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Evaluation of across-wind dynamic response for rectangular high rise buildings
Abstract
According to Taylor's Frozen Assumption about turbulence, an analytical solution of spectral density function of pressure fluctuation in across-wind direction was derived from the governing equation of flow movement in turbulence theory. All of the turbulence-mean components in the source term of pressure governing equation had been taken into account. If an appropriate turbulence integral scale is adopted, the spectrum density function value will correspond well to the results from full scale measurements. The function value near the basic natural frequency of building is larger than that from wind tunnel test. The displacement and the acceleration value evaluated with this fluctuating pressure load are larger than those from Japanese design code.
To research across-wind-induced vibration response of ultra high voltage (UHV) transmission tower and that of tower-line coupling system, taking a certain 1000 kV transmission line as research object, through wind tunnel test of aeroelastic model the across-wind-induced vibration responses of both single tower and tower-line coupling system under turbulent flow are researched. Test results show that in turbulent wind field the across-wind-induced vibration response and the along-wind-induced vibration response of single transmission tower are in the same order of magnitude. In tower-line coupling system, the across-wind acceleration response of the tower is larger than that of the single tower; the across-wind displacement response at the end of the crossbeam is larger than that of the single tower and the across-wind displacement response at the tower body is smaller that that of the single tower. The influence of high order vibration modes on the acceleration and displacement responses cannot be neglected, and there is a certain extent of background response involved in displacement response. Thus in the wind force proofing design of UHV transmission tower the influence of across-wind response should be taken into account.
An analytical solution to spectral density function of across-wind load fluctuation acting on the structure flank is presented from the original fluid movement equation in turbulence theory under certain assumptions. The spectral density function of wind load fluctuation could be derived from the CFD wind average velocity and fluctuating velocity distribution according to Taylor's Frozen Assumption of turbulence. All the T-M contributions have been taken into account in the analysis process. This could be regarded as an effective verification of the datum from wind tunnel test and datum from full scale observation. The analysis of structure dynamic response induced by this kind of wind load fluctuation could then be achieved without the expensive wind tunnel test.
The characteristics of across-wind loading and the mathematical model of tall buildings are theoretically studied, based on wind tunnel tests. Across-wind excitation on tall buildings is divided into across-wind turbulence and vortex-shedding components. Based on the wind tunnel test results of 10 typical tall building models, the excitation characteristics and the mathematical models of these two excitation components are investigated in some details. Using the test results, the aerodynamic force coefficients and shape coefficients of the two components are derived. In particular, power spectrum density and coherence functions of the vortex excitation are analyzed.
Tall buildings under wind action usually oscillate simultaneously in the along-wind and across-wind directions as well as in torsional modes. While several procedures have been developed for predicting wind-induced loads and responses in along-wind direction, accurate analytical methods for estimating across-wind and torsional response have not been possible yet. Simplified empirical formulas for estimation of the across-wind dynamic responses of rectangular tall buildings are presented in this paper. Unlike established empirical formulas in codifications, the formulas proposed in this paper are developed based on simultaneous pressure measurements from a series of tall building models with various side and aspect ratios in a boundary layer wind tunnel. Comparisons of the across-wind responses determined by the proposed formulas and the results obtained from the wind tunnel tests as well as those estimated by two well-known wind loading codes are made to examine the applicability and accuracy of the proposed simplified formulas. It is shown through the comparisons that the proposed simplified formulas can be served as an alternative and useful tool for the design and analysis of wind effects on rectangular tall buildings.
This paper describes the results of full-scale measurements of wind pressure and wind-induced response acceleration for an 18 storey building 68 m high. It also gives estimates of the response acceleration of this building in accordance with the AIJ Standard for Loads and External Forces on Buildings and Structures, the National Building Code of Canada, and the method suggested by Ohkuma and co-workers. The values of estimated response acceleration correspond to the values of the full-scale measurements.