Analysis On Shear Lag, Distortion And Ultimate Bearing Capacity Of Box-Section Beam Under Eccentric Load

Neither Euler-Bernoulli beam thoery nor Timoshenko beam thoery did take into account the properties of thin-walled bar, such as the shear lag effect and the distortion effect, which are both three dimentional mechanical models. In order to reduce the variables and simplify the problems, this thesis presents a one dimentional dispersed Spline Finite Point Method (SPFM) to analyze the shear lag effect and the distortion effect. Since safty of structure is the priovity, this study analyzes ultimate bearing capacity (UBC) of the thin-walled box beam under eccenric loads on the basis of the Elastic Modulus Reduction Method (EMRM). The main contents of thesis are:(1) Taking the additional deflection as the genaeralized displacement of the shear lag effect, this thesis presents a spline finite point method to analyze the distortion effect of box section beam because the method has high accuracy and less variables. Subdomain analysis is used to analyze the box beam, which is divided into several subdomains and then assembled to an integrate structure for the integrate analysis, accoding to the compatibility of displacement. The shear lag effect of box beam is solved by the SFPM, which is a simple, flexible, accurate and effective approach but has advantages of both Ritz method and finite element method (FEM).(2) On the basis of the distortion thoery under load decomposition, this thesis treats the distortional angle of the thin-walled box beam as the foundamental variables. The thin-walled box beam is dispersed by spline nodes along the length, and the displacement field is constructed. A spline finite point method is presented for analyzing on the distortion of thin-walled box beam acoording to the principle of minimum potential energy after establishing the total potential energy function considered warping and transverse bending deformation. Keeping a certain precision, SFPM costs small computing expense but enhances the computing efficiency. The distortion effect of box beam with a variable cross section can be analyzed according to the compatibility of displacement between subdomains.(3) Using of the traditional generalized yield function (GYF) to analyze the bearing capcacity (UBC) of stucture leads to an unstable result. To circumvent the disadvantage, a homogeneous generalized yield function (HGYF) of the thin-walled box beam under both bending and torsion is presented on the basis of principle of regressive analysis. Based on this, the ulmate bearing capacity of the thin-walled box beam under eccentric loads is studied. Numerical examples verify the accuracy of EMRM and the stability of the result.