Simulation Study on Sunshine Temperature Field of a Concrete Box Girder of the Cable-Stayed Bridge

Abstract

This paper investigates the distribution of the sunshine temperature field in bridge structures. To implement thermodynamic boundary conditions on the structure under the influence of sunshine, this study utilized the FILM and DFLUX subroutines provided by ABAQUS. Based on this method, the sunshine temperature field of the concrete box girder of a cable-stayed bridge was analyzed. The results showed that the simulated temperature values were in good agreement with the measured values. The temperature difference between the internal and external surfaces of the box girder under the influence of sunshine was significant, with the maximum negative temperature difference appearing around 6:00 a.m. and the maximum positive temperature difference appearing around 2:00 p.m. The temperature gradient of the box girder section calculated by the method presented a C-shaped distribution pattern, which differs from the double-line distribution pattern specified in the current “General Specifications for Design of Highway Bridges and Culverts” in China (JTG D60-2015). Furthermore, a sensitivity analysis of thermal parameters using the proposed simulation method for the sunshine temperature field of the concrete box girder was conducted, and the results indicated that the solar radiation absorption coefficient had a significant impact on the temperature field. A 30% increase or decrease in the solar radiation absorption coefficient caused the maximum temperature change on the surface of the structure to exceed 10 °C. This paper provides an accurate simulation of the sunshine temperature field of the concrete box girder of a cable-stayed bridge, and the research results are significant for controlling bridge alignment and stress state during the construction period, ensuring the reasonable initial operating state of the bridge, and enhancing the sustainability of the structure.

1. Introduction

The temperature field of a bridge structure in the natural environment is constantly changing due to passive or active heat transfer between the structure and the external environment, such as solar radiation, convective heat transfer, and radiative heat transfer. The causes of temperature change in the bridge structure can be divided into the daily temperature cycle, the sudden temperature change, and the seasonal temperature cycle. Among these, the daily temperature cycle and the seasonal temperature cycle are the two key aspects of the bridge temperature field. The former is mainly generated by the effects of daily temperature variation, solar radiation, and sunshine shadow occlusion, while the latter is generated by the effects of seasonal climate change and annual temperature amplitude. This paper focuses on simulating and discussing the daily temperature cycle of the concrete box girder of a cable-stayed bridge. The concrete girder of a cable-stayed bridge is always exposed to the atmospheric environment, resulting in temperature differences between the surfaces of the structure under the influence of sunlight and environmental factors. These differences include an overall temperature difference between the external surfaces and the local temperature difference between the internal and external surfaces in the thickness, which form a non-uniform temperature field within the structure. The temperature difference between the external surfaces is caused by the difference in solar radiation received by the sunny surface and the shaded surface, leading to changes in the alignment of the concrete girder. The direction and magnitude of the alignment change will vary with the position of the sun and the angle of light exposure, making it challenging to monitor the alignment of the concrete girder during the construction phase [1]. Moreover, this temperature difference can also lead to changes in the stress state of the structure. The local temperature difference in the direction of the wall thickness is caused by the inconsistent environmental boundary conditions between the internal and external surfaces of the structure. The temperature on the external surface of the structure changes significantly with changes in atmospheric temperature and solar radiation, while the air in the inner cavity of the structure does not flow and the thermal conductivity of the concrete is poor, resulting in a much smaller temperature change on the internal surface of the structure. Research has shown that when the temperature difference between the internal and external surfaces is too large, the resulting temperature stresses can reach live load levels [2,3,4,5,6], which may cause concrete cracking and affect the safety and stability of the structure and, therefore, the sustainability of bridge operations. Therefore, conducting in-depth research on the sunshine temperature field of the concrete box girder of cable-stayed bridges is essential for ensuring the reasonable initial operation state of the bridge and enhancing the sustainable performance of the structure. Many scholars have carried out extensive research on the sunshine temperature field of the concrete box girder. Zuk [7] studied the measured temperature field of a bridge and found that the temperature difference between the internal and external surfaces of the concrete structure is the highest in summer, with a maximum value of up to 22 °C. The temperature of the external surface of a steel-concrete composite beam located near the Hardware River was tested. The test results show that the temperature difference between the upper and lower surfaces of the concrete bridge deck can reach up to 19° during the day, and the temperature difference at night is small. For steel beams, the internal vertical temperature difference is not obvious; the influence of atmospheric temperature, wind speed, solar radiation, and other related environmental factors on the temperature field of the structure is discussed for the first time, and the temperature difference equation of the composite concrete beam bridge deck is summarized in his paper. Hambly and Rao [8,9] monitored the temperature field of a real bridge under direct solar radiation and summarized the temperature gradient distribution mode of the concrete box girder. Churchward [10] analyzed the influence of atmospheric temperature, wind speed, solar radiation, and other related environmental factors on the temperature field of the structure and derived the temperature distribution function of the vertical section of the box girder under the combined action of the DTMAX and sunshine parameters. Hoffman [11] found that the temperature variation in the longitudinal direction of the bridge is small, and variations in solar radiation and atmospheric temperature cause a non-linear temperature gradient along the vertical height direction in the main girder section. Xia et al. [12] combined field measurements with finite element simulations to calculate the temperature distribution of different components of the bridge structure and analyze the displacement and strain response of the structure. The analysis results showed that the displacement of the bridge in the longitudinal and transverse directions was consistent with the monitoring data. Liu et al. [13] studied the influence of temperature on the elevation of towers and girder sections of a large-span concrete cable-stayed bridge and summarized the influence of temperature change on the elevation of the key positions of the girder and tower. Wu et al. [14] monitored the temperature field of a steel-concrete combined box girder bridge and found that the concrete and steel box girders had different forms of temperature gradient functions. The results were compared with the gradient patterns specified in the code, which showed that the temperature gradient distribution patterns specified in the code differed from the actual distribution patterns to some extent.

To summarize, research on the sunshine temperature field of concrete box girders has primarily relied on the analysis of measured temperature data from actual engineering or test models. Although this method can collect real temperature data at specific measuring point positions, there are limitations due to the number of measurement points and monitoring conditions, which often result in significant data errors and may not fully reflect the actual temperature field distribution of the structure. In contrast, the numerical simulation method is not limited by these conditions and can achieve a rapid calculation of the structural temperature field. Consequently, this method has been favored by many researchers and engineers and has become one of the mainstream methods for calculating and researching the structural temperature field of bridges.

