Two Dimensional Micromechanics Based Computational Model for Spherically Voided Biaxial Slabs (SVBS)

Abstract

The demand for reducing the weight-to-stiffness and strength ratios of solid reinforced concrete slabs, while improving their span limit, has led to the emergence of spherically voided biaxial slab (SVBS) systems. However, the presence of the spherical voids makes the structural analysis of SVBS inherently challenging because of the heterogeneous and periodically varying complex cross-sectional geometry. Current analysis procedures heavily rely on proprietary manufacturer information with a recommendation of treating SVBS as solid reinforced concrete slabs and applying global reduction factors without giving regard to the microstructures of the SVBS itself. This dissertation presents new load-response analysis models that use a finite element based micromechanical homogenization procedure for predicting the elastic structural behavior of SVBS. Firstly, a representative volume element (RVE) or unit cell of a selected SVBS has been established and analyzed to determine the equivalent RVE stiffness properties, i.e. the extensional stiffness matrix [A], the coupling stiffness matrix [B], and the bending stiffness matrix [D]. Independent unit strains and unit curvatures are prescribed to the RVE in ANSYS, and the resulting resultant moments and forces are used to calculate the [A], [B] and [D] matrices. A procedure combining finite element analysis and Timoshenko's beam theory is proposed for determining the transverse shear stiffness matrix [E] with an acceptable margin of error. The micromechanical homogenization procedure is then verified by applying it to a homogenous isotropic RVE for which results can be determined analytically. Secondly, the ABDE matrices of the RVE are used to analyze a full-scale 2D orthotropic SVBS floor system by Mindlin-Reissner and Kirchhoff-Love plate theories which are programmed in MATLAB. Thirdly, parametric studies are presented investigating stiffness variations in five different configurations of SVBS, selection of alternative RVE type, and the effect of span length on SVBS efficacy. The results from this dissertation can play a role in the development of SVBS design guidelines, which currently do not exist in the US.