Cost Optimization of Concentric Loaded Rectangular Combined Footings Using Different Matlab Solvers

Conventional design methods for combined footings comprise a series of iterations. Generally, this involves an initial guess for the dimensions which are evaluated as guided by the existing design code. This is then followed by several iterations to reduce the cost without any detriment to structural safety. In most cases, the result from the final iteration does not reflect the minimum cost design. This necessitates optimization models capable of establishing efficient and accurate designs within a short period, especially under several design variables. For this purpose, an optimization model for concentric loaded rectangular combined footings was developed in this research. The model was built in a general form and can perform optimization with different soil and material properties. The model encompasses an accurate objective function, subjected to the structural, geotechnical, and logical constraints to satisfy the requirements of the strength and serviceability limit states in accordance with ACI 318-11M specifications. The model works to find the minimal construction cost ofthe structure, adequate dimensions, and steel areas in different sections that correspond to that minimal cost. The model was developed using five solvers available within the MATLAB Global Optimization toolbox. Model capabilities were investigated by optimizing a case of concentric loaded rectangular combined footing with a known solution. The model capabilities were also assessed by testing the effect of using different material properties v and varying site conditions on the resulting objective function. The optimization results showed identical results compared to the conventional design methodology. The results also showed the cost tends to decrease with the use of higher steel grades for all load variations. Moreover, there was no major effect for the concrete compressive strength in the range of 20 to 35 MPa on the value of the objective function. However, for higher concrete strengths \u3e35MPa, the objective function value increased significantly. The influence of changing the foundation depth was significant in terms of cost reduction for the depth ranges between 0.5 to 2.0m, then the cost remained almost constant with the depth increase. Finally, the results showed no significant impact of the column shape on the total cost