Along-wind response in prismatic structures, design statements in Mexico

H. Hernández-Barrios1, C. Muñoz-Black2, A. López-López3.

1Professor of Civil Engineering, Universidad Michoacana de San Nicolás de Hidalgo, Morelia,Michoacán, México, hugohbarrios@yahoo.com.mx

2Researcher, Gerencia de Ingeniería Civil, Instituto de Investigaciones Eléctricas, Cuernavaca,Morelos, México, cjmb@iie.org.mx

3Civil Engineering Coordinator, Gerencia de Ingeniería Civil, Instituto de InvestigacionesEléctricas, Cuernavaca, Morelos, México, alopez@iie.org.mx

ABSTRACT

At present, the Aeolian design of structures in Mexico is based on a consideration of thestatements specified by the Civil Works Design Manual-Wind Actions [1], MDOC as per Spanishabbreviation, and the Complementary Practical Standards [2], NTC as per Spanishabbreviation, to the Constructions Regulation of Federal District. Both these codes for winddesign employ the standards in the original model proposed by Davenport. However, becausethe MDOC update is in process, in this paper are presented diverse formulations suggested inmajor International Codes and Standard of wind design with the suggestion, to consider them inthe new version of the MDOC. It is concluded that for prismatic structures and for the designconditions in Mexico, the approach recommended by the Eurocode [3] is the best estimation forthe along-wind response.

INTRODUCTION

Many wind sensitive structures are susceptible to along wind dynamic loads. This is the case oftowers, chimneys, tall buildings, suspension bridges, cable roof structures, pipes, transmissionlines, etc. Based on the recommendations of Liepmann, the method of the Dynamic ResponseFactor (DRF) to consider the dynamic loads due to the wind on a structure was proposed byDavenport [4]. The original model of the DRF, considers within the structural response thecontribution of the first vibration mode solely. This depends on the linear fundamental modeshape of the structure itself and determines that the structure response can be separated into twocomponents: the background response (quasi-static) and the resonant response. Diverse authorshave proposed modifications to this model, among them are Vellozzi and Cohen [5], Vickery,Simiu and Scanlan [6], Solari y Kareem [7] and Drybre and Hansen [8]. Some of the moreimportant Codes and Standards of wind design load, for example: the Eurocode [3], JapaneseCode [9], Canadian Code [10], the American Standard [11], Australian-New Zealand Standard[12] and the Construction Code [13], have adopted these modifications.

The Civil Works Design Manual-Wind Actions [1] in Mexico (MDOC) is the majorreference to design wind sensitive structures, and suggests guidelines and procedures forassessing the along-wind effects on tall structures as well as other wind effects. TheComplementary Practical Standard to the Constructions Regulation of Federal District, NTC, [2]is the official code design applicable only in Mexico City, the country’s capital..

Although the 10-minute average period is the meterorological standard for the basic windvelocity in many countries of continental Europe, in continental America the 3-second averageperiod is common except in Canada which has adopted a one-hour average period.

The last version of the Civil Works Design Manual-Wind Actions was reviewed in 1993.More recently the Constructions Regulation of Federal District (Mexico City), was reviewed in2004. Both standards define the basic wind velocity as 3s gust, and both codes adopt theequivalent static wind load used in the original model of Gust-loading factor proposed byDavenport [2]. The dynamic response in both codes is obtained following similar backgroundand procedure as in the Canadian Code [10]. However the Gust-loading factor, based in one houraverage time, is converted to 3s average time. This produces some confusion in the applicationof the procedure. The MDOC update is in process, and in order to determine the next guidelinesand procedures for assessing the along-wind effects on tall structures and other wind effects,diverse formulations proposed in major International Codes and Standards were reviewed andconsidered.

METHODOLOGY

The procedures suggested by diverse codes of design to quantify the longitudinal response ofprismatic structures in the wind direction are analyzed. In the formulation of any procedures andcalculations, the equivalent dynamic force and wind load effects depend on the mean windvelocity profiles, turbulence intensity, wind spectrum, turbulence length scale, and correlationstructure of the wind field. An overview of the definitions or descriptions these windcharacteristics in codes and standards is provided in this paper. To facilitate a convenientcomparison, the expressions were rewritten with the original expressions in the codes.Furthermore, all the multiplier factors in the codes were assumed equal to the units consideredand the average wind velocity was taken equal to that suggested in each code.

