504 International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 504-507

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Appropriate Design Wind Speeds for Structures

B. Dean Kumar Associate Professor, Department of Civil Engineering, JNTUH, CE Kukatpally, Hyderabad,500085, deankumar@yahoo.com B. L. P. Swami Professor, Department of Civil Engineering, Vasavi College of Engineering, Ibrahimbagh, Hyderabad, 500032, blpswami@yahoo.com Y. Balakoti Reddy Trainee Engineer, GVK Power and Infrastructure Pvt. Ltd, Hyderabad, koticivil@gmail.com

ABSTRACT: The code IS 875 (Part 3) 1987 deals with the wind effects on the structures. The code gives the basic wind speeds for the country. The basic wind speed is arrived by considering 3 seconds gust at a height of 10m. For arriving at these values wind records over a period of time are observed and a statistical analysis is done to arrive at the basic wind speed. The basis of the analysis is not discussed in the code and the wind data is also old. In this paper an attempt has been made to point out the deficiencies in the wind map of the country. For this purpose wind speed records for some stations in south India have been collected. Various distribution methods are used to arrive at the appropriate basic wind speeds. Further the coastal areas of the country are subjected to high winds due to short duration effects like cyclones etc. The study includes the speeds produced due to these extraordinary winds. Based upon this study a comparison is made with the basic wind speed given in the existing code and suitable conclusions are drawn. KEY WORDS: Basic wind speed, wind records, gust, extraordinary winds, distribution method

INTRODUCTION: Wind engineering analyses the effect of wind in the natural and built environment and the damage due to the wind. For a structural Engineer the interest is in strong winds which may cause discomfort. With the structures becoming tall and slender the effect of wind on these structures is becoming critical. The extreme wind estimates is used to arrive at design load which the structure must withstand during its lifetime. The distribution of wind speeds is also important in determining serviceability of buildings. Fisher and Tippet (3) developed the general theory for asymptotic extreme value distribution. These distributions are well known as Type I, Type II and Type III. Gumbel (4) used Type I distribution for predicting the extreme floods in United States. Thom (10, 11) preferred Type II distribution for the prediction of extreme wind speeds in the United States. Davenport (2) was the first one to apply the concepts of Probability and Statistics for determining design wind speeds.

STUDY OF WIND IN INDIA: In India the study of extreme winds is done to a very limited extent. Ayyar and Goyal (1) used Type I distribution for analysis. Jain (6) used Type II distribution for analyzing the data of important stations. Swami et al (8) have studied the metrological data the various stations in the country. They have arrived at the extreme mean hourly winds in India. Swami et al (9) have done a critical review of the methods for correcting the sampling errors in the extreme wind speeds. Lakshmanan et al (7) have studied the wind speed data available in 70 meteorological stations for obtaining basic wind speed. The authors concluded that there is need for upgrading the certain regions of the country to higher wind zones.

DESIGN WIND SPEEDS IN INDIA: IS Code (5) is the Indian standard that gives wind forces and their effects both static and dynamic. This code should be taken into account when designing buildings, structures and components.

DETAILS OF THE PRESENT STUDY: In the present study Type I, Type II distribution has been used for statistical analysis of extreme wind speeds for 8 stations of South India. Also correlation between Type I and Type II given by Simiu and Filliben is used for analysis. The data for which has been collected from the meteorological department. The wind speeds have been computed over chosen return periods. The possibility of errors due to poor quality of data and inadequate choice of the probabilistic model is taken care by correcting the predicted extreme wind speeds for the sampling errors mainly with the appropriately associated confidence levels.

