Determination of Calculated Temperature Values for Dumbbell-Shaped CFST Arches

Literature Overview

The paper by Huang Fuyun, Chen Baochun, and Ke Tingxian (Fuzhou University and Fuzhou Ring Road Expressway Co., Ltd., 2011), published in the Journal of Fuzhou University (Vol. 39, No. 2, pp. 266-275), addresses a practically critical but often underappreciated aspect of steel-concrete composite bridge design: the determination of calculated temperature values for dumbbell-shaped concrete-filled steel tube (CFST) arch ribs. Funded by the Fuzhou University Talent Fund (0822460), this study combines finite element analysis validated by field temperature measurements with analytical calculations to establish recommended temperature values for design purposes.

Core Technical Content

Dumbbell-shaped CFST arch ribs consist of two parallel steel tubes (chord tubes) connected by transverse diaphragms, with the space between the tubes filled with concrete. This cross-sectional geometry is commonly used in medium-to-large span arch bridges in China, particularly in the southeastern provinces where temperature variations are significant. The thermal behavior of such arches is complex because the temperature distribution is non-uniform across the cross-section due to solar radiation, ambient air temperature, and wind effects.

Key Temperature Parameters

The study employs a finite element method (FEM) validated by measured temperature fields from an actual bridge. The FEM model accounts for: (1) solar radiation heat flux on the exposed surfaces of the steel tubes; (2) convective heat transfer between the tubes and ambient air; (3) conductive heat transfer through the concrete core; and (4) the thermal lag effect due to the thermal mass of the concrete.

Interpretation of Technical Points

Closing Temperature Determination

The calculated closing temperature is the temperature at which the arch rib is closed (i.e., the temporary construction supports are removed and the arch becomes self-supporting). The study finds that the closing temperature should be taken as the average air temperature over the 28 days following concrete placement, adjusted for the specific chord tube diameter. This is because:

1. The concrete continues to gain strength during the 28-day curing period, and the thermal expansion of the steel tubes during this period is partially accommodated by the plastic deformation of the young concrete.
2. The chord tube diameter affects the thermal lag — larger diameter tubes experience greater temperature gradients between their outer and inner surfaces, leading to a delayed thermal equilibrium.
3. The average 28-day temperature provides a statistically representative value that accounts for daily and seasonal temperature fluctuations.

Effective Temperature Determination

The maximum effective temperature is found to be approximately equal to the local maximum air temperature, while the minimum effective temperature is approximately equal to the local minimum daily average air temperature. This finding is somewhat counterintuitive because one might expect the effective temperature to be higher than the air temperature due to solar heating of the steel tubes. However, the study shows that for dumbbell-shaped cross-sections, the concrete core acts as a thermal buffer, and the overall effective temperature (averaged over the cross-section) does not significantly exceed the ambient air temperature extremes.

Recommended Temperature Values for Fujian Province

These values are specific to the climate of Fujian Province and should not be applied to other regions without appropriate adjustment. The temperature range (difference between maximum and minimum effective temperatures) in Fujian is approximately 42-46°C, which is significantly larger than in northern China but comparable to other subtropical regions.

Standards Analysis

The study critically examines the temperature provisions in JTG D60-2004 (General Specifications for Design of Highway Bridges and Culverts), which is the primary Chinese highway bridge design code. The key observations include:

1. Uniform temperature assumption: JTG D60-2004 assumes a uniform temperature rise of 15°C for thermal expansion calculations, which is conservative for most bridge types but may not accurately represent the thermal behavior of CFST arch ribs.
2. Temperature gradient: The code provides temperature gradient models for concrete decks but does not specifically address the temperature gradient in CFST arch ribs.
3. Closing temperature: The code does not provide explicit guidance on the determination of closing temperature for CFST arches, leaving this to the designer's judgment.

The study recommends that designers use the specific temperature values derived from validated FEM analysis rather than relying on the generic provisions of JTG D60-2004. This approach, while more computationally intensive, provides a more accurate representation of the thermal effects and avoids unnecessary conservatism that can lead to over-designed structural sections.

Integration with Engineering Practice

In the design of CFST arch bridges, the temperature effects must be considered in conjunction with: (1) dead load effects; (2) live load effects; (3) wind load effects; (4) construction stage effects; and (5) shrinkage and creep of the concrete core. The thermal effects in CFST arches are particularly significant because:

• The steel tubes have a thermal expansion coefficient of approximately 12×10⁻⁶/°C, while the concrete has approximately 10×10⁻⁶/°C. This differential expansion creates internal stresses at the steel-concrete interface.
• The arch geometry amplifies thermal effects because thermal expansion of the arch rib creates additional thrust at the supports, which is proportional to the temperature change and the arch rise-to-span ratio.
• The dumbbell-shaped cross-section has a relatively low moment of inertia compared to solid cross-sections, making it more sensitive to thermal warping effects.

For welding and fabrication of CFST arch ribs, the temperature effects have practical implications:

1. Welding sequence: The welding sequence for the steel tubes and diaphragms should be planned to minimize residual stresses that could interact adversely with thermal stresses. A symmetric welding sequence from the center outward is typically recommended.
2. Welding heat input: The heat input during welding of CFST arch ribs should be controlled to minimize the heat-affected zone (HAZ) width. For Q345 steel tubes with wall thicknesses of 12-20 mm, a heat input of 15-25 kJ/cm is typical for SAW welding.
3. Post-weld heat treatment: For thick-walled tubes (t > 25 mm), post-weld heat treatment (PWHT) at 550-650°C for a duration of 1 hour per 25 mm of wall thickness may be required to relieve welding residual stresses.

Key Questions and Reflections

A significant question that arises from this study is the interaction between temperature effects and long-term structural behavior. The concrete core in a CFST arch rib undergoes shrinkage and creep over time, which can partially counteract or amplify the thermal effects depending on the temperature history. The study does not address this interaction explicitly, but it is an important consideration for long-term structural assessment.

Another reflection is the importance of field measurements in validating analytical models. The study's use of measured temperature fields from an actual bridge is a strength that should be emulated in future research. Without field validation, analytical temperature predictions may have significant errors due to unmodeled factors such as paint absorption, vegetation shading, and wind tunneling effects.

Study Insights and Implications

This paper provides practical, region-specific temperature values that can be directly used in the design of CFST arch bridges in Fujian Province. The methodology — combining validated FEM analysis with analytical calculations — is sound and reproducible. The critical examination of JTG D60-2004 provisions is valuable for engineers who must navigate between code compliance and engineering judgment.

The broader implication is that temperature effects in CFST arch bridges should not be treated as secondary effects to be estimated with generic code provisions. They are primary effects that can govern the design of certain structural details, particularly at the arch springings and crown where thermal stresses are concentrated. Future research should extend this work to include probabilistic temperature analysis, considering the variability in solar radiation, wind speed, and ambient temperature over the design life of the bridge.