Supplementary File S1
Central-axis RB bending steady-demand estimator

File
Supplementary_File_S1_Central_Axis_RB_Bending_Steady_Demand_Estimator.html

Purpose
This self-contained browser-based estimator implements the analytical steady-demand relations for central-axis reinforcing-bar bending. It reports optional outputs for:

- steady bending force from the bilinear hardening formulation;
- steady shaft torque from the bilinear hardening formulation;
- steady bending force from the power-law hardening formulation;
- steady shaft torque from the power-law hardening formulation.

The bilinear and power-law outputs can be enabled or disabled independently. This allows the estimator to be used when only one set of hardening parameters is available.

Recommended use
When the required power-law parameters are available, the power-law formulation is recommended because it generally provided the closest overall agreement, while the bilinear formulation remains a simpler alternative when only a tangent hardening modulus is available.

Material-data requirement
The power-law parameters K and n should be obtained from the post-yield true stress-true total strain response used in the analytical formulation, rather than fitted directly from engineering stress-strain data. The bilinear tangent modulus E_H should also be determined consistently from the corresponding true stress-strain response.

Reference input ranges
- RB diameter, d: 8–16 mm
- Fulcrum roller radius, R_1: 10–35 mm
- Rotating bending roller radius, R_2: 10–35 mm
- Bending-roller rotation radius, R_3: 55–110 mm

Inputs
- d: RB diameter, mm
- R_1: fulcrum roller radius, mm
- R_2: rotating bending roller radius, mm
- R_3: bending-roller rotation radius, mm
- E_e: elastic modulus, MPa
- sigma_y: yield stress, MPa
- E_H: bilinear tangent hardening modulus, MPa; used only when bilinear output is enabled
- K: power-law strength coefficient, MPa; used only when power-law output is enabled
- n: power-law hardening exponent; used only when power-law output is enabled

Use
Open the HTML file in any modern web browser. No internet connection, external library, server connection, installation, or macro permission is required.

Notes
- Units must be kept consistent: MPa = N/mm², geometry in mm, force in N, and torque in N·mm or N·m.
- The visible implemented relations include the bilinear and power-law sectional bending-moment expressions together with the load-transfer relations. L_N is the normal-force moment arm, L_r is the moment arm of the equivalent tangential contact-resistance component, and L_eff is the effective load-transfer arm.
- Inputs outside the reference ranges are flagged by the estimator; calculations remain available when the input geometry satisfies the model requirements.
- The estimator includes an embedded geometry schematic, a calculation-report copy function, CSV export, and collapsible model notes.
- The estimator applies the analytical model within the assumptions adopted in the manuscript, representing the RB as an equivalent smooth round bar. Local transverse-rib effects on tool-bar contact, surface deformation, and force/torque fluctuations are not captured.
- The estimator is provided for supplementary use only. Input selection and interpretation of the outputs should follow the assumptions, analytical formulation, and limitations described in the manuscript.
