Study On Non-linear Analysis Method Of Steel Structure And Its Implementation In Software

Steel structures have many advantages, including high strength, low weight, fast construction, etc., that they have been widely used in engineering, especially for constructing large span, large space structures and high-rise buildings. Traditionally, steel structures are designed by the two-step method, which includes two steps that first calculating the internal force of members using linear-elastic method, and then designing the members separately under the guides of codes (In those guides, the interaction among members is considered by using effective length factor). As been widely recognized, the two-step method has many shortcomings. Alternatively, with the development of modern computer technology and calculation theory of structure, the advanced analysis method has been developed. The advanced analysis method can consider the nonlinear response of structures, the effects of deficiencies and other factors on the loading capacity of structures, etc.. By the advanced analysis method, only a full-phase global analysis is needed to design the structure. The nonlinear analysis is the key component for an advanced analysis. In this dissertation, the theory of geometric nonlinearity and material nonlinearity of steel structures will be presented. A non-linear programming is developed and added to the common design software of steel structure, USSCAD, to realize the nonlinear analyzing ability of the software.The mechanism of space bars is very simple that the bars can only have axial displacements. The dissertation has derived the tangent stiffness matrix of space bars by equilibrium equations and UL formulations respectively. In nonlinear analysis of space bars, the results by using the derived matrix from equilibrium equations and UL formulations are the same as the results by using the tangent stiffness matrix from TL formulations.The geometric nonlinearity analysis is more complex for space beams than that for space bars. The dissertation derives the tangent stiffness matrix of space beams by beam-column theory and the theory of nonlinear finite element by UL formulations. The characteristics of unchangeable and disable to be directly added for space rotations are proved, and then the methods of rotation matrix and quaternion are present for the superposition of space rotations. The idea of co-rotational is used to update the local coordinate system for space beams in each iteration process and to calculate the natural deformations of the ends of beams. In the process of nonlinear analysis, the unbalance forces are very important, which can affect the accuracy of final result. Here, two methods of calculating the internal force are present in detail, which are the natural deformation method and the external stiffens method.Currently the tapered members are used widely in the light steel plants, but there has no accurate mechanical model for this kind of element. The dissertation proposes a new approach to solve this problem, by adopting the method of equivalent moment of inertia to establish the mechanical model of tapered members. For the condition where the centriod of the section does not coincide with the corresponding node, two revised matrixes are used. The dissertation derives the theory of geometric nonlinear analysis for tapered members by the UL formulation.The key of material nonlinear analysis for space beams is that of defining the plastic model of members. Generally there are two models:distributed plasticity model and concentrated plasticity model. For elastic-perfectly plastic material the dissertation takes the elastic-plastic hinge method and the refine plastic hinge method deriving the elastic-plastic tangent stiffness matrix. The elastic-plastic state of members is judged by the limit yield surface equation of LRFD. Then the method of calculating the elastic-plastic internal force of beams is presented. At last in order to follow the yield criterion, it is necessary to revise the force-points which are deviant from the yield surface.By the nonlinear analysis theory of this dissertation, the programming can be easily designed, to complete the ability of nonlinear analysis for the steel software of USSCAD. The methods for solving nonlinear equations are Newton-Raphson method, modified Newton-Raphson method and arc-length method. The convergence criterion of iterations uses the infinite norm of unbalanced forces. The programming takes the object-oriented technique and C++ is adopted as the programming language. With the help of ObjectARX provided by the Autodesk Company, it achieves the secondary development of AutoCAD2007. Using the programming interface provided by the Microsoft Office, it is conveniently to realize the automatical generation of calculation book in the style of Microsoft Word. The results of several numerical examples designed by USSCAD show that the accuracy of nonlinear analysis theory can fulfill the requirements for engineering usages. Furthermore, the software is able to implement nonlinear analysis for large-sized space structures.Finally, the dissertation introduces the studies on the progressive collapse, and the provisions in some foreign codes for structure design about progressive collapse. The tie force method and the alternate path method are included for analyzing the capacity of structures to resist the progressive collapse. Following with the alternate path method and the modification method of load specified by USA' GSA code, a case study on progressive collapse analysis of a steel frame (which is designed under the guides of Chinese steel structures code) is given.