ALONG-WIND RESPONSE FOR TALL BUILDINGS, AUSTRALIAN/NEW ZEALAND STANDARD[12]

The Australian/New Zealand Standard [12] describes forces, moments, deflection, accelerations,and the like, in terms of a mean value plus the average maximum velocity likely to occur in a 10min period. However, the regional wind speeds RV has been corrected to consider approachingterrain, structure height, and local interference (adjacent buildings) to a benchmark of a height of10.0 m in open country terrain (category 2). The values represent the maximum 2s to 3 s gustoccurring within 1h at a height of 10 m, in open country terrain with a roughness length

0 0 020z . m (e.g., airport). Although the basic velocity is defined as 3 s gust, it is converted tothe 1 h mean wind velocity to evaluate the Dynamic Response Factor and the wind-inducedresponse of wind structures.

The Dynamic Response Factor dynC approximately accounts for the background

(quasistatic) and resonant components of the loading by being applied to the quasi-static gustloading. The factor incorporates the effects of correlation (size reduction) and resonance. Thisfactor differs from the Gust Factor, G , which was applied to the mean wind loading distribution(moment). The equation for the Dynamic Response Factor contains two dynamic terms, one forthe background effects (Ie:, sub-resonant) which accounts for the quasi-static dynamic responsebelow the natural frequency, and one for resonant effects that depends on the gust energy andaerodynamic admittance at the resonant frequency, and on the damping ratio for the structure.The resonant contribution is small for structures with natural frequency greater than 1 Hz 1T s . The dynamic response factor for structures with small frontal area then approaches thesquare of the ratio of peak gust wind speed to the mean wind speed, i.e., the dynamic method

will give similar loads to the static method. For structures with large frontal dimensions, thereduction produced by a low background factor sB may result in the Dynamic Analysis givinglower loads than the static analysis. The Australian/New Zealand Standard considers that if thestructure has a first mode fundamental period, T , less than 1s, then 1 0dynC . and it is greater

than 5s, it is not covered by this Standard. The procedure for the Dynamic Response Factor dynC

in the Australian/New Zealand Standard is summarized in Table 1. The Dynamic ResponseFactor dynC increases with increasing height on the structure.

Table 1: Procedure of Dynamic Response Factor in the AS/NZS 1170.0:2002 Standard [12]

hL is a measure of the integral turbulence length scale at height h :0 25

8510

.

hhL

hI is the turbulence intensity 1 v hP g I

Reduced frequency

3

3 5s

aH

des,

θn h

N .V

3

4s

a ohB

des,

θn b

NV

Where3sdes,

θV is the design wind speed and h is the average roof height of a structure above the ground, ohb is

the average breadth of the structure between 0 and h (m).

Aerodynamicsadmittance functions

11h

H

RN P

11b

B

RN P

Size reduction factor h bS R R

24 v

tv

n S (n )E

π σ

longitudinal powerspectral density

2 5

2 6

4

1 70 8

v

v

n S (n ) xσ

. x

3s

a h

des,

θn L

x PV

Background factor, where shb is the average breadth of the

structure between s and h 2 2

1

0 26 0 461

ssh

h

B. h s . b

L

Resonant factor 24v

sv

n S (n )πR Sζ σ

Where ζ is the ratio of structural damping tocritical damping of a structure

sH is the height factor for the resonant response :2

1ssHh

Peak factor 2 600R e ag log n with 600 10T s min utes ; and 3 7vg . .

Dynamic responsefactor

3

2 21 2

1 2s

h v s R s sdyn

v h

I g B g H RC

g I

ALONG-WIND RESPONSE FOR TALL BUILDINGS, EUROCODE [3]

The Eurocode [3] defines the fundamental value of basic wind, 0b,V , as the 10-minute mean

wind velocity with an annual risk of being exceeded of 0.02, irrespective of direction and season,at a height of 10 m above ground level in terrain Category II. Category II is flat open countryterrain with low vegetation and isolated obstacles with separations of at least 20 m in height. Therecommended value of air density is 31 25ρ . kg m , which is relatively high and relates to verylow temperatures at low altitude. The mean wind velocity mV z at a height z above the terrain

depends on the terrain roughness and orography and on the basic wind velocity, 0b,V , and it will

be determined using the equation,

0 07

00 0

00 19

0 05

.

m dir season b,z zV z C z . ln C C V. z

(1)

where dirC is the direction factor, seasonC is the season factor, 0C is the orography factor, and

0z is the roughness length. The intensity turbulence vI z at height z is defined as the standarddeviation of the turbulence divided by the mean wind velocity,

0

0

Iv

kI z

zC z lnz

for 200mínz z m (2a)

v v mínI z I z for mínz z(2b)

where Ik is the turbulence factor, once recommended value for it is 1.0.

