Spline Function Metnod For High-Rise Steel Frame Structure Stability Analysis

With many advantages, steel structure is more and more widely used in construction, now has become one of China's major structural system. Compared with the reinforced concrete structure, steel structure has some advantages, such as high strength, light weight, good anti-seismic performance, design flexibility, easy construction, short construction period, in line with industrial requirements, meet the requirements of sustainable development and so on. Steel frame, one of the most popular styles of steel structure, is flexible in column arrangement, large in column space, excellent in plastic performance, good for anti-seismic, simple in construction and widely used in many high-rise buildings.Since steel has high strength and excellent ductility, frame members is slender, thin-walled and light in high-rise steel frame system. In axial compression or bending, the structure may be local or global instability, and then stability factors control the ultimate strength of steel frame and its components. So stability analysis is very important while analyzing steel frames.Among so many methods for structure stability analysis, the finite element method is widely used. But traditional finite element method has much unknown quantity, resource occupation and calculation. Much finite element software can not track the loading path in many cases. The real ultimate stability state can not be achieved.This thesis aims to study the spline function methods for high-rise steel frame structure stability analysis. The main works includes:(1) Based on Kirchhoff thin-plate theory, the spline element-free method (SEFM) computation format for elastic thin plate stability analysis is established. The spline element-free method computation format for the stability analysis of thick/thin plate is established based on Mindlin-Reissner theory, which takes deflection and shear strains as the independent field variables. The critical force is determined by eigenvalue buckling. The general program is composed by C language. The results of examples shows that this method has many advantages such as high precision, rapid convergence, less degree of freedom, no shear locking phenomenon, easy to be programmed, applicable for the stability analysis of the plate with various boundaries and various thickness. It can be used to analyze the plate in frame structure.(2) Using beam-to-column theory and stable function, the stiffness matrix of beam-to-column which considered geometric nonlinear is developed. The computation format of QR method for the geometric nonlinear stability analysis of plan steel frame is conducted and adopted to programming by C language. The examples show that the effecting of geometry nonlinear to the stability analysis of steel frames can not be neglected. QR method has simple computation format and high precision, not only can calculate the critical load of whole instability of structure, but also can track the entire loading path. QR method has great advantages on steel frame stability analysis.(3) Based on the geometric nonlinear stability analysis, taking both material nonlinearity and geometric nonlinearity into account, using the stiffness matrix of beam-to-column developed in this thesis, the nonlinear stability analysis incremental stiffness equation by load incremental method is established. Plastic hinge model is used to establish the QR method format for double nonlinear stability analysis of steel frame. The Euler-modified-Newton method is used to solve the nonlinear equations. The tangent stiffness method is applied to trace the nonlinear equilibrium path of the structure. General computer program is composed by C language. Through typical examples, the effecting of material nonlinearity to structure stability is analyzed, which proofs the feasibility and superiority of QR method for double nonlinear stability analysis of steel frame. QR method has simple computation format, less unknown and high precision, do not need to modify the computational grid and the degree of freedom of structure to meet the appearance of plastic hinges, takes the overall instability as the termination condition. So the subsequent incremental calculation will not be terminated by local buckling damage.(4) A software of steel frame structure stability analysis which programmed by the algorithm of this thesis is introduced. It can be used to analyze the stability of plane frame and plate. Then takes the Guangxi Tobacco Industrial Co., Ltd. Research and Development Center Building as example, uses that software to analyze its stability, assess the stability of the structure.