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Any structure designed intelligently and responsibly aspires to be as light as possible. Its function is to support live loads. The dead loads of the structure itself are a necessary evil. The smaller the ratio between a structures dead load and the supported live loads, the lighter the structure. We realize immediately that a suspension bridge with knotted cables is obviously lighter than a truss bridge with welded bars which in turn is lighter than a box girder bridge from concrete. This consequently leads us to the question why so few suspension bridges are being built and only for large spans and we intuitively understand that the demand for lightness is not sole criterion when designing structures. Indeed, natural loads are the enemy of lightweight structures. These structures tend to deform heavily under snow and temperature changes, they are sensitive towards windinduced vibrations, they may tear (the structural engineers trauma of Tacoma), but they literally make light work of earthquakes. Another stern adversary of lightweight structures are todays high labour costs and the imprudent use of natural resources. This promotes the massiveness and hinders the filigree.
178 LIGHTWEIGHT STRUCTURES Jorg Schlaich Prof. Dr Ing. Drs.h.c. University of Stuttgart, Germany Any structure designed intelligently and responsibly aspires to be "as light as possible". Its function is to support "live loads". The dead loads of the structure itself are a necessary evil. The smaller the ratio between a structure's dead load and the supported live loads, the "lighter" the structure. We realize immediately that a suspension bridge with knotted cables is obviously lighter than a truss bridge with welded bars which in turn is lighter than a box girder bridge from concrete. This consequently leads us to the question why so few suspension bridges are being built and only for large spans and we intuitively understand that the demand for lightness is not sole criterion when designing structures. Indeed, "natural loads" are the enemy of lightweight structures. These structures tend to deform heavily under snow and temperature changes, they are sensitive towards wind-induced vibrations, they may tear (the structural engineers' trauma of Tacoma), but they literally make light work of earthquakes. Another stern adversary of lightweight structures are today's high labour costs and the imprudent use of natural resources. This promotes the massiveness and hinders the filigree. But before we discuss how to design lightweight structures we need to ask ourselves whether or not lightweight structures today are worth the effort to be promoted and developed. The answer is yes! From an ecological, social and cultural perspective lightweight structures have never been more contemporary and necessary than today. The ecological point of view: Lightweight structures are material-efficient because the materials strengths are optimally used. Thus no resources are wasted. Lightweight structures may usually be disassembled and their elements are recyclable. Lightweight structures curtail the entropy and therefore are superior in meeting the requirement for a sustainable development. The social point of view: Lightweight structures create jobs because filigree structures demand carefully designed labour-intensive details with a great expenditure in planning and above all manufacture. The intellectual effort replaces the physical effort, now time and craftsmanship supercede the extruding press - the joy of engineering instead of massiveness. But as long as our modern economy equals working hours with costs, we merely pay the mining costs of the raw materials and the overall "external costs" are not even added, lightweight structures will be more expensive than bulky structures with the same function. Therefore lightweight structures might be attributed with an elitist air. It is true that only banks and insurance companies, and sometimes museums, can afford lightweight structures, but nobody in the field of residential or ordinary industrial buildings. And the engineers and architects wallow in this elitist glow (a stark contrast to the pioneers' spirit of lightweight structures: Buckminster Fuller, Vladimir Suchov, Frei Otto). They continue to push this structural exhibitionism and do not even notice that 98 % of the structures around them crave for their attention, thus their actions are highly antisocial - the author know what he is talking about and stands accused. The cultural point of view: Lightweight structures, built responsibly and disciplined, may contribute heavily to an enriched architecture. Light, filigree and soft evokes more pleasant sensations than heavy, bulky and hard. In the typical lightweight structure the flow of forces is visible and the enlightened care to understand what they see. Thus