Along Wind

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

H. Hernndez-Barrios1, C. Muoz-Black

2, A. Lpez-Lpez

3.

1Professor of Civil Engineering, Universidad Michoacana de San Nicols de Hidalgo, Morelia,

Michoacn, Mxico, [email protected]

Researcher, Gerencia de Ingeniera Civil, Instituto de Investigaciones Elctricas, Cuernavaca,Morelos, Mxico, [email protected]

3Civil Engineering Coordinator, Gerencia de Ingeniera Civil, Instituto de Investigaciones

Elctricas, Cuernavaca, Morelos, Mxico, [email protected]

ABSTRACT

At present, the Aeolian design of structures in Mexico is based on a consideration of the

statements specified by the Civil Works Design Manual-Wind Actions [1], MDOC as per Spanishabbreviation, and the Complementary Practical Standards [2], NTC as per Spanish

abbreviation, to the Constructions Regulation of Federal District. Both these codes for wind

design employ the standards in the original model proposed by Davenport. However, because

the 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 in

the 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 for

the 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, transmission

lines, etc. Based on the recommendations of Liepmann, the method of the Dynamic Response

Factor (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 the

contribution 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 two

components: the background response (quasi-static) and the resonant response. Diverse authors

have 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 more

important Codes and Standards of wind design load, for example: the Eurocode [3], Japanese

Code [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 major

reference to design wind sensitive structures, and suggests guidelines and procedures forassessing the along-wind effects on tall structures as well as other wind effects. The

Complementary Practical Standard to the Constructions Regulation of Federal District, NTC, [2]

is the official code design applicable only in Mexico City, the countrys capital..Although the 10-minute average period is the meterorological standard for the basic wind

velocity in many countries of continental Europe, in continental America the 3-second average

period is common except in Canada which has adopted a one-hour average period.
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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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 in

2004. Both standards define the basic wind velocity as 3s gust, and both codes adopt the

equivalent 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 background

and procedure as in the Canadian Code [10]. However the Gust-loading factor, based in one hour

average 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 guidelines

and 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 and

considered.

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 and

calculations, the equivalent dynamic force and wind load effects depend on the mean wind

velocity profiles, turbulence intensity, wind spectrum, turbulence length scale, and correlation

structure 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 convenient

comparison, 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 considered

and the average wind velocity was taken equal to that suggested in each code.

ALONG-WIND RESPONSE FOR TALL BUILDINGS, AUSTRALIAN/NEWZEALANDSTANDARD

[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 10

min period. However, the regional wind speedsR

V has been corrected to consider approaching

terrain, structure height, and local interference (adjacent buildings) to a benchmark of a height of

10.0 m in open country terrain (category 2). The values represent the maximum 2s to 3 s gust

occurring within 1h at a height of 10 m, in open country terrain with a roughness length

00 020z . m (e.g., airport). Although the basic velocity is defined as 3 s gust, it is converted to

the 1 h mean wind velocity to evaluate the Dynamic Response Factor and the wind-inducedresponse of wind structures.

The Dynamic Response Factordyn

C approximately accounts for the background

(quasistatic) and resonant components of the loading by being applied to the quasi-static gust

loading. The factor incorporates the effects of correlation (size reduction) and resonance. This

factor 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 response

below 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


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will give similar loads to the static method. For structures with large frontal dimensions, the

reduction produced by a low background factors

B may result in the Dynamic Analysis giving

lower loads than the static analysis. The Australian/New Zealand Standard considers that if the

structure has a first mode fundamental period, T , less than 1s, then 1 0dyn

C . and it is greater

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

C

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

.

h

hL

hI is the turbulence intensity 1 v hP g I

Reduced frequency

3

3 5

s

aH

des,

n hN .

V

3

4

s

a ohB

des,

n bN

V

Where3s

des,V 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

1

1h

H

RN P

1

1b

B

RN P

Size reduction factor h bS R R

2

4 vt

v

n S (n)

E

longitudinal powerspectral density

2 5

2 6

4

1 70 8

v

v

n S (n)x

. x

3s

a h

des,

n Lx PV

Background factor, wheresh

b is the average breadth of the

structure between s and h

2 2

1

0 26 0 461

s

sh

h

B

. h s . b

L

Resonant factor24

vs

v

n S (n )R S

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

sH is the height factor for the resonant response :

2

1s

s

H h

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

Dynamic responsefactor

3

2 21 2

1 2s

h v s R s s

dynv h

I g B g H RC

g I


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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. The

recommended value of air density is3

1 25 . 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

0

0 190 05

.

m dir season b,

z zV z C z . ln C C V

. z

(1)

wheredir

C is the direction factor,season

C is the season factor,0

C is the orography factor, and

0z is the roughness length. The intensity turbulence vI z at height z is defined as the standard

deviation of the turbulence divided by the mean wind velocity,

00

Iv

kI z

zC z ln

z

for 200mn

z z m (2a)

v v mnI z I z for mnz 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 the

Eurocode. Once obtained, the Structural Factor value it will calculate the equivalent dynamic

force. The Eurocode suggests that for buildings with less than 15m in height the value of s dc c

may be taken as 1.0, and for framed buildings which have structural walls and which are less

than 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.


