ASCE 7-10 Wind Loads Ronald Cook1, Larry Griffis2, Peter Vickery3, Eric Stafford4 1
Civil and Coastal Engineering, University of Florida,
[email protected] Structures Division, Walter P. Moore and Associates,
[email protected] 3 Applied Research Associates,
[email protected] 4 T. Eric Stafford & Associates,
[email protected] 2
ABSTRACT ASCE 7-10 “Minimum Design Loads for Buildings and Other Structures” contains several changes regarding wind loads. The major editorial change is a complete reorganization to a multiple-chapter format as done previously for seismic loads with the objective being to make the provisions easier to follow. Technical changes include the introduction of new wind speed maps to be used with a 1.0 load factor for LRFD and a 0.6 load factor for ASD, the reintroduction of Exposure D for water surfaces in hurricane-prone regions, and revised wind-borne debris regions. A new simplified procedure for buildings up to 160 ft has been added based on the provisions for buildings of all heights. INTRODUCTION The major changes to the wind load provisions of ASCE 7 introduced in ASCE 7-10 are: • • • • •
Reorganization of wind load provisions Wind speed maps Re-introduction of Exposure D in hurricane-prone regions Wind-borne debris region Simplified procedure for buildings ≤ 160 ft
This paper presents a general background on the basis for these changes. Thirty other changes related to wind loads were included in ASCE 7-10. The majority of these changes were editorial but some did include technical changes. These include: • • • •
Minimum wind loads Improved exposure and roughness examples Revisions to low-rise “envelope” method Rooftop equipment
REORGANIZATION OF WIND LOAD PROVISIONS The wind load provisions of Chapter 6 in ASCE 7 have been reorganized into 6 new Chapters. In recent years, there has been much discussion about the layout and presentation of the wind load provisions in ASCE 7. While, ASCE 7-98 did make some improvements to the format (introduction of the 3 Methods), much of the important information was buried deep within the paragraph numbering. In addition, Method 2 Analytical Procedure actually contained several analytical methods embedded within the section (e.g., Buildings of All Heights and Low-rise Buildings). While the provisions were technically correct and properly numbered, understanding and applying the appropriate wind loads could be somewhat cumbersome. The primary goals of the reorganization effort were to keep the section numbering smaller and to locate major subject areas as distinct chapters. Additionally, it was desired to order the wind provisions in a logical sequence for the general structural design community. Accomplishing these goals led to the creation of 6 distinct chapters and the relocation of the provisions into their most logical new chapter. For example, the provisions for determining MWFRS loads are in separate chapters from Components and Cladding. Additionally, the different methods for determining MWFRS loads are located in the 3 separate chapters – Chapter 27 Directional Procedure (formerly buildings of all heights in Method 2); Chapter 28 Envelope Procedure (formerly low-rise buildings in Method 2); and Chapter 29 Other Structures and Building Appurtenances (formerly embedded in Method 2). Each chapter was again subdivided into “parts” where deemed appropriate for clarity. For example in Chapter 28 the analytical method for determining wind loads for low-rise buildings is identified as Part 1 and the simplified method for determining wind loads for low-rise buildings is identified as Part 2. Similar subdivisions occur in Chapters 27 and 30. To ease the transition to the new format and to facilitate improved awareness of the provisions applicable to the various methods, each chapter and parts contain tables that specifically identify and outline the steps and provisions applicable for that respective chapter or part. Table 27.2-1 shown below is an example of one of the outlines presented for Part 1 in Chapter 27.
