An Approximate Dynamic Analysis of Tube Structures
Chang, Peter Chun Po
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https://hdl.handle.net/2142/69914
Description
Title
An Approximate Dynamic Analysis of Tube Structures
Author(s)
Chang, Peter Chun Po
Issue Date
1982
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Abstract
In the design of high-rise structures, the tube concept has been widely accepted as an effective means to resist lateral loads arising from earthquakes or wind. Because finite element analyses of these structures are costly and time-consuming, an approximate method of analysis is needed. The object of this investigation is to develop a model for the approximate analysis of tube buildings that can replace the discrete beams and columns of a building by an equivalent continuum.
The properties of the model representing tube structures, multi-cell tubes and tubes reinforced by cores and by braces are derived. For these structures, the model considered includes the effect due to shear lag as well as the effects due to shear and flexual deformation. Once the model properties are obtained, the governing differential equations can be found using the Principle of Minimum Potential Energy. Because of the complexity of these equations, they are solved using an approximate technique; the fourth-order Runge-Kutta method is used. The results of the approximate method are compared with those resulting from a finite element analysis. This comparison demonstrates that the approximate analysis provides a high degree of accuracy for all the structures investigated.
The dynamic analysis of a structure requires the knowledge of its frequencies and mode shapes. These dynamic properties are calculated using the Rayleigh-Ritz method. Once the dynamic properties are found, the global response of the structure can be found using a spectral analysis or a time-history analysis. A practical example of the design of a 51-story building is given. In this example, the versatility and effectiveness of the approximate analysis for the preliminary design is stressed. The final design is also analyzed using the finite element method. The global response as well as the computational time used for both methods of analysis are compared. The comparison clearly indicates that the approximate analysis yields results that are comparable to those from the finite element analysis but requires much less effort. Thus the value of the model as a powerful tool for design of buildings is demonstrated.
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