Across-wind loads and effects of super-tall buildings and Structures

作者：GU Ming & QUAN Yong

国籍：US

出处：science china Technological Sciences

Abstract

Across-wind loads and effects have become increasingly important factors in the structural design of super-tall buildings and structures with increasing height. Across-wind loads and effects of tall buildings and structures are believed to be excited by inflow turbulence, wake, and inflow-structure interaction, which are very complicated. Although researchers have been focusing on the problem for over 30 years, the database of across-wind loads and effects and the computation methods of equivalent static wind loads have not yet been developed, most countries having no related rules in the load codes. Research results on the across-wind effects of tall buildings and structures mainly involve the determination of across-wind aerodynamic forces and across-wind aerodynamic damping, development of their databases, theoretical methods of equivalent static wind loads, and so on. In this paper we first review the current research on across-wind loads and effects of super-tall buildings and structures both at home and abroad. Then we present the results of our study. Finally, we illustrate a case study in which our research results are applied to a typical super-tall structure.

Introduction

With the development of science and technology, structures are becoming larger, longer, taller, and more sensitive to strong wind. Thus, wind engineering researchers are facing with more new challenges, even problems they are currently unaware of. For example, the construction of super tall buildings is now prevalent around the world. The Chicago Sears Tower with a height of 443 m has kept the record of the world’s tallest building for 26 years now. Dozens of super-tall buildings with heights of over 400 m are set to be constructed. Burj Dubai Tower with a height of 828 m has just been completed. In developed countries, there are even proposals to build “cities in the air” with thousands of meters of magnitude. With the increase in height and use of light and high-strength materials, wind-induced dynamic responses, especially across-wind dynamic responses of super-tall buildings and structures with low damping, will become more notable. Hence, strong wind load will become an important control factor in designing safe super-tall buildings and structures.

Davenport initially introduced stochastic concepts and methods into wind-resistant study on along-wind loads and effects of buildings and other structures. Afterward, researchers developed related theories and methods, and the main research results have already been reflected in the load codes of some countries for the design of buildings and structures. For modern super-tall buildings and structures, across- wind loads and effects may surpass along-wind ones. Although researchers have been focusing on the complex problem for over 30 years now, the widely accepted data-base of across-wind loads and computation methods of equivalent static wind loads have not been formed yet. Only a few countries have accordingly adopted the related con-tents and provisions in their codes.

Therefore, studying across-wind vibration and the equivalent static wind loads of super-tall buildings and structures is of great theoretical significance and practical value in the field of structural design of super-tall buildings and structures. The current paper thus reviews the research

situation of across-wind loads and effects of super-tall buildings and structures both at home and abroad. Then, the research results given by us are presented. Finally, a case study of across-wind loads and effects of a typical super-tall structure is illustrated.

Mechanism of across-wind loads and effects

Previous researches focused mainly on the mechanism of across-wind load. Kwok pointed out that across-wind excitation comes from wake, inflow turbulence, and wind-structure interaction effect, which could be recognized as aerodynamic damping. Solari attributed the across-wind load to across-wind turbulence and wake excitations, considering wake as the main excitation. Islam et al. and Kareem claimed that across-wind responses are induced by lateral uniform pressure fluctuation due to separation shear layer and wake fluctuation. Currently, the mechanism of across-wind load on tall buildings and structures has been recognized as inflow turbulence excitation, wake excitation, and aero elastic effect. Inflow turbulence and wake excitation are essentially the external aerodynamic force, which is collectively referred to in the present paper as aerodynamic force. Meanwhile, aero elastic effect can be treated as aerodynamic damping. Across-wind aero-dynamic force no longer conforms to quasi-steady assumption as the along-wind one; thus, the across-wind force spectra cannot be directly expressed as a function of inflow fluctuating wind velocity spectra. Wind tunnel test technique for unsteady wind pressures or forces is presently a main tool for studying across-wind aerodynamic forces. The wind tunnel experiment technique mainly involves the aero-elastic building model experiment technique, high frequency force balance technique, and rigid model experiment technique for multi-point pressure measurement. Using data of across-wind external aerodynamic force and across-wind aerodynamic damping, across-wind responses and the equivalent static wind load of buildings and structures can be computed for the structural design of super-tall buildings and structures.

Across-wind aerodynamic force

As stated above, the across-wind aerodynamic force can be obtained basically through the following channels: identifying across-wind aerodynamic force from across-wind responses of an aero elastic building model in a wind tunnel; obtaining across-wind aerodynamic force through spatial integration of wind pressure on rigid models; obtaining generalized aerodynamic force directly from measuring base bending moment using high frequency force balance technique.

Identification of across-wind aerodynamic force from dynamic responses of aero elastic building model.

