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基于结构约束探索不规则网状钢和玻璃外壳形式Sigrid Adriaenssens, M.ASCE1; Laurent Ney2; Eric Bodarwe3; and Chris Williams4摘要:在对荷兰阿姆斯特丹荷兰海事博物馆顶部覆盖的一种高效的结构形式进行探究的文章中,作者简要讨论了作用力对最早的玻璃屋顶覆盖物的影响。在20世纪末到21世纪初,外露的钢骨架玻璃壳设计慢慢出现。这些设计形式在从雕塑到几何再向结构转变。通过荷兰海事博物馆钢玻璃壳屋顶的发展,对它的挑战性设计的讨论得出了设计者在基于一个诗意的几何思想的基础上,对寻求有效的结构链形式的探索。本文提出了一种建筑结构设计方法。这种方法稍微适和用数值模拟方法探索目的是在所有的的三角化、四面性和五面性的网面中实现平面化的结构链模形。然而,如何通过分析玻璃面的途径将其很好的解决并呈现给人们为实现平面化向人们提出了挑战。对照此种方法得到麦克斯韦互惠网络图。最后,雕琢出的平面向人们展示了典雅、耐用。DOI:10.1061 /(土木)ae.1943 - 5568.0000074。2012美国土木工程师学会。CE数据库主题词:设计;钢材;玻璃;古迹;屋顶;荷兰。关键词:形状;概念设计;模型探究;钢玻璃壳体结构;历史意义的庭院;平面化感官;结构约束;麦克斯韦互惠网络。正文:随着工业革命的兴起,玻璃金属结构出现受两个因素支配: 其一、在人口过多的城市, 社会对绿色和安静的空间的渴望;其二、新的建筑材料(玻璃和铁) 的出现。在十八世纪初,第一温室装以玻璃的屋顶出现在人们生活的中。它们的高昂的建设和维护成本(由于玻璃和必需的供暖系统)让它们成为精英阶层的标志。他们的弯曲形状 (1) 嵴沟连跨型 例如, 查特斯沃思庄园, 英国(建于1834年), 与(2) 拱形, 例如, 裘园(伦敦市郊著名植物园), 英国 (建于1844年) (Kohlmaier and Von Sartory 1991)允许稀疏的阳光进入室内并照在柑橘和柠檬树上(因此,名称橘园)。其他品种的温室植物、灌木和奇异的植物也被安置在橘园。其中棕榈树, 扮演着大量的宗教色彩,是尤其令人印象深刻的和有名的植物,从而也把温室的形象进一步提升。十九世纪中期,温室类型学已全面发展,由此便产生了文化室、暖房以及冬景花园例如, 皇家温室、拉肯,比利时(建于1876年)现于Fig. 1 (Woods and Swartz 1988).冬季花园是本文特别感兴趣的,因为它是一个社交场合,与一栋私人豪宅或公共建筑及其接近。在十九世纪下半叶,大规模生产的负担得起的铁进一步鼓励了高层和大跨度由钢材和玻璃建成的展厅的设计和施工。大量光线进入展览区的建筑物,如水晶宫、英国(建于1851年)(如图所示在Fig. 1)。其如网状的钢结构骨架是预制的,后来被拆除,从海德公园搬运至伦敦南部的西登哈姆。不幸的是,它在1936年毁于火灾。19世纪后半期和20世纪早期,公共建筑物屋顶的设计和施工又经历了一个很大的提升,冬景花园不再种植植物,而是覆盖在重要的历史公共建筑的庭院上方例如 , 大英博物馆的大院子, United Kingdom, 英国; 见 Fig. 1; the Deutschen Historischen Museum, and Museum fur Hamburgische Geschichte, 德国(如期分别在2001和2004年建成的Schlaich Bergermann and Partners); 和the Smithsonian Institute,Washington, DC (Foster and Partners, and Buro Happold in 2001)。顶部覆盖玻璃的单层钢骨架的形状由雕塑、几何、物理以及施工条件等因素共同决定。最近这些结构的重新崛起,伴随着由数字化设计演化出的工具,使得设计师能够开发和分析出更多大胆和自由的几何设计。单层玻璃钢骨架结构今天的设计师(有过设计和工程背景)在设计这些非种植植物的冬季花园时主要遵循以下四个因素: 实施现状,建筑美学,建筑几何形状和建筑物结构效率等。现代冬季花园在过去的二十年里, 存在着这样与历史有关的公共建筑,它们已经能够通过扩展建筑物的中部空间适应室内或室外气候。那些狭小的建筑物通常利用中部空间提供光亮。钢结构玻璃外壳为设计的挑战提供了唯一的解决方案。历史的显示,设计师在研发设计壳体结构的过程中往往会受到一系列约束条件的限制。其限制条件通常包括高度的限制以及强加于现有建筑物,尤其是水平方向,最大负荷的限制。大英博物馆法院屋顶是滑动轴承支撑,这样就没有水平推力落在历史博物馆的砌体墙上(威廉姆斯2001)。回顾最近的设计我们就会意识到,推动钢结构玻璃壳结构设计的因素主要是建筑形态美学而非结构的性能。建筑美学利用可用几何数字建模工具,更多的建筑师通过把他们的工作建立在审美(通常是主观的)条件上来实现结构的布景效果。它们的结构设计主要取决于结构形式的创新,而非结构的重力荷载条件。因此,这种特殊的设计方法可以解决结构缺乏结构效率的问题。不幸的是, 这种结构解决方案通常必须使用一些笨拙的、重要的材料来构造这些建筑形态。这些自由延伸的构造会在建筑物产生不利的内力,也会在建筑物的表面造成无法预料的其它不利力的影响。这些形状依靠弯曲支撑受力-最有效的基本负荷的方法。然而,设计师往往忽略这样一个事实,即建筑物自由的结构形式由传统的建筑和结构方式构造产生。弗兰克盖里,普利兹克奖建筑师, 促进了这种建筑设计进程, 他传达过这种建筑设计的想法而没有过这种建筑设计(Shelden2002)。一个合理化的设计,在初步设计阶段,需要超越传统布局经验而且要以结构的完整性设计为中心(Leach et al . 2004)。形成一个初步的建筑结构形态需要一个强大的工程师和承包商团队。例如, Nuovo Polo Fiera Milano, 意大利 (建于2004年) (Guillaume et al. 2005) 的屋顶壳体设计概念是由建筑师马希米亚诺福克萨斯,然后交给结构工程师和承包商Mero TSK 集团解决结构上和构造上的关系后确定的(见图 2) (Basso et al. 2009)。几何造型几何学是一种工具, 古代建筑模型的构造就已经使用。当然,这也一直受到立体解析几何和设计者想象力强加的规则的限制。几个世纪以来,建筑学已经能够围绕简单的几何图形来判断建筑物在结构和构造上的质量。 我们可以从花之圣母大教堂的圆顶及其最近的混凝土外壳的设计中找到这样的例子。花之圣母大教堂的圆顶,意大利(建于1436年),由菲利普布鲁内莱斯基;其最近的混凝土外壳,费利克斯坎德拉(Moreyra Garlock and Billington 2008) 旋转弯曲型屋面,移动型屋面,和大小可变型屋面能让它们更好的组合成壳体屋面结构,并分散成一个个小小的单元。在这种背景下, 耶尔格施莱希和汉斯舍贝尔在钢壳结构的工作是一种创新。他们设计了将屋面分为平面四边形网格方法,能够获得正确的移动型屋面,和大小可变型屋面。柏林动物园的HippoHouse,德国(建于1996年),由建筑师设计Grieble和Schlaich Bergermann以及合作伙伴(Schober 2002,Glymph et al . 2004)利用这种方法设计的一个优美的钢壳,见图3。通过结构形式考虑结构效率几乎所有传统的结构设计原理(从材料选取、剖面图,节点类型, 整体微分几何、和支撑条件), 整体微分几何学都是确定一个壳体结构是否是稳定的,安全的,足够的支撑。每个拥有精美结构网络的大跨度壳体结构都是由大量细小模块组成。第一个此类结构的设计在于设置精确的边界条件,在这个精确的边界内外壳的形状可以向外拓展。在实现膜强度的稳定性,曲线形状是至关重要的。弯曲的壳体需要通过寻找“正确”的几何形状来避免因自重而只有膜起作用的结果。薄膜效应使材料的性能得以充分发挥。结构设计最重要的的挑战首先在于确定约束骨架的壳体的三维(3 d)表面。在二十世纪,建筑师和工程师高迪(Huerta 2003),奥托(Otto et al .1995), 易思乐(Billington 2008)尝试利用物理形式寻找这样一种方法,在对于一个给定的材料,建立一组边界条件和重力荷载,以寻找有效的三维结构形状。