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Alongwind actions on structures may produce a great number of stress cycles and lead to significant damage accumulation. A critical analysis of the pertinent methods proposed in the literature provides evidence of the necessity of improving the level of approximation, taking into account the bandwidth spectral properties of the stress processes. This paper pursues this aim by establishing an advanced broadband formulation. Applying the cycle counting method based on the narrow-band assumption, two discrete cycles histogram expressions are first suggested, which lead to an tipper and lower bound of the fatigue damage. As the gap between the two bounds may be very large, a more refined counting method is formulated, based on a bimodal representation of the alongwind induced stress power spectral density functions; the low- and high-frequency spectral contents are associated, respectively, with the quasistatic and the resonant parts of the response. Some examples highlight the properties of the proposed procedure and show the good agreement between the bimodal approach and the numerical results. DOI: 10.1061/(ASCE)0733-9445(2006) 132:6(899) CE Database subject headings: Fatigue life: Gaussian process; Stress; Damage.

The modeling and simulation of the wind field along structures is a fundamental step in tile analysis of their wind-excited response. The proper orthogonal decomposition (POD) provides efficient tools to formulate a model of the turbulence field based on principal components. This paper proposes a representation of turbulence based on a double application of the proper orthogonal decomposition. Considering a linear domain anti generalizing an analogous previous solution concerning the classical components, closed form expressions for the eigenvalues and eigenfunctions of the principal turbulence field are obtained. Based on this representation, a very efficient simulation scheme for the three correlated turbulence components along a linear domain is introduced. DOI: 10.1061/(ASCE)0733-9399(2005)131:12(1302) CE Database subject headings: Turbulence; Wind forces; Models; Simulation.

The wind-excited vibrations of structures induce fluctuating stresses that lead to fatigue damage accumulation and may determine structural failure without exceeding ultimate strength. This paper proposes a mathematical model aimed at deriving the histogram of the stress cycles, the accumulated damage, and the fatigue life of slender vertical structures exposed to simultaneous alongwind and crosswind vibrations. Wind climate is modeled by the joint density function of the mean wind velocity and direction. Wind-induced actions consist of aerodynamic forces on the stationary structure and of aeroelastic forces due to the structural motion. Aerodynamic actions on the stationary structure are caused by the turbulence of the oncoming flow, dealt with through quasisteady theory, and by the vortex wake, considered as independent from turbulence. Aeroelastic forces are aimed at reproducing the lock-in phenomenon. The static and the quasistatic parts of the structural response are evaluated by the influence function technique, taking all modes of vibrations into consideration. The resonant part of the response is related to the fundamental alongwind and crosswind modes only. The probabilistic accumulation of damage due to aerodynamic actions on stationary structures is estimated by a counting cycle method inspired by narrow band processes. The damage in lock-in conditions is superimposed by counting stress cycles deterministically. The examples illustrate the application and the effectiveness of the proposed procedure, focusing attention on the role of upper modes and wind directionality. CE Database subject headings: Buffeting; Crosswind; Wind loads; Fatigue life; Vortex shedding; Wind direction.

The present study is the logical successor to a preceding paper, in which a procedure was developed for treating the peak wind velocity and the equivalent pressure on rigid bodies in a unified way. Based upon this formulation the present paper sets out a closed-form solution (CFS2) of the dynamic alongwind response of structures that substantially generalizes a previous solution (CFS1) given by the author. The method introduced makes the gust-buffeting problem formally consistent by defining an equivalent static pressure on flexible structures from which the equivalent pressure on rigid structures can be derived as a limiting solution. Furthermore, it leaves the user free of calculating the dynamic alongwind response associated with any model of the oncoming wind and with any structural modal shape; under this point of view, CFS1 can be regarded as a particular case of CFS2.

Although the peak wind velocity, the equivalent pressure on rigid bodies, and the dynamic alongwind response of flexible structures are component parts of the gust buffeting problem, different procedures have been developed in the technical literature with reference to each of these subjects. This fact gives rise to conflicting solutions and noticeable inconsistencies of results, especially when these procedures are applied to boundary situations. On the basis of this consideration, this paper and a companion paper propose a revised and generalized formulation of the wind buffeting problem and a unified definition of gust factor. The present paper analyzes the themes of the peak wind velocity and of the equivalent pressure solving both problems in closed form. This goal is pursued by introducing a new general expression of the power spectrum of the alongwind turbulence and by applying the equivalent wind spectrum technique. In the context of this formulation, several well-known specific procedures can be conceptually regarded as particular cases of this more general treatment.

