Parametric study on effective spacing of self‑tapping screws in curved glulam beams considering plasticity-damage behavior: Experimental and numerical analyses

Self-tapping screws (STSs) have been recognized as an effective solution to prevent transverse splitting in curved glulam beams. However, a systematic parametric investigation into the STSs arrangement in curved glulam beams and their interaction with beam geometry remains limited. In this study, a refined three-dimensional finite element (FE) model of the curved glulam beams with STSs was developed using Abaqus/Explicit, in which a novel elasto-plastic damage constitutive model for timber was implemented via a VUMAT subroutine. The proposed constitutive law featured a modified Yamada-Sun yield criterion, kinematic hardening rule, and exponential damage evolution. The model was validated against six groups of four-point bending tests on curved glulam beams. The results revealed that the STSs reinforcement significantly postponed the radial damage initiation and reduced its evolution, resulting in a considerable increase in load-bearing capacity. Nevertheless, due to radial damage and cracking accumulation during bending, the ultimate load of some curved beams did not fully attain their bending capacity. Subsequently, a comprehensive parametric analysis was conducted, covering the commonly adopted design ranges of beam depth H , curvature parameters H / R w,m , and longitudinal screw spacings S L . The results demonstrated that increasing H / R w,m or S L / H drastically reduced the capacity ratio η and elevated the radial damage factor d 2 . Moreover, the sensitivity of both η and d 2 to changes in spacing was strongly amplified by H / R w,m . Based on the parametric analysis, a conservative exponential formula was finally proposed as a function of H / R w,m to determine the effective screw spacing that ensured η > 0.9 and d 2 < 0.9. However, given the limited experimental scope of this study, the FE‑derived formula requires further validation through additional testing.