In the daily temperature cycle, the bridge structure heats up during the day due to solar radiation and cools down at night when the ambient temperature decreases and the structure dissipates heat into the environment. The sunshine temperature field of the bridge structure is strongly time-varying due to the changes in solar radiation intensity and ambient temperature. Therefore, to achieve a refined simulation of the sunshine temperature field, accurate thermodynamic boundary conditions must be applied to the calculation model of the structure. This involves reflecting the heat transfer and heat exchange between the structure and the external environment through appropriate parameter models to accurately describe the changes in ambient temperature and solar radiation intensity at different times. In this study, the thermodynamic boundary conditions of the structure were imposed using the FILM and DFLUX subroutines provided by ABAQUS. This was based on previous research on the boundary conditions of the sunshine temperature field of bridge structures. This provided a simple and efficient method for the rapid analysis and prediction of the temperature field of the concrete box girders of cable-stayed bridges. The research results of this study are significant for controlling bridge alignment and stress state during the construction period, ensuring a reasonable initial operating condition of the bridge, and enhancing the sustainability of the structure.

2. Heat Transfer Boundary Condition

The heat transfer of the object should satisfy Fourier’s Law [15,16], which states that the rate of heat transfer is proportional to the temperature gradient in the object. The differential equation of heat transfer without an internal heat source can be expressed as follows:

$$\mathsf{\rho }\mathrm{c}\frac{\partial \mathrm{T}}{\partial \mathsf{\tau }}=\frac{\partial }{\partial \mathrm{x}}\left({\mathrm{k}}_{\mathrm{x}}\frac{\partial \mathrm{T}}{\partial \mathrm{x}}\right)+\frac{\partial }{\partial \mathrm{y}}\left({\mathrm{k}}_{\mathrm{y}}\frac{\partial \mathrm{T}}{\partial \mathrm{y}}\right)+\frac{\partial }{\partial \mathrm{z}}\left({\mathrm{k}}_{\mathrm{z}}\frac{\partial \mathrm{T}}{\partial \mathrm{z}}\right)$$

(1)

here, $\mathsf{\rho }$ is the density of the material, $\mathrm{kg}/{\mathrm{m}}^3$; $\mathrm{c}$ is the specific heat capacity of the material, $\mathrm{J}/\left(\mathrm{kg}·℃\right)$; ${\mathrm{k}}_{\mathrm{x}}$, ${\mathrm{k}}_{\mathrm{y}},$ and ${\mathrm{k}}_{\mathrm{z}}$ are the thermal conductivity of the structure in $\mathrm{x}$, $\mathrm{y},$ and $\mathrm{z}$ directions, respectively, $\mathrm{W}/\left(\mathrm{m}·℃\right)$.

Heat exchange between the bridge structure and the external environment, under the influence of sunshine, mainly includes solar radiation, convective heat transfer, and radiation heat transfer, as shown in Figure 1.

$$\mathrm{q}={\mathrm{q}}_{\mathrm{s}}+{\mathrm{q}}_{\mathrm{c}}+{\mathrm{q}}_{\mathrm{r}}$$

(2)

here, $\mathrm{q}$ is the heat flux density for comprehensive heat transfer on the structural surface, $\mathrm{W}/{\mathrm{m}}^2$; ${\mathrm{q}}_{\mathrm{s}}$ is the solar radiation heat flux density absorbed by the structural surface, $\mathrm{W}/{\mathrm{m}}^2$; ${\mathrm{q}}_{\mathrm{c}}$ is the heat flux density for convective heat transfer between the structural surface and the external environment, $\mathrm{W}/{\mathrm{m}}^2$; and ${\mathrm{q}}_{\mathrm{r}}$ is the heat flux density for radiation heat transfer between the structural surface and the external environment, $\mathrm{W}/{\mathrm{m}}^2$.

Researchers have proposed several solar radiation models to consider the influence of the atmosphere on solar radiation [17,18,19,20,21,22], building upon existing research in the field of meteorology. To keep the input parameters for the model as simple as possible, the Duffie model [19] has been selected in this study for the calculation of solar radiation.

2.1. Solar Radiation Effect

Solar radiation on the external surface of the structure mainly comprises direct solar radiation (${\mathrm{I}}_{\mathrm{D}}$), sky radiation (${\mathrm{I}}_{\mathrm{C}}$), and ground reflected radiation (${\mathrm{I}}_{\mathrm{R}}$), as shown in Figure 2. Thermal radiation on the surface of the bridge can be classified into long-wave radiation and short-wave radiation, with solar radiation being a type of short-wave radiation.

The total solar radiation heat flux ${\mathrm{q}}_{\mathrm{s}}$ of the total solar radiation on the surface of the structure is given by the following equation [23,24]:

$${\mathrm{q}}_{\mathrm{s}}={\mathsf{\epsilon }\mathrm{I}}_{\mathrm{SOR}}$$

(3)

here, ${\mathrm{I}}_{\mathrm{SOR}}$ is the total intensity of solar radiation on the structure’s surface, $\mathrm{W}/{\mathrm{m}}^2$; $\mathsf{\epsilon }$ is the short-wave radiation absorption coefficient of the concrete surface.

2.1.1. Calculation of Sun Position Parameters

The declination angle $\mathsf{\delta }$, the elevation angle ${\mathsf{\alpha }}_{\mathrm{s}}$ and the azimuth angle ${\mathsf{\gamma }}_{\mathrm{s}}$, which are the relative position parameters between the sun and ground level, can be calculated [25] based on the laws of solar operation in astronomical knowledge.