This method employs across-wind dynamic responses of the aero elastic building model, combining the dynamic characteristics of the model to identify across-wind aerodynamic force. Melbourne and Cheung performed aero elastic model wind tunnel tests on a series of circular, square, hexagon, polygon with eight angles, square with reentrant angles and fillets, and tall or cylindrical structures with sections contracting along height. However, further studies showed that across-wind aerodynamic damping force and aerodynamic force mixed together make it difficult to extract aerodynamic damping force accurately. As such, the method has been seldom used.

Wind pressure integration method.

Researchers have recommended wind pressure integration to obtain more accurately the across-wind aerodynamic forces on tall buildings. Islam et al .  adopted this method to obtain across-wind aerodynamic forces on tall buildings and structures. Cheng et al. experimentally studied across-wind aerodynamic forces of typical buildings under different wind field conditions and derived empirical formulas for the power spectrum density of the across-wind aerodynamic force reflecting the effects of turbulent intensity and turbulent scale. Turbulent intensity was found to widen the bandwidth of PSD of the across-wind aerodynamic force and reduce the peak value. However, turbulent intensity was determined to have almost no effects on total energy. Thus, researchers have recognized the quantitative rules of variation of across-wind aerodynamic force with wind condition to some extent. Liang et al. examined across-wind aerodynamic forces on typical rectangular buildings in a boundary layer wind tunnel using this method, thus proposing empirical formulas for PSD of across-wind aerodynamic forces of tall rectangular buildings and an analytical model for across-wind dynamic responses. Ye and Zhang decomposed across-wind turbulence excitation and vortex shedding excitation in across-wind aerodynamic forces on typical super-tall buildings. The results showed that the across-wind turbulence contributed much less to across-wind aerodynamic force than the wake excitation. Based on a large number of results, we derived PSD formulas for the across-wind turbulence excitation and the wake excitation, and further derived a new formula for the across-wind aerodynamic force. The first- and higher-mode generalized across-wind aerodynamic forces can be calculated through the integration of pressure distribution on rigid building models, which is an important advantage of this method. However, given the need for a large number of pressure taps for very large-scale structures in this kind of method, synchronous pressure measurements are difficult to make. Moreover, for buildings and structures with complex configurations, accurate wind pressure distribution and aerodynamic force are difficult to obtain using this kind of method.

High frequency force balance technique.

Compared with the pressure measuring technique, high frequency force balance technique has its unique advantage for obtaining total aerodynamic forces. The test and data analysis procedures are both very simple; hence, this technique is commonly used for selection studies on architectural appearance in the initial design stage of super-tall buildings and structures. Currently, this technique is widely used for total wind loads acting on super-tall buildings and structures, and for dynamic response computation as well.  The high frequency force balance technique has been gradually developed since the 1970s. Cermak et al. were the first to use this technique for building model measurement. They initially pointed out that the balance-model system should have a higher inherent frequency than the concerned frequency of wind forces. The five-component balance developed by Tschanz and Davenport marked the maturity of balance facility.

Kareem conducted an experimental study on across-wind aerodynamic forces on tall buildings with various section shapes in urban and suburban wind co research showed that for the buildings with , uncertainties of wind and structural parameters have small effects on PSD of the across-wind aerodynamic force, and the correlation between the along-wind aerodynamic force and the across-wind aerodynamic force or the torsion moment is negligible, but there is a strong correlation between the across-wind aerodynamic force and the torsion moment. This conclusion is important for the development of three-dimensional refined wind load model. Particularly, Gu and Quan and Quan et al. made detailed studies on the effects of the side ratio of a rectangular building, cross-section shape of a building, aspect ratio of a building, and wind field condition on the PSD of the across-wind aerodynamic force of tall buildings using a five-component balance. In fact, based on a large number of wind tunnel test results, formulas for across-wind aerodynamic force coefficients of the typically tall buildings have been derived by us and other researchers, some of which are listed in Table 1. In addition, in Table 1, the formula derived by Gu and Quan has already been adopted in related design codes in China.

Across-wind aerodynamic damping

In 1978, Kareem performed an investigation on across-wind dynamic responses of tall buildings based on both of the aero elastic model technique and the wind pressure integration method. He found out that the across-wind dynamic responses calculated with the across-wind aerodynamic forces obtained from the wind pressure tests at a certain test wind velocity range were always smaller than those of the aero elastic model of the same building model. This important result made researchers realize the existence of across-wind negative aerodynamic damping.