STATISTICAL ANALYSIS BY TYPE I DISTRIBUTION: The probability function of the extreme wind speed variable ‘v’ is expressed as

( ≤V) (1) The solution of the above equation yields the expression in the form of a reduced variate

(2) Where ‘α’ and ‘U’ are scale and location parameters respectively. Solution by Graphical Method: The scale and location parameters are calculated by using Eq. (2). The extreme wind speed data set is arranged in ascending order by assigning a rank ‘m’ to each sample. If the total sample size is ‘n’ then the probability of nonoccurrence of a particular wind speed of rank ‘m’ is

(3) Knowing the relative probability of each wind speed as given by Eq. (3), the reduced variate ‘Y’ is calculated by using Eq. (2). By taking the wind speed variable on the X-axis and the reduced variate on the Y-axis, a straight line may be fitted. The slope of the Straight line fitted is equal to ‘α’ and the intercept on the Y-axis is equal to ‘–αU’. From which ‘U’ is calculated. The scale and location parameters for the Hyderabad and Vishakhapatnam stations are tabulated as shown in table 1.

505 Appropriate Design Wind Speeds for Structures

International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 504-507

TABLE 1: SCALE AND LOCATION PARAMETERS BY GRAPHICAL METHOD

Station Name α U Hyderabad 0.075 72.0 Visakhapatnam 0.0667 93.5

Solution by Analytical Method: From statistical considerations, the mean and standard deviation of the wind speed variable are calculated to give analytical expressions for the Type I parameter. To calculate the scale and location parameter the following equations are used.

(4)

(5)

Where E(X) and are the mean and the standard deviation of the sample data and 0.5772 is the Euler’s Constant. Using the Eq. (4) and Eq. (5) the scale and locations parameters are calculated for Hyderabad and Vishakhapatnam stations as shown in table 2.

TABLE 2: SCALE AND LOCATION PARAMETERS BY ANALYTICAL METHOD

Return Period Analysis: The probability of nonoccurrence in a period of ‘R’ years is

(6) Using the above equation along with Eq. (1) and then taking logarithms of the equations we get the following equation

(7) Using the Eq. (7) the extreme wind speeds for different chosen return periods are obtained using the scale and location parameters obtained from both the graphical and analytical methods.

STATISTICAL ANALYSIS BY TYPE II DISTRIBUTION: To describe the cumulative probability distribution, Thom used the expression,

(8) Where, is the scale parameter and is the shape parameter. Taking logarithm on both the sides of the Eq. (8) and comparing with Eq. (2) we get the following equations

(9) (10)

Using the Eq. (9) and (10) and following the same procedure as in the case of graphical method we arrive at the scale and shape parameters for Hyderabad and Vishakhapatnam, stations as shown in table 3 below.

TABLE 3: SCALE AND LOCATION PARAMETERS BY THOM’S METHOD

Station Name β2 γ Hyderabad 71.81 6.41 Visakhapatnam 92.11 6.897

Return Period Analysis: Using Thom’s probability distribution given by Eq. (8) and compare with Eq. (6). Taking logarithms on both sides we get the following expression for extreme wind speeds.

(11) Where, R is the years and VR is extreme wind speed in kmph. Using the Eq. (11) the extreme wind speeds for any chosen return periods can be calculated. The extreme wind speeds for Hyderabad and Vishakhapatnam obtained from Thom’s method are tabulated in table 4.

TABLE 4: EXTREME WIND SPEEDS FOR DIFFERENT RETURN PERIOD’S FROM THOM’S METHOD

Station Extreme wind speed in kmph for Different Return Periods 25 Years 50 Years 100 Years

Hyderabad 118.65 132.19 147.29Visakhapatnam 146.89 162.43 179.60

CORRELATION BETWEEN TYPE I AND TYPE II: Simiu and Filliben used the following expression for obtaining the correlation between Type I and Type II.

