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Publication# Tragverhalten und Bemessung von Holz-Glas-Verbundträgern unter Berücksichtigung der Eigenspannungen im Glas

Résumé

The construction principles of "Timber-Glass-Composite-Girders" demand practical and theoretical research to ensure reliable designs. Toward this objective the mathematical description of load-bearing and the non-rigid bond is the subject of this work, i.e. to define the contributing parameters for the design of these girders. The non-rigid-bond of the adhesive joint is of great importance because of its influence on the load-bearing of the system as a whole. The loading of girders is dominated by permanent forces thus leading to the obligation of knowing the long-term behaviour of the system and its components. The definition of the characteristic values, taking into account the long-term load-bearing, is an intrinsic part of this investigation. It can be shown that the load-bearing of the girders depends on the fracture of the glass panes. The properties of glass-fractures are a function of the residual internal prestresses due to the heat-strengthening of the panes. The load-bearing, particularly the post-cracked behaviour, changes with respect to the intensity of these internal prestresses. The timber is able to reinforce the cracked glass, leading to a ductile load-bearing behaviour as in the girders, with a dependency upon the size of the remaining fractures. A model based on the differential equations of the non-rigid bond is defined in order to calculate the loading-peaks of the adhesive joint and the material loading itself. The characteristic values of the non-rigid bond, such as the number and distances between cracks and the load introducing length, were evaluated in tests on composite slabs and small scale girders. The existing calculation models which take into account non-rigid bonding were modified to adapt the influence of the width and thickness of the adhesive joint. In order to calculate the stressing of the material the existing calculation models were adapted to calculate the post-cracked situation. The load-bearing behaviour of glass-panes bent with respect to its strong neutral axis needs other safety-considerations than panes, bent off their plane. It is shown that the existing safety considerations subject to the use of glass can not easily be adapted onto the composite girders. The bending with respect to the strong neutral axis and the reinforcement of the glass of the timber demands a different hypothesis to adapt the fractural mechanical analysis and to establish a safe limit conception. This is part of the performed research of this document. The following descriptions present briefly the obtained results: Depending on the quality of the glass (residual stresses due to heat-strengthening, e.g. annealed glass, heat-strengthened glass, fully tempered glass), the ductility and the mode of failure of the girders does change. As a result of its failure mode, annealed glass without internal prestresses offers the highest remaining load-carrying potential after the first crack has appeared. This ductility and thus the structural safety, diminishes with an increasing degree of internal prestressing due to thermal treatment. Heat-strengthened glass (with various degrees of prestressing, various residual stresses) shows a decrease in remaining load-carrying capacity with an increasing degree of prestressing until it fails in a brittle mode as fully toughened glass does. This has to be well considered in respect to safety considerations. Girders with panes made of glass having internal residual stresses due to heat strengthening below 50N/mm2 are considered to collapse ductily, residual stresses bigger than 50N/mm2 cause brittle failure. The effective stiffness of the girders decreases under permanent loads in function of the bondage. Both, timber and adhesive take part in this decrease; the influence of both of the involved materials has been defined. Since the design of conventional glass constructions which uses the concept of principle stresses cannot be adapted, unidirectional shear stresses had to be determined for the shear strength of glass, which is defined as 25N/mm2 for annealed glass. The characteristic values of the adhesive to define the non-rigid bonds have been determined, likewise the influence of the width and thickness of the adhesive joint. The load introducing length, the distances between cracks and the number of cracks are defined with tests on composite slabs. A model to describe the theoretical bond with the defined parameters based on the differential equations was developed. This model allows the calculation of the material stressing at the load introduction and on both sides of a crack. To calculate the stressing of glass and timber existing calculation models which take into account non-rigid bonding were modified to adapt the influence of the width and thickness of the adhesive joint. In order to calculate the stressing of the material the existing calculation models were adapted to calculate the post-cracked situation. The safety factors for the influences of the glass surface, environmental conditions, load duration and the parameters of fracture mechanical analysis as developed as they are known for semi-probabilistic safety concepts for glass constructions cannot easily be adopted. The bending with respect to the strong neutral axis demands a different hypothesis in order to adapt the fractural mechanical analysis and to develop the safety parameters. For the reliable design of timber-glass-composite-girders a contribution to the appropriate use of probabilistic, semi-probabilistic and deterministic safety concepts are given. A realised construction (Hotel "Palafitte" in Monruz (NE)) shows an example and the experience made in designing girders.

