Extension of Classical PFI theory for Bending Behavior in Special Steel Plate Shear Walls using Nonlinear Analyses for Different Steel Grades

Steel Plate Shear Walls (SPSWs) have emerged as one of the most efficient and dependable lateral force–resisting systems in contemporary earthquake engineering. Their notable post-yield stability, high initial and cyclic stiffness, and exceptional capacity for hysteretic energy dissipation distinguish them from many conventional structural systems, making them especially attractive for deployment in regions characterized by elevated seismic hazard. Since their introduction into modern structural design practice in the early 1970s, SPSWs have witnessed a steady rise in application, particularly in mid- and high-rise buildings where rigorous performance objectives and stringent serviceability requirements demand structural mechanisms that exhibit both robustness and predictability under extreme loading conditions. In this study, an extensive analytical and numerical investigation is undertaken to evaluate the seismic performance of Special Steel Plate Shear Walls (SSPSWs) across a diverse range of structural heights, including 1-, 3-, 5-, 8-, 10-, 15-, 18-, 20-, and 30-story configurations. Each model is developed within the framework of performance-based seismic design, enabling a direct assessment of system behavior under varying levels of seismic demand. Two steel grades—conventional structural steel and low-grade steel (LGS)—are incorporated to explore the extent to which material strength and ductility influence both global system response and localized behavioral phenomena such as yielding patterns, shear band formation, and boundary-frame interaction. A suite of nonlinear static and dynamic analyses is performed to capture the evolution of inelastic deformation, progression of local and global damage, stiffness degradation trajectories, and cumulative energy dissipation mechanisms. Complementing these numerical simulations, the classical Plastic Flexural Interaction (PFI) theory is adopted to analytically characterize the flexural response of the SPSW systems. A systematic comparison between analytical predictions and detailed numerical results is conducted to evaluate the applicability, accuracy, and inherent limitations of the PFI framework when extended to steel grades with varying mechanical properties. This integrated analytical–numerical methodology provides a comprehensive perspective on the interplay between material nonlinearity, geometric effects, and system-level seismic behavior. The findings of this research clearly demonstrate that the application of LGS steel significantly enhances the overall seismic performance of SPSWs. Notable improvements include meaningful reductions in lateral displacement demands, increased initial and post-yield stiffness, substantial gains in load-bearing and lateral resistance capacity, and more uniform distribution of inelastic deformation throughout the wall height. The enhanced ductility and reduced yield strength associated with LGS steel facilitate earlier activation of energy-dissipating mechanisms, delay the onset of local or global instabilities, and ultimately contribute to a measurable enhancement in collapse-prevention capacity. Additionally, reductions in performance-point displacements and global seismic demand highlight the potential of LGS steel as a viable and advantageous alternative to conventional grades in high-performance seismic applications. Building on these observations, the study proposes an extended formulation of the PFI theory that more accurately captures the flexural response of SPSWs across steel grades of differing strengths. This refined model enables practical prediction of critical response parameters without relying on computationally intensive simulations, thus offering a valuable tool for preliminary design, rapid assessment, and performance-oriented decision-making. Collectively, the outcomes of this research advance current understanding of SPSW behavior, particularly with regard to material-dependent response mechanisms, and provide a strong foundation for future refinement of design provisions and next-generation seismic standards incorporating low-grade steel systems.