Static Performance of Rectangular Steel Tube-Concrete Members Under Biaxial Eccentric Compression with Torsion

Literature Overview

This paper by Liu Jiepeng, Zhang Sumei, and Guo Lanhui from the School of Civil Engineering, Harbin Institute of Technology, published in the Journal of Harbin Institute of Technology (2006, Vol. 38, Issue 5), investigates the static behavior of rectangular steel tube-confined concrete (STC) members subjected to biaxial eccentric compression, with particular attention to the torsion of the cross-sectional deformation axis. Supported by the National Natural Science Foundation of China (Grant 59808004) and the Heilongjiang Provincial Outstanding Youth Fund, the study develops a fiber-based computational model that accounts for cross-sectional deformation axis torsion and validates it against experimental data.

Core Technical Content

The research addresses a fundamental gap in the understanding of STC member behavior under combined biaxial eccentric loading. Under uniaxial eccentric compression, the deformation axis of a cross-section typically aligns with the load eccentricity direction. However, under biaxial eccentric loading, the interaction between the two eccentricity components can induce torsion of the deformation axis—a phenomenon that significantly affects load-bearing capacity but is not adequately captured by conventional design codes.

Fiber Model Methodology

The authors establish a computational method based on the fiber model approach, in which the cross-section is discretized into numerous small elements (fibers), each assigned appropriate stress-strain constitutive relationships for concrete, steel tube, and the interface. The key innovation is the incorporation of cross-sectional deformation axis torsion into the equilibrium and compatibility equations. The nonlinear analysis program, designated RA, solves the resulting system of equations iteratively to determine the load-deformation response and ultimate capacity.

The constitutive models used for the constituent materials follow established approaches:

Influence of Biaxial Eccentric Loading on Axial Capacity

The study demonstrates that biaxial eccentric loading significantly reduces the axial load-bearing capacity of rectangular STC members. This reduction is attributed to the torsion of the cross-sectional deformation axis, which creates non-uniform stress distributions that do not align with the applied load directions. The torsion effect is more pronounced in rectangular sections compared to circular sections because the geometric asymmetry amplifies the coupling between bending in the two principal directions.

The comparison with design codes reveals important discrepancies:

• Eurocode 4 (EN 1994-1-1): Overestimates the axial capacity (Nu) of biaxial eccentrically loaded rectangular STC members.
• Chinese Code (GB 50017 or relevant standard): Also overestimates Nu, though the degree of overestimation may differ from Eurocode 4.

This finding has significant implications for the safety and economy of STC member design under biaxial loading conditions. Designers relying solely on code provisions without considering deformation axis torsion may produce unsafe designs for members subjected to combined eccentricities.

Validation Against Experimental Results

The program RA produces results that show good agreement with experimental data, confirming the validity of the fiber model approach with deformation axis torsion. The agreement in both load-displacement curves and failure modes indicates that the model captures the essential mechanics of the problem.

Standards and Code Analysis

The overestimation of axial capacity by both Eurocode 4 and the Chinese code highlights a limitation in current design methodologies for STC members under biaxial eccentric loading. The codes typically employ interaction curves or simplified interaction equations that assume the deformation axis remains aligned with the load eccentricity direction, neglecting the torsion effect.

For engineers practicing in regions governed by these codes, the following recommendations emerge:

1. For members subjected to significant biaxial eccentricities, apply a reduction factor to the code-predicted axial capacity, or use the fiber model approach for detailed analysis.
2. The torsion effect is most critical for rectangular sections with high aspect ratios and for members with relatively thin steel tubes relative to the concrete core.
3. In seismic design, where biaxial loading is inherent due to the three-dimensional nature of earthquake response, the torsion effect should be explicitly considered.

Engineering Practice Integration

In practical engineering, biaxial eccentric loading occurs frequently in STC columns supporting eccentric beams, at frame joints with moment transfer in two directions, and in columns subjected to combined vertical and lateral loads. The study's findings suggest that current design practices may be non-conservative for such members.

A practical approach for engineers would be:

• For preliminary design, use code provisions but apply a cautionary reduction factor (e.g., 10%–20%) to the biaxial interaction capacity.
• For final design of critical members, perform detailed fiber-based nonlinear analysis incorporating deformation axis torsion.
• For research and development of new structural systems, adopt the RA program or equivalent tools to generate design charts that account for torsion effects.

Key Questions and Reflections

Several questions remain open. First, the study focuses on static loading; the behavior under cyclic or dynamic loading, where deformation axis torsion may evolve differently, requires further investigation. Second, the model assumes a specific constitutive behavior for the concrete-steel interface; the sensitivity of results to interface modeling assumptions should be explored. Third, the applicability of the findings to circular STC members, which exhibit different geometric symmetry characteristics, warrants separate study.

The study also raises the question of whether the observed torsion effect can be mitigated through design modifications, such as adding internal stiffeners or adjusting the steel tube geometry to reduce geometric asymmetry.

Study Insights and Implications

This research makes a significant contribution to the understanding of STC member behavior under biaxial eccentric loading. The demonstration that deformation axis torsion substantially reduces axial capacity and that current codes overestimate this capacity is a critical finding that should inform future code revisions. For practicing engineers, the study provides both a theoretical framework and a computational tool for more accurate assessment of STC members under complex loading conditions.

The practical implication is clear: engineers designing rectangular STC members for biaxially eccentric loading must move beyond simple code-based interaction checks and adopt more sophisticated analysis methods that capture the torsion of the deformation axis. This is particularly important for seismic design, where the three-dimensional loading state is unavoidable and the consequences of underestimating deformation demands can be catastrophic.