The solar declination, also referred to as the solar inclination, is the angle between the solar ray and the Earth’s equator at noon. This parameter is primarily used to describe the different seasons and can be approximately calculated according to FOR (4):

$$\mathsf{\delta }={23.45}^{°}\sin \left[\frac{{360}^{°}}{365}\left(284+\mathrm{N}\right)\right]$$

(4)

here, $\mathrm{N}$ is the annual accumulated day, which is the total number of days from January 1 to the current date. The solar declination ranges from $-{23.45}^{°}~{23.45}^{°}$, with a value of $+{23.5}^{°}$ during the summer solstice, zero during the spring and autumn equinoxes, and $-{23.5}^{°}$ during the winter solstice.

$$\sin \left({\mathsf{\alpha }}_{\mathrm{s}}\right)=\cos \left(\mathsf{\phi }\right)\cos \left(\mathsf{\delta }\right)\cos \left(\mathsf{\tau }\right)+\sin \left(\mathsf{\phi }\right)\sin \left(\mathsf{\delta }\right)$$

(5)

$${\mathsf{\gamma }}_{\mathrm{s}}=\mathrm{sign}\left(\mathsf{\tau }\right)\mid {\cos }^{-1}\left[\frac{\sin \left({\mathsf{\alpha }}_{\mathrm{s}}\right)\sin \left(\mathsf{\phi }\right)-\sin \left(\mathsf{\delta }\right)}{\cos \left({\mathsf{\alpha }}_{\mathrm{s}}\right)\cos \left(\mathsf{\phi }\right)}\right]\mid$$

(6)

In the above formula, ${\mathsf{\alpha }}_{\mathrm{s}}$ is the solar elevation angle, which is $0^{°}$ at sunrise and sunset. $\mathsf{\phi }$ is the geographical latitude, which is positive in the Northern Hemisphere and negative in the Southern Hemisphere, and the value range is $-{90}^{°}~{90}^{°}$; $\mathsf{\tau }$ is the solar hour angle, and the solar hour angle at noon is exactly $0^{°}$, $\mathsf{\tau }=\left(\mathrm{t}-12\right)\times {15}^{°}$, where $\mathrm{t}$ is the true solar hour; the ${\mathsf{\gamma }}_{\mathrm{s}}$ is positive to the west and negative to the east, and the value range is $-{180}^{°}~{180}^{°}$; the $\mathrm{sign}$ is a symbol function.

The relative position relationship between the structural plane and the sun is shown in Figure 3. The incident angle $\mathrm{i}$ of the solar ray, the angle between the solar ray and the external normal $\mathrm{n}$ of the structural surface, is calculated by the following FOR (7) [26]:

$$\cos \mathrm{i}={\sin \mathsf{\alpha }}_{\mathrm{s}}\cos \mathsf{\beta }+{\cos \mathsf{\alpha }}_{\mathrm{s}}\sin \mathsf{\beta }\cos \left({\mathsf{\gamma }}_{\mathrm{s}}-\mathsf{\gamma }\right)$$

(7)

where $\mathsf{\beta }$ is the inclination angle of the structural surface relative to the horizontal plane, and the value range is $0^{°}~{180}^{°}$. When it is greater than ${90}^{°}$, the surface is downward; $\mathsf{\gamma }$ is the angle between the exterior normal $\mathrm{n}$ of the structural surface and the positive south direction, ranging from $-180° \mathrm{to} 180°$. The direction is positive to the west and negative to the east.

2.1.2. Intensity of Solar Radiation

Direct solar radiation is a component of the radiation intensity that reaches the earth’s surface after undergoing multiple attenuations, such as absorption and scattering. In engineering calculations, Bouguer’s Formula (8) is commonly used to estimate the intensity of direct solar radiation reaching the surface of the earth [27]:

$${\mathrm{I}}_{\mathrm{D}0}={\mathrm{I}}_0{\mathrm{P}}^{\mathrm{m}}$$

(8)

where ${\mathrm{I}}_0$ is the solar constant, which represents the radiation intensity of the upper bound of the atmosphere projected onto the Earth’s surface in unit time, $\mathrm{W}/{\mathrm{m}}^2$; $\mathrm{m}$ is the atmospheric optical quality; $\mathrm{P}$ is the composite atmospheric transparency coefficient [26].

$${\mathrm{I}}_0=1367\left[1+0.033\cos \left({360}^{°}\mathrm{N}/365\right)\right]$$

(9)

$$\mathrm{m}=\frac{1}{\sin \left({\mathsf{\alpha }}_{\mathrm{s}}\right)}$$

(10)

$$\mathrm{P}={0.9}^{{\mathrm{t}}_{\mathrm{u}}{\mathrm{k}}_{\mathrm{a}}}$$

(11)

$${\mathrm{t}}_{\mathrm{u}}={\mathrm{A}}_{\mathrm{tu}}-{\mathrm{B}}_{\mathrm{tu}}\cos \left(\frac{{360}^{°}\mathrm{N}}{365}\right)$$

(12)

where ${\mathrm{t}}_{\mathrm{u}}$ is the Linke turbidity coefficient, which is related to time and geographical location; ${\mathrm{k}}_{\mathrm{a}}$ is the relative atmospheric pressure at different altitudes, and its value varies with altitude [25]. Both ${\mathrm{A}}_{\mathrm{tu}}$ and ${\mathrm{B}}_{\mathrm{tu}}$ are empirical parameters representing the annual average value and variation range of the Linke turbidity coefficient ${\mathrm{t}}_{\mathrm{u}}$ under different atmospheric conditions. The values of ${\mathrm{A}}_{\mathrm{tu}}$ and ${\mathrm{B}}_{\mathrm{tu}}$ can be determined from

Table 1. The Linke turbidity coefficient.

Region	${\mathbf{A}}_{\mathbf{t}\mathbf{u}}$	${\mathbf{B}}_{\mathbf{t}\mathbf{u}}$
Mountain area	2.2	0.5
Village	2.8	0.6
City	3.7	0.5
Industrial area	3.8	0.6

[25].

Solar radiation is scattered by air molecules, aerosol molecules, and other particles in the atmosphere before reaching the surface of the bridge structure. The part of solar radiation that can reach the surface of the bridge structure after being subjected to this effect is called solar scattered radiation. The intensity of solar scattered radiation ${\mathrm{I}}_{\mathrm{C}0}$ ($\mathrm{W}/{\mathrm{m}}^2$) on the horizontal surface of a bridge can be calculated according to Equation (13) [28]:

$${\mathrm{I}}_{\mathrm{C}0}=0.5{\mathrm{I}}_0\frac{1-{\mathrm{P}}^{\mathrm{m}}}{1-1.4\ln \left(\mathrm{P}\right)}\sin \left({\mathsf{\alpha }}_{\mathrm{s}}\right)$$

(13)

As the Earth’s surface absorbs and reflects solar radiation, a portion of solar radiation reaching the surface can be reflected on the surface of the bridge structure. This portion of the solar radiation is called ground-reflected radiation.

The horizontal ground reflected radiation intensity ${\mathrm{I}}_{\mathrm{R}}$ ($\mathrm{W}/{\mathrm{m}}^2$) can be calculated using FOR (14) [29,30]:

$${\mathrm{I}}_{\mathrm{R}0}={\mathrm{R}}_{\mathrm{e}}\left[{\mathrm{I}}_{\mathrm{D}}\sin \left({\mathsf{\alpha }}_{\mathrm{s}}\right)+{\mathrm{I}}_{\mathrm{C}}\right]$$

(14)

where ${\mathrm{R}}_{\mathrm{e}}$ is the short-wave emissivity of the surface or water surface, typically taken at 0.2 for the ground [31].

