Approximate analysis of quadrilateral slabs having various cases of boundary conditions and aspect ratios

Abstract

This paper provides an approximate analysis of quadrilateral slabs having various cases of aspect ratios and boundary conditions based on actual two-way action. Nine slabs with different boundary conditions, each having 11 aspect ratios were analyzed using SAP2000 software, thereafter, robustly validated against mathematical solutions. In this article, the hydrostatic point phenomenon was established as a reference point for identifying the slabs with actual two-way action and as a growth reference for other cases. This allows for the use of growth models for the hydrostatic and deviatoric moment tensors. The innovative selection of the extreme positive point moment facilitates the introduction of materials nonlinearity into the design. The plate shorter dimension was used for moment normalization in both directions to preserve the directional influence of the dimensions and to isolate the hydrostatic phenomenon. Through starting at a point of hydrostatic phenomenon occurrence and via fixing one of the plate’s dimensions and extending the other (for any boundary conditions), the extreme point’s Mohr circle develops from the hydrostatic point phenomenon as a growth in the hydrostatic component and drastic growth in the deviatoric component. Subsequently, the largest principal moment develops a higher magnitude as the aspect ratio increases. Furthermore, the non-identical boundary conditions on two perpendicular directions result in a deviation of the two-way action.