@Article{cmes.2026.086319,
AUTHOR = {Hashem Al-Madwami, Amira Abo Kaf , Haibin Yin},
TITLE = {Steady Bending Force and Shaft Torque in Central-Axis Bending of Reinforcing Bars: Mechanics-Based Analytical Modelling and Finite Element Assessment},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {},
YEAR = {},
NUMBER = {},
PAGES = {{pages}},
URL = {http://www.techscience.com/CMES/online/detail/28127},
ISSN = {1526-1506},
ABSTRACT = {A mechanics-based analytical framework is developed for estimating the steady bending force and shaft torque in central-axis bending of reinforcing bars (RBs). Analytical expressions are derived for the sectional bending moment and are subsequently linked to the machine-level force and torque through the roller-system load-transfer geometry. Three constitutive descriptions are considered, namely elastic-perfectly plastic, bilinear hardening, and power-law hardening, to examine the influence of post-yield material response on bending-demand estimation. The analytical formulations are assessed using a section-level pure-bending finite element model, a process-level three-dimensional finite element model with tool-bar contact, and reported smooth round-bar torque measurements and FE results for torque and circular-roller-force. The results show that representation of post-yield hardening is essential for reliable estimation of RB bending demand. At the section level, the mean relative error remains below 1% for the power-law formulation and below 5% for the bilinear formulation, whereas the elastic-perfectly plastic model deviates by about 30%–35%. At the process level, the mean relative errors of the power-law formulation remain below 7.5% for torque and below 10% for force; those of the bilinear formulation remain below 11% for torque and below 15% for force. Against the reported torque measurements, the elastic-perfectly plastic model underestimates the two reported steady torque levels by 36.02%–38.81%, whereas the hardening-based formulations give relative errors of 5.31%–7.48%. The parametric study further shows that RB diameter and strength grade govern the steady bending force and shaft torque primarily through sectional bending resistance, whereas machine-geometry parameters act primarily through the external load-transfer condition. Within the adopted assumptions, the proposed framework provides a mechanics-based quantitative tool for preliminary estimation and parametric assessment of steady bending force and shaft torque demand in central-axis RB bending systems.},
DOI = {10.32604/cmes.2026.086319}
}