JUN 1988
NBR 6123
Wind loads on Edifications
ABNT - Associação
Brasileira de Normas
Técnicas
Sede:
Rio de Janeiro
Av. Treze de maio, 13 – 26°andar
CEP: 20003 – Caixas Postal 1680
Rio de Janeiro - RJ
Procedure
Origin: Project NB-599/1987
CB-02 - Brazilian Committee for civil construction
CE-02:003.16 - Commission for Studies of the Wind Loads on Edifications
NBR 6123 - Building Construction - Bases for design of structures - Wind loads Procedure
Descriptions: Wind. Edifications
Incorporates the erratum nº 1 of Dec 1990
Re-printing of NB-599 of Dec 1987
66 pages
Key words: Wind. Edification
SUMMARY
1 Purpose
2 Symbols
3 Definitions
4 Procedure for calculations of wind loads on
edifications
5 Velocity profile of the wind
6 Aerodynamic coefficients for current edifications
7 Force coefficient for prismatic bars and reticulated
structures
8 Force coefficient for walls, plates and isolated roofs
9 Dynamic effects due to atmospheric turbulence
APPENDIX A - Normalized velocity S2 and time
intervals
APPENDIX B - Statistic factor S3 for a probability Pm
and life span of edification of m years
APPENDIX C - Location and altitude of meteorological
stations
APPENDIX D - Calculation of internal pressure
coefficients
APPENDIX E - Aerodynamic coefficients for curved
roofs
APPENDIX F - Additional information
APPENDIX G - Effect of the neighborhood
APPENDIX H - Dynamic effects on slender and
flexible edifications
APPENDIX I – Determining the of dynamic response
due to atmospheric turbulence
Index
1 Purpose
1.1 This Norm sets forth the required considerations of
loads due to static and dynamic actions of the wind for
edification design.
1.2 This Norm is not applicable to edifications with unusual
shapes, dimensions and location, whose cases demand
specific studies to calculate the wind loads and their effects.
Test results from wind tunnel procedure, simulating natural
wind profile can be used to replace the coefficients present
in this Norm.
2 Symbols
This Norm adopts the symbols in 2.1 and 2.3.
2.1 Capital Roman letters
A
- Area of a flat surface on which the wind load is
calculated, from form coefficients Ca and Cf
(perpendicular load to the surface) and the friction
coefficient Ci (tangent load to the surface)
Reference area for the calculation of the force
coefficients.
Ae
Effective frontal area: area of orthogonal projection
of the edification, structure or structural member on
a plane perpendicular to the wind direction (“shade
area”); used to determine the force coefficient.
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Al – Influence area corresponding to the coordinate i
T – Fundamental period of the structure
Aq – Reference area
V0 – Basic velocity of the wind: velocity of a 3s gust,
occurring on an average of once in 50 years, at 10 m
above ground, in flat open country
Ca – Drag coefficient; Ca = Fa /qA
Cai – Drag coefficient to the coordinate i
Vk – Basic velocity of the wind:
Vk = V0 S1 S2 S3
Ce – External form coefficient; Ce = Fe /qA
Cf – Force coefficient; Cf = Ff /qA
p
– Design velocity:
Fy – Friction coefficient; C1 = F1 /qA
p
= V10 mimj1 (10) S1 S3 = 0,69 V0 S1 S3
Cf – Internal form coefficient; Cf = Ff /qA
Cx – Force coefficient in direction x; Cx = Fx /qA
Cy – Force coefficient in direction y; Cy = Fy /qA
F – Load on a flat surface of area A, perpendicular to
the
respective surface
t (h) – Mean Wind velocity over t seconds in a height
h above ground
t (z) – Mean Wind velocity over t seconds in the
height z above ground, for the category i (not
considering the parameters S1 and S3)
xi – Overall wind in the direction of coordinate i
Fl = Friction force on a flat surface of the area A,
tangent to the respective surface
– Mean load xi
Fa – Drag force: component of the wind load in the
direction of the wind
– Fluctuating component of xi
Fe – External load to the edification, acting on a flat
surface of the area A, perpendicular to the
respective surface
Fg – Overall wind load: resulting from all the wind loads
on edification, or part of it
Fi – Internal load to the edification, acting on a flat
surface of area A, perpendicular to the respective
surface
2.2. Small Roman letters
a – Largest side – the largest horizontal dimension of
edification
Dimension between the supports of a structural member
b – Smallest side – the smallest horizontal dimension of
edification
Fr – Gust effect factor
Dimension of a structural member according to the wind
direction
Fx – Wind load component in the direction x
Meteorological parameter used to determine S2
Fy – Wind load component in the direction y
c – Reference dimension in prismatic bars of flat
façades
L – Height h or width lf of the frontal surface of
edification, to determine the time interval t
Profile dimensions (L= 1800m) used to determine the
dynamic amplification coefficient
Distance from the edge of a plate or wall to the point
application of F
Cas – Surface drag coefficient
Cp – Pressure coefficient: Cp = Cpe - Cpi
Pm – Probability of a certain wind velocity to occur, at
least, once in a period of m years
Q - Static variable (force, flexure moment, stress, etc)
or geometric (deformation, displacement, torsion)
Cpe – External pressure coefficient: Cpe = ∆pe /q
Cpi – Internal pressure coefficient: Cpi = ∆pi /q
Re – Reynolds number
Ca – Width of a prismatic bar, measured in a
perpendicular direction to the wind
S1 – Topographic factor
d – Diameter of a circular cylinder
S2 – Factor that considers the influence of the roughness
of the terrain, the dimension of the edification or part of
it, and its height above ground.
Diameter of the circle of a dome
S3 – Factor based on probability concepts
Level difference between the base and the top of a hill
or slope
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NBR 6123/1988
ea – Eccentricity in the direction of dimension a, in
relation to the vertical geometric axis of the edification
eb – Eccentricity in the direction of dimension b, in
relation to the vertical geometric axis of the edification
f - Rise of a barrel vault or dome
Zx– height above ground from which the mean velocity
profile is defined by the roughness of the terrain on
windward side of the change line of the roughness
Zr– Reference height: zr=10m
2.3 Greek letters
Natural vibration frequency
h – Height of edification above ground, measured to top
of the plat band, to or roof overhang level. Height of the
wall or plate
α – Incidence angle of the wind, measured between the
wind direction and the largest side of the edification
ß - Central angle between the direction of the wind and
the radius passing by the considered point in the
periphery of a circular cylinder
Height to determine the mean velocity
∆ P – Effective pressure on a surface point of the
edification
∆ P = ∆ Pa - ∆ Pi
l – Length of the bar, wall or plate
l1 – Width: horizontal dimension
perpendicular to the wind direction
of
edification
Reference dimension in the frontal surface of
edification
l2 – depth: dimension of edification in the direction of the
wind
m – life span of the edification, in years
m0 – Discreet reference mass
m1 – Discreet mass corresponding to the coordinate i
∆ Pe – Effective external pressure: on a point of the
external surface of the edification and the atmospheric
pressure of the wind acting on the windward side of the
edification, in the air flow not disturbed by the presence
of obstacles
∆ Pi – Effective internal pressure: difference between the
atmospheric pressure on a point of the internal surface
of the edification and the atmospheric pressure of the
wind acting on the wind ward (windward) side of the
edification, in the air flow not disturbed by the presence
of obstacles
η - Protection factor, in parallel reticulated structures
n – Number of degrees of liberty
θ – Inclination angle of roof slopes
p – Exponent of the Potential Law of variation of S2
q – Wind dynamic pressure, corresponding to the profile
velocity Vk1, in Normal conditions of pressure (1atm =
1013,2 mbar = 101320 Pa) and temperature (15º);
2
2
q = 0,613 V k ( q: N/m ; Vk: m/s)
t – Time interval to determine the mean velocity of the
Wind
Inclination angle of the mean surface of slopes and
hill sides, in a two-dimensional air flow
ξ - Mechanical amplification coefficient
Φ – Index of exposed area: effective frontal area of a
reticulate structure by the frontal area of the surface
limited by the frame of the reticulated structure
Ψ - Ψ = mi/m0
xi – Displacement corresponding to the coordinate i
ξ – Damping ratio
xn – Vibration mode
3- Definitions
z - Height above ground
This Norm adopts the definitions within 3.1 and 3.9.
zo– Roughness length
3.1 Windward
zo1– Roughness length of the terrain located on
windward side of a roughness change point
zo2– Roughness length of the terrain located on leeward
side of a roughness change point
zg– Gradient height: height of the boundary atmospheric
layer
Region from where the wind blows, in relation to the
edification
3.2 Reticulated structure
Every structure made of straight bars
3.3 Overpressure
zi– Height of the structural member i above ground level
Height above ground up to which the mean velocity
profile is defined by the roughness of the terrain on
leeward side of the change point of the roughness for z01
< z02
Every pressure above the reference atmospheric
pressure (Positive sign)
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3.4 Leeward
4.2.1. Pressure coefficients
Region opposite to where the wind blows, in relation to
the edification.
As the wind load depends on the pressure difference on
the opposite faces of the part of the edification under
study, the pressure coefficients are given by the external
surfaces and internal surfaces. To comply with this
Norm, effective pressure ∆ P , on a point the edification
surface, is the value defined by:
3.5 Suction
Effective pressure below the reference atmospheric
pressure (negative sing)
∆ P = ∆ Pe - ∆ Pi
3.6 Frontal Surface
Where:
Surface defined by the orthogonal projection of the
edification, structure or structure member on a plane
perpendicular to the direction of the wind (“shade
surface”)
∆ pe = effective external pressure
∆ pi = effective internal pressure
Therefore:
3.7 Basic wind
∆p = (Cpe - Cpi ) q
Wind corresponding to the basic velocity V0.
Where:
3.8 High turbulence wind
Cpe = external pressure coefficient: Cpe =∆ Pe /q
Wind following the described i 6.5.3
Cpi = internal pressure coefficient : Cpi =∆ Pi /q
3.9 Low turbulence wind
Wind identified in all the other cases
4
Procedure for calculation of wind load on
edifications
The positive values of the external or internal pressure
coefficients correspond to overpressures, and the
negative values correspond to suctions.
The wind loads on edification must be calculated
separately for:
A positive value for ∆p indicates an effective pressure
with the direction of an external overpressure, and a
negative value for ∆p indicates an effective pressure
with the direction of an external suction.
a)
Claddings and fixing parts (tiles, glasses, frames,
panels, etc);
4.2.4 Form coefficients
b)
parts of the structure (roofs, walls, etc);
c)
the structure as a whole.
The form loads on a flat edification element of area A act
perpendicularly to it, calculated:
F = Fe - Fi
4.1 Wind on partially built structures
Where:
The wind loads on a partially built structure depends on
the method and the building sequence. It is acceptable
to admit that the maximum velocity profile of the wind,
Vk1 will not occur within a short period of time. Therefore,
the verification for safety in a partially build structure can
be carried out with a smaller profile velocity1).
Fe = external load to the edification, acting on the flat
surface of area A
Fi = internal load to the edification, acting on the flat
surface of area A
Therefore:
4.2 Determination of the wind static loads
F = (Ce - Ci) qA
The wind static loads are determined as follows:
Where:
a)
the basic velocity of the wind, V0, adjusted to
the place where the structure will be built, is
determined according to the provisions in 5.1;
Ce = external form coefficient: Cpe = Fe /q
Ci = internal form coefficient : Ci = Fi /q
b)
c)
the basic velocity of the wind is multiplied by
the factors , S1, S2 and S3 and to obtain the
Profile velocity of the wind, Vk for the part of
the edification to be considered, according to
5.2 -5.5:
Positive values of the form coefficients, external and
internal, correspond to overpressures and negative
values correspond to suctions.
Vk = V0 S1 S2 S3
A positive value F indicates that this load acts towards
the interior, and a negative value indicates that this load
acts towards the exterior of the edification.
the profile velocity of the wind permits the
determination of the dynamic pressure by the
expression:
q = 0,613 Vk2
where (units S1 ): q in N/m2 and Vk in m/s
(1)
see 5.4 and group 5 .Table 3
For the cases in this Norm the internal pressure
uniformly distributed in the interior of the edification
consequently, on flat internal surfaces, Cpi = Ci
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NBR 6123/1988
4.2.3 Force coefficient
5.2 Topographic factor, S1
The overall wind load on edification or part of it, Fg1 is
obtained by the vector sum of the wind loads acting on it
.
The topographic factor S1 considers the topographic
variations of the terrain and is determined as follows:
The overall load component in the direction of the wind,
drag force Fa, is obtained by:
a)
flat, slightly uneven terrain: S1 = 1,0:
b)
slopes and hills;
Fa = Ca q Aa
- long slopes and hills where a twodimension air flow blowing in the direction
indicated on Figure 2 can be admitted:
Where:
- in the point A ( hills) and in the points A and
C ( slopes); S1 = 1,0;
Ca = drag coefficient
Aa = effective frontal area of the orthogonal projection
of the edification, structure or structural member on a
plane perpendicular to the direction of the wind (“shade
area”)
- in the point B [S1 is a function S1 (z)]:
θ ≤ 3º S1 (z) = 1,0
6 ≤ θ ≤ 17º ; S1 (z) = 1,0 +
Generically, a certain component of the overall load is
obtained by:
+ [ 2,5 – z/d] tg (θ - 3º) ≥ 1
F = Cf q Aa
θ ≤ 45º S1 (z) = 1,0 +
Where:
Cf = force coefficient, specified in each case: Cx
1
Cy1,
+ [ 2,5 – z/d] 0,31 ≥ 1
etc
A= reference area, specified in each case
[linear interpolation for 3º< θ < 6º < 17< θ
<45]
4.3 Determining the dynamic effects of the wind
To determine the dynamic effects dynamic effects due to
atmospheric turbulence, see calculation steps in
Chapter 9 and examples in Appendix 1.
Where:
5
d = level difference between the base and the
top of the slope or hill.
Profile velocity of the wind
Z = Mean height from ground surface in the point
considered
5.1 Basic velocity the wind V0
The is basic velocity the wind V01 is the velocity of a
gust, exceeded on average, once in 50 years, at 10 m
above ground, in flat open country.
Note: Figure 1 show the isopleths graph of the basic
velocity in Brazil, with 5m/s intervals (see Appendix C)
Θ = mean inclination of the slope or hill side
Note: Between A and B and B and C, the factor S1 is
obtained by linear interpolation.
c)
deep valleys, protected from the wind of any
direction : S1 = 0,9
5.1.1 As a rule, it is assumed that the basic wind can
blow from any horizontal direction.
The values indicated in 5.2-b) and 5.2-c) are an initial
approach and must be considered with precaution by.
5.1.2 In case of doubt concerning to the selection of the
basic velocity, and in extremely important works, a
specific study is recommended to determine V0. In that
case, preferential directions can be considered for the
basic wind, provided that they are properly justified.
If a more accurate knowledge of the topography is
necessary, or if the complexity of the topography makes
it difficult for the application of these indications, wind
tunnel procedure on topographic models, or
anemometric measures on the terrain in question are
recommended.
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Vo = in m/s
Vo = maximum mean velocity on 3s, which
can be exceeded on average once
in 50 years, at 10 m above ground
level in a flat open plane
Figure 1 - Isopleths of the basic velocity Vo (m/s)
7
NBR 6123/1988
a) Talude: Slope
b) Morro: Hill
Figure 2 - Topographic Factor S1 (z)
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NBR 6123/198
5.3 Roughness of the terrain, edification dimensions
and height above ground: Factor S2
The mean height of the top of the obstacles is equal to
3,0m.
The factor S2 considers the combined effect of the
roughness of the terrain, the variation of the wind
velocity with the height above ground and the edification
dimensions, or part of the edification dimensions, or part
of the edification in question.
Category lV; Terrain covered by plenty of obstacles and
not sparse, in forest, industrial or urbanized zones.
Examples;
For strong winds in neutral stability, the wind velocity
increases with the height above ground. This increase
depends on the roughness of the terrain and the time
interval considered to determine the velocity. This time
interval is related to the edification dimensions, as small
edifications and edifications elements are more affected
by short length gusts than the big edifications. For these
ones, it is more appropriate to consider mean wind
calculated with a larger time interval.
-
zones of parks and woods with lots of trees;
-
small towns and surrounding areas;
-
suburbs of large cities, densely built;
-
industrial areas, fully or partially developed.
The mean – height for the top of the obstacles is equal
to 10m.
5.3.1 Roughness of the terrain
This category also includes zones with larger obstacles,
which still cannot be considered in category V.
This Norm ranks the roughness of the terrain in five
categories (2) :
Category V: terrain covered by numerous, large, tall and
not sparse obstacles. Examples:
Category l: smooth surfaces of large dimensions, with
more that 5 km of extension, measured in the direction
of the acting wind. Examples:
-
calm sea (3) :
-
lakes and rivers;
-
forests with tall trees, with isolated crown
trees;
-
central areas f large cities;
-
developed industrial complexes.
The mean height for the top of the obstacles is equal or
greater than 25m.
-
swamps without vegetation.
5.3.2 Edification dimensions
Category ll: Open even terrain, or reasonably even, with
scattered obstacles, such as trees and low edifications.
Examples:
-
flat coastal zones;
-
swamps with thin vegetation;
-
aviation fields;
-
prairie and moor;
-
farm with fence or walls.
Wind velocity varies continuously and its mean value
can be calculated on any time interval. It has been
confirmed that the shortest interval of the usual
measures (3s) corresponds to gusts whose dimensions
envelope properly obstacles up to 20 m in the direction
of the mean wind.
The longer the time interval used for the calculation of
the mean velocity, the longer the distance covered by
the gust.
In order to define the actions of the wind, it is necessary
to consider the building or no structural continuity along
the edification, such as:
The mean height of the obstacle tops is considered less
than or equal to 1,0m.
-
Category lll : Flat or undulated terrain with obstacles,
such as fence or walls, few windbreaks of trees, low and
sparse edifications. Examples:
edifications with junctions separating the
structure in two or more structurally
independent parts,
-
edifications with low rigidity in the direction
perpendicular to the wind, therefore, with low
capacity for load distribution.