为钢壳结构找到一个缆索系统的重要性首先在于这样一个事实,自重(钢和玻璃引起的重力负载) 主要贡献的负载被抵消。子模块需要轴向加载使截面轮廓最有效地受力。利用数值模拟形式寻找方法力密度法(Schek 1974)和动态松弛法(1965天)已经成功地应用于轻便系统,其模型是由内部预应力和建筑物边界范围条件的水准设定。然而,当谈到缆索系统的形状并不取决于初始预应力而是由重力负载 (如案例中的砖石、混凝土或钢壳) 决定时,更少的数值模拟方法被应用。这主要因为很难找到最优形式对于那些依靠拉伸和压缩膜应力相互抵消的壳体结构。基利恩和奥科申朵夫(2005) 为静定系统呈现了一种基于粒子-弹簧系统的面料仿真模型的结构形状探索工具,该系统是用龙格-库塔求解器求解。布劳克和奥科申朵夫(2007)发表了应力网络分析来确定纯压力体系。对于荷兰海事博物馆屋顶的初始设计大赛项目, 动态松弛法通常是用于预应力系统,该法适应处理重力加载下,张力和压力下的三维缆索体系。在NSA庭院竞争设计钢玻璃壳体结构在不久的将来,荷兰海事博物馆计划彻底的改造项目。十七世纪历史建筑成为受限空间阻碍了游客的运行。博物馆的院子需要集成到旅客流通空间,且要规避天气影响,保持最小的室内温度。这样,一个邀请设计大赛被举办,为这座历史建筑增加更多附加价值一个新的玻璃屋顶产生了。2005年,奈伊和其合作伙伴,一个总部位于布鲁塞尔的工程设计咨询公司, 钢和玻璃结构外壳设计赢得了这次比赛。外壳的制造和施工在2009年和2011年之间。2012年,该项目被授予阿姆斯特丹建筑奖。Finding the Form of an Irregular Meshed Steel and Glass ShellBased on Construction ConstraintsSigrid Adriaenssens, M.ASCE1; Laurent Ney2; Eric Bodarwe3; and Chris Williams4Abstract: In the context of the search for an efficient structural shape to cover the Dutch Maritime Museum courtyard in Amsterdam, Netherlands,the authors briefly discuss the driving design factors that influenced the earliest glass roof coverings. The trends that emerged during thelate 20th and early 21st century in the design of skeletal steel glass shells are exposed. These design developments range from sculptural togeometric and structural intentions. The discussion of the competition design development of the Dutch Maritime Museum steel glass shellroof shows the quest for a structurally efficient catenary form based on a poetic geometric idea. This paper presents a construction-driven designmethodology that slightly adapts the numerical form found catenary shape with the objective of achieving planarity in all the triangulated, foursidedand five-sided mesh faces. The challenge of facet planarity is gracefully solved by an analytical origami approach and presented. Thisapproach is compared with finding the Maxwell reciprocal network diagram. The final faceted shape shows elegance and structural efficiency.DOI: 10.1061/(ASCE)AE.1943-5568.0000074. 2012 American Society of Civil Engineers.CE Database subject headings: Design; Steel; Glass; Historic sites; Roofs; Netherlands.Author keywords: Shape; Conceptual design; Form finding; Steel glass shell; Historic courtyard; Planarity faces; Construction constraint;Maxwell reciprocal network.IntroductionIn the wake of the Industrial Revolution, glass metal structuresappeared as a result of two factors: societys desire for green, quietspaces in overpopulated cities, and the scientific emergence of newconstruction materials (glass and iron).In the early nineteenth century, the first greenhouses with aglazed roof appeared as living spaces. Their tall construction andmaintenance costs (because of the glass and the required heatingsystem) made them style icons of the elite. Their curved shapes(1) ridge and furrow e.g., Chatsworth, United Kingdom (builtin 1834), and (2) vaulted, e.g., Kew, United Kingdom (built in1844) (Kohlmaier and Von Sartory 1991) allowed the sparsesunlight into the space and hit the citrus and lime trees (hence, thename orangery). Other varieties of tender plants, shrubs, andexotic plants were also housed in the orangery. The introductionof the palm tree, an impressive and prestigious plant with largereligious significance, pushed the shape of the greenhouse furtherupwards.In the middle of the nineteenth century, the development ofgreenhouse typologies was in full swing, and resulted in culturehouses, conservatories, and winter gardens