CHAPTER 6
CHAPTER 6
WIND LOADS – C6-1 –
WIND LOADS
Outline
6.1
General
6.1.1
Scope of application
6.1.2
Estimation principle
6.1.3
Buildings for which particular wind load or wind induced vibration is taken into account
6.2
Horizontal Wind Loads on Structural Frames
6.2.1
Scope of application
6.2.2
Equation
6.3
Roof Wind Load on Structural Frames
6.3.1
Scope of application
6.3.2
Procedure for estimating wind loads
6.4
Wind Loads on Components/Cladding
6.4.1
Scope of application
6.4.2
Procedure for estimating wind loads
A6.1
Wind Speed and Velocity Pressure
A6.1.1
Velocity pressure
A6.1.2
Design wind speed
A6.1.3
Basic wind speed
A6.1.4
Wind directionality factor
A6.1.5
Wind speed profile factor
A6.1.6
Turbulence intensity and turbulence scale
A6.1.7
Return period conversion factor
A6.2
Wind force coefficients and wind pressure coefficients
A6.2.1
Procedure for estimating wind force coefficients
A6.2.2
External pressure coefficients for structural frames
A6.2.3
Internal pressure coefficients for structural frames
A6.2.4
Wind force coefficients for design of structural frames
A6.2.5
Peak external pressure coefficients for components/cladding
A6.2.6
Factor for effect of fluctuating internal pressures
A6.2.7
Peak wind force coefficients for components/cladding
A6.3
Gust Effect Factors
A6.3.1
Gust effect factor for along-wind loads on structural frames
A6.3.2
Gust effect factor for roof wind loads on structural frames
A6.4
Across-wind Vibration and Resulting Wind Load
A6.4.1
Scope of application
– C6-2 –
Recommendations for Loads on Buildings
A6.4.2
A6.5
Procedure
Torsional Vibration and Resulting Wind Load
A6.5.1
Scope of application
A6.5.2
Procedure
A6.6
Horizontal Wind Loads on Lattice Structural Frames
A6.6.1
Scope of application
A6.6.2
Procedure for estimating wind loads
A6.6.3
Gust effect factor
A6.7
Vortex Induced Vibration
A6.7.1
Scope of application
A6.7.2
Vortex induced vibration and resulting wind load on buildings with circular sections
A6.7.3
Vortex induced vibration and resulting wind load on building components with circular
sections
A6.8
Combination of Wind Loads
A6.8.1
Scope of application
A6.8.2
Combination of horizontal wind loads for buildings not satisfying the conditions of
Eq.(6.1)
A6.8.3
Combination of horizontal wind loads for buildings satisfying the conditions of Eq.(6.1)
A6.8.4
Combination of horizontal wind loads and roof wind loads
A6.9
Mode Shape Correction Factor
A6.9.1
Scope of application
A6.9.2
Procedure
A6.10
Response Acceleration
A6.10.1
Scope of application
A6.10.2
Maximum response acceleration in along-wind direction
A6.10.3
Maximum response acceleration in across-wind direction
A6.10.4
Maximum torsional response acceleration
A6.11
Simplified Procedure
A6.11.1
Scope of application
A.6.11.2
Procedure
A6.12
Effects of Neighboring Tall Buildings
A6.13
1-Year-Recurrence Wind Speed
Appendix 6.6
References
Dispersion of Wind Load
CHAPTER 6
CHAPTER 6
WIND LOADS – C6-3 –
WIND LOADS
Outline
Each wind load is determined by a probabilistic-statistical method based on the concept of
“equivalent static wind load”, on the assumption that structural frames and components/cladding
behave elastically in strong wind.
Usually, mean wind force based on the mean wind speed and fluctuating wind force based on a
fluctuating flow field act on a building. The effect of fluctuating wind force on a building or part
thereof depends not only on the characteristics of fluctuating wind force but also on the size and
vibration characteristics of the building or part thereof. These recommendations evaluate the
maximum loading effect on a building due to fluctuating wind force by a probabilistic-statistical
method, and calculate the static wind load that gives the equivalent effect. The design wind load can
be obtained from the summation of this equivalent static wind load and the mean wind load.
A suitable wind load calculation method corresponding to the scale, shape, and vibration
characteristics of the design object is provided here. Wind load is classified into horizontal wind load
for structural frames, roof wind load for structural frames and wind load for components/cladding. The
wind load for structural frames is calculated from the product of velocity pressure, gust effect factor
and projected area. Furthermore, a calculation method for horizontal wind load for lattice structural
frames that stand upright from the ground is newly added. The wind load for components/cladding is
calculated from the product of velocity pressure, peak wind force coefficient and subject area. For
small-scale buildings, a simplified procedure can be applied.