lightweight structures with their rational aesthetics may solicit sympathies for technology, construction and engineers. They may help us to escape the wide-spread monotony and drabness in today's structural engineering which in turn will become again an essential part of the building culture. How to create lightweight structures? When designing lightweight structures we have to: firstly remember a most unfavourable characteristic of the dead loads: The thickness of a girder under bending stress, supporting only itself, increases not only proportional to its span (which is often falsely assumed), but also with the span's square! For example if the girder with a span of 10 m has to be 0.1 m thick, its thickness increases with a span of 100 m not only 1 Of old but 10 x lOfold. Consequently the girder has to be 10 m thick and its total weight increases by the factor 1000! 179 Already Galileo Galilei was aware of the importance of scale. He demonstrated this by comparing the tiny thin bone of a bird with the corresponding big bulky one of a dinosaur (Fig. 1). This teaches us that increasing spans increase the weight of structures, consequently gratuitous large spans are to be avoided. Fig 1 Galilei's demonstration of the scale effect But this law of nature about scale may be circumvented with some tricks, by secondly avoiding elements stressed by bending in favour of bars stressed purely axial by tension or compression, i. e. dissolving the girder. Basically this is always possible as demonstrated by the truss girder. With struts and ties the entire cross-section is evenly exploited without anything superfluous. Bending completely stresses only the edge fibers while in the center dead bulk has to be dragged along. Here ties in tension act apparently more favourable than struts in compression because they only tear if the material fails, while slender struts fail due to buckling, i. e. a sudden lateral evasive movement. This can easily be tested with a long bamboo stick. We cannot break it with our bare hands, but if we bear down on it, it buckles quickly. thirdly these efficient tension stressed elements becomeeven more efficient with increasing tension strength P and decreasing density of the material y, i. e. with increasing rupture length p/y. This clear value represents the length a thread can reach hanging straight down until it tears under its dead load. Wood is more efficient than steel and natural and artificial fibers do even better. These first three approaches to lightweight structures introduce us already to the entire multitude of forms in bridge engineering. We recognize (Fig. 2, starting from the top) the dissolution of the girder into the truss and then (left) the arch structures which carry their loads mainly by compression and their inversion (right) the suspension structures which make use of the especially favourable tensile forces. At the bottom are the most marginal structures, the pure arch or the cable suspended between two rock faces. But these latter ones are useless, because they deform too much under loads. But in between the upper and lower structures there are the most diverse solutions: arches and suspended cables stiffened by secondary girders in bending and all kinds of fastenings, deck-stiffened arches, strutted frames (left) as well as cable bridges and suspension bridges etc. (right). The further we move down in Fig. 2 the lighter it becomes but also the more critical with respect to wind- induced vibrations - and this represents the challenge and the attraction of bridge engineering. r compression-tension-v i^I^ ^TTTrrrr-ry Voiiiid/ Fig 2 The evolution of bridges The keen observer of today's bridge engineering will find that a rather pragmatic attitude prevails, structures are being built "as heavy as justifiable". Solid girders are used up to a span of about 100 m, arches resp. trusses up to approximately 250 m. Dead loads at least five times the live loads are tolerated. Beyond approximately 300 m the dead load becomes so dominant that, as the only alternative, tensile "lightweight structures" remain: up to about 1000 m self-anchored suspension and cable-stayed bridges and for even greater spans back-anchored suspension bridges. The Pont de Normandie in France spanning 856 m and the Tatara-Bridge in Japan spanning 890 m are the world's largest cable-stayed bridges. The largest suspension bridge with a span of 1990 m is the Akashi bridge in Japan. The suspension bridge proposed for the 180 crossing of the Straits of Messina spanning 3500 m is to be suspended from 4 cables each 1.7 m in diameter. These cables consume already half of their loadbearing capacity to support themselves and only one half remains for the actual bridge and the live load which remains insignificant compared to the dead load of the cables and the deck. By definition this is by no means lightweight, but at such span, today's