Optimisation of Multigonal Corner Combined Footings: A Mathematical Model for Minimum Dimensions Under Varying Load and Soil Conditions Using Python and Maple
Nigusie Tsehay Demeke1, Getasew Kindie Mihiretu2, Girma Moges Teshager3, Girmay Mengesha Azanaw4
1Nigusie Tsehay Demeke, Department of Civil Engineering, Institute of Technology, University of Gondar, Gondar, Ethiopia.
2Getasew Kindie Mihiretu, Department of Civil Engineering, Institute of Technology, University of Gondar, Gondar, Ethiopia.
3Girma Moges Teshager, Department of Civil Engineering, Institute of Technology, University of Gondar, Gondar, Ethiopia.
4Girmay Mengesha Azanaw, Department of Civil Engineering, Institute of Technology, University of Gondar, Gondar, Ethiopia.
Manuscript received on 15 July 2026 | First Revised Manuscript received on 06 August 2026 | Second Revised Manuscript received on 04 September 2026 | Manuscript Accepted on 15 September 2026 | Manuscript published on 30 September 2026 | PP: 9-24 | Volume-14 Issue-10, September 2026 | Retrieval Number: 100.1/ijese.H264614090826 | DOI: 10.35940/ijese.H2646.14090826
Open Access | Editorial and Publishing Policies | Cite | Zenodo | OJS | Indexing and Abstracting
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Foundations are important in structural engineering, as they transfer loads to the ground. Designing combined footings on uneven ground is challenging because of load eccentricity, soil heterogeneity, and material efficiency. Traditional methods, based on oversimplified soil-pressure assumptions, fail. This paper introduces a new model for optimal multigonal corner combined footing design that minimises size while adapting to varying loads and soil strengths. The model allows flexible footing slopes (90° to 0°) to position the load and geometric centres, ensuring uniform stress distribution and preventing eccentric loading. Optimised in Python for numerical accuracy and in Maple for symbolic calculation, the model is validated through numerical analysis and shows significant improvements in material efficiency and cost savings compared with traditional practices. The result is better footing regions, with lower b1 and b2 in end columns and greater n and m, which improves stress distribution and reduces load eccentricity. The model is recommended for designing corner combined footings with four continuous lines of property. Practical recommendations and future research on smaller dimensions and column-spacing effects on footing design conclude the paper.
Keywords: Footing Optimisation; Multigonal Corner Combined Footings; Mathematical Modelling; Python and Maple.
Scope of the Article: Civil Engineering