Innovative Systems Of Corrugated Shells Rationalizing The Design And Erection Processes For Free Building Forms

S t r e s z c z e n i e Artykuł prezentuje innowacyjną metodę kształtowania swobodnych form architektonicznych budynków i ich systemów morfologicznych zadaszonych złożonymi powłokami wykonanymi ze stalowych arkuszy fałdowych przekształconych z postaci płaskiej do postaci powłokowej. Interdyscyplinarny charakter pracy wynika z różnorodności i złożoności rozpatrywanych zagadnień. Za pomocą metody tworzone są złożone systemy morfologiczne budynków ze zintegrowanych postaciowo wielosegmentowych dachów powłokowych i płaskościennych elewacji. Metoda nakazuje utworzenie przestrzennej, parametrycznej sieci złożonej z wielu pojedynczych czworościennych geometrycznych utworów pozwalających zbudować spójne i atrakcyjne formy architektoniczne łatwo adoptowalne do zróżnicowanych warunków brzegowych w tym do istniejących warunków otoczenia. Powyższa sieć oraz algorytm metody umożliwiają racjonalizację procesów projektowania i wznoszenia swobodnych form budowlanych. Złożoność form geometrycznych budynków oraz zmian postaciowych arkuszy fałdowych przekształcanych do postaci powłokowej wymaga opracowania złożonych formuł matematycznych oraz innowacyjnych programów komputerowych wspomagających proces kształtowania swobodnych form. K e y w o r d s : Buildings; Corrugated roof shells; Effective transformations; Integrated free forms; Morphological systems. 1/2017 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 29 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T The Si les ian Univers i ty of Technology No. 1/2017 A . P r o k o p s k a , J . A b r a m c z y k the sheeting depends on a mutual position and curvature of the directrices. The transformations are effective if freedom of transversal width increments of each fold of the sheeting is ensured. In this case, the transformed sheeting is characterized by: a) orthotropic geometrical and mechanical properties; b) big mutual displacements of the subsequent folds; c) small strain; d) big deformations of fold’s flanges and webs out of their planes. Due to the above big displacements and effective shape transformations, great freedom in shaping the roof shell forms is achieved, so a variety of the architectural forms of the shell roofs and entire buildings is really great. However, some important restrictions of the sheet’s shape transformations have to be taken into account. The basic one concerns the fact that each effectively transformed fold is contracted in the half of its span and stretched at its both crosswise ends. Therefore, two or more complete corrugated shell sheetings cannot be joined to each other along their crosswise ends, that is perpendicularly to their fold’s directions, to obtain one resultant smooth shell. They can only be set up along their crosswise ends Fig. 1, to obtain a ribbed roof shell structure with regular edge pattern on its surface. Some innovative computer programs aiding the design process are elaborated because of the complexity of a mathematic description of the geometrical models used. 2. CRITICAL ANALYSIS OF KNOWLEDGE Simple shell structures composed of the corrugated shells have been used in a few various architectural configurations [1]. The structures are most often umbrella roofs supported by very few columns [2, 3]. They are used for achieving: a) large spans, b) greater architectural attractiveness, c) skylights letting the sunlight into the building interior [4]. Adam Reichhart has arranged the complete corrugated shells, see Figs. 1, 2, on horizontal or oblique planes as continuous ribbed structures [5]. Prokopska and Abramczyk have been continuing the problems carried on by professor Reichhart. They have proposed a way of geometrical integration of shell roof forms with oblique plane elevation walls to obtain the innovative, attractive and multi-variant architectural forms as morphological systems of buildings [6, 7]. Blaszczynski has presented principles of shaping roofs of various shapes starting with planar hipped roof ends [8]. Abramczyk has elaborated a preliminary version of a geometrical method of shaping shell structures [9, 10]. The method allows to use: a) oblique walls and columns [11], b) curvilinear directrices [12], c) regular reference surfaces to arrange regularly and effectively [4, 13] the corrugated complete shells in three-dimensional space, d) lines of curvature on the reference surface [10], e) an integration of the plane curved roof directrices with oblique complex elevations composed of plane folded walls [4], f) lines of striction of warped surfaces for modelling the complete shells to achieve effectiveness of the sheet shape transformations [12, 8]. At the preliminary stage that is during assembling the nominally planar sheets onto the roof directrices, the neutral surface of each fold is transformed into a shell shape, so initial effort and geometrical imperfections of the shell folds appear