Optimization of post-tensioned concrete slabs for minimum cost

Abstract

We present a methodology and computational procedure for optimization of arbitrary post-tensioned slabs. The method is not restricted to any predefined cable layout and therefore non-trivial, curved cables patterns emerge, achieving nearly 50% savings in cost and cable mass. The cost function that is minimized accounts for the material and labor costs with a penalty on complex cable layouts, leading to a more realistic cost estimate. Stress and deflection constraints are imposed so that the optimized layouts satisfy the requirements for limit states of serviceability. Together with curvature constraints and an explicit representation of the cables’ geometry, a computational design process is obtained that yields optimized designs that do not require additional post-processing. Furthermore, a Pareto optimum front is generated from a large set of optimized designs, demonstrating the critical trade-off between cable mass and construction complexity. Subsequently, the Pareto front can be utilized for decision making: finding the most suitable balance between material and construction costs, according to the added cost of constructing complex cable patterns.