Constitutive Relationship of Steel Tube Concrete Under Axial Tension

Literature Overview

The paper by Pan Youguang and Zhong Shantong (1990), published in Industrial Construction (Vol. 20, No. 4, pp. 30-37), addresses a fundamental yet under-explored topic: the constitutive behavior of steel tube concrete (STC) members under axial tension. This work was supported by the National Natural Science Foundation of China and represents an early contribution to understanding the tensile response of composite steel tube concrete systems. The authors are affiliated with Harbin Institute of Architecture and Engineering (now Harbin University of Science and Technology).

Core Technical Content

The study employs the compatibility of deformation conditions to analyze the stress-strain behavior of STC members under axial tension. A central finding is that the core concrete imposes a radial constraint on the steel tube, which effectively raises the proportional limit and yield point of the steel tube. Within the commonly used range of STC configurations, the yield point is enhanced by approximately 10%. This finding is counterintuitive from a purely steel tube perspective, because conventional understanding suggests that the steel tube alone governs the tensile response, with the concrete contributing negligibly to tensile capacity.

Fundamental Mechanics of Tensile Behavior

Under axial tension, the steel tube tends to contract radially due to the Poisson effect. The core concrete, being in a state of confinement, resists this radial contraction. This resistance manifests as a radial compressive stress on the steel tube wall, which effectively increases the axial stress required to reach yielding. The mechanism is analogous to the confinement effect observed under compression, but operates in reverse: under compression, the steel tube confines the concrete; under tension, the concrete confines the steel tube.

The authors analyzed the stress state in both the steel tube and the core concrete using equilibrium and compatibility conditions. The resulting constitutive model accounts for the interaction between the two materials and provides a more accurate prediction of the tensile response than a simple superposition of individual material responses.

Interpretation of Technical Points

The 10% Yield Point Enhancement

The reported enhancement of approximately 10% in the steel tube yield point is a significant finding with direct implications for design. In structural engineering practice, the tensile capacity of STC members is often conservatively estimated by considering only the steel tube cross-section, neglecting the contribution of the core concrete. This study demonstrates that such a simplification is overly conservative and that the composite action provides a measurable enhancement in tensile performance.

The magnitude of the enhancement depends on the relative stiffness of the steel tube and the core concrete, as well as the geometric parameters of the cross-section. For thin-walled tubes with a high concrete-to-steel area ratio, the enhancement may be more pronounced because the concrete provides greater radial resistance to the tube contraction.

Constitutive Model Development

The constitutive model developed by Pan and Zhong is based on the following key assumptions and steps:

The model captures the nonlinear interaction between the steel tube and the core concrete throughout the loading process. In the elastic range, the enhancement is modest because the radial stresses are relatively small. As the steel tube approaches yielding, the radial constraint from the concrete becomes more significant, leading to a progressive enhancement of the axial stress capacity.

Standards and Design Implications

The constitutive relationship established in this study has implications for the design of STC members subjected to tensile loading, which is common in cable-stayed bridges, tension members in long-span structures, and seismic-resistant structural systems where axial tension develops under lateral loading. Current design codes typically do not account for the composite tensile behavior of STC members and instead use simplified approaches that underestimate the tensile capacity.

For engineers practicing in accordance with standards such as GB 50017 or CECS 38, the findings of this study suggest that the tensile design provisions could be refined to incorporate the composite action between the steel tube and the core concrete. This would lead to more economical and accurate designs, particularly in applications where tensile capacity is a governing design criterion.

Engineering Practice Cases

In the design of cable-stayed bridge pylons using STC columns, the tensile capacity of the pylon under asymmetric loading is a critical design consideration. The composite tensile behavior characterized in this study can be used to evaluate the safety margin of existing pylon designs and to optimize the cross-sectional dimensions of new designs. Similarly, in the design of STC columns in seismic-resistant structures, the tensile response under cyclic loading is important for assessing the energy dissipation capacity and the post-yield behavior.

A practical consideration is the potential for concrete cracking under tensile loading. Once the concrete cracks, its ability to confine the steel tube is significantly reduced, and the tensile response may transition from a composite behavior to a predominantly steel-dominated behavior. The constitutive model should account for this transition, and engineers should consider the cracking threshold when assessing the tensile performance of STC members.

Key Questions and Reflections

A question that arises from this study is whether the 10% enhancement in yield point is conservative or optimistic for practical design purposes. The study was conducted in 1990, and the materials and testing techniques available at that time may have been less sophisticated than those available today. Modern testing techniques, including digital image correlation and fiber optic sensing, could provide more detailed measurements of the stress-strain distribution within the composite member and potentially refine the constitutive model.

Another reflection concerns the applicability of the model to different cross-sectional shapes. The study appears to focus on circular steel tubes, which are the most common configuration. However, square and rectangular tubes are also widely used in structural applications, and the radial constraint mechanism may differ for these shapes due to the presence of corners and flat faces. Future research should extend the constitutive model to non-circular cross-sections.

Study Insights and Implications

The work by Pan and Zhong is a foundational contribution to the understanding of STC tensile behavior. The demonstration that the core concrete enhances the steel tube yield point by approximately 10% challenges the conventional design assumption that the concrete contributes negligibly to tensile capacity. For engineers, this finding means that STC members may have a greater tensile safety margin than currently assumed in design, which can be leveraged for more efficient structural designs. The constitutive model developed in this study provides a theoretical basis for refining design codes and for conducting more accurate structural analyses of STC members under tensile loading. The key takeaway is that the composite action in STC members is a bidirectional phenomenon: under compression, the steel tube confines the concrete; under tension, the concrete confines the steel tube, and both mechanisms contribute to the overall structural performance.