# Damping and Natural Period Evaluation of Tall RC Buildings Using Full-Scale Data in Korea
## 1 Introduction  
In recent years, the main usage of reinforced concrete (RC) structures in Korea has shifted from low-rise residential and commercial buildings to high-rise buildings. Because an increasing number of high-rise RC buildings are being built, especially in cities such as Busan and Incheon, which are periodically hit by typhoons, wind-induced motion and corresponding serviceability issues have attracted considerable attention. Natural period and damping ratio are most important factors for estimating the design wind load and wind-induced response in the design of tall buildings [1]. In particular, the natural period of a building is the most important variable from the viewpoint of calculating wind load. Because a detailed analysis model for this purpose is not available in the initial design stage, wind load can be approximated using an empirical formula [2]. However, the Korean Building Code (KBC 2009) does not specify an empirical formula to estimate the natural period for wind design as it does for seismic design [3]. Instead, KBC 2009 introduced a few empirical formulas from foreign codes in the commentary. Consequently, engineers have to choose the values of natural period and damping ratio somewhat arbitrarily based on experience. [PERSON] et al. [4], however, reported a considerable discrepancy between the values obtained using foreign codes and the directly measured natural periods and damping ratios of existing RC buildings taller than 150 m in Korea. This is because residential buildings with concrete shear wall systems are more popular in Korea than in foreign countries and because the heavier gravitational load due to theunique floor heating system called \"ondol,\" with an additional unreinforced concrete layer measuring 10-15 cm in thickness in residential buildings, warrants the use of larger columns or shear wall sizes than those used in foreign countries. Consequently, the damping ratio provided in foreign codes may not necessarily be directly applicable to the design of tall buildings in Korea. In this paper, the ambient vibrations of actual RC buildings in Korea are measured to construct a database of wind design parameters, such as natural period and damping ratio. For this purpose, the ambient vibration of 36 RC buildings with heights of 44.8-305 m is measured. In addition to the full-scale measurement results of 36 buildings, the data of 22 buildings presented in [5,6] are added to cover most of the RC buildings in Korea with heights less than 100 m. Thus, the data of 58 buildings were used in this study to evaluate the empirical formulae provided in various design codes and research papers. Furthermore, the design formulae of natural frequency and damping ratio for wind design are proposed based on the database. The heights of 58 buildings considered in this study ranged from 24.4 m to 305 m.  
Empirical Formulae for Computing Natural Period of Reinforced Concrete (RC) Buildings for Wind Design  
A formula to compute the natural period of a building for wind design is not provided in KBC 2009. Instead, the following approximate formula for estimating the natural period is provided for in the seismic design of RC moment frames:  
\[T=0.073H^{0.75} \tag{1}\]  
where \(T\) is the natural period, and \(H\) is the building height (m). ASCE 7-10 [7] presents two empirical formula based on the results of finite element analysis and wind tunnel tests of a building shorter than 91 m (300 ft). \[T=0.0670H^{0.9} \tag{2}\]  
\[T=0.043H \tag{3}\]  
Equation (2) is for RC moment frames, and Equation (3) is for RC buildings with structural systems other than the moment frame. Unlike the finite-element-analysis-based empirical formula in ASCE 7-10, empirical formulae based on measured data are more frequently proposed and used in the wind design of buildings. The first empirical formula based on measured data was proposed by [PERSON] [8]. He used the data of 185 buildings, of which 52 were RC buildings.