2.1.3. Solar Radiation Intensity on Arbitrary Surface

The direct solar radiation intensity ${\mathrm{I}}_{\mathrm{D}}$, the sky scattered radiation intensity ${\mathrm{I}}_{\mathrm{C}},$ and the ground reflected radiation intensity ${\mathrm{I}}_{\mathrm{R}}$ on the structural surface with an inclination angle of $\mathsf{\beta }$ are:

$$\left\{\begin{array}{c}{\mathrm{I}}_{\mathrm{D}}={\mathrm{I}}_{\mathrm{D}0}\cos \left(\mathsf{\theta }\right)\\ {\mathrm{I}}_{\mathrm{C}}={\mathrm{I}}_{\mathrm{C}0}\frac{1+\cos \left(\mathsf{\beta }\right)}{2}\\ {\mathrm{I}}_{\mathrm{R}}={\mathrm{I}}_{\mathrm{R}0}\frac{1-\cos \left(\mathsf{\beta }\right)}{2}\end{array}\right.$$

(15)

Under the influence of sunshine, there are different temperature differences on the surface of the bridge structure due to varying inclination angles, azimuth angles, and heights from the ground of the bridge components. However, the different components of the structure or different parts of the same component will be projected onto the surfaces of other components under the influence of sunshine, causing solar rays’ shading. Three-dimensional shading will result in large temperature gradients on the surface of the bridge. The shadow occlusion relationship between the component and the component is complicated under the action of three-dimensional sunshine.

Based on existing research, the shading caused by solar ray irradiation can be categorized into no occlusion, self-occlusion, mutual occlusion, and permanent occlusion [32], as illustrated in Figure 4.

The total amount of solar radiation ${\mathrm{I}}_{\mathrm{SOR}}$ received by any surface should satisfy FOR (16) according to the shadow occlusion relationship of the structural surface shown in Figure 4.

$${\mathrm{I}}_{\mathrm{SOR}}=\left\{\begin{array}{c}{\mathrm{I}}_{\mathrm{D}}+{\mathrm{I}}_{\mathrm{C}}+{\mathrm{I}}_{\mathrm{R}} \mathrm{Sunlight} \mathrm{area}\\ {\mathrm{I}}_{\mathrm{C}}+{\mathrm{I}}_{\mathrm{R}} \mathrm{Shadow} \mathrm{area}\end{array}\right.$$

(16)

As shown in Figure 5, the sun’s trajectory varies in different seasons, and the intensity of solar radiation received on the surface of the same structure varies significantly. Figure 5b shows the variation of solar radiation intensity on the same horizontal surface at different times of the year, as calculated using the above solar radiation model for the ${40}^{°}$ north latitude.

2.1.4. Validation of the Solar Radiation Model

Compare the measured data with the theoretical values calculated by the above theoretical formula to verify the accuracy of the solar radiation model.

The measured data were obtained by monitoring the solar radiation intensity on a sunny day in March in the ${40}^{°}$ north latitude area, as reported by Song et al. [33]. The comparison between the calculated value of the model and the measured values is shown in Figure 6. It can be observed from the figure that the simulated values of the radiation model used in this article agree well with the measured values, indicating that the radiation model is accurate and can be used to simulate the solar radiation intensity for the calculation of the structural sunshine temperature field.

2.2. Convective Heat Transfer Effect

Convective heat transfer refers to the process of mutual heat transfer between the structural surface and the surrounding environment due to the temperature difference. The heat flux density q generated by convective heat transfer between the structural surface and the atmospheric environment ${\mathrm{q}}_{\mathrm{c}}$ ($\mathrm{W}/{\mathrm{m}}^2$) can be calculated by Newton’s law of cooling [34]:

$${\mathrm{q}}_{\mathrm{c}}={\mathrm{h}}_{\mathrm{c}}\left({\mathrm{T}}_{\mathrm{a}}-\mathrm{T}\right)$$

(17)

where ${\mathrm{T}}_{\mathrm{a}}$ is the ambient temperature, $℃$; $\mathrm{T}$ is the surface temperature of the bridge structure, $℃$; and ${\mathrm{h}}_{\mathrm{c}}$ is the convective heat transfer coefficient, $\mathrm{W}/\left({\mathrm{m}}^2·℃\right)$.

The convective heat transfer coefficient h is related to the shape of the structure, wind speed, ambient temperature, and other factors. The FOR (18) is usually used to calculate the temperature field of a bridge structure [35,36].

$${\mathrm{h}}_{\mathrm{c}}=2.5\left(\sqrt[4]{{\mathrm{T}}_{\mathrm{a}}-\mathrm{T}}+1.54\mathrm{v}\right)$$

(18)

where $\mathrm{v}$ is wind speed, $\mathrm{m}/\mathrm{s}$.

2.3. Radiation Heat Transfer Effect

The nature of radiation heat transfer is the emission of electromagnetic waves from a heat source. Radiation heat transfer occurs continuously between the surface of the bridge structure and the surrounding environment. The surface of the structure not only absorbs radiation from the atmosphere and the ground but also emits radiation to the surrounding environment. Unlike solar short-wave radiation, the thermal radiation generated by radiation heat transfer is long-wave radiation.

