Axial Force-Strain Relationship of Steel Tube Concrete Arch Ribs

Literature Overview

Jiang Lei, Liu Yongjian, and Hou Beibei (2016), from the School of Highway, Chang'an University, published a study in the China Journal of Highway and Transport on the axial force-strain relationship of steel tube concrete (SRC) arch ribs. The research was supported by the National Natural Science Foundation of China (Grants 51178051 and 51378068), the Ministry of Transport Construction Science and Technology Program (2013 318 812 410), and the Shaanxi Provincial Department of Transportation (13-26K). The paper addresses a fundamental challenge in bridge engineering: accurately determining the stress distribution between the steel tube and concrete core throughout the entire axial compression process of SRC arch ribs.

Theoretical Analysis and Derivation

Interaction Mechanism

The study begins with a theoretical analysis of the interaction mechanism between the steel tube and concrete core in SRC members. Based on the plane section assumption, the authors analyze the stress state changes of both the steel tube and concrete at different stages of axial compression. The core insight is that when composite action develops, both the steel tube and concrete are subjected to multiaxial stress states:

The core concrete experiences triaxial compression, which increases its longitudinal stress capacity.
The steel tube experiences biaxial stress, which reduces its longitudinal stress capacity due to the Poisson effect and the lateral confining pressure it exerts on the concrete.

Derivation of Axial Force-Strain Expressions

Using the mechanical equilibrium relationship, the authors derive calculation expressions for the longitudinal stress-strain behavior of both the steel tube and concrete, and subsequently obtain their respective axial force-strain relationships. The derivation accounts for:

The elastic stage, where both materials deform proportionally.
The transition stage, where concrete cracking and steel yielding begin.
The plastic stage, where significant interaction forces develop between the two materials.

Validation and Results

Comparison with Experimental Data

The proposed formulas were validated against two datasets:

Validation Dataset	Number of Specimens	Comparison Metric	Result
Ultimate load capacity of SRC short columns	425	Mean ratio of calculated to experimental	0.969
Ultimate load capacity of SRC short columns	425	Standard deviation	0.140
Ultimate load capacity of SRC short columns	425	Coefficient of variation	0.144
Load-strain curves of SRC short columns	7	Curve shape comparison	Good agreement

The mean ratio of 0.969 indicates that the proposed formula slightly underestimates the ultimate load capacity, which is a conservative bias favorable for engineering design. The coefficient of variation of 0.144 demonstrates good consistency across the extensive dataset.

Comparison with Dual-Element Model

A critical finding emerges when comparing the proposed formula with a dual-element model commonly used in finite element analysis. During the elastic stage, both approaches yield consistent results. However, upon entering the plastic stage, the dual-element model continues to allocate axial force between the steel tube and concrete based solely on stiffness ratios, which overestimates the load-carrying capacity of the steel tube. This leads to results that are unsafe (non-conservative), whereas the proposed formula provides more accurate predictions.

Engineering Practice Significance

Implications for Arch Bridge Design

For SRC arch rib bridges, accurate determination of the axial force distribution between the steel tube and concrete is essential for:

Designing the steel tube thickness and material grade.
Specifying the concrete strength and mix design.
Assessing the structural capacity under extreme loading conditions.
Evaluating the long-term performance under sustained loads.

The proposed method provides a more reliable basis for these design decisions compared to conventional approaches that neglect the interaction effects in the plastic range.

Practical Recommendations

Design Aspect	Recommendation
Elastic stage analysis	Either the proposed formula or dual-element model may be used
Plastic stage analysis	The proposed formula should be preferred for accuracy
Ultimate capacity assessment	The proposed formula provides conservative estimates suitable for design
Interaction effects	Must be considered in plastic analysis to avoid unsafe results

Study Insights and Reflections

This paper addresses a fundamental gap in the analytical treatment of SRC members. The conventional dual-element model, while convenient for finite element implementation, fails to capture the true interaction behavior in the plastic range. The proposed analytical approach, based on rigorous mechanical equilibrium and the plane section assumption, provides a more physically realistic representation of the composite behavior.

The finding that the dual-element model overestimates the steel tube's contribution in the plastic stage has important implications for the safety of existing SRC arch bridges. Engineers should be aware that conventional analysis methods may not adequately capture the actual stress redistribution that occurs as the structure enters the plastic range. This is particularly relevant for seismic design, where structures are expected to undergo significant inelastic deformation.

Summary

The study provides a rigorous analytical framework for determining the axial force-strain relationship in SRC arch ribs, validated against extensive experimental data. The proposed formula demonstrates good accuracy with a conservative bias, making it suitable for engineering design. The critical finding regarding the inadequacy of the dual-element model in the plastic stage should be noted by all engineers involved in SRC bridge design and assessment. The work represents a significant contribution to the theoretical understanding of SRC composite action and provides practical tools for more reliable structural analysis.