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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

z

L z

ifmn

z z

mnL z L z if mnz z

00 67 0 05 . . ln z

Background response factor

2

0 63

1

1 0 90

.

s

B

b h.

L z

Reduced frequency

14 6

,x

hm

n hN .

V z ;

1

4 6,x

Bm

b nN .

V z

2

2

1 11

2

hN

hh h

R eN N

for 0h

N 1h

R for 0h

N

Aerodynamics admittancefunctions 2

2

1 11

2

BN

B

B B

R eN N

for 0B

N ; 1B

R for 0B

N

Size reduction factor h h B bS R

No-dimensional power spectraldensity function

2 5 3

6 8

1 10 2

vL

v

nS z,n . xS z,n

. x

m

nL zx

V z

Resonant factor 12

24

v s ,x

s v

n S z ,nR S

Where2

ss

is the

damping ratio, percent

critical for buildings,s

is

the total logarithmicdecrement of damping

The up-crossing frequency2

1 2 20 08

,xR n . Hz

B R

The limit of 0 08. Hzcorresponds to 3

pk .

Peak factor

0 602 3

2p

.k ln

ln

T is the average timefor the mean wind velocity

(10 minutes), 600T s

Structural Factor

2 21 2

1 7

p v s

s d

v s

k I z B Rc c

I z

ALONG-WIND RESPONSE FOR TALL BUILDINGS, UNITEDSTATES 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 the

updated code consistent with the former version. The ASCE provides mean wind velocity

profiles 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,


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10zz

L

(3)

The mean hourly wind speed at height z,

10

z

zV b V

(4)

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

1 610

zI c

z

(5)

The constants in the expressions 3 to 5 are reported in ASCE-2005 [11]. The procedure

for 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 factor2

0 63

1

1 0 63

.

z

Q

B h.L

Reduced frequency14 6

h

z

n hN .

V 14 6

B

z

n BN .

V 115 4

L

z

n LN .

V

Aerodynamics admittance functions

2

2

1 11

2

hN

hh h

R eN N

for 0h

N 1h

R for 0h

N

2

2

1 11

2

BN

BB B

R eN N

for 0B

N 1B

R for 0B

N

221 1 1

2LN

LL 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 3

v

v

n S (n ) . x

. x

where1 z

z

n Lx

V

Resonant factor2

2

1 v

s v

n S (n)R S

wheres

is the damping ratio, percent critical for buildings

Peak factor

1

1

0 5772 3600

2 3600R

.g ln n

ln n

where 3600 1T s h

3 4Q

g . 3 4v

g .

Gust Effect Factor

2 2 2 21 1 7

0 9251 1 7

Q Rz

fv z

. I g Q g RG .

. g I


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

The Japan Code [9] suggests the Gust Effect Factor,D

G , is to be obtained utilizing the

equivalent 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 MD

D D D D

M M gG

M M M

(6)

where:D max

M ,D

M andMD

are maximum value, mean value and rms of overturning

moment at the base of the building, respectively.D max

M andMD

involve load effect due to

the dynamic response of the building, and it is composed by using the background component

and resonance component.

The basic wind speed0

U corresponds to the 100-yearrecurrence 10-minute mean wind

speed 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 isthe projected area at height Z,

DG is the gust effect factor and 2Hq N m is the velocity

pressure, defined by,

21

2H Hq (8)

where 31 22m

. kg m is the air density and HU m s is the design wind velocity.

Turbulence intensityZ

I is defined according to the conditions of the construction site,

Z rz gI

I I E (9)

In this paper, the topography factor is taken to be 1 0gI

E . and the turbulence intensity

on flat terrain categories is,0 05

0 10

.

rZG

ZI .

Z

forb G

Z Z Z (10a)

0 05

0 10

.

brZ

G

ZI .

Z

forb

Z Z (10b)

where Z m is the height above ground, bZ , GZ and , are parameters determining the

exposure factor (Table A6.3, in the code).Table 4 shows the expressions to obtain the Gust Effect Factor,D

G , suggested by the

Japan Code.


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

0 50

10030

.

Z

ZL

for 30

gm Z Z

100Z

L for 30Z m

zL is the turbulence scale Z m is the

height above ground,G

Z is the parameter

determining the exposure factor

Reduced frequency andAerodynamics

admittance functions

10

2 4495

min

D

H H

f HN .

U

0 502

0 90

1H .H

.R

N

10

3

min

DB

H

f BN

U

1

1BB

RN

D H BS R R

Power spectral densityfunction

2 5

2 6

4

1 71

v

v

n S (n ) xF

x

where

10min

D H

H

f Lx

U

RMS of Overturningmoment coefficient

0 56

0 49 0 14

0 63

1

'

g .

