International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 10 Issue: 07 | July 2023
p-ISSN: 2395-0072
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A Stochastic Approach to Determine Along-Wind Response of Tall Buildings Sitaram Vemuri1, Srimaruthi Jonnalagadda2 1
Structural Engineer, Assystem Stup; Honorary Professor, V R Siddhartha Engineering College, Vijayawada, AP, India ----------------------------------------------------------------------***---------------------------------------------------------------------------2
Abstract: Wind velocity is turbulent in nature and hence its variation with time is random. The interaction of the
turbulent wind with the building generates random vibrations in the building. When the frequency of the turbulent wind force comes in line with the natural frequency of the building, it produces resonant amplification of the building response that is undesirable for structural safety and dwellers comfort. This paper probes the application of theory of random vibration in determining the peak along wind response of a conventional tall building, rectangular in configuration. Velocity power spectral density function is a focal point in mathematical modeling of turbulent wind velocity. Different expressions for velocity power spectral density function were proposed by Simiu, Harris and Kaimal. They are used to derive corresponding displacement power spectral density functions. A peak in the displacement power spectral density function plot is observed at a frequency equal to the natural frequency of the building. The expected value of peak along wind response is calculated using principles of random vibration theory. Numeric computing software MATLAB is used for solving the mathematical equations involved in the analysis. All the three velocity power spectral density functions produced nearly equal peak displacement at the tip of the building wherein, Harris velocity power spectral density function has an edge over the others. A brief comparison of all the velocity power spectral density functions is also presented.
Keywords: Wind analysis, Power Spectral Density function, Random vibration, Stochastic process, Tall buildings, Along wind response
1. Introduction Tall buildings are vulnerable to heavy sway caused by the wind. Basically, wind flow is designated with its speed or velocity. The flow of wind in a terrain can be described using the boundary layer theory, where the ground acts as a viscous boundary layer. The wind flow is naturally turbulent. But, there is a mean wind speed, be it hourly mean or 3-sec averaged, that carries the turbulent wind. Thus, one can say that, the wind speed is fluctuating randomly about its mean wind speed. Fig. 1 shows a typical wind velocity time history. Thus one can find a scope in applying the random vibration theory to analyze flow properties of wind. As per that theory, any periodic function having a definite periodicity can be written as summation of sines and cosines of different frequencies which is well known as fourier expansion of periodic functions. It even can be extended to non periodic functions. A random process can explicitly be defined as a periodic function with infinite periodicity. A random process is said to be stationary if its statistical properties (mean, standard deviation, etc) doesn’t change with time [1]. Wind velocity time history is assumed to be a stationary random process about the mean speed. Velocity power spectral density function (PSD) has been a pivot point in mathematical modeling of wind velocity. As mentioned earlier, in a typical wind velocity time history, the velocity at any point of time can be decomposed as mean wind velocity (be it hourly mean, 3-sec averaged, etc) summed up with fluctuating component of velocity about the mean value. Now, using fourier expansion, this fluctuating component, at any instant of time can be written as the summation of eddies of different frequencies (circular frequencies). Thus each eddy has a definite wave number. The velocity of eddy per unit wave number is called as velocity power spectral density function. Mathematically it is the spectrum of power of fourier coefficients of velocity fluctuations for different frequencies. Various expressions for velocity power spectral density function were proposed by many researchers, of which expressions proposed by Simiu, Harris and Kaimal are
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