These recommendations introduce the wind directionality factor for calculating the design wind
speed for each individual wind direction, thus enabling rational design considering the building’s
orientation with respect to wind direction. Moreover, the topography factor for turbulence intensity is
newly added to take into account the increase of fluctuating wind load due to the increase of
fluctuating wind speed.
Introduction of the wind directionality factor requires the combination of wind loads in along-wind,
across-wind and torsional directions. Hence, it is decided to adopt the regulation for the combination
of wind loads in across-wind and along-wind directions, or in torsional and along-wind directions
explicitly. Furthermore, a prediction formula for the response acceleration of the building for
evaluating its habitability to vibration, which is needed in performance design, and information of
1-year-recurrence wind speed are newly added. Besides, information has been provided for the
dispersion of wind load.
– C6-4 –
Recommendations for Loads on Buildings
Notation
Notations used in the main text of this chapter are shown here.
Uppercase Letter
A (m2): projected area at height Z
AR (m2): subject area
AC (m2): subject area of components/cladding
A0 (m2): whole plane area of one face of lattice structure
AF (m2): projected area of one face of lattice structure
B (m): building breadth
B1 (m): building length in span direction
B2 (m): building length in ridge direction
B0 , BH (m): width of lattice structure in ground and width at height H
BD : background excitation factor for lattice structure
C1 , C 2 , C3 : parameters determining topography factor Eg and EI
C D , C R , C X , C Y : wind force coefficients
C L' , CT' : rms overturning moment coefficient and rms torsional moment coefficient
Ce : exposure factor, which is generally 1.0 and shall be 1.4 for open terrain with few
obstructions (Category II). When wind speed is expected to increase due to local
topography, this factor shall be increased accordingly.
Cg : overturning moment coefficient in along-wind direction
Cg' : rms overturning moment coefficient in along-wind direction
C f : wind force coefficient. For horizontal wind loads, wind force coefficient C D defined
in A6.2 with k Z = 0.9 shall be used. For roof wind loads, wind force coefficient C R
defined in A6.2 shall be used.
C pe : external pressure coefficient
C pe1 , C pe2 : external pressure coefficients on windward wall and leeward wall
C pi : internal pressure coefficient
*
C pi
: factor for effect of fluctuating internal pressure
C r : wind force coefficient at resonance
ĈC : peak wind force coefficient
Ĉ pe : peak external pressure coefficient
D (m): building depth, building diameter, member diameter
DB (m): building diameter at the base
Dm (m): building diameter at height of 2H / 3
E : wind speed profile factor
EH : wind speed profile factor at reference height H
CHAPTER 6
WIND LOADS – C6-5 –
EI : topography factor for turbulence intensity
Eg : topography factor for wind speed
EgI : topography factor for turbulence intensity
E r : exposure factor for flat terrain categories
FD : along-wind force spectrum factor
F : wind force spectrum factor
GD : gust effect factor for along-wind load
GR : gust effect factor for roof wind load
H (m): reference height
H S (m): height of topography
I T (kgm2): generalized inertial moment of building for torsional vibration
I Z : turbulence intensity at height Z
I rZ : turbulence intensity at height Z on flat terrain categories
K D : wind directionality factor
L (m): span of roof beam
LS (m): horizontal distance from topography top to point where height is half topography
height
LZ (m): turbulence scale at height Z
M (kg): total building mass
M D (kg): generalized mass of building for along-wind vibration
M L (kg): generalized mass of building for across-wind vibration
R : factor expressing correlation of wind pressure of windward side and leeward side
RD : resonance factor for along-wind vibration
RL : resonance factor for across-wind vibration
RT : resonance factor for torsional vibration
RRe : resonance factor for roof beam
S D : size effect factor
U 0 (m/s): basic wind speed
U1 (m/s): 1-year-recurrence 10-minute mean wind speed at 10m above ground over flat and
open terrain
U1H (m/s): 1-year-recurrence wind speed
U 500 (m/s): 500-year-recurrence 10-minute mean wind speed at 10m above ground over
flat and open terrain
U H (m/s): design wind speed
*
*
U Lcr
, U Tcr
: non-dimensional critical wind speed for aeroelastic instability in across-wind
and torsional directions
U r (m/s): resonance wind speed
U T* : non-dimensional wind speed for calculating torsional wind load
– C6-6 –
Recommendations for Loads on Buildings
U r* : non-dimensional resonance wind speed
W D (N): along-wind load at height Z
WL (N): across-wind load at height Z
WT (Nm): torsional wind load at height Z
WLC (N): across-wind combination load
WR (N): roof wind load
WSC (N): wind load on components/cladding obtained by simplified method
