# Shear Strength of Trapezoidal Corrugated Steel Webs for Horizontally Curved Girder Bridges
## 1 Introduction
[PERSON] [8] proposed \(36\leq k_{g}\leq 68.4\), \(36\) for a four-edge simple support and \(68.4\) for a four-edge fixed support, while [PERSON] [9] and [PERSON] et al. [10] suggested \(32.4\) for a four-edge simple support and \(60.4\) for a four-edge fixed support, and [PERSON] and [PERSON] [11] suggested \(50\) for composite girders with CSWs. The Guide to Stability Design Criteria for Metal Structures adopted \(31.6\) for a four-edge simple support and \(59.2\) for a four-edge fixed support [12]. [PERSON] et al. [13] presented the transition curves of the elastic global shear buckling capacity from the case of a four-edge simple support to the case of a four-edge fixed support using the Rayleigh-Ritz method, but provides only the curves for the plate dimensions (\(l\times h\)) of \(1\) m \(\times\) 1 m and \(2\) m \(\times\) 1 m.  
Figure 1: Curved composite girder bridges with corrugated steel webs (CSWs): (**a**) Altwipferrund Viaduct; (**b**) Yuwotou Bridge. CSW: corrugated steel web. Finally, the interactive shear buckling formula for CSWs is determined by local shear buckling, global shear buckling and the yield stress of the plate material [14], but the way these parameters are to be combined is still the subject of debate. Important work has been done by [PERSON] et al. [10], [PERSON] [15], [PERSON] et al. [16], [PERSON] et al. [17], [PERSON] [18] and [PERSON] et al. [14], etc., and various interactive shear buckling formulas of CSWs were proposed. For practical applications, [PERSON] et al. [19] recommended that the capacity of CSWs was controlled by the smaller value of local and global buckling, and a semiempirical formula for the inelastic buckling stress when the elastic buckling stress is larger than 80% of the yield stress was proposed. [PERSON] et al. [20] proposed a lower bound equation by combining local and global shear buckling equations of CSWs. [PERSON] et al. [21] proposed a shear buckling parameter formula for trapezoidal CSWs with no need to calculate either local, global or interactive shear buckling parameters. [PERSON] [2] proposed a shear buckling parameter formula for curved CSWs. [PERSON] et al. [22] carried out eight H-shape steel girders with CSWs and proposed a formula for the shear strength prediction of trapezoidal CSWs. [PERSON] et al. investigated the shear behavior of linearly tapered bridge girders with CSWs [23], and high-strength steel corrugated web girders [24]. [PERSON] and [PERSON] [25] experimentally and numerically studied the shear stress distribution in trapezoidal CSWs. [PERSON] et al. [26] studied the ultimate shear behavior of HCGs with trapezoidal CSWs and proposed an approximate method to calculate the shear strength of these girders. The ultimate shear strength of curved girders uses the equation of straight girders introducing a modification factor to account for the curvature of curved girders. [PERSON] et al. [27] theoretically and numerically studied the elastic global shear buckling of HCGs with CSWs and proposed a global shear buckling stress formula for a four-edge simple support. From the studies mentioned above, it is clear that a lot of work has been done related to the shear behavior of straight girders with CSWs, but limited work to HCGs. The curvature of HCGs may indeed have an influence on the buckling of CSWs. Therefore, a comprehensive study is necessary to understand whether the shear buckling formulas for CSWs for straight girders are appropriate for HCGs, and if so, to which extent. In this study, the CSW in HCGs is treated as an orthotropic cylindrical shallow shell constrained by the concrete flanges and diaphragms. First, the analytical formula for the elastic global shear buckling stress for three boundary conditions is deduced by the Galerkin method. Then, a parametric study based on a linear buckling analysis is performed to analyze the effect of the curvature radius and girder span on the shear buckling stress. Finally, a series of tests performed on three box girders with CSWs is discussed.