Structural Parameter Sensitivity Analysis of Multi-Arch Rib Wide-Span Special-Shaped Steel Tube Concrete Arch Bridge

Literature Overview

This paper by Li Jie, Du Xin, Zhang Bo, and Liang Yan from the School of Civil Engineering, Zhengzhou University, published in China Foreign Highway (Vol. 40, Issue 5, 2020, pp. 105-112), presents a comprehensive sensitivity analysis of structural parameters for a multi-arch rib wide-span special-shaped steel tube concrete (SC) arch bridge. The study was supported by the Henan Provincial Science and Technology Program (192102310227) and the National Natural Science Foundation of China (51608488).

The research employs the ALGOR finite element software to establish a refined finite element model of a specific arch bridge, investigating the effects of second-stage dead load, overall temperature change, arch rib steel tube concrete infilling, arch rib steel tube wall thickness, and cable forces (including middle hanger cables, edge hanger cables, and horizontal tie cables) on structural deformation and stress. The study further explores the sensitivity of edge arch rib crown stress to multiple parameters and derives regression formulas through experimental design methods.

Core Technical Points and Finite Element Modeling Approach

The finite element modeling approach used in this study is of particular interest from a metallurgical and materials perspective. The ALGOR software was used to create a refined model, which implies that the mesh density was sufficient to capture stress concentrations at critical locations such as weld joints, tube-to-tube connections, and the interface between the steel tube and the infilled concrete.

The multi-arch rib configuration represents a significant departure from conventional single-arch rib designs. In this configuration, multiple parallel arch ribs are connected by transverse beams and hanger cables, creating a spatial structural system. The "special-shaped" designation likely refers to non-circular cross-sections of the arch ribs, which could be elliptical, rectangular, or other custom shapes designed to optimize the load-carrying capacity and stiffness distribution.

From a steel tube fabrication standpoint, the arch ribs require large-diameter steel tubes, typically ranging from 1000 mm to 2000 mm in diameter with wall thicknesses of 12 mm to 30 mm. The steel grade commonly used is Q345B or Q390B, with higher grades (Q460 or Q550) potentially used for longer spans or heavier loads. The fabrication of such large-diameter tubes involves plate rolling, longitudinal seam welding, and circumferential seam welding.

The following table summarizes the key structural parameters investigated and their effects:

Steel Tube Concrete Arch Rib Design and Welding Considerations

The arch rib steel tube is the primary load-bearing element of the bridge, and its design and fabrication quality directly determine the structural safety and service life. The steel tube must withstand significant compressive and bending stresses, as well as potential buckling under axial compression. The concrete infilling within the steel tube provides additional compressive strength, improves the buckling resistance, and enhances the overall ductility of the arch rib.

From a welding perspective, the fabrication of the arch rib steel tubes involves several critical weld types:

1. Longitudinal Seam Welds: These welds join the rolled steel plate into a cylindrical tube. For large-diameter tubes, submerged arc welding (SAW) is the preferred process, providing excellent penetration and weld quality. The weld must achieve full penetration with no lack of fusion, slag inclusion, or undercut. The weld metal and HAZ must meet the impact toughness requirements of the base steel, typically ≥47 J at -20°C for Q345B per GB/T 1591.
2. Circumferential Seam Welds: These welds join individual tube segments to form the complete arch rib. The circumferential welds are typically performed using multi-pass SAW or flux-cored arc welding (FCAW). The welding position is often horizontal or 6G, requiring qualified welders and controlled welding sequences to minimize residual stress and distortion.
3. Connection Welds: The arch rib steel tubes are connected to the transverse beams, hanger cable anchorages, and bearing plates through welds or bolted connections. Where welding is used, the connection welds must be designed to transfer the full design load without fracture or excessive deformation.

The concrete infilling process within the steel tube is also critical. The concrete must be properly compacted to avoid voids and honeycombing, which would reduce the effective cross-sectional area and create stress concentrations. The concrete mix design should ensure adequate workability for pumping through the tube, with a slump of 160-200 mm and the use of superplasticizers to achieve the required flowability. The concrete strength grade is typically C40 to C60, depending on the design requirements.

Temperature Effects and Thermal Stress Analysis

The finding that overall temperature change has the most significant effect on the structural mechanical behavior is of great practical importance. Steel has a thermal expansion coefficient of approximately 12×10⁻⁶ /°C, which means that a temperature change of 30°C in a 200 m span arch bridge would produce a free thermal expansion of approximately 72 mm. In a restrained structure, this thermal expansion generates significant thermal stresses that can be comparable to or even exceed the dead load stresses.