WSf (N): wind load on structural frames
Wr (N): wind load at height Z
X S (m): distance from leading edge of topography to construction site
Z (m): height above ground
Z b , Z G (m): parameters determining exposure factor
Lowercase Letter
aDmax , aLmax (m/s2), aTmax (rad/s2): maximum response acceleration in along-wind,
across-wind and torsional directions at top of building
b (m): projected width of member
f (m): rise
f1 (Hz): The smaller of f L and f T
f D , f L , f T (Hz): natural frequency for first mode in along-wind, across-wind and torsional
directions
f R (Hz): natural frequency for first mode of roof beam
g aD , g aL , g aT : peak factors for response accelerations in along-wind, across-wind and
torsional directions
g D , g L , g T : peak factors for wind loads in along-wind, across-wind and torsional
directions
h (m): eaves height
k1 : factor for aspect ratio
k 2 : factor for surface roughness
k 3 : factor for end effects
k 4 : factor for three demensionality
k C : area reduction factor
k rW : return period conversion factor
k Z : factor for vertical profile for wind pressure coefficients or wind force coefficients
l (m): smaller value of 4 H and B , minimum value of 4 H , B1 and B2 , member
length
la1 (m): smaller value of H and B1
la2 (m): smaller value of H and B2
CHAPTER 6
WIND LOADS – C6-7 –
q H (N/m2): velocity pressure at reference height H
q Z (N/m2): velocity pressure at height Z
r (year): design return period
rRe : coefficient of variation for generalized external pressure
x (m) : distance from end of component
Greek Alphabet
α : exponent of power law for wind speed profile
β : exponent of power law for vibration mode
γ : load combination factor
δ , δ L , δ T : mass damping parameter for vortex induced vibration, across-wind vibration
and torsional vibration
φ D , φ L , φT : mode correction factor for vortex induced vibration, across-wind vibration and
torsional vibration
ζ D , ζ L , ζ T : critical damping ratio for first translational and torsional modes
ζ R : critical damping ratio for first mode of roof beam
ϕ : solidity
λ : mode correction factor of general wind force
λU : U 500 / U 0
μ : first mode shape in each direction
ν D (Hz): level crossing factor
θ (°): roof angle, angle of attack to member
θ S (°): inclination of topography
ρ (kg/m3): air density
ρ S (kg/m3): building density which is M /( HDm DB )
ρ LT : correlation coefficient between across-wind vibration and torsional vibration
6.1
6.1.1
General
Scope of application
(1) Target strong wind
Most wind damage to buildings occurs during strong winds. The wind loads specified here are
applied to the design of buildings to prevent failure due to strong wind. The strong winds that occur in
this country are mainly those that accompany a tropical or extratropical cyclone, and down-bursts or
tornados. The former are large-scale phenomena that are spread over about 1000km in a horizontal
plane, and their nature is comparatively well known. Down-bursts are gusts due to descending air
flows caused by severe rainfall in developed cumulonimbus. Since the scale of these phenomena are
very small, few are picked up by the meteorological observation network. It is known that tornados are
– C6-8 –
Recommendations for Loads on Buildings
small-scale phenomena several hundred meters wide at most having a rotational wind with a rapid
atmospheric pressure descent. The characteristics of the strong wind and pressure fluctuation caused
by tornados are not known. The number of occurrences of down-bursts and tornados is relatively large,
but their probability of attacking a particular site is very small compared with that of the tropical or
extratropical cyclones. However, the winds caused by down-bursts and tornados are very strong, so
they often fatally damage buildings. These recommendations focus on strong winds caused by tropical
or extratropical cyclones. However, the minimum wind speed takes into account the influence of
tornadoes and down-bursts.
(2) Wind loads on structural frames and wind loads on components/cladding
The wind loads provided in these recommendations is composed of those for structural frames and
those for components/cladding. The former are for the design of structural frames such as columns and
beams. The latter are for the design of finishings and bedding members of components/cladding and
their joints. Wind loads on structural frames and on components/cladding are different, because there
are large differences in their sizes, dynamic characteristics and dominant phenomena and behaviors.
Wind loads on structural frames are calculated on the basis of the elastic response of the whole
building against fluctuating wind forces. Wind loads on components/cladding are calculated on the
basis of fluctuating wind forces acting on a small part.
Wind resistant design for components/cladding has been inadequate until now. They play an
important role in protecting the interior space from destruction by strong wind. Therefore, wind
resistant design for components/cladding should be just as careful as that for structural frames.
