Zhuojin Pipe Fitting Co., LtdTheoretical Analysis and Experimental Study of Steel Pipe Concrete Members under Combined Bending and Torsion
Literature Overview
This landmark paper by Han Linhai and Zhong Shantong, published in Industrial Construction in 1994, represents a foundational contribution to the understanding of steel pipe concrete (SRC) members subjected to combined bending and torsion. The authors, affiliated with the Institute of Engineering Mechanics, China Earthquake Administration, and Harbin Institute of Technology, conducted both theoretical analysis and experimental verification on twelve test specimens. The research was supported by the National Natural Science Foundation of China and addressed a critical gap in structural design methodology for SRC members under complex loading conditions.
Core Technical Content
The authors recognized that in practical engineering structures—particularly those subjected to seismic loading—steel pipe concrete members rarely experience pure axial, pure bending, or pure torsional loading. Instead, combined loading states with varying proportions of axial force, bending moment, and torsional moment are the norm. The theoretical analysis presented in this paper systematically considered different loading paths, which is essential because the stress-strain state of a composite member is path-dependent due to the nonlinear material behavior of both steel and concrete.
The theoretical framework was built upon the fundamental assumptions of plane sections remaining plane after deformation and the compatibility of strains between the steel pipe and the concrete core. The constitutive relationships for both materials were incorporated into the analysis, accounting for the confinement effect of the steel pipe on the concrete core, which enhances both the strength and ductility of the concrete under compressive loading.
Twelve experimental specimens were designed and tested to validate the theoretical predictions. The test matrix varied the relative proportions of bending moment and torsional moment to cover the full range of interaction between these two load components. The experimental results demonstrated good agreement with the theoretical analysis, confirming the validity of the analytical approach.
| Loading Condition | Dominant Stress State | Primary Failure Mode | Ductility Characteristic |
|---|---|---|---|
| Pure bending (M) | Tension on one side, compression on the other | Steel pipe yielding on tension side | Moderate ductility |
| Pure torsion (T) | Shear stress throughout the section | Steel pipe shear yielding | Low ductility |
| Combined M + T | Complex biaxial stress state | Progressive steel pipe yielding | Depends on M/T ratio |
| Combined N + M + T | Full three-component loading | Steel pipe local buckling or rupture | Highly path-dependent |
Interaction Equation Development
The most significant practical contribution of this study is the derivation of a unified bearing capacity interaction equation for steel pipe concrete members under combined bending and torsion. This equation provides a continuous relationship between the pure bending capacity, pure torsional capacity, and the combined bending-torsion capacity, thereby enabling designers to evaluate the structural adequacy of SRC members under any combination of these loading components.
The interaction equation takes the form of a normalized relationship where the applied bending moment and torsional moment are expressed as fractions of their respective pure load capacities. The exponent in the interaction equation governs the curvature of the interaction surface and was calibrated based on both theoretical analysis and experimental data. This approach is consistent with the methodology used in steel design codes for interaction between bending and shear, extended here to include torsion.
The development of this interaction equation resolved a significant practical problem: prior to this work, designers had to rely on separate, independent formulas for pure bending and pure torsion, with no systematic method for evaluating combined loading conditions. The unified interaction equation enables a rational and code-compliant design approach for SRC members in complex structural systems.
Connection with Engineering Practice
From a welding and fabrication standpoint, the performance of steel pipe concrete members under combined bending and torsion is intimately linked to the quality of the pipe manufacturing process and any field or shop welds connecting the pipe to adjacent structural elements. For spiral welded pipes, the helical weld seam introduces anisotropic properties that can affect torsional behavior. For longitudinal welded pipes (ERW, HFW, LSAW), the longitudinal weld seam orientation relative to the principal bending axis is a critical design consideration.
When steel pipe concrete members are connected to other structural elements through welded joints, the weld design must accommodate the complex stress state that develops under combined loading. The HAZ of the weld may become a critical location for crack initiation under cyclic bending and torsional loading, particularly in seismic applications. Fracture mechanics-based assessment of the weld HAZ, considering the combined stress state, is essential for ensuring adequate fatigue and fracture resistance.
| Welding Process | Heat Input (kJ/mm) | HAZ Width (mm) | Recommended for SRC Connections |
|---|---|---|---|
| SMAW | 1.5–3.0 | 8–15 | Field connections, repair welding |
| FCAW | 2.0–4.0 | 10–18 | Shop fabrication, thick sections |
| SAW | 3.0–6.0 | 15–25 | Longitudinal pipe welds, girth welds |
| PAW | 2.0–5.0 | 8–15 | High-productivity shop fabrication |
| GTAW | 0.5–1.5 | 3–8 | Root pass, thin-walled pipe connections |
Key Questions and Reflections
The study raises the question of how the derived interaction equation should be modified to account for the effects of concrete shrinkage and creep on the long-term load distribution between the steel pipe and concrete core. Under sustained combined bending and torsion, creep in the concrete core may lead to a progressive transfer of bending moment and torsional moment from the concrete to the steel pipe, potentially exceeding the elastic capacity of the steel pipe.
Another important consideration is the effect of loading path on the ductility of SRC members under combined bending and torsion. The authors acknowledged that different loading paths can lead to different failure modes and ultimate capacities, but the interaction equation provides a single, path-independent relationship. In seismic applications, where loading paths are inherently unpredictable and may involve repeated reversals, the adequacy of a path-independent interaction equation requires careful consideration of cyclic degradation effects.
Study Insights and Implications
This research by Han Linhai and Zhong Shantong established a rigorous theoretical and experimental foundation for the design of steel pipe concrete members under combined bending and torsion. The unified interaction equation provides a practical design tool that bridges the gap between theoretical analysis and engineering application. For welding engineers, the study highlights the importance of ensuring that welded connections to SRC members can accommodate the complex stress states that develop under combined loading, particularly in seismic regions where ductile performance is paramount.
The experimental validation with twelve specimens provides confidence in the theoretical framework, but the sample size is relatively modest by modern standards. Future research should expand the experimental database to include higher-strength steel pipes, larger diameter-to-thickness ratios, and more diverse loading histories. Nevertheless, this paper remains a cornerstone reference for the design of steel pipe concrete structures subjected to complex combined loading conditions.