pneumatic structures In doing so it examined structures in nature. these structures respond to load in nature. to see how they solved the relationship The development of lightweight structures Grid shells between form and efficiency. The most has now reached the stage where the limits Heavyweight cable roofs. interesting and important work stemmed from of what can be designed and built are the Prestressed tents and cable networks are a study of soap film surfaces, forms whic h limitations of materials, the limitations of the doubly-curved saddle surfaces and are often are generated by the characteristics of the soap designer's inventiveness, and not, as has developed from soap bubble models. The film itself, a uniform surface tension. Modelling been hitherto the case, the limitation of soap bubble, which is a uniform surface techniques to generate soap film surfaces analysis and specification methods. When tension membrane, helps to ensure that were developed. Model work led to an we talk of these structures we are talking of surface curvature is adequate everywhere in appreciation of the transient nature of the free forms, which must be in equilibrium the surface. Prestressing is achieved by soap film surface ; the surface form is with themselves and w ith a set of appl ied stressing one set of cables or membrane dependent upon the load conditions acting forces. Usually they are very light so that, in fibres against another. The more curved the upon it. It also led to the realization that the initial condition, gravity loads are not very surface. the more effective the prestress as a modelling techniques generally were the best important. However, to counteract non­ means of providing surface stiffness. It way to study and understand the relationship uniform applied loads, either snow or wind­ follows, therefore, that large differences in between geometry and equilibrium for these induced, they are almost always prestressed, curvature across the surface can lead to surfaces. The modelling techniques brought either by air pressure or directly through substantially different properties, e.g. a soft with them too an indication of the way in tensioning of the net and fabric elements. To area or a stiff area, in different parts of the which real structures could be created. It is an understand the physical characteristics of any surface. It is also necessary to generate essential part of the study of lightweight particular lightweight form it is still important surfaces which can be prestressed. This is 2 structures that the forms, the initial load to work with models. One has to learn particularly important when dealing with stiff Fig. 1 Fig.2 Soap bubble (Zambian settling tents) Grid shell model (Photo : Ove Arup & Partners) (Photo : Courtesy of Frei Otto) Fig.3 Fig.4 Aeroelastic model for Berlin roof project, a heavyweight cable roof Cable net at Munich (Photo : Courtesy of Frei Otto) (Photo : Joachim Schock) materials such as Teflon fibreglass because situation the crucial supporting element is the a stiff rubber fabric, in the same way as in a they do not allow the fabric to redistribute internal air itself, and the distortion of the air standard dinghy. Until the level of prestress the stress if locally overstressed areas occur. mass and structure under application of loads in the fabric has been overcome, the tubes Surfaces which are easy to prestress are also is clearly large and dependent upon the act as a rigid element. Generally the structures surfaces which have a relatively uniform exact load distribution. A detailed treatment are designed so that for all normal working curvature throughout. The characteristic of of air structures has been carried out else­ load conditions prestress is high enough to low shear modulus which has been already where. It can be noted, however, that the ensure no wrinkling 3 and others have mentioned is very important in detailing dynamic modelling and analysis techniques suggested that the ultimate strength of a prestress nets and fabric tents. Shear distor­ developed for the prestressed tents are prestressed fabric rib is twice that at the tion can lead to large displacements across appropriate in air structures as well. The onset of first wrinkling. Obviously this has the diagonal of the net members and can only form of air structures is not as restricted as one got to be verified in particular cases as it be controlled by curvature and prestress. might think from looking at those normally depends upon the form of the structure. This shear distortion is one reason why cable available. Modelling techniques show that by Structural forms are achieved in the same way networks are not more popular than they are. introduction of stiffer elements in the surface, as with other fabric structures. Because the The category of prestress networks also free and unusual forms can be achieved. The air volume inside a fabric rib is relatively small includes radial cable trusses and prestress stress levels in air-supported structures are and the pressure high, the system is much ring structures. Where they have shear or generally substantially lower than the stress more sensitive to air leakage, as only a sma ll diagonal cable elements, as in the Jaworth levels in prestressed nets and fabric tents. amount of air loss is needed to effectively system, they may be treated as normal This means that they are not as sensitive to destress the surface. It is for that reason that structures when prestressed. This means fabrication error or material quality and special care has to be taken with the surface that the prestress level should be sufficient consequently the largest structures tend to be covering and, to date, the only membranes to counteract normal working loads. Where air-supported. Also because their geometry which have proved satisfactory for pneumatic shear diagonals do not occur, the behaviour is a simple rounded pure form, they have a structures are rubber-based membranes. is similar in character to normal cable net­ better controlled air flow over them and Grid shells are doubly-curved, convex surfaces works. The geometry at any time is dependent consequently can be influenced by their which are generated by freely hanging chain on the loading as well as the member design and where they are situated in the networks. The system was first proposed by lengths. Various studies have been carried out landscape. They are, however, susceptible Frei Otto and was used by him to generate the on their behaviour' and the definition of the to wind buffeting.
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