Second-Order Effect And Series-Parallel-Circuit Models For Multiple Structures

Shearing property of frames and bending property of shear walls, bracing and tube structures are fully used in multiple structures system. Connected with diaphragm of the slabs, these structures are sharing the same horizontal deformation, and the interaction between them is advantageous to the steel frame.The present research of dual or multiple structures usually consider shear wall (or bracing, tube structure) as a flexural type cantilever, whose shear deformation is ignored. And ignoring its flexural deformation, frame is considered as a shear type cantilever, which means the gravity stiffnesses of frame columns are infinite. The interaction is provided by rigid links between these cantilevers, and their deformations are compatible. Different from plain solid web structure, vierendeel structure and lattice structure are wildly used in shear wall and tube structure of dual structure system, such as steel frame-shear wall structure and steel frame-core structure in practical engineering. The shear deformations for vierendeel and lattice structure occupy a high proportion of total deformation, when the structure deforms laterally under horizontal load or buckles integrally under vertical load. The shear deformations are even proportionately larger than bending deformations in some steel trusses and braced frames. That means errors are bound to produced when simplification is taken in traditional theory of structure to these structures.Both bending and shear deformations were considered, and the substructures of dual, multiple structures were considered as flexural-shear structures in this thesis. Based on these, interaction among substructures, total horizontal deformations of the structure, second-order effect were studied intensively. A series of models and computational methods were proposed in this thesis.Based on Timoshenko elastic stability theory, substructures were equal to Timoshenko cantilevers considering both bending and shear deformations. From constant to varied, these equivalent cantilevers were studied, and a series of moment second-order factors formulas were proposed for models with multifarious cross-sections under multifarious loads. The accuracy of these formulas was proved to be suitable by finite element method. These proposed formulas not only simplified the calculation in moment second-order factors, but also provides convenience for follow-up researches.Second-order elastic analytical equations were deduced for constant cross-section dual structures under lateral and vertical loads at the top of the structure. By analyzing the interaction between the substructures of dual structure, the concept of stiffness amplification factor and its computational method are proposed. According to these, simplified method for second-order factors of dual structures is also proposed.By studying dual and multiple structure systems with varied cross-section stiffnesses and axial forces along the height, equivalent methods are proposed for both stffnesses and loads. With the proposed method for second-order factors under constant cross-section stiffnesses and axial forces, the second-order factors for the equivalent structures are obtained. The comparisons with finite element method show that, after equivalent, the proposed method is acceptable for multiple structure systems with varied cross-section stiffnesses and axial forces along the height.Based on stiffness amplification factor which describes the interaction between two substructures, the difference between two second-order factors for both substructures is considered. According to the superposition principle, the series-parallel-circuit model for second-order horizontal deformation of dual structures is proposed. With the equivalent method used in calculating second-order factor, the series-parallel-circuit models for both linear elastic and second-order horizontal deformations of dual structures can be extend to multiple structures with varied cross-section stiffnesses and axial forces, which is more close to the structures in practical engineering.Considering the multiple structures with both bending and shear stiffness, the results for second-order factors and horizontal deformations, obtained by the series of proposed and finite element method, have good agreements. And these formulas are simple, having wider application and clear meaning.