Design of Glass Panes for Uniformly Distributed Loads

Design of Glass Panes for Uniformly Distributed Loads Miguel Rui Sousa de Almeida Mechanical Engineering Department, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal E-mail : miguelrui412@gmail.com October 2013 Abstract In recent years, the glass area of the building has increase, in many cases occupying the entirety of the walls. The glass must meet several requirements, and its thickness is often constrained by the cost and mechanical strength due to the wind action The design of a fill glass when subjected to differential pressure evenly distributed, resorts to standards. They use in their methodology, approaches and assumptions that may differ partially or entirely among themselves The main objective of this paper is to analyze and compare the differences in results of three reference standards: French Standard, European Standard and the ASTM Standard. Given the differences in results obtained by using these three standards, was chosen to study theoretically and experimentally the double glass placed vertically. It was also conducted an experimental at National Laboratory of Civil Engineering ( LNEC ) in order to obtain practical results, for correlation with the results obtained by the standards under study. The European standard provides more consistent results with the experimental study compared to the French and ASTM standard, that in some cases admit a lower design thickness for glass, then for the same thickness they allow a higher applied pressure. Another important aspect in the study and that is not adequately covered in the standards is the influence of the support and sealing on the behavior of the glass. A major constraint is beneficial in reducing the deformation of the glass but can be harmful to their ability to resist actions that subject. Keywords: Glass, Standard, Design, Double Glazing, Stiffness 1

1. Introduction The glass-like material has been an increasing use in various civil engineering applications. Its use is present from the simplest to the huge window facades completely covered by this material so unique. Its unique characteristics, the level of transparency and luminosity give it a high aesthetic level, so have been stimulating the industry to get new and better solutions in their use. Despite increased use of glass over the past few years, its most common application continues to be related to nonstructural applications of the kind windows and doors. This factor is a lack of confidence that industry as in the glass, since it is considered a material with a brittle behavior which by their failure mode does not allow stress distribution through plastic deformation, leading the total collapse of the structure so that a crack reaches its critical value. With a value of reasonable tensile strength near 50 MPa for simple glass (annealing), but may amount to 200 MPa, if we speak of a tempered glass. [1]. The application of glass in windows and doors is nevertheless subject to the same risks in structural applications, since a window must be able to withstand diverse efforts of both human and environmental nature. More specifically the actions of wind, thermal stresses, impacts, among others. It is thus essential to good design of a glass structure to achieve the levels of safety and comfort required. For correct design of a glass structure refers to various methods and standards, and uses these in their methodology, approaches, formulations and assumptions that may differ partially or almost complete each other [2]. This document has as main objective, is to analyze and compare the differences and the results provided from three reference standards in the glass industry: French standard (NF), European Standard (EN) and standard from American Society for Testing and Materials (ASTM), for a specific insulating glass unit. As previously stated, solutions for structural glazing are numerous, and for this study we chose to study the insulting units, with two panes (double glazed). The choice fell on the double glass because it is widely used in society and provides more study elements of interest than monolithic glass (a glass plate). After this theoretical analysis, was carried out experimental work at the National Laboratory of Civil Engineering (LNEC), the Center for Acoustics, Lighting Components and facilities in order to obtain practical results for possible comparison between the results obtained by various standards study. 2

