A Theory Of Stability For Frames And Mega-Frames Considering The Effects Of Shear Deformations

A vast amount of research was focused on the theory of rigid frame structures in the last several decades, including the stability theory, the second order theory and the lateral stiffness. However, the traditional research only paid attention to the bending deformations of the rigid frames' components, ignoring the shear deformations. Recently, more and more mega-frame structure type and outrigger-braced structure type are applied in the realistic buildings. These types of structures share the common characteristics that they both adopt the mega components, and the mega components always have the lattice type cross sections or the truss type. When we use the traditional frame theory to analyze these mega-components, it will lead to great error because the shear deformations have a large proportion of the total deformations. This thesis will analyze the theory of rigid frame and mega-frame structures considering the effects of shear deformations.First of all, this thesis describes several methods of analyzing the effect of shear deformations, and discusses the basic assumptions and the differences between these methods. Particularly, introduce the method which is used in this thesis to analyze the different type structures.The second chapter analyses the elastic stability of bars considering the effect of the shear deformations. The influences of the bars' shear deformations to their critical loads are mainly discussed. The first and second order slope displacement equations for the beam element are proposed, where the effect of shear deformations are taken into account. These equations are the research basis of the whole thesis. They can be used to establish the equilibrium equations of all kinds different structure types.The simple formulae for the sway and non-sway buckling critical loads of the bars, which has arbitrary rotational restraints at both ends, are proposed respectively. Comparing with the accurate solutions, the proposed formulae have excellent accuracy. The internal relationships between the bars' sway buckling critical loads with their lateral stiffness have been concluded, and according to the relationship, the simple formula for the critical load of the bar with insufficient lateral support has been proposed.The effects of beams' shear deformations to the frames' stabilities are mainly discussed. According to the research, when the frame buckles in sway mode, no matter how different between the axial loads in the columns, we can reduce the linear bending stiffness of the beams to take account of its shear deformations, when the frame buckles in non-sway mode, the shear deformations of the beams can be ignored. And a simplified approach for the frames' critical loads is proposed, considering the shear deformations of frames' components, the inter-column and the inter-storey interactions. The frames' linear storey lateral stiffness has been studied, considering the shear deformations of components. According to the research, it is found that the linear lateral stiffness of certain storey is not only relative to the stiffness of columns and beams in that storey, but also to the stiffness of columns and beams in the upper and lower storeys and to the comparative value of lateral loads in different storeys. A simplified method has been proposed to calculate the linear storey lateral stiffness of rigid frames. And it is also found that when the different types of lateral and vertical loads acting on the frame, the stiffness of rotational restraints provided by beams at both ends of columns will vary greatly, even in some extreme situation, it could be negative, while the traditional frame theory thinks the value is always positive.The stability of stepped columns which have lattice type cross sections has been studied, considering the shear deformations of the columns. And the buckling formulae of stepped columns have been given. According to these buckling formulae, the numerical tables for different coefficient values have been provided. Meanwhile, a simplified formula for the critical loads of the stepped columns has been derived, comparing with the analytical solutions, it has great accuracy. The analytical solutions for the first order and second order lateral stiffness of the upper and lower columns have been proposed.The stability of the dual system with different heights, including the flexural substructure higher-the shear one lower, the flexural substructure lower-the shear one higher and the dual flexural-shear substructure systems with different heights, has been studied respectively. The analytical and the approximate solutions for the critical loads of these dual systems are been proposed. According to the research, we may found that with the relative heights of two substructures varying, the total critical loads of the dual systems will change accordingly. And when in the case the relative height equal to the optimum relative height, which is not equal to 1, and the total critical loads will get the maximum value.This thesis analyzes buckling of single-outrigger-braced frame-core structures in which the shear-deformable outrigger locates at an arbitrary height of the structure. By analyzing a simplified model of the outrigger-braced structure, the contributions of component rigidities and the location of the outrigger to the overall stiffness of the structure are identified. A continuous model, where the exterior frames are modeled as shear-deformable-only vertical cantilevers and the action of the outrigger is replaced by a rotational restraint at the outrigger-core connection, is used to analyze the bucking of a single-outrigger braced structure. It is found that the total critical load of the outrigger-braced structure is the sum of the critical loads of the frames and the core with the outrigger when they both function as independent structures. FE buckling analysis verified this conclusion. A simple formula for the buckling load of the structure is proposed. Compared with accurate solution, the proposed formula has excellent accuracy. Second order analysis is carried out for three types of lateral loads, with the concentrated vertical load acting at the top of the structure, amplification factors for the lateral displacement and moments of various members are analyzed and an approximate equation with good accuracy is presented.