(12) Where ‘ ’and ‘U’ are scale and location parameters. ‘ ’ which defines the upper tail of the distribution is termed as the tail length parameter. The probability plot correlation coefficient is given by

(13)

Where (14)

(15) n is the sample size and D is the Probability Distribution tested. In terms of the ‘Xi’and ‘Mi(D)’, the estimated location and scale values are obtained by the following equations

(16)

(17) The predicted wind speed VN for various intervals N is given by

(18)

Where ‘γopt’ is the optimal value of ‘γ’ and GXγopt (p) is the percent point function of the best fitting extreme value distribution. Using Eq. (13), Eq. (16) and Eq. (17) probability plot correlation coefficient, scale and location parameters are obtained for tail length parameter. Return Period Analysis: Using the Simiu and Filliben expression given by Eq. (12) and taking logarithms on both sides of the above equation yields the following expressions for extreme wind speeds.

(19) Using the Eq. (19) we obtain the extreme wind speeds for different return periods. The table 7 below gives the extreme wind speeds for different return periods for Hyderabad and Vishakhapatnam stations.

Station Name Α U Hyderabad 0.0857 72.42 Visakhapatnam 0.0745 92.76

506 B. Dean Kumar, B. L. P. Swami, Y. Balakoti Reddy

International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 504-507

TABLE 5: EXTREME WIND SPEEDS BY THOM’S METHOD

PERCENTAGE RISK AND CONFIDENCE LEVELS IN THE PREDICTED WIND SPEEDS: To arrive at the basic wind speeds for structural design certain corrections are required to be applied to the calculated extreme wind speeds and the resulting speeds are thereby modified by specifying suitable confidence intervals. There are two methods for calculating the confidence interval for different confidence levels. In terms of the standard deviation (σ) of a percent point function such as wind speed ‘v’ for a chosen probability P(v) of the annual series of extreme wind speeds, the 68%,95% and 99% confidence levels correspond to σ,2σ and 3σ respectively. Method of Moments: The deviation from the predicted value of extreme wind speed in the method of moments is expressed as

(20)

Where, R is the return period in years, n is the sample Size, σX is the Sample Standard deviation, YR is the variate in terms of the return period and is given by the following expression YR= (21) Using the Eq. (21) the variate in terms of the return period YR is calculated. The standard deviation σX for the sample is obtained from the analytical method. Substituting the values , σX and n into the Eq. (20), the respective confidence intervals for the return periods for the 68%, 95% and 99% confidence levels are obtained. Table 6 gives the confidence intervals for different return periods.

TABLE 6: CONFIDENCE INTERVALS AS PER METHOD OF MOMENTS

Return Period 50 Years

Confidence levels

68% 95% 99%

Hyderabad 6.27 12.55 18.82 Vishakhapatnam 9.82 19.64 29.46

W.M.O Method: As per the W.M.O. technical note, 1974, the confidence interval is expressed as,

(22)

Where (23)

and are the mean and standard deviation of the reduced variate y and these are obtained directly from the sample ranks in Type I distribution. This method is applied to both the graphical and analytical methods of Type I distribution. Using the Eq. (22) and Eq. (23) the

confidence intervals for different confidence levels are obtained.

DESIGN WIND SPEEDS COMPUTED FOR TYPICAL STATIONS: For normal buildings and structures a 50 year return period is chosen allowing a risk of about 63%. In the absence of proper codal provisions in respect of design wind speeds, the above procedure based on the data analysed assumes special importance. Applying the 99% confidence intervals obtained from both the method of moments and W.M.O methods to the wind speeds calculated from graphical, analytical, Thom’s and Simiu and Filliben methods the design wind speeds are obtained. The table 7 below shows the design wind speeds obtained as detailed above from the above four methods.

TABLE 7: DESIGN WIND SPEEDS OBTAINED FROM DIFFERENT METHODS

Methods Design Wind Speeds in kmph Hyderabad Vishakhapatnam

Graphical 41.00 52.00 Analytical 38.00 49.00 Thom’s 43.00 54.00 Simu and Filliben

42.00 51.00

DESIGN WIND SPEEDS AND COMPARISON WITH CODAL VALUES: The wind speeds obtained from the above methods are compared with the basic wind speed given by the code. The wind speeds obtained from Type I distribution are the best suitable for interior parts of the country. The Type II best defines the coastal parts of the country. But the correlation between Type I and Type II given by Simiu and Filliben can be considered to be rational in defining for the entire country. Table 8 gives the comparison of wind speeds obtained from the statistical analysis and those given by the IS code.

