Dynamic Behavior Study On Stiffened Plates Of Long-span Bridges With Steel Box Girder

Due to the low structural height, light self-weight, great load capacity, and easymanufacture of the steel box girder, it is used widely in long-span bridges. On the basis ofprevious research and design code of some countries and combining the construction featuresof stiffened plates of steel box girder, the dynamic behavior of stiffened plates of steel boxgirder is investigated through both theoretical derivation and numerical analysis. The mainresearch work in this thesis is as follows:(1) Energy principle is used to investigate the linear vibration of the stiffened plate ofsteel box girder. In this work, the basic assumption are as follows: first, it is considered to be astiffened plate in double directions; both longitudinal stiffeners and transverse diaphragms areconsidered to be beam elements according to the equivalent principle of mass and rigidity, andthe torsional effect is taken into account; the plate is computed according to the classical thinplate theory without the torsional effect taken into account. Second, the eccentricity ofstiffeners is taken into consideration, as well as the membrane strain energy of the plate. Third,the mode shape function of the plate is expressed by the product of two independent beamfunctions.(2) A combined plate beam element method is presented to investigate the localvibration of the steel bridge deck with trapezoidal stiffeners. The top plate is taken as shellelement. The trapezoidal stiffener is taken as plate beam element, and its displacement modelis built according to the deformation coordinate relationship between plate and stiffener. Thestiffness matrix, consistent mass matrix and consistent load matrix of the combined platebeam element are obtained based on energy-variation principle. The local vibration of thesteel bridge deck with trapezoidal stiffeners can be analyzed through finite element program.(3) An approach is presented to study dynamical buckling of stiffened plates with fouredges simply supported. The Hamilton principle and modal superposition method are used toderive the eigenvalue equations of the stiffened plate according to energy of the system. Theinitial geometrical imperfection is considered in the equations. Detailed discussion on how theinitial geometrical imperfection, the number and the flexural rigidity of stiffeners influencethe critical load is carried out.(4)The strain and kinetic energy of both the plate and stiffeners are established, and thenLagrange equation is used derive the governing equation of motion. Single-modal method ispresented to investigate the nonlinear vibration of stiffened plates with four edges simplysupported, four edges clamped and moving boundary conditions. For the free vibration, the exact single-mode solution can be obtained according to the integral of nonlinear differentialequations and the initial conditions. For the stiffened plates with four edges simply supportedand four edges clamped, the relationship between nonlinear natural frequency and itsamplitude is discussed with the number of stiffeners in the two directions varying. For thenonlinear forced vibration of stiffened plates with four edges simply supported and four edgesclamped, the first approximation solutions of the non-resonance and the primary resonance ofthe single-mode system are obtained by means of the method of multiple scales. Numericalexamples for different stiffened plates are presented to discuss the steady response of thenon-resonance and the amplitude-frequency response of the primary resonance. For thenonlinear vibration of stiffened plates with moving boundary conditions, the effect caused byboundary movement is transformed into equivalent excitations and the damping of the plate istaken into account as viscoelastic damping. Numerical examples for different stiffened platesare presented to discuss the steady response of the non-resonance and theamplitude-frequency response of the primary parametric resonance and primary resonance.(5) Double-modal nonlinear dynamic response of stiffened plates is investigated withfour edges simply supported and four edges clamped. The damping of the plate is taken intoaccount as viscoelastic damping.The governing equations of motion, which are derived byusing the Lagrange equation, are reduced to a two-degree-of-freedom nonlinear system byassuming mode shapes. Three-to-one internal resonance is taken into consideration, and themethod of multiple scales is used to investigate the double-modal motion. Finally, numericalexamples for different stiffened plates are presented to discuss the steady response andamplitude-frequency response of the primary resonance.(6) The dynamic stability of stiffened plates under in-plane periodic excitation isinvestigated with four edges simply supported and four edges clamped. The governingequation of parametric vibration is derived through Hamilton principle. Selecting the (1,1)thmode, the governing equation is converted into Mathieu-Hill equation, which can be sovledthrough Fourier series. Finally, numerical examples for different stiffened plates are presentedto discuss how the number and rigidity of stiffeners influence the unstable region.