The Tensile Membrane Action of Non-orthogonal Composite Slabs at Elevated Temperatures

Abstract
In order to generalize the applicability of nonlinear numerical investigation of the structural behavior of slab panels at high deflections, which utilizes tensile membrane action in the slabs, the meshing of such floor systems cannot be restricted to orthogonal grids. A separate but related issue is that nonlinear numerical modelling of internal slab panels with continuity across their edges has shown that the way in which their boundary conditions are defined can have a considerable influence on their predicted membrane forces in various situations. This research investigates the behaviour of the membrane forces in orthogonal and non-orthogonal composite slabs at elevated temperatures by means of numerical modelling. With different continuity conditions at slab panel edges, the effects of various boundary conditions on the tensile membrane action of non-orthogonal slabs at high deflections are identified. In order to achieve this end, a penalty function method is first developed which allows boundary conditions to be defined in terms of relationships between different degrees of freedom in the system’s global coordinates, as opposed to the conventional binary “free or restrained” choice for individual degrees of freedom. This allows boundary conditions either to be defined with respect to axes inclined to the global system, or to link displacements at different nodes. This easily defines suitable boundary conditions for non-orthogonal slabs, and also allows the continuity of internal panels to be realistically modelled.
In terms of simplified design methods, it is often possible to divide internal floor areas of a building into rectangular or square panels, but the problem of slabs at or near the edges of non-orthogonal buildings still exists. This thesis attempts to begin to extend these methods to non-orthogonal slabs by determining the optimal small-deflection yield-line failure patterns for quadrilateral slabs of different geometries. Simplified design methods assume that the enhancement of capacity due to tensile membrane action increases continuously with vertical deflection. However, as slab deflection increases, through-depth cracks which may or may not coincide with the yield lines can occur, and these cause progressive reduction of the enhancement of load capacity. Optimizing assumed yield-line patterns by using a plastic work balance method, the research establishes and validates two existing yield-line patterns for trapezoidal slabs. Further studies to determine the precise yield-line patterns of trapezoidal slabs are made by gradually changing of the geometrical parameters.

A new plastic energy method which includes the internal work dissipation during rebar extension has been extended to triangular slabs. The post-yield-line behaviour of such slabs has been demonstrated. This research validates and compares the enhancement factor performance from the new plastic energy method to the existing simplified design method. An investigation of the influence of different reinforcement meshes and geometry on the enhancement of load-carrying capacity of isosceles triangular slabs has been carried out.