(2)
(3)
-
granges, country houses, except for the parts
with woods;
-
farms with fence or walls;
-
suburbs, considerably far from the downtown,
with low and sparse houses
According to the designer, intermediate categories can be considered, with proper interpolation of the values of p and b or of S2
indicated in 5.3.3, or in Appendix A
For rough sea, the value of the exponent p for 1 h can achieve 0,15, for very strong wind. Usually, p = 0,12
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NBR 6123/198
The following classes of edifications were chosen, parts
of edification and its elements, with time interval for the
calculation of the mean velocity of, respectively, 3 s, 5 s
and 10 s:
always considering the gust factor Fr corresponding to
category II. The expression above is applicable until the
height zg, that defines the upper frame of the
atmospheric layer.
Class A: All cladding units, their fixing elements and
individual parts of structures without cladding.
All the edification whose horizontal or vertical
dimension does not exceed 20m.
The parameters that permit the determination of S2 for
the five categories in this Norm are presented on Table
1.
Class B: All the edification or part of edification to which
the biggest horizontal or vertical dimension of
the frontal surface is between 20m and 50m.
The values of S2 for the several categories of terrain
roughness and dimension classes of the edifications
defined in this Norm are given on Table 2.
Class C: All edification or part of edification to which the
biggest horizontal or vertical dimension of the
frontal surface exceeds 50m.
For the study of cladding elements, it is recommended
the use of factor S2, corresponding to the top of
edification. This recommendation is based on the fact
that in the windward façade and in the lateral façades,
the wind is deflected downwards; consequently increase
of the dynamic pressure in the lowest part of the
edification. For the same reason, the factor S2 is
considered constant up to10m high in category V.
For all the edification or part of edification to which the
biggest horizontal or vertical dimension of the frontal
surface exceeds 80m, the corresponding time interval
can be determined according to the indication in
Appendix A.
5.3.3.1 The Appendix A indicates the determination of
factor S2 for time intervals between 3 s e 1h and for any
terrain roughness.
5.3.3 Height above ground
The factor S2 used in the calculation of the wind velocity
in a height z above the general ground level is obtained
by the expression
S2 = b Ft (z/10)º,
Table 1 - Meteorological parameters
Zg
Classes
Parameter
Category
A
B
C
b
1,10
1,11
1,12
p
0,06
0,065
0,07
b
1,00
1,00
1,00
Ff
1,00
0,98
0,95
p
0,085
0,09
0,10
b
0,94
0,94
0,93
p
0,10
0,105
0,115
b
0,86
0,85
0,84
p
0,12
0,125
0,135
b
0,74
0,73
0,71
p
0,15
0,16
0,175
(m)
I
II
III
IV
V
250
300
350
420
500
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Table 2 - Factor S2
Category
Z
I
II
III
IV
V
(m)
Class
Class
Class
Class
Class
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
≤5
1,06
1,04
1,01
0,94
0,92
0,89
0,88
0,86
0,82
0,79
0,76
0,73
0,74
0,72
0,67
10
1,10
1,09
1,06
1,00
0,98
0,95
0,94
0,92
0,88
0,86
0,83
0,80
0,74
0,72
0,67
15
1,13
1,12
1,09
1,04
1,02
0,99
0,98
0,96
0,93
0,90
0,88
0,84
0,79
0,76
0,72
20
1,15
1,14
1,12
1,06
1,04
1,02
1,01
0,99
0,96
0,93
0,91
0,88
0,82
0,80
0,76
30
1,17
1,17
1,15
1,10
1,08
1,06
1,05
1,03
1,00
0,98
0,96
0,93
0,87
0,85
0,82
40
1,20
1,19
1,17
1,13
1,11
1,09
1,08
1,06
1,04
1,01
0,99
0,96
0,91
0,89
0,86
50
1,21
1,21
1,19
1,15
1,13
1,12
1,10
1,09
1,06
1,04
1,02
0,99
0,94
0,93
0,89
60
1,22
1,22
1,21
1,16
1,15
1,14
1,12
1,11
1,09
1,07
1,04
1,02
0,97
0,95
0,92
80
1,25
1,24
1,23
1,19
1,18
1,17
1,16
1,14
1,12
1,10
1,08
1,06
1,01
1,00
0,97
100
1,26
1,26
1,25
1,22
1,21
1,20
1,18
1,17
1,15
1,13
1,11
1,09
1,05
1,03
1,01
120
1,28
1,28
1,27
1,24
1,23
1,22
1,20
1,20
1,18
1,16
1,14
1,12
1,07
1,06
1,04
140
1,29
1,29
1,28
1,25
1,24
1,24
1,22
1,22
1,20
1,18
1,16
1,14
1,10
1,09
1,07
160
1,30
1,30
1,29
1,27
1,26
1,25
1,24
1,23
1,22
1,20
1,18
1,16
1,12
1,11
1,10
180
1,31
1,31
1,31
1,28
1,27
1,27
1,26
1,25
1,23
1,22
1,20
1,18
1,14
1,14
1,12
200
1,32
1,32
1,32
1,29
1,28
1,28
1,27
1,26
1,25
1,23
1,21
1,20
1,16
1,16
1,14
250
1,34
1,34
1,33
1,31
1,31
1,31
1,30
1,29
1,28
1,27
1,25
1,23
1,20
1,20
1,18
300
-
-
-
1,34
1,33
1,33
1,32
1,32
1,31
1,29
1,27
1,26
1,23
1,23
1,22
350
-
-
-
-
-
-
1,34
1,34
1,33
1,32
1,30
1,29
1,26
1,26
1,26
400
-
-
-
-
-
-
-
-
-
1,34
1,32
1,32
1,29
1,29
1,29
420
-
-
-
-
-
-
-
-
-
1,35
1,35
1,33
1,30
1,30
1,30
450
-
-
-
-
-
-
-
-
-
-
-
-
1,32
1,32
1,32
500
-
-
-
-
-
-
-
-
-
-
-
-
1,34
1,34
1,34
5.4 The statistic factor S3
The statistic factor S3 is based on statistic concepts, and
considers the safety degree required and the life span of the
edification. According to the definition in 5.1, the basic
velocity V0 is the wind velocity which presents a mean
recurring period of 50 years. The probability that the velocity
V0 is equaled or exceeded in this period is of 63%
destined to be dwellings, hotels, offices, etc (group 2). In
case of non-existence of a specific Norm about safety in
edification, or pertinent indications in the structural Norm, the
minimum values for factor S3 are the indicated on Table 3.
5.4.1 Appendix B indicates the determination of factor S3 for
other levels of probability and for other periods of exposition
of the edification to the wind load.
The probability level (0,63) and the life span (50years)
adopted are considered appropriate for Normal edification
Table 3 – Minimum values of the statistic factor S3
Group
Description
S3
1
Edification whose total or partial ruin can affect the safety or
possibility of help to people after a destructive storm (hospitals,
fire brigade quarters and security forces, communication centers,
etc).
Edifications for hotels and residences. Edifications for commerce
and industry with high occupation factor.
Edification and industrial facilities with low occupation factor
(Claddings, silos, rural building, etc).
Vedações (tiles, glasses, cladding panels, etc).
1,10
2
3
4
5
Temporary edifications structures of groups 1 to 3 during the
construction.
1,00
0,95
0,88
0,83
11
NBR 6123/198
5.5 Changes in the roughness of the terrain
5.5.1 If there is a change in the terrain category, with the
roughness length changing from Z01 to Z02, the wind will
run a certain distance before a new profile is established
in full for the mean velocities, with height Zg; The change
in the profile starts near the ground, and the new profile
increases its height Zx, as the distance X measure from
the category changing line grows. This profile of mean
velocities is determined as follows.
5.5.1.2 Transition for a category of lower roughness (Z01
> Z02)
The height Z is determined by the expression
Zg = A Z02 (x/ Z02 ) 0,8
Where :
A = 0,73 – 0,03 In (Zg / Z02 )
5.5.1.1 Transition for a Category of higher roughness
(Z01 < Z02)
The profile of the mean velocities (factors S2) is defined
this way (see Figure 3-b):
The heights Zx and Zi are determined by the expression
Zx = A Z02 ( x/ Z02 ) 0,8
a)
from height Zx above, the factors S2 are
considered, corresponding to the terrain farther
from the edification (Z01);
b)
from height Z below, the factors S2 are
considered, corresponding to the terrain
surrounding the edification , not exceeding,
however, the value of S2 determined in height Zx
for the terrain of roughness Z01;
Zy = 0,36 Z02 ( x/ Z02 ) 0,75
Where :
A = 0,63 – 0,03 In (Z02 / Z01 )
The profile of the mean velocities (factors S2) is defined
this way (see Figure 3-a):
a)
from height Zx above, the factors S2 are
considered, corresponding to the terrain farther
from the edification (Z01);
b)
from height Z below, the factors S2 are
considered, corresponding to the terrain
surrounding the edification (Z02);
5.5.2 The boundary layer height, Zg in the profiles of
mean velocity fully developed, the roughness lengths Z
are the following.
Category
c)
l
ll
lll
lV
V
Zg (m):
250
300
350
420
500
Z0 (m):
0,005
0,07
0,30
1,0
2,5
in the transition zone, between Z and Zx , consider
a new linear variation of factor S2
Perfil para:
Figure 3 – Profile of S2 at leeward of a roughness change.
12 NBR 6123/198
6 Aerodynamic
coefficients
for
current
edifications (also see Appendix E and F)
6.1 External form and pressure coefficients
6.1.1Values for external form and pressure coefficients for
several types of edifications and for critical directions of the
wind are given on Tables 4-8 and on Figures and Tables in
Appendix E and F. Surfaces where considerable pressure
variations occur were subdivided, and coefficients are given
for every part.
6.1.2 High suction zones appear near openings of walls
and roofs, being located according to the incidence angle of
the wind. Therefore, these high suctions do not appear in
these zones simultaneously, having specific Tables
presenting mean values of external pressure coefficients
(Cpe mean). These coefficients must only by used for the
calculation of wind loads on the respective zones,
applicable to the dimension, verification and anchorage of
cladding elements and the secondary structure.
6.1.3 For the calculation of cladding elements and fixing
parts to structural members, the factor S2 corresponding to
class A must be used, with the mean value of Ce or Cpe
applicable to the zone in which the respective element is
located. For calculation of the main structural members, the
factor S2 corresponding to classes A, B or C must be used,
with the value of Ce applicable to the zone in which the
respective structural member is located.
6.1.4 In order to determine the external pressures in a
cylindrical edification of circular cross-section, the values of
Cpe given on Table 9 must be used. These coefficients
apply only to air flow above the critical area, that is to say,
for the Reynolds number Re > 420000 and with the wind
acting perpendicularly to the axis of the cylinder, of
diameter d. the Reynolds number is determined by the
expression:
Re = 70000Vrd”
For Vk in meters per second and d in meters
6.1.5 The coefficients on Table 9 apply to vertical axis
cylinder (stacks, silos, gasometers, reservoirs, etc),
provided that, for the last situation, the free distance
between the cylinder and the ground is not smaller than the
cylinder diameter. These coefficients depend on the relation
h/d, between the cylinder length and its diameter, in case of
free action of the wind on one end of cylinder only. In case
of free wind action on both ends of the cylinder, the value of
h to be considered for the calculation of the relation h/d
must be half of the cylinder length.
6.1.6 The coefficients on Table 9 also apply to the cases
in which the terrain is subdivided by flat horizontal and
vertical surfaces, sufficiently long relatively to the crosssection of the cylinder, so as to produce flow conditions
similar to the ones proved by the wind.
6.2 Internal pressure coefficients
6.2.1 If the edification is totally air tight, the pressure in its
interior will not vary in time and regardless the velocity of
the external air flow. However, the walls and/ or roofs of the
edification are usually considered as closed, in Normal
operational conditions, and as a consequence of accidents,
allow the air glow to pass, provoking a change in the test
desired conditions. While the permeability does not exceed
the limits established in 6.2.3, it is presumable that the
external pressure shall be calculated according to the
specifications below.
6.2.2 This Norm considers impermeable the following
building element and claddings: cover-slabs and reinforced
or concrete curtain walls; masonry, stone, brick, block walls
and similar, without doors, windows or any other openings.
The other constructive elements and claddings are
considered permeable. Permeability occurs due to the
presence of openings, such as panel junctions in walls and
tiles, breaches in doors and windows, ventilation in tiles and
roofs, openings of doors and windows, stacks, etc.
6.2.3 The permeability index of one part of the edification
is defined by the relation between the area of the openings
and the overall area of that part. This index must be as
accurate as possible. As a general indication, the typical
index of permebeability of edification for offices or dwelling,
with all doors and windows closed, lies within 0,01% and
0,05%. In order to apply items in 6.2, except for the case of
dominant opening, no wall or roof slope permeability index
can exceed 30%. This index must be determined carefully,
as the changes in permeability during the edification life
span, may lead to harmful loading values.
6.2.4 This Norm considers the dominant opening the one
whose area is greater or equal to the total area of the
openings which make up the permeability considered on all
external surface of the edification (including the roofing, in
case of permeable or inexisting sheathing). This dominant
opening can occur by accident, such as the breaking of
fixed glasses caused by wind pressure (over pressure or
suction), by objects thrown by the wind or other reasons.
6.2.5 For edifications with permeable internal walls, the
internal pressure can be considered uniform. In this case,
the following values must be adapted for the internal
pressure coefficient Cpi:
a) two opposing faces equally permeable; the
other
impermeable faces:
- wind perpendicular to one permeable face:
Cpi = + 0,2;
- wind perpendicular to one impermeable face:
Cpi = - 0,3;
13
NBR 6123/1988
b) four faces equally permeable: Cpi = -0,3
or 0 (consider the most harmful value);
c) dominant opening in one face: the other faces equally
permeable:
- dominant opening in the windward face.
Ratio between the area of all the openings in the windward
face and the total area of the openings in all the faces
(walls and roof, according to the conditions in 6.24)
undergoing external suction:
6.2.6 For effectively air-tight edifications and with fixed
windows which have a negligible probability of being broken
by accident, consider the most harmful of the following
values:
Cpi = -0,2 or 0
6.2.7 When unnecessary or impossible to determine with
reasonable accuracy the permeability relation of 6.2.5-c),
the same value for the external form coefficient shall be
taken for the internal pressure coefficient, C,, (for wind
incidence between 0° and 90°), indicated in this No rm for
the dominant opening zone, both in walls and in roofs.
1…………………………………………………… Cpi = +0,1
1,5 ……………………………………………….. Cpi = +0,3
2 …………………………………………………. . Cpi = +0,5
3 …………………………………………………. . Cpi = +0,6
6 or more ……….………………………………. . Cpi = +0,8
- dominant opening in the leeward face.
6.2.8 Roof openings will influence the efforts on the walls
when the sheathing is permeable (natural porosity,
trapdoors and illumination boxes not air-tight, etc) or
inexisting. Otherwise, openings will only be considered for
the study of the roof structure of the sheathing itself.
6.2.9 The value of Cpi can be limited or monitored
positively by deliberate distribution of permeability in the
walls and roof, or by a ventilation device acting as a
dominant opening, placed with proper external pressure
value. Examples of such devices:
Take the value of the external form coefficient, Ce’,
corresponding to this face (see Table 4).
- dominant opening in a face parallel to the wind.
- ridges with ventilation in roofs undergoing suctions
for all wind directions, provoking reduction of the
ascensional force on the roof;
- Dominant opening not located in a zone of high external
suction.
Take the value of the external form coefficient C”,
corresponding to the opening place in this face (see Table
4).
- Dominant opening located in a zone of high external
suction.
Ratio between the dominant opening area (or area of the
openings located in this zone) and the total area of the
other openings located in all the faces undergoing external
suction:
- permanent openings in the walls parallel to the wind
direction and located near the windward edges (high
external suction zones), provoking considerable
reduction of the ascensional force the roof.
6.2.10 In the application field of Table 9, in order to
calculate the wind loads on the wall of a cylindrical
edification, when there is an open top, the following values
for Cpi must be taken:
h/d ≥ 0,3……………………………………… Cpi = -0,8
h/d < 0,3……………………………………… Cpi = -0,5
0,25………………………………………… Cpi = -0,4
0,50 ………………………………………. ..Cpi = -0,5
0,75…………………………………………. Cpi = -0,6
1,0 ………………………………………….. Cpi = -0,7
1,5 …………………………………………..Cpi = -0,8
3 or more ……….…………………………..Cpi = -0,9
High external suction zones are hachured on Tables 4 and
5 mean Cpe.
6.2.11 For the cases not covered in 6.2.5 to 6.2.7, the
internal pressure coefficient can be determined according
to the indication in Appendix D.
14 NBR 6123/1988
Table 4 - External pressure and form coefficients for walls of edifications of rectangular plan
Values of Ce for
α= 0°
Relative height
0,2 or h (the
smaller)
α= 90°
Mean Cpe
A1 + B 1
A2 + B2
C
D
A
B
C1 + D1
C2 + D2
1≤a≤ 3
b 2
-0,8
-0,5
+0,7
-0,4
+0,7
-0,4
-0,8
-0,4
-0,9
2 ≤ a/b ≤ 4
-0,8
-0,4
+0,7
-0,3
+0,7
-0,5
-0,9
-0,5
-1,0
1≤a≤ 3
b 2
-0,9
-0,5
+0,7
-0,5
+0,7
-0,5
-0,9
-0,5
-1,1
2 ≤ a/b ≤ 4
-0,9
-0,4
+0,7
-0,3
+0,7
-0,6
-0,9
-0,5
-1,1
1≤a≤ 3
b 2
-1,0
-0,6
+0,8
-0,6
+0,8
-0,6
-1,0
-0,6
-1,2
2 ≤ a/b ≤ 4
-1,0
-0,5
+0,8
-0,3
+0,8
-0,6
-1,0
-0,6
-1,2
h≤1
b 2
1/2 ≤ h/b ≤ 3/2
3/2 ≤ h/b ≤ 6
b/3 ou a/4 ( o maior dos dois, porem 2h) : b3/a4 (the biggest, however 2 h)
2h ou b/2 ( o menor dos dois ): 2h or b2 (the smallest)
c)
Notes: a) For a/b between 3/2 and 2, proceed linear interpolation
b) For wind at 0º, on parts A3 and B3, the form coefficient Ce, has the
following values:
-
for a/b = 1: the same value for parts A2 and B2;
-
for a/b ≥ 2: Ce = -0,2
-
for 1 < a/b < 2: linear interpolation
d)
For each one of both wind incidences (0º or 90º), the mean external
pressure coefficient Cpe, is applied to the windward part of the walls
parallel to the wind, at a distance equal to 0,2b or h, considering the
smaller value.
