Shear strength model for solid RC railway bridge piers considering stirrup strain localization and longitudinal tension shift

Railway bridge piers differ from highway bridge piers in terms of cross-sectional dimensions, reinforcement configurations, shear span ratios, and axial load ratios. For solid railway bridge piers, these characteristics may increase their susceptibility to brittle flexural-shear failure under severe earthquakes. Existing shear strength models for reinforced concrete (RC) bridge piers, most of which were developed for highway bridge piers or conventional RC columns, often provide inaccurate predictions for railway bridge piers because they assume uniform stirrup strain distributions and neglect the tension shift effect in longitudinal reinforcement. Moreover, current seismic design codes provide limited specific guidance for the shear design of railway bridge piers. In this study, 19 tests on solid RC railway bridge piers that failed in flexural-shear were compiled and analyzed. A novel shear strength model is proposed that explicitly accounts for both non-uniform stirrup deformation, referred to as strain localization, and longitudinal tension shift, two mechanisms commonly overlooked in existing models. The model parameters were calibrated using 16 test results and validated against the remaining three independent tests. The proposed model achieves a mean predicted-to-measured shear strength ratio of 1.005 and a coefficient of variation of 0.074, representing a 26%–33% reduction in variability compared to the best existing models. The primary novelty lies in the explicit incorporation of strain localization via a reduction factor C₀ = 0.5 and tension shift via a calibrated term Vt with C₁ = 0.04, both of which are ignored in existing code-based models. The proposed model provides a rational basis for the seismic design and shear strength evaluation of solid RC railway bridge piers.