# Geometrical Parametric Study on Steel Beams Exposed to Solar Radiation
## 1 Introduction  
Climate change is becoming more noticeable with time and has been the focus of hundreds of research works during the last few years. It is agreed that climate change and global warming can impact all aspects of human life, including the construction industry [1, 2]. Short-duration cold waves were also reported to impose undesirable temperature-induced stresses, especially for large bridge structures [3]. Some types of structures, like bridges, are under the direct influence of climate variations due to their outside exposure [4, 5, 6]. Wide differences in temperature between seasons could induce larger end displacements for simply-supported superstructures or higher end-restraint moments for continuous spans [7, 8, 9]. On the other hand, wider daily temperature differences lead to higher vertical and lateral (if any) temperature gradients in the sections, which may induce unfavorable sectional flexural stresses [10, 11, 12, 13, 14, 15]. Self-equilibrating stresses are the type of stresses that are induced to equilibrate the nonlinear sectional deformations due to nonlinear temperature gradients along the depth or width of a bridge's superstructure [16]. Previous studies showed that self-equilibrating stresses can be high enough to initiate surface cracking of bridge girders, which impacts the long-term serviceability and results in unplannedrehabilitation costs [10; 17]. A recent study [18] on a large span steel space dome showed that seasonal changes of environmental thermal loads can lead to an axial stress of up to 20 MPa. The geometry and configuration of the bridge superstructure play a major role in the distribution of sectional temperature gradients in both directions or across the thickness of these sections, where lateral gradients are significant in the case of concrete box-girders, while these gradients are noticeably small compared to vertical gradients in precast I-girders. Wider temperature gradients would be imposed in thick sections, while the gradient across the thickness of steel sections is almost zero. Several recent field, experimental and numerical studies aiming to investigate the possible impacts of temperature changes on concrete [19; 20; 21; 22; 23; 24; 25; 26] and composite [12; 27; 28; 29] gliders have been published. However, only a few focused on the influence of geometrical aspects and girder superstructure configuration. [PERSON] et al. [30] constructed three experimental concrete I-girders. The three girders were AASHTO Type-I girders, but with different top flange configurations. Thermocouples were placed in the sections vertically along the webs and horizontally along the flanges. The authors showed that significant temperature gradients were recorded during the pre-deck placement. They concluded that the current design gradient model differs from the recorded gradient distribution, and there is a lack of a model to capture the flanges' significant lateral gradients. [PERSON] et al. [31] constructed an experimental concrete box-girder segment with an unconventional configuration where the bottom flange was noticeably larger and wider than the top flange. The section was instrumented with thermocouples at different locations to evaluate the changes of temperature gradient shape with time. The authors concluded that the design temperature gradient models of most of current bridge codes are not suitable for the tested unconventional configuration. Moreover, their results revealed large lateral temperature gradients that affect the stress distribution in the section. A previous study on concrete I-girders [32] compared the thermal gradients of I-girders during construction (before deck slab placement) and after the placement of deck slab on a parallel series of I-girders. The research revealed that the lateral bottom-flange's gradient was reduced by 3 \({}^{\circ}\)C after slab placement due to the shading effect from the overhanging slab.