# Numerical Study on Temperature Distribution of Steel Truss
## 4 FEM Model Considering Shadow Effect and Simulation Process  
The 3D FEM model for the whole steel truss aqueduct is shown in Figure 6. In the model for the whole aqueduct, shell elements are used for simulating the steel planes and beam elements for truss structures. As the superstructures remain similar along the length and thickness, the temperature of the steel aqueduct has almost no change in the longitude direction under solar radiation [20]. Thus, for the sake of convenience and timesaving, only the mid-span cross-section is modeled and analyzed. A simplified 3D finite element model of the mid-span section with a small length is established using Solid 70 element to analyze the temperature distribution, as shown in Figure 7. The origin of coordinates is set in the middle of the floor of the water channel. In the analysis, the solar radiation and longwave radiation are simulated by applying an equivalent heat generation rate, and heat convection is considered through the surface thermal load. The thermal boundary condition of the model is illustrated in Figure 8. Under solar radiation, the azimuth angle of each surface, angle of incidence at each hour, and the shadow condition are varied. The differences induce the distinct solar radiation and need to be discussed separately. Five types of surfaces are classified in Figure 8, namely Type \(a\), \(b\), \(c\), \(d\), and \(e\). Type \(a\) surfaces represent the upper surfaces of top chords, which are under direct and diffuse radiation throughout the sunshine duration. Type \(b\) surfaces are the inner surfaces of the truss aqueduct, which are influenced by shadow induced by the outer truss members and top chords. Type \(c\) surfaces are the inner walls of the aqueduct, which directly contact and transfer heat with water when water exists. According to the specifications for load design of hydraulic structures (DL5077-1997), the convection coefficient of water is so large that it could be considered as infinity. Thus, in this study, the temperatures of the inner walls, which contact with water, are the same as those of surrounding water. The temperatures of water are set as 33 \({}^{\circ}\)C and 2 \({}^{\circ}\)C in summer and winter, respectively. Type \(d\) surfaces are similar to type \(b\) surfaces, in which part of the surfaces is under sunshine  
Figure 6: 3D finite element model (FEM) of the steel truss aqueduct. Figure 7: 3D FEM model of heat conduction. during the day. Type \(e\) surfaces are the lower surfaces and only affected by ground reflected radiation, ambient air temperature, and water if contacted. In order to consider the shadow effect of diagonal and vertical bracing conveniently, they are transferred into a box girder equivalently. Due to the existence of the top chord and the equivalent box girder, the solar radiation can only be applied on the part of the inner surfaces of the truss aqueduct, as shown in Figure 9. Only the surfaces exposed to yellow areas are under the solar radiation at that time. These shadow areas change with time, and thus the calculations of shadow areas on the inner surfaces of the aqueduct by time are required. Based on the FEM model, the numerical simulation process for the truss aqueduct under solar radiation in ANSYS software is shown in Figure 10.  
Figure 8: Thermal boundary condition on the FEM model. Figure 9: Illustration for local shadow effects of the equivalent box girder and top chord to the truss aqueduct. The temperature fields of the aquduct in summer (mid-July) and winter (mid-January) were calculated using the proposed model and method over 72 h, which were sunny without rain, separately. As discussed above, water has a large specific heat capacity, and the temperature of the water is relatively stable during a few days. The water level inside the aquduct, which is changed with seasons and transportation demands, will significantly influence the temperature distribution of the aquduct.