TY  - EJOU
AU  - Al-Madwami, Hashem 
AU  - Kaf, Amira Abo 
AU  - Yin, Haibin 

TI  - Steady Bending Force and Shaft Torque in Central-Axis Bending of Reinforcing Bars: Mechanics-Based Analytical Modelling and Finite Element Assessment
T2  - Computer Modeling in Engineering \& Sciences

PY  - 
VL  - 
IS  - 
SN  - 1526-1506

AB  - 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.
KW  - Elastic-plastic bending; strain hardening; sectional bending resistance; central-axis reinforcing-bar bending; steady bending force; shaft torque; finite element assessment

DO  - 10.32604/cmes.2026.086319