Bracing systems for three-ribbed arch bridges against out-of-plane buckling

This paper is concerned with the design of bracing systems for three-ribbed parabolic arch bridges against out-of-plane buckling. Typical bracing systems for the three-ribbed arch bridges include K-bracing system and X-bracing system as well as transverse bracing system. The buckling criterion of the braced funicular three-ribbed arch bridge is derived from an exact matrix stiffness method (MSM) with a 14 × 14 s-order element stiffness matrix of three-dimensional beam-column elements that allows for torsional and warping deformations. The lateral torsional buckling load and mode are given by the lowest eigenvalue and eigenvector associated with the assembled structural stability stiffness matrix. A comparison study between different bracing system configurations suggests that the three-ribbed arches with the integral K- or X-bracing system (a K/X-bracing across the three arch ribs) have lower lateral torsional buckling loads than their arch counterparts with the independent K- or X-bracing system (the adjacent arch ribs are connected by K/X-bracing respectively), because the latter ones could provide more restraint on the middle arch rib to avoid early lateral torsional instability. Further, a bracing utilization efficiency index (defined as the normalized buckling capacity over material usage for bracing system) is proposed to quantify the effect of bracing systems in improving the lateral torsional buckling capacity of arch bridges. Highly efficient bracing systems that maximize the lateral torsional buckling load of three-ribbed arch structures with the lowest bracing material usage are then recommended.