# Research on Effective Design Methods of Core Beam of Full Bridge Aeroelastic Model
## 1 Introduction  
Suspension bridges and cable-stayed bridges are sensitive to the effect of wind loads, due to their light mass, large flexibility, and small damping [1; 2; 3; 4; 5], and the dynamic response of the long-span bridges under wind actions has an increasing relevance as the lengths of the spans grow [6; 7]. So, the evaluation of wind resistance performance is essential for large-span bridges and other important structures [8]. Despite computational fluid dynamics [9; 10] and semi-analytical approaches [11; 12], wind tunnel tests remain the most direct and reliable way that investigates the aeroelastic behavior of a full bridge due to many complex factors [13; 14].  
Among various reduced-scale models that can be tested in the wind tunnel to study the aeroelastic response of a real bridge, the full-bridge model can more realistically simulate various aerodynamic actions of the real bridge under the action of wind, as well as the interaction between the main vibration modes of the structure [15; 16; 17]. A large number of wind tunnel tests on the full-bridge aeroelastic models have been carried out to study the aerodynamic performances of the prototype bridge [18; 19; 20; 21; 22; 23; 24; 25]. According to these references, the full-bridge reduced model tests require a faithful representation of the phenomena that are going to be studied when carried out in boundary layer wind tunnels. This requires a series of critical tasks [26; 27; 20; 28]. One of them is a precise reproduction of the geometry of the model, otherwise slight variations will deeply affect the results [27; 29]. Therefore,very high requirements have been put in place throughout the design, and production of the reduced-scale model. The reduced-scale models consist of core beams and \"clothing\", where the former provides required stiffness, and the latter simulates the aerodynamic configuration [30]. Furthermore, the mass properties of the core beam and the clothing combined should be similar to those of the real bridges. Obviously, the determination of the section geometric parameters of the core beam is particularly important.  
Targeted inertial moments of the core beam are calculated based on the similarity relationship with the prototype bridge [30]. The inertial moments of the core beam, including two bending moments of inertia and one torsional constant, are controlled by the section geometric parameters. The inertial moments determined by the section parameters should be as close as possible to the targeted ones.  
However, the common cross-sections of the core beams are various, such as rectangular, circular, U-shaped and \(\pi\)-shaped sections [31; 32; 33], the ranges of the section geometric parameters are ambiguous. It is difficult to obtain an analytical solution of the torsion constant. Therefore, it is extremely difficult to determine the section geometric parameters of the core beam even if all the targeted inertial moments are modeled accurately. At present, the trial-and-error method is commonly used to determine the section parameters of the core beam, which is complex, is tedious and has low accuracy. The U-shaped cross-section has been the most widely used for core beams of bridge decks, and the rectangular section is generally used for the core beams of bridge towers [33].  
In order to determine which geometric parameters of the core beam the model targeted inertial moments effectively, three numerical solutions of the torsion constant are proposed, and two optimization methods for geometric parameters are presented in this study. The first optimization method is the optimization in ANSYS, and the other one is the genetic algorithm. The advantages and disadvantages of the concerned methods are presented.