A Closed-Form Design Method for U-Shaped Springs in Aeroelastic Modeling of Truss-Girder Suspension Bridges

TL;DR

This paper presents a novel closed-form design method for U-shaped springs in aeroelastic models of suspension bridges, significantly reducing design time and improving accuracy through analytical equations and derivative-free optimization.

Contribution

It introduces a closed-form analytical approach for designing U-shaped springs, replacing trial-and-error methods and enabling rapid, accurate optimization for aeroelastic modeling.

Findings

The method accurately predicts elastic stiffness for suspension bridge models.

Optimization reduces design time to several seconds.

Experimental validation confirms the method's reliability.

Abstract

Aeroelastic model testing is essential for evaluating the wind resistance performance of long-span suspension bridges. In these models, truss girders are commonly modelled by a discrete-stiffness system incorporating U-shaped springs to simulate elastic stiffness properties, including vertical bending, lateral bending, and torsional rigidity. The design of these U-shaped springs significantly influences the accuracy of aeroelastic model tests for truss-girder suspension bridges. Traditional design approaches, however, lack an analytical foundation, relying instead on trial-and-error searches across the full parameter space, which is computationally intensive and time-consuming. To overcome these limitations, this study introduces a novel design method that establishes closed-form equations for U-shaped spring design. The method simplifies the truss girder's supporting condition to a cantilever configuration and determines the corresponding elastic stiffness using the principle of elastic-strain energy equivalence. These closed-form equations transform the design process into a non-smooth optimization problem, accounting for precision constraints inherent in practical fabrication. Derivative-free optimization algorithms, including the Nelder-Mead method, Pattern Search method, and Genetic Algorithm, are employed to identify a globally optimal solution. The proposed method is validated through its application to a representative suspension bridge with a truss girder, with numerical and experimental results confirming its accuracy and reliability. This approach enhances aeroelastic model design techniques for long-span bridges by providing a theoretical framework for the design of U-shaped spring, reducing the optimization process to several seconds.