Improved Deflection Theory For Self-anchored Suspension Bridges And In-plane Free Vibrations Of Stiffening Girders

The self-anchored suspension bridge is different from the earth-anchored suspension bridge.It does not need to build a huge anchored which makes the self-anchored suspension bridge more compact and more beautiful.It not only saves the cost of building anchors in the project,but also provides a new way for the construction of suspension bridges without terrain construction conditions;The self-anchored suspension bridge is better than the earth-anchored suspension bridge,which is increasingly used in urban bridges,and the span is also in the forefront of the world.Studying and analyzing the static force characteristics of the self-anchored suspension bridge and the bending free vibration in the plane of the stiffening girder has certain reference significance for the preliminary design,parameter optimization design and engineering practice of self-anchored suspension bridge.The purpose of this study is to establish the analytical solution and mode shape of the various frequencies of the free vibration in the bending plane of the stiffened girder under static load,displacement and the dead load under the self-anchored suspension bridge.This paper takes a double-tower three-span self-anchored suspension bridge as an example.Based on the deflection theory,the differential equation of force of self-anchored suspension bridge structure under live load is established.By improving the boundary conditions of the main cable at the top of the main tower,the calculation process is simplified,and the calculation efficiency of the initial stage is improved.The Newton-Raphson iterative method is not needed to solve the nonlinear equations.It directly gives the axial force of the stiffening girder of the self-anchored suspension bridge under live load,the boom force,the main cable tension,the stiffening girder and the main cable deflection,and the horizontal shortening of the stiffening girder.On this basis,the elongation caused by the introduction of the boom under the live load during the calculation process improves the accuracy of the deflection theory applied to the self-anchored suspension bridge structure calculation.The static calculation efficiency and calculation accuracy of the self-anchored suspension bridge are improved comprehensively.Based on the Hamiltonian principle,the partial differential equations of the distributed parameter system function form,the differential equations of the free vibration of the self-anchored suspension bridge stiffening girder in the plane are established.By introducing continuous cross-boundary conditions and solving this equation,the analytical solutions of the various frequencies of the free vibration of the stiffening girder in the self-anchored suspension bridge can be obtained,and the analytical solution of the mode function can be obtained.Based on the multi-parameter self-anchored suspension bridge model established in this paper,the influence of various parameters on the static force of the self-anchored suspension bridge and the free vibration characteristics of the stiffened girder is studied by parameter analysis,which provides a reference for the parameter optimization and conceptual design and preliminary design of the self-anchored suspension bridge.