Table 2 shows the expressions to obtain the Structural Factor, s dc c , suggested by theEurocode. Once obtained, the Structural Factor value it will calculate the equivalent dynamicforce. The Eurocode suggests that for buildings with less than 15m in height the value of s dc cmay be taken as 1.0, and for framed buildings which have structural walls and which are lessthan 100 m high and whose height is less than 4 times the in-wind depth, 4 0h d . , the value of

s dc c may be taken as 1.0.

Table 2: Expressions for the Structural Factor in the BS EN 1991-1-4-4 Code [3]

L z is the integral lengthscale of turbulence

300200

αzL z

if mínz z

mínL z L z if mínz z

00 67 0 05α . . ln z

Background response factor

20 63

1

1 0 90

.

s

B

b h.L z

Reduced frequency

14 6 ,xh

m

n hN .

V z ;

14 6 ,x

Bm

b nN .

V z

22

1 1 12

hNh

h h

R eN N

for 0hN 1hR for 0hN

Aerodynamics admittancefunctions 2

21 1 1

2BN

BB B

R eN N

for 0BN ; 1BR for 0BN

Size reduction factor h h B bS Rη R η

No-dimensional power spectraldensity function

2 5 3

6 8

1 10 2v

Lv

nS z,n . xS z,nσ . x

m

nL zx

V z

Resonant factor 12

24v s ,x

s v

n S z ,nπR Sζ σ

Where2

ss

δζ

π is the

damping ratio, percentcritical for buildings, sδ is

the total logarithmicdecrement of damping

The up-crossing frequency2

1 2 2 0 08,xRν n . Hz

B R

The limit of 0 08. Hzcorresponds to 3pk .

Peak factor

0 602 32p

.k ln

νT

ln

νT

T is the average timefor the mean wind velocity(10 minutes), 600T s

Structural Factor

2 21 2

1 7p v s

s dv s

k I z B Rc c

I z

ALONG-WIND RESPONSE FOR TALL BUILDINGS, UNITED STATES STANDARD [11]The ASCE Code [11] is based on a similar background as that of the Eurocode [7] and hasresulted in very similar formulations in these codes, except that the 0.925, in the expression forcalculation gust effect factor (Table 3) is an adjustment factor used to make the wind load in theupdated code consistent with the former version. The ASCE provides mean wind velocityprofiles based on both 3 s and 1 h averaging times, whereas the Eurocode utilizes averagingtimes of 10 min for the mean velocity profiles.

The integral length scale of turbulence,

10zzL

(3)

The mean hourly wind speed at height z,

10

α

zzV b V

(4)

Where V is the basic wind speed corresponds to a 3 s in exposure C category (maps) and theturbulence intensity,

1 610zI c

z

(5)

The constants in the expressions 3 to 5 are reported in ASCE-2005 [11]. The procedurefor Gust Effect Factor is summarized in Table 3.

Table 3: Procedure of Gust Effect Factor in the ASCE/SEI 7-2005 Standard [11]

Background response factor 20 63

1

1 0 63.

z

QB h.L

Reduced frequency 14 6hz

n hN .

V 14 6B

z

n BN .

V 115 4L

z

n LN .

V

Aerodynamics admittance functions2

21 1 1

2hN

hh h

R eN N

for 0hN 1hR for 0hN

22

1 1 12

BNB

B B

R eN N

for 0BN 1BR for 0BN

22

1 1 12

LNL

L L

R eN N

for 0LN 1LR for 0LN

Size reduction factor 0 53 0 47h B LS R R . . R

Longitudinal power spectral density 2 5 3

7 47

1 10 3v

v

n S (n ) . xσ . x

where 1 z

z

n Lx

V

Resonant factor 22

1 v

s v

n S (n )R S

ζ σ

where sζ is the damping ratio, percent critical for buildings

Peak factor 1

1

0 5772 36002 3600

R.g ln n

ln n where 3600 1T s h

3 4Qg . 3 4vg .

Gust Effect Factor

2 2 2 21 1 70 925

1 1 7Q Rz

fv z

. I g Q g RG .

