Zhuojin Pipe Fitting Co., LtdEarthquake Damage Assessment of Circular Steel Tube Members Based on Modified Park-Ang Model
Literature Overview
This paper by Liu Xiang, Zhu Nanhai, and Chen Lujun from Jiangxi University of Science and Technology, published in Chinese Journal of Computational Mechanics (2022, Vol. 39, No. 6, pp. 737-745), presents a modified Park-Ang damage model for circular steel tube members subjected to seismic loading. The research is supported by the National Natural Science Foundation of China (51768024), the Jiangxi Provincial Natural Science Foundation (20181BAB206039), and the Jiangxi University of Science and Technology Young Talent Support Program (JXUSTQJYX2018009).
Core Technical Framework
The Park-Ang damage model is a widely used cumulative damage model for seismic assessment, originally expressed as:
D = (delta / delta_u) + beta (integral of dE_p) / (f_y delta_u)
where D is the damage index, delta is the maximum displacement, delta_u is the ultimate displacement, beta is the model combination coefficient, E_p is the plastic energy dissipated, and f_y is the yield strength.
The modification for circular steel tube members involves:
| Parameter | Original Park-Ang | Modified for Circular Steel Tube |
|---|---|---|
| Ultimate displacement | Material-dependent | Derived from skeleton curve |
| Combination coefficient beta | Constant | Function of axial ratio, slenderness ratio, and diameter-to-thickness ratio |
| Damage limits | Generic values | 0.02, 0.41, 1.00 |
| Energy dissipation | Bilinear assumption | Skeleton curve-based |
The key innovation is the derivation of the combination coefficient as a function of the member's geometric and loading parameters, rather than treating it as a constant. This is achieved through back-calculation of the damage factor at the failure point (where D = 1.0) and curve fitting to establish the relationship with the governing parameters.
Damage Classification Criteria
The modified model establishes four damage levels with corresponding damage factor limits:
| Damage Level | Damage Factor Range | Description |
|---|---|---|
| Basically intact | 0.00 - 0.02 | No visible damage, elastic behavior |
| Slight to moderate damage | 0.02 - 0.41 | Local yielding, minor deformation |
| Severe damage | 0.41 - 1.00 | Significant plastic deformation, buckling |
| Failure | 1.00 | Collapse, loss of load-bearing capacity |
The convergence of the damage factor to 1.0 at ultimate failure with low dispersion validates the modified model's accuracy. The damage factor of 0.41 as the boundary between moderate and severe damage is a practical threshold for post-earthquake assessment decisions.
Parameter Relationships and Engineering Application
The combination coefficient beta is expressed as a function of:
- Axial compression ratio: Higher axial ratios reduce the damage capacity, requiring a larger beta to account for the reduced energy dissipation capacity.
- Slenderness ratio: Slender members are more susceptible to buckling, which reduces the effective plastic deformation capacity and requires adjustment of beta.
- Diameter-to-thickness ratio: Thin-walled tubes with higher D/t ratios are more prone to local buckling, which limits the plastic deformation range and affects the damage accumulation rate.
For engineering practice, the following implications emerge:
- Post-earthquake damage assessment of circular steel tube members can be performed using the modified Park-Ang model with the established damage factor limits.
- The combination coefficient should be calculated from the member's specific parameters rather than using generic values, as the parameter-dependent relationship significantly affects the accuracy of damage estimation.
- The damage factor of 0.41 serves as a practical threshold for determining whether a member requires repair or replacement. Members with damage factors above 0.41 should be considered for replacement due to the risk of insufficient residual capacity.
- The model is particularly applicable to thin-walled circular steel tubes, where the damage accumulation is dominated by local buckling and plastic deformation at the cross-section level.
Key Questions and Reflections
A significant question is the applicability of the modified model to thick-walled steel tubes or steel tubes with internal concrete infill, where the damage mechanisms differ substantially. The model is developed for empty thin-walled circular steel tubes, and the confinement effect of concrete or the increased buckling resistance of thick-walled tubes would alter the damage accumulation behavior. Additionally, the model does not account for the effect of loading direction or the interaction between local buckling and global buckling, which are important considerations for complex structural systems.
Summary
This study provides a practical and validated modified Park-Ang damage model for circular steel tube members, with damage factor limits of 0.02, 0.41, and 1.00 for damage classification. The parameter-dependent combination coefficient, derived from axial compression ratio, slenderness ratio, and diameter-to-thickness ratio, represents a significant improvement over the conventional constant-coefficient approach. For steel tube engineers, the model provides a quantitative tool for post-earthquake assessment, enabling data-driven decisions on repair versus replacement. The convergence of damage factors to 1.0 at failure with low dispersion confirms the model's reliability for practical application in seismic damage assessment of circular steel tube structures.