Comparative Evaluation of Beam-Based Modeling Approaches for 90˚ Pipe Elbows against Shell Element Analysis: Parametric Study across Diameter-to-Thickness Ratios

Abstract

This paper presents a systematic parametric comparison of two beam-based modeling approaches for 90˚ long-radius pipe elbows—the ASME B31.3 flexibility factor method and the Equivalent Straight Elbow (ESE) method—against shell element analysis. Twelve geometric cases covering four nominal pipe sizes (NPS 6” to 24”) and three wall thickness schedules (Sch 10/40/80), with diameter-to-thickness ratios ( D / t ) from 15.3 to 96.0, were analyzed using SAP2000 under in-plane bending, out-of-plane bending, and axial loading. Results show that the ASME B31.3 method systematically overestimates elbow flexibility, with errors of 10.9% to 25.6% under in-plane bending and up to 63.2% under out-of-plane bending, increasing monotonically with D / t ratio. The analytical ESE method consistently underestimates flexibility by 16.5% to 22.7% for in-plane bending and 47% to 81% for out-of-plane bending. Stress intensification ratios between shell and beam models range from 2.8 to 11.7, confirming that beam elements cannot capture ovalization-induced stress amplification. Based on these findings, the ASME B31.3 method is recommended for in-plane bending analysis when D / t < 50 and moderate conservatism (error ≤ 15%) is acceptable. The analytical ESE method without finite element calibration is not recommended for general-purpose elbow modeling.