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

Literature Overview

The paper by Zha Xiaoxiong, Zhong Shantong, and Tang Jiaxiang, published in the Chinese Journal of Computational Mechanics (1999, Vol. 16, No. 1, pp. 52–57), presents a nonlinear finite element analysis of steel tube concrete (STC) members subjected to combined compression, bending, and torsion with initial stresses. The authors, affiliated with Huazhong University of Science and Technology and Harbin University of Architecture, address a practically important problem: the presence of initial stresses in the steel tube due to fabrication tolerances, welding residual stresses, and construction-induced deformations significantly affects the load-bearing behavior of STC members in large-span bridges and high-rise buildings.

Significance of Initial Stress in Steel Tube Concrete

Initial stresses in the steel tube of STC members arise from multiple sources:

• Welding residual stresses: Longitudinal and hoop residual stresses develop during the welding of longitudinal seams in welded tubes, or during the welding of end connections. These stresses can reach values approaching the yield strength of the steel.
• Cold-forming residual stresses: For cold-formed steel tubes, the plastic deformation during bending introduces residual stresses that affect the post-buckling behavior.
• Geometric imperfections: Out-of-roundness, ovality, and flatness deviations in the steel tube introduce initial bending moments and torsional moments that are equivalent to initial stresses.
• Construction-induced stresses: Pre-stressing, erection stresses, and differential settlement can introduce initial stresses in the completed structure.

The presence of initial stresses reduces the effective cross-sectional area available to resist applied loads and can trigger premature local buckling. In STC members, the interaction between the initial stress in the steel tube and the confining action on the concrete core creates a complex nonlinear problem that requires careful numerical modeling.

Finite Element Model Development

The authors developed a nonlinear finite element program based on two key constitutive models:

1. Steel constitutive model: A kinematic hardening model was adopted to capture the Bauschinger effect, which is important for members subjected to cyclic or reversed loading. The kinematic hardening law describes the evolution of the yield surface in stress space as plastic deformation accumulates, accounting for the shift in the yield point upon load reversal.
2. Concrete constitutive model: A boundary-based model was used to describe the behavior of confined concrete, accounting for the confinement effect of the steel tube on the concrete core. The model captures the triaxial stress state of the concrete and the nonlinear stress-strain relationship under confinement.

The finite element mesh was designed to capture the nonlinear behavior at critical locations, including the steel-concrete interface, potential buckling zones, and regions of high stress concentration. The solution algorithm employed an incremental-iterative approach to handle the geometric and material nonlinearities inherent in the problem.

Key Results and Findings

The analysis revealed several important findings:

• Initial stress sensitivity: The presence of initial stresses can reduce the ultimate load capacity of STC members by 10–25%, depending on the magnitude and distribution of the initial stress field.
• Failure mode transition: Higher initial stresses promote a transition from global buckling to local buckling failure mode, which is less ductile and more sudden.
• Confinement effectiveness: The confining effect of the steel tube on the concrete core is partially compromised by initial stresses in the tube, as the tube's ability to resist outward expansion of the concrete is reduced.
• Computational efficiency: The proposed constitutive models and solution algorithm achieved significant savings in computational time compared to conventional approaches, while maintaining acceptable accuracy.

Implications for Steel Tube Fabrication and Welding Quality

From a metallurgical and welding engineering perspective, this paper highlights the critical importance of controlling welding residual stresses in steel tubes used for STC structures. Welding residual stresses in the longitudinal seam of welded tubes can be reduced through several methods:

• Stress-relief welding: Adding a stress-relief weld along the length of the seam to redistribute residual stresses.
• Post-weld heat treatment: Normalizing or stress-relieving the tube after welding to reduce residual stresses below 50% of the yield strength.
• Controlled welding sequences: Using multi-pass welding with controlled heat input to minimize residual stress magnitudes.
• Shot peening or mechanical vibration stress relief: Applying compressive surface stresses to counteract tensile residual stresses.

The welding procedure specification (WPS) for tubes intended for STC applications should include provisions for residual stress control, with verification through magnetic stress measurement or X-ray diffraction methods.

Study Insights and Reflections

This paper is a pioneering contribution to the numerical analysis of STC members that accounts for initial stresses, a factor that is often neglected in design codes but is critical in practice. The authors' choice of kinematic hardening for steel and boundary-based modeling for concrete reflects a deep understanding of the underlying material behavior. For practicing engineers, the key message is that the fabrication quality of steel tubes—particularly the residual stress state—has a measurable impact on the structural performance of STC members. This insight should inform welding procedure qualification, non-destructive testing requirements, and acceptance criteria for tubes used in critical STC applications such as bridge decks and high-rise building columns.