6.1.2
Estimation principle
(1) Classification of wind load
A mean wind force acts on a building. This mean wind force is derived from the mean wind speed
and the fluctuating wind force produced by the fluctuating flow field. The effect of the fluctuating
wind force on the building or part thereof depends not only on the characteristics of the fluctuating
wind force but also on the size and vibration characteristics of the building or part thereof. Therefore,
in order to estimate the design wind load, it is necessary to evaluate the characteristics of fluctuating
wind forces and the dynamic characteristics of the building.
The following factors are generally considered in determining the fluctuating wind force.
1) wind turbulence (temporal and spatial fluctuation of wind)
2) vortex generation in wake of building
3) interaction between building vibration and surrounding air flow
CHAPTER 6
WIND LOADS – C6-9 –
vibration direction
vibration direction
wind turbulence
a) fluctuating wind force caused by
wind turbulence
Figure 6.1.1
vortices
b) fluctuating wind force caused by
vortex generation in wake of building
Fluctuating wind forces based on wind turbulence and vortex generation in wake of
building
Fluctuating wind pressures act on building surfaces due to the above factors. Fluctuating wind
pressures change temporally, and their dynamic characteristics are not uniform at all positions on the
building surface. Therefore, it is better to evaluate wind load on structural frames based on overall
building behavior and that on components/cladding based on the behavior of individual building parts.
For most buildings, the effect of fluctuating wind force generated by wind turbulence is predominant.
In this case, horizontal wind load on structural frames in the along-wind direction is important.
However, for relatively flexible buildings with a large aspect ratio, horizontal wind loads on structural
frames in the across-wind and torsional directions should not be ignored. For roof loads, the
fluctuating wind force caused by separation flow from the leading edge of the roof often predominates.
Therefore, wind load on structural frames is divided into two parts: horizontal wind load on structural
frames and roof wind load on structural frames.
along-wind load
wind load on
structural frames
wind load
wind load on
components/cladding
small-scale building
simplified
procedure
Figure 6.1.2
horizontal wind load
across-wind load
roof wind load
torsional wind load
wind load on
structural frames
wind load on
components/cladding
Classification of wind loads
(2) Combination of wind loads
Wind pressure distributions on the surface of a building with a rectangular section are asymmetric
even when wind blows normal to the building surface. Therefore, wind forces in the across-wind and
torsional directions are not zero when the wind force in the along-wind direction is a maximum.
– C6-10 –
Recommendations for Loads on Buildings
Combination of wind loads in the along-wind, across-wind and torsional directions have not been
taken into consideration positively so far, because the design wind speed has been used without
considering the effect of wind direction. However, with the introduction of wind directionality,
combination of wind loads in the along-wind, across-wind and torsional directions has become
necessary. Hence, it has been decided to adopt explicitly a regulation for combination of wind loads in
along-wind, across-wind and torsional directions.
(3) Wind directionality factor
Occurrence and intensity of wind speed at a construction site vary for each wind direction with
geographic location and large-scale topographic effects. Furthermore, the characteristics of wind
forces acting on a building vary for each wind direction. Therefore, rational wind resistant design can
be applied by investigating the characteristics of wind speed at a construction site and wind forces
acting on the building for each wind direction. These recommendations introduce the wind
directionality factor in calculating the design wind speed for each wind direction individually. In
evaluating the wind directionality factor, the influence of typhoons, which is the main factor of strong
winds in Japan, should be taken into account. However, it was difficult to quantify the probability
distribution of wind speed due to a typhoon from meteorological observation records over only about
70 years, because the occurrence of typhoons hitting a particular point is not necessarily high. In these
recommendations, the wind directionality factor was determined by conducting Monte Carlo
simulation of typhoons, and analysis of observation data provided by the Metrological Agency.
(4) Reference height and velocity pressure
The reference height is generally the mean roof height of the building, as shown in Fig.6.1.3. The
wind loads are calculated from the velocity pressure at this reference height. The vertical distribution
of wind load is reflected in the wind force coefficients and wind pressure coefficients. However, the
wind load for a lattice type structure shall be calculated from the velocity pressure at each height, as
shown in Fig.6.1.3.
qH
qZ
qH
H
qH
H
house
dome
Figure 6.1.3
Z
H
high-rise building
lattice type structure
Definition of reference height and velocity pressure
(5) Wind load on structural frames
The maximum loading effect on each part of the building can be estimated by the dynamic response
analysis considering the characteristics of temporal and spatial fluctuating wind pressure and the
CHAPTER 6
WIND LOADS – C6-11 –
dynamic characteristics of the building. The equivalent static wind load producing the maximum
loading effect is given as the design wind load. For the response of the building against strong wind,
the first mode is predominant and higher frequency modes are not predominant for most buildings.