2. Theory The most important physical properties of glasses SLSG (silico-sodocalcic) are summarized in Table 2.1. Table 2.1 Physical properties of glasses SLSG(adapted from [2]). Proprieties SLSG Density 2500 kg/m 3 Elastic Modulus 70 GPa Poisson Coefficient 0,23 A pressure uniformly applied to the outer glass results in deformation, this deformation causes a reduction in the volume of the cavity which in turn leads to an increase in air pressure contained in the cavity. Thus, the applied load is transferred to the air inside the cavity and then the air applies pressure over the inner glass. In this situation one may say that the air acts as a spring. In this case adds up to the fact that the inner pane when pushed by positive pressure also deform, but in order to increase the cavity volume of air. Therefore, it becomes that the resulting pressure in the air cavity is dependent on the volume change of the air cavity [3]. By Boyle's law [4]: This volume change caused by each of the glasses can be obtained by integrating dual function of deformation of the glass when subjected to a uniform pressure: (2.1) The deformation function of glass can be obtained considering the theory for thin plates, with the proper boundary conditions at all four sides. The flexural rigidity of the glass has an important influence on the magnitude of the change in volume of the cavity. This rigidity depends mainly on: Glass thickness Boundary conditions Dimensions of Glass Behavior of plate (Linear, Non- Linear) Have been choose to study three reference standards in the industry, but at the same time use different methods in their analysis, in order to compare the results. These standards are: Standard French, ASTM and European Standard, specifically NF P 78-201-4: 2006 [5] ASTM E1300-12 [6] pren 13474-2[7]. These different standards do not take into account all types of glazing configurations, loads, restraints, or the condition of the surface. They are mostly limited to simple glass, laminate and isolation units, and primary considered to be rectangular glasses with two, three or four sides simply supported. In the following sections will be mentioned the most important factor and what the solution presented in each standard to the isolation unit double glazed, single-pane, 3

rectangular, vertical and subject to wind action in study. 3. Material and Protocol The outer glass designation refers to glass which is uniform pressure applied, the other being the inner glass, se figure 3.2. 3.1 Material The insulating unit we used in our tests is an double glazing, both annealed, both with a 4 mm, and an air cavity of 8mm separating them. As the dimensions of the isolation unit for the above glass area was measured: 1820 mm in height and 745 mm width. On the right side of the insulating unit, a hole was made in order to pierce the rubber stopper and the interlayer, with the aim of placing a pressure tap within the air cavity to be possible to measure the pressure in cavity air throughout the test (figure 3.1). 3.2 Protocol Fig 3.2 Experimental setup. Fig 3.1 Pressure tap within the air cavity The performance of the tests was carried out in a pressure chamber. The chamber contains a sensor to measure the value of the existing pressure. Was used a computer program to input pressure and its application time and make the recording of experimental data. At the same time this device also comprises three comparators (c1, c2, c3) placed in the inner glass pane of the glass unit isolation and thus reads every instant of its values. They are also used other five analog comparators, with the aim of reading the deformation of the inner and outer glass at certain points relevant to this study (c4, c5, c6, c7, c8). The protocol for the tests to perform was the following: 1. Placing an analog comparator in the center of the outer pane (c8), this being inside the pressure chamber. 2. Placement of the comparators control device (c1 to c3) along the vertical axis of symmetry of the inner glass. At the highest point, the center and at the lowest point of the glass (see figure 3.3). 3. Placement of the comparator, c7, in the vertical symmetry axis of the inner glass, at the midpoint between the center of the glass and the lowest point of the glass (see figure 3.3). 4. Placement of the analog comparators in the inner glass. In the horizontal 4

symmetry axis ends (c4, c5) and the midpoint between end and center of the glass (c6) (see figure 3.3). 4. Results and Discussion In addition to the experimental results, it was also used for comparison of the results provided by standards, the values obtained through theoretical analysis performed based on the theory of thin plates. 4.1 Pressure differences on panes Fig 3.3 Schematic representation of the experimental setup. 5. Tube placed inside the air cavity connected to digital micro manometer. 6. Pressure difference applied in steps of - 500 Pa, from -1500 up to -4000Pa. 7. From the comparators c1 to c3, there are made five readings to compare, using the computer program at each step of pressure. 8. For analog comparators, read and record the new values indicated for each pressure step. 9. The readings of the comparators must be performed within a time interval of 10 s+50s, and 10s are for pressure stabilization and registration of the comparators c1 to c3 and the other 50s for the remaining comparators. 10. Carry out the average of 10 readings at each step micro manometer pressure, and record the obtained value. The French Standard does not provide a result for this division pressure because their study is conducted for the unit as a whole, and therefore not represented in the figure 4.1 shown below. For the European Standard, this "sharing" of pressure is well defined, and the value of the pressure applied uniformly affected by a safety factor on the action of the wind γq = 1,5. To ASTM Standard, the pressure difference for each glass is also carried out however there s not any safety factor for the action of the wind. Fig 4.1 Pressure difference for the outer glass. If at these results were taken the safety coefficients and compared with the results obtained by theoretical analyzes made, we obtain the following figure 4.2: 5

