Dynamic Impact Coefficient Analysis of Large-Span Steel Tube Concrete Arch Bridges

Literature Overview

The paper by Zhao Luwei, Wang Guichun, Li Huayang, and Sun Yuxiang, published in the Structural Engineer (2019, Vol. 35, No. 2), investigates the dynamic impact coefficient of large-span steel tube concrete (STC) arch bridges by considering vehicle-bridge coupled vibration. Using the Maocao Street STC arch bridge as a case study and a typical three-axle truck as the vehicle model, the authors established structural analysis models using the finite element method and multi-rigid-body dynamics models for the vehicle. The effect of bridge deck irregularity was considered, and the Newmark-β method was used to solve the vibration differential equations. The results show that the impact coefficient typically exceeds the values calculated according to codes, increases rapidly with road surface irregularity, and exhibits random behavior with respect to vehicle speed. This research is highly relevant to our field because the steel tubes used in arch bridges are subjected to complex dynamic loading conditions, and the welding quality of the steel tube connections directly influences the dynamic response and fatigue life of the structure.

Core Technical Approach

Vehicle-Bridge Coupled Vibration Modeling

The vehicle-bridge coupled vibration model is a sophisticated approach that considers the interaction between the vehicle dynamics and the bridge structural dynamics. The vehicle is modeled as a multi-rigid-body system with multiple degrees of freedom, including the sprung mass, unsprung mass, and the suspension system. The bridge is modeled as a finite element structure with appropriate boundary conditions and material properties. The coupling between the vehicle and the bridge is established through the contact force at the wheel-bridge interface, which depends on the bridge deck deflection, the vehicle suspension dynamics, and the road surface irregularity.

Newmark-β Method for Time-Domain Analysis

The Newmark-β method is a widely used numerical integration method for solving second-order differential equations of motion. It is particularly suitable for the analysis of dynamic systems with nonlinear behavior, such as vehicle-bridge coupled systems. The method requires the selection of two parameters, α and δ, which control the accuracy and stability of the numerical solution. For the analysis of impact coefficients, the parameters should be selected to ensure sufficient accuracy in capturing the high-frequency dynamic response, which is critical for the evaluation of the impact effect.

Effect of Bridge Deck Irregularity

The bridge deck irregularity is a critical factor in the dynamic impact analysis. The irregularity introduces additional dynamic excitation that is superimposed on the static load of the vehicle. The irregularity profile is typically characterized by a power spectral density function, which describes the amplitude distribution of the irregularity as a function of spatial frequency. The effect of the irregularity on the impact coefficient is significant: as the irregularity increases, the impact coefficient increases rapidly, which can lead to a substantial increase in the dynamic load on the bridge structure.

Technical Parameter Analysis

Connection with Steel Pipe and Welding Practice

The steel tubes used in STC arch bridges are typically large-diameter, thick-walled tubes that are fabricated by welding. The welding quality of these tubes is critical for the structural integrity and dynamic performance of the bridge. From my experience with large-diameter welded steel tubes, the following considerations are essential:

First, the longitudinal welds in the steel tubes must be thoroughly inspected using non-destructive testing (NDT) methods such as ultrasonic testing (UT), radiographic testing (RT), and magnetic particle testing (MT). Any defects detected in the welds must be repaired according to the relevant welding repair procedures. The weld repair procedure must be qualified to ensure that the repaired weld has adequate mechanical properties and fracture toughness.

Second, the circumferential welds that connect the steel tube segments must be designed and executed with particular care. These welds are subjected to cyclic loading during the service life of the bridge, and any defects in the welds can lead to fatigue cracking. The welding procedure should be optimized to produce welds with low residual stress, fine microstructure, and high toughness. Post-weld heat treatment may be necessary to relieve residual stresses and to improve the toughness of the HAZ.

Third, the steel tube geometry must be controlled to minimize stress concentrations. The transition between the steel tube and the concrete infill, as well as the connection between the steel tube and the hanger system, must be designed with smooth transitions and adequate fillet radii. The welding of these transition regions should be performed with special attention to the weld geometry and the heat input to avoid excessive distortion and residual stress.

Key Questions and Reflections

A significant question that arises from this research is how to accurately predict the dynamic impact coefficient for STC arch bridges in practice. The vehicle-bridge coupled vibration analysis provides a more accurate prediction than the empirical formulas in the codes, but it requires detailed information about the vehicle dynamics, the bridge structural properties, and the road surface irregularity. In practice, this information may not be readily available, and the analysis may be too complex for routine design. Therefore, simplified methods that capture the essential physics of the dynamic interaction are needed.

Another important consideration is the effect of the steel tube welding quality on the dynamic response of the bridge. The welding residual stress and the microstructural changes in the HAZ can affect the local stiffness and damping of the bridge structure, which in turn influences the dynamic response. However, the current analytical models typically assume that the bridge structure is linearly elastic, which does not account for the local non-linear behavior introduced by the welding defects and residual stresses. This is an area that requires further investigation.

Study Insights and Implications

This research provides valuable insights into the dynamic behavior of STC arch bridges and highlights the importance of considering vehicle-bridge coupled vibration in the design of these structures. The finding that the impact coefficient typically exceeds the code values suggests that the current design codes may be unconservative for STC arch bridges, particularly when the road surface irregularity is significant. This has important implications for the safety and serviceability of existing bridges and for the design of new bridges.

For engineering practice, I would recommend that the design of STC arch bridges incorporate a comprehensive dynamic analysis that considers the vehicle-bridge coupled vibration, the road surface irregularity, and the material non-linearity of the steel tubes. The welding quality of the steel tubes should be ensured through rigorous quality control measures, including weld procedure qualification, in-process monitoring, and post-weld NDT. The dynamic response of the bridge should be monitored during the construction and service phases to verify the design assumptions and to detect any anomalies that may indicate structural deterioration.

Future research should focus on the development of simplified dynamic analysis methods that can be used for routine design, the effect of welding defects on the dynamic response of STC arch bridges, and the long-term durability of the steel tubes under cyclic dynamic loading. The integration of welding metallurgy, structural dynamics, and materials science is essential for the development of safe and efficient STC arch bridges.