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For centuries, the use of glass in buildings was essentially restricted to functions such as windows and glazing. Over the last decades, continuous improvements in production and refining technologies have enabled glass elements to carry more substantial superimposed loads and therefore achieve a more structural role. The structural design of such elements, however, remains problematic. Current widely used design methods suffer from notable shortcomings. They are, for instance, not applicable to general conditions, but are limited to special cases like rectangular plates, uniform lateral loads, constant loads, time-independent stress distributions and the like. Some model parameters combine several physical aspects, so that they depend on the experimental setup used for their determination. The condition of the glass surface is not represented by user-modifiable parameters, but is embedded implicitly. The design methods contain inconsistencies and give unrealistic results for special cases. Different models yield differing results and several researchers have expressed fundamental doubts about the suitability and correctness of common glass design methods. The lack of confidence in "advanced" glass models and the absence of a generally agreed design method result in frequent time-consuming and expensive laboratory testing and in inadequately designed structural glass elements. The present thesis endeavours to improve this situation. After outlining the fundamental aspects of the use of glass as a building material, an analysis of present knowledge was conducted in order to provide a focus for subsequent investigations. Then a lifetime prediction model for structural glass elements was established based on fracture mechanics and the theory of probability. Aiming at consistency, flexibility, and a wide field of application, this model offers significant advantages over currently used models. It contains, for instance, no simplifying hypotheses that would restrict its applicability to special cases and it offers great flexibility with regard to the representation of the surface condition. In a next step, possible simplifications of the model and the availability of the model's required input data were discussed. In addition to the analysis of existing data, laboratory tests were performed and testing procedures improved in order to provide more reliable and accurate model input. In the last part of the work, recommendations for structural design and testing were developed. They include, among other things, the following: Glass elements that are permanently protected from damage can be designed by extrapolation of experimental data obtained from as-received or homogeneously damaged specimens. The design of exposed glass elements whose surfaces may be damaged during their service lives (for example, because of accidental impact or vandalism), however, should be based on a realistic estimation of the potential damage (design flaw). Appropriate predictive models and testing procedures are proposed in this thesis. If substantial surface damage has to be considered, the inherent strength contributes little to the resistance of heat treated glass. Therefore, quality control measures that allow the use of a high design value for the residual surface stress are very efficient in terms of economical material use. Results from laboratory testing at ambient conditions represent a combination of surface condition and crack growth. The strong stress rate dependence of the latter, which was demonstrated in this thesis, diminishes the accuracy and reliability of the results. The problem can be addressed by the near-inert testing procedure that was developed and used in this thesis. The application of the proposed models and recommendations in research and practice is facilitated by GlassTools, the computer software that was developed as part of this thesis.

Stability of load carrying elements in glass The increasing demand in modern architecture for more slender and lighter structures requires the use of new construction materials. Glass, a material that has been used for a long time in windows as a filling material, has much to offer in this regard due to its very high compressive strength and transparency. For this reason, there is a growing trend to extend the use of glass sheets to load carrying elements such as columns, beams and panels. Due to their high slenderness and high compressive strength, such elements tend to fail because of instability (i.e. column buckling, lateral torsional buckling or plate buckling). At the moment little knowledge exists about the load carrying behaviour of glass structural elements, and existing design methods for other materials (i.e. steel) have been found to be unsuitable for direct transfer to the design of glass panels. With this in mind, the main objectives of the current thesis are: The study of the load carrying behaviour of glass elements which may fail due to lack of stability by means of laboratory tests and analytical and numerical models, as well as the study of the main influencing parameters. Discussion of possible design methods for glass elements which may fail due to lack of stability for the three main stability problems (column buckling, lateral torsional buckling and plate buckling) and proposition of possible aids for design such as buckling curves. The main influencing parameters (dispersion of the glass thickness, initial deformation) on the load carrying behaviour of glass elements which may fail due to lack of stability have been measured and are evaluated herein using statistical methods. The breakage stress, the thermal prestress and the effective tensile strength are defined and explained. Existing models to determine the tensile strength of glass are discussed. The column buckling behaviour of single layer and laminated safety glass is studied by means of column buckling tests, which are compared to analytical and numerical models. The models are used to study the influence of the main parameters, particularly the shear connection due to the interlayer (PVB) in laminated safety glass, on the load carrying behaviour and buckling strength of glass elements. On the basis of this study different possible design methods for column buckling of glass elements in compression are proposed and discussed. It is shown that a second order stress analysis is the most appropriate method for glass. As a further simplification, the cross section of a laminated safety glass structural element can be modelled as a monolithic cross section with an effective thickness. Analytical and numerical models for the lateral torsional buckling of glass beams are also verified by a comparison to test results. Along with a study of the main parameters, different methods to determine the lateral torsional buckling strength are discussed, and it is shown that buckling curves for lateral torsional buckling should be developed for glass beams using a slenderness ratio based on effective tensile strength. As a result of numerical simulations, recommendations for the future development of lateral torsional buckling curves of glass beams are given. The column buckling behaviour of single layer and laminated safety glass is also studied by means of column buckling tests, analytical and numerical models. It is shown that glass panels have a large post critical load carrying capacity but the way the loads are introduced into the panels, as well as the buckling shape, have an important influence on the plate buckling capacity. A design method with buckling curves using a slenderness ratio based on effective tensile strength seems applicable for the design of glass panels. As a result of numerical simulations, recommendations for the future development of plate buckling curves for plate glass elements under compression are given.

Sofia Colabella, Corentin Jean Dominique Fivet, Endrit Hoxha

This paper presents the design and construction of a 36m2 gridshell, the rigidity of which is achieved through the bending of an initially flat grid of 210 reclaimed skis. The generated waste for its production is near zero as it is mostly built from discarded material. Its construction process is such that it can be disassembled and reassembled multiple times without scaffolding and by means of traditional tools only. After a brief introduction on the need for reducing embodied carbon and waste in structures through reuse, the paper sets up the constraints that have driven the definition of the pavilion, the main one being the extension of the lifetime of high-performance sport equipment by reclaiming their intrinsic mechanical properties. The paper then details the encountered unusual aspects in the design process and how they have been overcome – i.e. sporadic material supply, categorization of mechanical properties, physical alteration of these properties, and uncertainties in the numerical modelling of both the structural analysis and the construction process. Eventually, we conclude that reclaimed skis as a material have the potential to be as good as conventional timber when designing elastic gridshells. A series of future directions for this emerging field of research are also laid out.

2017