materials do not permit anything lighter - we have reached the limit - unless, steel cables can be replaced by plastic fibres with a significantly greater p/y-value. A strikingly ingenious trick to achieve lightness should be addressed briefly, i. e. fourthly prestress or pretension which permits to transform unfavourable compression stress into favourable tension stress (Fig. 3). The example shows a quadrangle of slats with crossed cables. The diagonal cable receiving compression will not become slack but shares the load because it is prestressed. Initially before applying the outer load this cable was exposed to pretension, thus when compressed it will not experience compression but a reduction of tension which is the static equivalent. This procedure permits the creation of very light cable girders and cable nets which act like ideal structures with tension and compression resistant elements or like membrane shells. Fig 3 The principle of prestress Top left: Unstiffened kinematic system Top right: The diagonal in compression becomes slack and only the diagonal in tension is active. Bottom left: Prestress: before loading the diagonals are shortened i. e. pretensioned Bottom right: In a prestressed system both diagonals share the load The basic principles of lightweight bridges also apply to buildings such as roofs over large sports arenas or fair pavilions or industrial plants lending an individual character and a human scale to these structures. Since the gap between these cable girders still has to be spanned with transversal girders using bending and thus resulting in semi-heavy or semi-light roofs, the final step is inevitable: fifthly the use of lightweight spatial structures, or double curved space structures with pure axial stress, called membrane stresses (Fig. 4). These structures are not only extremely light but they also open up a whole new world in architecture, an unsurpassable variety of forms which is not yet exhausted, by no means. Just like bridges, these structures transfer their loads predominantly by compression shells or domes (Fig. 4, left), or by tension cable nets and membranes (right). In between are the plane space structures - the slabs and the space frames. i i-l * l t l t I i„; I * 1 Fig 4 The evolution of lightweight spatial structures Despite the extremely thin walls of shells and space domes their curved shape stabilizes and prevents them from the dreaded buckling. And applying prestress protects the extraordinarily lightweight nets and membrane from the effects of wind-induced vibrations. The two principal directions of the nets and membranes are mechanically stressed against each other resulting in the typical saddle-shape with an anticlastic curvature, or, if pneumatically stressed by creating an internal air pressure or a vacuum, resulting in a dome shape with synclastic curvature. This can be mastered with modern computers. Manufacture and, as a consequence, costs are more likely to limit the scope of these lightweight spatial structures. Expensive formwork and complicated cutting patterns are required for the manufacture of these double- curved surfaces (Fig. 5). The details of tensile structures and membranes are complicated and have to be manufactured with extreme precision. 181 But in recent years the textile membrane structures have made a remarkable progress. Since they may be folded they are even used as convertible structures. This marked the beginning of a whole new era in structural engineering completely changing life in our capricious climate. The future is now! STRUCTURE I MANUFACTURE I GEOMETRY SQUARE NET TRIANGULAR NET TEXTILE MEMBRANE THIN METAL SHEET MEMBRANE free restricted free restricted Fig 5 The geometry and manufacture of typical double-curved lightweight structures Fig 6a The cable net cooling tower at Schmehausen (1974) Achieving lightness is a heavy burden, because lightweight structures challenge the boundaries set by the theories of statics and dynamics. The fancy materials put the technologies to the test and the complicated three- dimensional structures dare the manufacturing procedures. Lightweight structures tempt the dedicated engineer, because they - exemplary for this profession - equally and simultaneously address his knowledge, his ability and his experience as well as his fantasy and his intuition. With lightweight structures the engineer is able to award the adequate visual expression to an ingenious and efficient structure thus contributing to building culture. Over the years, the author and his colleagues tried to apply these principles of lightweight to all types of structures including bridges and to towers even (Fig. 6), but out of space reasons, this report will be restricted to lightweight roofs, leaving out even the wide and interesting field of concrete shells (Fig. 7). Fig 6b The Killesberg lookout tower in Stuttgart (under design) Fig 