Study On Effective Length Of Variable Cross-Section Pier

With the development of highway in mountainous area and city road, variable cross-section Pier is widely applied in the modern bridge engineering for its reasonable mechanical property and low cost in material. The coefficient of effective length of the uniform cross section pier is proposed referring to the standard of"Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts". But the general formula of coefficient of effective length of the variable cross-section Pier is not put forward in this standard. The bearing capacity of variable cross-section Pier can be calculated exactly by the method of FEM, which is lack of applicability and efficiency. Basing on the theories of virtual rigid joint and conversion inertia moment, mechanical balanced principle is applied in this paper to research the following works by energy method and transfer-matrix method.①The length of pier body considering the influence of pile foundation is investigated. It is important to calculate the effective length of pier and ensure the length of the component. The pier body is effected by pile and foundation soil. According to the point bearing pile, friction pile and driven pile, virtual rigid joint method is proposed. M-method is used to calculate the horizontal displacement and rotation on the top pile.②The conversion inertia moment of the uniform cross section pier which is equivalent to the variable cross-section Pier is investigated. The inertia moment of pier shaft is the important parameter in the calculation of effective length. The variable cross-section pier is equivalent to the uniform cross section pier in the condition of the same critical load referring to the method of effective length upon stability theory. The formula of conversion inertia moment of variable cross-section is deduced and simplified by Rayleigh-Ritz method and transfer-matrix method to improve its applicability and precision.③The formula of constraint stiffness of the top pile is investigated. The precision of effective length is effected by the constraints of top pile. According to the formula of virtual rigid joint and conversion inertia moment, the formula of anti-pushing rigidity is simplified through equivalent Euler column. The solution of the formula of anti-pushing rigidity is proved comparing with the data of real engineering. ④Combining the investigated content, the coefficient of effective length of the variable cross-section pier is calculated by the differential equation of Euler column in stability theory .Solid model established by the general FEM software of ANSYS is calculated and compared with all the solution of formula.