Transformed Corrugated Shell Units Used as a Material Determining Unconventional Forms of Complex Building Structures.

Jacek Abramczyk

doi:10.3390/ma14092402

Abstract

This article is an insight into interdisciplinary topics in the field of civil engineering, morphology, architecture, mechanics, and computer programming. A novel method for shaping unconventional complex roofs in which regular folded units transformed into various shells are used as a complex substitute material is proposed. The original method’s algorithm for building systems of planes defining diversified polyhedral networks in the three-dimensional space by means of division coefficients of the subsequently determined vertices is presented. The algorithm is based on the proportions between the lengths of the edges of the reference network, the location and shape of the ruled shell units included in the designed complex roof structure, so it is intuitive. The shell units are made up of nominally flat folded sheets transformed effectively into shell forms whose static-strength properties are controlled by geometric quantities characteristic of ruled surfaces. The presented original approach to the shaping of the shell roof structures determining specific complex building forms allows us to go beyond the limitations related to the orthotropic structure of the folded roof sheeting and the shape transformations.

Highlights

Since the transverse flexural stiffness and torsional stiffness of a nominally flat thinwalled steel sheet of open profile and folded in one direction are small, a small load applied perpendicularly to the neutral surface of the sheet causes a significant initial shape change
A few ways of determination of the vertices belonging to the investigated reference networks were developed by Abramczyk [1,17,21]
The coefficients define the positions of: (1) the vertices of the sought-after reference network Γ with respect to a few intuitively adopted specific points of Γ, (2) the planes of Γ, (3) the points SAij, SBij, SCij, and SDij belonging to ωr, and (4) the vertices Aij Bij, Cij and Dij of Bv determining the multi-shell roof structure Ω

Summary

Introduction

Since the transverse flexural stiffness and torsional stiffness of a nominally flat thinwalled steel sheet of open profile and folded in one direction are small, a small load applied perpendicularly to the neutral surface of the sheet causes a significant initial shape change. The loaded sheets connected by their longitudinal edges into a nominally flat single strip are spread on at least two mutually skew directrices to change their forms from flat into ruled shells, depending on the shape and the mutual position of the directrices [1] (Figure 1). If a freedom of the fold’s changes manifesting especially in the fold’s width increments is ensured during spreading and fixing all folds to the roof directrices, the folds tend to obtain such shell forms that their longitudinal axes remain straight lines and their contraction appears at a half-way along the length of each shell fold. Since the length of the thin-walled steel sheets is relatively small and the aforementioned geometric and structural limitations of the effectively transformed sheets are very important boundary conditions, it is impossible to obtain a single smooth shell roof of a medium span [1,2] (Figure 2). The complete transformed shell sectors are joined by means of their transverse edges into ribbed structures, so that the shape of each shell sector is characterized by a contraction passing through the halves of all folds at their length to optimize the initial stresses [3]

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