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Figure :1 Traditional glass uses
Traditionally, the use of glass in buildings has been limited to windows (see Figure 1). Used in this way glass is subject only to transient wind loading and its self weight, conditions where its brittle nature and variable strength are not significant. However, over time interest in using glass in construction has grown. 

Figure :2 Modern glass usage
Architects, fascinated with the concept of a transparent building, increased natural light levels or an open work environment, have used glass in greater and greater quantities. The most obvious example today is the fully glass clad modern skyscraper. With these developments the size of the glass panelling used has increased and the method of connection has become more complicated (see Figure 2), but the way in which the glass is loaded has remained essentially the same.

In recent years designers have begun to use glass in much more structural applications. Instead of panes of glass being supported on metal beams and columns, glass is now being used to support itself through glass structural members. The aesthetic result is a totally transparent structure (see Figure 3a). The engineering consequence is that the glass must now sustain long term, inplane loading.
Figure :3a New glass structures

The properties of glass are such that it seems to behave quite differently when the loading is long term rather than short term and transient. In fact, the glass appears to become weaker as the duration of loading increases. This problem has been of little importance to traditional designers for whom the maximum load period is a several second wind gust. For the new applications, however, it is crucial to the design.

One might ask why glass is used in these new applications if it is so badly suited to them. The basic answer is cost. Glass is a mass produced product with cheap raw materials, and is therefore one of the cheapest fully transparent materials available. For example, the cantilevered structure shown in Figure 3b had some acrylic material included in the plies of the beams to provide a degree of ductility in case of failure. Although the volume of glass used in the other plies and the roof sheeting greatly exceeded that of the three individual acrylic plies, it was the cost of the acrylic which was greater. It can therefore be seen that glass is a crucial material if the new transparent architecture is to be widespread, because of its price. The cost is that a new structural design philosophy must be developed to account for the new application.
Figure :3b Cantilevered glass canopy, Tokyo, Japan

The term “glass” is often applied in the materials sciences to mean any substance which does not exhibit long range order on the molecular scale. In this thesis the term “glass” shall correspond to the popular understanding of the word, which is the substance which is used in windows. This soda-lime silica glass is a solid, non-crystalline, brittle material. It is perfectly linear elastic until failure, with a Young’s modulus of 70MPa, similar to that of aluminum. Its failure is governed by fracture, which occurs at cracks on the glass surface. In most cases these cracks are too small to be seen by eye. Owing to variation in the size of the cracks there is variation in the failure stress. Values for short-term strength might range from 20-200MPa.

Glass also undergoes a loss in strength with duration of loading, which is commonly referred to as “static fatigue”. The long term strength of glass is often quoted in the range 7-20MPa. This variation in strength depends on a myriad of factors. It is predominantly affected by the surface finish but is also influenced by glass type, environmental conditions (especially humidity), production effects and others. Essentially, glass is highly predictable under normal operation, but the point at which failure occurs can appear quite random.

The literature concerning the material properties of glass is extensive. Griffith (1920) presented experimental results on glass with introduced flaws of various sizes to show that it was the flaws which determined the strength of the glass. His work is the foundation of modern fracture mechanics, which is the field that is used to describe glass failure in the material sciences. Due to the perfect linear elastic behaviour of glass it has often been the material of choice for experimentalists when investigating fracture mechanics. This means that considerable information on glass is available.

Until recently there was little information publicly available on structural design of commercial glass. This was due to competition between glass manufacturers who also performed most of the engineering design for glass in structures. A major advancement in public glass engineering theory came with the paper of Beason & Morgan (1984). This paper focused on lateral loading of glass plates, as wind-loaded building cladding was the main use for glass at this time. The work of Beason & Morgan became the basis for many glass design codes around the world. Later modifications were suggested, such as by Fischer-Cripps & Collins (1995) and Sedlacek et al. (1995), which account for more localised loading conditions and more accurate fracture mechanics phenomena. The most recent method, proposed by Overend et al. (1999), allows for any load, support and plate geometry through the use of an equivalent stress procedure. The various design methods and scarce public information on glass have been collected in a single volume by Jofeh (1999). All of this previous work, however, has been tailored to applications of panels of glass being loaded out-of-plane.

The work on glass at The University of Oxford began when an engineering consultancy approached the Civil Engineering Department seeking assistance with a structural glass design. At this early stage the research comprised a number of fourth year undergraduate projects. Investigations of in-plane glass beam bending, column compression and contact loading were conducted. The variability in glass failure strength was demonstrated by Fair (1996) who loaded a series of annealed and heat toughened beams in bending. Strength variability was also encountered by Wren (1998) who tested cylindrical glass columns. In his experiments Wren also had to deal with a new problem: failure originating at the connections. Scarr (1997) investigated the stresses which occur due to a bearing pad connection (similar to that shown in Figure 4). It was shown that the inability of glass to redistribute stresses plastically results in high local stresses due to contact loading. A series of different bearing materials was used. It was found that materials of low Young’s modulus were most efficient at transmitting  the applied load evenly to the glass. It was also noted that small imperfections on the surface of the glass can greatly affect the resulting stress profile.
Figure :4 Glass being supported on pads
The projects described above focused on determining the strength of glass and the stresses developed within it under certain loading regimes. In his M.Sc thesis, Crompton (1999) studied a number of design theories and their applicability to glass. This thesis therefore represents the first real comment on glass design methods from the work conducted at Oxford. Crompton studied the various design philosophies that have been widely used in Structural Engineering over the last century. These included Permissible Stress, Plastic and Limit State Design theories. He followed their development with the major construction materials: steel, reinforced concrete, masonry and timber.

