Hiperbolik paraboloitlerin yapı endüstrisindeki yeri
Hyperbolic paraboloids (Hypar) in the building industry
Yazar: MUHAMMED EMİN AKYÜREK
Danışman: DR. ÖĞR. ÜYESİ NABİ VOLKAN GÜR ; DR. ÖĞR. ÜYESİ MEHMET SELİM ÖKTEN
Mimar Sinan Güzel Sanatlar Üniversitesi / Fen Bilimleri Enstitüsü / Mimarlık Ana Bilim Dalı / Yapı Bilgisi Bilim Dalı
Derece: Yüksek Lisans, 2020
Konu: Mimarlık = Architecture ; İnşaat Mühendisliği = Civil Engineering

Özet:
Hiperbolik paraboloit çift eğrilikli bir yüzey türüdür. Bu yüzey türünün yapı endüstrisinde bir strüktür olarak kullanımı betonarmenin yaygınlaşmasıyla birlikte mümkün olmuştur. Bu strüktür şeklini yapı endüstrisinde tanıtan Felix Candela, çeşitli yüzeylerin birbiriyle entegrasyonuyla birçok yapı ortaya koymuştur. Her noktasında çekme ve basınç gerilmelerini karşılaması onu diğer kabuk yapılara oranla daha ince ve estetik kılmıştır. Öte yandan kalıp işçiliği, donatı yerleştirilmesi, beton dökümü, yalıtım ve kaplama katmanlarının teşkilinin zorluğu nedeniyle bu strüktürlerin uygulanması belirli bölgelerle sınırlı kalmıştır. Bunun yanında ilerleyen yapı teknolojisi ve yeni malzemelerin türetilmesiyle birlikte çeşitli çağdaş uygulamaların ortaya çıkmasını sağlamıştır.
Hiperbolik paraboloit biçimli betonarme ince kabuk teknolojisini takip eden ilk strüktür tipi ahşap kabuklar olmuştur. İngiltere'de Booth ve Tottenham önderliğinde gelişen bu strüktür ile, kalıp maliyeti neredeyse ortadan kaldırılmış, dolayısıyla ekonomik yapılar ortaya konmuştur. Benzer şekilde ahşap ızgara kabuk strüktürler ile esneklik ve narinlik düzeyi artırılarak, malzeme cinsinden kıyasla; ahşap betonarmeye göre daha uzun yıllar tevarüs etmiştir. Bunun yanında, her ne kadar sayıca az olsa da kablo ağı, çadır veya hibrit sistemli strüktürler gibi denemeler de mevcuttur. Bunlar, geniş açıklık geçtiği ölçüde birçok yönden verimli yapıların oluşumuna meydan sağlamıştır.
Dünyanın çeşitli yerlerinde, birçok malzeme ve yöntemle hipar strüktürlerin inşa edilmesine rağmen ülkemizdeki varlığı neredeyse yok gibidir. Strüktürün karmaşık görünen geometrisi, inşasının da güç olacağı kanısını beraberinde getirmiştir. Bunun yanında mimar-inşaat mühendisi işbirliğinin yeterince sağlanamaması ile birlikte strüktürün kurgusu sağlanamamış ve yapısal davranışı gözlemlenememiştir. Uygulama yoksunluğunun en önemli nedeni, hiperbolik paraboloitlerin geometrisinin ve yapım yöntemlerinin bilinmemesidir. Nitekim mimarlık ve inşaat mühendisliği eğitimleri, öğrencileri klasik strüktürlerin ötesine geçme yolunda yeterince ilgi uyandıramamıştır.
Bu çalışmada hipar biçimli strüktürlerin geometrisinin, strüktürel kurgusunun, yapısal davranışının ve hangi malzeme veya tekniklerle inşa edilebileceğinin bilinmesi sağlanmaya çalışılmıştır. Bu yolda çeşitli incelemeler yapılarak maket ve model gibidenemelerle biçimin tanımlı geometrisi vurgulanmış; yüzeyin yük altındaki davranışı gözlemlerle birlikte ifade edilmiştir. Hipar biçimli strüktürler sınıflandırılarak tarihsel gelişimi, yapım yöntemleri ve çağdaş yapı örnekleriyle birlikte incelenmiştir. Elde edilen bulgular; yapım yöntemi, geçilen açıklık, kullanılan malzeme gibi etmenler baz alınarak kıyaslanmış ve değerlendirilmiştir. Böylece yapı tasarımcısına, hipar biçimli strüktürler için analitik bir tasarlama teorisi ortaya konmuştur. Hipar yüzeyin Türkiye'deki olası serüvenine yönelik; öncelikle kent mobilyaları, parklar, durak ve pergoleler gibi küçük ölçekli yapıların yapımı önerilmektedir. Böylece bu strüktür belirli deneysel evrelerden geçerek oditoryum, stadyum veya cami gibi geniş açıklıklı yapılarda bir taşıyıcı sistem alternatifi olarak yer edinebilecektir.
