Temperature Stress Calculation for Steel Tube Concrete Arch Bridges

Literature Overview

The paper by Chen Baochun, Xu Aimin, and Sun Chao (2000), published in the China Journal of Highway and Transport, addresses a practical and often overlooked issue in the design of steel tube concrete (STC) arch bridges: the determination of the temperature differential value used in structural analysis. Temperature-induced stresses are a significant design load case for arch bridges, as the arch action is highly sensitive to thermal expansion and contraction. For STC arch bridges, the thermal behavior is more complex than for conventional concrete or steel arches because the steel tube and the enclosed concrete have different coefficients of thermal expansion, leading to differential thermal strains and internal stresses within the composite section.

Core Technical Concept: Closure Temperature

The study introduces the concept of "calculation closure temperature" for STC arch bridges, which is distinct from the conventional closure temperature used in conventional bridge design. The closure temperature is the reference temperature at which the bridge is constructed and closed, and it serves as the baseline for temperature stress calculations. For STC arch bridges, the study demonstrates that the calculation closure temperature is primarily determined by three factors: the tube diameter, the average temperature of the concrete within one month after casting, and the closure temperature of the empty steel tube.

This finding is significant because it challenges the conventional practice of using a single ambient temperature as the reference for thermal analysis. In STC structures, the thermal history of the concrete within the steel tube—including curing temperature, hydration heat, and subsequent thermal equilibrium—plays a critical role in determining the internal stress state. The study's approach of considering the actual thermal conditions during construction provides a more accurate basis for temperature stress analysis.

Thermal Analysis of STC Sections

The study conducted temperature field measurements on STC members and performed computer analysis of temperature variation values for STC arch bridges. The thermal behavior of an STC section is governed by the heat transfer characteristics of the composite section, including the convective and radiative heat exchange between the steel tube inner surface and the concrete, the thermal conductivity of the concrete, and the thermal mass of the section.

The temperature field within an STC section is not uniform; it varies radially from the outer surface of the steel tube to the center of the concrete core. This temperature gradient generates differential thermal strains between the steel and concrete, which are partially restrained by the bond between the two materials. The resulting internal stresses can be significant, particularly during the early stages of concrete curing when the hydration heat is still being dissipated.

Engineering Practice Implications

For the design of STC arch bridges, the study's findings have direct implications for the calculation of temperature-induced forces and displacements. Engineers should not simply assume a uniform temperature change across the section; instead, they should account for the temperature gradient and the differential thermal expansion between steel and concrete. The calculation closure temperature should be determined based on the actual construction conditions, including the concrete casting temperature, the ambient temperature during curing, and the tube geometry.

In practice, this means that the thermal analysis of an STC arch bridge should incorporate a finite element model that captures the two-dimensional temperature distribution within the section, the temperature-dependent material properties of both steel and concrete, and the bond-slip behavior at the steel-concrete interface. The temperature loads should be applied as time-dependent boundary conditions that reflect the actual thermal history of the structure.

Study Insights and Reflections

The emphasis on the calculation closure temperature is a refreshing departure from the oversimplified thermal models often used in bridge design. In many design codes, temperature effects are treated as a uniform temperature change applied to the entire structure, which is an acceptable approximation for homogeneous sections but inadequate for composite sections like STC. The study's approach of considering the actual thermal conditions during construction provides a more physically realistic basis for thermal analysis.

The finding that the calculation closure temperature depends on the tube diameter is particularly important for practical design. Larger diameter tubes have greater thermal mass and slower heat dissipation, resulting in higher internal temperatures and longer equilibration times. This means that the thermal stress state of a large-diameter STC arch is more complex and more sensitive to construction timing than that of a small-diameter STC arch. Engineers should account for this size effect when designing STC arch bridges of different scales.

Reference Value and Outlook

This study provides valuable guidance for the thermal analysis of STC arch bridges, which are increasingly used in modern bridge engineering due to their excellent structural performance and rapid construction capability. The concept of calculation closure temperature and the methodology for determining it based on construction conditions offer a practical framework for more accurate thermal stress calculations. Future research should extend to the long-term thermal performance of STC arch bridges, including the effects of seasonal temperature variations, solar radiation, and the aging of concrete on the thermal stress state. The integration of field monitoring data with finite element models would further validate and refine the thermal analysis methodology proposed in this study.