Responsive Parametric Building Free Forms Determined by Their Elastically Transformed Steel Shell Roofs

Abstract

The article concerns the unconventional architectural forms of buildings roofed with transformed shells made up of thin-walled steel fold sheets, and a parametric description of how they are shaped. Complicated deformations of flanges and webs, as well as the complex static–strength work of the folds in a shell roof, demand the creation of simplified models regarding the parameterization of such shells and their integration with the general forms of the buildings. To obtain favorable results, it was necessary to write computer applications because of both the complicated problems related to the significant limitations of the transformations, as well as the great possibilities of shaping shell roofs by means of directrices of almost free shape and mutual position. The developed procedures enable the prediction of shapes and states of all the folds in the designed shell. They take account of two basic conditions related to these restrictions, which guarantee that the folds encounter little resistance when matching their transformed forms to the roof directrices, and that their initial effort was as low as possible. The developed procedures required solving a number of issues in the fields of architecture, civil engineering, and structures, and are illustrated with an example of shaping one unconventional architectural form. The interdisciplinary study explains a new insight into shaping such forms.

Transformed Shell Roof Structures as the Main Determinant in Creative Shaping Building Free Forms Sensitive to Man-Made and Natural Environments

“…Reichhart developed a specific method for calculating the arrangement and the length of the supporting lines of all folds in transformed corrugated shell sheeting [11], but it is effective only for the cases where the fold's longitudinal axes are perpendicular to roof directrices or very close to those [13]. The author significantly improved the Reichhart concept and has proposed an innovative method [13,18], so that the transformation would cause the smallest possible initial stresses on the shell folds resulting from this transformation.…”

“…Therefore, two or more complete corrugated shell sheets cannot be joined with their crosswise ends, that is perpendicular to the fold's directions, to obtain one resultant smooth shell [17]. They can only be set together with their transverse ends ( Figure 2), to obtain an edge roof shell structure with regular edge pattern on its surface [18,19]. For engineering developments, each shell fold can be modelled with a simplified smooth sector of a warped surface [20,21] including hyperbolic paraboloid [22,23].…”

“…The transverse ends of transformed folds cannot be extended to the positions predicted by conventional methods, because this action causes a radical increase in stresses of the deformed thin-walled profiles [11,13,14]. The fold's fixing points along all roof directrices must be precisely calculated either by the Reichhart method [11], if the longitudinal fold's axes are close to perpendicular to the directrices, or by the author's method [13,18]. For these calculations based on precisely calculated supporting conditions, diversified for the subsequent folds in a roof shell, and the stiffness of these folds resulting from their geometrical and mechanical properties can be applied.…”

“…The visible result of different stress values at both transverse ends of the same shell fold is that the transverse contraction of the fold does not pass halfway along its length, on the contrary, it is shifted closer to one of these ends. The condition defined by the author is employed in his innovative method of shaping individual roof shells (monograph) [13] and implemented in the application he developed [18] in the Rhino/Grasshopper program used for parametric modeling of engineering objects.…”

“…The author presented wide possibilities of shaping free form structures composed of many individual free forms [13,17]. He developed the concept and coherent rules for creating such complex structures covered with plane-walled folded elevations and multi-segment transformed shell roof structures [18,19]. The developed algorithms allowed a radical increase in the variety of shapes of these forms [19,22,32,33].…”