Nonlinear Static Mechanical Properity Of The Suspension Bridges

The mechanical behaviors of the susp ension bridges under st atic load are the basis for the design of susp ension bridge.It is helps to analyze the complex behavior of susp ension bridges more accurately that researching the nonlinear st atic p roblems of susp ension bridges.In practical engineering,the nonlinear p roblem of the susp ension bridges is st udied usually by the finite element simulation and exp erimental methods.However,these two methods are not conducive to revealing the changing laws of the susp ension bridges mechanical behavior.So far,there is a few the nonlinear analytical solution formula of the susp ension bridge p roposed by the researchers,although analytical formulas can clearly reveal the change law of mechanical behavior.In this dissertation,first ly,the results of finite element numerical simulation are compared with the analytical solution of linear vertical bending that are obtained by Galerkin method.The results show that there is a certain error between the linear analytical solution and the finite element solution when the load is large.Therefore,the nonlinear analytical solution formula of the susp ension bridge under vertical static force is obtained by the perturbation method and Galerkin method.Because of Galerkin method,the accuracy of analytical solution is reduced,but the process and form of solution become simpler.The results show that the non-linear solution under uniform load is in good agreement with the finite element results,and the accuracy of the non-linear solution under concentrated load meets the accuracy requirements of the finite element results.The st atic linear and nonlinear analytical solution of the susp ension bridge are compared with the finite element simulation.The results show that the non-linear solution has higher accuracy,and it reveals the non-linear relationship between the vertical displacement and the sag of the main cable.The non-linear relationship uncovers the law that the minimum value of the vertical deformation changes with the load.Afterwards,the effects,they include main cable sag,elast ic modulus of cable,beam bending rigidity and mass p er unit length,on the static nonlinear mechanical behavior of the suspension bridge were st udied by the analytical solution.When the mechanical behavior is analyzed by linear theory,it is found that the vertical disp lacement varies monotonously with the change of these factors.However,the nonlinear theory shows that these factors have more the complex influence on the mechanical behavior of the suspension bridges.These influences are manifest ed in the following two asp ects.First,under the large uniformly distributed load,when the sag or elast ic modulus of the main cable is small,the vertical displacement will not change monotonically with the change of sag or elastic modulus.Second,under the uniformly distributed load or the large concentrated load,when the unit mass of the bridge is small,the vertical disp lacement will not change monotonously with the change of unit mass.In this dissertation,the nonlinear analytical solution is a foundation of the further research of the complex mechanical behavior of the susp ension bridges,and the solutions may provide some references for the engineering applications.