# Dynamic Response of Slender Vertical Structures Subjected to Thunderstorm Outflows
## 1 Introduction
[21] adopted the EPSD to generalize the wind loading chain approach from stationary winds to thunderstorms. Based on such models, the gust factor technique from [PERSON] [22] was generalized to nonstationary winds by [PERSON] and [PERSON] [23], who introduced suitable equivalent parameters, and subsequently, [PERSON] et al. [13] removed the hypothesis of long-pulse duration. More recently, closed-form solutions to simplify its application from a design perspective were proposed by [PERSON] and [PERSON] [24] under the hypothesis of long-pulse duration. Subsequently, [PERSON] and [PERSON] [25] proposed a new closed-form solution that accounts for the transient dynamic effects of both the nonstationary response and the presence of a background wind. Although this approach is surely convenient and user-friendly, it has the shortcoming of being slightly conservative when the system becomes flexible and low-damped. Moreover, the closed-form solution proposed by [PERSON] and [PERSON] [25], which accounts for the thunderstorm wind speed parameters and the transient effects in the dynamic response, was developed for SDOF systems, and its reliability when applied to MDOF systems needs to be assessed. In this framework, this study aims to address these shortcomings by pursuing two main objectives: the extension of the Thunderstorm Gust Response Factor (TGRF) technique to the analysis of vertical structures, assessing its reliability, and the comparison between the maximum dynamic response due to thunderstorms and synoptic events. The extension of the TGRF technique to the case of slender vertical structures is pursued by accounting for the variation in the mean wind speed with the height, and for the partial correlation of the turbulent fluctuations along the structure. A suitable model from the literature is introduced to describe the vertical profile of the mean wind speed, while the partial correlation is accounted for through the coherence function from stationary winds, which is suitably adapted to the thunderstorm case as proposed by [PERSON] [18]. Subsequently, the reliability of the TGRF is assessed by comparing the related maximum response with the one estimated via TDA based on a large number of full-scale thunderstorm records, and the TRS technique. Finally, the maximum dynamic response induced via thunderstorms is compared with the one induced by stationary synoptic winds. The comparison between thunderstorm- and synoptic-induced dynamic responses is based on the definition of three factors depending on the reference: wind velocity, the mean wind vertical profile, and the gust response factor. Two structures of different heights and dynamical properties are considered as case studies: a steel lighting pole, representative of a low-rise structure, and a reinforced concrete telecommunications tower, representative of a taller structure. The paper is organized as follows: Section 2 outlines the analytical formulation, starting with the extension of the EPSD-based approach to continuous systems and deriving the dynamic response of a slender vertical structure along with its maximum value through the TGRF technique. Section 3 illustrates the numerical applications, including the structure case studies chosen, the wind speed data utilized, the modeling of the wind loading, and the comparison between the estimate of the maximum dynamic response using the TGRF, TDA, and TRS techniques. Section 4 outlines the comparison between the dynamic response induced by synoptic winds and thunderstorm outflows, estimated following a design-based approach and by investigating the role of different assumptions for the turbulence intensity profile. Finally, Section 5 derives the conclusions and prospects of this research. Appendix A reports the models of the vertical profiles of the wind speed and turbulence intensity, and the model for the integral length scale adopted in this study.