6c The Leipzig Fair tower, Volkwin Marg, architect (1995) Fig 7 The 12 ram thick GRC-(Glass fibre Reinforced Concrete) Shell at Stuttgart (1977) (following Candela's Xochimilco design). It started with a real highlight, the cable net tent for the Munich Olympic Games in 1972 (Fig. 8). This exemplifies the almost unlimited freedom of shapes which the cable net with quadrangular mesh offers. By changing the angles of the original square net it can adapt to almost any surface. Since this roof has been published widely let us proceed to a later cable net over an ice- skating rink at the same site in Munich which is elliptic in plan (88 x 67 m) (Fig. 9a). The cable net (mesh width 75 x 75 cm) is suspended from an arch spanning 104 m in the longitudinal direction and 18.5 m high, andstressed at its periphery using guyed masts there. Fig 8 cable net roof for the Munich Olympics, Behnisch und Partner and Frei Otto, architects (1972) The interesting point is that the arch not only carries the net but that simultaneously the net stabilizes the arch. In order to permit a complete prefabrication of the net and a simple erection but also to separate visually the arch from the net, the trussed arch is triangular in section with the suspenders fixed to its bottom chord (Fig. 9c). With that it was possible to first erect the arch (which had to be temporarily guyed because, as mentioned, alone it was not stable), spread the net underneath and then lift it in its final position below the arch and stretch it by tilting the guyed masts. Whereas the slots between the edge cable underneath the arch were covered with clear acrylic Fig 9a The cable net roof over an ice-skating rink at Munich, Kurt Ackermann und Partner, architects (1985) glass, the cable net itself was to be covered with a PVC/polyester membrane, expecting from it not only an economical solution but also a pleasant interior atmosphere. To fix the membrane on the cable net, a wooden grid was used because wood can as well be bolted to the joints of the cable net as the membrane may be attached to it with nails. This on the other side raised the question of fire protection of the arch, which we 183 Fig 9b Interior view could overcome by reducing the amount of wood close to the arch to a minimum. There the spacing of the wooden grid is 75 x 75 cm, following the cable net. We could do so because from there the snow would slide down to the flatter region of the roof, thus the reduced snow load would permit the 75 x 75 cm mesh to be spanned by the membrane alone. As a logical consequence the grid in the lower parts along the periphery of the roof had to be closer with additional wooden slats supporting the membrane there. At the end we were very happy in finding that the satisfaction of two technical requirements - fire and snow load - resulted in a beautiful visual appearance, because due to the reduced density of the grid from the periphery towards the arch, the transparency increases from the lower part to the higher part of the roof, thus suggesting more internal height or volume than really exists and thus producing in this ice- skating ring a gay and relaxed atmosphere (Fig. 9b). Concerning membrane structures we were for many years reluctant to try our own designs because many of those built in the sixties exposed a surprisingly painful discrepancy between their beautiful overall shape and their nasty details without a tendency towards improvement in the years to follow. Finally, however, we welcomed the invitation of the contractors Hochtief of the Jeddah Airport roofs to advise them in the detailing and during the construction of this SOM/Horst Berger design (completed 1982) as well as of Philipp Holzmann of the Riyadh Stadium roof to do the final design and the construction supervision of this Ian Fraser/Horst Berger conceptual design (completed 1984) for them. These two roofs gave us a chance to develop our own hopefully improved details and to gather overall experience with membrane structures. Besides the large roof over the temporary grandstand for the Munich Olympic swimming hall in 1972 the real chance to design and build original and own membrane Fig 9c Details of the ridge cable arrangement structures came only about ten years ago and we even started with their most challenging species, the convertible roofs: The inflated cushion for the Roman Arena in Nimes, France, with an elliptic plan 88 x 57 m is installed there each year in fall and removed in spring (Fig. 10). It goes back to an earlier design for the Roman Arena in Verona, Italy, where we had even proposed to fill it with helium and to fly it to the periphery of the town to serve there as a temporary shed during the summer. Fig 10 The Roman Arena convertible roof in Nimes, France, with F. Geipel and N. Michelin, architects (1988) 184 It was only last year, when we could apply the same principle to a