Analytic solution of free vibration of simply-supported thin-walled box girder by perturbation method
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(1.Department of Civil Engineering, University of Science and Technology Beijing, Beijing 100083, China; 2.Power China Road Bridge Group Co., Ltd., Beijing 100048, China)

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TU311.3,U448.21

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    Abstract:

    To investigate the shear lag effect of thin-walled box girder on the dynamic characteristics, a new approach was developed to analyze the free vibration of box girders based on the modal perturbation method. The natural modes of vibration of the corresponding prismatic Euler beam with the same length and boundary conditions were used as Ritz base functions. Then, the new method can transform the set of partial differential equations governing the transverse vibration of the box girder into a set of nonlinear algebraic equations. For the simply-supported beams, the algebraic equations were further simplified as quadratic equation with one unknown, so that the exact eigenvalues and eigenvectors could be obtained. The analytical vibration modes of the box girder were used to propose the shear lag coefficients of modes, which illustrates the relationship between the natural frequency and shear lag effect. Numerical examples were used to analyze the shear lag coefficients of modes varying with the ratio between span and width, the second moment of area ratio between flange slab and the full section. The numerical results show that the maximum shear lag coefficients of modes located at the web of the box girder are greater than 1, which are positive shear lag effect. As the increase of modes order, the reduction of the ratio between span and width and the increase of the second moment of area ratio between flange slab and the full section, the shear lag coefficients and shear lag effect would be more remarkable.

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History
  • Received:September 12,2015
  • Revised:
  • Adopted:
  • Online: December 16,2016
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