Keywords: stochastic approach, spectral density function, nonlinear dynamic analysis.

High-speed computing and advanced finite element procedures provide the capability of detailed analysis of cable structures. Nowadays, the most common approach to cable net analysis is the nonlinear dynamic analysis by forward matrix-upgrade-integration in the time domain. By means of the time history of the loading, the step-by-step analysis proceeds where the equilibrium of the dynamic forces at the end of each time increment is established by minimization of the total potential energy [1]. However, deterministic analysis requires considerable time and effort.

The accuracy of the calculated response and the stability considerations of the numerical integration operator used in the analysis typically requires the selection of small time increments, especially when the structure exhibits significant nonlinearities. Furthermore, the current approaches to calculate the equilibrium position of a nonlinear structure are based on iterative procedures. Owing to the random nature of some sources of dynamic excitations, structural analysis in the time domain should be done under a family of time histories of loading with comparable statistical properties.

Considering the demands and limitations of nonlinear deterministic time-domain analysis, this paper suggests a simplified approach to perform a spectral analysis of cable roofs under a family of wind loadings with defined characteristics. This simplified rational analysis method of cable roofs presented here is convenient for structural designers. This method is based on the fact that in most cable roof designs, the response is typically weakly nonlinear as the kinematics are not very large, and the dominant frequencies will only slightly vary with the amplitude of the response of the structure. Therefore, the dynamic response of weakly nonlinear structures can be obtained superposing the static response of the structure under the mean wind speed and the maximum probable response of the structure due to the fluctuating component of wind velocity applying spectral density function or power spectra of the fluctuating component of wind velocity and statistical theory [2].

The present work also extends the proposed approach to involve a larger number of significant degrees of freedom to improve its accuracy. The approach can have direct applications to the dynamic analysis of cable-stayed bridges, cable beams, cable nets and roofs and guyed masts. The proposed method is illustrated with two examples of common cable roofs from real cases, one with circular and the other with rectangular boundaries. In order to validate and check the accuracy of the method, the results are compared with those obtained from a detailed nonlinear incremental time-step dynamic analysis using ADINA (Automatic Dynamic Incremental Nonlinear Analysis) under a series of synthetic wind loading time histories [3].

1

G.D. Stefanou, "Dynamic response of tension cable structures due to wind loads", Computers & Structures, 43(2), 365-372, 1992. doi:10.1016/0045-7949(92)90154-R

2

H.A. Buchholdt, "An introduction to cable roof structures - second edition", Thomas Telford, 1999.

3

S.A. Ghafari Oskoei, G. McClure, "Dynamic analysis of cable roofs under transient wind; a comparison between time domain and frequency domain approaches", Journal of Tsinghua University - Science and Technology, 13(S1), 53-57, 2008.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)