Optimization of post-tensioned concrete floor slabs

The proposed study will focus on the design of flat plate slabs, with a particular concern for high-rise buildings. The slab has a crucial role within these structures, acting as a diaphragm to transfer the forces – seismic forces and gravity loads – to the members supporting the floor, providing a “level-to-level redistribution of forces”. The present work aims to formulate a methodology to design thin post-tensioned reinforced concrete slabs for complex architectural projects. Complexities considered include asymmetrical slabs, the non-regularity of columns and, very long spans. For architectural and structural reasons, flat slabs are becoming thinner. This trend can reduce building height and/or allow more floors in a single building. From a structural perspective, the thinning of slabs primarily reduces the amount of material used and allows for a reduction in structural weight. For high-rise constructions, smaller walls and foundations is a crucial factor. The main objective of the research will focus on the use of post-tensioning in order to reduce: 1. Thickness and weight of slabs by finding the optimal location of post-tensioning. As we can imagine this will save on the amount of rebar used thanks to the use of post-tensioning. 2. Slab deflections for very long spans. The goal is to achieve increased structural performance of a building structure and reduce overall cost construction. The first task requires finding tools to predict optimal post-tensioned layouts/profiles. This can be accomplished by separating the problem into two parts: the in-plane behavior and the out-of-plane behavior. The out-of-plane behavior can be studied using the force density method. This method would determine the vertical drape of cable networks defined by the post-tensioning tendons through changing the coordinates of the fixed nodes or the force densities of the cables. The in-plane problem can be analyzed using plate theory. The main objective is to determine the directions of the stresses within the plate. The topology optimization will give a good initial evaluation if applied by scaling the intensity of the stresses to differentiate the banded tendons from the uniform ones. A complete understanding of the post-tensioning concrete slab behavior is indispensable to perform the optimization procedure, therefore a number of factors, such as cracking, deflection, creep and shrinkage must also be taken into account when finalizing the optimized design. First, the design criteria used to design post-tensioning concrete slabs, both in a traditional and in an optimized way, will be presented. Subsequently, topology optimization will be applied to define the optimized tendons profile and layout, which will then be updated using a FEM software in order to evaluate the accuracy of the results and to verify their compliance with the design criteria and code specifications Finally, an evaluation of the rebar quantities, both for prestressing and ordinary design, for use in the optimized design will be carried out with a comparison between the optimized and traditional layout to be performed. One step further in the research would consist of considering construction constraints (construction techniques, feasibility, time and cost) to adapt the obtained optimized profiles to a possible utilization on site.