To determine the drag coefficient, Ca, the graph on Figure 4 (low
turbulence wind) or Figure 5 (high turbulence wind – see 6.5.3) must
be used.
15
NBR 6123/1988
Table 5 - External form and pressure coefficients, for roofs with two slopes, symmetric, in edification with rectangular
Relative height
h/b ≤ ½
1/2 ≤ h/b ≤ 3/2
3/2 ≤ h/b ≤ 6
θ
Values of Ce for
α=90°
(A)
plan.
Mean Cpe
α= 0°
EF
GH
EG
FH
0°
5º
10º
-0,8
-0,9
-1,2
-0,4
-0,4
-0,4
-0,8
-0,8
-0,8
-0,4
-0,4
-0,6
-2,0
-1,4
-1,4
-2,0
-1,2
-1,4
15º
20º
30º
-1,0
-0,4
0
-0,4
-0,4
-0,4
-0,8
-0,7
-0,7
-0,6
-0,6
-0,6
-1,4
-1,0
-0,8
-1,2
45º
60º
0°
5º
10º
+0,3
+0,7
-0,8
-0,9
-1,1
-0,5
-0,6
-0,6
-0,6
-0,6
-0,7
-0,7
-1,0
-0,9
-0,8
-0,6
-0,6
-0,6
-0,6
-0,6
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-1,5
-1,5
15º
20º
30º
-1,0
-0,7
0,2
-0,6
-0,5
-0,5
-0,8
-0,8
-0,8
-0,6
-0,6
-0,8
-1,8
-1,5
-1,0
-1,5
-1,5
-1,5
-1,5
-1,2
-1,0
-1,0
45º
60º
0°
5º
10º
+0,2
+0,6
-0,8
-0,8
-0,8
-0,5
-0,5
-0,6
-0,6
-0,6
-0,8
-0,8
-0,9
-0,8
-0,8
-0,8
-0,8
-0,7
-0,8
-0,8
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-1,5
-1,5
--1,0
-1,2
15º
20º
30º
-0,8
-0,8
-1,0
-0,6
-0,6
-0,5
-0,8
-0,8
-0,8
-0,8
-0,8
-0,7
-1,8
-1,5
-1,5
-1,8
-1,5
-1,5
-1,5
-1,2
-1,2
40º
50º
60º
-0,2
+0,2
+0,5
-0,5
-0,5
-0,5
-0,8
-0,8
-0,8
-0,7
-0,7
-0,7
-1,0
-2,0
-1,2
--1,0
-1,2
-1,2
-1,2
-1,1
-1,1
-1,1
--1,0
-1,2
Detalhe 1: Detail 1
Notes:
a)
b)
c)
d)
The form coefficient Ce in the lower face of the is
equal to the one of the corresponding wall.
In the zones around the past of the edification
salient to the roof (stacks, reservoirs, towers,
etc), consider a form coefficient Ce = 1,2, up to a
distance equal to half of the dimension of the
diagonal seen in plan.
In the special eave roof, the mean Cpe = -2,0
For the wind at 0º, in the parts I and J, the form
coefficient Ca has the following values:
a/b = 1: the same value of the parts F and H; a/b
≥ 2 :Ca = -0,2
Linear interpolation for the intermediate values
of a/b.
Vento: Wind
b/3 ou a/4 ( o Maior dos dois porém ≤ 2 ): b/3 or
a/4 (the biggest of both, however ≤ 2)
y=h ou 0,15 b ( o menor dos dois ): y=h ou 0,15
b the smallest of both
16 NBR 6123/1988
Table 6- External pressure and form coefficients, for one-slope, in edifications with rectangle plan, with h/b <2
Vento: Wind
Corte AA: section AA
Y = h or 0,15b (take the smaller value)
Surfaces H and L refer to the whole respective quadrant
Θ
Values of Ce the incidence angle of the wind
90 º (C)
H
5º
10º
15º
20º
25º
30º
-1,0
-1,0
-0,9
-0,8
-0,7
-0,5
45º
L
-0,5
-0,5
-0,5
-0,5
-0,5
-0,5
H
0º
L
-1,0
-1,0
-1,0
-1,0
-1,0
-1,0
-0,9
-0,8
-0,7
-0,6
-0,6
-0,6
-45º
HeL
HeL
(A)
(B)
-1,0
-1,0
-1,0
-0,9
-0,8
-0,8
-0,5
-0,5
-0,5
-0,5
-0,5
-0,5
-90 º
H
L
H
L
-0,9
-0,8
-0,6
-0,5
-0,3
-0,1
-1,0
-1,0
-1,0
-1,0
-0,9
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0
-1,0
-1,0
-1,0
-1,0
-0,9
-0,6
Mean Cpe
θ
5º
10º
15º
20º
25º
30º
H1
-2,0
-2,0
-1,8
-1,8
-1,8
-1,8
H2
L1
L2
He
Le
-1,5
-1,5
-0,9
-0,8
-0,7
-0,5
-2,0
-2,0
-1,8
-1,8
-0,9
-0,5
-1,5
-1,5
-1,4
-1,4
-0,9
-0,5
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
-2,0
(A) up to a depth equal to b/2
(B) from b/2 to a/2
(C) consider symmetrical values to the other side of symmetry axis parallel to the wind.
Note: for winds at 0º, in parts I and J, referring to the respective quadrants, the form coefficients Ce has the following values:
a/b = 1, the same value of the parts H and L a/b = 2 Ce = -0,2. Proceed linear interpolation for intermediate values of a/b.
17
NBR 6123/1988
Table 7 - External pressure and form coefficients for multiple roofs, symmetric with equal trusses with h ≤ a
Vento: wind
y = h or O,1b (take the smaller value)
y = b or O,1ba (take the smallest of the three values)
Roof
inclination
Incidence
angle of
the wind
Ce
Mean Cpe
First
truss
First
intermediate
truss
θ
α
5º
10º
20º
30º
45º
Roof
inclination
0º
<45º
Last truss
a*
b*
c*
d*
m*
n*
x*
z*
-0,9
-1,1
-0,7
-0,2
+0,3
-0,6
-0,6
-0,6
-0,6
-0,6
-0,4
-0,4
-0,4
-0,4
-0,4
-0,3
-0,3
-0,3
-0,3
-0,4
-0,3
-0,3
-0,3
-0,2
-0,2
-0,3
-0,3
-0,3
-0,3
-0,4
-0,3
-0,3
-0,3
-0,2
-0,2
-0,3
-0,4
-0,5
-0,5
-0,5
Incidence
angle of
the wind
θ
Other
intermediate
trusses
-2,0
-1,5
Ce in the distance
α
b1
b2
b3
90º
-0,8
-0,6
-0,2
Notes: a) Friction forces:
- for α = o°, the horizontal friction forces must be deter mined according to the Table values;
- for α = 90°, the horizontal friction forces must be dete rmined according to 6.4.
b) Information about multiple roofs are still incomplete Cases different from the ones considered on Tables 7 and 8 and
Appendix F, must be studied separately.
18 NBR 6123/1988
Table 8 - External pressure and for coefficients for multiple, asymmetric, of equal trusses roofs, with
1
smaller slope inclination of 60° and h ≤ a
y = h or O,1 b (take the smaller value)
y = b or O,25 ba (take the smallest of the three values)
b1 = b2 = h
Ce
Incidence
angle of the
wind
First
truss
First
intermediate
truss
Other
intermediate
trusses
Last truss
α
a*
b*
c*
d*
m*
n*
x*
z*
0º
+0,6
-0,7
-0,7
-0,4
-0,3
-0,2
-0,1
-0,3
180º
-0,5
-0,3
-0,3
-0,3
-0,4
-0,6
-0,6
-0,1
Incidence
angle of
the wind
Mean Cpe
-2,0
-1,5
Ce in the distance
b1
b2
b3
-0,8
-0,6
-0,2
α
90º
Notes: a) Friction forces:
- for α = o°, the horizontal friction forces must be deter mined according to the Table values;
- for α = 90°, the horizontal friction forces must be dete rmined according to 6.4.
b) Information about multiple roofs are still incomplete cases different from the ones considered on Tables 7 and 8 and
Appendix F, must be studied separately.
19
NBR 6123/1988
Table 9 - External pressure distribution on cylindrical edifications of circular cross-section
External pressure coefficient Cpe
β
0°
10°
20°
30°
40°
50°
60°
70°
80°
90°
100°
120°
140°
160°
180°
Rough surface with salience
Smooth surface
h/d=10
h/d≤2,5
h/d=10
h/d≤2,5
+1,0
+0,9
+0,7
+0,4
0
-0,5
-0,95
-1,25
-1,2
-1,0
-0,8
-0,5
-0,4
-0,4
-0,4
+1,0
+0,9
+0,7
+0,4
0
-0,4
-0,8
-1,1
-1,05
-0,85
-0,65
-0,35
-0,3
-0,3
-0,3
+1,0
+0,9
+0,7
+0,35
0
-0,7
-1,2
-1,4
-1,45
-1,4
-1,1
-0,6
-0,35
-0,35
-0,35
+1,0
+0,9
+0,7
+0,35
0
-0,5
-1,05
-1,25
-1,3
-1,2
-0,85
-0,4
-0,25
-0,25
-0,25
6.3 Drag coefficients
The drag coefficients indicated in this item are applicable to
bodies of constant or slightly variable cross- sections.
6.3.1 For wind acting perpendicular to each one of the
façades of edification rectangular in plan and set on
ground, the graph on Figure 4 must be used, or, for the
exceptional case of high turbulence wind (according to the
requirements in 6.5.3), the graph of Figure 5. The drag
coefficients are given, in those Figures, according to the
relations h/lt and lt / l2
6.3.2 The drag coefficients given on Table 10 depend on
the relation h/l, between the length of the body and the
reference dimensions l, and, in several cases, the Reynolds
number, expressed by:
6.3.4 If the wind can pass freely through both ends of the
body, the value of h to be considered for the calculation of
the relation h/lt must be half the length of body. If the body
is confined in both ends by surfaces, long enough relatively
to the transversal cross-section of the body the relation h/l,
is considered infinite. If the confinement in the previous
conditions exists in only one end, the value h to be
considered for the calculation of the end, the value h l1
must be the real length of the body.
6.3.5 Although the values given on Table 10 refer to closed
bodies, they can be applied to bodies with one end open,
such as stacks, since the relation h/lt is superior to 8.
6.3.6 The drag force is calculated by the expression:
Fa= Ca q Ae
Re= 70000 Vk lt (Vk in m/s; l1 in m).
The coefficients are applicable to bodies of vertical axis and
set on the ground on a flat surface, with extension enough
(relatively to the section transversal to the body) to originate
flow conditions similar to the provoked by the terrain
6.3.3 The coefficients on Table 10 are also applicable to the
case of horizontal axis bodies, since the free distance
between the body and the terrain (or equivalent surface) is
not smaller than the reference dimension l1. The wind is
considered acting perpendicularly to the axis of the body, of
length h.
For the cases where the coefficient Ca depends on the
Reynolds number, it may result more adverse the adoption
of a velocity inferior to the profile velocity, because the
reduction of the dynamic pressure q can be overcome by
the increase of the drag coefficient Ca.
20 NBR 6123/198
Vento: wind
Figure 4 - Drag coefficient Ca^ for parallelepiped edifications under low turbulence wind
6.4 Frictional coefficient
6.4.1 In certain edifications, a friction force (force in the
direction of the wind, originated from the roughness and
ribs) must be considered, in addition to the ones calculated
according to 6.1 and 6.2.
6.4.2 For current edifications of rectangular plan, this
friction force must be considered only when the relation l2/h
or l2/li is greater than 4. for these edifications, the friction
force F1 is given by:
F1 = Cp q l1 (l2 – 4 h) + Cp q 2 h (l2 -4 h), if h ≤ l1
And by
F1 = Cp q l1 (l2 – 4 l1) + Cp q 2 h (l2 -4 l1), if h ≥ l1
In each formula, the first term of the second member
corresponds to the friction for on the roof, and the second
term, to the frictional force on the walls.
The terms are given separately in order to permit the use of
different values of Cp and q in the several surfaces.
6.4.3 The values of Cp are the following:
a) Cf = 0,01 for surfaces without ribs transversal to
the wind direction;
b) Cf1 = 0,02 for surfaces with round ribs
(undulations) transversal to the wind direction;
c) Cf1 = 0,04 for surfaces with rectangular ribs
transversal to the wind direction.
6.4.4 For isolated roofs, the friction force is determined
according to the indications in 8.2.
21
NBR 6123/1988
6.5 Reductions in the form and drag coefficients
6.5.1 Generally, the aerodynamic coefficients given in this
Norm were obtained from tests in which the air flow was
moderately mild, similar to the flat open ground wind (low
turbulence wind). In the high turbulence wind present in
large cities, there is a reduction of suction on the leeward
wall of parallelepiped edifications, therefore presenting
reduction of the respective coefficients, except for
edifications with a depth/ width ratio of 1/3 or less.
The effects of the neighborhood are only considered
up to the height of the to of the edification (s) located
nearby, within a circle whose diameter is equal to the
height of the identification in question, or equal to six
times the smallest side of the edification, b, taking the
smaller of these two values.
7 Force coefficients for prismatic bars and
reticulated structures
7.1 Prismatic bars
6.5.2 For parallelepiped edifications, exposed to high
turbulence wind, the following reductions are accepted:
a) form coefficient on the leeward wall: consider 2/3 of
the value given on Table 4 ( wall B for α =90º and
wall D for α = 0º);
7.1.1 The force coefficients refer to prismatic with
infinite length (two-dimension flow). For prismatic bars
with finite length, the force coefficients must be
multiplied by on factor K that depends on the relation l /
Cα , for :
b) drag coefficient: use the graph of Figure 5.
l = length of the prismatic bar
6.5.3 Edification can be considered under high turbulence
wind when its height does not exceed in two times the
mean height of the surrounding edifications, these ones
lying in the direction of the acting wind, at a minimum
distance of:
-
500 m for edification up to 40 m high;
-
1000m for edification up to 55 m high;
-
2000m for edification up to 70 m high;
-
3000m for edification up to 70 m high;
Note: Values for the reduction factor K are given on
Table 11.
7.1.2 When a prismatic bar is connected to a plate or
wall in a way that impedes the free air flow around this
end of the bar, the relation l/cα must be doubled to
determine k. When both ends of the prismatic bar are
obstructed this way, the relation l/cα must be
considered infinite.
6.6 Eccentricity of drag forces
6.6.1 The effects of the eccentricity of drag forces must be
considered, when appropriate.
6.6.2 For parallelepiped edifications, the design must
consider:
- the wind loads acting perpendicularly to each of the
façades, according to the specifications in this
Norm;
-
-
Cα = width of the prismatic bar measured in
perpendicular direction to the wind (orthogonal
projection of the bar section on a straight perpendicular
to the wind direction – (see note b on Table 12).
the eccentricities caused by the wind acting
obliquely, or by the effect of the neighborhoods.
The torsion efforts generated are calculated
considering the loads, acting respectively, with the
following eccentricities , in relation to the vertical
geometric axis;
edifications not affected by the effects of the
neighborhood:
7.1.3 Bars whose dimensions and wind profile velocity
are under a flow characteristic above critical, may
demand additional calculations to check if the larger
loads do not occur with wind velocity below maximum,
under a sub-critical flow characteristic.
7.2 Prismatic bars of flat faces
The force coefficients and given on Table 12 refer to
two directions mutually perpendicular, x and y, as
indicated in the Figure.
The force coefficients refer to the wind acting
perpendicularly to the longitudinal axis of the bar. The
corresponding loads are calculated by:
-
load in the direction X = Fx = Cx q k l c;
-
load in the direction y = Fy = Cx q k l c
7.3 Prismatic bars of circular cross-section
ea= 0,075a and cf = 0,075b
-
edifications affected by the
neighborhood:
effects
of
the
ea= 0,15a and cf = 0,15b1,
for ea measured in the direction of the smallest side, a,
and eb measured in the direction of the smallest side b.
For circular cross-section prismatic bars, the drag
coefficients Ca depend on the Reynolds number, Re, an are
given on Table 13. The values of Ca given in this Table
apply to all the roughness surfaces distributed uniformly, of
height smaller than 1/100 of the diameter d of the bars, that
is to say, are valid for all Normal surface sheathing.
