Simplified Torsional Calculation for Thin-Walled Centrifugally Cast Concrete-Filled Steel Tubes

Literature Overview

The paper by Jin Weiliang, Qu Chen, Fu Jun, and Zhang Li, published in Journal of Zhejiang University (Engineering Science) (Vol. 37, No. 1, 2003, pp. 5-9), presents a simplified calculation methodology for the full-process torsional behavior of thin-walled centrifugally cast concrete-filled steel tubes (CFST). Based on the analysis of 22 experimental specimens, the authors propose a three-stage torsional failure concept and develop simplified formulas for elastic and plastic torsional moments using a direct double-linear method consistent with international research and domestic codes.

Three-Stage Torsional Failure Concept

The experimental data from 22 thin-walled centrifugally cast CFST specimens revealed a distinct three-stage failure pattern under pure torsional loading:

Stage	Description	Material Behavior	Deformation Characteristic
Elastic stage	Linear relationship between torque and twist	Both steel and concrete in elastic range	Uniform shear stress distribution
Elasto-plastic stage	Nonlinear torque-twist relationship	Steel yielding initiates; concrete still elastic	Shear stress redistribution
Plastic stage	Torque plateau or gradual increase	Full plasticity in steel; concrete contributes through friction and confinement	Large plastic deformation with stable load

This three-stage concept provides a clear framework for understanding the progressive failure mechanism and enables the development of practical design formulas that capture the essential behavior without requiring complex numerical analysis.

Simplified Calculation Formulas

Elastic Torsional Moment

The elastic torsional moment of the composite section is calculated based on the combined stiffness of the steel tube and concrete core. The key innovation is the introduction of a composite modulus expression that accounts for the geometric parameters of the section:

Parameter	Symbol	Effect on Composite Modulus
Hollow rate (void ratio)	-	Reduces effective concrete contribution
Steel ratio	ρ	Increases composite stiffness
Slenderness ratio	λ	Affects boundary condition effects

The composite modulus is expressed as a function of these parameters, allowing engineers to rapidly estimate the torsional stiffness of CFST members with varying geometric configurations.

Plastic Torsional Moment

The plastic torsional moment formula accounts for the full yielding of the steel tube wall and the contribution of the concrete core through frictional resistance and confinement effects. The centrifugal casting process produces a denser, more uniform concrete-steel interface, which enhances the frictional bond and improves the plastic torsional capacity compared to conventionally cast CFST members.

Direct Double-Linear Method

The authors employ the direct double-linear method, which is consistent with international research approaches and domestic code provisions (such as GB 51248 and JGJ/T 70). This method provides a practical framework for calculating the deformation behavior at each torsional stage by using two linear segments to approximate the nonlinear torque-twist relationship. The method's simplicity makes it suitable for hand calculations and preliminary design, while its accuracy—validated against the 22 experimental specimens—ensures reliability for detailed design.

Centrifugal Casting Process Implications

The centrifugal casting process is critical to the performance of these CFST members. During centrifugation, the concrete mixture is spun at high rotational speed, causing the heavier steel aggregate to migrate toward the steel tube wall while the lighter paste concentrates toward the core. This produces a non-uniform concrete density profile with a denser layer adjacent to the steel tube, which enhances the bond strength and the confinement effect. The thin-walled nature of the steel tube (typically D/t > 50) makes it susceptible to local buckling under torsional shear stress, but the centrifugally cast concrete provides lateral support that delays buckling and allows the tube to reach its full plastic capacity.

Quality Control for Centrifugal CFST Production

Quality Parameter	Acceptance Criteria	Inspection Method
Steel tube wall thickness uniformity	±10% of nominal	Ultrasonic thickness measurement
Concrete fill density	Minimum 2200 kg/m³	Core sampling or GPR
Interface bond quality	No voids or delamination	Ultrasonic pulse velocity
Steel tube concentricity	Within ±5 mm	Dimensional survey
Centrifugation speed consistency	±5% of design speed	Process monitoring records

Key Reflections

This research provides a valuable simplified calculation methodology for the torsional design of centrifugally cast CFST members, which is particularly relevant for applications such as transmission tower legs, bridge piers subjected to torsional loading, and industrial equipment supports. The three-stage failure concept and the direct double-linear method offer engineers a practical design tool that balances accuracy with computational simplicity. The parametric expressions for composite modulus in terms of hollow rate, steel ratio, and slenderness ratio enable rapid evaluation of design alternatives during the preliminary design phase. However, the methodology is based on pure torsional loading, and the interaction between torsion and other load components (bending, axial compression, shear) requires additional investigation. The centrifugal casting process quality is a critical factor that directly influences the bond strength and composite action, and engineers should ensure that the manufacturing process meets the quality standards necessary to achieve the predicted structural performance. This work represents a significant contribution to the practical design of CFST members in torsion and should be referenced alongside current code provisions for composite structural design.