Nonlinear Seismic Analysis of Steel Tube Concrete Arch Bridges with Cross Bracing

Literature Overview

This paper by Du Qian, Xia Xiushen, Chen Xingchong, and Sun Xuexian from Lanzhou Jiaotong University presents a nonlinear seismic analysis of steel tube concrete (STC) arch bridges incorporating cross bracing members. The study utilizes the OpenSees platform to establish a dynamic analysis finite element model, validated against the first five natural vibration periods obtained from a Midas Civil model. Incremental dynamic analysis (IDA) is conducted using a strong earthquake record to determine the yielding sequence of cross bracing members and to investigate the nonlinear development patterns of bracing elements in large-span STC arch bridges. The research is funded by the National Natural Science Foundation of China (51368033, 51668035) and the China Railway Corporation Science and Technology Research and Development Program (2015G002-B).

Core Technical Findings

Nonlinear Behavior of Cross Bracing

The incremental dynamic analysis reveals that cross bracing members near the 3/8 and 5/8 span locations of the arch rib are the first to yield under transverse strong earthquake excitation. This yielding sequence is critical for understanding the overall seismic response of the bridge, as the bracing members serve as the primary load transfer mechanism between the arch rib and the main girder system.

The study compares two constitutive models for the cross bracing members: linear elastic and bilinear. The bilinear model accounts for the plastic yielding and hardening behavior of the bracing members, providing a more realistic representation of the structural response under seismic loading.

Key Section Response Comparison

The following table presents the comparative results between linear elastic and bilinear constitutive models for critical cross-sections:

Critical Section	Linear Elastic Model	Bilinear Model	Change Trend
Arch foot	Large internal forces	Slightly reduced	Minimal change
1/4 arch rib	High internal forces	Reduced internal forces	Significant reduction
Arch crown	Maximum internal forces	Reduced internal forces and displacement	Progressive reduction with more yielding units

The results demonstrate that as more bracing units yield, the reduction in internal forces and displacements at the 1/4 arch rib section and arch crown becomes more pronounced. This indicates that the plastic yielding of bracing members provides an effective energy dissipation mechanism, redistributing forces away from critical sections.

Nonlinear Development Patterns

The nonlinear development of cross bracing follows a predictable pattern that can be utilized for seismic design optimization:

Initial yielding occurs at the 3/8 and 5/8 span locations, where the interaction between the arch rib and main girder generates the highest shear demands.
As seismic intensity increases, yielding propagates to adjacent bracing members, creating a distributed plastic hinge zone.
The arch crown and arch rib-main girder connection areas also experience yielding, but at higher seismic intensities than the 3/8 and 5/8 locations.
The progressive yielding of bracing members provides a ductile failure mode, preventing sudden collapse of the bridge structure.

Engineering Practice Implications

Seismic Design Considerations

The research provides several important implications for the seismic design of STC arch bridges:

Bracing Member Design: Cross bracing members should be designed with sufficient ductility to accommodate plastic deformation without fracture. The design should ensure that yielding occurs in the bracing members rather than in the arch rib or main girder connections.
Constitutive Model Selection: The bilinear constitutive model provides a more accurate representation of seismic response compared to the linear elastic model. Engineers should use nonlinear models for performance-based seismic design of STC arch bridges.
Force Redistribution: The plastic yielding of bracing members leads to significant force redistribution, reducing internal forces at critical sections. This redistribution effect should be considered in seismic design, as it can lead to more economical and efficient structural designs.
Yielding Sequence Control: The design should aim to control the yielding sequence of bracing members to ensure a ductile failure mode. The 3/8 and 5/8 span locations should be designed to yield first, providing early energy dissipation and protecting more critical structural elements.

Design Recommendations

Based on the research findings, the following design recommendations are proposed for STC arch bridges:

Cross bracing members should be designed with a ductility ratio of at least 3.0 to ensure adequate energy dissipation capacity.
The yielding strength of bracing members should be calibrated to ensure that yielding occurs at the 3/8 and 5/8 span locations first, followed by progressive yielding at other locations.
Nonlinear finite element analysis should be used for seismic design verification, with the bilinear constitutive model adopted for bracing members.
The seismic design should account for the force redistribution effects of bracing member yielding, which can lead to reduced demands on critical sections.

Key Technical Questions and Reflections

The study raises important questions about the current seismic design practices for STC arch bridges. Traditional design methods often assume linear elastic behavior for bracing members, which may lead to overly conservative designs or, in some cases, non-conservative estimates of seismic demand. The research demonstrates that the nonlinear behavior of bracing members significantly affects the overall seismic response, and this behavior should be explicitly considered in design.

Another important consideration is the interaction between the arch rib and bracing members under seismic loading. The arch rib acts as a primary load-carrying element, while the bracing members provide lateral stability and load transfer between the arch rib and main girder. The nonlinear interaction between these elements is complex and requires careful modeling to capture the true seismic response.

The research also highlights the importance of the 3/8 and 5/8 span locations as critical zones for bracing member design. These locations experience the highest shear demands due to the interaction between the arch rib bending and the main girder loading. Engineers should pay special attention to the design of bracing members at these locations, ensuring adequate ductility and connection strength.

Study Insights and Implications

This research provides valuable insights for the performance-based seismic design of STC arch bridges. The findings demonstrate that the nonlinear behavior of cross bracing members plays a critical role in the overall seismic response, and this behavior should be explicitly considered in design. The progressive yielding of bracing members provides an effective energy dissipation mechanism, leading to a ductile failure mode that is desirable from a seismic design perspective.

For engineers involved in the design of STC arch bridges, this research underscores the importance of using nonlinear analysis methods for seismic design verification. The bilinear constitutive model provides a practical and accurate representation of bracing member behavior, and should be adopted for performance-based seismic design. The research also highlights the need for careful attention to the yielding sequence of bracing members, as this sequence directly affects the overall seismic performance and failure mode of the bridge.

Future research should investigate the effects of different earthquake characteristics on the seismic response of STC arch bridges, including the influence of earthquake duration, frequency content, and pulse-like characteristics. The research should also explore the development of simplified design methods that account for the nonlinear behavior of bracing members, making performance-based seismic design more accessible to practicing engineers.