Elastic Torsional Stress Analysis of Centrifugal Steel Pipe Concrete Structures

Literature Overview

This paper by Jin Weiliang and Qu Chen, published in Journal of Dalian University of Technology (2003, Vol. 43, No. 5, pp. 654-658), presents a rigorous analytical framework for determining torsional stresses in centrifugally cast steel pipe concrete (CFSC) composite members. The authors employ fundamental elasticity theory combined with a variational approach to derive closed-form expressions for cross-sectional and interlayer shear stresses under pure torsion.

Core Technical Framework

Structural Characteristics of CFSC Members

Centrifugal steel pipe concrete is manufactured by spinning a steel pipe shell with concrete slurry at high rotational speeds (typically 300–600 rpm), producing a dense, homogeneous concrete core with enhanced bond strength at the steel-concrete interface. The resulting composite section exhibits:

Non-uniform material distribution across the cross-section (steel tube + concrete core)
Potential interfacial slip under torsional loading
Complex stress distribution that cannot be captured by simple thin-walled tube theory
Significant coupling between warping and torsion in non-circular sections

Analytical Methodology

The authors establish the governing equations based on:

Equilibrium equations in cylindrical coordinates for a composite cylinder under torsion
Assumed stress function form satisfying boundary conditions at the outer surface and the steel-concrete interface
Complementary energy variational principle applied to the layered material system to approximately satisfy compatibility conditions

The key innovation is the treatment of the steel-concrete interface as a potential slip plane, where interfacial shear stress develops to maintain compatibility between the two materials. The variational approach minimizes the total complementary energy of the system, yielding approximate but physically consistent solutions.

Key Formulas and Results

The derived expressions provide:

Cross-sectional shear stress distribution τ(r,θ) as a function of radial position and material layer
Interfacial shear stress τ_interface at the steel-concrete boundary
Warping displacement function for non-circular sections
Torsional rigidity GJ of the composite section accounting for material mismatch

Parameter	Steel Tube Component	Concrete Core	Interface
Shear modulus	G_s = 80 GPa	G_c = 30 GPa (for C40 concrete)	Effective G_int
Polar moment of inertia	J_s = π/32 × (D⁴ - d⁴)	J_c = πd⁴/32	—
Shear stress at outer surface	τ_s = T·R/(G_s·J_s)	—	—
Shear stress at interface	τ_s_int = T·d/(G_s·J_s)	τ_c_int = T·d/(G_c·J_c)	τ_interface

Engineering Relevance

Design Implications for CFSC Members

For structural engineers designing CFSC columns, beams, or bridge piers subjected to torsional loads:

The interfacial shear stress is the critical design parameter governing bond integrity
Under pure torsion, the maximum interfacial shear stress occurs at the steel-concrete interface and can exceed the concrete's tensile strength
The composite torsional rigidity is less than the sum of individual component rigidities due to interface compliance
For circular sections, the warping effect is zero, simplifying the analysis significantly

Comparison with Existing Design Approaches

Method	Accuracy	Complexity	Applicable Cases
Thin-walled tube theory	Low (error >30%)	Simple	Thin-wall, small eccentricity
Thin-walled tube theory	Low (error >30%)	Simple	Thin-wall, small eccentricity
Full 3D FEA	High	Very complex	Any geometry, any loading
This paper's analytical method	Moderate-High (error <10%)	Moderate	Circular/elliptical CFSC under torsion
Empirical design codes	Variable	Simple	Code-specified conditions only

Study Reflections

This paper represents an important contribution to the analytical understanding of CFSC members, which have gained increasing popularity in seismic design due to their excellent ductility and energy dissipation capacity. The authors' approach of combining classical elasticity with variational methods provides engineers with a transparent, physics-based tool for preliminary design and verification.

The practical significance extends beyond pure torsion — understanding interfacial shear behavior under torsion informs the design of connection details, splice joints, and the overall structural system's torsional response. For engineers working with centrifugal CFSC products (which are increasingly manufactured in China for infrastructure projects), this analytical framework provides a basis for validating finite element models and interpreting test results.

One limitation worth noting is that the analysis assumes elastic behavior throughout, which is appropriate for serviceability checks but insufficient for ultimate limit state design where concrete cracking and steel yielding must be considered. Engineers should use this framework for initial sizing and then supplement with nonlinear analysis for detailed design.