Crompton commented that Limit State Design was a derivative of Plastic Design, and therefore had an emphasis on ultimate load and strength. He showed that its application to masonry was not rigorous, as masonry rarely fails due to being over-stressed, but more frequently as a result of stability issues. Stability, as with other non-stress related actions, is poorly incorporated into current Limit State Design methods. Crompton proposed that of the four major construction materials  listed above, glass was most similar to timber. This was mainly due to the variability in brittle failure stress for both materials. Indeed, Crompton concluded that of the present design methods available a Permissible Stress design similar to that used for timber was preferential to a stress based Limit State Method as used for steel or concrete when dealing with glass.

Crompton (1999) also went on to investigate a topic of current interest in glass engineering: alternative load paths. It is common in glass construction to use more than one glass member in each structural element, resulting in the widespread use of multi-ply beams, for example. Since glass is a brittle material, the failure of any single element could lead to global structural failure unless alternative load paths are provided. The consequences of failure are another reason for this added redundancy. Should the sole load path fail then overhead shards of glass could fall and seriously injure people below.

In his investigation Crompton studied the case of a multi-ply beam with a constant overall width. The same probabilistic strength statistical parameters were applied to each ply in the glass member. It was shown that as the number of plies increased, the probability of failure under a given load decreased. Hence, having alternative load paths provides greater safety in design and is more economical, as the volume of glass required for a particular stress and probability of failure reduces with increasing plies. In practical terms in-plane loading means that it is the edge of the glass member which experiences the greatest stresses, such as the bottom face of a simply supported glass beam. Glass is often heat or chemically strengthened to provide a layer of compression over its surface. Although aspects of this are discussed, the focus here is on the basic annealed state of the glass. More general, localised residual stresses are also omitted in this somewhat preliminary treatment of structural glass.

In the traditional uses of glass (see Figures 1 and 2) the compressive loads encountered are modest, and generally similar in magnitude to the tensile stresses likely to be generated. Since glass failure arises at zones of tension it is therefore the tensile stresses, rather than the compressive ones, which are critical in design. In the new structural glass applications, greater concentrations of load are found in compressive members, such as columns. Hence, an understanding of the failure mechanism in the absence of global tensile stresses is required in order to develop a rigorous design method for these members. A mathematical analysis of compressive failure in an infinite plane has only been dealt with relatively recently by such authors as Ashby and Hallam (1986) and Vaughan (1998), although experimental investigations of the failure mechanism are somewhat older, for example Hoek and Bieniawski (1965). In this thesis the failure mechanism is applied to edge cracks in compression, as edge cracks are critical in structural glass. This is done through a rigorous fracture mechanical analysis using a novel technique based on distributed dislocations.

Connections are more important for glass than for other materials because of its brittle nature. Due to the absence of plastic flow, the stress concentration which occurs at the connection cannot be relieved. To reduce this concentration it is normal for a layer of “soft” material to be inserted between the glass and the generally hard connecting piece, which might be a metal pin or support pad.

In traditional Civil engineering design with ductile materials, bearing connections, such as those shown in Figure 4, are often designed by simply assuming an even distribution of “bearing” stress along the pad length. Owing to its brittleness, this is insufficient for glass and so a more rigorous analysis of these contact stresses is required.

In the case of the rigid plastic interlayer, a slip line field theory approach is used to determine the contact loading. For the elastic interlayer, stress functions for the layer and half plane are used to calculate the contact stresses. This is done for all possible combinations of full adhesion and lubrication on the top and bottom faces of the interlayer. Distributed edge dislocations are then introduced to allow for a finite degree of friction on the half plane surface.

The stress profile results for the glass due to the contact loading show that the interlayer achieves its goal of reducing the possible stress concentrations and eliminating tension. The work on compression loading of columns in the literature demonstrates that there need not be a global tensile stress for brittle fracture to occur. It is the presence of a crack, and its behaviour in the applied stress field which determines failure. The fracture mechanical analysis used earlier for compression loading is applied later to the contact stresses of the
interlayer connection.

Although structural glass design was the impetus for the compression and connection analysis, the work also has a more general application to other situations encountered in fracture and contact mechanics. The solutions to the problems are valid, and computationally efficient, for any linear elastic material being loaded under the prescribed conditions. In many cases the solution method is described so that it may be applied to any specified stress profile. Some problems, such as the growth of cracks in compressive stress fields, are applicable to other situations, such as squat cracks in rail heads.

References
  • Crompton P.R., “Assessment of Design Procedures for Structural Glass”, M.Sc Thesis, Department of Engineering Science, The University of Oxford, 1999.
  • Fair L., “Structural Glass”, 4th Year Project Thesis, The Department of Engineering Science, The University of Oxford, 1996.
  • Fischer-Cripps A.C., Collins R.E., “Architectural Glazings: Standards and Failure Models”, Building and Environment, Vol. 30, No. 1., pp. 29-40, 1995.
  • Griffith A.A., “The phenomena of rupture and flow in solids”, Philosophical Transactions of the Royal Society of London, Series A, Vol. 221, pp. 163-198, 1920.
  • Jofeh C., Structural Use of Glass in Buildings, The Institution of Structural Engineers, London, 1999.
  • Wren S., “Testing of Structural Glass Columns”, 4th Year Project Thesis, The Department of Engineering Science, The University of Oxford, 1998.
  • Sedlacek G., Blank K., Güsgen J., “Glass in structural engineering”, The Structural Engineer, 73, No. 2, pp. 17-22, 1995.
  • Wren S., “Testing of Structural Glass Columns”, 4th Year Project Thesis, The Department of Engineering Science, The University of Oxford, 1998.

 








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