Geometrical Non-Linear Analysis Of Reinforced Concrete Beams Due To Chloride Ingression

The theory of nonlinear analysis is the foundation of the whole process analysis of structure.Meanwhile,the nonlinear theory is also an important application foundation widely used in large span and space structures.With the deepening of theoretical research and the increasingly advanced methods,we can provide powerful and accurate analysis and design capabilities for the future.What's more,the accuracy of analysis and the depth of analysis directly improve the design quality of complex structures and the analysis quality of complex parts in structure.For the needs of practical applications,it is necessary to systematically discuss the nonlinear analysis theory in the structure,especially in the space structure.During the process for nonlinear analysis,the iterative method,the calculation method and the stiffness matrix will have a great influence on it.The accuracy of the stiffness matrix not only affects the accuracy of the calculation results,but also affects the convergence of the critical point.In this paper,the nonlinear analysis theory of beam column element is derived and deduced,and the tangent stiffness matrix with geometric nonlinearity is mainly derived.Based on the theories,nonlinear analysis programs are developed.And some typical examples are used to verify and evaluate the applicability and correctness of the theory and procedure.Then combining fiber beam-column element theory with cellular automata(CA)effectively,nonlinear analysis and durability life evaluation of corroded reinforced concrete beams are carried out.The research content is as follows:Firstly,the nonlinear analysis theory of plane beam column element based on the finite element method is derived and deduced.On the basis of the modified Lagrange(UL)formulation and the principle of minimum potential energy,ignoring the shear and torsion,the shape function is determined by defining the force and deformation of the plane beam element.Furthermore,the elastic stiffness matrix and geometric stiffness matrix of the plane beam column element are derived,and tangent stiffness matrix for plane nonlinear analysis is obtained,and the transformation relation between the plane local coordinate and the global coordinate is further obtained.Secondly,the nonlinear analysis theory of spatial beam column element based on the finite element method is derived and deduced.On the basis of the modified Lagrange(UL)formulation,ignoring the shear and torsion,the displacement interpolation function is determined by defining the force and deformation of the spatial beam element with two nodes and ten degrees of freedom.Furthermore,the elastic stiffness matrix and geometric stiffness matrix of the spatial beam column element are derived,and tangent stiffness matrix for spatialnonlinear analysis is obtained,and the transformation relation between the spatial local coordinate and the global coordinate is further obtained.Thirdly,the nonlinear analysis theory of spatial fiber beam-column element on the basis of the stiffness method is derived and deduced.On account of the basic assumptions of the fiber model,the introduction of the analytical model,the dispersion of the fiber section and the partition of the fiber size,the displacement interpolation function is determined by defining the force and deformation of the spatial beam element with two nodes and ten degrees of freedom.In addition,the elastic stiffness matrix and geometric stiffness matrix of the spatial fibre beam-column element are derived,and tangent stiffness matrix for spatial nonlinear analysis is obtained.Fourthly,nonlinear analysis programs corresponding to the nonlinear analysis theory of beam-column element based on the finite element method and that of spatial fiber beam-column element on the basis of the stiffness method are programmed by using MATLAB.Four classic examples of Williams frame,cantilever beam,Lee 's Frame and portal frame are selected to analyzed by means of nonlinear analysis program.It's shown that the calculated results are more or less agree with the experimental results and the calculation results in other literature,which verify the obtained theories well.Besides,the effect of several factors,such as unit division,section fiber dispersion and fiber size division on the results of geometric nonlinear analysis is discussed in course of analysis,and more precise parameter selection is obtained.Lastly,combining the theory of fiber beam-column element with chloride ion diffusion CA model,taking reinforced concrete continuous beam in erosive environment as an example,the chloride ion diffusion in beam section is simulated by cellular automata method,and the damage factor-time curve of steel bars is obtained.Then introducing the damage factor into the nonlinear analysis of reinforced concrete continuous beam,the displacement-time evolution of the key points and the relationship between the bending moment and curvature of the section at different corrosion times are obtained.Finally,by comparing the resistance of the structure with the internal force of the structure,the durability life evaluation of the structure is completed.