Stability Theory Of Thin-Walled Steel Components With Physical Defects And Its Applications

The effects of crack on the elastic deflection and the ultimate bearing capacity of thin-walled columns under both axially and eccentrically load were studied systematically by use of a local-global approach, where the local analysis for crack was according to one-dimensional model and the global analysis for column was according to three-dimensional model. And the stability theory and the method for determining ultimate bearing capacity of cracked steel-column were established. Thus a series of useful theoretical results were obtained, which are essential to evaluating the safety and durability of a damaged steel structure.Firstly, the development in nonlinear theories of stability for thin-walled structures was reviewed and a systematic exposition of the theoretical significance and application prospect of this study was made. Secondly, in order to take account of the effects of the cracks in structures, the expression of the stress intensity factor (SIF) of center cracked thin-walled members was achieved by means of the crack-section stress field (CSSF) method. Then, the elastic deflection of an eccentric thin-walled column with a model-I crack were calculated by mean of Rayleigh-Ritz energy method, where the plane crack model and spatial crack model where employed respectively. Furthermore, the control equations of the equilibrium path of the elastic buckling were derived for cracked columns subjected to both axial and eccentric compressive load. And an analytical model of the equilibrium path of both before and post buckling was suggested for the cracked column under axial load, where the crack closure and fracture condition are considered. Finally, the two-criteria approach to analyze the failure of thin-walled columns has been suggested and the analytical equations for determinate the ultimate bearing capacity were given. In addition, a simple test method for determining the uniaxial ductile damage curves of thin-slab was studied systematically and a numerical iterative-fit method was suggested for determining the material damage constants of the non-linear equations of Lemaiter-Chaboche's damage model. Based on above damage test results, the application of the theory of elastic-plastic damage in stability analysis of the steel structures was discussed preliminarily. The main works and achievements of this dissertation are as follows:(1) The crack-section stress field (CSSF) method for determining the stress intensity factor (SIF) of center cracked thin-walled bars was proposed and a universal expression of the dimensionless stress intensity factors for thin-walled and center-cracked members with unequal-thickness sections was acquired by use of the equilibrium condition of semi cracked member. The key to CSSF method is to establish a normal stress distribution model on the cracked cross section according to the numerical results of the finite element analysis and expression of the local or global stress field of an infinite center cracked plate. In comparison with the existing finite SIF results of thin-walled members, the simple formula given in this paper are simple and reliable to evaluate the residual bearing capacity or working life of engineering cracked thin-walled structures.(2) A method for determining the elastic deflection of the eccentric thin-walled column with model-I crack has been developed according to the plane crack model and spatial crack model respectively and a trigonometric series solution of the elastic deflection equation was obtained by mean of Rayleigh-Ritz energy method, where the change in elastic energy caused by introducing the crack was considered. Especially, A universal analytical-solution of the maximum deflection for cracked columns with various cross-sections was developed, that is useful to examine analytically the elastic buckling behavior and to estimate the ultimate bearing capacity. By comparison with the current rotational spring model and the equivalent stiffness method, the main advantage of the present solution is that the effect of axial compression on crack closure is considered.(3) The governing equation for whole process of an eccentric compressive column with model I crack was established, based on above analytical expression of the maximum deflection and an analytical model of the equilibrium path of both before and post buckling was suggested for the a cracked axial column, where the crack closure and fracture condition are considered. The equilibrium path model shows that when an excessive lateral interfering deflection appears the cracks will have the critical load decreased, while when the lateral interfering deflection is small the cracks will have no effects on critical load but post-buckling process. Thus the unreasonable conclusions in some references that cracks have certainly effects on critical load were corrected.(4) After the equations of ultimate yielding and fracture load were established for cracked eccentric column, the perfect equations for determining the stability factors were derived according to the two-failure criteria, i.e., yielding and fracture criteria. And effects of some factors on the critical transition crack-length, slenderness and eccentricity from yielding failure to fracture failure were investigated respectively.(5) For the two complex cases of a T-section column with a single-side crack and a multi-step compressive rectangular column with arbitrary number of cracks, thel expressions of the elastic deflections were obtained. And hence the governing equation for the buckling equilibrium path and the computational programs were established.(6) A simple test technique by use of clip gage for determining the uniaxial ductile damage curves of thin-slab was studied systematically and a numerical iterative-fit method was suggested for fitting the non-linear damage equation of Lemaiter-Chaboche's model. Some special techniques for measuring damage parameters of materials, such as the specimen size requirements, gauge length, the stability of the repeated-unloading elastic modulus and measuring and controlling of large strain, were proposed and discussed. The results tested from the thin-slabs of LY12-CZ aluminum alloys showed that the test method suggested for determining the uniaxial ductile damage curves of thin-slabs is feasible and effective.(7) The calculation method for determining the elastic-plastic buckling load was improved by introducing the material model of exponential strengthening and nonlinear plastic damage model into Shanley's theory. The interactive equation for finding the elastic-plastic stability coefficients was derived and an example of its application was gived and analyzed.(8) For some sections of columns, the influence of crack on the elastic deflection and ultimate bearing capacity of thin-walled columns was studied. And the differences between plane crack model and spatial crack model and their application limitation were discussed. A number of curves and tables of numerical results were given and analyzed in this dissertation.