Table 27.2-1 Steps to Determine MWFRS Wind Loads Enclosed, Partially Enclosed and Open Buildings of All Heights Step 1: Determine risk category of building or other structure, see Table 1.4-1 Step 2: Determine the basic wind speed, V, for the applicable risk category, see Figure 26.5-1A, B or C Step 3: Determine wind load parameters: ¾ Wind directionality factor, Kd , see Section 26.6 and Table 26.6-1 ¾ Exposure category, see Section 26.7 ¾ Topographic factor, Kzt, see Section 26.8 and Table 26.8-1 ¾ Gust Effect Factor, G, see Section 26.9 ¾ Enclosure classification, see Section 26.10 ¾ Internal pressure coefficient, GCpi, see Section 26.11 and Table 26.11-1 Step 4: Determine velocity pressure exposure coefficient, Kz or Kh, see Table 27.3-1 Step 5: Determine velocity pressure qz or qh Eq. 27.3-1 Step 6: Determine external pressure coefficient, Cp or CN ¾ Fig. 27.4-1 for walls and flat, gable, hip, monoslope or mansard roofs ¾ Fig. 27.4-2 for domed roofs ¾ Fig. 27.4-3 for arched roofs ¾ Fig. 27.4-4 for monoslope roof, open building ¾ Fig. 27.4-5 for pitched roof, open building ¾ Fig. 27.4-6 for troughed roof, open building ¾ Fig. 27.4-7 for along-ridge/valley wind load case for monoslope, pitched or troughed roof, open building Step 7: Calculate wind pressure, p, on each building surface ¾ Eq. 27.4-1 for rigid buildings ¾ Eq. 27.4-2 for flexible buildings ¾ Eq. 27.4-3 for open buildings
Additionally, a table was added to the commentary that provides a crossreference of all sections, figures, and tables between ASCE 7-05 and ASCE 7-10. Sections applicable to ASCE 7-05 are shown in the left column in numerical sequence so that users familiar the ASCE 7-05 may easily locate the applicable sections in ASCE 7-10. WIND SPEED MAPS Multiple Maps. The decision to move to multiple ultimate, limit state, or strength design wind speed maps to be used in conjunction with a wind load factor of 1.0 for LRFD instead of using a single map coupled with an importance factor and a wind load factor of 1.6 was made because: • •
An ultimate or strength based map brings the wind design approach more in line with that used for seismic design in that they both essentially eliminate the use of a 1.0 load factor for strength design. The multiple map approach eliminates the inconsistencies in the use of the importance factor that strictly varies with location and between the hurricane and non-hurricane regions.
• •
The new maps establish uniformity in the return period for the design basis winds, and they more clearly convey that information The new maps, by providing the design speeds directly, more clearly inform owners and their consultants about the storm intensities for which their designs are performed.
The hurricane importance factor specified in ANSI A58.1 1982 and ASCE 793 was eliminated from the 1995 Edition of ASCE 7 by incorporating it into the wind speed contours. Consequently, at no time since the introduction of ASCE 7-95 have the wind speed contours in the hurricane prone region been representative of a 50 year return period wind speed, although most users erroneously thought this was the case. In the development of the wind speed map used in ASCE 7-98 the Wind Load Task Committee (WLTC) re-visited the hurricane importance factor inherent in the Standard since 1982 primarily because it was recognized that the importance factor varied with location along the coast and using a constant value of 1.05 was not appropriate. This spatially varying factor was incorporated into the map by dividing the 500 year wind speeds by the square root of the load factor, which at the time was expected to be 1.5, not the value of 1.6 that was finally recommended by the load factor committee. In ASCE 7-10, the approach taken to determine the return periods associated with different occupancy category importance factors began with the premise that the nominal wind load, computed using the methods given in ASCE 7-05, when multiplied by the wind load factor, represents a limit state or strength load. Furthermore, it was assumed that the variability of the wind speed dominates the calculation of the wind load factor. This is an approximation, and depends on the uncertainty in the various components of the wind loading chain (Davenport, 1983). The wind speed uncertainty is combined with uncertainties in pressure coefficient, exposure factor, gust factor and modeling errors. Since these errors combine as sums of squares, and because the uncertainty effect of the wind speed is doubled as it appears in the wind load equation as a pressure, the net result is the wind speed uncertainty contributes in the range of 70% to 80% of the total uncertainty. Regardless of the exact contribution of the wind speed uncertainty to the total uncertainty, the return period for the ultimate, or strength, design point for ASCE 710 was determined using the approximation where all the uncertainty was treated through the wind speed variability. Using this approach, the limit state wind load, WT, is given as: WT =CFV502WLF Iv