The radiation heat transfer between the structural surface and the external environment in this article is calculated using FOR (19) [25,37].

$${\mathrm{q}}_{\mathrm{r}}={\mathrm{h}}_{\mathrm{r}}\left({\mathrm{T}}_{\mathrm{a}}-\mathrm{T}\right)-{\mathrm{q}}_{\mathrm{rn}}$$

(19)

$${\mathrm{h}}_{\mathrm{r}}={\mathrm{C}}_0\mathsf{\epsilon }\left[{\left(\mathrm{T}+273.15\right)}^2+{\left({\mathrm{T}}_{\mathrm{a}}+273.15\right)}^2\right]\left(\mathrm{T}+{\mathrm{T}}_{\mathrm{a}}+546.3\right)$$

(20)

$${\mathrm{q}}_{\mathrm{rn}}=\left(1-{\mathsf{\epsilon }}_{\mathrm{a}}\right)\frac{1+\cos \left(\mathsf{\beta }\right)}{2}{\mathsf{\epsilon }\mathrm{C}}_0{\left({\mathrm{T}}_{\mathrm{a}}+273.15\right)}^4$$

(21)

where ${\mathrm{h}}_{\mathrm{r}}$ is the radiation heat transfer coefficient, $\mathrm{W}/\left({\mathrm{m}}^2·℃\right)$; ${\mathrm{C}}_0$ is the Stefan–Boltzmann constant, taking $5.67\times {10}^{-8}\mathrm{W}/\left({\mathrm{m}}^2·{\mathrm{K}}^4\right)$; ${\mathsf{\epsilon }}_{\mathrm{a}}$ is the atmospheric radiation coefficient, its value range is $0.74~0.95$, generally taken as 0.82; $\mathsf{\epsilon }$ is the radiation emissivity of the structure, generally $0.85~0.95$; and ${\mathrm{q}}_{\mathrm{rn}}$ is the heat flux density of the inclined plane caused by the sky radiation effect, $\mathrm{W}/{\mathrm{m}}^2$.

2.4. Daily Temperature Model

Ambient temperature changes are mainly influenced by solar radiation on an ideal sunny day (without clouds or rain). The daily temperature starts to gradually rise after sunrise and typically reaches its peak around 14:00~15:00, after which it begins to fall gradually. To simulate the sunshine temperature field of the bridge structure, it is reasonable to assume that the atmospheric temperature varies as a sinusoidal function throughout the day. In this study, the segmental sinusoidal function model shown in Figure 7 is used to simulate the changes in temperature throughout the day with the following equations [38,39]:

$$\left\{\begin{array}{c}{\mathrm{T}}_1=0.5\left[{\mathrm{T}}_{\mathrm{sum}}+\Delta \mathrm{T}\sin \left(\frac{\mathsf{\pi }\left(\mathrm{t}+30\right)}{24}\right)\right] 0\le \mathrm{t}<6 \\ {\mathrm{T}}_1=0.5\left[{\mathrm{T}}_{\mathrm{sum}}+\Delta \mathrm{T}\sin \left(\frac{\mathsf{\pi }\left(\mathrm{t}-10.5\right)}{9}\right)\right] 6\le \mathrm{t}<15\\ {\mathrm{T}}_1=0.5\left[{\mathrm{T}}_{\mathrm{sum}}+\Delta \mathrm{T}\sin \left(\frac{\mathsf{\pi }\left(\mathrm{t}-9\right)}{12}\right)\right] 15\le \mathrm{t}\le 24\end{array}\right.$$

(22)

where $\mathrm{t}$ is the moment, hour; ${\mathrm{T}}_{\mathrm{sum}}={\mathrm{T}}_{\max }+{\mathrm{T}}_{\min }$; $\Delta \mathrm{T}={\mathrm{T}}_{\max }-{\mathrm{T}}_{\min }$; ${\mathrm{T}}_{\max }$ is the daily maximum temperature, taking the temperature at 3:00 p.m., $℃$; and ${\mathrm{T}}_{\min }$ is the daily minimum temperature, taking the temperature at 6:00 a.m., $℃$.

Since the solar altitude angle is zero at sunrise and sunset, the sunrise moment $t_c$ and the sunset moment $t_c$ can be calculated using FOR (23) [25]:

$$\left\{\begin{array}{c}{t}_c=12-\frac{1}{15}{\cos }^{-1}\left(-\tan \delta \tan \varphi \right)\\ t_s=12+\frac{1}{15}{\cos }^{-1}\left(-\tan \delta \tan \varphi \right)\end{array}\right.$$

(23)

where $\delta$ is the solar declination; $\varphi$ is the geographical latitude.

The accuracy of the daily temperature change model was verified by comparing the simulated values with the measured temperature data. Figure 8 displays the comparison between the simulated and measured ambient temperatures on 17 May 2019, in the area of ${116}^{°}{20}^{\prime }$ east longitude and ${39}^{°}{56}^{\prime }$ north latitude.

As shown in Figure 8, the simulated temperature changes are in good agreement with the measured temperature changes, and the maximum temperature difference is only $1.9 °\mathrm{C}$. Therefore, it can be used to accurately simulate the temperature changes of environmental objects in engineering calculations.

3. Methods

3.1. Methodology for Simulation of Sunshine Temperature Fields

In this article, the DFLUX and FILM subroutines are provided by the ABAQUS platform for the redevelopment of the software to calculate the sunshine temperature field of the structure. Figure 9 shows the secondary development interface of the subroutine. The DFLUX subroutine can apply the surface heat source controlled by the custom heat source equation to the surface of the selected structure [40]. This is used to load the solar radiation heat load onto the surface of the structure. At the same time, the sunshine shadow recognition algorithm is introduced into the DFLUX subroutine to distinguish the sunshine shadow surface of the structure. The FILM subroutine is used to define the heat transfer coefficient related to ambient temperature and model parameters [40]. Hence, the convective heat transfer and radiation heat transfer-generated heat transfer coefficients between the structural surface and the surrounding environment are loaded by the FILM subroutine. Figure 10 shows the specific loading situation.

3.2. Validation of the Simulation Method

The experimental model in Reference [41] is taken as a case, and the measured temperature value in the literature is compared with the simulated temperature value in this paper to verify the accuracy of the above temperature field simulation method.

3.2.1. Brief Description of the Case

The experimental model is a concrete-curve box girder with a total span of 10 m along the centerline of the bridge, a radius of curvature of 12 m, and a central angle of ${48}^{°}$. The main girder is a single-cell box section with a roof width of 1.7 m, a floor width of 0.62 m, a minimum vertical web thickness of 0.1 m, and a box girder height of 0.36 m. The section of the box girder is depicted in Figure 11. The test model bridge is located at ${118}^{°}{38}^{\prime }$ east longitude and ${32}^{°}{05}^{\prime }$ north latitude, and it exhibits an east-west orientation.

The simulation values of temperature at measuring points A, B, C, and D in the mid-span section of the experimental model were compared with the measured temperature values to verify the accuracy of the above sunshine temperature field simulation method. The arrangement of the measuring points is shown in Figure 11.

