Analysis Of Shear Lag Effect And Stochastic Finite Element Based Reliability On Box-Girders

Box-girders is a thin-walled beam with box section, which is widely used in bridge and building. The classical Euler beam theory does not hold for bending box-girders under external load because of the shear lag effect, the stress is non-uniformly distributed along flange cross section. Investigations show that shear lag effect can reduce the bending stiffness of box-girders, result in cracks or serious accident such as local collapse. Moreover, in practical engineering, the material porperties, member size and external load are random physical quantities. With the progressive of computation theory and powerful of information processing ability of computer, it is need to handle practical engineering problems using uncertain computational mechanics model, based on which reliability is calculated. Therefore, it is necessary to study shear lag effect, stochastic analysis and reliability analysis comprehensively and deeply. The main contents of the thesis include:1. The additional deflection of box-girder was defined for characterizing the nonuniformity of normal stress along flange section. The potential energy functional is developed using external loads instead of inner forces. A set of4th order ordinary differential equations on additional deflection is derived as well as the boundary conditions, based on which the closed form solutions of the additional deflection were achieved. Furthermore, the shear lag coefficients based on deflection was presented to investigate the variation of shear lag effect on box girders, and examined the effects of the boundary conditions and the section’s geometric dimensions on the shear lag. 2. The deflection, additional deflection and their first derivatives are chosen as nodal displacement parameters of the box-girder element, so that a one-dimensional finite element is developed for shear-lag effect on box girders, analyzed the shear lag effect and its variation law under different boundary conditions. Studies show that the shear lag coefficient based on the additional deflection can take place of the conventional one based on the stress; the one-dimensional finite element method has high precision.3. Hierarchical Stochastic Finite Element Method was built for structure with large randomness in elastic modulus and external loads. This method established a set of base vector using hierarchical expand method, and the control equations of Hierarchical Stochastic Finite Element Method were built based on variational principle. The simplified formulae of stiffness elements and load array elements were derived on the basis of chaos polynomial, and the expression of node displacements were given under different order base vector, then derived the formulae for the mean and the covariance of node displacement were derived. Stochastic element methods were built for box-girders, including Monte Carlo Stochastic Analysis, Perturbation Stochastic Analysis and Hierarchical Stochastic Analysis in this paper.The statistical characteristics of structure response were analyzed using these three stochastic finite methods, and the calculate results were compared. Researches indicate that the results calculate by Hierarchical Stochastic Finite Element Method tallied with the Monte Carlo Simulation Method under stochastic parameters with large variations, and had high computational efficiency.4. Calculation methods for reliability index based on Hierarchical Stochastic Finite Element Method were established, including embedded iterative algorithm based on cheking point and separate iterative algorithm based on mean value point. Studied using Monte Carlo simulation method to calculate reliability index by sampling and statistics, combined Perturbation Stochastic Finite Element Method and iterative algorithm for structural reliability analysis to calculate reliability index. Reliability of box-girder was analyzed using reliability analysis methods based on these three methods and calculations were compared. Studies manifest that accuracy of separate iterative algorithms based on mean value point of Hierarchical Stochastic Finite Element Method and of perturbation stochastic finite element method based on design point, are higher comparing with the algorithm accuracy of Monte Carlo stochastic finite element method. What is more, as the variation of stochastic parameter is lager, the accuracy of separate iterative algorithm based on mean value point is higher than that of perturbation stochastic finite element method based on design point.