(1)
where CF is a component/structure specific coefficient that includes the effects building height, geometry, terrain, etc. V50 is the 50 year return period wind speed, WLF is the wind load factor, and Iv is the occupancy importance factor applied to the wind load. In order to estimate the magnitude of IH, the committee required that the annual probability of exceeding the limit state wind load in hurricane and non-
hurricane regions be the same. Recalling that the nominal design wind speed in the non-hurricane regions of the United States is associated a 50 year return period, the WLTC sought to determine the return period associated with the wind speed producing the limit state load in a non-hurricane region. As defined in ASCE 7-95 through the present, in the non-hurricane regions of the United States, the ratio of the wind speed for any return period, T, to the 50 year return period wind speed is: VT V50 = [0.36 + 0.1ln(12T )]
(2)
where VT is wind speed associated with the strength load condition having an annual exceedance probability of 1/T. This strength load, WT, for an occupancy Category II structure (Iv=1.0) occurs when: WT = C F VT2 = C F V502 W LF
(3)
Consequently from (2) and (3), VT V50 can be represented as an algebraic function in the form:
VT V50 = [0.36 + 0.1ln(12T )] = WLF
(4)
From (4), the return period T associated with the limit state wind speed in non-hurricane regions is for Occupancy Category II structures is:
T = 0.00228 exp(10 WLF )
(5)
Using the wind load factor of 1.6 as is currently specified in ASCE 7-05, from (5) we get T = 709 years~700 years for Occupancy Category II structures. In the case of Occupancy Category I and Occupancy Categories III and IV, WLF in (3), (4) and (5) is replaced with WLF Iv, yielding return periods of 294 years (rounded to 300) for Occupancy Category I and 1700 years for Occupancy Categories III and IV. The return periods of 294 and 1700 years were computed with the more accurate definition of importance factor obtained from the square of (3) with T= 25 years for Occupancy Category I and 100 years for Occupancy Category III and IV, rather than using the rounded values given in ASCE 7-05 which yield return periods of 309 years and 1780 years. In ASD the wind speed from any of the three maps are used in conjunction with a WLF of 0.6, which is the rounded result of an ASD WLF that is equal to 1/ 1.6 = 0.623. Hurricane Simulation Model Updates. The design wind speeds given in ANSI A58.1 1982 and all versions of ASCE since that time have been comprised of a combination of hurricane and non-hurricane winds. The non-hurricane wind speeds are the same as those that have been in ASCE 7 since 1995 (adjusted to different return periods). The hurricane winds which are derived from a simulation model
differ due to updates in the hurricane modeling. The hurricane wind speeds were developed using the hurricane hazard model described in Vickery et al. (2009b). These hurricane wind speeds are combined with the statistical model for nonhurricane wind speeds given in Peterka and Shahid (1998) to develop maps that consider both hurricane and non-hurricane winds. The major differences between the simulation models described Vickery et al. (2000a,b) (used to define the design wind speeds in ASCE 7-98 through ASCE 7-05) to those in the current model (Vickery et al., 2009b) are: • • • •
A new intensity model includes ocean mixing to limit hurricane A new statistical model for Holland B parameter A new filling (storm weakening after landfall) model A new wind field model
In addition to changes to the simulation model itself, the new maps were developed using a 100,000 year simulation vs. a 20,000 year simulation for the old map. The maps were developed using predicted wind speeds at 2851 points vs. the 208 points used to develop the old map, resulting in a much more precise representation of the change in contours as one moves inland away from the coast.
