Flexural Design of Reinforced Concrete Sections by Analytical Stress Integration: Algorithm, Implementation, and Validation

Resumen

This paper presents the formulation and computational implementation of MSolver, a tool developed to determine the moment capacity envelope of reinforced concrete sections subjected to axial load and biaxial bending. The formulation is based on the analytical integration of concrete stresses according to the parabola–rectangle stress block and on the discrete contribution of reinforcement, in accordance with ABNT NBR 6118:2026. The nonlinear axial equilibrium equation is solved using the Van Wijngaarden–Dekker–Brent method. The tool was implemented in C++ and compiled to WebAssembly for multiplatform execution in a web environment. The implementation was verified by comparing the resisting envelopes obtained with those produced by the SECC and OblqCALCO programs for an asymmetric polygonal section subjected to different axial load levels. The results showed good agreement among the solutions, indicating consistency in the adopted formulation and confirming the suitability of the proposed tool as a computational basis for future applications associated with the revised constitutive relationship of the Brazilian standard.