Finite Element Analysis of Initial Stress Effects on Steel Tube Concrete Axially Compressed Members

Overview of the Study

This foundational 1997 paper by Zha Xiaoxiong and Zhong Shantong of Harbin University of Architecture represents one of the earliest theoretical investigations into the effect of initial (residual) stresses in the steel tube on the compressive behavior of steel tube concrete (CFT) members. The authors treated the CFT member as a composite material and used the finite element method (FEM) to analyze, for the first time from a theoretical perspective, how initial stresses in the steel tube affect the combined mechanical performance indicators and the ultimate load-bearing capacity of axially compressed CFT members. The theoretical results were validated through a series of comparative tests on axially compressed members with and without initial stresses. This research is particularly significant because it was conducted at a time when CFT structures were gaining widespread adoption in China, and the understanding of residual stress effects was still in its infancy.

Technical Background and Significance

Initial Stresses in Steel Tubes

Initial stresses (also called residual stresses or pre-stresses) in steel tubes can arise from multiple sources:

1. Manufacturing processes: Hot rolling, cold drawing, welding, and forming introduce plastic deformation and subsequent elastic recovery, creating residual stress fields.
2. Welding: The thermal cycles during welding create localized plastic deformation and residual stresses, particularly at the weld seam and heat-affected zone (HAZ).
3. Cooling and contraction: Differential cooling rates between the outer and inner surfaces of the tube wall create through-thickness residual stresses.
4. Strain hardening and work hardening: Plastic deformation during manufacturing increases the yield strength locally, creating a non-uniform stress-strain state.

These initial stresses are self-equilibrating (the net force and moment on any cross-section is zero) but they significantly affect the stress distribution under external loading.

Composite Material Approach

The authors' approach of treating CFT as a composite material is a key methodological contribution. In this approach:

• The steel tube and concrete core are considered as two distinct but bonded material phases.
• The composite behavior is analyzed using micromechanics principles, where the overall response is derived from the individual material responses and their interaction.
• The initial stress field in the steel tube is treated as an initial condition that modifies the stress-strain relationship of the composite.

This approach allows for a more rigorous analysis than the traditional strut-and-tie or simplified interaction model approaches, which often neglect the detailed stress distribution within the composite section.

Finite Element Methodology

Model Description

The FEM model incorporated the following key features:

• Geometry: CFT column with circular or square steel tube and concrete core, loaded axially at both ends.
• Material models:
• Steel tube: Elastic-plastic material with initial stress field imposed as a body force or initial condition.
• Concrete: Elastic-plastic material with confinement-dependent strength and ductility (the steel tube provides lateral confinement to the concrete).
• Boundary conditions: Axial compression applied through end plates, with appropriate constraints to simulate realistic end conditions (pinned, fixed, or partially restrained).
• Mesh: Appropriate element density to capture the stress gradients, particularly near the steel-concrete interface and at the end plates.

Analysis Cases

The study compared two sets of cases:

1. With initial stress: The steel tube has a residual stress field (typically tensile on the outer surface and compressive on the inner surface, or vice versa, depending on the manufacturing process).
2. Without initial stress: The steel tube is stress-free, representing an idealized condition.

Key Results

The results consistently show that initial stresses in the steel tube have a detrimental effect on the compressive performance of CFT members. The reduction in ultimate capacity is attributed to the following mechanisms:

1. Premature yielding: The initial tensile stresses in the steel tube reduce the additional stress that can be applied before yielding occurs. This means the steel tube yields at a lower external load than a stress-free tube.
2. Reduced confinement: Once the steel tube yields, its ability to provide lateral confinement to the concrete core is reduced. The confined concrete, which typically has enhanced strength and ductility compared to unconfined concrete, loses some of its confinement benefit.
3. Accelerated local buckling: The initial stress field, particularly if it includes compressive stresses in certain regions of the tube wall, can accelerate the onset of local buckling. Local buckling of the steel tube is a critical failure mode for CFT columns, especially those with relatively thin walls.
4. Non-uniform stress distribution: The initial stress field creates a non-uniform stress state that can lead to premature failure at specific locations (e.g., the outer surface of the tube) before the full cross-section capacity is mobilized.

Validation Through Experimental Testing

The authors conducted comparative tests on axially compressed CFT members with and without initial stresses to validate the FEM predictions. The experimental setup likely included:

• Specimens: CFT columns with identical geometry and material properties, but with controlled introduction of initial stresses (e.g., through controlled plastic deformation of the steel tube before concrete filling).
• Loading: Axial compression applied monotonically to failure.
• Instrumentation: Strain gauges on the steel tube surface, load cells, and displacement transducers to measure the load-deformation behavior.
• Comparison: The experimental results were compared with the FEM predictions to assess the accuracy of the model.

The experimental validation confirmed the FEM predictions, demonstrating that the theoretical model accurately captures the effect of initial stresses on CFT member behavior. This validation is important because it establishes confidence in using the FEM approach for design purposes.

Engineering Practice Implications

Design Considerations

1. Residual stress assessment: Engineers designing CFT structures should assess the residual stress levels in the steel tubes used. This can be done through:

• X-ray diffraction (XRD) residual stress measurement
• Hole drilling method
• Neutron diffraction (for deeper penetration)
• Process simulation (FEM analysis of the manufacturing process)

1. Stress relief treatment: If residual stresses are found to be significant, stress relief heat treatment should be applied before concrete filling. Typical parameters:

• Temperature: 550–650°C
• Soak time: 1 hour per 25 mm of wall thickness
• Cooling: Furnace cool or controlled air cool

1. Design safety factors: If residual stresses