1000 990 980
B= B= B= B=
970 960 950
0.75 1 1.3 1.5
940 930 0
1
2
3
4
5
6
7
8
Distance from Storm Center (r/RMW)
9
60 B= B= B= B=
50 40 -1
Pressure e (hPa)
1010
(ms )
1020
Gradient Balance Wind Speed
The primary reason for the reduction in wind speeds produced by the 2009 model compared to those obtained using the previous model is through the modeling of the Holland B parameter. The details of Holland B parameter are discussed in Holland (1980) as well as Vickery et al. (2010), among others. Figure xx1 shows the impact of changes in B on the radial variation of the wind speeds and pressures for a hurricane with constant values of central pressure, radius to maximum wind speed (RMW) and translation speed. 0.75 1 1.3 1.5
30 20 10 0 0
1
2
3
4
5
6
7
8
9
Distance from Storm Center (r/RMW)
Figure 1 Effect of B on azimuthally averaged radial profiles of wind speed and pressure Figure 1 shows that as B increases, the radial variation of both wind speed and pressure increases, and the maximum wind speed increase. It can be shown that in a stationary hurricane the maximum gradient level wind speed, VGmax, in a hurricane is proportional to the square root of B in the form VG max ∝ BΔp where Δp is the
difference between the low pressure at the center of the hurricane and the high pressure well away from the storm center. With all else equal, in a stationary hurricane, a 10% decrease in either B or Δp corresponds to a 5% decrease in the maximum wind speed in the hurricane, indicating that both variables are important. As discussed in Vickery and Wadhera (2008), B has statistically significant correlations with RMW (increasing as RMW decreases), latitude (decreasing as latitude increases) and sea surface temperature (SST) (decreasing with decreasing SST). In an attempt to incorporate a relationship between latitude, SST, RMW and B using a single parameter, B over open water, is modeled as:
B = 1.7642 − 1.2098 A + ε ;
r2=0.345, σB = 0.226
(6)
where A is a non-dimensional parameter that incorporates SST, RMW and latitude. In (6) the numerator of A is a function RMW and latitude and the denominator is a function of central pressure and SST. The two most important parameters controlling the behavior of B in (6) are RMW and latitude. The model for B used in Vickery et al. (2000b) is: B = 1.38 + 0.00184 Δp − 0.00309 RMW + ε ;
r2=0.026, σB = 0.381
(7)
Note that in (7) there is no dependence on latitude and that the r2 value is much lower and the error term is much higher than in (6). The reduction in r2 and the associated decrease in the error term, σB, plays an important role in the reduction of wind speeds associated with rarer events, as these events are driven by the tails of the input distributions rather than the means. Whereas Figure 1 shows the importance of B from the viewpoint of a single storm, Figure 2 shows the effect of the new statistical model for B on predicted wind speeds though comparisons of predicted hurricane gust wind speeds at Wilmington, NC and Miami, FL. In the Wilmington case, the use of the new model for B reduces the 100 year return period gust wind speed by 9.4%, and in the Miami case a 6.8% reduction occurs. For a 700 year return period, the reductions are 10.9% and 9.3% for Wilmington and Miami respectively.
