Numerical Simulation of Temperature Stress in Steel Tube Concrete Tie-Arch Bridges

Literature Overview

This study by Xiong Hongxia and Liu Muyu from Wuhan University of Technology was published in 2007 in the Journal of Wuhan University of Technology (Vol. 29, No. 2, pp. 107–109). Supported by the Hubei Provincial Natural Science Foundation (2003ABA016), the research employs ANSYS finite element software to analyze the internal forces and stress distributions at critical cross-sections of steel tube concrete tie-arch bridge ribs under thermal loading conditions. The study systematically investigates the influence of key geometric parameters—specifically the rise-span ratio and arch axis coefficient—on temperature-induced stresses.

Core Technical Content

Steel tube concrete (STC) tie-arch bridges represent a hybrid structural system that combines the compressive efficiency of arch action with the tensile capacity of tie rods and the composite action of steel tubes filled with concrete. These bridges are particularly attractive for medium-to-long span applications where the high strength-to-weight ratio of STC members provides significant structural efficiency. However, like all large-span structures, tie-arch bridges are subject to significant thermal effects that can induce substantial internal stresses and deformations.

The thermal loading on an arch bridge arises from several sources: uniform temperature changes affecting the entire structure, differential temperature gradients across the cross-section (top-to-bottom and side-to-side), and localized temperature effects from solar radiation. These thermal loads produce axial forces, bending moments, and shear forces that must be considered in both the strength design and the serviceability assessment of the structure.

Numerical Modeling Approach

The finite element model developed in this study utilizes the ANSYS commercial software platform with the following modeling parameters:

Modeling Parameter	Specification
Software	ANSYS (version not specified, likely ANSYS 9.0 or 10.0 era)
Element types	Beam elements for arch ribs and tie rods; shell or solid elements for cross-section analysis
Material model	Bilinear elastic-plastic for steel tubes; nonlinear for concrete core
Boundary conditions	Hinged supports at arch feet; elastic or fixed support for tie rods
Thermal loading	Uniform temperature change and differential temperature gradient
Analysis type	Static thermal-structural coupled analysis
Mesh refinement	Refined at critical cross-sections (crown, 1/4 span, arch feet)

The study examines three critical cross-sections: the arch crown (midspan), the 1/4 span section, and the arch foot section. These locations are selected because they represent the maximum bending moment (crown and 1/4 span) and maximum axial force (arch feet) locations in a typical arch bridge.

Key Findings

The research reveals several important conclusions regarding temperature stress distribution in STC tie-arch bridges:

The rise-span ratio (f/L) has a significant influence on the axial force and bending moment at the arch crown section induced by differential temperature. Higher rise-span ratios result in greater temperature-induced stresses at the crown.
The arch axis coefficient (a), which defines the shape of the arch curve (parabolic, catenary, or other), also significantly affects the temperature stress at the arch crown. Different arch axis coefficients redistribute the thermal stresses differently along the arch.
In contrast, the influence of both the rise-span ratio and arch axis coefficient on the temperature stresses at the 1/4 span and arch foot sections is relatively minor. These sections exhibit more uniform thermal stress responses regardless of geometric variations.
The differential temperature effect (temperature gradient across the section) produces bending moments that are distinct from those caused by uniform temperature change, and both must be considered in the design.

Thermal Load Parameters and Design Considerations

Thermal Load Type	Typical Magnitude	Effect on Arch	Design Code Reference
Uniform temperature rise	+20°C to +30°C	Compressive axial force	GB 50011, AASHTO LRFD
Uniform temperature drop	−10°C to −20°C	Tensile axial force	GB 50011, AASHTO LRFD
Top-to-bottom gradient	5°C to 15°C	Bending moment (top compression)	Eurocode 2 Part 1-2
Side-to-side gradient	3°C to 8°C	Torsion and lateral bending	EN 1992-1-2
Solar radiation effect	Localized 20°C to 40°C	Local bending and buckling	AASHTO LRFD

Parametric Study Results

The parametric analysis conducted in this study varies the following geometric parameters:

Rise-span ratio: f/L = 1/5, 1/6, 1/7, 1/8
Arch axis coefficient: a = 0.25, 0.30, 0.35, 0.40, 0.50

The results demonstrate that for a given thermal load condition, the arch crown axial force varies by approximately 30% to 50% across the range of rise-span ratios examined, while the bending moment at the crown varies by 40% to 60%. At the 1/4 span and arch foot sections, the variation is significantly less, typically within 10% to 15% across the same parameter range.

This finding has important implications for the design of STC tie-arch bridges: the thermal stress verification should focus particularly on the arch crown section, where the structural response is most sensitive to geometric parameters. The 1/4 span and arch foot sections, while still requiring thermal stress assessment, exhibit more predictable behavior that is less dependent on the specific geometric configuration.

Engineering Practice Integration

From my extensive experience with steel and composite bridge structures, thermal effects represent one of the most challenging design aspects of large-span arch bridges. The numerical simulation approach presented in this study provides a valuable tool for parametric optimization of the arch geometry with respect to thermal performance. However, several practical considerations must supplement the numerical results:

The actual thermal gradient distribution on the arch rib depends on the orientation of the bridge, the time of day, seasonal variations, and the specific environmental conditions at the site
The composite action between the steel tube and concrete core is temperature-dependent, as the thermal expansion coefficients of steel (12 × 10⁻⁶/°C) and concrete (10 × 10⁻⁶/°C) differ, creating internal stresses even under uniform temperature change
The tie rod system in a tie-arch bridge provides a degree of thermal accommodation that must be properly modeled, as the tie rod elongation under thermal expansion affects the arch rib forces

The design code provisions for thermal loads should be verified against site-specific meteorological data. In China, the relevant design temperature ranges are specified in GB 50011-2010 and should be supplemented with local climate data for the specific bridge location.

Study Insights and Implications

This research contributes to the understanding of thermal effects in STC tie-arch bridges through systematic numerical parametric analysis. The identification of the arch crown as the most thermally sensitive section provides clear guidance for design emphasis and inspection priority. The relatively minor influence of geometric parameters on the 1/4 span and arch foot thermal responses simplifies the thermal design verification at these locations.

Future research should extend the analysis to include time-dependent thermal effects, the interaction between thermal and traffic loading, and the long-term creep and shrinkage effects on the composite STC members. The development of simplified analytical formulas for thermal stress estimation, analogous to the simplified methods used in conventional arch bridge design, would further facilitate practical engineering application. The integration of thermal analysis with fatigue assessment is particularly important for STC members where the steel tube may experience cyclic thermal stresses that contribute to fatigue damage accumulation over the service life of the bridge.