A Procedure for Predicting the Fatigue Damage of Structural Members in Unsteady Winds

Abstract

Abstract The practice of assuming fill, steady state, vortex-induced vibration response, to wind is excessively conservative [1]. This paper presents a practical methodfor estimating the reduction of the fatigue damage rate due to the naturalunsteady fluctuations in wind speed. Two dimensionless parameters are shown tobe particularly important. The first is the ratio of the lock-in bandwidth tothe turbulence intensity level of the wind. The second is the ratio of thelength of time the wind speed remains in the lock-in interval to the rise timeof the member to steady state response levels. The paper also shows that onemust account for the discrete nature of wind speed and direction scatterdiagrams in estimating the probability of occurrence of the critical windspeed. Introduction A 1992 review [2] of state-of-the-art design calculations for wind-inducedfatigue damage of structural members revealed substantial excess conservatismdue to the assumption of steady state structural response to wind. Further workwas recommended to establish the effect of unsteady wind speed variations, turbulence, and finite structural response rise time. These factors have nowbeen investigated by means of wind tunnel tests, analysis of extensive NorthSea wind records, and development of appropriate dynamic and probabilisticmodels. The theoretical results, wind tunnel data, and statistical analysis of the winddata have been published in two recent papers and a Ph.D. thesis [3, 4 &5]. This paper synthesizes these results in the form of a proposed, practicalprocedure for predicting the fatigue life of structural members excited byvortex shedding in wind. In this paper the members are assumed to vibrate in the first mode in thecross-flow direction. The only types of members studied are restrained at bothends, with boundary conditions which may vary from pinned to fixed. Otherstructural configurations such as cantilevers could be addressed by the methodsdescribed here, but no emphasis has been given to such applications in thisstudy. Assumptions, Definitions and Objectives Accepted practice in the industry today is to compute D,,, the steady statefatigue damage rate that results from wind at the critical wind speed, V,, which causes maximum vibration response. This damage rate is then multiplied bythe fraction of the year that the wind is expected to blow at or near to thecritical velocity for that member. [n this paper three adjustment factors, YoY1 and Y1introduced, so as to obtain theadjusted damage rate, D,, as shown below, (MATHEMATICAL EQUATION AVAILABLE IN FULL PAPER) The first two factors, Y0 and Y1, account forthe unsteady behavior of natural winds and the finite rise time required by thestructural member to reach steady state, given the wind is at the critical windspeed. The third correction factor, Ybin, accounts for the use ofdiscrete wind speed and direction scatter diagrams rather than smooth windspeed probability density functions.