3.2.2. Setting of Model and Material Parameters

The concrete box girder is a hollow and closed structure, which makes it difficult to determine boundary conditions such as convective and radiative heat transfer between the internal surface of the box girder and the air inside. In the absence of directly measured data on the inner air temperature, this study uses heat conduction to simulate the heat transfer process between the internal surface of the box girder and the air in the inner cavity [42,43]. The finite element model takes into account the continuous changes in temperature and heat flux density at the interface between concrete and air. The eight-node linear heat transfer hexahedral solid element “DC3D8” provided in ABAQUS is used to simulate the concrete box girder and the air inside, and the two are connected using the “TIE” function in the program. The finite element model and meshing are shown in Figure 12 and Figure 13, respectively.

Since the temperature change caused by sunshine has little effect on the thermal parameters of concrete structures, they can be considered fixed values [42].

Table 2. Thermal parameters of materials.

Thermal Parameter	Concrete	Air
Density $\left(\mathrm{kg}/{\mathrm{m}}^3\right)$	2400	1.29
Thermal Conductivity $\left(\mathrm{W}/\left(\mathrm{m}·℃\right)\right)$	2.5	0.025
Specific Heat Capacity $\left(\mathrm{J}/\left(\mathrm{kg}·℃\right)\right)$	900	1010
Radiation Absorption Rate	0.5	/
Longwave radiative emissivity	0.9	/
Longwave radiation absorptivity	0.9	/

shows the thermal parameters of the materials used in the model.

3.2.3. Results Analysis

The accuracy of the proposed sunshine temperature field simulation method was verified by comparing the simulated temperature field values from 0 h on 13 August 2013 to 24 h on 14 August 2013 with the measured values of the temperature field during the corresponding period. The initial temperature field was obtained by introducing the temperature field calculation results of the first 3 days into the calculation model to eliminate the influence of the initial temperature of the model on the simulation results. The thermal parameters of the materials used in the model are shown in Table 2. The atmospheric temperature data for the calculation date are shown in

Table 3. Atmospheric temperature.

Date	Weather Conditions	$\mathbf{Maximum} \mathbf{Temperature}/℃$	$\mathbf{Minimum} \mathbf{Temperature}/℃$
10 August 2013	Clear	39.0	29.0
11 August 2013	Clear	39.0	30.0
12 August 2013	Clear	39.0	29.0
13 August 2013	From sunny to cloudy	39.0	28.0
14 August 2013	Clear	38.0	27.0

.

Figure 14 and Figure 15 show the contours of the calculated temperature field, and Figure 16 presents a comparative analysis of the simulated and measured temperature field values obtained using the sunshine temperature field simulation method proposed in this paper. The trend of the simulated and measured temperature field values is similar. Although the simulation results for the roof differ significantly from the measured results during the period from 10 a.m. to 5 p.m. on 13 August, the two are more consistent at other locations. The maximum errors between the simulated values and the measured values at points A, B, C, and D are 2.9 °C, 2.5 °C, 2.8 °C, and 2.8 °C, respectively. The weather changed from sunny to cloudy during the period from 10 a.m. to 5 p.m. on 13 August, and the direct solar radiation weakened, resulting in a large difference between the simulation results and the measured results for the roof.

Table 4. The deviation between the simulated and measured results.

Measuring Point	$\mathbf{Maximum} \mathbf{Deviation}/℃$	$\mathbf{Mean} \mathbf{Value} \mathbf{of} \mathbf{Deviation}/℃$
A	2.5	1.5
B	2.9	1.9
C	2.8	1.4
D	2.8	1.5

shows that the mean deviations between the simulated values and the measured values of the temperature at points A, B, C, and D are 1.5 °C, 1.9 °C, 1.4 °C, and 1.5 °C, respectively.

In summary, the proposed simulation method for the concrete box girder temperature field in this article provides results that are in good agreement with the actual situation, indicating that it can be used to accurately simulate the sunshine temperature field of bridge structures and analyze their temperature effects.

4. Results

In the daily temperature cycle of a bridge structure, solar radiation heats up the structure during the day, while the ambient temperature decreases at night and the structure dissipates heat into the environment to cool down. The sunshine temperature field of the bridge structure exhibits strong time-varying characteristics due to the changes in solar radiation intensity and ambient temperature. This section focuses on simulating and discussing the daily temperature cycle of the concrete box girder of a cable-stayed bridge.

4.1. Example Introduction

A single-box, three-cell concrete box girder with a length of 400 m (ignoring the diaphragm plate) is selected as an example to calculate the temperature field to analyze the sunshine temperature field of the closed concrete box girder, including the tuyere, which is 38.5 m. The vertical thickness of the upper and lower floors and the inclined webs on both sides is 0.55 m, and the thickness of the middle web is 0.8 m. The detailed dimensions of the box girder section can be seen in Figure 17. The bridge is located at ${116}^{°}{20}^{\prime }$ east longitude and ${39}^{°}{56}^{\prime }$ north latitude, with a north-south orientation. The meshing of the model section is shown in Figure 18.

The roof has no shading effect during the day; the bottom plate has been self-shielding; and the two outer inclined webs are exposed to the sun only for a short time during the day. Therefore, the ${\mathrm{T}}_1$~${\mathrm{T}}_8$ measuring points in Figure 19 are selected to analyze the time-varying temperature of the internal and external surfaces of the roof, the bottom plate, and the outer inclined web. Among them, ${\mathrm{T}}_1$, ${\mathrm{T}}_3$, ${\mathrm{T}}_5,$ and ${\mathrm{T}}_7$ are the temperature measuring points on the external surface, and ${\mathrm{T}}_2$, ${\mathrm{T}}_4$, ${\mathrm{T}}_{6,}$ and ${\mathrm{T}}_8$ are the temperature measuring points on the internal surface.

The influence of wind speed on the structural temperature is mainly reflected in the effect of the convective heat transfer coefficient on the surface of the structure; therefore, it cannot be ignored in the calculation of the convective heat transfer coefficient. In the absence of actual measurement data, many scholars often assume the wind speed as $1.0 \mathrm{m}/\mathrm{s}$ when analyzing the temperature field of bridge structures [44,45]. Therefore, this article also assumes the same value for the wind speed when analyzing the sunshine temperature field of the concrete box girders. The material parameters and environmental parameters required for analysis are shown in

Table 5. Thermal parameters of materials.

Thermal Parameter	Concrete	Air
Density $\left(\mathrm{kg}/{\mathrm{m}}^3\right)$	2400	1.29
Thermal Conductivity $\left(\mathrm{W}/\left(\mathrm{m}·℃\right)\right)$	2.5	0.025
Specific Heat Capacity $\left(\mathrm{J}/\left(\mathrm{kg}·℃\right)\right)$	900	1010
Radiation Absorption Rate	0.6	/
Long-wave radiative emissivity	0.9	/
longwave radiation absorptivity	0.9	/

and

Table 6. Weather conditions.

