Based on the previous research work, a new idea is proposed for analyzing the impact of solar radiation on the substructure of bridges. Investigation is conducted in the thermodynamic phenomena and temperature stress of a dual-column pier. Research is led to the thermal conductivity of concrete structure and the values of the environmental parameters under solar radiation. An analytical code is written for the thermal analysis of the dual-column pier using the parametric modeling function of FE software, by means of which the temperature distribution of the bridge structure is computed under solar radiation. Using the thermal analytical results, the temperature stress of the dual-column pier is further calculated. The results tell that the temperature gradient distribution curve inside the concrete of the pier fits favorably the curve defined in the design specification and coincides quite well with real situation, which verifies the new idea proposed in this paper. Under the solar radiation which is a time-variable nonlinear temperature load to the bridge, the maximum principal stress is found at the corner of the pier with the sign of negative, which is believed to threaten the safety of the substructure of bridge and is necessary to arouse emphasis.
Solar radiation induces transient variation of temperature stress in the bridge structures, and this nonlinear temperature stress which is time-variable tends to bring about a potential safety hazard to the bridge structure. According to some reports, it can be found that the solar radiation may be one of the reasons to blame for the failure of some bridges [
As shown in Figure
Flowchart of the analytical thought.
To accurately analyze the temperature effect on the reinforced concrete bridge piers under the solar radiation, it is necessary to choose a reasonable method to obtain the temperature field of the bridge pier. And the thermodynamic parameters need to be determined firstly. Obviously, the temperature field of the reinforced concrete pier changes as the solar radiation varies in a day. The time-varying temperature field of the concrete pier is closely related to the material properties and some surroundings influence factors, such as the geographical position and orientation of the pier system, the intensity of the solar radiation, the heat exchange coefficient, the atmosphere temperature, and the environment in which the pier system locates.
The heat exchange coefficient, also known as natural convection heat transfer coefficient, is defined to account for the amount of heat that is transferred between materials and objects (whether in gaseous state or in liquid state or in solid state) which have different temperatures [
The heat exchange coefficient by solar radiation
Convective heat exchange coefficient
From (
Average values of thermal exchange coefficient with the wind velocity
Orientation of bridge components |
|
|
|
---|---|---|---|
w/(m2·°C) | w/(m2·°C) | w/(m2·°C) | |
On the surface exposed to the sun | 3.9 | 7.1 | 11.0 |
On the surface in the shade | 4.0 | 7.5 | 11.5 |
In the perspective of civil engineering calculations, the values of thermal exchange coefficients listed in Table
To obtain the temperature field, some thermophysical parameters need to be determined for the material of concrete, including the heat conductivity coefficient, the specific heat capacity, and the linear expansion factor. The main factor that has a notable influence on the thermal parameters (such as the heat conductivity coefficient and the specific heat capacity) of the concrete material is the mixing proportion. With regard to the normal weight concrete, the heat conductivity coefficient is within the limits of 1.86~3.49 W/(m·s·°C), and the specific heat capacity is ranged in 800~1200 J/(kg·°C). The linear expansion factor usually remains constant under the normal atmospheric temperature, and the value of 1.0 × 10−5/°C can be used for normal weight concrete, reinforced concrete, and also prestressed concrete during the regular engineering calculation.
The amount of solar radiation on the ground surface is influenced by the angle of the sunlight and the cloud coverage. When the sunlight angle is small (in the morning or at the nightfall), the distance of sunlight travelling in the air is much farther, and therefore the amount of energy dissipated during travelling is much larger. In the meantime, if the cloudiness is increased, the sunlight energy is lost at a larger rate. The amount of energy reaching the surface of an object is also affected by the incidence angle of the sunlight. The surficial temperature of concrete structure under solar radiation can be obtained by
The atmospheric temperature adopted in the model calculation is chosen from a series of data collected at a site in Chongqing, which can represent the typical atmospheric temperature in one day. Table
Atmospheric temperature collected at site
Collection time | 6:00 | 8:00 | 11:00 | 12:30 | 14:30 | 17:00 | 18:00 |
|
|||||||
Atmospheric temperature (°C) | 13.2 | 16.4 | 32.1 | 34.3 | 36.6 | 28 | 20.4 |
The absorption coefficient on the concrete structure surface is taken as
In Table
Typical values for the solar radiation intensity
Region | Orientation | Local time | |||||||
---|---|---|---|---|---|---|---|---|---|
6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||
Chongqing, China | S | 16 | 47 | 79 | 119 | 200 | 252 | 270 | 252 |
W (E) | 16 | 47 | 79 | 104 | 122 | 133 | 138 | 340 | |
N | 124 | 153 | 131 | 104 | 122 | 133 | 138 | 133 | |
H | 81 | 270 | 487 | 686 | 844 | 945 | 980 | 945 |
E, S, W, N, and H refer to the vertical planes, respectively, normal to the eastern direction, the southern direction, the west direction, and the northern direction, and the horizontal plane.
Based on the theory of solar radiation [
APDL scripts are compiled from the total analytical process based on the code of ANSYS, and the temperature field is analyzed by addition of convectional boundary conditions on the elements. Figure
Flowchart of thermal field analysis.
For illustrative purpose, the substructure of the example bridge is a dual-column pier, and the superstructure is prestressed concrete T-shaped girder of simply supported span. The main size of the bridge pier is shown in Figure
Dimensions of the bridge pier.
The element of SOLID70 is developed by ANSYS, which can be used to perform 3D steady-state thermal conductivity analysis and 3D transient thermal conductivity analysis. The element has 8 nodes and each node only has a temperature DOF. The SOLID70 is applied when temperature field analysis is performed. When constructing the FE model for the bridge pier, the element of SOLID45 is used, for this element has 6 DOFs at each node and can be used to account for the effects of plastic behavior, creep, expansion, stress stiffening, large deformation, and large strain.
