A noble analytical solution for the size of rectangular footing subjected to axial, bending, and surcharge load

This paper introduces a comprehensive mathematical framework for the design of rectangular reinforced concrete footings under axial load, surcharge, and biaxial moments, accounting for both fully and partially supported contact conditions. The proposed method presents a set of closed-form equations obtained via integration, which incorporate changes in soil pressure distribution resulting from eccentric loading. As the noble contribution, a key parameter named compression fraction λ, is added to differentiate between complete and partial soil-footing interaction. The model incorporates surcharge—a component overlooked in previous formulations—and generalizes the concept of equal width typically employed in footing design. Parametric analyses reveal the model’s responsiveness to fluctuations in vertical load, moments, soil bearing capacity, and aspect ratio. Results indicate consistent and rational tendencies, with the footing area expanding under elevated loads or diminished bearing capacity, and contracting with increased soil strength. A comparison with Landeros’s model demonstrates that the proposed method produces more economical designs, with footing area reductions of up to 49.91%. The incorporation of surcharge and the capacity to manage partial compression render the presented equations a reliable and effective resource for structural engineers pursuing precise and material-efficient footing designs under complex loading scenarios.