and have to be taken into account. Reichhart has designed corrugated shell sheeting supported by very stiffen frameworks or planar girders with additional intermediate members and roof bracings [14]. Such an activity is aimed at designing the transformed folds as thin-walled beams with open cross-sections simply supported at their ends [15, 16]. His method does not take account of changing the cross-section shapes along the fold’s length [12, 17] as well as various kinds of buckling because the maximum degree of the fold transformation is restricted [5]. The behavior of the corrugated hyperbolic paraboloid roofs under a characteristic load at the service work stage is analyzed in [18, 19, 20]. The co-operation between the corrugated hyperbolic 30 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 1/2017 Figure 1. The simple shell structures arranged on the horizontal and oblique planes INNOVATIVE SYSTEMS OF CORRUGATED SHELLS RATIONALIZING THE DESIGN AND ERECTION PROCESSES FOR FREE BUILDING FORMS paraboloid sheeting and its structural system and the influence of the co-operation on the balance state of the entire free form building is considered in [3, 22]. A way of decomposing a load vector into directions similar to directions of two any rulings belonging to two various families of a hyperbolic paraboloid is proposed in [21] by Egger, Fisher and Resinger. It is assumed there that a set of the shell folds produces an orthotropic continuous shell. However, the directions similar and perpendicular to the fold’s neutral axes are not analyzed. Reichhart has proposed a very general concept of decomposing of the load vector acting on a warped surface [5]. The concept enables decomposing the load vector in the directions similar to the subsequent fold direction. The utilization of the folded steel sheeting for roofing considerably improves the processes of building design and erection due to: a) the unification of the folded sheets, b) light, fast and easy transport, erection and assembly, c) a possibility of easy adding various equipments of the building including installations, d) ease of mass production and prefabrication including manufacturing with help of so-called factory on wheels, e) elimination of delays resulting from bad weather. In addition, the sheeting is economic and recyclable material, which enables protecting the natural environment and controlling phases of roof damage as well as co-operation with a building framework [20]. The profiled steel sheets can be manufactured as folded panels with the help of the factory on wheels, that is the technology and technique ABM MIC worked up by US army [19], It enables enable achieving the great diversity in shaping free roof forms due to the competent and effective shape transformations, which can lead to many innovative solutions in terms of shape, strength and stability. The great possibility of shaping free forms is the reason of elaborating the proposed original method. 3. AIM, RANGE AND MEHODOLOGY The aim is to present the new method of shaping free form building structures roofed with diversified systems of many complete corrugated shells made up of folded sheets transformed effectively from plane into spatial shapes. The issues presented are a continuation of the analyses conducted by professor Reichhart in terms of the shell roof sheeting [5, 14]. A general definition of a system is adopted from [23], where the system is an active integrity regarded as a group or set of objects connected by a certain form of regular cooperation or interdependences meeting required functions. Following the method proposed bellow in details, the main system here is defined as a building system formed from: a) a set of such simpler systems that are complete members whose work, effort and stability have to be evaluated during designing, b) complete covers of the roof and elevations. Following the above general definition of the system, it is established that: a) a complete roof shell is regarded as a system of the effectively transformed folds – simple supported thin-walled beams of open A R C H I T E C T U R E 1 /2017 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 31 a Figure 2. The architectural model, framework, shell roof structure and control structure created during defining the building free form A . P r o k o p s k a , J . A b r a m c z y k cross-sections, bracings and members supporting the folds; b) a roof structure is a system of the complete shells divided from each other by ribbing; c) a folded elevation is a system of complete plane parts – walls; d) the complete wall is a system of columns, beams, bracings connected one to another; e) a final system used in this work is a building structure – the sum of the roof shell system and the folded elevation system including a spatial framework stiffening the entire system. The building structure is also called free form building or complex building, Fig. 2. The diversified systems of the roof structures created