Gradient-based algorithmic cross-frame cross-section optimization for skewed steel I-girder integral abutment bridge deck placement response

Abstract

Steel I-girder integral abutment bridges (IABs) often have fixed bearings during construction, which can induce considerable flange lateral bending response during deck placement when the bridges are skewed, especially at cross-frames near girder ends. Cross-frames are important load-carrying members for skewed bridge construction; however, they are often designed using standardized uniform cross-sections across a bridge after considering all pertinent load cases. In lieu of traditionally-used iterative design processes that rely on engineering judgements, this study adopted an algorithmic approach to optimize cross-frame cross-sections as a practical, efficient, and reliable solution to refine load distribution and reduce flange lateral bending stress for skewed steel I-girder IABs during deck placement. Gradient-based Method of Moving Asymptotes was used to optimize an IAB considering skew variations between 15º-60°. The bridges were simulated for deck placement with 3D models in CSI Bridge, using modeling strategies verified with existing field measurements and 3D models in ABAQUS (validated in prior research). The optimization achieved around 20 % decrease for peak bottom and top flange lateral bending stresses (the objective function), while the total cross-frame volume (the constraint) decreased by about 30 % for all bridges. Bridge cross-section stiffness and cross-frame slenderness ratio satisfied design requirements after optimization, and girder movement had only slight changes. The adopted optimization approach provided insights on lateral bending response of skewed IABs during deck placement – optimization was generally achieved by reducing cross-sections of the first intermediate cross-frames (where stress concentrates for the original designs) to redistribute lateral load internally, while original bridges with various skew had different optimized designs due to their differences in stress distribution. Based on the application presented in this paper, the proposed algorithmic approach can be implemented to optimize other structural designs with appropriate definition of parameters, objective functions, and constraints, especially to solve structural problems with response concentration.