. g I

ALONG-WIND RESPONSE FOR TALL BUILDINGS, JAPAN CODE [9]

The Japan Code [9] suggests the Gust Effect Factor, DG , is to be obtained utilizing theequivalent static wind force of along-wind response design. The Gust Effect Factor is based onthe overturning moment as described by the equation,

1D max D D MD D MDD

D D D

M M gσ g σ

GM M M

(6)

where: D maxM , DM and MDσ are maximum value, mean value and rms of overturning

moment at the base of the building, respectively. D maxM and MDσ involve load effect due tothe dynamic response of the building, and it is composed by using the background componentand resonance component.

The basic wind speed 0U corresponds to the 100-year–recurrence 10-minute mean windspeed over a flat and open terrain (category II, in the code) at an elevation of 10 m. The along-wind loads on structural frames are calculated from,

D H D DW q C G A (7)

where DW N is the along-wind load at height Z, DC is the wind force coefficient, 2A m is

the projected area at height Z, DG is the gust effect factor and 2Hq N m is the velocity

pressure, defined by,21

2H HqρU

(8)

where 31 22 mρ . kg m is the air density and HU m s is the design wind velocity.

Turbulence intensity ZI is defined according to the conditions of the construction site,

Z rz gII I E (9)

In this paper, the topography factor is taken to be 1 0gIE . and the turbulence intensity

on flat terrain categories is,0 05

0 10α .

rZG

ZI .Z

for b GZ Z Z (10a)

0 05

0 10α .

brZ

G

ZI .

Z

for bZ Z (10b)

where Z m is the height above ground, bZ , GZ and α , are parameters determining theexposure factor (Table A6.3, in the code).

Table 4 shows the expressions to obtain the Gust Effect Factor, DG , suggested by theJapan Code.

Table 4: Procedure of Gust Effect Factor in the AIJ Code [9]

0 50100

30

.

ZZL

for 30 gm Z Z

100ZL for 30Z m

zL is the turbulence scale Z m is the

height above ground, GZ is the parameter

determining the exposure factor

Reduced frequency andAerodynamics

admittance functions

10

2 4495min

DH

H

f HN .

U

0 502

0 90

1H .

H

.RN

10

3min

DB

H

f BN

U 1

1BB

RN

D H BS R R

Power spectral densityfunction

2 52 6

4

1 71

v

v

n S (n ) xFσ x

where

10 min

D H

H

f Lx

U

RMS of Overturningmoment coefficient

0 560 49 0 14

0 63

1

'g .

Hk

. .α

CBH.

L

HB

0 07 1

0 15 1

Hk .B

Hk .B

12013 B

RN

0 57 0 3 2 0 053 0 042A . .α R . . α

Resonant factor 2 24 4

vD D 'D v g

n S (n )π AR Sξ σ C

Dξ is the damping ratio, percent critical for buildings

Overturning momentcoefficient

1 13 3 6gC

α

The up-crossingfrequency 1

DD D

D

Rv f

R

Peak factor 2 600 1 2D Dg ln v . the average time for the mean wind velocity(10 minutes) 600T s

Gust Effect Factors10

21 2 1min

'g

D H D D Dg

CG I g R

C

ALONG-WIND RESPONSE FOR TALL BUILDINGS, CANADIAN CODE [10]The wind load calculation procedure in Canadian Code [10] is called the Dynamic Procedure,and is intended for determining overall wind effects, including amplified resonant response. Thewind pressure is based on mean hourly wind speed for the probability of being exceeded per year

of 1 in 50 (return period of 50 years). The Canadian Code considers that buildings whose heightis greater than 4 times their minimum effective width, or greater than 120m and other buildingswhose light weight, low frequency and low damping properties make them susceptible tovibration shall be designed considering the dynamic effects of wind. The Canadian Codeemploys a high gust energy factor, proposed by Davenport that is only on the mean wind speedand the ground roughness, and is independent of the height.

Table 5 shows the expressions to obtain the Gust Effect Factor, suggested by theCanadian Code.