e.g., the Royal greenhouses,Laeken, Belgium (built in 1876) shown in Fig. 1 (Woods andSwartz 1988). The winter garden is of particular interest to thispaper because it defines a social meeting place adjacent to a privatemansion or public building.Mass production of affordable iron in the second half of thenineteenth century further encouraged the design and constructionof tall and large span exhibition halls made of cast and wrought ironand glass. Plenty of light entered the exhibition areas of buildings,such as the Crystal Palace, United Kingdom (built in 1851) (shownin Fig. 1). Its filigree iron structural skeleton was prefabricated, andit was subsequently dismantled and moved from Hyde Park toSydenham in South London. Unfortunately, it was destroyed by firein 1936.The second half of the 20th and the early 21st centuries experienceda new uprising of the design and construction of roofs oversocial gathering places, winter gardens without plants, coveringcourtyards of historically important public buildings e.g., the greatcourtyard of the British Museum, United Kingdom; see Fig. 1; theDeutschen Historischen Museum, and Museum fur HamburgischeGeschichte, Germany (both Schlaich Bergermann and Partners, builtin 2001 and 2004, respectively); and the Smithsonian Institute,Washington, DC (Foster and Partners, and Buro Happold in 2001).The shapes of these glass-covered, single-layered steel skeletalshells were driven by a combination of sculptural, geometric,physical, and constructional considerations (Williams 2000). Therecent re-emergence of these structures goes hand in hand with theevolution of digital design tools that enable the designer to developand analyze more free and daring geometries.Single-LayeredSteelSkeletalShellsCoveredwithGlassTodays designers (either from an architectural or engineeringbackground) of these nonbotanical winter garden shells seem tobe guided by one or more of the following four driving factors: Fig. 1. (a) Laeken winter garden (Belgium, built in 1875) still serves asa social meeting place. (Jackson 2007; reprinted with permission fromthe photographer); (b) prefabricated Crystal Palace (United Kingdom,built in 1851) was dismantled soon after its intended use (reprintedfrom /wiki/File:Crystal_Palace.PNG,originally from Tallis History and Criticism of the Crystal Palace.1852); (c) British Museum Courtyard (United Kingdom, built in 2000)steel roof adds value to the museum by expanding the useable circulationspace (image by authors)imposed existing situation, sculptural architectural esthetics,geometric shape, and structural efficiency through form.Imposition on an Existing Situation: The ModernWinter GardenIn the last two decades, existing historically relevant publicbuildings with a central open courtyard have been adapted to extendthe useable floor area to an indoor/outdoor climate. Thesegenerally narrow buildings count on the courtyard for daylight.Steel and glass shells offer a unique solution to this design challenge.The historic context for these shells imposes a series ofdesign constraints within which the designer has the freedom todevelop the shells form. The boundary conditions often includeheight restrictions and limits upon the maximumextra load that canbe imposed on the existing building, particularly in a horizontaldirection. The British Museum Court Roof is supported on slidingbearings so that no horizontal thrust is exerted on the historicmasonry walls of the museum (Williams 2001). In the reviewingthe design