Estimation Practical Frequency Formulas for Vertical Vibration of Extradosed Cable-stayed Bridge Based on Energy Method

To calculate vertical frequency of extradosed cable-stayed bridge conveniently,a extradosed cable-stayed bridge with double-towers was taken as a research object,while the tower was rigidly connected with the girder and supported by the pier. Frequency formulas for the first symmetric and asymmetric vertical vibration modes were induced by the Rayleigh method and the nominal unity mass anti-bending rigidity concept was proposed. Finally,the presented theoretical formulas were validated by the engineering project,and the application condition was discussed. The results indicate that constraint condition has a great influence on vertical frequency,which should be correctly considered in frequency calculation. The error between values calculated by the proposed formulas and the finite element method( FEM) meets with the requirement of conceptive design. The proposed formulas can be applied to extradosed cable-stayed bridge,but the vertical frequency formulas in the wind-resistant design specification cannot be applied to the such bridge.