Date	Weather Conditions	$\mathbf{Maximum} \mathbf{Temperature}/℃$	$\mathbf{Minimum} \mathbf{Temperature}/℃$
5 September 2022	Clear	28.0	14.0
6 September 2022	Clear	29.0	15.0
7 September 2022	Clear	32.0	17.0
8 September 2022	Clear	32.0	19.0

. The results of the continuous calculation of the temperature field in the first three days are used as the initial temperature field for subsequent calculations to eliminate the influence of the initial temperature field on the calculation results.

4.2. Time-Varying Analysis of Temperature Field

Figure 20 shows the two-dimensional temperature distribution cloud map of the example at a typical time of the day. Figure 21 shows the time-varying curves of the surface temperature of the roof, floor, and inclined web of the concrete box girder. It can be observed that the temperature on the external surfaces of the roof, floor, and inclined web of the concrete box girder fluctuates greatly during the day, while the temperature on the internal surface changes slightly. The minimum temperature of each surface appears at around 6 a.m. The maximum temperature of the external surface of the roof appears at around 2 p.m., reaching about 44.3 °C, and the temperature difference between its internal and external surfaces can reach 16.5 °C. The change range of the external surface temperature of the floor and the inclined web is smaller than that of the roof. This is because the floor is always in a self-occlusion state and not exposed to the sun, while the two inclined webs are also exposed to the sunshine for a shorter period during the day and receive less direct solar radiation. As a result, the magnitude of the corresponding surface temperature variation is smaller compared to the surface of the top slab, which is always exposed to the sun. The maximum value of the temperature on the floor and the inclined web occurred at around 3 p.m., with a maximum value of approximately 31.0 °C, and the maximum temperature difference between the external surface and the internal surface is approximately 6.5 °C.

4.3. Vertical Temperature Gradient

A large temperature gradient is often generated in the direction of the beam height due to the low thermal conductivity of concrete. If the temperature of the roof is higher than the temperature of the web, it is referred to as the vertical positive temperature difference distribution mode, also known as the heating gradient. Conversely, when the temperature of the web is higher than the temperature of the roof, it is referred to as the vertical negative temperature difference distribution mode, also known as the cooling gradient. The difference between the maximum and minimum temperatures in the height direction of the beam represents the maximum gradient temperature difference.

The concrete box girder of the cable-stayed bridge is generally a multi-box structure. The outer web is affected by external factors and the temperature in the box, while the middle web is only affected by the temperature in the box. The time-varying analysis of the temperature field of the concrete box girder shows that the temperature of the top plate changes the most, and the temperature of the bottom plate and the outer web surface on both sides is the same. The temperature distribution of path $\mathrm{a}$ and path $\mathrm{b}$ in Figure 19 at different times is selected to analyze the vertical temperature gradient of the concrete box girder.

4.3.1. Temperature Distribution of the Path $\mathrm{a}$

Figure 22, Figure 23 and Figure 24 show the temperature changes of path $\mathrm{a}$ at different times of the day. According to the figures, the most unfavorable vertical negative temperature difference occurs at 6 a.m., which is 6.6 °C, while the most unfavorable vertical positive temperature difference appears at 2 p.m., which is about 17.3 °C.

4.3.2. Temperature Distribution of the Path $\mathrm{b}$

Figure 25, Figure 26 and Figure 27 show the temperature change of path $\mathrm{b}$ at different times of the day. According to the figure, the most unfavorable vertical negative temperature difference in a day occurs at 6 a.m., which is 6.7 °C; the most unfavorable vertical positive temperature difference appears at 2 p.m., about 17.2 °C.

4.3.3. Most Unfavorable Temperature Gradient

The above analysis shows that the most unfavorable heating gradient and the most unfavorable cooling gradient of paths a and b appear at the same time and both show a C-shaped distribution. Among them, the most unfavorable vertical negative temperature difference occurred at 6 a.m., about 6.7 °C, and the most unfavorable vertical positive temperature difference appeared at 2 p.m., about 17.2 °C.

There are significant differences in the regulations for the vertical temperature gradient of concrete box girders among different national bridge specifications. To quantify the differences, the most unfavorable temperature gradient distribution pattern calculated in this article is compared with the most unfavorable temperature gradient pattern recommended in several national specifications.

Table 7. The most unfavorable vertical temperature gradient value.

Temperature Gradient Mode	$\mathbf{Heating} \mathbf{Gradient}/°\mathbf{C}$	$\mathbf{Cooling} \mathbf{Gradient}/°\mathbf{C}$
In this paper	17.2	6.7
JTG D60-2015 [46]	25.0	12.5
AASHTO [47]	21.0	10.5
BS-5400 [48]	13.5	8.4

shows the most unfavorable vertical temperature gradient values in this article and several national specifications. The data in the table shows that the difference between the most unfavorable vertical temperature gradient value in this article and the most unfavorable vertical temperature gradient value in the General Specifications for Design of Highway Bridges and Culverts (JTG D60-2015) is the largest, with a difference of 7.8 °C and 5.8 °C for the heating gradient and cooling gradient, respectively.

As the most unfavorable vertical temperature gradients of paths a and b are the same, the most unfavorable distribution pattern of path a is chosen here for comparison with the temperature gradient distribution patterns of various national specifications. Figure 28 shows the distribution mode of the most unfavorable cooling gradient, and Figure 29 shows the distribution mode of the most unfavorable heating gradient. It can be seen from the figures that the most unfavorable temperature gradient distribution pattern obtained in this article is closest to the provisions in the British BS-5400 specification, followed by the difference with the American AASHTO specification, and the difference with the Chinese JTG D60-2015 specification is the largest. It should be noted that temperature variations within a certain range from the external surface are more pronounced due to the poor thermal storage properties of concrete. For the cooling gradient, the turning points for temperature change occur at 0.45 m from the top surface and 0.4 m from the bottom surface, respectively; for the heating gradient, the turning points for temperature change occur at 0.4 m from the top surface and 0.3 m from the bottom surface, respectively, which is closer to the BS-5400 specification.

