Optimal Design of Fibrous Concrete Beams Through Simulated Annealing

In this paper formulation and solution technique using Simulated Annealing for optimizing the moment capacity of steel fiber reinforced concrete beams, with random orientated steel fibers, is presented along with identification of design variables, objective function and constraints. Steel fibers form an expensive constituent of steel fiber concrete and therefore it is important to determine ways and means of using these fibers in a judicial way with care consistent with economy for achieving the desired benefits. The most important factors which influence the ultimate load carrying capacity of FRC are the volume percentage of the fibers, their aspect ratios and bond characteristics. Hence an attempt has been made to analyze the effective contribution of fibers to bending of reinforced fiber concrete beams. Equations are derived to predict the ultimate strength in flexure of SFRC beam with uniformly dispersed and randomly oriented steel fibers. Predicted strengths using the derived expressions have been compared with the experimental data. A reasonable agreement (within the range of ±20 percent!) was evident with different types of steel fibers, aspect ratio, and material characteristics. A computer coding has been developed based on the formulations and the influence of various parameters on the ultimate flexural strength is discussed. A computer algorithm that conducts a random search in the space of four variables-beam width, beam depth, fiber content and aspect ratio-to yield an optimum solution for a given objective function (ultimate moment (Mu)) is presented. The outlined methods provide a simple and effective tool to assess the optimum flexural strength of steel fiber reinforced concrete beams. Using the results obtained the influence of various parameters on the ultimate strength are discussed. Particular attentions are given to the construction practice as well as the reduction of searching space. It has been shown that within a reasonable and finite number of searching the developed algorithm is able to yield optimum solutions for the given objective function.