Table 5: Procedure of Gust Effect Factor in NRCC 48192 Code [10]

Background turbulence factor

914

40 2 3

4 1 13 1 1 1457 122

H xB dxxH xw

x

Reduced frequency andAerodynamics admittance

functions

1

83

h,terrain" n"

nh

H

f HN

V ; 1

1hh

RN

1

10

h,terrain" n"

nB

H

f wN

V ; 1

1BB

RN

Size reduction factor3 h BπS R R

Gust energy ratio

2

2 4 321

v

v

nS n xFσ x

where

1

1220

h,terrain" n"

nD

H

fx

V

Resonant factor

21 v

s v

n S nR S

ζ σ

where2

ss

δζ

π is the critical damping ratio in the along-wind direction

The up-crossing frequency ns

SFν fSF

ζ B

Peak factor0 57722p.g ln

νT

ln

νT

Where T=3600s

Coefficient of variation e

σ K B Rμ C

K is a factor related to the surface roughnesscoefficient of terrain and it taken

0 08K . for exposure A0 10K . for exposure B0 14K . for exposure C

eHC is the exposure factor at the top of building, based on the profile of mean wind speed (commentary I [10])

Gust Effect Factor 1g pσC gμ

EXAMPLE OF COMPARISON

A comparison of the analyzed procedures was elaborated initially through an applicationexample, where it is assumed that the wind speed is 3 40 23sU . m/s ( 600 25 62sU . m/s or

3600 26 47sU . m s ), at a 50-year recurrence, in terrain type B or equivalent (suburban areas,wooded areas or other terrain with numerous closely spaced obstructions). In order to make thecomparison all the multiplier factors in the codes were assumed equal to the unit and the averagewind velocity was taken equal to that which was suggested in each code. The along windresponse due to the dynamic effect of the wind is calculated for the following properties of thestructure: m88.182H (height), m48.30B (width), m48.30L (depth), 1 0 20n . Hz (firstmode natural frequency of vibration in the along-wind direction), 01.0 (structural damping

ratio), a linear fundamental mode shape, building density 192 03 3m . kg/m , air density of31 22ρ . kg m and the 1 30dC . .

By applying each one of the design codes previously described, results are shown inTable 6. In this Table it is noted that the higher value of the dynamic response factor is the oneobtained with the Canadian Code, nevertheless, is not the one that gives higher equivalent staticforces. The design code that gives higher equivalent forces is the Eurocode. The differencebetween the dynamic response factors is in the order of 2.47, but the difference between thegreatest force and the minor force is on the order of 1.54 times. The previous remarks leads tothe conclusion that to compare the dynamic response factors proposed by diverse design codes isan incorrect method, since the wind speed averaging time in each one of them is different. Thus,it is necessary to compare the magnitude of the results between the equivalent forces. Theexisting differences between the proposed equivalent static forces by the analyzed codes, are dueto several factors, among them can be mentioned: the wind speed averaging time, the turbulenceintensity of the site, the used turbulent length scale and the power spectral density.

Table 6: Comparison of results for the application example

Standard or Code DRF DRFDRF /maxEquivalent force

(N) FF /max

AIJ [9] 11.2DC 1.24 700,21DW 1.46ASCE/SEI 7-2005 [11] 06.1fG 2.47 166,27F 1.17AS/NZS [12] 08.1dynC 2.45 624,20F 1.54Eurocode [3] 71.1dscc 1.53 788,31wF 1.00NBC 2005 [10] 62.2gC 1.00 062,27F 1.18

PARAMETRIC STUDY

Additionally, a parametric study for the along wind response based on the slenderness ratio, H/B,and natural period of one prismatic structure has been elaborated. The natural period of multi-story buildings was calculated using the expression,

15nT (11)

Where n is the numbers of story and T (s) is de natural period, so than if height of each storey is2.5m, one building with H=37.5 m has a natural period of T=1.0 s. Generally, the terraincategories are defined differently in each code. Table 7 shows the equivalence between thedifferent terrain categories in each code.

Table 7: Equivalence between different terrain categories

Code Cat. Code Cat.

AIJEurocodeASCE 7

NBC 2005AS/NZS

VIVBC4

AIJEurocodeASCE 7

NBC 2005AS/NZS

IIIIIIBB3

Code Cat. Code Cat.

AIJEurocodeASCE 7AS/NZS

IIIIC2

AIJEurocodeASCE 7

NBC 2005AS/NZS

I0DA1

Figure 1 illustrates a comparison of gust effect factor by terrain category and buildingheight for 4H B , 1 0D B . and 3 10 140 23 25 62 26 47s min hV . m s U . m s V . m s .,for each code or standard. The gust effect factor becomes large with terrain category andbuilding height, except in Japan and Canadian Code, for all terrain categories.

Once calculated, the gust effect factor, the equivalent static force along-wind iscalculated. Figure 2 shows the equivalent static force on reference height obtained for each codereviewed considered one structural damping ratio 0 01ξ . , hold constant the air density

31 22ρ . kg m , one projected area of 10 m2 and 1 30dC . . Figure 2 notes that there is slightdifference in the equivalent static forces results, and in all cases the ASCE-7 produced higherequivalent forces for this H/B, but this is not true for others slenderness ratio, H/B [15].