Fig 4.2 Real pressure difference for the outer glass. Is possible to note the similarity of the values provided by the standards with the values found by analysis of plates that was made, which thus leads to the conclusion as to the proper approach to the rules on the first phase of their study. 4.2 Maximum deformation The results provided by the different standards with regard to the maximum deflection are shown in Figure 4.3, taking into account that the French Standard maximum deflection if for the whole insulating glass unit, in ASTM maximum deflection is in the center of the outer glass or inner, because the value of maximum deformation is the same for both glasses (for the unit under study). European Standard maximum deformation occurs at the center of the outer glass, because is the one subjected to a greater pressure difference. Fig 4.3 Maximum deformation in the outer glass When you look at the curve of maximum deformation values obtained by ASTM and European Standard (see figure 4.3), it is clear that their behaviors are almost identical. Both use an approximation non - linear in calculating its deformed leading to values quite similar. The French Standard appears to use a smart way to circumvent the lack of nonlinear analysis. For this, use an approach which results in a linear line with a slope smaller than the linear simulation for edges supported situation, this leads to overestimated values at low pressures, but which for values of elevated pressure where the effect of " membrane" passes to act, this can approach the values provided by the non- linear solutions. It can be concluded that the approximations provided by standards under study are very good compared to the finite element simulation of a plate support. 4.3 Limit value In the design of glass subjected to wind action, meet the threshold pressure that our scaled unit can support is of 6

fundamental interest. This can be done by the different standards in study, despite the different shape is made. Those results are shown in table 4.1. Table 4.1 Limit values for different standards in study. European Standard Knowing the limit value of the insulating unit under consideration (in the case of European Standard is the allowable stress value (ƒg,d), in the case of ASTM Standard Load resistance (LR) and in the case of the French Standard is resistant thickness (e R )) can be calculated the value of maximum pressure difference just before reaching the limit of the unit. The European standard is thus the most conservative of all. P max (Pa) W max (mm) 1300 5,284 Limit Value 17,782 (MPa) Coef. Security Wind 1,5 French Standard 1875 6,458 5,55 (mm) 1,5 ASTM Standard 2268 8,210 2267,89 (Pa) 1 By observing figure 4.4 we can see that with increasing uniform pressure applied, the pressure in the cavity becomes lower than indicated by European Standard. With the evolution of the uniform pressure applied, there is a reduction of air pressure in the cavity, this means that the outer glass is now slightly more rigid in relation to the inner glass. This is due to the fact that the outer pane is in contact with EPDM (silicone) sealant witch introduces a bending moment in the edges, increasing the rigidity of the glass. This helps to reduce the maximum deformation of the glass (can be observed by the looking of figure 4.5), but also introduces extra stresses on the edges of the glass. This resulted in a greater constriction for both glass panes, but a greater rigidity to the outside than to the inside, hence the difference of values for the air pressure in the cavity. 4.4 Experimental Results The figure 4.4 represents the evolution of air pressure in cavity during the test. Fig 4.5 - Maximum deformation on the inner glass, for the test. Fig 4.4 - Air pressure in the cavity recorded in test. It was then made an estimation of the effective stresses present in the insulating unit during the test, in order to 7