Anahtar kelimeler: Hiperbolik Paraboloit, Betonarme Kabuk, Ahşap Kabuk, Izgara Kabuk, Kablo Ağı Strüktür

Abstract:
Hyperbolic paraboloid is a type of anticlastic surface with double curvature. This surface is formed by translating a parabola perpendicularly to another parabola in the opposite direction or by shifting the two ends of a line (generatrix) on curved or straight directix in different planes. It will be understood that, the hyperbolic paraboloid may be formed not only by the curvature (translational element) being parabola, but also by being straight line. In addition, the directix of the hyperbolic paraboloids as the ruled surface does not need to be curved. In this case, all of the elements that form the surface are line segment. In this sense, the hypar is divided into two categories depending on whether the edges are straight or curved. Hyperbolic paraboloid surfaces with straight edges are formed by shifting the two ends of a oblique line to the plane on two other oblique lines opposite but not parallel to each other. If so, the sections taken from the surface give hyperbola and parabola as on the curved edge surface. If it's needed to objectify hypar; it is a form that resembles the passage between two mountains, the form of a chips or the saddle of a horse.
Hypar, is generally a shell structure transfer the load with surface activity. It has constant and equal shear stresses at every point thanks to its anticlastic curvatures. That is to say, the buckling response caused by the compressive force acting in one direction is prevented by the tensile force acting in the other direction. The torsional force acting on the surface is less than the tensile and compressive force and is generally prevented by side beams. Due to this advantages, hypar can be produced in more delicate dimensions than other forms. This reduces costs by reducing the amount of material used.
Hypar-shaped structures have been widely applied from past to present under the following three headings: reinforced concrete thin shell, wooden shell and cable net structures. It has been one of the most widely practiced forms in the 20th century because of structural effectiveness. Beside, low amount of material required for construction and its aesthetic view are features that makes it popular. In addition, combination of both curved-edged and straight-edged hyperbolic paraboloids in various sizes and shapes, supported at various points provided innovation and diversity in its architectural design.
The use of this surface as a roof construction in the building industry has become possible with the spread of reinforced concrete. Felix Candela, introducing this structure to the building industry, built several structures by integrating various surfaces. Balancing the tensile and compressive stresses at every point, makes it thinner and more aesthetic than other shell forms. On the other hand, it was not easy to introduce hypar concrete shells to the construction industry. One of the most important reasons for this is the fact that these surfaces, which are a double curvature mathematical form, are not well known by either designers nor constractors. Beside, erection of wooden formwork is difficult and expensive. Therefore, the production of these surfaces, which are applied as reinforced concrete shell system, has been limited in certain regions with similar works of the same construction team. Causes such as cracking of concrete shells over time, rusting of reinforcement and construction difficulties have led researchers to try recent technologies such as use of a membrane as a mold, use of shotcrete and reinforcing concrete with a fabric. Consructing the old with less and more perfect are inadequate efforts due to the lack of implementation in the industry. In addition, with the advancing construction technology and the derivation of new materials, various contemporary applications have emerged.
Cast in-situ concrete shell structure implementations seem to have been abandoned because of many construction problems. However the adventure of hypar, which gained momentum with Candela, continued with Nowicki's pioneering cable net structure, wooden shell with Catalano, gridshell with Natterer and Otto.
The cable net structure, which has been constructed in various places since the 1950s, has become a structure alternative that provides efficiency in many ways rather than being a trend with its rapid construction and wide span effectiveness. Stabilize the cable net with reinforced concrete has expanded the possibilities of the structure by transforming it into a monolithic surface. One of the first examples is found in the Philips Pavilion review. Similarly, the Saddledome Stadium, which has a circular plan, appears to be connecting the cable net with precast elements and in-situ cast concrete.
Another structure following the hypar-shaped reinforced concrete thin shell technology is wooden shells. With this structure, was developed under the leadership of Booth and Tottenham in England, formwork cost was almost eliminated and thus more economic roof structures were revealed. Wood shells became an architectural style in England between 1957-1975 with the elegance and aesthetics it offers. With standardization in these structures, construction could be faster, easier and cheaper. This feature procures wooden shells to be a structure system alternative in different periods and regions. Thus, it became known the literature.
In addition to examples where the surface has become a complete shell, there are also examples of structures formed with linear beams. These structures, which was gained to the literature as gridshell, are especially preferred in free-form structures. The auditorium in the Paraiso Park, which consists of a multi-layered wooden grid and Antwerp Law Court which was formed with laminated beams are the examples of gridshell. In addition to these, various materials and methods such as bamboo pergola, prefabricated stone and steel tie integrated canopy are encountered in various regions.
These studies show that the search for re-implementation of this form under various structure classifications in accordance with today's construction technology continues. The reason for this is undoubtedly the structural efficency provided by this form, the ability of the surface to be build in various forms and the aesthetic effect it offers to the designers.
Despite the construction of hypar structure with many materials and methods in many regions of the world, there is almost no presence in Turkey. The complex geometry of the structure led to the belief that its construction would be difficult. In addition, with the lack of collaboration between architect and civil engineer, establishment of the structure and its structural behavior could not be observed. The most important reason of implementation deprivation is that the geometry and construction methods of hyperbolic paraboloids are not well known. As a matter of fact, the architectural and civil engineering education have not aroused enough interest for the students to go beyond the classical structures.
In this study, it is aimed to understand the hypar geometry, structural design and behavior and the materials or techniques that can be constructed with hypar-shaped structures. In this way, various examinations have been conducted and the defined geometry of the form has been emphasized through experiments such as both physical and digital models. The behavior of the surface under load is expressed with observations on models. Hypar-shaped structures are classified and examined with their historical development, construction methods and contemporary building examples. Findings were compared and evaluated on the basis of factors such as construction method, span, material used. Thus, an analytical resource was presented fort he design theory of hypar-shaped structures.
Keywords: Hyperbolic paraboloid, Concrete Shell, Wooden Shell, Gridshell, Cable Net Structure