Nonlinear Stability Analysis of Single-Rib Inclined-Braced Steel Tube Concrete Arch Bridge

Literature Overview

The paper by Liu Muyu, Sun Xiangdong, Yuan Weiguo, and Gong Kai, published in Bridge Construction in 2009, presents a nonlinear stability analysis of a single-rib inclined-braced steel tube concrete (SRC) arch bridge. The study uses the Guangwu Expressway Shuangfeng to Pingtai section K111+495 overpass as a case study. The authors employ the commercial finite element software ANSYS to perform a comprehensive stability analysis that considers both geometric and material nonlinearity. The analysis reveals that the first-order elastic buckling mode is an out-of-plane symmetric buckling of the arch rib, with a stability safety factor greater than 15. However, when both geometric and material nonlinearity are considered simultaneously, the stability safety factor decreases by 40% to 50%, demonstrating the significant influence of material nonlinearity on structural stability.

Structural Configuration and Analysis Setup

The single-rib inclined-braced SRC arch bridge is a relatively new bridge type that combines the structural efficiency of a single arch rib with the lateral stability provided by inclined braces. The single rib is a steel tube filled with concrete, which provides both the axial stiffness of the steel tube and the compressive strength of the concrete. The inclined braces connect the arch rib to the bridge deck, providing lateral restraint and transferring loads between the rib and the deck.

The finite element model was constructed in ANSYS using appropriate element types for the different structural components. The arch rib was modeled with beam elements that can capture both bending and torsional behavior, while the inclined braces were modeled with similar elements. The bridge deck was modeled with shell elements to capture its two-dimensional behavior. The material models for the steel and concrete were defined to include the nonlinear stress-strain relationships, including the yielding of steel and the cracking and crushing of concrete.

Stability Analysis Results and Discussion

The analysis was performed under multiple load cases representing different live load configurations on the bridge deck. The results show that the first-order linear elastic buckling mode is consistent across all load cases, indicating that the buckling mode is primarily governed by the structural geometry rather than the specific load pattern. The out-of-plane symmetric buckling mode of the arch rib is the dominant instability mode, which is expected for a single-rib arch bridge where the lateral restraint is provided by the inclined braces.

The stability safety factor under linear elastic analysis is greater than 15, which appears to provide a very high safety margin. However, this value is significantly reduced when geometric nonlinearity is considered, and the reduction is much more dramatic when material nonlinearity is also included. The 40% to 50% reduction in the stability safety factor due to the combined effect of geometric and material nonlinearity is a critical finding that has direct implications for the design of SRC arch bridges.

The analysis also reveals that the stability safety factors under different live load cases are relatively similar, with only small differences between cases. This indicates that the structural stability is not highly sensitive to the specific live load configuration, which simplifies the design process by allowing the use of representative load cases rather than exhaustive case-by-case analysis.

Material Nonlinearity Effects on Stability

The significant influence of material nonlinearity on the stability safety factor is the most important finding of this study. Under high compressive stresses, the concrete in the arch rib begins to crack and eventually crush, while the steel tube approaches or exceeds its yield strength. These material nonlinearities reduce the effective stiffness of the arch rib, which in turn lowers the buckling load. The effect is particularly pronounced in the lower part of the arch rib where the axial compression is highest.

From a steel pipe engineering perspective, this finding highlights the importance of material quality control in the fabrication of SRC arch ribs. The mechanical properties of the steel tube, including the yield strength and the strain-hardening behavior, directly affect the stability performance of the arch. Similarly, the concrete quality, including its compressive strength and the bond with the steel tube, influences the composite action that provides the arch rib with its effective stiffness. Any deviation from the specified material properties will reduce the actual stability safety factor below the design value.

Engineering Practice Implications

The findings of this study have several important implications for the engineering practice of SRC arch bridge design and construction. First, linear elastic stability analysis is not sufficient for the design of SRC arch bridges, and nonlinear analysis should be used to obtain a realistic estimate of the stability safety factor. Second, the material properties of both the steel tube and the concrete should be verified through testing of representative specimens from the actual production batch, rather than relying solely on the specified material grades. Third, the construction sequence and the quality of the concrete infill should be carefully controlled to ensure that the composite action is achieved as assumed in the design analysis.

For steel pipe fabricators, the dimensional accuracy of the arch rib tubes is critical. Any deviation from the designed radius of curvature, straightness, or wall thickness uniformity will affect the buckling behavior and reduce the stability safety factor. The welding quality of the tube joints is also important, as weld defects can initiate buckling and reduce the effective load-bearing area. Non-destructive testing of welds should be performed to ensure that the welds meet the required quality standards.

Study Insights and Recommendations

The nonlinear stability analysis methodology presented in this study provides a reliable and practical approach for evaluating the stability of SRC arch bridges. The use of commercial finite element software makes the methodology accessible to practicing engineers, and the case study provides a concrete example of the analysis procedure. However, the study is limited to the as-built condition and does not consider the construction stage stability, which is often the governing condition for large arch bridges. Future research should extend the analysis to include the construction stage, considering the progressive loading of the arch rib and the temporary support conditions.

The study also does not consider the effect of temperature on the stability, which is an important factor for large-span bridges exposed to solar radiation. Temperature gradients across the arch rib cross-section can induce additional stresses that reduce the stability margin. The combination of thermal effects with the material nonlinearity should be investigated to provide a more comprehensive assessment of the structural stability.