Simplified Seismic Analysis Method for Steel Pipe Concrete Lattice Girder Bridges under Rare Earthquakes

Literature Overview

This paper by Ou Zhijing, Lin Jianmao, Xie Mingqin, and Wang Jinze from Fujian University of Technology and Fujian Transportation Research Institute Co., Ltd., published in Earthquake Resistance Engineering and Retrofitting in 2021 (Vol. 43, No. 1, pp. 132-139), presents a simplified seismic analysis method for steel pipe concrete lattice girder bridges under rare earthquakes. The study was supported by the National Natural Science Foundation of China (Grant No. 51408128), Fujian Provincial Natural Science Foundation (Grant No. 2017J01471), and Fujian Provincial University New Century Outstanding Talent Support Program (Grant No. GY-Z15108). The research is based on the engineering background of the Ganhaizi Special Bridge.

Core Viewpoints and Technical Approach

The study addresses the challenge of seismic analysis of steel pipe concrete lattice girder bridges, which are increasingly used in modern bridge engineering due to their high strength, lightweight, and aesthetic advantages. The authors established a finite element model of the bridge using Midas Civil software and conducted time-history analyses under rare earthquake conditions using both elastic and elastic-plastic methods.

The key findings are as follows:

Development of the Equivalent Elastic Method

The authors proposed an "equivalent elastic method" for simplified seismic analysis of steel pipe concrete lattice girder bridges under rare earthquakes. This method achieves results that are in good agreement with the more computationally intensive elastic-plastic fiber element method, while significantly improving computational efficiency. The method was validated against multiple earthquake waves, different seismic intensity levels, and various peak ground acceleration values, demonstrating its robustness and reliability across a range of seismic scenarios.

The equivalent elastic method works by calibrating the elastic stiffness and damping properties of the bridge model to reproduce the key seismic response characteristics observed in the elastic-plastic analysis. This allows engineers to perform rapid seismic assessments using standard linear analysis tools, without the need for non-linear finite element analysis software or specialized expertise in fiber element modeling.

Interpretation of Technical Points

Fiber Element Method as Benchmark

The fiber element method used as the benchmark in this study is a well-established approach for non-linear seismic analysis of reinforced and prestressed concrete members. In the fiber element formulation, the cross-section of each structural member is discretized into multiple fibers, each of which follows its own constitutive stress-strain relationship. This allows the method to capture the non-linear behavior of the steel pipe concrete members, including the yielding of the steel pipe, the crushing of the concrete core, and the interaction between the steel and concrete components.

The agreement between the elastic and elastic-plastic methods in terms of displacement and bending moment response mode shapes is an important finding. It indicates that for steel pipe concrete lattice girder bridges, the elastic mode shapes are a reasonable approximation of the elastic-plastic mode shapes, at least for the fundamental modes that govern the seismic response. This is the basis for the validity of the equivalent elastic method.

Validation Across Multiple Scenarios

The validation of the equivalent elastic method against multiple earthquake waves, seismic intensity levels, and peak ground acceleration values is a critical aspect of the study. Seismic response is highly sensitive to the characteristics of the input ground motion, and a simplified method that is only valid for a single earthquake or intensity level would have limited practical value. The fact that the method performs well across a range of scenarios demonstrates that it captures the essential physics of the seismic response, rather than merely fitting to a specific case.

Implications for Bridge Design Codes

The development of a validated simplified seismic analysis method for steel pipe concrete lattice girder bridges has direct implications for bridge design codes and standards. Currently, many bridge design codes do not provide specific provisions for the seismic design of steel pipe concrete structures, and engineers often resort to detailed non-linear analysis for seismic assessment. The equivalent elastic method provides a practical alternative that can be incorporated into design codes as a simplified procedure for seismic analysis of these structures.

Integration with Engineering Practice

The equivalent elastic method is particularly valuable for the preliminary design and screening of steel pipe concrete lattice girder bridges. In the early stages of design, when multiple bridge configurations are being evaluated, the ability to perform rapid seismic assessments using standard linear analysis tools can significantly accelerate the design process and reduce engineering costs.

For detailed design and code compliance, the equivalent elastic method can be used as a verification tool to check the results of more detailed non-linear analysis. If the simplified and detailed methods agree, the detailed analysis can be confirmed as reliable. If there are significant discrepancies, the detailed analysis should be reviewed for modeling errors or inappropriate assumptions.

The method is also useful for seismic retrofitting assessments of existing steel pipe concrete bridges. Engineers can use the equivalent elastic method to rapidly evaluate the seismic performance of existing bridges and identify those that require retrofitting, without the need for detailed non-linear analysis of every bridge in the inventory.

Key Questions and Reflections

One important question is the range of applicability of the equivalent elastic method. The method was developed and validated for steel pipe concrete lattice girder bridges, but whether it can be extended to other types of steel pipe concrete structures, such as solid web columns, box girders, or shear walls, is not addressed in the study. The lattice configuration, with its relatively slender members and open cross-section, may have specific characteristics that make the elastic approximation more valid than for other structural configurations.

Another consideration is the effect of geometric non-linearity on the seismic response. For tall lattice bridges, geometric non-linearity (P-delta effects) can be significant, and the equivalent elastic method should be evaluated for its ability to capture these effects. If geometric non-linearity is important, the method may need to be supplemented with geometric stiffness considerations.

Study Insights and Implications

This paper provides a practical and validated simplified seismic analysis method for steel pipe concrete lattice girder bridges under rare earthquakes. The equivalent elastic method achieves good agreement with the detailed fiber element method while significantly improving computational efficiency, making it suitable for routine engineering practice. The study contributes to the development of design standards for steel pipe concrete bridges by providing a simplified procedure that can be incorporated into seismic design codes. For practicing bridge engineers, the method offers a practical tool for seismic assessment that balances accuracy with efficiency, and can be readily applied using standard analysis software without specialized training in non-linear analysis.