The resistance of laminated glass to blast pressure loading and the coefficients for single degree of freedom analysis of laminated glass

Abstract

For terrorist explosions or accidental explosions in urban areas, the greatest threat of death and serious injury comes from the effects of glass fragments. Laminated glazing has been proven by trials and experience of actual events to eliminate the risk of significant fragment injury to people behind the glazing, and also to provide substantial protection from blast injury effects, provided that after cracking it remains as a continuous membrane substantially attached to the supporting frame. However, design of laminated glazing is currently based on extrapolation from testing, with limited understanding of the material behaviour that underlies the behaviour under blast loading. This thesis presents an investigation into the application of a simplified method of dynamic analysis for laminated glass, the development of parameters derived from the properties of the materials in laminated glass and the behaviour of laminated glass systems that can be applied to the design of laminated glazing to resist blast loading. The development of the single degree of freedom method for analysis of dynamic response is reviewed from its inception use for analysis of glazing, through its adaptation for reinforced concrete analysis, to its modern use for analysis of glazing. Although the principles of the method are widely applicable, some procedures established for elastic-plastic reinforced concrete analysis in the 1950s are not appropriate for glazing, and should be treated with care. Coefficients for analysis of reinforced concrete date from approximate analyses in the 1950s and 60s and are not accurate. New calculations using advanced yield line models and finite element analysis have been used to provide alternative coefficients for rectangular panels supported on four edges. The elastic analyses for reinforced concrete are linear because they are based on small-deflection theory. Deflections of most uncracked glass panes exceed the limits of this theory. The development of practical non-linear large-deflection analyses in the 1980s was dependent on numerical methods and computer analysis, but they have previously only been applied to resistance and cracking. New non-linear finite element analyses refine the existing resistance data, and data from the same calculations has been used to derive large deflection single degree of freedom parameters for dynamic analysis and to assess the reaction distribution. The cracking of glass arises from small flaws in its surface, and can be very variable in its onset. In addition, the strength is sensitive to the loading rate. Statistical approaches have been based on quasi-static tests, either assuming a normal distribution, or using a more complex Weibull distribution. However, statistical refinement gains little, as strengths then need to be increased for the faster loading under blast. Back-analysis of extensive blast tests had been used to establish deterministic lower bound design cracking strengths for different types of glass. These have been applied in this thesis for design, and back-analysis of blast trials indicates that the design cracking strengths are lower bound. Formulae for a monolithic pane with equivalent behaviour to a laminated glass pane are proposed that would allow the large deflection analysis to be applied to laminated glass up to cracking of the final ply. The results of some blast trials of uncracked laminated glass are reported which are consistent with an equivalent monolithic analysis. They indicate that laminated glass under blast can be taken as fully composite to temperatures approaching 20ºC, but that it is not fully composite at 29ºC or above. Unfortunately, there is currently no data to indicate the performance in the critical temperature range between. After laminated glass cracks, the resistance is provided by an interlayer of the viscoelastic polymer, Polyvinyl Butyral. Though research is ongoing, non-linear viscoelastic material models for finite element analyses have not yet been developed to the point that they can reproduce the full range of behaviour observed in the tensile tests over the range of temperatures and elongation rates which are reported in the thesis. Instead, the results of the tensile tests are fitted to a simple bilinear material model by back-analysis of the tensile tests to give three stiffness and strength parameters that vary with temperature and strain rate. Non-linear finite element analyses of PVB membranes corresponding to two series of laminated glass blast trials are used to produce single degree of freedom parameters for membrane response. The blast trials are reported, and back-analysis of the deflection histories is used to estimate the ratio of the PVB material strain rates and the observed laminated glass strain rates for the best-fit calculated response. This ratio, found to have a mean value of 3.8, is expected to reflect the stiffening of PVB by attached glass fragments, together with other factors. However, the scatter in the data is large, so the reliability of this figure should be viewed with this in mind. Laminated glass providing blast protection is normally maintained close to room temperature, so a design based on a room temperature of 23ºC is proposed, using single degree of freedom data that is a composite of the uncracked data up to cracking and the membrane data after that point. For normal laminated glazing where the observed strain rate is expected to be about 10 /s, design membrane properties based on a PVB strain rate of 40 /s are proposed, but this may need to be modified for other cases. Typical design cases for marginal behaviour are analysed on this basis, and also for material properties at temperatures 6ºC higher and lower than 23ºC, to assess the sensitivity of the design to likely temperature variations. These indicate that a margin of 16-21% may be needed on deflection limits to allow for temperature increases, but that the calculated deflections would still be below the maximum deflections observed in the trials without PVB failure. The analyses indicate that the peak reactions are unlikely to be sensitive to temperature. However, they indicate that a margin of safety of 2.4 will need to be incorporated in the design anchorage strength to resist in-plane tension in the PVB membrane at reduced temperature. The thesis develops an improved design method under blast loading for laminated glass and double glazing incorporating laminated glass, although some of the values used in the method should be considered tentative. The thesis also indicates a level of anchorage strength sensitivity to temperature reductions that needs to be taken into account in practical glazing designs.