Analytical Solution and Exact Effective Thickness of Multilayered Laminated Glass Cantilevered Balustrades

Cantilevered laminated glass balustrades present design challenges. The cross-sectional warping allowed by the end constraint induces such strong asymmetrical deformations that traditional methods, defining the effective thickness of a monolith with equivalent bending properties, cannot be accurate. By using a recently proposed refined zig-zag theory for laminates, we analytically solve the representative problem of a short simply supported laminated beam with a long cantilevered overhang. The variables are the beam displacement and the mean sectional shear angle, defining the zig-zag warping of the cross section. Geometric and natural boundary conditions, as well as the matching condition 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. Comparisons are made with other approaches that that, however, apply only to three-layered packages. The expressions proposed here can be directly used in the design practice.