Cold Deformation of Glass

Mick Eekhout
Dries Staaks

1. Introduction

In modern architecture the customary flat glass façades are supplemented by curved surfaces and occasionally by geometrically complicated curved glass façades, mainly in conjunction with ‘blob’ or ‘liquid design’. Amongst others cold deformation of laminated and insulated glass panels has been realised recently in order to attain the desired non-flat glass surfaces. The development of advanced computer programs describing the complex geometry of surfaces makes extreme designs possible: so-called "blob-architecture" (blob = binary large objects). Part of their curved envelope has to be transparent. Common heat formed glass sheets, adopted from the automotive industry, are used for that purpose. However, contrary to automotive design for series production, building design is unique, up to the building components. Heat-formed glass sheets need a special formwork for warping at high temperature. That makes this process expensive for a small number of
identically shaped glass sheets. Thus, for building envelopes cold bent glass sheets (with slight bending) are more favourable. The research concerning the geometrical pattern of single and double curved glass sheets and the stresses caused by curving and the practical applications preceding (and
challenging) this research are the subject of this paper.

2. Applications

2.1 Cold bent façade of the Municipal Floriade Pavilion, Haarlemmermeer, the Netherlands

One of the innovations Octatube made for this pavilion, designed by Asymptote Architects from New York, is executed in the south façade. This façade has two glass surfaces of approximately 6x6 m2, each divided in 3x3 panels of maximally 2x2 m2. The glass panels are frameless: usually 4
corner points. Cold bending of 12 panels took place at the construction site by pressing two pairs of
two additional points at the lower and upper edge by 50% of the allowable stresses outward with a camber of 80 mm over 2m.

2.2 Twisted façade of the Town Hall of Alphen aan den Rijn, the Netherlands

In September 2001, Octatube was approached to design an alternative for the ‘spaghetti’ glass strips
at the rear façade of the Town Hall Alphen a/d Rijn, designed by Erick van Egeraat. The design of this façade asked for several transparent glass strips curling randomly around an ‘egg’-shaped building façade, causing a twist at the bottom and top of the ribbon. Our concept was to consider all window frames redundant and focus on the development of the glass panels instead. After structural
analysis and a test with a prototype of a cold twisted double glass panel, the definitive proposition was developed. Flat double glass panels would be twisted on the building site, forced in upper and lower continuous U-profiles, fitted with rubber elements and finally waterproofed with sealant.
Although the risk was high, the cost price was transparent, thus we could give the client a considerable reduction of the total cost. Cold twisting proved to be a practical and above all economic innovation, which resulted in the first cold twisted pre-tensioned double glass façade in
the world. Twisting up to 40mm out-of-plane of each panel max 900x2000mm.

These two projects introduced the need for a theoretical foundation and further research.

3. Single Curved Glass Sheets

The simplest shape of a single curved surface is part of a cylinder. The glass pane has a constant curvature, with a radius R, equal to half the diameter of the cylinder. This means that the maximum stresses in the glass sheet are directly-proportional to the thickness of the pane t, and inverselyproportional to the radius of curvature R. For surfaces with a small radius of curvature we need thin
panes of toughened glass. The stresses are permanently present, and reduce the capacity to withstand loads by self weight (in the case of non-vertical panes) and wind.

4. Double Curved Glass Sheets

The appearance of the distortion of the panes in Alphen aan den Rijn (chapter 2.2), magnified through the mirror-effect of glass gave rise to questions about the exact deformation of twisted glass panes. The research focused on point-fixed quadrangular glass panels as part of a double curved façade. Within a complex geometry the flexible silicon connections of point-fixed façades are able to match the varying angles
between panes. A typical quadrangular panel of any double curved façade is supported by four pin joints, three of which lie in the same geometrical plane and one out-of-plane. Though dependent on the position of the four joints, the glass panel will deform in its own way. In experiments by increasing warping, the deformed shape of the pane suddenly changes from one geometrical mode to another. This phenomenon is caused by buckling of one of the diagonals, causing unwanted uneven reflections of the glass.
The first mode consists of a double curved shape, the second mode approximates a single curved shape. The point of transition from the first to the second mode was determined dependent of plate geometry. In general
maximum stresses will occur near the corners, more and more exceeding first order equilibrium stresses while deformation dZ increases.

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The Authors

Mr. Mick Eekhout Prof. Dr. Octatube Space Structures Prof. Dr. Ir. Mick Eekhout is professor for product development at the faculty of architecture at Technical University Delft, The Netherlands. He runs his own architectural office since 1975. In 1983 ... Read more