of recently realized steel shells, the driving design factormore often seems to be architectural scenographic esthetics ratherthan structural performance.Sculptural Architectural EstheticsWith the available geometric digital modeling tools, more architectsbase their work on esthetic (and often subjective) considerations toachieve scenographic effects. This sculptural design intent can beappreciated for its inventiveness of plastic forms, but not for itsconsideration of gravity loads. This particular design approach thusraises questions from a structural point of view with respect to theresulting lack of structural efficiency. Unfortunately, the structuralsolutions necessary to make these sculptural shapes possible typicallyuse an awkward and significant accumulation of material.These free-form shapes often lead to unfavorable internal forces andunder loading do not allow membrane stresses to develop within thesurface. These shapes then rely on bending actionthe least effectiveof all basic load carrying methods. Designers often ignore thefact that the free form is made up of conventional constructional andstructural means. Frank Gehry, the Pritzker prize-winning architect,promotes this architectural process, which expresses sculpturalintentions but is disconnected from any sculptural intent (Shelden2002). A rationalization is needed at the preliminary design stagethat goes beyond this scenographic experience and concentrates onthe structural integrity of the design (Leach et al. 2004).The evolution of an initial sculptural shape into a constructablestructure needs a strong team of engineers and contractors. For example,the conceptual design for the shell of the Nuovo Polo FieraMilano, Italy (built in 2004) (Guillaume et al. 2005) was developedby the architect Massimiliano Fuksas and then handed over to theengineers Schlaich Bergermann and Partners and contractor MeroTSK Group for the development of the structural and constructionalrationale for the project (see Fig. 2) (Basso et al. 2009).Geometric ShapeGeometry is a tool that has been used since antiquity for the developmentof architectural shapes. These forms are thus limited bythe rules imposed by analytical geometry and the designers imagination.Through the centuries, architecture has developed around“simple” geometries chosen for their constructive or structuralqualities. Examples can be found in the design of the cupola ofthe cathedral Santa Maria del Fiore, Italy (built in 1436), by FilippoBrunelleschi and more recently the thin concrete shells by FelixCandela (Moreyra Garlock and Billington 2008). Surfaces of revolution,translational surfaces, and scale-trans surfaces lend themselvesexcellently to shell action and discretization into subelements.In this context, the work of Jorg Schlaich and Hans Schober on steelshells is innovative. They devised a method to find the right translationalor scale-trans surface that can be divided into four-sidedplanar meshes. The HippoHouse of the Berlin Zoo, Germany (builtin 1996), designed by architect Grieble and Schlaich Bergermannand Partners (Schober 2002, Glymph et al. 2004) exploits this approachin an elegant steel shell, as shown in Fig. 3.Structural Efficiency through FormOf all traditional structural design elements (ranging from materialchoice, profile sections, node type, global geometry, and supportconditions), global geometry mostly decides whether a shell will bestable, safe, and stiff enough. The shell spans large distances withFig. 