Global structural analysis of central cores supported tall buildings compared with FEM
The focus of this article is to present an approximate method of calculation based on the equivalent column theory. This approximate method of calculation may be successfully applied in the case of tall buildings. Knowing the geometrical and stiffness characteristics of the structure, applying the equivalent column theory may determined: the displacements in both directions, the rotation of the structure, critical load, shear forces, bending moments for each resisting element and the torsional moment of the structure. The results obtained using the approximate calculation method will be compared with the results obtained using an exact calculation based on F.E.M.: Autodesk Robot Structural Analysis and ANSYS 12.1.
Vibration analysis of doubly asymmetric, three-dimensional structures comprising wall and frame assemblies with variable cross-section
Abstract A global analysis approach to modelling doubly asymmetric, three-dimensional, multi-bay, multi-storey, wall–frame structures is presented in a form that enables the lower numbered natural frequencies to be determined approximately with the certain knowledge that none have been missed. It is assumed that the primary walls and frames of the original structure run in two orthogonal directions and that their properties may vary in a step-wise fashion at one or more storey levels. The structure therefore divides naturally into uniform segments between changes of section properties. A typical segment is then replaced by an equivalent shear–flexure–torsion coupled beam whose governing differential equations are formulated using a continuum approach and posed in the form of a dynamic member stiffness matrix. The original structure can then be re-modelled as a sophisticated stepped cantilever in the usual way. Since the mass of each segment is assumed to be uniformly distributed, it is necessary to solve a transcendental eigenvalue problem, which is accomplished using the Wittrick–Williams algorithm. A parametric study on a series of wall–frame structures of varying height with different plan configurations is given to compare the accuracy of the current approach with datum results from fully converged finite element analyses.
Estimating Periods of Vibration of Tall Buildings
A hand method of estimating the period of free vibration of building structures, for use in determining the minimum base shear for their earthquake design, is presented. The method is for structures that have uniform properties through their height, and that are symmetrical in plan and symmetrically loaded so that they do not twist. The structures may consist of rigid frames, coupled walls, wall-frames and braced frames, or any combination of these. The basis of the method is that all of the above described types of bent behave as members of a family of shear-flexure structures whose static deflections can be predicted by coupled wall theory. A method of decoupling the static deflection into a flexural component and a shear plus flexure wall-frame type of component is extended to dynamic behavior of a corresponding decoupled eigenvalue approach, to determine the periods of free vibration. The derivation of the method, an assessment of its accuracy, and a worked example to illustrate its application are presented.