ASCE 7-2005 Eurocode

AS/NZS AIJ

NBC 2005Figure 1: Variation of the gust effect factor by terrain category and building height

ASCE 7-2005 Eurocode

AS/NZS AIJ

NBC 2005Figure 2: Variation of the equivalent static force by terrain category and building height

CONCLUDING REMARKS

The Australian/New Zealand Standard, Canadian Code and Japan Code, prescribe a length scaleformulation independent of terrain, Counihan [14] suggests a decreasing function of terraintoughness. Canadian Code employs a gust energy factor, proposed by Davenport that dependsonly on the mean wind speed and the ground roughness, and is independent of height.

In order to compare the estimates of wind load effects based on the codes and standardsconsidered, to compare only the dynamic response factors is not correct, since the wind speed

averaging time in each one of them is different. Thus, it is necessary to compare the magnitudeof the results between the equivalent static forces. The existing differences between the proposedequivalent forces by the analyzed codes, are due to several factors, among them can bementioned: the wind speed averaging time, the turbulence intensity of the site, the used turbulentlength scale and the power spectral density.

It is concluded that for the prismatic structures and for the design conditions in Mexico,the approach recommended by the Eurocode [3] is the best estimation for the along-windresponse. However, in Mexico the basic wind velocity is defined as 3 s gust, because of its needto be converted to 10 minutes mean wind velocity to evaluate the gusts loading factor and thewind-induced response of dynamics structures.

ACKNOWLEDGEMENT

The writers gratefully acknowledge support from Federal Electrical Utility (CFE-Mexico),Instituto de Investigaciones Electricas (IIE), University of Michoacan (UMSNH) and COECyT-Michoacan, for this study.

REFERENCES

[1] MDOC, Civil Works Design Manual-Wind Actions, Manual de Diseño de Obras Civiles, Diseño porViento, Comisión Federal de Electricidad-Instituto de Investigaciones Eléctricas, México, 1993.

[2] NTC, Complementary Practical Standards to the Constructions Regulation of Federal District,Normas Técnicas Complementarias al Reglamento de Construcciones del DF, Diseño por Viento, 2004.

[3] BS EN 1991-1-4-4:2005, Eurocode 1: Actions on structures, Part 1-4: General actions-Wind Actions,British Standard, 2005.

[4] A. G. Davenport, The application of statistical concepts to the wind loading of structures, Proc.Institution of Civil Engineers, 19,1961, 442-447.

[5] J. Vellozzi, E. Cohen, Gust response factors, J. Struct. Div., ASCE, 94 (6), 1968, pp. 1295-1313.

[6] E. Simiu, R. Scanlan, Wind effects on structures: Fundamentals and applications to design, 3rd, Ed.,1996, Wiley, New York, 688 pp.

[7] G. Solari, A. Kareem, On the formulation of ASCE 7-95 gust effect factor, J. Wind. Eng. Ind. Aerodyn.77 (1998) 673-684.

[8] C. Dyrbye, A. O. Hansen, Wind Loads on Structures, John Wiley and Sons, 1997, ISBN 0-471-95651-1.

[9] AIJ, Architectural Institute of Japan, Recommendations for Loads on Buildings, Chapter 6, WindLoads, 2004.

[10] NRCC 48192, National Research Council Canada, User’s Guide-NBC 2005 StructuralCommentaries Part 4 of Division B, 2005, ISBN 0-660-19506-2.

[11] ASCE/SEI 7-2005, Minimum Design Loads for Buildings and Other Structures, American Society ofCivil Engineers, 2005, ISBN 0-7844-0809-2.

[12] AS/NZS 1170.0:2002, Australian/New Zealand Standard, Structural design actions, Part 0: GeneralPrinciples, 2005, ISBN 0-7337 4469-9.

[13] ACS, Código de Construcción Modelo para Cargas por Viento, Asociación de Estados del Caribe.2004.

[14] Counihan, J. Adiabatic atmospheric boundary layer: a review and analysis of the data from theperiod 1880-1972, Atmos. Environ., 9, 1975, pp. 871-905.

[15] Hernández-Barrios, Factor de Amplificación Dinámica y Simulación de Ráfagas de viento, Reporteinterno del Proyecto 12.2, Coordinación de la Investigación Científica, Universidad Michoacana de SanNicolás de Hidalgo, 2004.