Wilmington, NC
Miami, FL Peak Gust Wind Speed (mph)
Peak Gust Wind Speed (mph)
200
B from Vickery, et al. (2000) B from Vickery and Wadhera (2008) 150
100
50
0 1
10 100 Return Period (years)
10
200 150 100 50
B from Vickery, et al. (2000) B from Vickery and Wadhera (2008)
0 1
10 100 Return Period (years)
1000
Figure 2. Effect of Holland B modeling on predicted wind speeds
RE-INTRODUCTION OF EXPOSURE D IN HURRICANE PRONE AREAS One of the more significant differences between the hurricane wind field models used in Vickery et al. (2000a) and Vickery et al. (2009) is in the modeling of the sea surface drag coefficient, Cd. In Vickery et al. (2009) the hurricane wind field model uses a representation of Cd, which reaches a maximum value at mean wind speeds of around 20 m/sec. This treatment of the Cd varies markedly from that used in Vickery et al. (2000a), where Cd increases monotonically with wind speed without limit. The change in the modeling of the Cd is due to the work described in Powell et al. (2003) which indicates that Cd does not continue to increase with increasing wind speed, but reaches a maximum or limiting value. A limiting value of Cd contradicts the findings given in the earlier works of both Powell (1980) and Garrett (1977), but has been supported by other research since 2003. The hurricane wind field model used to develop the ASCE 7-10 wind speeds models the limiting Cd through the use of an upper bound on Cd that varies with distance from the center of the hurricane Figure 3 presents the water-land gust wind speed ratios derived from the Vickery, et al. (2008) model (near the RMW), the ratios derived from the Vickery et al. (2000a) model (also near the RMW), and those implied in ASCE 7. The wind speed ratio is defined as the marine gust wind speed divided by the open terrain (defined as zo=0.03m) gust wind speed. In ASCE 7 this ratio is equal to K z evaluated in Exposure D at z=10 m. As indicated in Figure 3, the ratios produced by the new wind model are approximately consistent with the Exposure D ratio. Using model for Cd that does not have a limiting value the wind speed ratio approaches that of Exposure C in ASCE 7 as the wind speed increases, and thus for simplicity Exposure D was eliminated from the hurricane prone coastline in the 1998 Edition of ASCE 7.
Gust Wind Speed Ratio (Marine/Land)
1.20 1.15 ASCE 7 Exposure D
1.10 1.05
ASCE 7 Exposure C
1.00 0.95
Vickery et al. Vickery et al. Vickery et al. Vickery et al.
0.90 0.85
(2000a) (2008a), RMW=20 km (2008a), RMW=40 km (2008a), RMW=80 km
0.80 30
40
50
60
70
Mean Wind Speed at 10m Over Water (m/sec)
Figure 3. Gust wind speed ratio (Gust wind speed on land divided by gust wind speed over water). A gust wind speed ratio of 1 indicates no reduction in wind speed as wind moves from sea to land (i.e. marine roughness is the same as open terrain). WIND-BORNE DEBRIS REGIONS The primary changes to the wind-borne debris provisions in ASCE 7 are to accomplish relative coordination with the new ultimate wind speed maps that are now basis for determining design wind speeds. The language that triggers the Wind-borne Debris Region (WBDR) has been relocated to Section 26.10.3.1. The language is still similar but includes a couple of key changes. The appropriate map for the category of building under consideration is to be used for determining the application of the WBDR requirements. For Risk Category II buildings and Risk Category III buildings except health care facilities, the WBDR triggers are to be based on the wind speed map for Risk Category II buildings, Figure 26.5.1A. For Risk Category IV buildings and Risk Category III health care facilities, the WBDR triggers are to be based on the wind speed map for Category III and IV buildings, figure 26.5.1B. Using the Risk Category III and IV wind speed map does substantially increase the WBDR for these buildings and structures as compared with the provisions of ASCE 7-05 except around Jacksonville, Florida and the “big bend” region of Florida. Using the appropriate risk based map for the appropriate Risk Category provides a means for achieving a more risk consistent approach for defining WBDR, particularly with regards to life safety. The types of buildings and structures included in Risk Category III suggest that life safety is most important for health care facilities. Therefore, the expanded WBDR in Figure 26.5.1B applies to Risk Category III health care facilities. For Risk Category II buildings, there is a notable change in the geographic area that is now designated as a WBDR. The WBDR contained in the previous editions of ASCE 7 (1998, 2002, and 2005) were based on judgment and essentially applied the region in a strip of the coast along most of the Gulf of Mexico and