H

k

. .C

BH.L

H

B

0 07 1

0 15 1

Hk .

B

Hk .

B

1

201

3 B

R

N

0 57 0 3 2 0 053 0 042A . .

Resonant factor 2 24

4

vD D

'D vg

n S (n ) AR S

C

D

is the damping ratio, percent critical for buildings

Overturning momentcoefficient

1 1

3 3 6gC

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 1

min

'

g

D H D D D

g

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. The

wind pressure is based on mean hourly wind speed for the probability of being exceeded per year


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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 buildings

whose light weight, low frequency and low damping properties make them susceptible to

vibration 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 speed

and 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 1

31 1 1

457 122

H xB dx

xH xwx

Reduced frequency andAerodynamics admittance

functions

1

8

3h,terrain" n"

nh

H

f HN

V ;

1

1hh

RN

1

10

h,terrain" n"

nB

H

f wNV

; 11B

B

RN

Size reduction factor3 h B

S R R

Gust energy ratio

2

2 4 32

1

v

v

nS n xF

x

where

1

1220

h,terrain" n"

nD

H

fx

V

Resonant factor

2

1 v

s v

n S nR S

where2

ss

is the critical damping ratio in the along-wind direction

The up-crossing frequency ns

SF f

SF

Peak factor0 577

22p.

g lnln

Where T=3600s

Coefficient of variation e

KB R

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 p

C g


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EXAMPLE OF COMPARISON

A comparison of the analyzed procedures was elaborated initially through an application

example, where it is assumed that the wind speed is3

40 23s

U . m/s (600

25 62s

U . m/s or

360026 47

sU . 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 the

comparison 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 wind

response due to the dynamic effect of the wind is calculated for the following properties of the

structure: m88.182H (height), m48.30B (width), m48.30L (depth),1

0 20n . Hz (first

mode 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 22 . kg m and the 1 30

dC . .

By applying each one of the design codes previously described, results are shown in

Table 6. In this Table it is noted that the higher value of the dynamic response factor is the one

obtained 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 difference

between 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 to

the conclusion that to compare the dynamic response factors proposed by diverse design codes is

an 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. The

existing differences between the proposed equivalent static forces by the analyzed codes, are due

to 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 1.46

ASCE/SEI 7-2005 [11] 06.1fG 2.47 166,27F 1.17

AS/NZS [12] 08.1dynC 2.45 624,20F 1.54

Eurocode [3] 71.1dscc 1.53 788,31wF 1.00

NBC 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,

15

nT (11)


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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 terrain

categories 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.

AIJ

Eurocode

ASCE 7

NBC 2005

AS/NZS

V

IV

B

C

4

AIJ

Eurocode

ASCE 7

NBC 2005

AS/NZS

III

III

B

B

3

Code Cat. Code Cat.

AIJ

Eurocode

ASCE 7

AS/NZS

II

II

C

2

AIJ

Eurocode

ASCE 7

NBC 2005

AS/NZS

I

0

D

A

1

Figure 1 illustrates a comparison of gust effect factor by terrain category and building

height for 4H B , 1 0D B . and3 10 1

40 23 25 62 26 47s min h

V . 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 code

reviewed considered one structural damping ratio 0 01 . , hold constant the air density31 22 . kg m , one projected area of 10 m2 and 1 30

dC . . Figure 2 notes that there is slight

difference 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].


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ASCE 7-2005 Eurocode

AS/NZS AIJ

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


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ASCE 7-2005 Eurocode

AS/NZS AIJ

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

CONCLUDINGREMARKS

The Australian/New Zealand Standard, Canadian Code and Japan Code, prescribe a length scaleformulation independent of terrain, Counihan [14] suggests a decreasing function of terrain

toughness. Canadian Code employs a gust energy factor, proposed by Davenport that depends

only 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 standards

considered, to compare only the dynamic response factors is not correct, since the wind speed


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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 proposed

equivalent forces by the analyzed codes, are due to several factors, among them can be

mentioned: 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 need

to 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 Diseo de Obras Civiles, Diseo porViento, Comisin Federal de Electricidad-Instituto de Investigaciones Elctricas, Mxico, 1993.

[2] NTC, Complementary Practical Standards to the Constructions Regulation of Federal District,Normas Tcnicas Complementarias al Reglamento de Construcciones del DF, Diseo 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, Users Guide-NBC 2005 Structural

Commentaries 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.


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

[13] ACS, Cdigo de Construccin Modelo para Cargas por Viento, Asociacin de Estados del Caribe.2004.

[14] Counihan, J. Adiabatic atmospheric boundary layer: a review and analysis of the data from the

period 1880-1972, Atmos. Environ., 9, 1975, pp. 871-905.

[15] Hernndez-Barrios, Factor de Amplificacin Dinmica y Simulacin de Rfagas de viento, Reporte

interno del Proyecto 12.2, Coordinacin de la Investigacin Cientfica, Universidad Michoacana de SanNicols de Hidalgo, 2004.

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