convertible roof of the bull-fight arena Vista Alegre in Madrid/Spain (Fig. 11). The cushion has a diameter of 50 m. Its upper Polyester/PVC translucent membrane rises 7 m, its inner ET transparent membrane sags 5 m and is reinforced by a cable net with a 1.5/1.5 m mesh of 12 mm cables. The whole cushion can be lifted 11.4 m by winches along 12 vertical columns placed at the inner ring of the permanent cantilevering roof over the grandstand. ^^7~^zz— fir X X / J? 5000 SO.It Fig 11a Lifting roof, Vista Alegre, Madrid, Spain, with FHECOR engineers, for the fixed outer roof. Cross-section left side cushion in closed position, right side cushion in lifted position (1999) Fig lib The pneumatic cushion during installation The huge retractable roof covering 20,000 m_ with a PVC/Kevlar-membrane for the Olympic Stadium in Montreal, Canada (Fig. 12), could not be completed for the 1976 Olympic Games. When, during the mid- eighties, we were approached by Lavalin Consulting Engineers of Montreal to help them complete it now, the prescribed boundary conditions were so that this turned out to become certainly the most complex assignment we ever accepted. Though the result, as known, was not satisfactory but probably could not be better without accepting major changes of the original design by the architect, we learned a lot, so that we considered it as a pleasure to apply this experience when designing the roof for the bull-fight arena in Zaragoza, Spain, with its fixed circular outer roof and its central convertible part. This roof has the right size for a light and unobtrusive membrane and especially the convertible roof when seen in motion from underneath, resembling an opening and closing beautiful flower, confirms that membrane Fig 12 The Montreal Olympic Stadium convertible roof as seen from inside during closure, R. Taillibert, architect (1989) II Fig 13a The roof over the bull-fight arena at Zaragoza, Spain, total view, convertible inner part not yet installed (1989) Fig 13b From inside during operation of the convertible inner part structures deserve the attribute 'natural' (Fig. 13). In the case of the four completed large stadium roofs - some more are nearing completion or under design - for the Gottlieb-Daimler-Stadium in Stuttgart (Fig. 14), the Gerry Weber Centre Court in Halle with a translucent and convertible inner roof, the NSC Outdoor Stadium in Kuala Lumpur (Fig. 15) and the Estadio Olimpico de Sevilla (Fig. 16), primary cable structures are applied based on the spoked wheel principle with either two inner tension rings and one outer compression ring or vice versa. In spite of their huge size these make very light structures permitting the membranes really to come forward with their transparency resulting in a friendly and pleasant atmosphere. This is most important in the case of stadia to help calm aggressions which in other 185 places frequently resulted in fights, riots and panic attacks. The atmosphere during the Athletic World Championships 1993 at the Stuttgart stadium was most friendly - thanks to the light and pleasant membrane structure. Unfortunately, older stadia used to be rather ugly and obtrusive concrete monsters and if such an existing grandstand is to be covered - as in the case of Halle - there is no chance to improve the outer appearance even with the lightest membrane roof or with the most carefully designed details. Fig 14a The Daimler Stadium in Stuttgart; H. Siegel und Partner and Weidleplan, architects (1993) Fig 16a Estadio Olimpico de Sevilla. The folded membranes during erection; Cruz y Ortiz, architects (1999) Fig 16b Comparison of Stuttgart versus Sevilla membrane arrangement Fig 14b Interior view Whereas for Stuttgart, Kuala Lumpur and Halle we introduced radial cable girders between the inner and outer rings, as a primary structure with the membrane spanning between their lower (Stuttgart, Halle) or upper (Kuala Lumpur) cables and tied arches as a secondary structure, in case of the roof of the Estadio Olimpico de Sevilla (as earlier for the outer roof at Zaragossa), the membrane is an integral part of the primary structure: It is stressed between the upper and lower cables resulting in a folded plate geometry and loadbearing behaviour (Fig. 16 b). To our surprise in this case the architect was not interested in a translucent roof, but insisted to make the membrane opaque. Obviously the quality and success of membrane structures depends on their details, clean and simple details which are in harmony with the structure as a whole. This of course needs constant efforts and includes not only the "hardware" but also the cutting pattern of the membrane as well. If carefully designed, the geometry of the seams can reflect the flow of forces thus improving the visual appearance of membrane roofs. Three recent roofs may exemplify how we tried to follow this idea: Fig 15 The NSC Outdoor Stadium in