realize why the break did not occur in the outer glass when the present values of pressure were very above from the allowed by the standards under study (see table 4.1). It was found that the difference for effective stress at -4000 Pa in experimental situation against the theoretical stress due to the observed outer glass is approximately 2.42 MPa. It passes from a theoretical value of 26.19 MPa to 28.61 MPa. This value is above the allowable stress of 17,782 MPa according to European Standard for this glass, but if we remove the safety factor of the material, ϒ M =1,8 turns out to be below the limit of 32 MPa and therefore have not been found to rupture. The bending moment introduced by the edges resulted in an increase of 2.42 MPa for the outer glass. 5. Conclusions In this study we observed the extreme importance of nonlinear analysis, and the importance of the membrane effect ".It s no contemplation for high pressures when displacements are greater than the thickness of the glass results in a overestimation of the results that may be on the order of nearly 100%. It was also observed that the boundary conditions at which the glass is subject on borders, strongly affects his behavior, the level of effective stresses and deformation. In the European Standard, the values given can be obtained through an linear or nonlinear analysis, that situation is useful to conduct a deeper study. It is possible to calculate effective stress, maximum deflection, the air pressure in the cavity in the case of double glazed, pressure difference for each of the glasses and allowable stress for each type of glass and size desired. When the results provided by the European Standard are compared with the results obtained by a finite element analysis, we can determine the great similarity of the results, which demonstrates the excellent tool that is the European Standard for design glass when subjected to pressures evenly distributed. When compared to French and ASTM Standard they are more restrictive. In the case of French standard only know what is the maximum deflection of our glass, in the case of a double glass, only indicates the maximum deflection unit and if insulating unit supports or not the load to which it is subject. Use approaches easy to use and interpretation and quickly check the correct or incorrect dimensioning of our glass. The outputs of maximum deflection turn out to be acceptable when compared with those provided by European Standard, despite using only a linear approximation. As for ASTM Standard, their need to resort to graphics, and the latter being only available for normalize thicknesses, make your analysis more time consuming, limiting and prone to errors due to scales little detailed. There is a concern with the study of individual glass in the case of double glazing, and in the case of maximum deformation nonlinear analysis is taken into account and provides results at all similar to the European standard. With respect to the solutions provided by standards are more or less conservative, we reached the conclusion that they are all quite conservative. This is due to the existence of 8

a safety factor for the action of wind and a safety factor for the material. In the case of European standard a safety factor of 1.5 x 1.8, corresponding to the wind and the material in question, resulting in an overall safety factor of 2.7. This need to put a safety factor usually so high is to compensate for the uncertainty about the number of defects present on the surface of a glass which of course greatly affects their resistance to breakage. As was verified experimentally, one major constraint at the edges resulting in a lower amount of deformation due to the relative increase the stiffness of the glass panels, but on a larger effective stress in the outer pane and greater stress concentrations at the edges of the glass. These factors are due to the tensions introduced by the silicone sealant. The author concludes that in order to do a deeper study of the unit to design the European standard is the best, and that way, being aware of all the variables included in the process, you can go a little further in reducing the level of security, thereby achieving a more economical solution but also safe. The other standards are useful to be used in the first analysis of design, and ultimately provide good security to the designer. air pressure in the cavity due to mechanical and thermo-mechanical loads, 2003. [4] Charles Webster, The Discovery of Boyle s Law, in Archive for the History of the Exact Sciences, 2:441 502,1965. [5] NF P 78-201-4: 2006 - Building works - Glazing and mirror glass works - Memorandum for glass thickness calculation. Paris: AFNOR. DTU 39. [6] ASTM E 1300 12. Standard Practice for Determining Load Resistance of Glass in Buildings. American Society for Testing Materials, 2012. [7] pren 13474-2:2000. Glass in building Design of glass panes Part 2: Design for uniformly distributed load. CEN, 2000. [8] B.Sugarman,. Strength of Glass ( A Review). Material Science 2, 1967. [9] EN 1991-1-4:2005. Eurocode 1 - Actions on structures - General actions - Part 1-4: Wind actions. CEN 2005. [10] Ugural, A.C., Stresses in Plates and Shells, McGraw Hill Inc, 1981. [11] Timoshenko, S. and Woinowsky- Krieger, Theory of Plates and Shells, McGraw-Hill. [8] www.solidworks.com 6. References [1] HALDIMANN, M., Fracture strength of structural glass elements. Lausanne, 2006. [2] Haldimann, M., Luible, A. and Overende, M., Structural use of glass, IABSE-AIPC- IVBH, Zurique, Suiça, 2008. [3] E.M.P. Huveners, F. van Herwijnen & F. Soetens, s.d. Load Sharing in Insulated Double Glass Units. Determination of the 9