Session: Research & Development
Event: GPD Finland 2023
Analytical solution and exact effective thickness for multilayered laminated glass beams of arbitrary composition. Application to cantilevered balustrades.
Under the quasi-elastic approximation, assuming that the interlayer polymer is linear elastic with moduli parametrically depending on time and environmental temperature, we present a model for inflexed laminated glass beams in the pre-glass-breakage phase. This relies on a modified version of the refined zig-zag theory for composites, in which the glass plies are Euler-Bernoulli beams, whereas the interlayers provides for the shear- coupling of the glass plies. The field variables are the beam displacement and the mean sectional shear angle, defining the zig-zag warping of the cross section. A FEM implementation is proposed but, remarkably, the governing equations can be solved analytically, for multi-laminated packages of arbitrary composition, when the structure is statically determined.
The analytical solution is worked out for cantilevered laminated-glass balustrades, schematized as a short simply-supported laminated beam with a long cantilevered overhang. The cross-sectional warping allowed by the end constraint induces such strong asymmetrical deformation that traditional approaches based on the definition of the effective thickness of a monolith with equivalent bending properties, such as the Wölfel-Bennison or the EET methods, cannot be accurate. Geometric and natural boundary conditions, together with matching conditions at the intermediate roller constraint, necessary to solve the governing differential problem, are found variationally. The analytical solutions under concentrated and distributed loads exactly determine the effective thickness of the laminate, allowing for comparison with other recently proposed approximate approaches which, however, apply only to three-layered packages. The expressions proposed here can be directly used in the design practice.
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