7.3.1 The drag is calculated by:
Fa = Ca q k l d;
22 NBR 6123/1988
Table 10 - Drag coefficient Ca, for bodies of constant cross-section
Wind perpendicular to the plan of the Figure
h/ll
(A)
Re
X
-5
10
1/2
1
2
5
10
20
Smooth (metal,
concrete
masonry)
≥ 3,5
≥ 4,2
0,7
0,5
0,7
0,5
0,7
0,5
0,8
0,5
0,9
0,5
1,0 1,2
0,6 0,6
With roughness
or salience =
0,02 l1
All
0,7
0,7
0,8
0,8
0,9
1,0 1,2
0,8
0,8
0,9
1,0
1,1
1,2 1,4
≥ 4,2
≥7
0,5
0,2
0,5
0,2
0,5
0,2
0,5
0,2
0,6
0,2
0,6
0,2
≤7
≥8
0,8
0,8
0,8
0,8
0,9
0,9
1,0
1,0
1,1
1,1
1,3 1,7
1,3 1,5
r/l = 1/3
≤ 3,5
≥ 4,2
0,6
0,4
0,6
0,4
0,6
0,4
0,7
0,4
0,8
0,5
0,8 1,0
0,5 0,5
l1/ l2 = 1
≤7
≥8
0,7
0,5
0,8
0,5
0,8
0,5
0,9
0,5
1,0
0,6
1,0 1,3
0,6 0,6
≤2
≥ 3,5
0,3
0,2
0,3
0,2
0,3
0,2
0,3
0,2
0,3
0,3
0,3 0,4
0,3 0,3
Plan
With roughness
or salience =
0,08 l1
Ellipse
l1/ l2 = 1/2
Ellipse
l1/ l2 = 2
l1/ l2 = 1
∞
values
All
values
0,7
0,2
r / l1 = 1/6
l1/ l2 = 1/2
r / l1 = 1/2
23
NBR 6123/1988
To be continued
/ continuation
h/ll
(A)
Re
X
-5
10
Plant
l1/ l2 = ½
r / l1 = 1/6
l1/ l2 = 2
r / l1 = 1/2
l1/ l2 = 2
r / l1 = 1/4
r / a =1/3
r / a =1/12
∞
1/2
1
2
5
10
20
0,5
0,5
0,5
0,5
0,6
0,6 0,7
0,9
0,9
1,0
1,1
1,2
1,5 1,9
≤ 3,5
≥ 4,2
0,7
0,5
0,8
0,5
0,8
0,5
0,9
0,5
1,0
0,5
1,2 1,6
0,6 0,6
≤ 4,2
≥ 6
0,8
0,5
0,8
0,5
0,9
0,5
1,0
0,5
1,1 1,3
0,5 0,5
0,9
0,9
0,9
1,1
1,2
1,3 1,6
0,7
0,4
0,7
0,4
0,7
0,4
0,8
0,4
0,9
0,5
1,0 1,2
0,5 0,5
0,7
0,7
0,7
0,4
0,7
0,4
0,8
0,4
0,8
0,8
0,8
1,0
1,1
1,2 1,4
0,7
0,7
0,8
0,9
1,0
1,1 1,3
All
values
All
values
1,5
0,6
All
values
r / a =1/48
All
values
r / l1 = 1/4
r / l1 = 1/ 12
≤7
≥ 10
0,9
0,5
1,0 1,2
0,5 0,5
All
values
All
r / l1 = 1/48
values
24 NBR 6123/1988
/to be continued
/continuation
h/ll
(A)
Re
X
-5
10
Plant
r / l1 = 1/4
≤5
≥7
20
∞
1,1
0,5
1,3
0,5
1,6
1,7
2,1
0,9
0,7
1,0
0,8
1,1
0,9
1,3
1,1
1,2
1,2
1,3
1,4
1/2
1
2
5
0,7
0,4
0,7
0,4
0,8
0,4
0,9
0,4
1,2
1,2
1,2
1,4
0,7
0,7
0,7
0,7
0,8
0,7
1,0
1,0
1,1
10
1,0
0,5
All
1/48< r / l1 < 1/ 12
DODECAGON
l1/ l2
values
≤5
≥ 12
All
OCTAGON
l1/ l2
values
(A)
Linear interpolation for intermediate Re numbers:
Re = 70000 Vk l 1(VK in m/s; l1 in m)
Vento: wind
Figure 5 - Drag coefficient, Ca, for edifications parallelepiped under high turbulence wind
25
NBR 6123/1988
Table 11 - values of the reduction factor, K, for finite length bars
l/cα or l/d
Prismatic bars of circular cross-section under
subcritical regime
(Re < 4,2. 105)
Prismatic bars of circular cross-section under
above critical regime
(Re ≥ 4,2. 105)
Prismatic bars of flat faces
2
5
10
20
40
50
100
∞
0,58
0,62
0,68
0,74
0,82
0,87
0,98
1,0
0,80
0,80
0,82
0,90
0,98
0,99
1,0
1,0
0,62
0,66
0,69
0,81
0,87
0,90
0,95
1,0
Table 12 - Force coefficients, Cx and Cy, for prismatic bars of flat faces of infinite length
α
Cx
+ 1,9
+ 1,8
+ 2,0
- 1,8
- 2,0
Cy
+ 0,95
+ 0,8
+ 1,7
- 0,1
+ 0,1
Cx
+ 1,8
+ 2,1
- 1,9
- 2,0
- 1,4
Cy
+1,8
+1,8
.1,0
+0,3
-1,4
Cx
+1,75
+0,85
+0,1
-0,75
-1,75
Cy
+0,1
+0,85
+1,75
+0,75
-0,1
Cx
+1,6
+1,5
-0,95
-0,5
-1,5
Cy
0
-0,1
+0,7
+1,05
0
0°
45º
90º
135º
180º
Cx
+2,0
+1,2
-1,6
-1,1
-1,7
Cy
0
+0,9
+2,15
+2,4
+-2,1
Cx
+2,5
+1,85
0
-1,6
-1,8
Cy
0
+0,6
+0,6
+0,4
0
Cx
+1,4
+1,2
0
-
Cy
0
+1,6
+2,2
-
Cx
+2,05
+1,95
+0,5
-
Cy
0
+0,6
+0,9
-
α
Cx
Cy
Cx
Cy
Cx
Cy
Cx
Cy
0°
45º
90º
+1,6
+1,5
0
0
+1,5
+1,9
+2,0
+1,8
0
0
+0,1
+0,1
+2,1
+1,4
0
0
+0,7
+0,75
+2,0
+1,55
0
0
+1,55
+2,0
0°
45º
90º
135º
180º
α
Notes: a) In this Table, the force coefficients Cx and Cy are
given in relation to the dimension C, and not, as in the other Tables, in
relation to the effective frontal area Ae.
b) The dimension Cα is used to determine the reduction factor K (see Table 11)
VENTO: WIND
26 NBR 6123/198
table 13 – Drag coefficients, Ca1 for circular cross-section prismatic bars
and with infinite length
Flow profile (Re = 70000 Vk d)
Ca
[Vk in m/s; d in m]
Re < 4,2 . 105
Subcritical
1,2
5
Above
5
4,2 . 10 ≤ Re < 8,4 . 10
0,6
critical
8.4 . 105 ≤ Re < 2,3 . 106
0,7
Re ≥ 2,3 . 105
0,8
7.4 Wires and cables
For wires and cables, the drag coefficients Ca depend on
the Reynolds number value Re, and are given on Table 14:
r1 = radius of the secondary wires and cables of the
external layer of the cable
d = diameter of the defined circle of the section of the
wire or cable
l = wire or cable length
Where:
Ae = frontal area of the reticulate: area of orthogonal
projection of the bars of the reticulated structure
on a plane perpendicular to the wind direction
The graph in Figure 6 gives the values of the drag
coefficient Ca for a flat reticulate structure formed by
prismatic bars of flat faces, and the graph on Figure 7 gives
values of Ca for a flat reticulated structure formed by
circular cross-section bars. The index of the exposed area
ø is equal to the effective frontal area of the reticulated
structure divided by the frontal area of the surface limited
by the reticulate frame.
In reticulated structures made of circular cross-section
bars, the Reynolds number is obtained by.
7.4.1 For wires and cables perpendicular to the wind, the
force is calculated by:
Fa = Ca q l d
Re = 70000 Vkd (Vk in m/s; d in m)
Where:
If the direction of the wind (assumed horizontal) form an
angle α with the chord of the wire or cable, the load Fy1,
perpendicular to the chord, is calculated by:
Fy = Fa sen2 α
The load Fx1 in the direction of the chord is negligible.
7.5 Isolated flat reticulated structures
d = diameter of the truss bars
For reticulated structure made of flat face prismatic bars
and/or circular cross-section bars of one or more
diameters, the respective coefficients are applied
proportionally to the frontal areas of the respective bars
(areas of orthogonal projections of the bars on a plane
perpendicular to the direction of the wind – “shade area”).
The index of the exposed area always refers to the group of
all bars of the reticulated structure.
This Norm considers as reticulated structure every
structure made of straight bars.
7.5.1 The drag force is calculated by:
Fa = Ca q Ae
Flow profile
(Re = 70000 Vk d)
[Vk in m/s; d in m]
Table 14 - Drag force coefficient Ca1 for wires and cables with l/d > 60
Drag coefficient Ca for:
Smooth wire
Slightly smooth
Twisted cables
Twisted cables of
Wire
of thin wires
thick wires
(galvanized or)
painted)
r’d ≤ 1/30
r’d ≥ 1/25
Re ≤ 2,5 . 104
-
-
1,2
1,3
4
Re ≥ 4,2 . 10
-
-
0,9
1,1
Re ≤ 2,5 . 105
1,2
1,2
-
-
5
0,5
0,7
-
-
Re ≥ 4,2 . 10
For Re and r’/d intermediate, the values of Ca are obtained by interpolation
27
NBR 6123/1988
Figure 6 – Drag coefficient, Ca for flat reticulated structures formed by prismatic bars with salient corners or slightly
rounded
7.6 Multiple flat reticulated structures
Where:
This section applies to structures made of two or more
parallel flat reticulated members, equidistant and of
parallel sets, where the windward reticulate can have a
protective effect on the other reticulated structures.
The windward reticulate and all the parts of the other
reticulated structures are protected by the first and
must be calculated as indicated in 7.5. The wind loads
on the protected parts of the reticulated structures
must be multiplied by one protection factor η (see
Figure 8), which depends on the index of the exposed
area of the reticulate, located right at the windward of
the reticulate under study, and the respective relative
distance e/h.
Aa= effective frontal area of one face of the
reticulated tower: area of orthogonal projection of the
bars of one of the faces of the reticulated tower over a
plane parallel to this face.
7.6.1 For n reticulated, structures equal and equally
separate the drag coefficient of the group of n
reticulated structures, Can1 is obtained by:
Can = Ca1 [1+ (n-1)n]
7.7.2.1 For reticulate towers made of prismatic bars of
flat faces, with salient corners or slightly rounded, the
Values of the drag coefficient, Ca1, for the wind acting
perpendicularly to one of the faces, are given in the
graphs in Figure 9.
For reticulated towers of square cross-section, the drag
coefficient for the wind acting with an angle α in
relation to the perpendicular to the windward face, Caα ,
is obtained by:
Caα = Ka Ca
Where:
Where:
Ka = 1 +αº /125 ………..0º < α ≤ 20º
Ca1 = drag coefficient of one isolated reticulate,
determined according to 7.5.
Ka = 1, 16 ……………..20º ≤ α ≤ 45º
7.6.2 the drag force of the group of n reticulated
structures is calculated by:
Fan = Can q Ae
7.7 Reticulated towers
7.7.1 Reticulate towers of triangular cross-section can
be calculated according to 7.6, for wind acting
perpendicularly to each pair of parallel faces. The wind
load over the faces parallel to direction of the wind is
considered inexistent.
7.7.2 Reticulated towers of square or equilateral
triangular cross-section, whit reticulated structures of
equal faces, are special cases for which it may be
convenient to determine the overall wind load directly.
For those cases, the drag force is calculated by:
Fa = C a q A a
For reticulated towers of equilateral triangular crosssection the wind load can be admitted constant for any
incidence angle of the wind.
7.7.2.2 For reticulated towers made of prismatic bars of
circular section, the values of the drag force coefficient
ca, are given in the graphs in Figures 10 to 12.
7.7.2.3 In case of reticulate towers made of prismatic
bars of flat faces and/or of circular cross-section bars
of one or more diameters, the respective coefficients
are applied proportionally to the frontal areas of the
respective bar. The index of the exposed area always
refers to the group of all bars of one of the faces of the
tower.
7.7.2.4 The components of the drag force, Fa, on the
faces of the tower, are obtained multiplying Fa, by the
values given on Table 15,
28 NBR 6123/1988
Figure 7 - Drag coefficient, Ca for flat reticulated structure made of circular cross-section
prismatic bars
NBR 6123/1988
Vento: Wind
Ca1 = Ca Treliça isolada: Ca1 = Ca Isolated truss
Vento: Wind
Figure 8 - Protection factor, η, for two or more flat reticulated structures parallel equally distant
Vento: wind
Vento de qualquer direção: Wind of any direction
Figure 9 - Drag coefficient, Ca for reticulated towers of square and equilateral triangular cross-section
made of prismatic bars with salient corners or slightly rounded corners
29
30 NBR 6123/1988
Figure 10 - Drag coefficient, Ca1 for reticulated towers of square cross-section, made of circular section
bars-Wind acting perpendicularly to both parallel faces
Figure 11 - Drag coefficient, Ca1 for reticulated towers of square cross-section, made of circular crosssection bars-Wind acting according to a diagonal
31
NBR 6123/1988
Vento de qualquer direção: Wind of any direction
Figure 12 - Drag coefficient, Ca1 for equilateral triangular cross-section, made of circular cross-section
bars-Wind of any direction
Table 15 - Components of the drag force on the faces of reticulated towers of square or equilateral
triangular cross- section
Wind direction
Face I
Face II
Face III
Face IV
0
η__
l+η
0
0
0
0
0
N
0,20
0,20
0,15
0,15
T
0,20
0,20
0,15
0,15
N
0,57
0,11
0,11
__
T
0
0,19
0,19
__
N
0,50
0
0,37
__
T
0,29
0
0,21
__
N
0,14
0,14
0,43
__
T
0,25
0,25
0
__
N
l__
l+η
T
n : component perpendicular to the face
t : component parallel to the face
Note: The components of the drag force, Fa, are obtained multiplying Fa by the values given in this Table, where η is the
protection number defined in 7.6.
32 NBR 6123/1988
8 Force coefficients for walls, plates and isolated
roofs
8.1.1 The load F acts perpendicularly to the plane of the
wall or plate.
8.1 Rectangular walls and plates
8.1.2 Table 16 classifies the wall or plate according to the
flow conditions in their edges. Except for wall or plate under
two-dimension flow, the most adverse incidence of the verb
is oblique. This incidence and the application point of F are
given in this Table.
The wind load on a rectangular wall or plate is calculated
by:
F = Cf q A
8.1.3 The wall or plate is considered in two-dimension flow
when l/h > 60, in the absence of plates or walls-placed
parallel to the flow – in their ends, or when l/h ≥ 10, in case
of the presence of plates or walls in the conditions
mentioned before.
Where:
Cf = force coefficient, according to Table 16
q = dynamic pressure of the wind on the top of the wall
or plate
8.1.4 For intermediate values of l/h – without plates or
walls in the ends – and for ground distances between 0 and
0,25h, of Cf are obtained by linear interpolation.
A = area of the face: A = l h
l = length of the wall or plate
h = length of the wall or plate
Table 16 - Force Coefficients, Cf1 for rectangular walls and plates
l/h 50 (without end plates)
l/h 10 ( with end plates)
l/h = 10
l/h = 1
33
NBR 6123/1988
8.2 Isolated flat slope roofs
8.2.1 For isolated roofs, that is, roofs on supports of small
dimensions, which do not represent considerable obstacle
to the air flow, the wind load acts directly on the upper and
lower faces of the roof.
8.2.2 For isolated one or two slope roofs, flat, where the
free height between the ground and the lowest horizontal
ridge level of the roof meets the requirements in 8.2.3, and
for wind acting perpendicularly to the roof generarix, apply
the coefficients indicated on Tables 17 and 18. These
Tables give the values and directions of the pressure
coefficients, which comprise the actions perpendicular to
both faces of the roof. In cases where two loadings are
indicated, both respective load situations must be
considered independently.
8.2.3 The coefficients on Tables 17 and 18 apply only
when the following requirements are met:
- one-slope roofs (Table17): 0 ≤ tgθ ≤ 0,7,
h ≥ 0,51 l2;
- two-slope roofs (Table18): 0,07 ≤ tgθ ≤ 0,6,
h ≥ 0,51 l2;
where
8.2.7 In case of reticulated structures exposed directly to
the wind, the indications in 7.5 (isolated flat reticulated
structures) and in 7.6 (multiple flat reticulated structures)
must be adopted.
8.2.8 For
existing flanges along the roof, flat or
approximately flat, a uniformly distributed pressure must be
considered, with resulting load calculated by:
F = 1,3 q Ae, for the windward flange
F = 0,8 q Ae , for the leeward flange
for Ae being the effective frontal area of the plates and
elements alike which make the flange under study. The
previous expressions are valid for flanges which form, in
relation to the vertical, an angle of 30° at most. The loads
calculated this way comprise the pressures acting on both
flange faces, perpendicular to the wind direction.
8.2.9 For flanges parallel to the wind direction, friction
horizontal loads must be considered, calculated by the
expression:
Fat = 0,05 q Ae
and applied to the middle height of the flanges. These loads
comprise the wind acting on both faces of the flanges.
h = free height between the ground and the lowest
horizontal ridge of the roof
8.2.10 Each protective element must be calculated with
Cp = ±2,0.
l2 = depth of the roof
9 Dynamic effects due to atmospheric turbulence
θ = inclination angle of the roof slopes
9.1 General Provisions
8.2.4 In cases where the height h is inferior to the limit
established in 8.2.3, or when obstructions can be placed
under or near the roof, this must resist to the wind load, in
the obstruction zone, calculated for a closed edification and
of same roof, with Cpi = +0,8, for obstructions on the
leeward edge, and with Cpi = -0,3, for obstructions on the
windward edge.
8.2.5 For winds parallel to the roof generatrix, friction
horizontal loads must be considered by the expression:
For natural wind, the module and orientation of the instant
velocity of the air present fluctuations around the mean
velocity
, considered as gusts. Its is assumed that the
mean velocity stays constant during a time interval of 10
min or more, producing merely static effects on the
edifications, appointed as follows as mean response. On
the other hand the fluctuations of velocity can produce in
very flexible, especially tall and slender edifications,
important oscillations in the direction of the mean velocity,
here considered as fluctuant response.
Fat = 0,05 q a b
being a and b the roof plan dimensions. Theses loads
comprise the wind acting on the both faces of the roof.
8.2.6 Horizontal wind loads on plates placed above or
under the roof are calculated according to 8.1 (rectangular
walls and plates), the roof closed to the plate is considered
as the ground.
For edifications with a fundamental period T, equal or
smaller than 1 s, the influence of the fluctuant response is
less, having its effects considered in the determination of
the time interval adapted for the factor S2. However,
edifications with a fundamental period superior 1 s,
especially those weakly damped, can present important
fluctuant response in the direction of the mean wind. The
overall dynamic response, equal to the superposed
responses, mean and fluctuant, can be calculated
according to the specifications in this Chapter. Examples
are presented in Appendix I.
34 NBR 6123/1988
Table 17 - Pressure coefficient on isolated roofs with one flat slope
First loading
Second loading
Wind
Table 18 - Pressure coefficient on isolated roofs with two symmetric flat slopes
First loading
Second loading
Coefficien
ts
Positive directions
of the pressure
coefficients
9.2 Input data to determine the dynamic response in
the wind direction
9.2.1Design velocity
The design velocity, corresponding to the mean velocity
over 10 min at 10 m of height above ground, in category II
terrain, is obtained by:
Vp = 0,69 Va S1 S2
9.2.2 Dynamic profile of the structure
9.2.2.1Simplified continuous model
A simplified continuous model can be adapted for
edifications with constant section and mass distribution at
least roughly uniform. The simplified method is applicable
to structures supported exclusively on the base and with
height inferior to 150 m, being considered in their dynamic
response only the contribution of the fundamental mode.