To analyze the C-shaped temperature gradient distribution pattern obtained in this paper, the temperature variation between the upper and lower turning points is minimal, and the temperature distribution pattern resembles a straight line. On the other hand, the temperature distribution of the upper and lower turning sections is closer to an exponential function. Therefore, we used the exponential function presented in FOR (24) to fit the temperature values of the upper and lower turning sections [49,50], and the results of the fitting are shown in Figure 30 and Figure 31.

$$\mathrm{T}\left(\mathrm{x}\right)={\mathrm{T}}_0{\mathrm{e}}^{-\mathsf{\alpha }\mathrm{x}}+\mathrm{C}$$

(24)

where $\mathrm{C}$ is the temperature value at the temperature turning point, $°\mathrm{C}$; ${\mathrm{T}}_0$ is the temperature difference between the external surface of the box girder and the temperature turning point, $°\mathrm{C}$.

The minimum correlation coefficient of the fitted temperature data for the upper and lower transitions of the least favorable vertical negative temperature gradient and the least favorable vertical positive temperature gradient is 0.984, with good fitting accuracy.

Based on the analysis conducted in this study, the recommended distribution patterns for the cooling and heating gradients of concrete box girders in the construction stage are shown in Figure 32a,b, respectively. In these figures, the upper and lower transitional sections follow an exponential distribution, while the middle section follows a linear distribution.

5. Discussion

In the analysis of the temperature of concrete structures, parameters such as material density, thermal conductivity, specific heat capacity, solar radiation absorption coefficient, surface long-wave radiation absorption rate, wind speed, etc. are required. While the concrete density and specific heat capacity can be measured experimentally, the thermal conductivity of the material can also be deduced by inversion from the measured temperature data. However, determining the exact value of the long-wave radiation absorption rate of the concrete and the absorption coefficient of solar radiation on the surface of the concrete structure is challenging, with values ranging between 0.85 and 0.95 and 0.5 and 0.7, respectively. Additionally, measuring the wind speed at the surface of the structure is often difficult. This subsection focuses on the impact of three calculated parameters, namely the solar radiation absorption coefficient, the surface long-wave radiation absorption (or emission) rate, and the wind speed, on the temperature field calculations.

For the study, the control variables method was used to increase or decrease the calculated parameters individually by a margin of 30% while keeping the other parameters constant. The values of each parameter are shown in

Table 8. The values of parameters.

Parameter	Reduced by 30%	Unchanged (Original Value)	Increased by 30%
Wind speed ($\mathrm{m}/\mathrm{s}$)	1.4	2.0	2.6
Short-wave radiation absorption rate	0.42	0.60	0.78
Long-wave radiation absorption rate	0.63	0.90	1.17

.

The temperature values of $T_1$ measuring points on the roof are compared and analyzed, and the comparison results are shown in Figure 33.

From Figure 33, it is apparent that the solar radiation absorption coefficient has the greatest impact on the temperature calculation results, followed by the influence of changes in wind speed. The long-wave radiation absorption coefficient has the smallest impact on the temperature field calculation results while maintaining the same amplitude of change. The difference in the maximum temperature of the structural surface will reach about 13%, and the temperature change can be over 10 °C by increasing or decreasing the solar radiation absorption coefficient by 30%. This is because the solar radiation absorption coefficient determines how much solar radiation reaching the structural surface can be absorbed by the structure, and solar radiation is the primary cause of structural temperature change. Therefore, changes in this parameter have the greatest influence on the calculation results of the temperature field. The influence of wind speed on structural temperature is mainly reflected in the convective heat transfer coefficient between the structural surface and the external environment. The larger the wind speed, the larger the convective heat transfer coefficient, and the faster the heat dissipation of the structure. Decreasing wind speed will weaken the convective heat transfer process and reduce the heat dissipation speed of the structure. The long-wave radiation absorption coefficient mainly affects the radiation heat transfer between the structure and the external environment. However, the temperature change caused by this effect is relatively small. This results in the temperature change caused by changing the long-wave radiation absorption coefficient also being small.

In summary, it is important to choose a reasonable value for the solar radiation absorption coefficient to avoid significant deviations between the calculated temperature field and the actual results for concrete structures.

6. Conclusions

This study involves the development of a new simulation method using the user subroutine function of ABAQUS, which allows for the imposition of complex thermodynamic boundary conditions with ease. The accuracy of the simulation method was verified by comparing the simulated values of temperature with the measured values. Based on this simulation method, the sunshine temperature field of the concrete box girder of a cable-stayed bridge was analyzed. The main conclusions of this study are as follows:

(1)

The comparison between the simulated and measured temperature values of the experimental model reveals that the difference between the simulated and measured values is small, with a maximum deviation of 2.9 °C. This result verifies the accuracy of the simple simulation method of the sunshine temperature field used in this paper;

(2)

The analysis reveals a significant temperature difference between the internal and external surfaces of the box girder under the influence of sunshine, with the maximum negative temperature difference occurring around 6:00 a.m. and the maximum positive temperature difference occurring around 2:00 p.m.;

(3)

The most unfavorable vertical temperature gradient distribution pattern of the concrete box girder calculated in this paper is not completely consistent with the double-line distribution pattern specified in the current “General Specifications for Design of Highway Bridges and Culverts” in China (JTG D60-2015). The comparison with the vertical temperature gradient values of concrete box girders in different national specifications shows that the Chinese specification is more conservative, and the results of this study are closest to the British specification. Therefore, for the concrete box girders in the construction stage, it is recommended to adopt the C-shaped distribution pattern calculated in this paper for the cooling and heating gradients;

(4)

The sensitivity analysis of the parameters used to calculate the temperature field indicates that the solar radiation absorption coefficient has the greatest impact on the temperature calculation results, followed by wind speed changes, while changes in the long-wave radiation absorption coefficient of the structure surface have the smallest impact on the temperature field calculation results. Increasing or decreasing the solar radiation absorption coefficient by 30% can result in a difference of up to 13% in the maximum temperature of the structure’s surface and a temperature variation of 10 °C or more.

In this paper, a simple simulation method is proposed to study the temperature field distribution of bridge structures under sunshine, with a focus on the concrete box girder of cable-stayed bridges. The accuracy of the simulation method is validated by comparing the simulated and measured temperature values of an experimental model, and the results show a small difference. The research findings have significant implications for the control of bridge alignment and stress state during construction, ensuring a reasonable initial operating state of the bridge, and enhancing the sustainability of the structure. However, due to space limitations, only the sunshine temperature field of the concrete box girder is studied, and further research is needed to analyze the sunshine temperature field of other materials and bridge members.