Numerical Method to Obtain the Resistance of Reinforced Concrete and Composite Steel Concrete Sections Subjected to Axial Forces and Biaxial Bending Based on Simplex (Linear Programming)

Designing reinforced concrete sections of various shapes, including those with variable geometry, holes, and arbitrary distribution of reinforcing steel bars, is a common task in civil engineering involving reinforced concrete structures. This design process requires integrating non-linear stress fields over complex shapes due to the non-linear behavior of concrete in compression. In this paper, we propose a novel algorithm based on the simplex method to calculate the ultimate strength of reinforced concrete and steel concrete composite sections under biaxial bending and axial force. The proposed algorithm is validated by comparing its analytical results with methods suggested by other authors and with experimental results available in the literature.