Kuala Lumpur; interior view during construction; Weidleplan, architects (1997) 186 The Hamburg-Stellingen Ice-Skating Rink roof covers an existing ice field. Its light appearance results from the fact that it is supported by four masts only with additional cable supported props. As the membrane approaches these singular supports, its seams assume a concentric pattern with additional strengthening strips in order to visualize the concentration of the forces (Fig. 17). Fig 17a The roof over the Hamburg-Stelling Ice-Skating Rink from outside at night; Silcher, Werner, Redante und Partner, architects (1994) Fig 17b From inside. The roof over a grandstand at Oldenburg cantilevers from a number of masts using horizontal struts with cable supports and membrane panels in-between, tied down towards the masts. From a distance it looks rather simple and geometrical whereas from underneath it reveals again this clean and joyful appearance, typical for membrane structures (Fig. 18). 1 Fig. 18: The roof over a grandstand at Oldenburg (1996) Another effort to solve the difficult singular point supports of membranes resulted in a cloverleaf at the indoor pool adjacent to the Kuala Lumpur stadium (Fig. 19). If a rectangular area is to be covered at minimum cost, as in case of large exhibition halls for fairs, the unidirectional cable girders or hanging roofs usually are Fig 19a Kuala Lumpur Indoor Pool; Weidleplan, architects (1998) Fig 19b Cloverleaf, Kuala Lumpur Indoor Pool better suited than the double-curved cable nets or membranes. Three examples from our practice may illustrate this type of lightweight tension structure. For an exhibition hall 112 x 184m at the Hannover Fair we added 18 cable supported girders of 122 m span and 9 m depths, resulting not only in a simple and economic but also real light structure (Fig. 20). For another exhibition hall covering 210 x 110m we chose a sequence of three pure stress-ribbons from steel slats covered with wooden panels (Fig. 21). The same system, but much smaller and covered with glass, we applied earlier for a canopy at the Ulm railway station (Fig. 23). Finally most recently for another fair hall at Hannover we applied in a similar way a sequence of 4 full and two half bay stress ribbons at either end, covered with wood and supported in the cross-direction by self-anchored suspension structures: rather complicated, and perhaps at the brink between high-tech and high-effect (Fig. 22)! 187 Fig 20 Hall 4 at the Hannover Fair at night, Volkwin Marg, architect (1995 Fig 21 Hall 26 at the Hannover Fair inside, Thomas Herzog, architect (1996) i 4 i V Fig 22a Hall 8/9 at the Hannover Fair (model), Volkwin Marg, architect (1999) Fig 22b Hall 8/9 at the Hannover Fair. The transversal suspension structure during erection Fig 23 Suspended glass canopy in front of the Ulm railway station, H. Gaupp, architect (1992) This finally brings me to our glass-covered roofs, for which we developed what we call grid-domes. Based again on the structural principle of the square mesh or grid, which adapts by change of angles to a double- curved surface of any shape, first such a pure grid-dome is built and afterwards stiffened by diagonal cables. The glass-grid dome of the Neckarsulm indoor swimming pool is of pure spherical geometry (Fig. 24). In case of the roof over the courtyard for the Museum of the History of Hamburg two cylinders stiffened by spoked wheels intersect in a free transition surface of the dome shape (Fig. 25). Both roofs, and many more to follow, demonstrate the lightness of such shell-type structures. Double-curved glass covered grid-domes commonly and naturally call for spherically curved glass panes, since the four edges of a grid mesh are not in one plane, a real problem especially if double-glazing is required. In Neckarsulm we really got spherically shaped double- glazed glass - but never again! - in Hamburg we had simple glazing and enforced the necessary distortion to the glass. Fig 24 The glass-grid dome of the Neckarsulm indoor swimming pool from inside, K. Bechler, architects (1989) [...]... absence of discipline by geometrical manufacturing constraints must not result in chaotic shapes, but can be replaced by self-imposed order resulting in clean and beautiful structures The author is aware that he owes these rewarding structures to his creative and tireless partners and collaborators, imaginative architects, skillful manufacturers and last but not least trusting clients Fig 28 DG-Bank,... domes as discussed here or in other words, the work of Bauersfeld, Fuller, Wachsman, Schwedler, Mengeringhausen, Otto and others was characterized by the search for efficient reticulated space lattice structures with as many as possible slats and nodes of equal size and geometry for an economical pre-fabrication and assembly "Thanks" to computers with CAD, CAM, CNC this all appears to be Fig 27b The