Atlantic coast regions where the risk of a direct strike of a Category 3 or larger hurricane was high. The new criteria continue that judgment based definition by including the coastal areas that are approximately consistent with those given in prior editions of ASCE 7 for Risk Category II. A straight translation of the 110 and 120 mph wind speeds from ASCE 7-05 to the 700 year return period maps in ASCE 7-10 would yield triggers of 140 mph and 150 mph respectively. This would have eliminated the WBDR along most the Texas coast and substantially reduce the region in other areas that are considered to be in a WBDR in ASCE 7-05. This is due to the changes in the hurricane simulation model that reduces the magnitude of wind speeds for long return periods. However, while the applicability of the WBDR has essentially been shifted by 10 mph, the applicable region for Risk Category II and Risk Category III buildings excluding health care facilities has be substantially narrowed and eliminated in some places as compared to the regions applicable in ASCE 7-05 and prior editions. Significant reductions in the WBDR occur around Jacksonville, Florida, the Florida panhandle, and along the coast of North Carolina. SIMPLIFIED PROCEDURE FOR BUILDINGS ≤ 160 FT New to ASCE 7-10 is a simplified approach for determining design wind pressures applicable to buildings with a mean roof height h ≤ 160 ft. Design pressures for both roof and wall surfaces are determined directly from a set of tables. The method is based on the same principles that form the basis of the Directional Procedure defined in Chapter 27 Part1 for the MWFRS and Chapter 30 Part 3 for CC. MWFRS – Chapter 27 Part 2. The method for MWFRS covers two classes of buildings that are a function of building height. In addition to the normal limitations listed in Chapter 27 Section 27.1.2 regarding a regular building and absence of unusual dynamic characteristics, the requirements for each class are stipulated below: Class 1 Buildings: 1. 2. 3. 4.
Enclosed simple diaphragm building (as defined in Section 26.2) h ≤ 60 ft. 0.2 ≤ L/B ≤ 5.0 Kzt = 1.0 with exceptions as defined in Section 27.5.2
Class 2 Buildings: 1. 2. 3. 4. 5.
Enclosed simple diaphragm building (as defined in Section 26.2) 60 ft < h ≤ 160 ft. 0.2 ≤ L/B ≤ 5.0 Kzt = 1.0 with exceptions as defined in Section 27.5.2 The fundamental natural frequency shall not be less than 75/h where h is in feet.
The procedure can be applied for buildings with either rigid or flexible diaphragms as discussed in Section 27.5.4. Net wind pressures for wall and roof surfaces are determined from Tables 27.6-1 and Table 27.6-2 respectively. Tables are presented for all exposures, B, C and D and for wind speeds varying from 110 MPH to 200 MPH. A procedure is also specified for determining pressures for roof parapets (see Figure 27.6-2) and roof overhangs (see Figure 27.6-3). Loads from the tables are applied to the walls and roof simultaneously. The step by step procedure is defined at the front of Chapter 27 Part 2 Table 27.5-1. An excerpt from Table 27.6-1 for walls is shown below. An excerpt from Table 27.6-2 for roofs is also shown. For roofs, the procedure covers flat, gable, hip, monoslope and mansard roofs as referenced in Table 27.6-2. For wall pressures determined from Table 27.6-1, two pressures are tabulated for each building height and wind speed. The uppermost row in the table defines ph which is the roof pressure at the top of the building. The lower row (shown shaded) defines p0 which is the pressure at the base of the building. A linear variation of pressure between the two is to be used in design as shown at the front of Table 27.61. This linear variation has been developed to produce essentially the same story shears and overturning moments as the “exact” values from Part 1 of Chapter 27. It is to be noted that the procedure includes the calculation of the Gust Effect Factor based on conservative assumptions for building frequency and damping. Further details on the derivation of tabulated pressure values can be found in the commentary to ASCE 7-10.
