Open Access

ARTICLE

Steady Bending Force and Shaft Torque in Central-Axis Bending of Reinforcing Bars: Mechanics-Based Analytical Modelling and Finite Element Assessment

Hashem Al-Madwami^1,2, Amira Abo Kaf ³, Haibin Yin^1,4,*

1 School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan, 430070, China
2 Department of Mechanical Engineering, Faculty of Engineering, Sana’a University, Sana’a, 11311, Yemen
3 State Key Laboratory of Light Superalloys, Wuhan University of Technology, Wuhan, 430070, China
4 Hubei Engineering Research Center of Robotics and Intelligent Manufacturing, Wuhan University of Technology, Wuhan, 430070, China

* Corresponding Author: Haibin Yin. Email:

(This article belongs to the Special Issue: Mechanical Applications of Computational Methods and Machine Learning)

Computer Modeling in Engineering & Sciences 2026, 148(3), 8 https://doi.org/10.32604/cmes.2026.086319

Received 28 May 2026; Accepted 14 August 2026; Issue published 28 September 2026

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.

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Supplementary Material

Supplementary Material File

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