2. Nuovo Polo Fiera Milano (Italy, built in 2004; architect Massimiliano Fuksas, structural engineers Schlaich Bergermann and Partner and MeroTSK Group) illustrates how a sculptural shell is discretized in four-sided and triangulated (at the supports) meshesFig. 3. Hippo House (Germany, built in 1997), designed by architect Grieble and Schlaich Bergermann and Partners, shows the discretization ofa translational surface into planar quadrangular meshes (photograph courtesy of Edward Segal, reprinted with permission)a fine structural network (skeleton) of individual small subelements.The first design consideration lies in setting the exact boundaryconditions within which the shell shape can be developed. Thecurved shape is of vital importance to achieve stability throughmembrane stiffness. Shell bending needs to be avoided by findingthe “right” geometry, so that under the self-weight only membraneaction results. Membrane action makes efficient use of material. Theimportant structural design challenge lies in the determination ofa three-dimensional (3D) surface that will hold the skeletal shell.In the twentieth century, both architects and engineers Gaudi(Huerta 2003), Otto (Otto et al. 1995), and Isler (Billington 2008)experimented with physical form finding techniques, which fora given material, created a set of boundary conditions and gravityloading that found the efficient 3D structural shape. The importanceof finding a funicular shape for steel shells lies in the fact that theself-weight (gravity loads caused by steel and glass) contributeslargely to the load to be resisted. The subelements need to be loadedaxially to make most efficient use of the section profile.Numerical form finding techniques force density (Schek 1974)and dynamic relaxation (Day 1965) have been successfully appliedto weightless systems whose shape is set by the level of internalprestress and boundary supports. However, when it comes to funicularsystems whose shape is not determined by initial prestress butby gravity loads (such as the case for masonry, concrete, or steelshells), fewer numerical methods have been developed. This ismainly because of the difficulty of finding optimal forms for thoseshells that rely on both tensile and compressive membrane stressesto resist dead load. Kilian and Ochsendorf (2005) presenteda shape-finding tool for statically determinate systems based ona particle-spring system solved with a Runge-Kutta solver, used incomputer graphics for cloth simulation. Block and Ochsendorf(2007) published the thrust network analysis to establish the shapeof pure compression systems. For the initial design competition forthe Dutch Maritime Museum roof project, the dynamic relaxationmethod usually used for prestressed systems was adapted to dealwith 3D funicular systems with tension and compression elementsunder gravity loads.Competition Design for a Steel Glass Shell overthe NSA CourtyardThe Dutch Maritime Museum planned a thorough museum renovationin the near future. The restricted space in the seventeenthcentury historic building hinders the movement of visitors. Thecourtyard needed to be integrated into the museums circulationspace, sheltered from weather, and kept to a minimal indoor temperature.An invited design competition was held for a new glass roofthat added value to the historic building. In 2005, Ney and Partners,a Brussels-based engineering design consultancy, won this competitionwith a steel an

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