From a materials science perspective, the thermal cycling experienced by the bridge during its service life can lead to several degradation mechanisms:

• Thermal Fatigue: Repeated thermal expansion and contraction can cause fatigue cracking at weld joints and stress concentration points. The HAZ of welds is particularly susceptible to thermal fatigue due to the presence of coarse-grained grains and residual stresses.
• Creep: Under sustained compressive stress and elevated temperatures, the steel can experience creep deformation. Although steel creep is typically not a concern at ambient temperatures, it becomes relevant at temperatures above 200°C, which could occur in fire conditions or in regions with extreme solar radiation.
• Corrosion: Thermal cycling can accelerate corrosion by repeatedly breaking and reforming the corrosion product layer on the steel surface. The presence of concrete infilling provides some protection, but any voids or honeycombing in the concrete would expose the steel tube interior to moisture and corrosive agents.

The thermal stress analysis should be incorporated into the design process, and the thermal expansion joints and sliding bearings should be designed to accommodate the maximum expected thermal movement. The horizontal tie cables and hanger cables must also be designed to accommodate the differential thermal expansion between the arch rib and the deck.

Sensitivity Analysis Methodology and Regression Formulas

The use of experimental design methods to derive regression formulas is a practical and efficient approach to structural sensitivity analysis. Instead of performing a large number of finite element analyses for each parameter combination, the experimental design method allows for the identification of the most influential parameters and the derivation of approximate analytical expressions.

The regression formula derived in this study can be used to quickly estimate the structural response under different loading and parameter conditions without the need for full finite element analysis. This is particularly useful during the preliminary design phase, when rapid iteration is required to optimize the structural configuration.

From a quality control perspective, the sensitivity analysis results provide valuable guidance for inspection and testing priorities. Parameters with high sensitivity (such as temperature change and cable forces) should be given priority in monitoring and inspection programs. The edge arch rib crown stress, identified as the critical response variable, should be monitored using strain gauges or fiber optic sensors installed at the crown section of the edge arch rib.

Engineering Practice Integration and Recommendations

The findings of this study have several practical implications for the design and construction of multi-arch rib wide-span SC arch bridges:

1. Temperature Effect Compensation: The design should include adequate thermal expansion provisions, including expansion joints, sliding bearings, and cable tensioning systems that can accommodate thermal movements. The thermal analysis should consider the diurnal, seasonal, and solar radiation temperature gradients.
2. Cable Force Optimization: The cable forces (hanger cables and horizontal tie cables) have a significant influence on the structural behavior. The initial cable tension should be carefully optimized to minimize the permanent stress in the arch ribs and cables, considering the long-term effects of cable relaxation and creep.
3. Steel Tube Wall Thickness Selection: The wall thickness of the arch rib steel tube should be selected based on the buckling resistance requirements, considering both local buckling (governed by the diameter-to-thickness ratio) and global buckling (governed by the effective length and boundary conditions). The minimum wall thickness should also satisfy the minimum requirements for concrete infilling and corrosion protection.
4. Quality Control of Steel Tube Fabrication: The steel tube fabrication should follow strict quality control procedures, including ultrasonic testing of longitudinal and circumferential welds, dimensional inspection, and hydrostatic testing. The acceptance criteria should follow relevant standards such as GB/T 3091 (ERW pipe), SY/T 5037 (HFW pipe), or ASME B31.3 (process piping) as applicable.
5. Post-Construction Monitoring: A structural health monitoring system should be installed to track the long-term performance of the bridge, including strain, displacement, temperature, and cable force measurements. The monitoring data should be compared with the finite element model predictions to validate the model and detect any anomalies.

In conclusion, this study provides valuable insights into the structural behavior of multi-arch rib wide-span SC arch bridges through a systematic sensitivity analysis. The identification of temperature change as the most influential parameter underscores the importance of thermal analysis in the design of long-span steel structures. The derived regression formulas offer a practical tool for rapid structural assessment during the design phase. For engineers involved in the fabrication and welding of the arch rib steel tubes, the key message is that the structural performance is highly sensitive to the quality of the steel tube fabrication, including weld quality, dimensional accuracy, and concrete infilling integrity.