Giovanni Solari

Probabilistic 3-D turbulence modeling for gust buffeting of structures

Literature on turbulence modeling is rich in empirical, semi-empirical and theoretical spectral equations whose parameters assume deterministic values. Starting from a critical review of the state of the art, this paper proposes a unified model of atmospheric turbulence especially suited to determine the 3-D gust-excited response of structures. Unlike classical models, all parameters are assigned through first and second order statistical moments derived from a wide set of selected experimental measurements. A general discussion is also provided about model errors and other sources of randomness. Due to these properties the model proposed is suitable for carrying out reliability analyses which take into account the propagation of the uncertainties.

3-D gust effect factor for slender vertical structures

Original studies on gust factor buffeting dealt with the alongwind displacement of structures. Research on this topic carried out since the nineties followed two distinct lines: the first determines the maximum effects due to the alongwind response; the second extends the original method from the alongwind response to crosswind and torsional responses. This paper represents the junction point of these research lines with reference to cantilever slender vertical structures. It derives the most relevant effects associated with the three-dimensional (3-D) wind-excited response of this structural type and shows that a suitable definition of one non-dimensional quantity, referred to as the 3-D gust effect factor, provides such effects at any level through a wide set of experimental, numerical and analytical procedures. A new definition of a 3-D equivalent static force consistent with this method is also introduced and critically compared with previous analogous statements.

Dynamic alongwind fatigue of slender vertical structures

The wind-excited vibrations of structures induce fluctuating stresses around mean deformation states that lead to fatigue damage accumulation and can determine structural failure without exceeding design wind actions. This paper proposes a mathematical model aimed at deriving a histogram of the stress cycles, the accumulated damage and the fatigue life of slender vertical structures (e.g. towers, chimneys, poles and masts) in alongwind vibrations. The formulation, integrally in closed form, is based on a probabilistic counting cycle method inspired by narrow-band processes. An example illustrates the proposed procedure and shows, through the comparison with Monte Carlo simulations, the entity of the approximations involved by treating the response as narrow-banded instead of broad-banded.

Wind modes for structural dynamics: a continuous approach

Load on structural systems is often represented by a multi-dimensional and/or multi-variate random process. The cross-correlation often existing between loading components acting in different points of the structure introduces conceptual and computational difficulties in many practical problems. It is the case, for example, of the projection of the external load on the vibration modes in the modal analysis of linear systems or of the simulation of multi-correlated time series for a Monte Carlo-based analysis of non-linear structures. The use of the proper orthogonal decomposition (POD) introduces some formal simplifications in the solution of the aforementioned problems, but requires the evaluation of the eigenquantities of some statistical representations of the loading process. The knowledge of such quantities in analytic form yields computational advantages and enables important physical interpretations. In the present paper, an analytic expression of POD is developed for a class of processes, which includes models usually adopted to represent the atmospheric turbulence. Examples of linear analysis of a wind-excited slender structure and of simulation of turbulence fields are presented.

On the formulation of ASCE7-95 gust effect factor

Abstract Highlights of the formulation of the gust effect factor in recent revisions of the wind load provisions in ASCE7-95 are presented. The revised wind map is based on 50-year peak gust speeds in contrast with fastest mile speeds used in ANSI/ASCE7-93. The concepts of spatial and temporal averages are discussed, and the new gust effect factor (GEF) is introduced with its derivation detailed. Examples to illustrate the use of the new provisions in ASCE7-95 for flexible structures are provided.

Wind-excited response of structures with uncertain parameters

The wind-excited response of structures is classically evaluated by considering the model parameters as deterministic. Due to this assumption, the density function of the maximum response is so narrow and sharp as to make the expected maximum a suitable pseudo-deterministic representation of the maximum response. Based on Taylor series expansions retaining up to the first and second-order derivative terms, this paper provides closed form expressions of the first and second statistical moments of the maximum response taking the uncertainties of the parameters and the model error into account. It is shown that such uncertainties may spread and shift the density function of the maximum response to the point at which the classical value of the expected maximum is no longer representative of the structural behaviour.

Closed form prediction of 3-D wind-excited response of slender structures

Abstract This paper provides a concise, logical and operative scheme of a general procedure aimed at evaluating the alongwind, crosswind and torsional response of slender structures and structural elements. It also illustrates its application to the calculation of the 3-D wind-excited response of structures previously subjected to wind tunnel tests and full-scale measurements. The comparison between analytical and experimental results highlights the reliability of the procedure discussed herein.

Analytical estimation of the alongwind response of structures

Abstract The problem of the dynamic alongwind response of structures to forces induced by the atmospheric turbulence is studied in this work. Starting from the classical treatment of the problem, a general analytical formulation is developed with reference to three structural standard models called “point-like”, “vertical” and “horizontal”, respectively. The statement given to this paper stresses the advantages of this formulation in comparison with the traditional calculation procedures represented by the use of graphs and computer programs.

A turbulence model based on principal components

Literature on turbulence is very wide, providing several models for the power spectral density function of the single-point turbulence components, for the two-point coherence function of the same turbulence component and for the single-point coherence function of different turbulence components. On the other hand, no suitable and simple model seems to be available for representing the two-point coherence function of different turbulence components, in particular of the longitudinal and vertical turbulence components, which would be useful for modelling buffeting actions on bridges. The Proper Orthogonal Decomposition provides efficient tools to formulate a new model of the turbulence field based on principal components. Furthermore, it suggests physical principles and defines mathematical rules to establish an appropriate model of the two-point coherence function of the longitudinal and vertical components, completing the statistical model of turbulence. Embedded in a Monte Carlo framework, this new representation can be used to simulate multi-dimensional and multi-variate random turbulence fields.

Stochastic analysis of the linear equivalent response of bridge piers with aseismic devices

The dynamic response of bridge piers with aseismic devices to earthquake excitation is evaluated by the stochastic equivalent linearization technique. The seismic acceleration is schematized through a Gaussian stationary random process. The pier is considered linear elastic, the span is idealized as a rigid mass, the restoring force of the device is represented through a non-linear differential model. The study of the complex modes of the linearized system gives an interpretation of the mechanical behaviour, leads to a formally elementary solution and highlights some phenomena which are typical of the hysteretic systems, particularly of those marked by weak hardening. Even though the solution is limited to the stationary field, it brings out several noteworthy considerations about the effective non stationary behaviour of the structure.