Subsequently, researchers carried out numerous studies on the problem and developed effective methods for identifying aerodynamic damping. The first kind of method obtains aerodynamic damping by comparing the dynamic responses computed based on the aerodynamic forces from rigid building model tests and those from aero elastic model tests. The second one separates aerodynamic damping force from the total aerodynamic force measured from aero elastic building models or forced vibration building models. The third kind employs identification methods for extracting aerodynamic damping from random responses of aero elastic models. Moreover, researchers realized the effect law of factors, including structural shape, structural dynamic parameters, wind conditions, and so on, on aerodynamic damping, Isyumov et al. were the first researchers to propose a method for aerodynamic damping through comparing responses from a rigid building model test using HFFB technique with those of an aero elastic model of the same building. Cheng et al. adopted the method to study across-wind responses and aerodynamic damping of tall square buildings and proposed an aerodynamic damping formula.

Steckley initially developed a set of forced vibration devices for measuring total aerodynamic forces, including aerodynamic damping force and aerodynamic force. He measured the base bending moment of a tall building model, which was vibrated by a specially designed device. The aerodynamic force related to structure motion was separated from the total aerodynamic force, and then it was decomposed into aerodynamic stiff force and aerodynamic damping force to obtain aerodynamic damping. Vickery and Steckley proposed a negative aerodynamic damping model. Cooper et al.  attempted to measure wind pressure on a harmonically vibrating building model to obtain total aerodynamic force. Aerodynamic damping was then computed using a method similar to Steckley’s. The advantage of this kind of method is that the characteristics of real buildings do not have to be taken into consideration in wind tunnel tests, which makes this kind of method more convenient to use, especially in popularizing the test results. The main shortcoming of this kind of method is that it requires complicated devices, especially because a multi-component coupling device was not available until now.

Identifying aerodynamic damping based on the stochastic vibration responses of aero elastic building models can be performed using appropriate system identification techniques, which include frequency domain methods, time domain methods, and frequency-time domain methods. Among these methods, the random decrement method, one of the time domain methods, is broadly adopted to identify the aerodynamic damping of tall buildings and structures. Jeary introduced the random decrement technique to identify structural damping. Marukawa et al. employed the random decrement method to identify along-wind and across-wind aerodynamic dampings of tall buildings with rectangular sections. They analyzed the effects of building aspect ratio, side ratio, and structural damping on aerodynamic damping. Tamura et al. conducted a detailed study on the application of random decrement technique to identify the aerodynamic damping of super-tall buildings. Quan and Quan et al. adopted RDT to identify across-wind aerodynamic damping of the square-section tall buildings with different structural dampings in different wind fields and derived an empirical formula. These research results have been adopted into the related China Codes . Qin and Gu were the first researchers to introduce stochastic sub-space identification method into identification of aerodynamic parameters including aerodynamic stiffness and damping of long-span bridges, obtaining satisfying results. Compared with random decrement method, the stochastic sub-space identification method has more merits than RDT and MRDT and can overcome their main shortcomings i.e. weak noise-resistantce ability and need for large experimental data. Qin adopted this method to identify the aerodynamic damping of tall buildings.

Application to the codes

As stated above, although researchers have been focusing on across-wind loads on tall buildings for over 30 years now, the widely accepted database of across-wind loads and computation methods of equivalent static wind loads have not been developed yet. Moreover, only a few countries have adopted related contents and provisions in their codes.

Compared with the codes of other countries, the Architectural Association of Japan provides the best method for across-wind loads for structural design of tall buildings. Nevertheless, the formula for PSD of the across-wind force in the code can only be applied to tall buildings with aspect ratios of less than six, which seems difficult to meet the actual needs. In addition, the method takes across-wind inertia load of fundamental mode as across-wind equivalent static wind load including background and resonant components, making it seem questionable. Moreover, aerodynamic damping has not been considered in the method. In the present load code for the design of building structures (GB50009-2001) of China, only a simple method for calculating vortex-induced resonance of chimney-like tall structures with a circular section is provided, which is not applicable to the wind-resistant design for tall buildings and structures in general. In the design specification titled “Specification for Steel Structure Design of Tall Buildings” , our related research results have been adopted.

Concluding remarks

With the continuing increase in the height of buildings, across-wind loads and effects have become increasingly important factors for the structural design of super-tall buildings and structures. The current paper reviews researches on across-wind loads and effects of super-tall buildings and structures, including the mechanism of across-wind loads and effects, across-wind aerodynamic forces, across-wind aerodynamic damping, and applications in the code. Consequently, some of our research achievements involving across-wind forces on typical buildings, across-wind aerodynamic damping of typical buildings, and applications to the Chinese Codes are presented. Finally, a case study of a real typical tower, where strong across-wind loads and effects may be observed, is introduced. The recent trend in constructing higher buildings and structures implies that wind engineering researchers will be faced with more new challenges, even problems they are currently unaware of. Therefore, more efforts are necessary to resolve engineering design problems, as well as to further the development of wind engineering.