PSI - Issue 3

Alberto Lorenzon et al. / Procedia Structural Integrity 3 (2017) 370–379 A. Lorenzon et al. / Structural Integrity Procedia 00 (2017) 000–000

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2.2. Calculation of wind-induced fatigue damage Two main approaches have been proposed: -

Frequency domain-based methods developed from Davenport’s work. These methods calculate the total damage by considering the probability of the fluctuating stress related to different values of mean wind velocity (see Petrov (1998)). As pointed out in Repetto and Solari (2002) these methods are able to provide efficient results but are difficult to use in complex applications; moreover, the link between the stochastic characteristics of excitations and those of the structural response is easily determinable only when the structural model is linear (see Cluni et al. (2007)). In Repetto and Solari (2002) and Holmes (2002) a closed form formulations to assess the wind-induced fatigue damage in narrow band response hypothesis has been proposed. - Time domain-based methods calculate the total damage by applying deterministic methods, such as the rain-flow counting algorithm, to time series. Time series of turbulent flows can be obtained by performing Monte Carlo simulations or through wind tunnel test. This approach is easier to use but requires higher computational or experimental effort. Nevertheless, as pointed out in Repetto and Torrielli (2017), rain flow cycles counting of long time series is the approach that is most widely used in different fields and standard codes and is part of the framework of classical fatigue theory. As for the calculation of fatigue, some local approaches such as Strain Energy Density (SED) criterion (see Colussi et al. (2017); Lazzarin and Zambardi (2001)) have emerged which, coupled with the usual nominal stress method, are capable of conducting massive amounts of computations while guaranteeing robustness and affordable computational cost for not requiring an extremely fine mesh. 3. Literature review of wind-induced fatigue analysis of steel structures In literature, some analyses have been presented where an assessment of fatigue behavior of structures exposed to wind has been performed. A certain number of papers are here referred and described with the aim of identifying the key flow properties that were necessary for the studies. 3.1. High-rise, slender buildings Repetto and Solari extensively analyzed the fatigue behavior of slender steel structures in Repetto et al. (2014); Repetto and Solari (2002) and formulated a mathematical model in frequency domain in order to obtain the accumulated fatigue damage in closed form for slender vertical structures subjected to alongwind, crosswind and directional gust-excited vibrations. This is done by taking into account the probability distribution of in-site mean velocity and determining the histogram of the stress cycles by applying a probabilistic counting method of the cycles to an analytical solution of the dynamic response. Another approach used by the authors as a benchmark is based on a time-domain analysis based on the cycle counting of synthetic time series produced using Monte Carlo simulations. These approaches need a previous knowledge of the aerodynamic parameters of the structure. 3.2. Long span bridges In Cluni et al. (2007) an investigation of wind-induced cable fatigue has been performed. The fatigue damage was calculated in time domain. Wind tunnel experimental analyses were performed in order to evaluate the drag coefficient of the cable D C . The drag coefficient was then used to calculate the generic i-th component of the vector of nodal wind drag forces:

(16)

( ) 1

( ) ( ) C A U t U t   D a i i i

Di F t

2