Study On The Spatial Mechanical Properties Of Single-box Multi-cell Composite Box Girders With Corrugated Steel Webs Based On Finite Element Analysis

Single-box multi-cell composite box girders with corrugated steel webs(CBGCSWs)and variable height have been extensively used in the construction of medium-and long-span highway bridges in China,due to their excellent structural performance.However,the reduction of the thickness and bending resistance of the corrugated steel webs,and the enhancement of shear strength of steel-web material,which will lead to the obvious differences in spatial mechanical properties between box-section with corrugated steel webs and box-section with traditional solid webs.In order to reveal the spatial mechanical properties of single-box multi-cell CBGCSWs with variable height,and put forward a simplified beam finite element model.In this paper,a comprehensive and systematic study on the spatial mechanical properties of single-box multi-cell CBGCSWs with variable height has been conducted by means of theoretical derivation and case verification.The main contents of this study are as follows:(1)Based on the bending theory of thin-walled box girder,the distribution law of bending shear flow of single-box multi-cell CBGCSWs has been explained,and the components of warping displacement of different plate considering shear lag and shear deformation effect are reconstructed.The rationality of choosing the cosine function as the transverse distribution function of warping displacement has been theoretically demonstrated,and the calculation procedure of correction coefficient of shear lag function for the top lateral cantilever flange is designed.On the basis of the principle of minimum potential energy,the governing differential equations,considering both the influences of shear lag warping and shear deformation in webs,are derived for singlebox multi-cell CBGCSWs.(2)Selecting closed-form homogeneous solutions of the governing differential equations of the shear lag effect of single-box multi-cell CBGCSWs as the displacement interpolation function,the exact shape functions of the flange and web warping displacements under the shear lag effect can be determined with the given displacement boundary conditions at the rod end.Using the energy variational method,the beam segment model of single-box multi-cell CBGCSWs(B3CS)is established and the shear lag problem of a three-dimensional single-box multi-cell CBGCSWs can be simplified into a one-dimensional beam element model.Compared with the traditional beam element model,only one more degree of freedom is incorporated to consider the shear lag warping.The calculation accuracy and applicability of the B3 CS beam element model are verified by a series of case studies.With the B3 CS beam element model,the influences of web type,web shear deformation,and geometric parameters on the shear lag effect of CBGCSWs are presented,respectively.(3)Based on the Vlasov thin-walled theory and membrane-analogy method,the distribution of Saint-Venant(SV)torsional shear stress in the open and closed sections of single-box multicell CBGCSWs has been given,and the expressions of free torsional warping displacement of the open and closed sections can be furtherly established.According to the stress equilibrium condition and the geometric deformation compatibility equation,the distribution law of restrained torsional shear stress is proposed,and the equivalent relationship between the bending-torsional moment and the integrated moment of restrained torsional shear stress(secondary torque)is demonstrated.The main torsional angle of the box section is modified by including the additional torsional angle,which is induced by the secondary torsion,and the shear strain distribution considering the influence of SV torsion and secondary torsional moment deformation effect(STMDE)is established.Based on the principle of minimum potential energy,the governing differential equations of restrained torsion effect of single-box multi-cell CBGCSWs is derived considering both influences of non-uniform torsional warping and STMDE.(4)Selecting closed-form homogeneous solutions of the governing differential equations of restrained torsion of single-box multi-cell CBGCSWs as the displacement interpolation function,the exact shape functions of the flange and web warping displacements and tangential displacements under the restrained torsion effect can be determined with the given displacement boundary conditions at the rod end.Based on the energy variational method,the beam segment model of single-box multi-cell CBGCSWs(B2CTB)considering both the non-uniform torsional warping and STMDE is established and the restrained torsion problem of a three-dimensional single-box multi-cell CBGCSWs can be simplified into a one-dimensional beam element model.Compared with the traditional beam element model,only one more degree of freedom is incorporated to consider the STMDE.The calculation accuracy and applicability of the B2 CTB beam element model are verified by a series of case studies.With the B2 CTB beam element model,the influences of web type,STMDE,and geometric parameters on the restrained torsion effect of CBGCSWs are analyzed,respectively.(5)On the basis of the generalized coordinate method,the expressions of distortional warping displacement of the open and closed sections has been established.According to the stress equilibrium condition and the geometric deformation compatibility equation,the distribution law of distortional shear stress is analyzed,and the equivalent relationship between bending-distortional moment and integrated moment of distortional shear stress(distortional shear force)is proved.The main distortional angle of the box section is modified by including the additional distortional angle,which induced by the distortional shear force,and the shear strain distribution function considering the influences of the distortional shear deformation effect(DSDE)is established.Based on the principle of minimum potential energy,the governing differential equations of distortion effect of single-box multi-cell CBGCSWs is derived considering both influences of distortional warping and DSDE.(6)Selecting closed-form homogeneous solutions of the governing differential equations of distortion effect of single-box multi-cell CBGCSWs as the displacement interpolation function,the exact shape functions of the flange and web warping displacements and tangential displacements under the distortion effect can be determined with the given displacement boundary conditions at the rod end.Based on the energy variational method,the beam segment model of singlebox multi-cell CBGCSWs(B2CDB)considering both the distortional warping and DSDE is established and the distortion problem of a three-dimensional single-box multi-cell CBGCSWs can be simplified into a one-dimensional beam element model.Compared with the traditional beam element model,only two more degrees of freedom are incorporated to consider the distortional warping and DSDE.The calculation accuracy and applicability of the B2 CDB beam element model are verified by a series of case studies.With the B2 CDB beam element model,the influences of web type,DSDE,and diaphragm spacing arrangement on the distortion effect of CBGCSWs are illustrated,respectively.