To develop a numerically stable and computationally efficient macro-scale rigid body spring model (RBSM) for the nonlinear analysis of reinforced concrete (RC) and steel–concrete composite beams, addressing the convergence difficulties and high computational cost often encountered in post-peak softening regimes.
A macro-scale RBSM framework with multi-spring interfaces is proposed. A dummy spring-based stabilization strategy is introduced to maintain the positive definiteness of the global stiffness matrix during post-peak response, improving Newton–Raphson robustness without altering the physical stiffness. The framework is implemented in Python and validated through elastic cantilever benchmarks, RC beam bending tests (simply supported and continuous), steel–concrete composite beam experiments and a two-storey RC frame pushover analysis. Comparative assessments against OpenSees and Abaqus are also provided.
The proposed framework reliably predicts global load–displacement responses and failure modes under coarse discretization. It achieves peak load errors within 3.3% for RC beams and 1.3% for composite beams. The dummy-spring strategy enables stable load-controlled post-peak tracing, reducing iteration counts and computational cost compared with conventional displacement-controlled finite element simulations. A sensitivity analysis confirms that the results are insensitive to the dummy-spring stiffness over a wide range.
The current implementation is limited to 2D static monotonic loading of beam/column members, focusing on global response rather than detailed crack morphology. Future extensions include 3D, dynamic and collapse scenarios.
A novel combination of a macro-scale multi-spring RBSM and a dummy-spring stabilization strategy is presented. The work provides a systematic validation from member to structural level, including a new two-storey frame pushover benchmark and a detailed sensitivity study of the numerical stabilization parameter.