Generally, the retention of the first mode only leads to
mistakes lower than 10%.
It is admitted that the first vibration mode can be
represented accurately by the equation:
x = (z/h)y
Table 19 presents approximate values of y and equations,
approximate too, which permit the direct calculation of the
fundamental frequency f1 (Hz) and y can be obtained
through the use of methods of the structure vibration
theory. The critical damping ratio is also indicated on Table
19, depending on the on type of structure.
9.2.2.2Discreet mode
For general cases of edification with variable properties
with the height, it must be represented by means of a
discreet model, according to the scheme of Figure 13, in
which:
Xi = displacement corresponding to the coordinate i;
A1 – area of influence corresponding to the coordinate i;
mi = discreet mass corresponding to the coordinate i;
Cai = drag coefficient corresponding to the coordinate i;
Zi = height of the element i above ground;
Zr = reference height: Zr = 10 m;
n - number of degrees of liberty (i = 1, 2,… n).
In case of vertical structure with a symmetry plane, n
is also equal to the number of elements by which the
structure is divided (se Figure 13)
Generally, a model with n = 10 is sufficient for an adequate
precision to be obtained in the results. A larger number of
elements can be necessary, if the edification presents
important variations in its profile. Once defined the structure
model, through the application of the structure vibration
theory, the following must be determined: the natural
frequency fj (Hz) and the modal form Xj, corresponding to
mode j, for j = 1,2,….r, being r < n the number of modes
that will be held in the solution. As indicated in 9.2.21, the
retention of an only mode (r = 1) is usually sufficient, except
in case of very slender edifications and/ or with rigidity
strongly variable. In these cases, the contributions of
modes 1,2, etc., must be computed successively, until the
equivalent loads associated to the last mode calculated (j =
r) are negligible.
The critical damping ratio is ζ is indicated on Table 19,
depending on the type of edification. Other values can be
adapted, if properly justified.
35
NBR 6123/1988
Table 19 - Parameters to determine the dynamic effects
Y
ζ
T1 = 1 /f1
1,2
0,020
0,05h + 0,015h
(h in meters)
1,6
0,015
0,05 + 0,012h
Concrete towers and stacks, variable cross-section
2,7
0,015
0,02h
Concrete towers, masts and stacks, uniform cross-section
1,7
0,010
0,015h
Building with welded steel structure
1,2
0,010
0,29 √ h – 0,4
Steel towers and stacks, uniform cross-section
1,7
0,08
--
0,030
Type of edification
Buildings with porch structure in concrete, without curtain
walls
Buildings with concrete structure, with curtain walls to
absorb horizontal loads
Structures in wood
Orientação do vetor velocidade média: average speed vector orientation
Figure 13 - Scheme for discreet dynamic model
9.3 Calculation of dynamic response in the direction of
the wind
9.3.1 Simplified method
The variation of the dynamic pressure with the height is
expressed by the equation:
in which the first term within brackets corresponds to the
mean response and the second represents the maximum
amplitude of the fluctuant response, being:
The exponent p and the coefficient b depend on terrain
roughness category, according to the indicated on Table
20. the dynamic amplification coefficient ζ, function of the
edification dimensions, the critical damping ratio ζ, the
frequency f (through the adimensional relation
/fL), is
presented in the graphs of Figures 14 to 18, for the five
categories of terrain roughness considered in this Norm.
The pressure q (z) is a continuous function of the height z
above ground. The equivalent static load, which comprises
the static dynamic pressures of the wind, by height unit
results equal to q (z) l1, Ca, being l, the width or diameter of
the edification.
36 NBR 6123/1988
9.3.2 Discreet model
9.3.2.2 Combination of the modal contributions
9.3.2.1 Determining modal contributions
Where r modes are held in the solution (r >1), the combined
effect can be computed by the criterion of the square root
of the sum of the square values. After the response for
each mode j ( j=1, …. r) is obtained, all the concerning
variables to each mode must be determined. By indicating
with Qj a certain static variable (load, flexure moment,
stress, etc), or geometric (deformation, displacement,
torsion), corresponding to the mode j, the superposing of
effects is calculated by:
For each vibration mode J, with components (Xi ) = Yi the
overall wind load Xi in the direction of the coordinate i is
given by:
Xi = Xi =Xi
in which the mean load Xi is equal to (symbols: see 9.2.2.2)
Xi = q°b2 Cai Ai [zi/zr]2p
For: q° =0,613 Vp2 (q° in N/m2, Vp m/s)
The equation above is applicable when the natural
frequencies fj (j = 1, …..r) are reasonably separate, that is
to say, when there are not frequencies very near.
b , p indicated in Table 20
9.4 calculation of the dynamic response transversal to
the wind.
A fluctuant component Xi is given by
The random fluctuations of the mean velocity of wind are
responsible for vibration of the structure in the direction
perpendicular to the direction of the mean flow. The
resulting solicitations Yi in the direction perpendicular to the
direction of the wind can be calculated from the effective
loads in the direction of the wind, by the expression:
Xi = FH Ψi Xi
For : Ψi =mi /m°
Yi = 1/3Xi
When necessary, the response in the lateral direction must
be added to the response due to vortex shedding.
9.4 Calculation of the maximum accelerations for
comfort analysis
ßi = Cai Ai /Ai [zi/zr]
p
In case of edifications for human occupation, the induced
oscillations induced by fluctuating loads can provoke
discomfort for the people. If uj denotes the displacement
of the level z due to the fluctuating response on the mode
j, the maximum acceleration amplitude at this level can be
calculated by the expression;
In the equations above, m° and A° denote arbitrary
reference mass and area ξ, is the dynamic amplification
coefficient, presented on Figures 14 to 18 for the five
terrain categories in this Norm. For situations not
comprised by these Figures, ξ can be determined by
interpolation or extrapolation.
aj = 4 π 2 fj2 uj2
As a general indication, the maximum amplitude cannot
exceed 0,1 m/s2. The comfort analysis must be carried out
for the wind velocities with larger probability to occur than
the structural velocity, to be defined by the designer. It is
acceptable that the maximum amplitude of acceleration is
exceeded, on average, once every ten years.
Table 20 - Exponent p and parameter b
Category
l
ll
lll
lV
V
of
roughness
p
0,095 0,15 0,185 0,23 0,31
b
1,23
1,00
0,86
0,71 0,50
NBR 6123/1988
Figure 14 – Dynamic amplification coefficients, ζ for terrain of category I (L = 1800m; h in
meters)
37
38 NBR 6123/1988
Figure 15 – Dynamic amplification coefficients, ζ for terrain of category II (L = 1800m; h in
meters)
NBR 6123/1988
Figure 16 – Dynamic amplification coefficients, ζ for terrain of category III (L = 1800m; h in
meters
39
40 NBR 6123/1988
Figure 17 – Dynamic amplification coefficients, ζ for terrain of category IV (L = 1800m; h in
meters
NBR 6123/1988
Figure 18 – Dynamic amplification coefficients, ζ for terrain of category V (L = 1800m; h in
meters
41
42 NBR 6123/1988
Appendix A – Normalized velocity S2 and time interval
A.1 Factor S2
The profile velocity is defined by:
The factor S2 can be considered as an admensional
velocity, Normalized in V0:
Vkj = V0 S1 S2 S3
Regardless of the roughness categories defined in this
Norm, the factor S2 can be obtained by the expression>
Where:
S = b Frll (z/10)º
i = category of terrain roughness
= mean velocity over seconds, in height z above
ground, for the category i (not considering factors S1 and
S3)
Values for the parameters b, b Frll and p, for several time
intervals and five categories in this Norm are presented on
Table 21. The corresponding values to S2 are presented on
Table 22.
Table 21 - Parameters b, p, FrII
cat
I
II
III
IV
V
t(s)
3
5
10
15
20
30
45
60
120
300
600
3600
b
1,10
1,11
1,12
1,13
1,14
1,15
1,16
1,17
1,19
1,21
1,23
1,25
p
0,06
0,065
0,07
0,075 0,075
0,08
0,085 0,085
0,09
0,095 0,095
0,10
b
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
p
0,085
0,09
0,10
0,105
0,11
0,115
0,12
0,125 0,135 0,145
0,15
0,16
Fr
1,00
0,98
0,95
0,93
0,90
0,87
0,84
0,82
0,77
0,72
0,69
0,65
b
0,94
0,94
0,93
0,92
0,92
0,91
0,90
0,90
0,89
0,87
0,86
0,85
p
0,10
0,105 0,115 0,125
0,13
0,14
0,145
0,15
0,16
0,175 0,185
0,20
b
0,86
0,85
0,83
0,83
0,82
0,80
0,79
0,76
0,73
0,71
0,68
p
0,12
0,125 0,135 0,145
0,15
0,16
0,17
0,175 0,195 0,215
0,23
0,25
b
0,74
0,73
0,71
0,70
0,69
0,67
0,64
0,62
0,58
0,53
0,50
0,44
p
0,15
0,16
0,175 0,185
0,19
0,205
0,22
0,23
0,255 0,285
0,31
0,35
0,84
A.2 Time interval
To determine the time interval t, to be used to obtain the
mean velocity of the wind acting on edification, or part of
edification with the largest horizontal or vertical dimension
of the frontal surface exceeding 80m, the following
expression can be used;
T = 7,5 L/Vt (h)
Where :
L= height or width of the frontal surface of the edification
or part of edification under study, taking the larger
value
Vt(h) = Mean velocity of the wind over t seconds, on the
top of the edification or part of edification under study
– Vt(h) = S1 S2(h) V0
The calculation of Vt(h) can be done by successive
approximations.
43
NBR 6123/1988
Table 22 – Normalized velocity S2
cat
Z
(m)
10
15
20
30
3
1,06
1,10
1,13
1,15
1,17
5
1,04
1,09
1,12
1,14
1,17
10
1,01
1,06
1,09
1,12
1,5
15
1,00
1,05
1,08
1,11
1,14
20
0,97
1,02
1,05
1,08
1,11
30
0,95
1,00
1,03
1,06
1,09
45
0,92
0,97
1,01
1,03
1,07
60
0,90
0,96
0,99
1,02
1,05
120
0,86
0,92
0,95
0,98
1,01
300
0,82
0,87
0,91
0,93
0,97
600
0,79
0,85
0,88
0,91
0,94
3600
0,76
0,81
0,85
0,87
0,91
40
50
60
80
100
1,20
1,21
1,22
1,25
1,26
1,19
1,21
1,22
1,24
1,26
1,17
1,19
1,21
1,23
1,25
1,17
1,19
1,20
1,23
1,25
1,14
1,16
1,17
1,20
1,22
1,12
1,14
1,15
1,18
1,20
1,09
1,11
1,13
1,16
1,18
1,08
1,10
1,12
1,14
1,17
1,04
1,06
1,08
1,10
1,13
0,99
1,02
1,03
1,06
1,08
0,97
0,99
1,01
1,03
1,06
0,93
0,97
1,00
1,02
120
140
160
180
200
250
1,28
1,29
1,30
1,31
1,32
1,34
1,28
1,29
1,30
1,31
1,32
1,34
1,27
1,28
1,29
1,31
1,32
1,33
1,27
1,28
1,29
1,31
1,32
1,33
1,24
1,25
1,26
1,27
1,28
1,31
1,22
1,24
1,25
1,26
1,27
1,29
1,20
1,21
1,23
1,24
1,25
1,27
1,19
1,20
1,21
1,23
1,24
1,26
1,15
1,16
1,18
1,19
1,20
1,22
1,10
1,12
1,13
1,15
1,16
1,18
1,07
1,09
1,10
1,12
1,13
1,15
1,04
1,06
1,07
1,08
1,10
1,12
≤5
10
15
20
30
0,94
1,00
1,04
1,06
1,10
0,92
0,98
1,02
1,04
1,08
0,89
0,95
0,99
1,02
1,06
0,86
0,93
0,97
1,00
1,04
0,83
0,90
0,94
0,97
1,02
0,80
0,87
0,91
0,94
0,99
0,77
0,84
0,88
0,91
0,96
0,75
0,82
0,86
0,89
0,94
0,70
0,77
0,81
0,85
0,89
0,65
0,72
0,76
0,80
0,84
0,62
0,69
0,73
0,77
0,81
0,58
0,65
0,69
0,72
0,77
40
50
60
80
100
1,13
1,15
1,16
1,19
1,22
1,11
1,13
1,15
1,18
1,21
1,09
1,12
1,14
1,17
1,20
1,08
1,10
1,12
1,16
1,18
1,05
1,07
1,10
1,13
1,16
1,02
1,05
1,07
1,11
1,13
0,99
1,02
1,04
1,08
1,11
0,98
1,00
1,03
1,06
1,09
0,93
0,96
0,98
1,02
1,05
0,88
0,91
0,93
0,97
1,01
0,85
0,88
0,90
0,94
0,97
0,81
0,84
0,87
0,91
0,94
120
140
160
180
200
250
300
1,24
1,25
1,27
1,28
1,29
1,31
1,34
1,23
1,24
1,26
1,27
1,28
1,31
1,33
1,22
1,24
1,25
1,27
1,28
1,31
1,33
1,21
1,23
1,24
1,26
1,27
1,30
1,33
1,18
1,20
1,22
1,24
1,25
1,28
1,31
1,16
1,18
1,20
1,21
1,23
1,26
1,29
1,13
1,15
1,17
1,19
1,20
1,24
1,26
1,12
1,14
1,16
1,18
1,19
1,23
1,25
1,08
1,10
1,12
1,14
1,15
1,19
1,22
1,03
1,06
1,08
1,09
1,11
1,15
1,18
1,00
1,03
1,05
1,06
1,08
1,12
1,15
0,97
0,99
1,01
1,03
1,05
1,09
1,12
≤5
10
15
20
30
0,88
0,94
0,98
1,01
1,05
0,86
0,92
0,96
0,99
1,03
0,82
0,88
0,93
0,96
1,0
0,78
0,86
0,90
0,93
0,98
0,75
0,83
0,87
0,90
0,95
0,72
0,79
0,84
0,87
0,92
0,68
0,76
0,80
0,84
0,89
0,67
0,74
0,78
0,82
0,87
0,61
0,69
0,73
0,77
0,82
0,55
0,63
0,67
0,71
0,76
0,52
0,59
0,64
0,67
0,73
0,48
0,55
0,60
0,63
0,69
40
50
60
80
100
1,08
1,10
1,12
1,16
1,18
1,06
1,09
1,11
1,14
1,17
1,04
1,06
1,09
1,12
1,15
1,02
1,05
1,07
1,11
1,14
0,99
1,02
1,05
1,09
1,12
0,96
0,99
1,02
1,06
1,09
0,92
0,96
0,98
1,02
1,06
0,91
0,94
0,97
1,01
1,04
0,86
0,89
0,91
0,96
0,99
0,80
0,83
0,86
0,90
0,94
0,77
0,88
0,83
0,87
0,91
0,73
0,76
0,79
0,84
0,88
120
140
160
180
200
1,20
1,22
1,24
1,26
1,27
1,20
1,22
1,23
1,25
1,26
1,18
1,20
1,22
1,23
1,25
1,17
1,19
1,21
1,23
1,24
1,14
1,17
1,19
1,21
1,22
1,12
1,15
1,17
1,19
1,20
1,08
1,11
1,13
1,15
1,17
1,07
1,10
1,12
1,14
1,16
1,02
1,05
1,07
1,09
1,11
0,97
0,99
1,02
1,04
1,06
0,94
0,97
0,99
1,01
1,03
0,91
0,94
0,96
0,98
1,01
250
300
350
1,30
1,32
1,34
1,29
1,32
1,34
1,28
1,31
1,33
1,26
1,29
1,31
1,24
1,27
1,30
1,21
1,24
1,27
1,20
1,23
1,26
1,15
1,18
1,21
1,10
1,14
1,17
1,08
1,11
1,15
1,05
1,09
1,12
≤5
I
II
III
S2
1,28
1,31
1,33
To be continued
44 NBR 6123/1988
Continuation
cat
Z
(m)
10
15
20
30
3
0,79
0,86
0,90
0,93
0,98
5
0,76
0,83
0,88
0,91
0,96
10
0,78
0,80
0,84
0,88
0,93
15
0,70
0,77
0,82
0,85
0,90
Values of S2 for t (s)
20
30
45
0,67
0,64
0,60
0,74
0,71
0,67
0,79
0,76
0,72
0,83
0,80
0,76
0,88
0,85
0,81
60
0,57
0,65
0,70
0,73
0,79
120
0,51
0,59
0,63
0,67
0,73
300
0,45
0,53
0,57
0,61
0,67
500
0,42
0,49
0,54
0,57
0,63
3600
0,37
0,44
0,49
0,53
0,58
40
50
60
80
100
1,01
10,4
1,07
1,10
1,13
0,99
1,02
1,04
1,08
1,11
0,96
0,99
1,02
1,06
1,08
0,94
0,97
1,00
1,04
1,08
0,92
0,95
0,98
1,02
1,06
0,89
0,92
0,95
0,99
1,03
0,85
0,88
0,91
0,96
0,99
0,83
0,86
0,89
0,93
0,97
0,77
0,80
0,83
0,88
0,92
0,71
0,74
0,77
0,82
0,86
0,67
0,71
0,74
079
0,83
0,62
0,66
0,69
0,74
0,78
120
140
160
180
200
1,16
1,18
1,20
1,22
1,23
1,14
1,16
1,18
1,20
1,21
1,12
1,14
1,16
1,18
1,20
1,11
1,13
1,16
1,17
1,19
1,08
1,11
1,13
1,15
1,17
1,06
1,09
1,11
1,13
1,15
1,03
1,05
1,08
1,10
1,12
1,00
1,03
1,05
1,07
1,09
0,95
0,98
1,00
1,03
1,05
0,90
0,93
0,95
0,98
1,00
0,87
0,90
0,93
0,95
0,97
0,82
0,85
0,88
0,91
0,93
250
300
400
420
1,27
1,29
1,32
1,31
1,35
1,25
1,27
1,30
1,32
1,33
1,23
1,26
1,29
1,32
1,33
1,23
1,26
1,29
1,32
1,33
1,21
1,24
1,27
1,30
1,31
1,19
1,23
1,26
1,29
1,30
1,16
1,20
1,23
1,26
1,27
1,14
1,17
1,21
1,24
1,25
1,10
1,13
1,17
1,20
1,21
1,05
1,09
1,13
1,16
1,17
1,03
1,07
1,11
1,14
1,16
0,99
1,03
1,07
1,10
1,12
≤ 10
15
20
30
40
0,74
0,79
0,82
0,87
0,91
0,72
0,76
0,80
0,85
0,89
0,67
0,72
0,76
0,82
0,86
0,68
0,70
0,74
0,80
0,84
0,62
0,67
0,71
0,77
0,81
0,68
0,63
0,67
0,73
0,77
0,54
0,59
0,63
0,69
0,73
0,51
0,56
0,60
0,65
0,70
0,45
0,50
0,53
0,59
0,64
0,38
0,43
0,46
0,52
0,57
0,34
0,39
0,43
0,48
0,53
029
0,33
0,36
0,42
0,46
50
60
80
100
120
0,94
0,97
1,01
1,05
1,07
0,93
0,95
1,00
1,03
1,06
0,89
0,92
0,97
1,01
1,04
0,88
0,91
0,96
1,00
1,03
0,84
0,87
0,92
0,96
1,00
0,81
0,84
0,89
0,93
0,97
0,77
0,80
0,85
0,89
0,93
0,74
0,77
0,82
0,86
0,90
0,67
0,71
0,76
0,80
0,84
0,60
0,64
0,69
0,74
0,77
0,57
0,60
0,66
0,70
0,75
0,50
0,54
0,59
0,64
0,68
140
160
180
200
250
1,10
1,12
1,14
1,16
1,20
1,09
1,11
1,14
1,16
1,20
1,07
1,10
1,12
1,14
1,18
1,06
1,09
1,11
1,13
14,18
1,03
1,05
1,08
1,10
1,15
1,00
1,03
1,05
1,08
1,13
0,96
0,99
1,02
1,04
1,09
0,93
0,96
0,99
1,01
1,07
0,88
0,91
0,93
0,96
1,01
0,81
0,84
0,87
0,90
0,96
0,78
0,81
0,84
0,87
0,94
0,72
0,75
0,79
0,82
0,88
300
350
400
450
500
1,23
1,26
1,29
1,32
1,34
1,23
1,26
1,29
1,32
1,34
1,22
1,26
1,29
1,32
1,34
1,22
1,26
1,29
1,32
1,34
1,19
1,22
1,25
1,26
1,31
1,17
1,21
1,24
1,27
1,30
1,14
1,15
1,19
1,22
1,25
1,11
1,15
1,19
1,22
1,25
1,05
1,11
1,14
1,18
1,21
1,01
1,05
1,09
1,13
1,17
0,99
1,04
1,08
1,12
1,16
0,94
0,99
1,04
1,08
1,12
≤5
IV
V
45
NBR 6123/1988
Appendix B – Statistic factor S3 for probability Pm and life span of the edification in m years
For V0 the wind velocity that has a probability Pm to be
exceeded, in the place in question, at least once in a period
of m years. This velocity corresponds to the gusts of 3s of
duration, on edification of roughness category II (see 5.3.1),
at 10m height above ground. The relation between V0 and
the basic velocity defined in 5.1 is the following:
In case of lack of a specific Norm on safety in edifications,
or indications corresponding to the structural Norm in use, it
is the designer’s attribution to set a probability Pm and a life
span m, according to the edification profile.
