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This research presents a new mathematical framework for the optimal design of elliptical isolated footings under vertical load and two orthogonal moments. The suggested method considers the spatial variation of contact pressure between the footing and the supporting soil, facilitating an accurate representation of structural requirements. New formulations for bending moment, unidirectional shear, and punching shear are generated using volume integration, accurately representing the complex stress distribution beneath elliptical foundations. Lagrange multipliers are utilized to identify the crucial points of maximum and minimum contact stresses for elliptical and circular footing shapes. A thorough numerical analysis illustrates the benefits of the suggested strategy by contrasting its results with those of a conventional design methodology. The findings demonstrate that the newly created model produces more cost-effective designs while maintaining structural integrity and performance, underscoring its potential as a significant asset in engineering practice. A MATLAB code for design using new formulas is programmed and results obtained compared to those from literature and were more efficient and economic.
I like to express my profound appreciation to the editor and the anonymous reviewers for their invaluable feedback and insightful recommendations, which have markedly enhanced the quality of this paper. Their direction and constructive feedback have refined the text and ensured clarity in presenting the findings. I sincerely value their time and effort in evaluating this work.