# Numerical Study on Temperature Distribution of Steel Truss
## 1 Introduction  
To satisfy the demand for large span capability and various attractive geometrical surfaces, steel structures are widely used in numerous applications [1; 2; 3], of which one significant application is steel bridge [4]. Aqueducs [5] are special kinds of bridges for water transportation, which were usually made of reinforced concrete [6; 7; 8] or large volume concrete [9; 10; 11] in the past. Nowadays, new forms of steel truss aqueducs have been constructed like Magdeburg Water Bridge (2003) but are rarely seen in China. The analysis of structural behaviors of such type of aqueducs could be found in several references [12; 13], but the investigations on temperature effects of this kind under solar radiation are limited. An aqueduc has complex temperature boundary conditions. Different from common bridges, an aqueduct [14; 15; 16] has water flowing through. The temperature boundary conditions of an aqueduct are that the external surfaces contact the surrounding atmosphere and the internal surfaces directly contact the flowing water [9], which induce continuous heat exchange for the external surfaces with the atmosphere through radiation, convection, and conduction and stable temperature for the inner surfaces, respectively. Various natural environmental conditions have an influence on the temperature distributions of external surfaces like geographic locations, topography, and landforms, the orientation of aqueduct, seasons, solar radiation intensity, a variation of air temperatures, cloud, fog, rain, and snow. The temperature distributions of aqueducs are rather complicated consideringthe combination of those temperature boundaries, especially when an extreme weather condition is applied. Assuming a sudden rise or drop of ambient temperature happens, the differences in temperature boundaries will cause inhomogeneous temperature change and induce large nonlinear temperature gradients. The nonlinear temperature gradients along the directions of height, the width of the beam, and thickness of plate unquestionably cause significant deformation and stress of temperature under constraints [17; 18; 19], which threaten the safety and serviceability [11; 20] of aqueducts. Thus, the study of thermal stress of an aqueduct is a significant aspect of the design process, and temperature distribution is the prerequisite for stress analysis. Thermal stresses have different sources: daily solar radiation and annual ambient temperature change, among which the former renders a higher rate of temperature change and is the main source of thermal stresses. Numerous researchers have studied the solar radiation effect on bridges. [PERSON] and [PERSON] [21] proposed a conic distribution of sunshine temperature difference and derived a formula to calculate temperature stress of concrete box aqueduct. [PERSON] et al. [22] found that vertical deflection of concrete box girder during cantilever construction is greatly influenced by solar temperature gradient. [PERSON] et al. [23] used two-dimensional plane and three-dimensional solid finite element model (FEM) to study concrete box girder arch bridges. [PERSON] et al. [24] studied the mechanisms of solar radiation-induced behavior of Tamar Bridge through monitoring data and FEM. [PERSON] et al. [25] monitored the temperature field of a steel latticed shell structure and found that solar radiation has little effect on this kind of structure. [PERSON] et al. [26] developed a method to predict the 3D temperature distribution of different curved steel box girder bridges under solar radiation. Besides, several researchers [27; 28] did experiments on different shapes of steel members under solar radiation considering shadow effect, providing resources for thermal design. However, those studies have focused on relatively small concrete bridges [22; 23], composite bridges [24], steel shell [25], steel box girders [26; 27; 28], and steel members of I or H shape [29; 30], which have a relatively limited value of reference on the thermal studies of steel truss aqueducts.