Table 23 shows typical values of the S3 factor, whose
mathematical expression is
V0 = S3 V0
S3 = 0,54 [ - In (1- Pm)]
m
0,157
Table 23 - Statistic factor S3
Values of S3 for Pm
m
2
10
25
50
100
200
0,10
0,20
0,50
0,63
0,75
0,90
0,86
1,10
1,27
1,42
1,58
1,77
0,76
0,98
1,13
1,26
1,41
1,57
0,64
0,82
0,95
1,06
1,18
1,31
0,60
0,78
0,90
1,00
1,11
1,24
0,57
074
085
0,95
1,06
1,18
0,53
0,68
0,79
0,88
0,98
1,09
Under any circumstance a factor S3 smaller than the one indicated on Table 3 (see 5.4) can be adopted.
46 NBR 6123/198
Appendix C – Location and altitude of the meteorological stations
The numbers close to the full circles which appear on
Figure 1 identify the meteorological stations of the
“Serviço de Proteção ao Vôo”, Ministério da
Aeronáutica, whose registers were the base for the
elaboration of isopleths of this Figure.
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
Station
Afonsos
Anápolis
Amapá
Belém
Belo Horizonte
Brasília
Bagé
Boa Vista
Caravelas
Cachimbo
Cuiabá
Campinas
Curitiba
Campo Grande
Carolina
Cumbica
Fortaleza
Florianópolis
Foz do Iguaçu
Fernando de Noronha
Goiânia
Jacareacanga
Londrina
Lapa
Manaus
Maceió
Natal
Ponta Porã
Parnaíba
Petrolina
Pirassununga
Porto Alegre
Porto Nacional
Porto Velho
Recife
Rio Branco
Rio de Janeiro (Santo Dumont)
Santarém
São Luiz
Salvador
Santa Cruz
São Paulo (Congonhas)
Santos
Santa Maria
Teresina
Uberlândia
Uruguaiana
Vitória
Vilhena
The following Table presents a list, in alphabetical order,
with these stations, as well as their geographic coordinates.
Latitude
22°52’S
16°22’S
02°04’N
01°23’S
19°51’S
15°52’S
31°23’S
02°50’N
17°38’S
09°22’S
15°30’S
23°00’S
25°31’S
20°28’S
07°20’S
23°26’S
03°47’S
27°40’S
25°31’S
03°51’S
16°38’S
06°16’S
23°20’S
13°16’S
03°09’S
09°31’S
05°55’S
22°33’S
02°54’S
09°24’S
21°59’S
30°00’S
10°42’S
08°46’S
08°08’S
09°58’S
22°51’S
02°26’S
02°35’S
12°54’S
22°56’S
23°37’S
23°56’S
20°43’S
05°05’S
18°55’S
29°47’S
20°16’S
12°44’S
Longitude
43°22’W
48°57’W
50°32’W
48°29’W
43°57’W
47°65’W
54°07’W
60°42’W
39°15’W
54°54’W
56°06’W
47°08’W
49°11’W
54°40’W
47°26’W
40°28’W
38°32’W
48°33’W
54°35’W
32°25’W
49°13’W
57°44’W
51°08’W
43°25’W
50°59’W
35°47’W
35°15’W
55°42’W
41°45’W
40°30’W
47°21’W
51°10’W
48°25’W
63°54’W
34°55’W
57°47’W
43°10’W
54°43’W
44°14’W
38°20’W
43°43’W
46°30’W
46°16’W
53°42’W
42°49’W
48°14’W
57°02’W
40°17’W
60°08’W
Height (m)
31
1097
10
16
789
1061
180
140
4
432
182
648
910
552
181
763
25
5
180
45
747
110
570
439
84
115
49
660
5
375
598
4
290
125
11
136
5
12
64
13
4
802
3
85
59
923
74
4
652
47
NBR 6123/1988
Appendix D – Determining the internal pressure coefficient
The air flow through a small opening of the area A is
given by:
Q=KApV
(D.1)
Where:
K = flow coefficient
V= wind velocity in the opening
∑n1 ± A p= √│Cpe - Cpi│= 0
(D.4)
The experience shows that the previous expression
can be applied to larger openings (Windows, doors,
gates, ventilations, spread permeability, etc), since the
mean pressure coefficients are not considered in the
outskirts of the opening. These mean coefficients,
which will be referred as C*e and C*I can be both form
coefficient (C*e e C*I ) and mean pressure coefficients,
given in this Norm or obtained from other sources.
With this generalization to (D.4), we have:
(D.2)
P= specific mass of the air, considered constant
(that is to say, the air is considered incompressible)
For a number n of openings, once the balance is
established, the air mass going into the edification will
be equal to the one going out. That is:
Q= 0
According to (D.1) and (D.2)
∑n1 K A p = √2│∆Pe -∆ Pi │/ p= 0
With due approximation, K can be considered
constant. Bear in mind that:
∆Pe = Cpe q
e ∆Pi = Cpi q
(D.3)
(D.5)
The root is considered positive for all the terms
corresponding to openings with air admission (C*e >
C*I ), and negative for openings with air outing (C*e <
C*I ), that is, the root will have the same sing of C*e C*I . The calculation can be done with successive
approximations, with arbitrary values for C*I .
Examples:
1st) determine Cpi on an intermediate floor of a building
with dimensions a x b x h = 40 x 15 x 60m. The
permeability and mean external coefficients (Ce, Table
4) are given on Figure 19.
a (D.3) is:
Vento: Wind
Figure 19 - Internal pressure on floor- type of building
48 NBR 6123/1988
Place
Ce
Opening
area
Cl
+0,4
+0,7
+0,75
2
(m )
A
B
C 1 e D1
C2 e D 2
6,00
0,60
0,23
0,23
+0,8
-0,6
-1,0
-0,6
∑=
Ce - Cl
± A√..
Ce - Cl
± A√..
Ce - Cl
± A√..
+0,4
-1,0
-1,4
-1,0
-
+3,79
-0,60
-0,27
-0,23
+2,69
+0,1
-1,3
-1,7
-1,3
-
+1,90
-0,68
-0,30
-0,26
+0,66
+0,05
-1,35
-1,75
-1,35
-
+1,34
-0,70
-0,30
-0,27
+0,07
2nd) Determining Cpi in an industrial pavilion, with
geometric and aerodynamic profile indicated on Figure
20.
The
roof
is
considered
impermeable.
By the sign of the last summation, considering one
decimal position Cpi = +0,8
Place
Opening
area
Ce
Cl
0
-0,2
0,15
2
(m )
A
B
EF
GH
80
80
16
16
+0,7
-0,5
-1,2
-0,4
∑=
Ce - Cl
± A√..
Ce - Cl
± A√..
Ce - Cl
± A√..
+0,7
-0,5
-1,2
-0,4
-
+66,9
-56,6
-17,5
-10,1
-17,3
+0,9
-0,3
-1,0
-0,2
-
+75,9
-43,8
-16,0
-7,2
+8,9
+0,85
-0,35
-1,05
-0,25
-
+73,8
-47,3
-16,4
-8,0
+2,1
By the sign of the last summation, considering one
decimal position, Cpi = -0,1
considered for all the openings. Otherwise, it will be
necessary to consider the effective pressures
It is worth applying the expression (D.5) when there is
only one reference dynamic pressure, or so it can be
dynamic pressure, or, for ∆Ppi
constant inside the edification.
Planta: Plant
Vento: wind
Altura real de ventilação: ventilation actual height
- no lanternin (I) 0,020m: ridge vent (I) 0,020m
- nas venezianas fixas (2): 1,00m: on fixed sub-blinds (2): 1,00m
Figure 20 – Internal pressure in industrial pavilion
49
NBR 6123/1988
Place
Opening
area
Ce
Cl
-0,4
-0,6
-0,5
-0,45
2
(m )
A
B
EF
GH
20
80
16
16
Ce - Cl
± A√..
Ce - Cl
Ce - Cl
Ce - Cl
± A√..
+1,1
-0,1
-0,8
0
-
+21,0
-25,3
-14,3
0
-18,6
+1,3
+0,1
-0,6
+0,2
-
+22,8
+25,3
-12,4
+5,1
+42,9
+1,2
0
-0,7
+0,1
-
+21,9
0
-13,4
+5,1
+13,6
+0,7
-0,5
-1,2
-0,4
∑=
Ce Cl
+1,15
-0,05
-0,75
+0,05
-
± A√..
+21,4
-17,9
-13,9
+3,6
-0,8
3rd) the same pavilion of the second example, but with only
one windward gate.
By the last sign of the summation, considering one decimal
position, Cpi = - 0,5.
To obtain the highest value for internal pressure, the gates
are considered closed.
4th) the same pavilion of the second example, but the
façade with fixed shutter located at windward.
Opening
area
Place
Ce
+0,4
Ce - Cl
± A√..
2
(m )
A
EF
GH
Cl
80
16
16
+0,7
-1,2
-0,4
∑=
By the sign the last summation and considering one decimal
position, Cpi = + 0,5.
Notes: a) Higher accuracy will be achieved if it is possible to
determine the mean value of the pressure coefficient
on the frame of each opening (gates, doors, windows,
fixed shutter, special ventilation tiles, etc).
b) The fourth example shows the beneficial effect of
the
special eave (open), which reduces in 0,2 the
internal pressure coefficient, which would be,
without it,
+0,3
-1,6
-0,8
-
+43,8
-20,2
-14,3
+9,3
+0,5
Ce - Cl
± A√..
+0,2
-1,7
-0,9
-
+35,8
-20,9
-15,2
-0,3
equal to the value of the external form coefficient in
the area of the opening: +0,7. The value indicated in
6.2.5 is a little higher (+0,8), because the dominant
opening predicted there can be in an area a
pressure superior to the average (+0,7).
C) Tests have shown that, both in rectangular plan
pavilions and domes, the presence of special eaves
causes the reduction of the lift coefficient, which is
between 0,2 and 0,3.
50 NBR 6123/1988
APPENDIX E – Aerodynamic coefficients for curved roofs
E.1 Circular cross-section barrel vaults
E.1.1 The external pressures on curved surfaces depend
on the location of the separation points of the flow, which
vary according to the wind velocity, turbulence profile,
dimensions and relation among the dimensions of the
edification, curvature of the roofing external surface and
its roughness, etc.
E.1.2 The pressure coefficients presented on Tables 24
and 26 are based on essays carried out with flows
approximately uniform and of low turbulence, with a
subcritical Reynolds number, but with the model roof with
rough external surface. These values, therefore, are not
entirely valid for the actual edifications, but can be
considered as a reference for the design. Special studies
must be performed in case of edifications of large
dimensions or which are different from the simple form
indicated on Figure 21.
a) Wind perpendicular to the generatrix of the roof
The pressure coefficients of Table 24 correspond to the
wind blowing perpendicularly to the generatrix of the roof.
The arch is divided into six equal parts, with the
coefficient considered constant in each of them.
The pressure coefficients of Table 25 correspond to the
wind blowing parallel to the generatrix of the roof.
The roof is divided, in the direction of the wind, into four
equal parts, with the pressure coefficient considered
constant in each of them.
Suction ends can occur with oblique wind. The
corresponding pressure coefficient is given on Table 26.
b) Parallel wind to the generatrix of the roof
Figure 21- Circular cross-section vaults with 0,5 l2 < l1 < 3 l2 (l1 and l2 of part “a” of this figure)
51
NBR 6123/1988
E.1.3 The pressure coefficients presented on Table 27 and 29
are based on tests carried out with turbulent air flow, with an
external surface roughness of the roof of the model defining
points of separation of the flow corresponding to Reynolds
numbers above the critical region. There values must be
considered with precaution, because the distribution of the
pressures in curved surfaces depend on several factors, as
indicated in E.1.1.
The value of b of these tests corresponds to the wind
over terrain of category between I and II.
The tested models had a smaller plan dimension, b, equal to
20 m (Series S1) and 50m (Series S2). The profiles of the
simulated winds are the following:
The pressure coefficients on Table 27 correspond to the
wind blowing perpendicularly to the generatrix of the roof.
The arch is divided into six equal parts; the pressure
coefficient is considered constant in each one of the six
parts (see Figure 22.a)
- Series S1 – l1 = 11% and L1 /b = 1,5 (constant with the
height).
Where:
l1 =
intensity of the longitudinal component of the
turbulence
L1 =
macro scale of this component
- Series S2 – l1 = 15,5% and L1 /b = 1,6 (on top of the
roof).
The simulate wind is within categories III and IV
(p=0,23).
The pressure coefficients on Table 28 correspond to the
wind blowing parallel to the generatrix of the roof. The
roof is divided, in the direction of the wind, into four parts,
according to Figure 22-b; the pressure coefficient is
considered constant in each on of the four parts.
The pressure coefficients on Table 29 correspond the
suction ends that can occur with oblique wind. These
coefficients are considered constant in the respective
ranges (see Figure 22 –c).
24 - External pressure coefficients, Cpe, for the wind blowing perpendicularly to the roof generatrix
Cpe
f/l2
h/l2
0
1/8
1/4
1/2
1
5
1/8
1/4
1/2
1
1/5
1/10
1
2
3
4
5
6
+0,3
-0,5
-0,9
-1,2
-1,4
-1,6
-1,0
-1,2
-1,5
-1,6
-0,3
-0,5
-0,6
-0,7
-0,8
1,0
-0,4
-0,5
-1,0
-1,0
-0,6
-0,7
-0,8
-0,9
-0,9
-1,1
-0,4
-0,4
-0,7
-0,8
-0,7
-0,7
-0,8
-0,8
-0,9
-1,2
-0,4
-0,4
-0,5
-0,6
-0,6
-0,5
-0,4
-0,3
-0,4
-0,8
-0,4
-0,4
-0,4
-0,4
-0,2
-0,2
-0,2
-0,2
-0,4
-0,7
-0,3
-0,3
-0,3
-0,3
Table 25 – External pressure coefficients, Cpe, for
the wind blowing parallel to the
generatrix of the roof
Part of the A1 + A2
roof
Cpe
-0,8
B
C
D1 + D 2
-0,6
-0,3
-0,2
Table 26 – External pressure coefficients, Cpe, for
the wind blowing obliquely to the generatrix of the
roof
Part of the roof
Cpe
A1
D1
-1,8
-1,8
Table 27 - External pressure coefficients, Cpe, for the wind blowing perpendicularly to the generatrix of the roof
* For the series S2 : hb/b
Cpe
a/b
f/b
h/b
Series
1/5
S1
2
3
4
5
6
1/4
-0,3
-0,7
-0,8
-0,6
-0,4
-0,4
1/2
-0,9
-0,9
-0,9
-0,7
-0,5
-0,5
1/4
-1,0
-0,6
-0,6
-0,6
-0,4
-0,3
1/2
-1,0
-0,6
-0,7
-0,7
-0,5
-0,4
-1/9
+0,4
-0,6
-1,2
-0,9
-0,7
-0,7
4
1/10
S2
1
-5
-1/3
52 NBR 6123/1988
Vento: wind
a) Wind perpendicular to the generatrix of the roof
b) Wind parallel to the generatrix of
the roof
c) Oblique wind (local action)
Figure 22 - Vaults circular cross-section Barrel
Table 28 - External pressure coefficients, Cpe, for wind blowing parallel to the generatrix of the roof
Cpe for part
a/b
f/b
h/b
A
B
C
D
1/4
-0,8
-0,4
-0,3
-0,2
1/2
-0,8
-0,6
-0,3
-0,2
1/4
-0,8
-0,4
-0,3
-0,2
1/2
-0,9
-0,6
-0,3
-0,2
-1/9
-0,8
-0,4
-0,2
-0,2
Series
1/5
S1
4
1/10
S2
(A)
-5
For the series S2: hb/b
-1/3
53
NBR 6123/1988
Table 29 - External pressure coefficients, Cpe, for wind blowing obliquely to the roof generatrix
Series
a/b
f/b
1/5
S1
(A)
Cpe for the range
E
F
G
H
1/4
-1,6
--
--
--
1/2
-2,4
-1,2
--
--
1/4
-1,4
-1,4
--
--
1/2
-1,6
-1,8
--
--
-1/9
-1,5
--
-1,8
-1,5
4
1/10
S2
(A)
h/b
-5
-1/3
For the series S2: hb/b
E.2 Domes
Where:
The same way it happens to circular crosssection barrel vaults, only approximate values of
Cpe can be given for the domes, due to the
variation of pressure distribution with the wind
profile, the relation among the edification
dimension and the external surface of the dome.