C&C – Chapter 30 Part 4. The method for CC covers both wall and roof surfaces. Roof and wall pressures for flat, gable, mansard, hip and monoslope roof buildings are covered Table 30.7-2. Tabulated pressures are shown for five zones that include all wall and roof surfaces as shown in the figures in Table 30.7-2. The step by step procedure is defined at the front of Chapter 30 Part 4 in Table 30.7-1. Table 30.7-2 shows pressure for Exposure C only. However, pressures for all exposures can be determined by applying the Exposure Adjustment Factor shown in a graph within the table. Tabulated values are shown for an effective wind area of 10 sf but reduction factors are shown in graphs part of the table for other effective wind areas. The various factors are applied to the tabulated pressures according to Equation 30.7-1. A procedure is also specified for determining pressures on parapets (refer to Figure 30.7-1) and overhangs (refer to Figure 30.7-2). An excerpt to Table 30.7-2 is shown below.
OTHER CHANGES TO ASCE 7-10 WIND LOADS
OTHER CHANGES Minimum wind loads. Minimum wind load pressure was increased from 10 psf to 16 psf to account for the change in load factors. Improved exposure and roughness examples. New figures were added to the commentary to provide examples on how to determine exposure conditions for different roughness conditions around the building . Revisions to low-rise “envelope” method. The figure for determining MWFRS exterior pressure coefficients, GCpf, for low-rise buildings was revised to be consistent with that used in ASCE 7-98. Provisions for roof-top equipment. Provisions have been added to quantify both lateral and vertical wind loads on rooftop equipment. CONCLUSION This paper provides a general overview of the major changes to the ASCE 7 wind load provisions in ASCE 7-10. The reorganization and change in the return period of the wind speed maps has made the overall format of the wind load provisions similar to that of the ASCE 7 seismic provisions. Additional information on changes can be found in the ASCE 7-10 Commentary. REFERENCES Davenport, A.G. (1983), “The relationship of reliability to wind loading”, J. Wind Eng. Ind. Aerodyn. 13, 3-27 Garratt, J.R. (1977), “Review of drag coefficients over oceans and continents”, Mon. Wea. Rev. 105, 915–929 Holland, G. J., (1980), “An analytical model of the wind and pressure profiles in hurricanes Mon. Wea. Rev. 108, 1212-1218. Peterka, J. A. and Shahid, S (1998), “Design Gust Wind Speeds in the United States”. J. Struct. Eng. 124, 207Powell, M.D. (1980), “Evaluations of Diagnostic Marine Boundary-Layer Models Applied to Hurricanes”, Mon. Wea. Rev. 108, 757–766 Powell, M.D., P.J. Vickery, and T.A. Reinhold, (2003) “Reduced drag coefficients for high wind speeds in tropical cyclones”, Nature 422, 279-283.
Stafford, T. Eric (2010) “Significant Changes to the Wind Load Provisions of ASCE 7-10, An Illustrated Guide,” ASCE Press Vickery, P.J. and D. Wadhera, (2008), “Statistical Models of the Holland Pressure Profile Parameter and Radius to Maximum Winds of Hurricanes from Flight Level Pressure and H*Wind Data”, J. Appl. Meteor., 47, 2497-2517 Vickery, P.J., D. Wadhera, M.D. Powell and Y. Chen, (2009a) “A Hurricane Boundary Layer and Wind Field Model for Use in Engineering Applications”, J. Appl. Meteor., 48, 381-405 Vickery, P.J.; D. Wadhera, L.A. Twisdale Jr. and F. M. Lavelle, (2009b). “United States Hurricane Wind Speed Risk and Uncertainty”, J. Struct. Eng. 135, 301320 Vickery, P.J, P.F., Skerlj, A.C. Steckley and L.A. Twisdale, (2000a) “Hurricane wind field model for use in hurricane simulations”, J. Struct. Eng., 126, 12031221. Vickery, P.J., P.F. Skerlj and L.A. Twisdale Jr., (2000b) “Simulation of hurricane risk in the U.S. using an empirical track model,” J. Struct. Eng., 126, 1222-1237 Vickery P.J., D. Wadhera, J. Galsworthy, J. A. Peterka, P.A. Irwin, and L. A. Griffis (2010), “Ultimate wind load design gust wind speeds in the United States for use in ASCE-7”, J. Struct. Eng., 136, 613-625