Studies carried out on gust buffeting and aerodynamic admittance show that mode shape represents a sort of watershed. If the mode does not change sign along the structure axis, the problem admits a robust conceptual interpretation based on energy cascade and a simple closed-form solution. If, instead, the mode changes sign, the solution calls for numerical tools, and its physical interpretation definitely is unclear. The companion paper investigated this issue within the novel framework of the enhanced equivalent spectrum technique and derived a closed-form solution of the aerodynamic admittance that can be applied to any mode using quasi-steady theory. This solution is precise and simple for modes with a few changes of sign, but it becomes laborious with increasing mode shape complexity; in addition, it provides a partial conceptual interpretation. Both these limitations were overcome in this paper, in which the application of proper orthogonal decomposition led to a full conceptual interpretation of aerodynamic admittance and to a simple and general closed-form solution. Analyses were limited here to single modes; multiple arbitrary modes are left for future research, as is the generalization of these concepts to arbitrary influence functions. [ABSTRACT FROM AUTHOR]

The loading and response of structures due to gust buffeting is a dominant topic of wind engineering. One of its crucial aspects is the shape of vibration modes. Although numeric solutions are available for any mode, conceptual interpretations and closed-form solutions mainly are limited to the case in which the sign of the mode does not change along the structural axis. For modes that change sign, it is difficult, if not impossible, to recognize the physical role of the parameters that govern the problem and judge analysis results in qualitative form. This paper addressed this issue in the framework of quasi-steady theory by clarifying the relationship linking aerodynamic admittance with mode shape, showed that any mode may be brought back to a piecewise ensemble of regular modes with constant sign, and used this concept to obtain a closed-form expression for any aerodynamic admittance. This solution is simple for modes with few changes of sign, but becomes laborious as mode complexity increases. In addition, it provides a partial conceptual interpretation. Both of these limits were overcome in the companion paper, in which the use of proper orthogonal decomposition led to a full conceptual interpretation of aerodynamic admittance and a simple and general closed-form solution. [ABSTRACT FROM AUTHOR]

Modal transformation techniques are usually adopted in structural dynamics with the aim of decoupling the equations of motion. They are based on the search for an abstract space in which the solution of the problem results simplified. Analogous transformation techniques have recently been developed with the aim of defining a space where a multivariate stochastic process is expressed by a linear combination of one-variate uncorrelated processes. This paper proposes a method, called double modal transformation, by which the dynamic analysis of a linear structure is carried out through the simultaneous transformation of the equations of motion and the loading process. By adopting this technique, the structural response is obtained through a double series expansion in which structural and loading modal contributions are superimposed. Its effectiveness and application are discussed with reference to two classic wind engineering problems--the alongwind response and the vortex-induced crosswind response of slender structures--which provide a wide panorama of the most relevant properties of this procedure.

The analysis of wind actions and effects on structures involves the knowledge of the parent population and extreme value distributions of the mean wind velocity. In spite of an impressive amount of measurements, refined probabilistic models and detailed applications to the study of specific sites, there is an equally disheartening lack of available probabilistic information at the territorial scale, and, therefore, of tools effectively applicable in the engineering and codification sectors. Almost all of the international standards and codes report sufficiently reliable maps of the mean wind velocity with 50-year return periods. On the other hand, there are still few regulations that provide the distribution of the yearly maximum value of the mean wind velocity or such value as a function of the return period. Furthermore, no regulations provide the distribution of the parent population of the mean wind velocity that may be very important for serviceability and fatigue analyses. This paper introduces a joint representation of the parent population and extreme value distributions of the mean wind velocity of synoptic extratropical cyclones; starting from this model, simple but reliable expressions are derived, directly applicable in the engineering and codification sectors, aimed at bridging the gap described. The obtained expressions are critically examined, pointing out their advantages but also some apparent critical issues. A preliminary application of these expressions is carried out with reference to the Italian territory. [ABSTRACT FROM AUTHOR]

Wind-induced fatigue is a crucial topic in the design of wind-sensitive structures. Despite this, methods proposed in literature are mainly addressed to research, or they are too simplified for engineering applications. Thus, suitable engineering and standards procedures are almost totally lacking, which is a major shortcoming in structural and wind engineering. Starting from a closed-form solution (CFS) recently proposed by the authors, this paper develops a novel engineering approach to evaluate the alongwind-induced fatigue of structures and structural elements. This approach is based on a hierarchy of hypotheses that lead to a progressive simplification of the basic formulation. Two classes of formulas, referred to as Levels I and II CFSs, are obtained and critically discussed with special concern for input parameters. Level I CFS implies three further simplifications joined together by the common aim of providing refined approximations of the reference target solution. Level II CFS implies three different simplifications joined together by the common aim of providing easy solutions on the safe side. This set of CFSs is framed within a general procedure that any country, society, or engineer can easily personalize to a situation and requirement, ranging from numerical tools to manual engineering calculations and code provisions. [ABSTRACT FROM AUTHOR]