Temperature Field Analysis of Steel Tubes under Solar Radiation

Literature Overview

This 2011 study published in Space Structures by Liu Hongbo and colleagues from Tianjin University investigates the temperature field distribution in steel tubes subjected to solar radiation. The research is funded by the National Natural Science Foundation of China and the Tianjin Municipal Commission of Housing and Urban-Rural Development. The study is based on the ASHRAE clear sky model and finite element thermal analysis theory, examining the diurnal variation of the temperature field and the distribution patterns. Parameter analysis covers solar radiation absorptivity, ground radiation reflectivity, steel tube dimensions, and spatial orientation of the tube.

Core Findings and Technical Analysis

The study establishes that the temperature field in steel tubes under solar radiation exhibits significant diurnal variation, with peak temperatures occurring in the afternoon hours when solar radiation intensity is maximum. The temperature distribution is not uniform across the tube cross-section; the sun-facing surface reaches significantly higher temperatures than the shaded surface, creating a temperature gradient across the tube wall thickness. This temperature gradient induces thermal stresses that can affect the structural behavior of space steel structures.

Thermal Stress and Structural Implications

The temperature gradient across the steel tube wall creates differential thermal expansion between the outer and inner surfaces. For a steel tube with outer diameter D, wall thickness t, and temperature difference ΔT between the sun-facing and shaded surfaces, the induced thermal stress can be estimated using the formula σ = EαΔT/(1-ν), where E is Young's modulus, α is the coefficient of thermal expansion, and ν is Poisson's ratio. For structural steel with E = 206 GPa, α = 12 × 10⁻⁶ /°C, and ν = 0.3, a temperature difference of 30°C across the wall would induce a stress of approximately 83 MPa, which is significant relative to the yield strength of common structural steels.

The diurnal temperature variation also creates cyclic thermal loading. Over a typical year, a steel tube in an exposed location may experience thousands of thermal cycles. While the thermal stresses from solar radiation are generally lower than the mechanical design loads, the cyclic nature of the loading raises concerns about fatigue accumulation, particularly at welded joints, bolted connections, and geometric discontinuities in the steel tube structure.

Connection with Steel Pipe and Welding Engineering

From a welding and steel pipe manufacturing perspective, the thermal effects of solar radiation on steel tubes have several important implications. First, the temperature field in steel tubes used in space structures (such as stadium roofs, airport terminals, and exhibition halls) affects the residual stress distribution from the welding process. The welding residual stresses, which are typically compressive in the weld and tensile in the heat-affected zone (HAZ), interact with the thermal stresses from solar radiation. In the worst case, the superposition of these stress fields could push the local stress state beyond the yield point, leading to local yielding and potential fatigue initiation.

Second, the material selection for steel tubes in solar-exposed applications should consider the thermal properties of the steel grade. Carbon structural steels (Q235, Q345) and high-strength low-alloy steels (Q390, Q420, Q460) have similar thermal expansion coefficients, but their yield strengths differ significantly. For applications where thermal stress is a significant design consideration, higher-strength steels provide a larger margin against thermal yielding, but they may be more susceptible to hydrogen-induced cracking during welding if proper preheating and post-weld heat treatment are not applied.

Third, the surface condition of the steel tube—whether it is bare, painted, or coated—dramatically affects the solar radiation absorptivity. Bare steel has an absorptivity of approximately 0.7 to 0.9, while white-painted surfaces can reduce this to 0.2 to 0.4. The selection of surface finish should be considered as part of the structural thermal design, not merely as an aesthetic or corrosion protection measure.

Simplified Calculation Model Evaluation

The study proposes a simplified calculation model based on the combination of solar radiation time-history finite element analysis and steady-state thermal analysis. The model simplifies the complex transient thermal problem by separating it into a time-dependent component (representing the diurnal solar radiation variation) and a steady-state component (representing the average thermal state). This approach reduces the computational complexity significantly while maintaining acceptable accuracy for engineering design purposes.

The simplified model is validated through numerical examples, and the results demonstrate reasonable agreement with the full transient analysis. For practical engineering applications, the simplified model enables rapid assessment of thermal effects during the design phase without requiring extensive finite element computation for every design iteration. This is particularly valuable for preliminary design of large space steel structures where the thermal analysis needs to be performed for multiple structural configurations and orientations.

Key Questions and Reflections

An important question that the study does not fully address is the interaction between solar radiation thermal effects and the mechanical loads in steel tube structures. In reality, steel tubes in space structures are subjected to simultaneous mechanical loading (dead load, wind load, snow load) and thermal loading (solar radiation). The interaction between these load types can be complex, particularly when the structure is partially restrained against thermal expansion. The study focuses primarily on the thermal analysis, and a comprehensive structural analysis that incorporates both mechanical and thermal loads simultaneously would be more representative of actual engineering conditions.

Another reflection concerns the applicability of the ASHRAE clear sky model to different geographic locations. The solar radiation intensity and spectral distribution vary significantly with latitude, altitude, and atmospheric conditions. The clear sky model assumes clear atmospheric conditions, but in practice, cloud cover, humidity, and atmospheric particulates significantly reduce the actual solar radiation reaching the steel tube surface. Engineers should apply appropriate correction factors based on the specific geographic location of the structure.

Study Insights and Implications

The study provides a systematic framework for evaluating thermal effects of solar radiation on steel tube structures, which is essential for the design of large-span space structures. The parameter analysis identifies the key factors that influence the temperature field, enabling engineers to make informed decisions about material selection, surface treatment, and structural orientation. The simplified calculation model offers a practical tool for routine engineering design, bridging the gap between detailed thermal analysis and practical design requirements.

Reference Value and Outlook

This research contributes to the thermal design methodology for space steel structures and provides quantitative data that can be directly applied to engineering practice. The findings on surface absorptivity effects are particularly relevant for architects and engineers who can specify appropriate surface finishes to mitigate thermal stresses. Future research should extend to include the effects of reflected radiation from surrounding surfaces (such as glass facades and reflective roofing materials), which can create concentrated thermal loading on specific structural members, and should incorporate the long-term degradation of surface coatings under UV exposure.