On the size and shape of initial out-of-plane curvatures in structural glass components

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Abstract

For many structural glass components, buckling is known to be a major design issue, which is influenced significantly by several parameters. The latter include boundary conditions, slenderness and geometrical imperfections, in particular initial curvatures. However, in spite of their importance for building practice, experimental data for the latter are very poorly documented. Consequently, an extended experimental campaign is presented in which initial curvatures of 312 monolithic and laminated glass beams with a variable length, height, glass thickness, glass type and – wherever applicable – interlayer, have been accurately measured and analysed. Major conclusions have been drawn regarding the shape and the size of initial curvatures.

Research highlights

► We measure shape and size of initial curvatures of 312 glass beams. ► In general, sinus and parabola describe shape of curvature well. ► Curvature is influenced by lamination and tempering. ► No influence of geometry or interlayer type was observed. ► Characteristic value of initial imperfection amplitude is L/400.

Introduction

Over the last two decades, the use of glass as a load-bearing structural material has grown in a relatively spectacular way. Typical examples include glass stairs, roofs, accessible floors, beams, columns, shear walls, etc. [1], [2], [3]. Even if official design standards or recommendations for most of those applications are still lacking in most countries, a large number of scientific investigations has been carried out in this field, providing useful information for glass designing professionals. Amongst the research focusing on the load-bearing capacity of simple glass components (i.e. without connection devices, etc.), two major research areas could be detected.

A first group of researchers focuses on strength-related issues, such as brittleness, fracture mechanics and probabilistic reliability of glass. In particular the tensile strength of glass is of interest for structural applications, as it is well-known to be significantly lower than the compressive strength. Apart from the many contributions in specialised material science literature, several authors investigated these subjects from a structural engineering point of view [4], [5], [6], [7], [8], [9].

In addition, a second group of researchers concentrated on stability problems, such as flexural buckling, torsional buckling, lateral torsional buckling, plate buckling and shear buckling [10], [11], [12], [13], [14], [15], [16], [17], [18]. Those stability issues are of particular interest when glass elements, which are usually very slender, are subjected to axial compressive loads, as in such cases the (elastic) buckling load will often be more critical than the glass breakage load.

For designing purposes, most parameters influencing the buckling resistance of monolithic or laminated glass are relatively easily accessible (e.g. the glass geometry, which is a given; the interlayer properties, which are available from the manufacturer or in literature; or loading and mounting eccentricities, which follow from tolerances and from the design concept itself). However, information on initial shape imperfections, which according to several authors often play a rather important role regarding the stability of structural glass members [10], [11], [12], [18], is scarce and scattered. The typical influence of initial curvature on the elastic buckling resistance of a bar in compression is illustrated in Fig. 1.

Consequently, the main objectives of this contribution are the following:

  • (1)

    To present an extended experimental campaign and to discuss its results in order to determine the shape and the characteristic value of the maximum amplitude of initial geometrical imperfections (i.e. global bow) of various beam-like glass panes.

  • (2)

    To detect trends in imperfection shapes and sizes with respect to other parameters, such as glass thickness, geometric aspect ratio, glass type, lamination and interlayer material.

Section snippets

Test specimens

An extended experimental campaign has been executed to measure the initial curvature of a variety of glass beams, which have been subjected to buckling tests afterwards. However, the latter are beyond the scope of this contribution: the interested reader will find more details in literature [11], [12]. The current focus is on the initial curvature measurement campaign, which was divided in two parts and executed at two different research labs. The first part of the experiments was organised at

Measurement according to EN 1863-1 and EN 12150

In EN 1863-1 and EN 12150 a standard method is given to determine the overall and local bow of respectively heat-strengthened soda lime silicate glass [19] and thermally toughened soda lime silicate safety glass [20]. According to these standards, the glass pane should be placed in a vertical position and supported on its longer edge by two load-bearing blocks in the quarter points. Subsequently, the deformation in terms of global bow must be measured along the edges and diagonals of the glass,

Imperfection shape

Fig. 7a depicts the initial geometrical imperfections of the aluminium guiding rail, together with the results of three subsequent mirrored measurements on the same specimen, used to determine the imperfections of the guiding rail as explained in §3.2.2. Furthermore, Fig. 7b–d represent a general overview of the shape imperfections of all specimens obtained from manufacturer A, B, and C, respectively. To avoid the graphs to be too crowded, only the minimum and maximum are shown in black; the

Discussion

Several parameters are analysed below to determine their influence on the shape and magnitude of the initial imperfections of all glass specimens presented in §2.

Conclusions

In this contribution, an extended experimental campaign was presented to investigate the shape and size of initial geometrical imperfections (curvature) of structural glass components, i.e. glass beams, fins and columns. The most important conclusions are summarised below. However, it should be noted that only beam-like specimens (i.e. W<<L) have been investigated here. Consequently, one should be careful to adopt the conclusions when dealing with smaller aspect ratios L/W.

Acknowledgements

BRS (NL), GlasTrösch SA (CH), DuPont de Nemours (B), Lerobel (Groep Leroi, B), van Noordenne Groep (NL) and VIM - Verres Industriels Moutier SA (CH) (in alphabetical order) are gratefully acknowledged for the testing materials.

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1

Present address: RI ISA, Permasteelisa Group, Delta 5, 51000 Riejeka, Croatia.

2

Present address: Lucerne University of Applied Sciences and Arts, Technikumstrasse 21, 6048 Horw, Switzerland.

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