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Based on Hamilton principle,the governing differential equations and the corresponding boundary conditions of steel-concrete composite box girder with consideration of the shear lag effect meeting self equilibrated stress,shear deformation,slip,as well as rotational inertia were induced.Therefore,natural frequency equations were obtained for the boundary types,such as simple support,cantilever,continuous girder and fixed support at two ends.The ANSYS finite element solutions were compared with the analytical solutions by calculation examples and the validity of the proposed approach was verified,which also shows the correctness of longitudinal warping displacement functions.Some meaningful conclusions for engineering design were obtained.The decrease extent of each order natural frequency of the steel-concrete composite box-girder is great under action of the shear lag effect.The shear-lag effect of steel-concrete composite box girder increases when frequency order rises,and increases while span-width ratio decreases.The proposed approach provides theoretical basis for further research of free vibration characteristics of steel-concrete composite box-girder.
Based on Hamilton principle, the governing differential equations and the corresponding boundary conditions of steel-concrete composite box girder with consideration of the shear lag effect meeting self equilibrated stress, shear deformation, slip, as well as rotational inertia were induced.Therefore, natural frequency equations were obtained for the boundary types, such as simple support, cantilever, continuous girder and fixed support at two ends. ANSYS finite element solutions were compared with the analytical solutions by calculation examples and the validity of the proposed approach was verified, which also shows the correctness of longitudinal warping displacement functions. Some meaningful conclusions for engineering design were obtained. The decreased extent of each order natural frequency of the steel-concrete composite box-girder is great under action of the shear lag effect. The shear-lag effect of steel-concrete composite box girder increases when frequency order rises, and increases while span-width ratio decreases. The proposed approach provides theoretical basis for further research of free vibration characteristics of steel-concrete composite box-girder.