The two quarter-symmetry models, generated in Algor   FEA software, are of a 72 X 72 <sup />1</sup>⁄<sub>2</sub>-in. plate   of glass with foursided support. Tensile stress ( <i><sub>yy </sub></i>)   contours from a wind loading in the –<i>Z </i>direction show that   maximum stress is greater for laminated glass (left) than a monolithic   pane (right). Plus, maximum stresses occur at different points on the   plate surfaces, which are shown in the closeup views. The insets reveal   that, due to shear deformations on the interlayer, the stress distribution   through the thickness of the laminated plate differs from that of the   monolithic plate.

The two quarter-symmetry models, generated in Algor FEA software, are of a 72 X 72 12-in. plate of glass with foursided support. Tensile stress ( yy ) contours from a wind loading in the –Z direction show that maximum stress is greater for laminated glass (left) than a monolithic pane (right). Plus, maximum stresses occur at different points on the plate surfaces, which are shown in the closeup views. The insets reveal that, due to shear deformations on the interlayer, the stress distribution through the thickness of the laminated plate differs from that of the monolithic plate.


Recent FEA studies of architectural glass show that two bonded window panes are not as strong as one pane that has the thickness of the bonded pair. The study comes at a time when some in the architectural industry would like to rewrite building codes to allow substituting two-pane glass for the single pane design.

The most common configuration for laminated glass involves two pieces of the same thickness bonded together with a plasticized PVB interlayer. The interlayer used most often is a mixture of plasticizers and polyvinyl butyral (PVB) resin. "The adhesive interlayer is also a safety feature," says W. Lynn Beason, an associate professor of Civil Engineering at Texas A&M University in College Station, Tex., and engineering consultant. Should one pane break, its pieces are held to the other pane.

"Designers had assumed that the strength of architectural laminated glass with an interlayer equaled 60% of the strength of monolithic glass of equivalent thickness," said Beason. "The relationship assumes limited shear transfer through the interlayer," he adds. Research funded by PVB manufacturers recently redefined the relationship so the strength factor has been increased to 0.75 in most building codes throughout the United States. Some PVB researchers now say the structural behavior of laminated glass is equivalent to the structural behavior of monolithic glass for most common applications, so a laminated glass strength factor of 1.0 should be adopted. "Implementing the assumption would allow one-toone replacement of existing monolithic glass with laminated glass without altering window framing details," said Beason. "If the single-piece equivalency model is not valid, implementing it would result in an unconservative design and wider use of laminated glass, which could lead to failure of the glass at the design load."

Modeling and analyzing laminated glass presents several challenges. "The main ones are geometric nonlinearities, temperature-dependent materials, and the great difference in the layers' moduli," says Beason. He recently used FEA software to study the structural behavior of laminated glass for applications including athletic complexes and highprofile building applications.

"The structural characteristics of the plasticized PVB interlayer depend on temperature," says Beason. "It's stronger when cold and weaker when hot." If the interlayer is hot, it is soft, flexible, and limits the shear transfer between the two glass plates. As the stiffness of the interlayer approaches zero, the laminated plates behave independently without shear transfer. A cold interlayer transfers sufficient shear between the glass plates so the behavior of the laminated material approaches that of a uniform glass plate of the same overall thickness.

Beason modeled and analyzed laminated and monolithic glass in Algor FEA software to compare them. He created two models of a 72 X 72 X12-in. glass plate, one laminated and the other monolithic. The laminated model consisted of two glass layers with an interlayer. Both models used eight-node brick elements and were subjected to a simulated wind — a pressure load of 0.5 psi. Constraints represented continuous lateral support of all four edges, assuming the glass edges were simply supported and free to slip in plane.

Material properties defined for the glass and the PVB interlayer at 120°F included mass density, modulus of elasticity, Poisson's ratio, and shear modulus of elasticity. Material properties came from a study of laminated glass beams with architectural-grade plasticized PVB interlayers. Beason then performed a Mechanical Event Simulation with nonlinear materials to include effects of large deflection and strain. A final step compared the finite-element results with published theoretical and experimental results (Vallabhan, et al, 1993). They matched.

"The maximum principal stress revealed in the Algor finite-element model for the laminated glass plate is about 25% greater than for the monolithic glass plate," said Beason. "This happens because plane sections do not remain plane due to the mismatch in the moduli of elasticity between the glass and the interlayer. The structural behavior of laminated glass depends on the interaction of the plates and the interlayer. The stiffness of the plasticized PVB interlayer is many orders of magnitude less than that of glass. As a result, plane sections of the laminated design before loading do not necessarily remain plane after loading due to differences in deformation between the layers," he says.

Consequently, says Beason, FEA results do not warrant the general use of a singlepane equivalency for the design of architectural-grade laminated glass. The findings instead suggest that a monolithic equivalency could result in poor estimates of stresses and deflections for some common laminated glass situations, which might lead to broken windows.

"If a consensus can be reached regarding an appropriate design temperature," adds Beason, "FEA results can be combined with glass-failureprediction formulations to develop rational design criteria for architectural-grade laminated glass in general use. In the interim, it would be unwise to increase the laminated glass strength factor above 0.75 for architectural-grade laminated glass. What's more, FEA tools like Algor effectively complement traditional hand calculations for validating proposed changes to standards and codes."