A Minimal GBT Model for Distortional-Twist Elastic Analysis of Box-Girder Bridges

Francesca Pancella,Angelo Luongo

doi:10.3390/app11062501

Abstract

A simple and efficient method is proposed for the analysis of twist of rectangular box-girder bridges, which undergo distortion of the cross section. The model is developed in the framework of the Generalized Beam Theory and oriented towards semi-analytical solutions. Accordingly, only two modes are accounted for: (i) the torsional mode, in which the box-girder behaves as a Vlasov beam under nonuniform torsion, and, (ii) a distortional mode, in which the cross section behaves as a planar frame experiencing skew-symmetric displacements. By following a variational approach, two coupled, fourth-order differential equations in the modulating amplitudes are obtained. The order of magnitude of the different terms is analyzed, and further reduced models are proposed. A sample system, taken from the literature, is considered, for which generalized displacement and stress fields are evaluated. Both a Fourier solution for the coupled problem and a closed-form solution for the uncoupled problem are carried out, and the results are compared. Finally, the model is validated against finite element analyses.

Highlights

It is well-known that, when a mono-cellular box-girder undergoes torsion, induced by eccentric loads with respect to its longitudinal axis, its cross section suffers a distortion in its own plane, which modifies the original shape [1]
The phenomenon is dangerous, since flexure of the webs entails longitudinal normal stress, which adds to the tangential stresses of the Bredt theory of uniform torsion and to the normal stresses of the Vlasov theory of nonuniform torsion
Flanges and webs all suffer transverse bending, which would not be present if the cross section could maintain its shape

Summary

Introduction

It is well-known that, when a mono-cellular box-girder undergoes torsion, induced by eccentric loads with respect to its longitudinal axis, its cross section suffers a distortion in its own plane, which modifies the original shape [1]. Such a phenomenon is often referred to, in the technical literature devoted to bridges, as differential flexure, since a quota of the external torsional moment not equilibrated by the internal torsional moment is instead bared by internal forces triggered by equal and opposite flexures of the two webs. Flanges and webs all suffer transverse bending, which would not be present if the cross section could maintain its shape To limit such effects, diaphragms or bracings are occasionally introduced into the box-girder, but more often, these devices are omitted for construction simplicity.

Methods

Results

Conclusion