The flow of wind is complex because many flow situations arise from the interaction of wind with structures. However, in wind engineering, simplifications are made to arrive at design wind loads by distinguishing the following characteristics:

• Variation of wind velocity with height.

• Wind turbulence.

• Statistical probability.

• Vortex shedding phenomenon.

• Dynamic nature of wind-structure interaction.

The viscosity of air reduces its velocity adjacent to the earth's surface to almost zero, as shown in Fig. 1.1. A retarding effect occurs in the wind layers near the ground, and these inner layers in turn successively slow the outer layers. The slowing down is reduced at each layer as the height increases, and eventually becomes negligibly small. The height at which velocity ceases to increase is called the gradient height, and the corresponding velocity, the gradient velocity. This characteristic of variation of wind velocity with height is a well-understood phenomenon, as evidenced by higher design pressures specified at higher elevations in most building codes.

At heights of approximately 1200 ft (366 m) aboveground, the wind speed is virtually unaffected by surface friction, and its movement is solely dependent on prevailing seasonal and local wind effects. The height through which the wind speed is affected by topography is called the atmospheric boundary layer. The wind speed profile within this layer is given by

where

Vz = mean wind speed at height Z aboveground

Vg = gradient wind speed assumed constant above the boundary layer Z = height aboveground zg = nominal height of boundary layer, which depends on the exposure (Values for

Zg are given in Fig. 1.1.) a = power law coefficient

With known values of mean wind speed at gradient height and exponent a, wind speeds at height Z are calculated by using Eq. (1.1). The exponent 1/a and the depth of boundary layer Zg vary with terrain roughness and the averaging time used in calculating wind speed. a ranges from a low of 0.087 for open country of 0.20 for built-up urban areas, signifying that wind speed reaches its maximum value over a greater height in an urban terrain than in the open country.

Motion of wind is turbulent. A concise mathematical definition of turbulence is difficult to give, except to state that it occurs in wind flow because air has a very low viscosity—about one-sixteenth that of water. Any movement of air at speeds greater than 2 to 3 mph (0.9 to 1.3 m/s) is turbulent, causing particles of air to move randomly in all directions. This is in contrast to the laminar flow of particles of heavy fluids, which move predominantly parallel to the direction of flow.

For structural engineering purposes, velocity of wind can be considered as having two components: a mean velocity component that increases with height, and a turbulent velocity that remains the same over height (Fig. 1.1a). Similarly, the wind pressures, which are proportional to the square of the velocities, also fluctuate as shown in Fig. 1.2. The total pressure Pt at any instant t is given by the relation

where

Pt = pressure at instant t P = average or mean pressure P' = instantaneous pressure fluctuation

In many engineering sciences the intensity of certain events is considered to be a function of the duration recurrence interval (return period). For example, in hydrology the intensity of rainfall expected in a region is considered in terms of a return period because the rainfall expected once in 10 years is less than the one expected once every 50 years. Similarly, in wind engineering the speed of wind is considered to vary with return periods. For example, the fastest-mile wind 33 ft (10 m) above ground in Dallas, TX, corresponding

Figure 1.2. Schematic representation of mean and gust pressure. At any instant t, the pressure Pt = P' + P.

to a 50-year return period, is 67 mph (30 m/s), compared to the value of 71 mph (31.7 m/ s) for a 100-year recurrence interval.

A 50-year return-period wind of 67 mph (30 m/s) means that on the average, Dallas will experience a wind faster than 67 mph within a period of 50 years. A return period of 50 years corresponds to a probability of occurrence of 1/50 = 0.02 = 2%. Thus the chance that a wind exceeding 67 mph (30 m/s) will occur in Dallas within a given year is 2%. Suppose a building is designed for a 100-year lifetime using a design wind speed of 67 mph. What is the probability that this wind will exceed the design speed within the lifetime of the structure? The probability that this wind speed will not be exceeded in any year is 49/50. The probability that this speed will not be exceeded 100 years in a row is (49/50)100. Therefore, the probability that this wind speed will be exceeded at least once in 100 years is

This signifies that although a wind with low annual probability of occurrence (such as a 50-year wind) is used to design structures, there still exists a high probability of the wind being exceeded within the lifetime of the structure. However, in structural engineering practice it is believed that the actual probability of overstressing a structure is much less because of the factors of safety and the generally conservative values used in design.

It is important to understand the notion of probability of occurrence of design wind speeds during the service life of buildings. The general expression for probability P that a design wind speed will be exceeded at least once during the exposed period of n years is given by

Pa = annual probability of being exceeded (reciprocal of the mean recurrence interval)

n = exposure period in years

Consider a building in Dallas designed for a 50-year service life instead of 100 years. The probability of exceeding the design wind speed at least once during the 50-year lifetime of the building is

The probability that wind speeds of a given magnitude will be exceeded increases with a longer exposure period of the building and the mean recurrence interval used in the design. Values of P for a given mean recurrence interval and a given exposure period are shown in Table 1.1.

Wind velocities (measured with anemometers usually installed at airports across the country) are necessarily averages of the fluctuating velocities measured during a finite interval of time. The value usually reported in the United States, until the publication of the American Society of Civil Engineers' ASCE 7-95 standard, was the average of the velocities recorded during the time it takes a horizontal column of air 1 mile long to pass a fixed point. For example, if a 1-mile column of air is moving at an average velocity of 60 mph, it passes an anemometer in 60 seconds, the reported velocity being the average of the velocities recorded these 60 seconds. The fastest mile is the highest velocity in one day. The annual extreme mile is the largest of the daily maximums. Furthermore, since the annual extreme mile varies from year to year, wind pressures used in design are based on p = i - (i - pay n

where

TABLE 1.1 Probability of Exceeding Design Wind Speed During Design Life of Building

Mean

Annual recurrence Exposure period (design life), n (years) probability interval -

TABLE 1.1 Probability of Exceeding Design Wind Speed During Design Life of Building

Mean

Annual recurrence Exposure period (design life), n (years) probability interval -

Pa |
(1/Pa) years |

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