Curved bridges live load bending moment distribution using straight and curved girders

abstract: The present study focuses on comparative parametric analysis of curved precast concrete bridges using straight and curved I-girders. The live load bending moment distribution for girders was studied using the bridge curvature and its relationship with the results obtained for a straight bridge. FEM 3D models were developed with restrictions on the transverse live load positions and with two different load models types: HL-93 (AASHTO) and TB-450 (NBR 7188, 2013). The parametric analysis results were calculated using the Modification Factor (MF) and the Bending Moment Distribution Factor (BMDF), calculated from the structural analysis of each model at the midspan. Globally, an increase was found in the total bending moment for the curved bridge models in relation to the straight bridge. In the examples herein studied, the larger the bending radius, the larger the maximal bending moment in the bridge center. For the external girders, the MF increases with the increase of the L/R. For the internal ones, the MF decreases with the increase of the L/R. In addition, the occurrence of “Load Shift” was different from the rigid body behavior, for there was demonstrated a different bending moment variation between external girder (G1) in relation to its adjacent (G2). Therefore, the structural behavior of straight (SG) and curved girders (CG) was analyzed, revealing that, in the SG, a significant gap occurred in the BMDF between G1 and G2 girders for all curvatures. For L/R = 0.6, it caused a difference of 17.8% in the BMDF between the G1 and G2 girders, while on the curved girders, a difference of only 6.6% was found.

Shear Strength of Trapezoidal Corrugated Steel Webs for Horizontally Curved Girder Bridges

Curved composite girder bridges with corrugated steel webs (CSWs) have already been constructed around the world. However, limited work has been done on their shear behavior. In this paper, the corrugated steel web (CSW) in horizontally curved girders (HCGs) is treated as an orthotropic cylindrical shallow shell, and the analytical formula for the elastic global shear buckling stress is deduced by the Galerkin method. Calculation tables for the global shear buckling coefficient for a four-edge simple support, for a four-edge fixed support, and for the two edges constrained by flanges fixed and the other two edges simply supported are given. 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. Analytical and numerical results show that the difference of shear buckling stress of CSWs between curved girders and straight girders is small, so the shear design formulas for straight girders can be applied for curved girders. Finally, a series of tests were performed on three curved box girders with CSWs. Similar to CSWs in straight girders, the shear strain distributions of CSWs in HCGs are almost uniform along the direction of the web height and the principal strain direction angles are close to 45°. For the three specimens, CSWs carry about 76% of the shear force. In the destructive test, shear buckling after yielding occurred in all specimens which is in good agreement with the theoretical prediction, which means that the analytical formulas provide good predictions for the shear buckling stress of CSWs in HCGs and can be recommended for design purposes.

Study on Elastic Global Shear Buckling of Curved Girders with Corrugated Steel Webs: Theoretical Analysis and FE Modelling

Despite the construction of several curved prestressed concrete girder bridges with corrugated steel webs (CSWs) around the world; their shear behavior has seldom been investigated. Accordingly, this paper substitutes the lack of available information on the global elastic shear buckling of a plane curved corrugated steel web (PCCSW) in a curved girder. This is based on the equilibrium equations and geometric equations in the elastic theory of classical shells, combined with the constitutive relation of orthotropic shells. Currently, the global elastic shear buckling process of the PCCSW in a curved girder is studied, for the first time in literature, with an equivalent orthotropic open circular cylindrical shell (OOCCS) model. The governing differential equation of global elastic shear buckling of the PCCSW, as well as its buckling strength, is derived by considering the orthotropic characteristics of a corrugated steel web, the rational trigonometric displacement modes, Galerkin’s method and variational principles. Additionally, the accuracy of the proposed theoretical formula is verified by comparison with finite element (FE) results. Moreover, the expressions of the inner or outer folded angle and radius of curvature are given by the cosine theorem of the trigonometric function and inverse trigonometric function. Subsequently, parametric analysis of the shear buckling behavior of the PCCSW is carried out by considering the cases where the radius of curvature is constant or variable. This parametric analysis highlights the effects of web dimensions, height-to-thickness ratio, aspect ratios of longitudinal and inclined panels, corrugation height, curvature radius and folded angles on the elastic shear buckling strength. As a result, this study provides a theoretical reference for the design and application of composite curved girders with CSWs.

