shear hysteresis;  shear deformation;  Simple support box girder;  natural vibration;  Variational principle

Due to the shear hysteresis effect and shear deformation, the bending vibration frequency of the box girder tends to have a large error in the calculation according to the primary beam theory. Comprehensively considering the shear deformation and shear hysteresis effect of the box girder, the free vibration of the simple support box girder is analyzed by using the energy variational principle, and the analytical solution of the self-resonance frequency of each order of the simple support box girder considering the shear hysteresis effect and shear deformation is derived, which is generalized compared with the previous vibration fundamental frequency that can only be calculated. The verification example shows that the theoretical derivation of the proposed method is correct, and the calculation accuracy is greatly improved compared with the elementary beam theory. Finally, the effects of shear hysteresis effect and shear deformation on the self-vibration characteristics of box girder are discussed, and it is found that considering the shear hysteresis effect and considering shear deformation reduce the vibration fundamental frequency of simple support box girder, and the reduction of high-order vibration frequency of box girder is particularly obvious. And the width-span ratio of the box girder is a shadow