Special studies must be performed in case of
large dimension domes.
q = dynamic pressure of the wind or the top
of the dome
d = diameter of the circle of the dome base
E.2.1.2 The lift force acts vertically from bottom
to top.
E.2.1 Domes above ground
E.2.2 Domes on cylindrical walls
Typical distribution of isobars (lines of same Cpe)
for domes placed directly on the ground are give
on Figure 23, for f/d = 1/2 and 1/4.
E.2.1.1 Boundary values for the positive external
pressure coefficients (overpressures) and
negative (suctions) are given on Table 30, for
several relations rise / diameter (f/d).
For intermediate relations, the coefficients are
obtained by interpolation. The same Table
presents the values for the lift coefficient, C,
being the lift force calculated by the expression:
Fs = Cs q πd
4
2
A dome on a cylindrical wall presents a larger
variation of the values of the external pressure
coefficients than when it is placed directly on the
ground. Typical distribution of isobars are given
on Figure 24. There is no overpressure zone on
domes with f/d smaller than 1/5 and wall height
as of d/4.
E.2.2.1 Boundary values for the positive external
pressure coefficients (overpressures) and
negative (suctions) are given on Table 31. For
intermediate relations of f/d and h/d, the
coefficients are obtained by interpolation.
54 NBR 6123/1988
a)
Elevation
Vento: Wind
b) View from above: isobar lines of the external pressure coefficients for f/d = 1/2
Vento: wind
c) View from above: isobar lines of the
external pressure coefficients for f/d = 1/4
Figure 23 - Dome on the ground –isobar lines
Table 30 - Boundary values of the external pressure coefficients, Cpe, and the lift coefficients, Cs – Dome on the
ground
Cpe
f/d
1/15
1/10
1/8
1/6
1/4
1/2
Overlapping
Suction
+0,1
+0,2
+0,2
+0,3
+0,4
+0,6
-0,3
-0,3
-0,4
-0,5
-0,6
-1,0
Cs
0,15
0,2
0,2
03
0,3
0,5
55
NBR 6123/1988
a) Elevation
Vento: wind
b) View from above: isobar lines of the external pressure coefficients for f/d = 1/2 and h/d = 1/2
Vento: wind
c) View from above: isobar lines of the external pressure coefficients for f/d = 1/10 and h/d = 1
Figure 24 - Domes on cylindrical walls – isobar lines
Table 31 – Boundary values of the external pressure coefficients, Cpe and the lift coefficients–
Domes on cylindrical walls
f/d
h/d
1/2
1/4
1/2
1
1/6
1/10
1/15
1/20
1/6
1/10
1/15
1/20
1/4
1
Cpe
Lateral windward on top
+0,9
+0,8
+0,8
-1,5
-1,7
-1,7
-0,4
-0,4
-0,5
-0,1
-1,2
-1,4
-1,4
-1,4
-1,7
-1,5
-1,4
-0,9
-0,6
-0,5
-0,4
-1,1
-0,8
-0,5
-0,5
-0,4
-0,3
-0,3
-0,2
-0,4
-0,4
-0,4
-0,4
Note: For pressure coefficients on the cylindrical wall, the values given in Table 9 must be adopted.
56 NBR 6123/1988
APPENDIX F - Additional Information
For high suction zones, mean values for
pressure coefficients (mean Cpe) are presented,
which must be taken only for the calculation of
wind loads on the respective zones, applying to
the dimensioning, verification and anchorage of
the protective elements and of the secondary
structure.
Recent test results are presented in this
Appendix, which are applicable to edifications
with relations between dimensions indicated in
the respective Tables. Extrapolations can be
performed to proportions close to these ones.
The tests were carried out with simulation of the
main profiles of the natural winds, applicable to
any terrain category, with acceptable error.
The notes in 6.1.3 must be considered.
Surfaces where considerable pressure variations
occur, have been subdivided, and form
coefficients Ce are given for each of the parts.
Table 32 - External pressure and form coefficients for roofs with two slopes two-sloped, symmetric,
with central gutter, in rectangular edifications (use S2 corresponding to height h)
Ce
α = 90°
h/b
a/b
α = 0°
h/h
EF
GH
EG
FH
0,05
-0,6
-0,2
-0,7
-0,1
0,1 to 0,2
-0,7
-0,4
-0,7
-0,3
0,05
-0,8
-0,3
-0,4
+0,2
0,1 to 0,2
-0,8
-0,5
-0,5
-0,2
1
0,5
2
57
NBR 6123/1988
Table 33 – External form and pressure coefficients, for multiple roofs, with one vertical slope, of equal trusses.
Y=h or Otb (take the smaller value)
Y=h or Otb or 0,25a (take the smallest of the three values).
b1 = b2 = h
The ranges parallel to the biggest side of pavilion (of width y) include the vertical faces ( a*, c*, m*, x*)
Incidence
Ce
Roof
inclination angle of
First truss
First
Other
the wind
intermediate intermediate
θ
truss
trusses
α
a*
b*
c*
d*
m*
n*
10º
15º
30º
Last truss
x*
z*
0º
+0,6 -0,6
-0,5
-0,2
+0,2
-0,2
+0,2 -0,2
180º
-0,2 -0,1
-0,2
-0,1
-0,2
-0,2
-0,4
0º
+0,6 -0,7
-0,6
-0,2
+0,1
-0,2
+0,1 -0,3
180º
-0,2 -0,1
-0,2
-0,1
-0,2
-0,2
-0,5
0º
+0,7 -0,7
-0,5
-0,4
+0,1
-0,2
+0,1 -0,2
180º
-0,2 -0,1
-0,1
-0,1
-0,2
-0,1
-0,6 +0,1
-0,2
-0,2
*Ce = -0,3 on the second intermediate truss; *C = 0,5 on the last intermediate truss.
Ce in the distance
Incidence angle
of the wind α
Roof inclination
θ
b1
b2
b3
90º
10º
15º
30º
-0,8
-0,9
-06
-0,6
-0,2
-0,3
Notes: a) the relation between the dimensions a x b x h of the tested models is the following:
for θ = 10º and 15º 2 x 1 x ¼ and 2 x 1 x 1/8;
for θ = 30º 4 x 1 1/2, 4x1 x 1/3, 3 x 1 x 1/4 and 10 x 1 x 1/3
-
b) Friction forces
for α =90º; the horizontal forces must be determined
according to 6.4;
for α = 0º and 180º F’ = C’q a b, for C’ =0,1 for
α = 0º e C’ = 0,0018º + 0,02 for α = 180º
(8º angle in 8 degrees).
Mean Cpe
-2,0
-1,5
58 NBR 6123/1988
APPENDIX G – Effect of the neighborhood
There are certain situations when it is necessary to
consider the influence of edification located in the
neighborhoods of the edification under study. These
edifications can cause increase in the wind loads in
three different ways.
d* = the smaller of both dimensions:
- smaller side b;
G.1 By Venturini effect
Neighboring edifications can, due to their dimensions,
shape and orientation, cause a “funneling” of the wind,
accelerating the air flow, consequently changing the
pressures. This effect is mainly present in very near
edifications, where negative pressure coefficients
(suctions) have been observed, exceeding, in module,
the value 2.0. These suction ends are noticed on
opposing walls of both edifications, near the windward
ridge.
G.2 By deflection of the wind in the vertical
direction
Tall edifications deflect downwards part of the wind
acting on its windward façade, increasing velocity in
zones near the ground. Shorter edifications, located in
these zones, can have the wind loads increased by
this effect, with the form coefficients achieving values
between – 1,5 and 2,0.
G3 By the turbulence track
Edification located at windward of another one can be
affected by the turbulence generated in the track of the
edification windward, and may cause considerable
dynamic effects (“strike effects”) and changes in the
pressures. These are particularly important in
edifications with roofs and cladding panels made of
light materials.
G4 Determining the effect of the neighborhood
It is not possible to indicate numeric values for the
effect of the neighborhoods in a generic and normative
way.
These effects can be determined by wind tunnel
procedure, in which the neighborhood conditions and
the natural wind profiles that can influence in the
results are reproduced. The problem gets more
complicated with the possibility of adverse changes to
the neighborhood conditions during the life span of the
edification in question.
An approximate indication of the increases the can
affect the aerodynamic coefficients by effect of the
neighborhoods is given as follows:
For:
s = distance between the planes of the opposing
faces of the two tall, neighboring edifications, being a
and b the plan dimensions of the edifications (a x b
between 1 x 1 and 4x 1)
- semi diagonal
FV = effect of the neighborhood factor, defined
by:
FV = C on the neighboring edification
C on the isolated edification
C =
aerodynamic coefficient under study (Ce,
mean Cpe, Ca)
The representative values of FV are the following:
- for drag coefficients, Ca (see Figures 4 and 5);
for form coefficient, Ca and for the mean value
of the pressure coefficient, mean Cpe, on
opposing walls (parallel faces to the wind on
Table 4):
s/d* ≤ 1,0……….. FV = 1,3
s/d* ≥ 3,0……….. FV = 1,0
For form coefficient, Ce, and for mean value of the
pressure coefficient mean, Cpe, on the roof (see Table
5):
s/d* ≤ 0,5……….. FV = 1,3
s/d* ≥ 3,0……….. FV = 1,0
Linear interpolation for intermediate values of s/d*.
The effect of the neighborhood factors are considered
until the top height of the neighboring edifications.
The tests on which the previous recommendations are
based were performed with two or a few models of
height alike. In case of many neighboring buildings in
these conditions, the neighborhood factors will be
generally smaller, with possibility of being below 1.0.
However, there may be wind incidence that cause the
FV values to be close to the ones indicated previously,
mainly when there are “voids” in the neighborhood of
the building under study.
Effect of the neighborhoods on the torsion coefficient
Cp were considered in 6.6.
59
NBR 6123/1988
APPENDIX H - Dynamic effects on slender and flexible edifications
Some slender and flexible edifications show an
intrinsically dynamic behavior, when exposed to the
wind; the most adverse velocity in not always the
maximum wind velocity expected. The study of its
stability is necessary, through mathematical and/ or
experimental way, in a wide range of wind velocities.
The dynamic response to the wind excitation on the
edification depends not only on the external shape, but
also on the materials used, damping and structural
rigidity.
Generally, the vibrations are provoked by one or more
of the following causes:
Linear interpolation for intermediate values of Re.
For a plate perpendicular to the wind:
L = width l1
St = 0,14
For a rectangular cross-section, wind perpendicular to
the largest face:
L = width l1
St = 0,15
For profiles of flat faces:
H. 1 Cadenced vortex shedding
L = width l1
Movements transversal to the direction of the wind can
be produced by these vortexes, if one of the natural
frequencies of the structure, or a structural member is
equal to the shedding frequency of a pair of these
vortexes, within an expected velocity range for the
wind. This phenomenon can be particularly damaging
in stacks and metallic cylindrical towers.
St = 0,12 to 0,16 (generally)
The energy of the vortexes and the special correlation
of their shedding are influenced, among other factors,
by the oscillation of the structure or structural members
and by the wind turbulence profiles.
The effects on the structure or structural member
increase as the wind turbulence and the structural
damping reduction.
The critical velocity of the wind, Vcr, is the velocity for
which the frequency of detachment of a pair of
vortexes coincide with one of the natural frequencies
of the structure or structural element. This velocity is
obtained by the expression:
Vcr, = fl
St
Where:
f = natural frequency of the structure
L = profile dimension
St = Strouhal number
Dynamic effects are possible if the critical velocity id
equal or less than the mean maximum velocity,
expect for the place of the edification.
For circular cross-section (Re = 70000
L: cylinder diameter
St: 103 < Re < 2.105 – St = 0,20
Re > 105 – St = 0,28
d):
As an approximate indication, the mean velocity,
,
can be calculated in a time interval between 30s and
60s (10 to 30 shedding periods of a pair of vortexes,
depending on the structural damping).
As the wind velocity is variable according to the height,
the frequency of vortex shedding will also vary along
the height, reducing considerably the effects on the
structure or structural member, due the lack of
synchronism of the exciting force.
H.2 Gallop effect
The edification under dynamic effects caused by the
turbulence existing in the track of another edification.
These effects can be considerable, both on light and
slender edifications, and on very high and slender
buildings.
H.3 Gallop
The gallop effect occurs due to loads determined by
the movement and shape of the edification. Among the
forms sensitive to this phenomenon, are prismatic
edification of rectangular and triangular cross-section.
The gallop appears when a certain wind velocity is
exceeded, producing transversal oscillations to the
direction of the wind. These oscillation increase in
amplitude with the wind velocity, achieving much
higher levels than the ones caused by cadenced
vortexes. Slender light and flexible edifications, such
as void pillars of viaducts of great height as
susceptible to this phenomenon.
,
H.4 Draping
It is a dynamic effect involving two or more degrees of
liberty of the structure, with vibration coupling.
It is a typical phenomenon for slender structures with
proportion similar to the ones of an airplane wing, such
as a very tall and slender building, of rectangular
cross-section, not square-like.
H.5 Energy held by the atmospheric turbulence
Although wind gusts are a random phenomenon, the
mechanical admittance profiles can contribute for the
kinetic energy in the wind gusts provoke a nonnegligible oscillation on the edification. For further
details, see Chapter 9 and Appendix I.
60 NBR 6123/1988
Appendix I – Determining the dynamic response due to atmospheric turbulence
The dynamic pressure variation with the height is given
by the expression (q in N/m2, z in m);
I.1 Simplified method
The wind load will be determined, in the direction of
the mean velocity, on a building of square crosssection, 120,00m high and 24,00 of side, located on a
category IV terrain for velocity V0 = 45m/s and the
parameters S1 = 1,0 and S3 =1,0.
-
q(z)=298 [ (z/10)0,46 + 0,212(z/10)]
-
The following alternatives will be analyzed:
-
case a: building in concrete structure, on
which the horizontal loads are resisted
exclusively by porches.
-
Case b: the same, with resisting structure in
steel (welded junctions).
I.1.1 Firstly, it must be calculated (see 9.2.1):
p
-
case a: T1 = 1,85 s1 y =1, ξ =0,02;
-
case b; T1 = 2,8 s1 y =1, ξ =0,01.
I.1.3Determing the dynamic amplification coefficient ξ:
-
case a ;Vp / fl L= 31,05 x 1,85 x 1800 = 0,032
From the graph on Figure 17, we obtain, for:
l1/h=24/120=0,2 e ξ =0,02:
h (m) :
ξ
-
25
100
300
1,69
1,16
0,62
case b: Vp / fl L= 31,05 x 2,8 /1800 = 0,048
From the graph on Figure 17, we obtain, for:
l1/h=24/120=0,2 e ξ =0,01:
h (m) :
ξ
25
100
300
1,50
0,88
The values corresponding h = 120m can be
determined by graph interpolation, as illustrated on
Figure 25, resulting in:
-
case a: ξ = 1,07 (concrete);
-
case b: ξ = 1,40 (steel).
We calculate then (see 9.3.1);
Q0 b2 = 0,613 x 31,052 x 0,712 = 298N/m2
1+2 y = 1+ 2
= 1,345
1 + y + p 1+1+0,23
case b q(z)=298 [ (z/10)0,46 + (120/10)0,23
(z/120)1 x 1,345x 1,40]
q(z)=298 [ (z/10)0,46 + 0,277(z/10)]
On the top of the building, the dynamic pressure is
equal to N/m2 for building with reinforced concrete
structures and to 1925 N/m2 in case of buildings with
steel structure. The statistic method leads to single
value, of 1557 N/m2 (category IV, class C, low
turbulence wind):
Vk = V0 S1 S2 S3= 45 x 1 1,12 x 1 = 50,4m/s
=0,69 x 45x 1x 1 = 31,05m/s
I.1.2 The fundamental periods, for both cases, were,
based on measurement performed on similar
buildings. The modal form (parameter y) and the
critical damping ratio were obtained on Table 19.
case a: q(z)=298 [ (z/10)0,46 + (120/10)0,23
(z/120)1 x 1,345x 1,07]
q = 0,613 V2k = 1557 N/m2
I.1.4 The equivalent static load, by unit of height, is
obtained by the expression (see 9.3.1):
q (z) l1 Ca
for l1, the width of the building, equal to 24,00m. The
drag coefficient, Ca, is obtained from the graph on
Figure 4, or, for the rare cases of high turbulence wind,
the graph on Figure 5, with its value considered
invariable with Z.