TABLE 8: COMPARISON OF BASIC WIND SPEEDS Station Obtained Basic

Wind speed in m/sec

Basic Wind Speed as per IS Code in m/sec

Hyderabad 42 44 Visakhapatnam 51 50

CONCLUSIONS: • Type II distribution is suitable for extraordinary

winds like cyclones, hurricanes, typhoons etc. • In India the code used Type I distribution for arriving

at the basic wind speeds. But the Indian subcontinent is having variable wind climate. Hence no single distribution is suitable for India conditions.

• The wind speeds obtained are corrected for sampling errors using confidence intervals, but the code has not mentioned about these corrections.

• The basic wind speeds obtained are varying with the codal values. The wind speeds for coastal areas like Vishakhapatnam are more than the codal values as the extraordinary winds are not properly represented by Type I.

Station Extreme wind speed in kmph for Different Return Periods 25 Years 50 Years 100 Years

Hyderabad 118.57 127.85 136.79 Visakhapatnam 139.08 149.44 159.42

507 Appropriate Design Wind Speeds for Structures

International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 504-507

ACKNOWLEDGEMENTS: The authors are thankful to the JNTUH authorities for providing the facilities for bringing out this paper.

REFERENCES:

[1] Ayyar Harihara P.S, and Goyal.S.C., “Extreme Wind Speeds for India”, Indian Journal of Meteorology and Geophysics, 1972.

[2] Davenport. A. G, “The Buffeting of Structures by Gusts”, Proceedings of Symposium on Wind Effects on Buildings and Structures, NPL, Teddington, U.K, 1963.

[3] Fisher R.A and Tippet. L.H.C “Limiting forms of the frequency distribution of the largest or smallest member of a sample”, proc. of the Cambridge philosophical society, 1989, pp 180-190.

[4] Gumbel.E.J, “Statistics theory of extreme values and some practical applications”, Applied math series, vol.33, National Bureau of standards, Washington (DC), 1954.

[5] IS: 875 (Part 3)-1987, “Code of Practice for Design Loads (Other Than Earthquake) for Buildings and Structures”, Part 3 Wind Loads, Second Revision, Bureau of Indian Standards, NewDelhi, 1989.

[6] Jain. P.K., “Maximum Wind Pressure over India”, Indian Journal of Met. Geophysics, Vol.2, 1971,pp.571-574.

[7] Lakshmanan.N, Gomathinayagam.S, Harikrishna.P, Abraham.A and Chitra Ganapathi.S, “Basic Wind Speed Map of India with long term Hourly Wind Data”, Review Article, Current Science, Vol.96 No.7, April 2009.pp.911-922

[8] Swami. B.L.P, Seetaramulu, Kaveti, Chaudhry. K.K., “Study of Extreme Wind Speeds in India based on Gumbel’s Distribution”, Proceedings of the National Seminar on Tall Reinforced Concrete Chimneys, April 1985, New Delhi

[9] Swami. B.L.P, Seetaramulu, Kaveti, Chaudhry.

K.K., “A Critical Review of the Methods for Correcting the Sampling Errors in the Extreme Winid Speeds”, Journal of Structural Engineering, SERC, Madras, V.12, No.4, January 1986,pp.143-148

[10] Thom. H.C.S, “Towards a universal climatologically Extreme wind distribution”’ proceedings of the International Research Seminar o wind effects on Buildings and structures, vol.I, Ottawa, Canada, sept.11-14, (1967).

[11] Thom. H.C.S, “New Distributions of Extreme wind speeds in the united states”, Jl.struct.Div. ASCE, vol.No.ST7 paper 6038, pp 1787-1801 (1968).