Zhuojin Pipe Fitting Co., LtdAxial Force-Strain Relationship of Steel Tube Concrete Arch Ribs
Literature Overview
This paper by Jiang Lei, Liu Yongjian, and Hou Beibei from Chang'an University, published in the China Journal of Highway and Transport in 2016, presents a theoretical and analytical framework for determining the axial force-strain relationship of steel tube concrete (SRC) arch ribs under axial compression. The research was supported by multiple funding sources including the National Natural Science Foundation of China (51178051, 51378068), the Ministry of Transport Construction Science and Technology Project (2013 318 812 410), and the Shaanxi Provincial Department of Transportation Science Research Project (13-26K). The study addresses a fundamental question in bridge engineering: how do the steel tube and concrete core share axial loads throughout the entire loading history of an SRC arch rib, and how does this load sharing affect the ultimate bearing capacity and structural safety.
Theoretical Framework and Assumptions
The authors adopt the plane section assumption (Bernoulli's hypothesis) and analyse the stress state of both the steel tube and the concrete core at different stages of axial compression. The key theoretical contributions include:
- Derivation of longitudinal stress-strain expressions for both the steel tube and the concrete core based on mechanical equilibrium.
- Accounting for the composite action mechanism where the steel tube and concrete interact through radial pressure.
- Development of axial force-strain relationships for each component individually.
The fundamental assumption is that under axial compression, the steel tube and concrete core deform together (compatible deformation), but the internal stress distribution is not simply proportional to stiffness as assumed in simple composite models. Instead, the interaction between the steel tube and concrete creates a multi-axial stress state that modifies the longitudinal stress-strain behaviour of each component.
Composite Action Mechanism
The study reveals important insights into the composite action mechanism of SRC arch ribs:
| Component | Stress State Under Composite Action | Effect on Longitudinal Stress |
|---|---|---|
| Concrete core (central region) | Triaxial compression | Longitudinal stress increases |
| Steel tube | Biaxial stress (hoop + longitudinal) | Longitudinal stress decreases |
This is a critical finding. When composite action is fully developed, the concrete core is confined by the steel tube, resulting in a triaxial compressive stress state that enhances the longitudinal strength of the concrete. Simultaneously, the steel tube experiences hoop tension from the expanding concrete core, which reduces its longitudinal stress capacity due to the interaction between hoop and longitudinal stresses (von Mises or Tresca yield criterion). This load redistribution means that the steel tube carries less longitudinal load than a simple stiffness-proportional model would predict, while the concrete carries more.
Validation and Accuracy Assessment
The authors validated their proposed calculation formula against two datasets:
- Ultimate bearing capacity comparison: 425 SRC short column ultimate bearing capacity test results were compared with the proposed formula predictions.
- Load-strain curve comparison: 7 short column load-strain test results were compared with the proposed formula predictions.
- Arch rib analysis: A parabolic pure compression arch under uniformly distributed load was analysed using both the proposed formula and a dual-element model, comparing results in both elastic and plastic stages.
The accuracy metrics for the ultimate bearing capacity comparison are summarised below:
| Metric | Value |
|---|---|
| Mean ratio (calculated/test) | 0.969 |
| Standard deviation | 0.140 |
| Coefficient of variation | 0.144 |
A mean ratio of 0.969 indicates that the formula is slightly conservative (on the safe side), with a coefficient of variation of 0.144 indicating reasonable scatter. The load-strain curves predicted by the formula showed good agreement with experimental curves.
Comparison with Dual-Element Model
A particularly important finding is the comparison between the proposed formula and the dual-element model (which treats the steel tube and concrete as two separate elements sharing load proportionally to stiffness). The comparison revealed:
- In the elastic stage, both the proposed formula and the dual-element model produce consistent results, as composite action has not yet developed significantly.
- In the plastic stage, the dual-element model continues to allocate axial forces according to stiffness ratio, which overestimates the load carried by the steel tube and underestimates the load carried by the concrete. This leads to unconservative (dangerous) results.
- The proposed formula, which accounts for composite action and multi-axial stress states, provides more accurate and conservative predictions in the plastic stage.
This finding has significant implications for the design of SRC arch ribs, as many arch ribs operate in the plastic range under service and ultimate loads. Using the dual-element model for plastic-stage analysis could lead to underestimation of the concrete contribution and overestimation of the steel tube contribution, potentially resulting in unsafe designs.
Engineering Practice Implications
For bridge engineers designing SRC arch ribs, the findings have several practical implications:
- The proposed axial force-strain relationship should be preferred over simple stiffness-proportional models when analysing SRC arch ribs in the plastic range.
- The composite action mechanism means that the concrete core carries more load than expected, which can be leveraged in design optimisation to potentially reduce steel tube wall thickness while maintaining safety.
- The conservative bias of the proposed formula (mean ratio 0.969) provides a built-in safety margin, which is desirable for structural design.
- Engineers should be cautious when using dual-element models for plastic-stage analysis of SRC structures, as they can produce unconservative results.
Key Questions and Reflections
The study's theoretical framework is based on the plane section assumption, which is valid for short columns but may not hold for slender arch ribs with significant shear deformation. Additionally, the study focuses on axial compression, but actual arch ribs are subjected to combined axial and bending loads, particularly near the haunches and springings. The extension of the proposed axial force-strain relationship to combined loading conditions would be a valuable next step. Furthermore, the study does not address the effect of concrete age, temperature, or long-term creep on the composite action mechanism, which are relevant for long-span bridge applications.
Summary
This paper provides a rigorous theoretical framework for understanding the load-sharing mechanism between steel tube and concrete core in SRC arch ribs under axial compression. The most significant finding is that composite action creates a multi-axial stress state that increases the concrete's longitudinal stress and decreases the steel tube's longitudinal stress, a phenomenon that is not captured by simple stiffness-proportional models. The proposed formula has been validated against a large dataset of 425 test results with good accuracy and conservative bias. Bridge engineers should adopt this framework for plastic-stage analysis of SRC arch ribs to avoid the unconservative results that can arise from dual-element models. The work represents an important advancement in the analytical design of SRC arch bridge structures.