Development and Application of an Analytical Model for Horizontally Curved Bridge Decks

Abstract

This paper presents a reliable closed form analytical solution without any major simplification which can be used with confidence by designers for the analysis of statically indeterminate horizontally curved bridges idealized as curved girders. The unit load method, a method extracted from the Castigliano's second theorem is used to derive the proposed closed form analytical solution which is then used to obtain the influence line diagram of shear force, bending moment and torsion of the curved bridge girder and it is validated with the published test results and also with the finite element solution of a curved girder. Moreover, an extensive parametric study is conducted using the proposed analytical model to investigate the effect of various parameters such as curvature ratio, span length, number of cells and number of loading lanes on bending moment and torsion of the curved bridges subjected to Australian bridge design loads where the effect of all these parameters except the number of cells is found to be significant. Finally, a comparative study of the behaviour of horizontally curved bridges subjected to loads recommended by three different international bridge design codes is undertaken which concludes that the Eurocode LM1 predicts higher bending moment as well as torsion with respect to other codes.

Load distribution for composite steel–concrete horizontally curved box girder bridge

“…For the analysis of the statically indeterminate horizontally curved beam, the closed form analytical solution has recently been developed by the authors [13] which has been used to generate the influence line diagrams to predict the critical loading condition for the idealized horizontally curved beam subjected to moving loads (P). The detail of the analytical model is not presented here as it has been reported in [13].…”

“…The detail of the analytical model is not presented here as it has been reported in [13]. In this section, only the final equations which are used to calculate the total shear force (V), bending moment (M) and torsion (T) at any critical section within a curved beam ( Fig.…”

“…In this situation, the use of influence line diagrams for stress resultants of these structures are useful to estimate the maximum value of those stress resultants at the critical sections of the bridge deck. This problem was addressed by the authors in previous research [13]. A closed form analytical solution has been developed [13] in order to determine the influence line diagrams for statically indeterminate curved beams.…”

“…This problem was addressed by the authors in previous research [13]. A closed form analytical solution has been developed [13] in order to determine the influence line diagrams for statically indeterminate curved beams.…”

“…On the other hand, the closed form analytical solution for the influence line diagram of curved beams which has been developed by the authors [13] is used to calculate the stress resultant acting over the entire bridge deck section due to the same loading configuration. The stress resultants obtained from the finite element analysis for the individual girders and the total stress resultant obtained from the analytical solution are used to calculate the load distribution factors as the ratio between them.…”