Keywords: analysis, bending and torsion, curved I-beams, non-linear, top flange, uniformly distributed load, steel structure.

Steel I-section curved girders are often used in unpropped composite steel and concrete curved bridges because of their economy and convenience of construction. During construction, the steel curved girder carries a uniformly distributed load, due to its own weight and that of the concrete deck. Just after casting, the concrete deck has no stiffness, so that the steel girders act separately as individually simply supported curved girders, with much of the load acting at the top flange. A linear analysis is often thought to be sufficient for predicting the structural behaviour of unpropped composite steel and concrete I-section girders curved in-plan during construction. This linear analysis assumes that no lateral displacements take place during the deformation of the curved girder. However, when a steel I-girder curved in-plan is subjected to a vertical uniformly distributed load, it experiences a primary bending action about the major axis of the cross-section and a primary torsion action about the shear centre axis which produce primary vertical deflections perpendicular to the plane of the girder and twist rotations of cross-section. The primary bending and torsion actions and , vertical deflections and twist rotations couple together to produce a second-order bending action about the minor axis of the cross-section of the steel curved girder, which in turn produces lateral displacements in the plane of the girder. The interactions between these actions can grow rapidly, produce early nonlinear behaviour and even yielding, and lead to large deformations and a significant reduction of load carrying capacities of curved girders during construction. Hence, the predictions of a linear analysis may be very misleading for determining the behaviour of composite steel and concrete I-section girders curved in-plan during construction. To correctly predict the deformations and strength of the curved girder during construction, a nonlinear elastic and elastic-plastic analysis is needed.

Some attempts have been made to predict the nonlinear behaviour of I-section girders curved in-plan by calculating the "flexural-torsional buckling load" of the curved girder. The classical methods for predicting elastic buckling loads consider the bifurcation from a primary trivial prebuckling equilibrium path to an orthogonal buckling path. In the case of a curved girder, the torsional deformations are primary and not trivial, and so it is difficult to see the significance of bifurcation-type flexural-torsional buckling. Although mathematical buckling loads may be calculated for horizontally curved girders, they predict a hypothetical condition of neutral equilibrium. Therefore, a nonlinear analysis is needed to predict the flexural-torsional behaviour of I-section girders curved in-plan. However, most research hitherto has concentrated on linear elastic behaviour, as identified by the Structural Stability Research Council-Task Group 14 [1]. Research into the nonlinear inelastic behaviour of horizontally curved beams and girders is much needed.

The popular computer software ABAQUS has been used recently by a number of researchers for the analysis of curved I-beams and I-girders. However, the integration sampling points for calculating stress resultants in the ABAQUS beam element in space for open, thin-walled sections are defined at the mid-line of the wall thickness, where the shear stress is equal to zero, so that the influence of the uniform torsion shear stress is completely lost in the process of calculating the stress resultants. As torsion is one of the primary actions in curved girders and as it produces both longitudinal normal stresses due to warping torsion and shear stresses due to uniform torsion, the ABAQUS beam element may be not suitable for the nonlinear analysis of curved I-girders. In addition, the effects of load height are not accounted for in the ABAQUS beam element. Because of these deficiencies, the use of the ABAQUS beam element for the nonlinear analysis of curved I-girders may produce erroneous results.

This paper presents a 3D finite element model for the nonlinear elastic and inelastic analysis of beams curved in-plan and uses it to investigate the elastic and inelastic behaviour of unpropped composite steel and concrete I-section girders curved in-plan during construction. Numerical examples demonstrate that the finite element model is effective, efficient and accurate. Only a few curved beam elements are sufficient to predict the structural behaviour of curved I-girders accurately. Because the finite element model includes the additional nonlinear effects of the load height, it is suitable for the nonlinear analysis of curved I-girders subjected to a uniformly distributed load at the top flange of the cress-section.

It is found that the use of a linear theory may produce very misleading predictions of the structural behaviour of steel I-section girders curved in-plan during construction because early nonlinearity and even yielding may be induced by the primary coupling between the bending and torsion actions, and the vertical deflections and twist rotations. In general, the mathematical "flexural-torsional buckling load" predicts only a hypothetical condition of neutral equilibrium of curved girders, and a nonlinear analysis is needed to predict correctly the elastic and inelastic behaviour of composite curved girders during construction. The deformations and load carrying capacity of the composite curved girders during construction have to be checked, and some measures may need to be taken in order to prevent the composite girder from serviceability or strength failure during construction.

1

"Horizontally curved girders - a look to the future", Annual Report, Structural Stability Research Council - Task Group 14, Chicago, Illinois, 1991.

2

ABAQUS user's manual. Version 5.8. Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, Rhode Island, 1998.

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