Complex Spectral Method for Dynamic Analysis of Gable Frames: Undamped Systems

Abstract

Non-prismatic tapered members have been used extensively in modern steel structures. Economical design of such structures may be gained by reducing the member section in the low moment regions. In order to analyse and design a tapered I-beam member, it is necessary to develop an accurate and reliable analysis method. The conventional finite element method can be used to analyse structures with tapered I-beams. However, the number of elements and the computer memory and time in this method in order to obtain accurate results∼ especially under dynamic loading, can be large. This paper shows how the mathematical spectral theory can be used to formulate a matrix methodology in which the dynamic response of steel structures with tapered members can be obtained accurately with a lesser number of elements. A computer program based on this complex spectral element method is described, and numerical examples have been solved to demonstrate the efficiency of the method.

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