box girder;  shear hysteresis;  vibration;  variation;  Difference method

A theoretical method for the analysis of forced vibration shear hysteresis of thin-walled box girder is proposed. The differential equation and boundary conditions of forced vibration of box girder considering the shear hysteresis effect are derived by variational principle, the differential format of the equation solution is established, the stability and convergence of the differential format are demonstrated, and the Matlab programming is used. In the numerical solution, due to the coupling between the vertical displacement of the beam and the longitudinal maximum displacement difference function of the wing plate reflecting the shear hysteresis, the necessary hypothetical shape function in the finite element method cannot reflect the coupling relationship, so the finite difference method with stronger adaptability is adopted. The results show that the shear hysteresis effect is obvious when the thin-walled box girder vibrates, which significantly increases the amplitude of the mid-span displacement response and the stress response at the junction of the upper wing plate and the web.