Optimization of Reinforced Concrete Footings Used to Support Wind Loaded Structures

The application of optimization to the design of structures where the ability to sustain a large wind load is considered. This investigation was an outgrowth of research intended to increase the capabilities of engineers who design such structures as highway signs and elevated steam lines. A second objective was to see if optimization techniques could successfully be applied to this class of problems. The objective was to minimize the mass of the footing needed to support the structure. A model of a reinforced concrete footing which supports the structure is given. This model includes constraints which assure that the structure won’t overturn and that stresses in the footing and soil don’t exceed the strength of the respective materials. Optimization software (a conjugate gradient method) uses this model to find a design which minimizes the mass of the footing. Results for various loadings and configurations are presented. Analysis of the results indicate that for lightly loaded structures the optimal footing design tends to be a piling (large depth relative to length) while for a relatively heavily loaded structure the optimal design is more of a plate (large length relative to depth). A copy of the Fortran source code used to model the system and the optimization algorithm is available from either author.