Nonlinear Finite Element Analysis of Steel Tube Concrete Members Under Combined Compression Bending and Torsion with Initial Stress

Overview and Research Significance

The paper by Zha Xiaoxiong, Zhong Shantong, and Tang Jiaxiang, published in 1999 in the Journal of Computational Mechanics, addresses a critical and complex engineering problem: the nonlinear behavior of steel tube concrete (STC) members subjected to combined compression, bending, and torsion, particularly when initial stresses are present in the steel tube. This research is directly relevant to the design of STC structures in large-span bridges and super-tall buildings, where initial stresses arise from construction sequencing, thermal effects, prestressing operations, and residual stresses from manufacturing.

The inclusion of initial stress in the analysis is a significant advancement over earlier studies that assumed stress-free initial conditions. In practice, STC members are rarely stress-free at the time of service loading. The steel tube may carry residual stresses from cold-forming or welding, and the concrete core may have shrinkage and creep-induced stresses that develop during the curing period before structural loading is applied.

Theoretical Framework and Constitutive Models

The nonlinear finite element (FE) analysis presented in this paper is built upon two key constitutive models: the steel kinematic hardening model and the concrete interface boundary model. These models capture the essential nonlinear behavior of the STC member under complex loading conditions.

Steel Kinematic Hardening Model

The kinematic hardening model describes the evolution of the yield surface in stress space as plastic deformation accumulates. For steel tubes under combined loading, the yield surface translates in the direction of the plastic strain increment, capturing the Bauschinger effect where the yield strength in tension decreases after prior compression, and vice versa. The key parameters of the kinematic hardening model include:

The kinematic hardening model is particularly important for cyclic loading applications, such as seismic loading of STC members, where the Bauschinger effect significantly influences the energy dissipation capacity and cumulative damage accumulation.

Concrete Interface Boundary model

The concrete interface boundary model describes the mechanical interaction between the steel tube and the concrete core. This model captures the following phenomena:

• Bond-slip behavior: The relative slip between the steel tube inner surface and the concrete core surface, which develops progressively under increasing load.
• Confinement pressure: The radial pressure exerted by the steel tube on the concrete core, which increases as the concrete undergoes lateral expansion under axial compression.
• Interface cracking: The initiation and propagation of cracks at the steel-concrete interface, particularly under torsional and bending loads.
• Frictional sliding: The frictional resistance at the interface when relative slip occurs, which depends on the normal contact pressure and the friction coefficient.

Finite Element Model and Solution Methodology

The FE program developed in this study incorporates several distinctive features that improve computational efficiency while maintaining accuracy:

1. Element formulation: The steel tube is modeled using shell elements with kinematic hardening material properties, while the concrete core is modeled using solid elements with a confinement-dependent constitutive law. The interface is modeled using contact elements with frictional and bond-slip capabilities.
2. Initial stress incorporation: The initial stress state is applied as a pre-stress load case before the service loading is applied. This is achieved through a two-stage analysis: first, the initial stress state is established through thermal loading, shrinkage simulation, or direct stress application; second, the service loads (compression, bending, torsion) are applied incrementally.
3. Nonlinear solution algorithm: The Newton-Raphson iterative method with arc-length control is employed to trace the complete load-displacement response curve, including the post-peak descending branch. The arc-length method is essential for capturing snap-through and snap-back behavior that may occur in STC members under combined loading.
4. Computational efficiency: The authors report that their formulation significantly reduces computation time compared to conventional approaches, likely through optimized element formulations, efficient contact algorithms, and adaptive mesh refinement.

Combined Loading Interaction Effects

The interaction between compression, bending, and torsion in STC members creates complex stress states that cannot be captured by simplified interaction diagrams. The key interaction effects identified in this research include:

• Compression-bending interaction: The axial compression reduces the bending capacity of the STC member, but the interaction is not linear due to the confinement effect that becomes more pronounced at higher compression levels.
• Torsion-bending interaction: Torsional shear stresses interact with bending-induced shear stresses through the von Mises yield criterion, reducing the combined shear capacity below the sum of individual capacities.
• Compression-torsion interaction: Axial compression increases the torsional capacity of the STC member through the confinement effect, which is more significant for higher compression levels.
• Initial stress effects: The presence of initial stresses in the steel tube shifts the yield surface and modifies the interaction between the three load components. Compressive initial stresses reduce the residual tensile capacity of the steel tube, while tensile initial stresses reduce the residual compressive capacity.

Engineering Applications and Design Implications

The research findings have direct implications for the design of STC structures in the following areas:

Large-Span Bridges

In large-span bridges, STC members are commonly used as piers, towers, and cross-beams. These members are subjected to combined compression from dead and live loads, bending from eccentric loading and wind, and torsion from asymmetric traffic loading and wind. The initial stress state arises from construction sequencing, thermal gradients during casting, and prestressing operations. The nonlinear FE analysis presented in this paper provides the basis for accurate capacity assessment under these complex loading conditions.

Super-Tall Buildings

In super-tall buildings, STC columns are subjected to large axial compressions from gravity loads, bending from wind and seismic lateral forces, and torsion from eccentric loading and torsional wind moments. The initial stress state includes construction stresses from the incremental construction process, thermal stresses from diurnal temperature variations, and residual stresses from the steel tube manufacturing process.

Study Insights and Critical Evaluation

This research represents a significant contribution to the computational analysis of STC members, particularly in its treatment of initial stresses and combined loading. The development of a dedicated nonlinear FE program that efficiently handles the complex material and geometric nonlinearities of STC members is a valuable tool for engineers who need to assess the behavior of these members under realistic loading conditions.

One important insight from this study is that the initial stress state can significantly influence the ultimate capacity and failure mode of STC members. Engineers who neglect initial stresses in their design analyses may overestimate the residual capacity of STC members, particularly under combined loading conditions. The kinematic hardening model is essential for capturing the Bauschinger effect, which is critical for seismic design where cyclic loading is the governing design condition.

The concrete interface boundary model is another key contribution, as it captures the bond-slip behavior that governs the load transfer between the steel tube and the concrete core. This model is particularly important for members subjected to torsional loading, where the interface shear stresses are high and bond-slip can significantly reduce the torsional capacity.

In conclusion, this research provides a rigorous computational framework for the analysis of STC members under realistic combined loading conditions with initial stresses. The nonlinear FE program developed in this study is a powerful tool for engineers designing STC structures in large-span bridges and super-tall buildings, where the interaction between compression, bending, and torsion, combined with the initial stress state, governs the structural performance. The emphasis on computational efficiency makes this approach practical for routine design applications, not just research purposes.