Experimental study on shear behavior of curved box girders with corrugated steel webs

<p>Curved girder bridges with corrugated steel webs have already been constructed around the world; however, few works have been done on their shear behavior. To investigate the shear behavior of corrugated steel webs in curved girders, a curved box girder with corrugated steel webs was investigated and tested in current study. The method of three-point loading was used in the test. Test results indicate that the girder failed due to nonlinear shear buckling of the webs and the shear yield stress of the material was less than the elastic shear buckling stress of the corrugated steel webs. Failure of the corrugated steel webs was initiated by the local shear buckling of one of the corrugation panels, which propagated to other panels. In the failure stage, the interactive shear buckling occurred in outboard and inboard corrugated steel webs. In addition, many cracks appeared in the concrete top flange nearby the top supports and the concrete bottom flange between the 1/4 span to 3/4 span. The girder with corrugated steel webs can continue to resist the load after the occurrence of shear buckling. For the design of this type of curved box girder, it is necessary to consider the shear buckling of the corrugated steel webs.</p>

Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders

In this paper, a semi-analytical solution for free vibration differential equations of curved girders is proposed based on their mathematical properties and vibration characteristics. The solutions of in-plane vibration differential equations are classified into two cases: one only considers variable separation of non-longitudinal vibration, while the other is a synthesis method addressing both longitudinal and non-longitudinal vibration using Rayleigh’s modal assumption and variable separation method. A similar approach is employed for the out of- plane vibration, but further mathematical operations are conducted to incorporate the coupling effect of bending and twisting. In this case study, the natural frequencies of a curved girder under different boundary conditions are obtained using the two proposed methods, respectively. The results are compared with those from the finite element analysis (FEA) and results show good convergence.

Curved Box-Girders with Corrugated Steel Webs under Torsion Loading

It is known that coupled bending and torsional effect is a distinct characteristic of curved girders. According to mechanical characteristics of box girders with corrugated steel webs and theory of box girders, warping normal stress of box girders with corrugated steel webs caused by Torsion Loading is studied. On the basis of second theory of Wu, restrained torsion differential equation of box-girders with corrugated steel webs is proposed. Corrugated webs are assumed as orthotropic plates. Constraint torsional normal stress and shear stress are deduced using Initial parameters method. The results demonstrate that the method is more accurate compared with conventional ones, and it is connected with existing bridge calculation theory. The method is then a practical one in this respect.

Column Effective Length Factor and Girder Parametric Analysis for the Components of Xinqiao International Airport Terminal

The steel structure of Hefei Xinqiao International Airport Terminal was taken as a background of this article. The large-span frame is a typical frame of the structure. The curved box-girders are the critical parts of the whole frame. This paper focused on the mechanical properties of the curved girders, as well as the influence on box-columns connected with them. Stability problem is a key problem in the steel structure design, and effective length factor is a way to reflect the stability problem in code for design. In this paper, the whole model of the airport terminal was established to conduct eigenvalue buckling analysis to obtain effective length factors of the box-columns connected to the curved box-girder. In the finite model, a unified axial force was applied on the end of the box-column, and the elements of the box-columns and the adjacent members were refined. Then the effective length factors were derived through the buckling models. In this paper, the curved box-girders of Hefei airport building were studied using finite element software ANSYS. The local model of the curved box-girders were set up to study the mechanical properties of the curved girders including the ultimate capacity analysis. Parametric analysis of the girders was carried out, and the results could be used to guide the design. The results show that finite element method is a convenient way of calculating effective length factors for members with complex boundary conditions, and analysis of local models provides reasonable suggestions for design.