7.2 Basic Code and Standard Equations
7.2.1 Kinetic Energy of Wind Field
In assessing pressures or forces induced on buildings by wind, it proves convenient to have a simple and direct relationship between the upstream wind flow conditions at some suitable reference point and the induced pressure at any point on the surfaces of the building. Traditionally, the approach followed has been to develop a relationship utilizing the "mean"
kinetic energy of the approaching wind (qo) given by:
q = 1 2 U
o o
ρ 2 (Eq. 7.2.1-1)
where Uo is the mean wind speed referenced to some height above mean ground level and ρ is the mass density of the air. ASCE 7-98 expands Equation 7.2.1-1 to define "velocity pressure" (or stagnation pressure), q, (psf) given by the expression:
q = 0.00256 Kz KztKdV2Iw (Eq. 7.2.1-2) where,
V = Basic mean design wind speed in mph (3-second gust) at a height above ground of 10 meters (33 ft.) for terrain exposure category C.
Iw = Importance factor, a coefficient used to modify wind speed to provide a somewhat consistent level of risk based upon usage.
Kz= Velocity pressure exposure coefficient to account for variation in velocity with height above mean ground level as influenced by terrain exposure.
Kzt = Topographic factor that accounts for wind speed-up over hills, ridges, and escarpments.
Kd = Directionality factor.
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The numerical coefficient 0.00256 (lb-hr2-ft-2-miles-2) represents the "l/2ρ"
term in Equation 7.2.1-1 and is based on the mass density of the air (ρ) corresponding to atmospheric pressure at sea level (760 mm of mercury) and a temperature of 15°C. Different values of this constant should be employed where sufficient meteorological data are available to justify its use for a specific design application. Air mass density varies as a function of altitude, latitude, temperature, weather and season. Average and extreme values of air mass density and procedure for calculating the coefficient can be found in various references (e.g., Ref. B3.42).
Calculation of the velocity pressure (q) provides a measure of the portion of kinetic wind energy to be resisted by the structure in a given design application and hence, a careful evaluation of this quantity is warranted. A detailed discussion of each of the terms of Equation 7.2.1-2 follows.
Basic Wind Speed, V
ASCE 7-98 is based on a 3-second gust wind speed. A transition was made from fastest-mile wind speed to 3-second gust beginning with ASCE 7-95 (Ref. B3.43) for the following reasons.
1. Fastest mile oriented anemometers have been replaced by modern equipment with graphic strip chart readouts.
2. The peak gust is the easiest and most reliable wind speed to read from the newer graphs.
3. Three second gust speeds are closer to the speeds quoted in news media.
4. Structural members are designed by gust speeds. If another type wind speed is used, large corrections must be made by use of the gust effect factor.
A 3-second gust wind speed is defined as the maximum average speed of the wind averaged over 3 seconds passing through a wind speed measuring instrument at a certain height above a given terrain roughness over a specified period of time. For standardization purposes in codes and standards, that height is usually taken as 10 meters, terrain roughness as exposure C, and specified period of time as 50 years. The ASCE 7-98 basic wind speed has been updated from ASCE 7-95 based on a new and more complete analysis of hurricanes.
The non-hurricane 3-second gust wind speeds used in ASCE 7-98 are from Peterka and Shahid (Ref. B3.41). The values correspond to the annual, extreme, 3-second gust wind speeds with an annual probability of exceedence
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of 0.02 (50-year mean return interval) and were established from data collected at 485 weather stations for the contiguous United States. A wind speed shown for a given location on the 50-year map has a 2% probability of being exceeded in any given year and a 63% probability of being exceeded once in 50 years.
In using the basic design wind speeds given in the map, the following caveats should be noted:
1. Anomalies in wind speed exist for many regions of the country on a micrometeorological scale (denoted as special wind regions ASCE 7-98 Figure 6-1).
2. Experience has shown (Ref. B3.10) that wind speeds may be substantially higher in mountainous and hilly terrain, gorges, and ocean promontories. (This has been accounted for in ASCE 7-98 by introducing the topographic factor, Kzt.)
3. Increased wind speeds due to channeling effects produced by upstream natural terrain or large, nearby constructed features (for example, buildings) have not been considered.
4. Tornadic wind events were not included in developing the basic wind speeds given.
Velocity Exposure Coefficient, Kz
The velocity exposure coefficient (Kz) is introduced to take into consideration the variation of velocity with height as a function of ground roughness. ASCE 7-98 defines four exposure categories A, B, C, and D as depicted in Figure 7.2.1(a) which compares the mean speed variation with height for each of these four categories based upon a basic design speed of 100 mph for Exposure C. The coefficient (Kz) is given by:
⎪⎪
⎩
⎪⎪
⎨
⎧
⎟ <
⎟
⎠
⎞
⎜⎜
⎝
⎛
≤
⎟ ≤
⎟
⎠
⎞
⎜⎜
⎝
⎛
= α
α
ft 15 z z for
15
z z ft 5 1 z for
z 01 . 2
K 2/
g
g 2/
g
z (Eq. 7.2.1-3)
where,
z = height above mean ground level, in feet zg = gradient height given in Table 7.2.1, in feet α = exponential factor given in Table 7.2.1
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Figure 7.2.1(a)
Mean Wind Speed Variation With Height
Table 7.2.1
Exposure Category Constants
Exposure Category αααα zg
A 5.0 1,500
B 7.0 1,200
C 9.5 900
D 11.5 700
Experience and wind tunnel tests have confirmed that turbulence and mixing increases near ground level. To account for this fact, Kz, is assumed constant for the first 15 feet.
From Figure 7.2.1(a), it is seen that the selection of an appropriate exposure category significantly affects the design load as the velocity is squared in Equation 7.2.1-2.
The selection of an appropriate exposure category requires accurate knowledge of the terrain immediately surrounding the building site as well as sound engineering judgment. Although usually not possible, it would be prudent to consider possible changes in terrain that might occur in the future.
From Figure 7.2.1(a) it is seen that the velocity pressure for Exposure B, which is directly proportional to the square of the wind speed, may be only
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0.72 times that of Exposure C. Thus, the use of Exposure B, where applicable, could reduce the velocity pressure by 72 percent. As noted earlier in Section 1.4.4 of this Manual, IBC 2000 specifies that Exposure B shall be assumed unless the site meets the definition of another exposure.
Importance Factor, Iw
For wind loads, the importance factor, in effect, adjusts the wind speeds provided in the 50-year map to other levels of probability. Thus, coefficients of 1.15 and 0.87 are associated with annual probabilities of exceedence of 0.01 (100-year return period) and 0.04 (25-year return period), respectively.
Topographic Factor, Kzt
Wind speed-up effects at isolated hills, ridges, and escarpements constituting abrupt changes in general topography are incorporated with the topographic factor, Kzt. ASCE 7-98, Section 6.5.7, lists five conditions that must all be met before this effect needs to be considered.
Directionality Factor, Kd
This factor, which has been previously incorporated in the wind load factor for LRFD, has been separated out in ASCE 7-98. This factor accounts for the reduced probability of maximum winds coming from any given direction and the reduced probability of the maximum pressure coefficient occurring for any given wind direction.