I.2 Discreet model
The wind load will be determined, in the direction of
the mean velocity, in a reinforced concrete stack, with
the profile indicated on Table 34. The property of the
model adopted in the dynamic analysis are indicated
on Table 35. The fundamental vibration frequency of
the stack was calculated, resulting in ft = 0,26 H.z. The
from of the fundamental vibration mode is also given
on Table 35, for an adopted critical damping ratio ξ =
0,01. The drag coefficient, Ca =0,6, considering the
Reynolds numbers and the roughness of the stack
surface.
For V0 = 39,4 m/s, S1 = S3 = 1, the design velocity is
equal to:
p
= 0,69 x 40 = 27,2m/s
p
/ ft L = 27,2(0,26 x 1800) = 0,058
The terrain roughness is category III. From Figure 16
we obtain, for Vp / ft L = 0,58, values of ξ for h=25, 100
and 300m in relations l1/h=0 and 0,2. By graphic
interpolation, we obtain ξ =1,43. From Table 20, we
obtain p = 0,185 and b = 0,86
Then, we calculate (see 9.3.2):
q0 = 0,613 V2p = 0,613(27,2)2 = 453,52 N/m2
The graphic interpolation that permitted the
determination of ξ is shown on Figure 26, while Table
36 shows the calculation route for the determination of
the loads on the stack, for the fundamental mode of
vibration (j = 1).
NBR 6123/1988
Formulas (see 9.3.2.1) and the auxiliary values:
Estrutura de aço: steel strutucture
Estrutura de concreto: concrete structure
Figure 25 – Graphic determination of the dynamic amplification coefficient ζ
Interpolação linear: Linear interpolation
Figure 26 – Graphic determination of the dynamic amplification coefficient ζ
61
62 NBR 6123/1988
Table 34 - stack profile - height h = 180m
Z
(m)
180
130
80
35
0
External
diameter
Thickness of
the wall
mass
Inertia moment
(m)
4075
5,90
7,42
8,82
9,86
(m)
0,17
0,17
0,25
0,60
0,60
(Kg/m)
9400
10900
17400
38700
43600
(m )
6,4
12,6
36,2
131,6
187,9
4
Table 35 - Properties of the adopted model
Z
(m)
Xl
ml
(Kg)
Al
2
(m )
C a,l
180
165
150
135
120
105
90
75
60
40
20
1,00
0,83
0,68
0,56
0,46
0,36
0,28
0,20
0,14
0,07
0,03
70900
146200
153700
163100
174400
195000
232500
292500
463800
750000
1254000
36,3
76,4
81,6
86,9
93,0
99,9
107,2
114,0
141,4
173,2
282,5
0,6
0,6
0,6
0,6
0,6
0,6
0,6
0,6
0,6
0,6
0,6
Table 36 - Determining mean, fluctuant and overall loads on the stack for the fundamental mode (j = l)
I
Z
(m)
Al
2
(m )
A i/ A 0
Xi
ßl x/ Ca
Ψ1
1
2
3
4
5
6
7
8
9
10
11
180
165
150
135
120
105
90
75
60
40
20
36,3
76,4
81,6
86,9
93,0
99,9
107,2
114,0
141,4
173,2
282,5
0,0281
0,0591
0,0632
0,0673
0,0720
0,0773
0,0830
0,0882
0,1094
0,1341
0,2187
1,00
0,83
0,68
0,56
0,46
0,36
0,28
0,20
0,14
0,07
0,03
0,04797
0,08239
0,07093
0,06100
0,05245
0,04299
0,03490
0,02561
0,02134
0,01213
0,00746
0,0709
0,1462
0,1537
0,1631
0,1744
0,1950
0,2325
0,2925
0,4638
0,7500
1,2540
6
2
Ψ1X
2
1
0,07090
0,10072
0,07107
0,05115
0,03690
0,02527
0,01823
0,01170
0,00909
0,00368
0,00113
M°=10 Kg; A° = ∑ A l = 1292 m ; ∑ ßl xl =0,6 x 0,45917; ∑ Ψ1X
2
1
Xi
(KN)
Xi
(KN)
Xi
(KN)
21,29
43,38
44,73
45,81
46,94
47,99
48,64
48,35
55,22
58,22
73,47
30,27
51,81
44,63
39,00
34,26
29,98
27,80
24,98
27,73
22,42
16,06
51,57
95,12
89,36
84,81
81,20
77,97
76,44
73,33
82,95
80,64
89,53
= 0,39984
63
NBR 6123/1988
INDEX
Items
Page
1 Purpose …………………………………………………………………………………………………………………………..
1
2 Symbols ………………………………………………………………………………………………………...........................
1
2.1 Capital Roman Letters ………………………………………………………………………………………………………..
1
2.2 Small Roman Letters ………………………………………………………………………………………………………….
2
2.3 Greek Letters …………………………………………………………………………………………………........................
3
3 Definitions ………………………………………………………………………………………………………………………...
3
3.1 Windward ………………………………………………………………………………………………………………………
3
3.2 Reticulates structure …………………………………………………………………………………………………………..
3
3.3 Overpressure …………………………………………………………………………………………………………….........
3
3.4 Leeward ………………………………………………………………………………………………………………………...
4
3.5 Suction ………………………………………………………………………………………………………………………….
4
3.6 Frontal Surface ………………………………………………………………………………………………………………...
4
3.7 Basic Wind ……………………………………………………………………………………………………………………..
4
3.8 High Turbulence Wind ………………………………………………………………………………………………………..
4
3.9 Low Turbulence Wind …………………………………………………………………………………………………………
4
4 Procedure for the calculation of wind load on edifications …………………………………………………………………..
4
4.1 Wind on partially built structures ………………………………………………………………………………………...…..
4
4.2 Determining wind static roads ………………………………………………………………………………………….........
4
4.2.1 Pressure coefficients ………………………………………………………………………………………………….........
4
4.2.2 Form coefficients ……………………………………………………………………………………………………………
4
4.2.3 Force coefficients ……………………………………………………………………………………………………………
5
4.3 Determining the dynamic effects of the wind ……………………………………………………………………………….
5
5 Profile velocity of the wind ………………………………………………………………………………………………………
5
5.1 Basic velocity of the wind Vo …………………………………………………………………………………………………
5
5.2 Topographic factor, S1 ………………………………………………………………………………………………………..
5
5.3 Roughness of the terrain, dimensions of the edification and height above ground: Factor S2 ………………………..
8
5.3.1 Roughness of the terrain …………………………………………………………………………………………………..
8
5.3.2 Edification dimensions ……………………………………………………………………………………………………...
8
5.3.3 Height above ground ………………………………………………………………………………………………….........
9
5.4 Statistic factor S3 ……………………………………………………………………………………………………………… 10
5.5 Changes in the roughness of the terrain …………………………………………………………………………………… 11
5.5.1.1 Transition for a category of higher roughness (Z01 >Z02) …………………………………………………………….. 11
5.5.1.2 Transition for a category of lower (Z01 >Z02) ………………………………………………………………….............. 11
6 Aerodynamic coefficients for current edifications ……………………………………………………………………………. 12
6.1 External form and pressure coefficients ……………………………………………………………………………………. 12
6.2 Internal pressure coefficients ………………………………………………………………………………………………... 12
6.3 Drag coefficients ………………………………………………………………………………………………………………. 19
6.4 Friction coefficients …………………………………………………………………………………………………............... 20
6.5 Reductions in the form and drag coefficients ……………………………………………………………………………… 21
6.6 Eccentricity of drag forces …………………………………………………………………………………………………… 21
7 Force coefficients for prismatic bars and reticulated structures …………………………………………………………… 21
7.1 Prismatic bars …………………………………………………………………………………………………………………. 21
7.2 Prismatic bars of flat faces…………………………………………………………………………………………………… 21
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7.3 Prismatic bars of circular cross-section ……………………………………………………………………………………. 21
7.4res and cables …………………………………………………………………………………………………………………. 26
7.5 Isolated flat reticulated structures …………………………………………………………………………………………… 26
4.6 Multiple flat reticulated structures …………………………………………………………………………………………… 27
7.7 Reticulate towers ……………………………………………………………………………………………………………… 27
8 Force coefficients for walls, plates and isolated roof ………………………………………………………………………... 32
8.1 Rectangular walls and plates ………………………………………………………………………………………………... 32
8.2 Flat slope isolated roofs ……………………………………………………………………………………………………… 33
9 Dynamic effects due to atmospheric turbulence …………………………………………………………………………….. 33
9.1 General provisions ……………………………………………………………………………………………………………. 33
9.2 Input data to determine the dynamic response in the wind direction …………………………………………………… 34
9.2.1 Design velocity
p
………………………………………………………………………………………………………..
34
9.2.2 Dynamic profile of the structure …………………………………………………………………………………………… 34
9.2.2.1 Simplified continuous model …………………………………………………………………………………………….. 34
9.2.2.2 Discreet mode ……………………………………………………………………………………………………………
34
9.3 Calculation of the dynamic response in the direction of the wind ……………………………………………………….. 35
9.3.1 Simplified method …………………………………………………………………………………………………………... 35
9.3.2 Discreet model ……………………………………………………………………………………………………………… 36
9.3.2.1 Determining modal contributions ……………………………………………………………………………………….. 36
9.3.2.2 Combination of the modal contributions ……………………………………………………………………………….. 36
9.4 Calculation of the dynamic response transversal to the wind ……………………………………………………………. 36
9.5 Calculation of maximum accelerations for comfort analysis ……………………………………………………………... 36
APPENDIX A - Normalized velocity S2 and time internal …………………………………………………………………….
42
A.1 Factor S2 ………………………………………………………………………………………………………………………. 42
A.2 Time internal ………………………………………………………………………………………………………………….. 42
APPENDIX B - Statistic factor S3 for probability Pm and life span the edification in m years …………………………….. 45
APPENDIX C - Location and altitude of the meteorological stations ………………………………………………………... 46
APPENDIX D - Determining the internal pressure coefficients ………………………………………………………………. 47
APPENDIX E - Aerodynamic coefficients for curved roofs ………………………………………………………………....... 50
E.1 Circular cross-section Barrel vaults ………………………………………………………………………………………… 50
E.2 Domes …………………………………………………………………………………………………………………………. 53
E.2.1 Domes above ground ……………………………………………………………………………………………………… 53
E2.2 Domes on cylindrical walls …………………………………………………………………………………………………. 53
APPENDIX F - Additional information …………………………………………………………………………………………... 56
APPENDIX G - Effects of the neighborhood …………………………………………………………………………………… 58
G.1 By Venturini effect ……………………………………………………………………………………………………………. 58
G.2 By wind deflection in the vertical direction ………………………………………………………………………………… 58
G.3 The turbulence track …………………………………………………………………………………………………………. 58
G.4 Determining the effects of the neighborhood ……………………………………………………………………………… 58
APPENDIX H - Dynamic effects on slender and flexible edifications ……………………………………………………….. 59
H.1 Cadenced vortex shedding ………………………………………………………………………………………………….. 59
H.2 Gallop effect …………………………………………………………………………………………………………………... 59
H.3 Gallop ………………………………………………………………………………………………………………………….. 59
H.4 Draping ………………………………………………………………………………………………………………………... 59
H.5 Energy held by the atmospheric turbulence ………………………………………………………………………………. 59
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APPENDIX I - Determining the dynamic response to atmospheric turbulence ……………………………………………. 60
I.1 Simplified method ……………………………………………………………………………………………………………… 60
I.2 Discreet model …………………………………………………………………………………………………………………. 60
Figure 1 - Isopleths of the basic velocity Vo (m/s)………………………………………………………………………………
6
Figure 2 - Topographic factor S1 (Z) …………………………………………………………………………………………….
7
Figure 3 - Profile of S2 at leeward of a roughness change …………………………………………………………………… 11
Figure 4 - Drag coefficient, Ca, for parallelepiped edifications under low turbulence wind ……………………………….. 20
Figure 5 - Drag coefficient, Ca, for parallelepiped edifications under high turbulence wind ………………………………. 24
Figure 6 - Drag coefficient, Ca , for flat reticulated structures made of prismatic bars with salient or slightly rounded
corners………………………………………………………………………………………………………………………………. 27
Figure 7 - Drag coefficient, Ca , for flat reticulated structures made of circular cross-section bars ………………………. 28
Figure 8 - Protection factor, η, for two or more parallel flat reticulated structures equally distant ……………………….. 29
Figure 9 - Drag coefficient, Ca , for reticulated towers of square and equilateral triangular cross-section, made of
prismatic bars with salient and slightly rounded corners ……………………………………………………………………… 29
Figure 10 - Drag coefficient, Ca , for reticulated towers of square cross-section, made of circular cross-section bars Wind acting perpendicularly on both parallel faces …………………………………………………………………………… 30
Figure 11- Drag coefficient, Ca , for reticulated towers of square cross-section, made of circular cross-section bars Wind acting according to a diagonal …………………………………………………………………………………………….. 30
Figure 12 - Drag coefficient, Ca , for reticulated towers of equilateral triangular cross-section, made of circular crosssection bars-Wind of any direction ………………………………………………………………………………………………. 31
Figure 13 - Scheme for discreet dynamic model ………………………………………………………………………………. 35
Figure 14 - Dynamic amplification coefficient, ξ, terrain for category I (L = 1800 m; h in meters)………………………... 37
Figure 15 - Dynamic amplification coefficient, ξ, terrain for category II (L = 1800 m; h in meters)……………………….. 38
Figure 16 - Dynamic amplification coefficient, ξ, terrain for category III (L = 1800 m; h in meters)………………………. 39
Figure 17 - Dynamic amplification coefficient, ξ, terrain for category IV (L = 1800 m; h in meters)………………………. 40
Figure 18 - Dynamic amplification coefficient, ξ, terrain for category V (L = 1800 m; h in meters)………………………. 41
Figure 19 - Internal pressure on floor type of building ………………………………………………………………………… 47
Figure 20 - Internal pressure on industrial pavilion ……………………………………………………………………………. 48
Figure 21 - Circular cross-section barrel vaults with 0,5l2 < l1 <3l2 …………………………………………………………… 50
Figure 22 - Circular cross-section barrel vaults ……………………………………………………………………………….. 52
Figure 23 - Domes on the ground-Isobar lines ………………………………………………………………………………… 54
Figure 24 - Domes on cylindrical walls-Isobar lines …………………………………………………………………………... 55
Figure 25 - Graphic determination of the dynamic amplification coefficient ξ ……………………………………………… 61
Figure 26 - Graphic determination of the dynamic amplification coefficient ξ ……………………………………………… 61
Table 1 - Meteorological parameters …………………………………………………………………………………………….
9
Table 2 - Factor S2 ………………………………………………………………………………………………………………… 10
Table 3 - Minimum values of the statistic factor S3 ……………………………………………………………………………. 10
Table 4 - External pressure and form coefficients, for walls of edifications of rectangular plan ………………………….. 14
Table 5 - External pressure and form coefficients, for roofs with two slopes, in edifications of rectangular plan ……… 15
Table 6 - External pressure and form coefficients for roofs with one slope, in edifications of rectangular plan, with h/b
<2s…………………………………………………………………………………………………………………………………… 16
66 NBR 6123/1988
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Page
Table 7 - External pressure and form coefficients, for multiple roofs symmetric, with equal trusses, with h ≤ a
1
…………...
17
Table 8 - External pressure and form coefficients, for multiple roofs, asymmetric, with equal trusses, with the
1
smallest slope inclination of 60º and with h ≤ a ………………………………………………………………………………. 18
Table 9 - Distribution of external pressures distribution on cylindrical edifications of circular cross-section ……………. 19
Table 10 - Drag coefficient, Ca, for bodies of constant cross-section ……………………………………………………….. 22
Table 11 - Values of the reduction factor K for finite length bars ……………………………………………………………
25
Table 12 - Force coefficients, Cx and Cy, for prismatic bars of flat faces of infinite length ………………………………… 25
Table 13 - Drag coefficients, Ca, for prismatic bars of circular cross-section and infinite length …………………………. 26
Table 14 - Drag coefficient, Ca, for wires, and cables with l/d > 60 ………………………………………………………….
26
Table 15 - Drag force components on the faces of reticulated towers of square or equilateral triangular cross-section
31
Table 16 - Force coefficients Cf1, for walls and rectangular plates ………………………………………………………….. 32
Table 17 - Pressure coefficient on isolated roofs with one flat slope ………………………………………………………... 34
Table 18 - Pressure coefficients on isolated roofs with two symmetric flat slopes ………………………………………… 34
Table 19 - Parameters to determine the dynamic effects …………………………………………………………………….. 35
Table 20 - Exponent p and parameter b ………………………………………………………………………………………... 36
Table 21 - Parameters b, p, FrII........................................................................................................................................ 42
Table 22 - Normalized velocity S2 ……………………………………………………………………………………………….. 43
Table 23 - Statistic factor S3 ……………………………………………………………………………………………………… 45
Table 24 - External pressure coefficients, Cpe for the wind blowing perpendicularly to the generatrix of the roof ……… 51
Table 25 - External pressure coefficients, Cpe, for the wind blowing in parallel to the generatrix of the roof ………….... 51
Table 26 - External pressure coefficients, Cpe, for the wind blowing obliquely to the generatrix of the roof …………….. 51
Table 27 - External pressure coefficients, Cpe, for the wind blowing in perpendicularly to the generatrix of the roof ….. 51
Table 28 - External pressure coefficients, Cpe, for the wind blowing in parallel the generatrix of the roof ………………. 52
Table 29 - External pressure coefficients, Cpe, for the wind blowing obliquely the generatrix of the roof ……………….. 53
Table 30 - Boundary values of the external pressure coefficients Cpe and the lift coefficients, Ca –Domes on the
ground ………………………………………………………………………………………………………………………………. 54
Table 31 - Boundary values of the external pressure coefficients Cpe and the lift coefficients, Ca –Dome cylindrical
walls ………………………………………………………………………………………………………………………………… 55
Table 32 - External pressure and form coefficients, for roofs with two slopes, symmetric, with central gutter, in
edification of rectangular plan ……………………………………………………………………………………………………. 56
Table 33 - External pressure and for coefficients, for multiple roofs with one vertical slope, of equal trusses ………..... 57
Table 34 - Stack profile …………………………………………………………………………………………………………… 62
Table 35 - Properties of the adopted model ……………………………………………………………………………………. 62
Table 36 - Determining mean, fluctuant and overall loads on the stack for the fundamental mode (j =1)……….……… 62