The FE model is established as shown in Figure
FE model of the bridge pier.
The thermophysical parameters for the material of concrete are listed in Table
Thermophysical parameters for concrete.
Parameter | Unit | Variable name | Value |
---|---|---|---|
Heat conductivity coefficient | w/(m·°C) | KXX | 2.94 |
Convection coefficient | w/(m·°C) | HF | 11.0/11.5 |
Density | kg/m3 | DENS | 2500 |
Specific heat | J/(kg·°C) |
|
1050 |
Heat emission coefficient | w/(m2·°C) | CONV | 50 |
The heat conductivity coefficient changes as the solar radiation intensity is different. And therefore different material properties are defined for the structure surfaces since some surfaces are exposed to the sunshine while the others are shadow surfaces.
Analysis is performed of temperature distribution in the pier structure at the time of 6:00 a.m. in the morning and 18:00 p.m. in the afternoon, respectively. The instantaneous sunlight direction is set to be in the
The results corresponding to three representative moments are chosen for analysis. At 8:00 a.m., the incident angle of the sunlight is small, the top surface of the cap beam and the surfaces of the pier exposed to the sun are influenced by solar radiation, and the FE model is modified according to this situation. At 11:00 a.m., a similar case can be expected with the situation at 8:00, with the exception that the area of the pier exposed to the sunshine decreases as the incident angle of the sunlight increases. When the time turns to 14:30 p.m., the calculation method remains unchanged for analysis of structural temperature field and temperature gradient stress compared with the cases of 8:00 and 11:00 a.m. But at this time, the incident angle of the sunlight reaches the largest value in a day and the whole pier is located in the shadow of the cap beam; hence, the influence of solar radiation on the pier can be neglected. The temperature field nephogram for the bridge pier at different moments is shown in Figure
Temperature field at each moment.
8:00 a.m.
10:00 a.m.
14:30 p.m.
The calculated values of temperature over the structural surfaces with different orientations at different moments are shown in Table
Calculated values of the structural surface temperature.
Surface orientation | Moment | ||||||
---|---|---|---|---|---|---|---|
6:00 | 8:00 | 11:00 | 12:30 | 14:30 | 17:00 | 18:00 | |
S | 13.41 | 17.43 | 35.38 | 37.81 | 39.20 | 28.61 | 20.64 |
W (E) | 13.41 | 17.43 | 33.83 | 36.09 | 43.22 | 35.22 | 25.51 |
N | 14.81 | 18.10 | 33.83 | 36.09 | 38.19 | 29.99 | 22.24 |
H | 14.25 | 22.73 | 44.39 | 47.04 | 47.57 | 31.51 | 21.60 |
Variation curves of the temperature gradient inside the structure with respect to the vertical axis are plotted corresponding to two typical sections I and II shown in Figure
Temperature gradient of section I at the three moments.
Temperature gradient of section II at the three moments.
From Figures
Transform the elements of thermal analysis into elements of structural analysis and write the temperature field information recorded in TEMP.rth from thermal analysis into the load step files. Then define the analytical type as static analysis and resolve the problem. After reanalysis of the FE model, the temperature stress at every time step can be derived.
With the use of solid elements in the FE model, result of structural stress can be obtained. From the stress result, it can be found that, in the solar radiation cases at the moments of 8:00 and 11:00 a.m., respectively, the stress of the two columns is not evenly distributed in the
There is temperature difference on both the internal and external surfaces of the pier, and different distributions of tensile stress can be anticipated at different nodes of the same cross section. In order to better reflect this phenomenon, 14 typical nodes are selected in the pier model as shown in Figure
The nodes selected for stress analysis.
The thermal internal stress at the location of the selected nodes.
It cannot be difficult to find that the tensile stress at nodes 148 and 149 is the largest. Some tensile stress can also be found at the other nodes; although small in values, they can lead to much worse damage under the repeated solar radiation, for there is usually no prestressing steel mounted in the bridge pier. So much more attention is needed to be paid to the solar radiation influence on column pier, so that the unnecessary damage can be avoided in the bridge substructure.
A method is proposed in this paper for analysis of the temperature field and the temperature stress of the bridge substructure under solar radiation. Using the software of ANSYS, thermal analysis is performed for a dual-column pier under the solar radiation of different incident angles corresponding to the different moments from 6:00 a.m. to 18:00 p.m. The results corresponding to three typical moments are selected for presentation, and the temperature stress of the pier structure is analyzed based on thermal analysis. The following conclusions can be drawn. It can be found that the conduction of the thermal flux inside the structure is uniformly distributed, and the temperature distribution coincides quite well with the temperature gradient curves defined in the design codes, which can be served as a testimony that the method presented in this paper is reasonable. After comparing the results of the two cases in accordance with 11:00 a.m. and 14:30 p.m., respectively, it can be concluded that the amounts of solar radiation absorbed by the structure as well as the surficial location of the structure exposed to the sunshine are the two key factors which are most efficient in controlling the distribution of temperature difference stress. The tensile stress which is most hazardous to the safety of bridge structures can be found in the corners of the bridge piers, with the largest value of about 0.3 MPa. The repeated and accumulative characteristics of the solar radiation effect can lead to an unpredictable potential safety hazard to the bridges. And hence it is highly suggested that the structural stress induced by solar radiation should be considered during the design and construction of a column pier with large size.
The authors declare that there is no conflict of interests regarding the publication of this paper.