TEXAS A&M UNIVERSITY PROFESSOR EXAMINES THE STRUCTURAL BEHAVIOR OF LAMINATED GLASS WITH ALGOR

Modeling and analyzing laminated glass, such as plates used for window glass in commercial buildings, presents several technical challenges. According to Dr. W. Lynn Beason, an Associate Professor of Civil Engineering at Texas A&M University in College Station, Texas, "The main challenges are geometric nonlinearities, temperature-dependent material and the great difference between the moduli of the layers." As an engineering consultant, Beason used ALGOR finite element analysis (FEA) software to study the structural behavior of laminated glass for specific applications including glass in athletic complexes and high-profile building applications.

Laminated glass is manufactured by bonding multiple layers of glass together through the use of adhesive interlayers or a poured-in-place resin. "The adhesive interlayer ensures safety," said Beason, "because, if the external glass layers break, it adheres to the glass fragments and prevents them from exiting the window framing system." The interlayer material that is most often used is a mixture of plasticizers and polyvinyl butyral (PVB) resin. The most common laminated glass configuration involves two pieces of glass of the same thickness and type that are bonded together with a plasticized PVB interlayer.

"The structural characteristics of the plasticized PVB interlayer depend on temperature," explained Beason, "which makes it stronger when cold and weaker when hot." If the interlayer is hot, it is soft and flexible and the shear transfer between the two glass plates is limited. As the stiffness of the interlayer approaches zero, the laminated glass plates behave as though they are independent with no shear transfer. If the plasticized PVB interlayer is cold, there is sufficient shear transfer between the glass plates so that the behavior of the laminated glass approaches that of a monolithic (uniform or made of a single material) glass plate of the same overall thickness.

"Historically, it has been assumed that the strength of architectural laminated glass with an interlayer is equal to 60 percent of the strength of monolithic glass of equivalent thickness," said Beason, who has led development of three American Society for Testing and Materials (ASTM) standards for window glass. "Use of this relationship assumes that there is limited shear transfer through the interlayer." In recent years, research funded by PVB manufacturers has redefined the historic laminated glass strength relationship such that the strength factor has been increased to 0.75 in most building codes throughout the United States. Some PVB researchers recommend that the structural behavior of laminated glass is equivalent to the structural behavior of monolithic glass for most common applications and therefore a laminated glass strength factor of 1.0 should be adopted.

"Implementation of this monolithic equivalency assumption would allow one-to-one replacement of existing monolithic glass with laminated glass without altering existing window framing details," said Beason. "However, if the monolithic equivalency model is not valid, its implementation would result in the unconservative design and use of laminated glass, which could lead to failure of the glass at the design load."

Beason, who has more than 25 years of experience relating to the design of window glass, modeled and analyzed laminated and monolithic glass in ALGOR FEA software to compare them. "A few years ago, I used other FEA packages, namely Ansys and Abaqus, on a supercomputer to analyze these kinds of models because of the extensive calculations required for geometric nonlinearities. Now, I can get the same accuracy using ALGOR on a PC. Plus, its overall ease-of-use enables me to set up and analyze a model more quickly."

To compare the two glass types, Beason created two models of a 72 x 72 x 1/2 in. glass plate, one laminated and the other monolithic. The laminated glass model consisted of two glass layers with a PVB interlayer and the monolithic glass model was one solid piece of glass. Both models used 8-node brick elements and were subjected to a negative pressure load of 0.5 psi, which simulated a wind load. Constraints were defined to represent continuous lateral support of all four edges, which assumed the edges of the glass were simply supported and free to slip in plane.

Shown here are two quarter-symmetry ALGOR finite element models of a 72 x 72 x 1/2 in. plate of glass with four-sided support. Tensile stress (yy) contours from a wind pressure loading in the –Z direction illustrate that maximum stress is greater for laminated glass (left) than monolithic glass (right). Plus, the maximum stresses occur at different points on the plate surfaces, which are shown in the inset close-up views. The insets reveal that, due to shear deformations experienced by the interlayer, the stress distribution through the thickness of the laminated plate is very different from that of the monolithic plate.

Custom material properties were defined for the glass and PVB interlayer at a temperature of 120° F including mass density, modulus of elasticity, Poisson's ratio and shear modulus of elasticity. The material properties were obtained from a study of laminated glass beams with architectural-grade plasticized PVB interlayers, which was conducted in association with the specification of laminated glass for use in the Sydney Opera House in Australia (Hooper, 1973).

Beason then performed Mechanical Event Simulation with nonlinear materials to include the effects of large deflection and large strain. The validity of the finite element modeling procedure was established by comparing finite element results with published theoretical and experimental results (Vallabhan, et al, 1993), which matched.

"The maximum principal stress revealed in the ALGOR finite element model for the laminated glass plate is about 25 percent greater than for the monolithic glass plate," said Beason. "The reason this happens is that plane sections do not remain plane on the laminated glass because of the mismatch in the moduli of elasticity between the glass and the interlayer."

Beason explained, "The structural behavior of laminated glass is a function of the interaction of the glass plates and the plasticized PVB interlayer. The stiffness of the plasticized PVB interlayer is many orders of magnitude less than that of glass. As a result, plane sections through the thickness of laminated glass before loading do not necessarily remain plane after loading due to differences in deformation between the layers."

According to Beason, the FEA results suggest the general use of a monolithic equivalency for the design of architectural-grade laminated glass is not warranted. Rather, the findings concluded that use of a monolithic equivalency could result in poor estimates of both stresses and deflections for some common laminated glass situations, which might lead to glass breakage.

"If a consensus can be reached regarding an appropriate design temperature," said Beason, "results from finite element analyses can be combined with glass failure prediction formulations to develop rational design criteria for architectural-grade laminated glass in general use. In the interim, it is recommended that the laminated glass strength factor not be increased above 0.75 for architectural-grade laminated glass."

According to Beason, "FEA tools like ALGOR can be used quite effectively to complement traditional hand calculation methods for validating proposed changes to standards and codes."

W. Lynn Beason earned a Ph.D. at Texas Tech University. He frequently serves as a consultant on matters relating to the structural behavior of window glass.