Optimization of Multigonal Corner Combined Footings: A Mathematical Model for Minimum Dimensions Under Varying Load and Soil Conditions Using Python and Maple

Foundations are important in structural engineering, as they transfer loads to the ground. It is challenging to design combined footings on uneven ground due to load eccentricity, soil heterogeneity, and material efficiency. Traditional methods, based on oversimplified assumptions of soil pressure, fail. This paper introduces a new model for optimal multigonal corner combined footing design, with minimum size but with the capacity to adapt to varying loads and soil strengths. The model offers flexible footing slopes (90° to 0°) to place the load and geometric centers, offering uniform stress distribution and preventing eccentric loading. Optimized in Python for numerical accuracy and Maple for symbolic calculation, the model is computed using numerical analysis. The result is better regions of footing, with lower b1 and b2 in end columns, and greater n and m, which enhance stress distribution and lessen load eccentricity. The model is recommended for the design of corner combined footings with four continuous lines of property. Practical recommendations and future research for smaller dimensions and column spacing effects on footing design finalize the paper.