Unified Solution for Axial Compressive Bearing Capacity of CFST Columns Considering Initial Stress

Literature Overview

This paper by Li Yan, Zhao Junhai, Liang Wenbiao, and Wang Su from Chang'an University presents a theoretical framework for calculating the ultimate axial compressive capacity of concrete-filled steel tube (CFST) short columns that are subjected to initial stress. The work is grounded in the double-shear unified strength theory, which accounts for both the intermediate principal stress and the material's tension-to-compression strength ratio. A reduction coefficient incorporating the slenderness ratio effect is introduced, and the authors derive a unified analytical solution that has been validated against experimental data from the literature with good agreement. The study also proposes a new initial-stress influence coefficient and performs a parametric analysis of its constituent variables.

Core Technical Approach and Unified Strength Theory

The double-shear unified strength theory represents a significant advancement over classical failure criteria such as von Mises or Tresca, which do not adequately capture the behavior of concrete-like materials where the intermediate principal stress plays a non-negligible role. In CFST members, the confined concrete core experiences a complex triaxial stress state, and the steel tube itself undergoes biaxial to triaxial stresses depending on the loading condition and boundary restraints. The unified strength theory introduces a parameter $\beta$ that characterizes the material's tension-compression ratio, typically ranging from 0.7 to 0.8 for ordinary concrete, and a parameter $b$ that governs the influence of the intermediate principal stress, with $b = 0$ recovering the Tresca criterion and $b = 1$ recovering the von Mises criterion.

The initial stress condition is particularly relevant in engineering practice because CFST columns in multi-story buildings, offshore platforms, and bridge piers often carry pre-existing loads from upper structural elements before the full axial load is applied. This pre-stress state alters the stress distribution at the steel-concrete interface and modifies the confinement effectiveness. The authors introduce a slenderness-dependent reduction coefficient that bridges the gap between short-column idealization and practical long-column behavior, making the unified solution applicable to a broader range of member geometries.

Process and Standards Analysis

From a steel pipe manufacturing and welding standpoint, the initial stress in CFST columns is intimately connected to the fabrication and erection sequence. The steel tube is typically formed from rolled steel plates via ERW (Electric Resistance Welding) or LSAW (Longitudinal Submerged Arc Welding), and the weld heat-affected zone (HAZ) introduces residual stresses that constitute a form of initial stress. According to ASME B31.3 and GB/T 21835, the residual stress distribution in welded steel tubes follows a pattern of tensile residual stress near the weld root and compressive residual stress in the surrounding base metal, with magnitudes typically reaching 60–80% of the yield strength of the parent material.

When the steel tube is filled with concrete, the differential thermal contraction between the steel and concrete during curing introduces additional initial stresses at the interface. The steel tube, having a higher coefficient of thermal expansion, contracts more than the concrete, creating a tensile hoop stress in the steel and a compressive radial stress in the concrete. This self-confinement effect is beneficial for axial compressive capacity but can be detrimental if the initial stress state is not properly accounted for in design. The unified solution presented in this paper provides a rigorous basis for quantifying this effect, which is particularly valuable for engineers working with API 5L X65 or X70 grade line pipe adapted for structural applications.

Integration with Engineering Practice

In offshore platform construction, CFST columns are routinely subjected to cyclic loading from wave action and wind, and the initial stress state from fabrication residual stresses and self-confinement interacts with fatigue damage accumulation. The European standard EN 1993-1-1 and the Chinese standard GB 50017-2017 both provide simplified design formulas for CFST columns, but these formulas often assume a uniform initial stress state or ignore it entirely. The unified solution developed by Li et al. offers a more refined tool that can be integrated into finite element analysis workflows using software such as ABAQUS or ANSYS, where the initial stress can be applied as a boundary condition or as an initial field variable.

For pipe fitting fabrication, particularly for butt-weld fittings used in CFST column splices, the welding residual stress distribution around the circumferential weld seam follows patterns documented in ASME Section IX and AWS D1.1. The initial stress in the steel tube wall interacts with the weld residual stress, and their superposition can lead to localized yielding that reduces the effective confinement pressure. Engineers should consider stress-relief heat treatment or post-weld bending to mitigate these effects in critical applications.

Key Questions and Reflections

The paper raises an important question: to what extent does the initial stress from fabrication residual stresses and self-confinement actually alter the ultimate capacity compared to the idealized case? The authors' parametric analysis suggests that the initial stress influence coefficient is sensitive to the slenderness ratio and the confinement ratio, but the practical impact depends on the specific stress distribution pattern, which is rarely uniform in real components. This limitation highlights the need for experimental validation using instrumented specimens with strain gauges and pressure sensors at the steel-concrete interface.

Another reflection is the applicability of the unified strength theory to high-strength steel tubes (e.g., API 5L X100 or ASTM A500 Grade C) where the yield strength exceeds 500 MPa. At higher strength levels, the ductility of the steel tube decreases, and the confinement mechanism may become less effective due to reduced plastic deformation capacity. The unified solution should be extended to incorporate strain-hardening behavior and fracture mechanics considerations for these advanced materials.

Study Insights and Implications

This paper provides a rigorous theoretical foundation that bridges the gap between simplified design codes and the complex stress states encountered in real CFST columns. The unified solution's ability to account for initial stress, intermediate principal stress, and slenderness effects simultaneously makes it a valuable tool for advanced structural analysis. For engineers involved in steel pipe manufacturing and welding, the key takeaway is that the initial stress state is not merely a theoretical abstraction but a quantifiable factor that affects design capacity and should be considered in the fabrication quality control process. The proposed initial-stress influence coefficient offers a practical means of incorporating this factor into routine design calculations, and its parametric form allows for straightforward implementation in structural analysis software.