MS24.7 - Wind Induced Vibrations of Slender Structures

The wind induced vibration of flexible structures is an important topic in the field of wind engineering in terms of human comfort and safety, and of global instability of cable structures. In particular, cable structures used for roofs, for example, cable net and membrane tensile structures, are very sensitive to wind induced vibrations [1] because the axial force in a cable depends on its geometry. When the cable changes its geometry during the vibrations, it may either lose its tension or the cable tension may exceed the cable’s material strength. The wind structure interaction on flexible roofs is most frequently investigated through numerical analyses using forces time histories calculated by aerodynamic tests on rigid models. However, this approach fails to predict the effective dynamic deformation of the roof. This paper discusses results obtained from aeroelastic tests in a wind tunnel on flexible roofs. Accelerometric signals were acquired using very small and lightweight accelerometers (lighter than 1 g). The tested geometry was a saddle roof that recreates a cable net of a membrane hyperbolic paraboloid roof. The plan shape of the roof was square. The sum of the upward cables’ sag and downward cables’ sag was 1/10 of the roof span. The test model was constructed using a rigid steel structure for the supporting walls and very tiny steel ropes to simulate the cable net. In total, 39 × 39 ropes were used in the model. The membrane was recreated with silk fabric and linked to the net nodes. The wind induced accelerations were measured on 39 points located on the roof cable net nodes. Each cable was prestressed using a mechanical approach based on stayed bolts. Three different wind angles of attack were investigated and accelerations were measured under seven different inflow velocities. A significant flutter of the roof was observed under the highest velocity tested in the wind tunnel, even if collapses of either cables or the membrane were not observed. Signals were acquired with a sampling frequency of 1600 Hz for 1 minute, which corresponds to 3840 s in a real life scale (i.e. time scale it was equal to 0.0156). Signals were divided into 6 slots of 10 minutes (at the prototype scale) and the statistics of peaks were estimated and discussed through the cumulative distribution function plot. Quantiles of 79%, 93% and 95% of the wind induced acceleration were compared with the values provided in literature, codes and standards. The comparison showed that the values of accelerations provided in the literature are underestimated. In particular, electric and thermal installations suspended to the roof should be carefully designed taking into account the roof vibration. Codes and standards tend to neglect this aspect, even if, for sports arenas or meeting rooms, installations are large enough to pose a considerable risk in the event of a fall.

Thunderstorms and extra-tropical cyclones provide significantly different wind conditions: extra-tropical cyclones, commonly referred to as Atmospheric Boundary Layer (ABL) winds, provide stationary wind conditions over time intervals of 10 minutes-1 hour and a wind velocity profile increasing with the height; instead, thunderstorms are responsible for nonstationary wind conditions and are characterized by a nose-shaped velocity profile. Furthermore, the two phenomena are characterized by different extreme distributions and high return period thunderstorm wind speeds can be higher than those corresponding to extra-tropical cyclones. Despite these remarkable differences, a shared model for the estimate of the maximum response and wind loading provided by thunderstorms is, to date, not available. The authors proposed a formulation generalized to thunderstorms of the gust response factor from Davenport for Single-Degree-Of-Freedom systems [1]. The objective of the present paper is to extend the approach to slender vertical structures and compare the effects of thunderstorm outflows and extra-tropical cyclones in terms of maximum alongwind dynamic response. Since thunderstorms are usually considered more dangerous for mid-low structures while ABL winds are considered as dimensioning for higher structures [2], two case studies with different heights are chosen: a steel lighting pole with height H = 15.76 m and a reinforced concrete telecommunication tower with H = 98 m. Different reference wind velocities with 50 years return period are adopted for thunderstorm and ABL winds, based on the results of a statistical analysis carried out on wind speed data collected by an anemometer located in the port of Livorno [3]. A literature nose-shaped profile is adopted for thunderstorms considering four different heights of the nose tip. The wind speed associated with the ABL wind is modelled through a logarithmic vertical profile assuming five different values of the roughness length. The gust response factor associated with the ABL wind is derived through the Davenport formulation, while for thunderstorms the generalized gust response factor is adopted. The comparison is performed in terms of ratio of the maximum response to thunderstorms and ABL winds. Such ratio is governed by three main factors: the reference wind velocity, the vertical profile and the gust response factor. Overall, for the two structures analysed, thunderstorms mostly provide a greater response also for the higher structure, especially when the tip of the nose-shaped profile is close to its top. References [1] Roncallo, L., Solari, G., Muscolino, G., Tubino, F., 2022. Maximum dynamic response of linear elastic SDOF systems based on an evolutionary spectral model for thunderstorm outflows. Journal of Wind Engineering and Industrial Aerodynamics. 224, 104978. [2] Sengupta, A., Sarkar, P.P., 2008. Experimental measurement and numerical simulation of an impinging jet with application to thunderstorm microburst winds. Journal of Wind Engineering and Industrial Aerodynamics. 96, 345-365. [3] Zhang, S., Solari, G., Yang, Q., and Repetto, M. P., 2018. Extreme wind speed distribution in a mixed wind climate. Journal of Wind Engineering and Industrial Aerodynamics, 176, 239–253.

Full long-term analysis is the most accurate method to determine extreme buffeting responses in long-span bridges since it considers the variability of the wind turbulence and the variability in the short-term buffeting response which traditionally are neglected. Several authors have reported significantly higher responses using the long-term approach compared to the traditional approach. Hence, it is suggested to revisit the methods widely accepted in most of the design codes. Recently, the National Public Road Administration (NPRA), adopted this probabilistic approach by including the full long-term analysis in the latest version of the handbook for bridge design, N400. Nevertheless, a more elaborate regulation is required in the future to improve the guidelines. The principal weakness of the method lies in its relatively high computational demand. Methods have been proposed to increase the computational speed, but they are regularly based on inverse reliability methods which tend to give only approximate solutions. On the other hand, using surrogate modeling approaches based on machine learning algorithms offer a reasonable alternative to reduce the computational demand of the full long-term method. The approach is simple, a surrogate model of the short-term buffeting response is trained with some few but strategically selected wind conditions. Then, the full long-term analysis is executed using fast estimations from the surrogate model instead of making a time-consuming complete structural analysis. This paper contains an overview of the extreme buffeting response of the Sulafjord bridge, a 3200m long-span single suspension bridge located in western Norway. This paper examines a framework for the full long-term analysis with a surrogate model based on Gaussian Process Regression. This type of algorithm uses a Bayesian updating strategy that optimizes the amount of training simulations, thus enhancing the computational speed of the analysis. The results from the examined framework were compared with the exact solution from the full long-term analysis. The comparison showed that the proposed framework has a high degree of accuracy, with 2.1% error and yet, using just less than 1% of the original computational demand. The simplicity and accuracy of this framework offers an attractive pathway to set the tone for further steps of implementation in the industry and contribute significantly to the future regulation.