# Shear Strength of Trapezoidal Corrugated Steel Webs for Horizontally Curved Girder Bridges
## 1 Introduction  
The steel-concrete composite girder with CSWs is known as a new type of bridge structure to overcome the weight problem of common concrete box girders. Compared with concrete webs, CSWs have low longitudinal stiffness due to the accordion effect, so CSWs mainly carry the shear force and barely carry axial force [1]. Because of this characteristic, CSWs fail due to shear buckling or yielding. Therefore, the shear buckling stability of CSWs is one of the most important considerations in the design of this kind of composite girder bridges. Curved composite girder bridges with CSWs (see Figure 1) have already been constructed around the world, for example, the Meaux viaduct in France, the Altwipfergrund viaduct in Germany, the Nakano viaduct in Japan, the Yuwotou bridge and No. 3 East River bridge in China, etc. However, so far, limited research has been conducted on the shear behavior of CSWs of HCGs. In practice, the shear buckling calculation of CSWs for HCGs usually adopts the corresponding formula of straightgirders which have been relatively well studied. It is widely accepted that for straight girder bridges, local shear buckling is the dominant failure mode in coarse corrugations, whereas global shear buckling becomes the dominant failure mode in dense corrugations and interactive shear buckling mode becomes dominant when the density is in between of the two above scenarios [2]. It is straightforward to understand that the shear buckling failure modes of CSWs in HCGs also consist of local shear buckling, global shear buckling, and interactive shear buckling. The local shear buckling of CSWs for straight girders is solved by analyzing a single flat panel constrained by adjacent panels and girder flanges under shear force. For this, the formula for the shear buckling stress of isotropic rectangular plates [3] can be applied. Because the single flat panel of CSWs in HCGs is under the same constraint conditions as in straight girders, the formula can also be applied to HCGs. [PERSON] et al. [4] numerically studied the local shear buckling of CSWs and found that the boundary conditions at the top and bottom edges were close to fixed, while the boundary conditions at the fold line between the flat and inclined panels lie between simply supported and fixed. The global shear buckling of CSWs for straight girder bridges is analyzed by assuming the whole web as an orthotropic rectangular plate constrained by concrete flanges and diaphragms, and has been studied by various researchers. [PERSON] and [PERSON] [5] derived the formula for calculating shear buckling loads by treating the corrugated plates as plates having different flexural rigidities in two perpendicular directions. [PERSON] [6] investigated the shear buckling behavior of stiffened plates reinforced by separate equally spaced stiffeners which were symmetrically arranged on two sides of the plates, and extended the deduced results to corrugated plates. [PERSON] and [PERSON] [7] investigated the global shear buckling behavior of corrugated metal diaphragms also by treating them as orthotropic plates and developed the formulas for the shear buckling load by the Ritz and the Energy method. [PERSON] [8] made a comparative analysis of the Bergmann-Reissner formula [5], the Hlavacek formula [6] and the Easley-McFarland formula [7], and proposed a more comprehensive and applicable global shear buckling formula of corrugated plates. Corrugated plates were originally applied in aircrafts and were gradually extended to civil engineering. The formula \(\tau_{g}^{e}=k_{g}\frac{(D_{g})^{1/4}(D_{g})^{3/4}}{H^{2}}\) was accepted to calculate the global shear buckling stress of CSWs for straight girders, where \(k_{g}\) is the global shear buckling coefficient depending on the edge conditions. Although a global shear buckling formula of CSWs has been proposed, researchers hold different views on the global shear buckling coefficient \(k_{g}\).