The horizontal wind load (along-wind load) distribution for structural frames is assumed to be equal to
the mean wind load distribution, because the first mode shape resembles the mean building
displacement. Specifically, the equivalent wind load is obtained by multiplying the gust effect factor,
which is defined as the ratio of the instantaneous value to the mean value of the building response, to
the mean wind load. The characteristics of the wind force acting on the roof are influenced by the
features of the fluctuating wind force caused by separation flow from the leading edge of the roof and
the inner pressure, which depends on the degree of sealing of the building. Therefore, the
characteristics of roof wind load on structural frames are different from those of the along-wind load
on structural frames.
Thus, the roof wind load on structural frames cannot be evaluated by the same
procedure as for the along-wind load on structural frames. Here, the gust effect factor is given when
the first mode is predominant and assuming elastic dynamic behavior of the roof beam under wind
load.
(6) Wind load on components/cladding
In the calculation of wind load on components/cladding, the peak exterior wind pressure coefficient
and the coefficient of inner wind pressure variation effect are prescribed, and the peak wind force
coefficient is calculated as their difference. Only the size effect is considered. The resonance effect is
ignored, because the natural frequency of components/cladding is generally high. The wind load on
components/cladding is prescribed as the maximum of positive pressure and negative pressure for
each part of the components/cladding for wind from every direction, while the wind load on structural
frames is prescribed for the wind direction normal to the building face. Therefore, for the wind load on
components/cladding, the peak wind force coefficient or the peak exterior wind pressure coefficient
must be obtained from wind tunnel tests or another verification method.
(7) Wind loads in across-wind and torsional directions
It is difficult to predict responses in the across-wind and torsional directions theoretically like
along-wind responses. However, a prediction formula is given in these recommendations based on the
fluctuating overturning moment in the across-wind direction and the fluctuating torsional moment for
the first vibration mode in each direction.
(8) Vortex induced vibration and aeroelastic instability
Vortex-induced vibration and aeroelastic instability can occur with flexible buildings or structural
members with very large aspect ratios. Criteria for across-wind and torsional vibrations are provided
for buildings with rectangular sections. Criteria for vortex-induced vibrations are provided for
buildings and structural members with circular sections. If these criteria indicate that vortex-induced
vibration or aeroelastic instability will occur, structural safety should be confirmed by wind tunnel
tests and so on. A formula for wind load caused by vortex-induced vibrations is also provided for
buildings or structural members with circular sections.
– C6-12 –
Recommendations for Loads on Buildings
(9) Small-scale buildings
For small buildings with large stiffness, the size effect is small and the dynamic effect can be
neglected. Thus, a simplified procedure is employed.
(10) Effect of neighboring buildings
When groups of two or more tall buildings are constructed in proximity to each other, the wind flow
through the group may be significantly deformed and cause a much more complex effect than is
usually acknowledged, resulting in higher dynamic pressures and motions, especially on neighboring
downstream buildings.
(11) Assessment of building habitability
Building habitability against wind-induced vibration is usually evaluated on the basis of the
maximum response acceleration for 1-year-recurrence wind speed. Hence, these recommendations
show a map of 1-year-recurrence wind speed based on the daily maximum wind speed observed at
meteorological stations and a calculation method for response acceleration.
(12) Shielding effect by surrounding topography or buildings
When there are topographical features and buildings around the construction site, wind loads or
wind-induced vibrations are sometimes decreased by their shielding effect. Rational wind resistant
design that considers this shielding effect can be performed. However, changes to these features during
the building’s service life need to be confirmed. Furthermore, the shielding effect should be
investigated by careful wind tunnel study or other suitable verification methods, because it is generally
complicate and cannot be easily analyzed.
CHAPTER 6
WIND LOADS – C6-13 –
Start
A6.1.1 Velocity pressure
A6.1.2 Design wind speed
A6.1.3 Basic wind speed
A6.1.4 Wind directionality factor
A6.1.5 Wind speed profile factor
A6.1.6 Turbulence intensity and turbulence
scale
A6.1.7 Return period conversion factor
A6.11 Simplified procedure
Outline of building
A6.1 Wind speed and velocity pressure
6.1.3 Buildings to be designed for particular
wind load or wind induced vibration
(1) across-wind, torsional wind loads
(2) vortex induced vibration,
aeroelastic instability
A6.12 Effects of neighboring tall buildings
Wind load on structural frames
Wind tunnel experiment
Wind load on components/cladding
A6.2.1 Procedure for estimating wind force coefficients
A6.2.2 External wind pressure coefficient
A6.2.3 Internal pressure coefficients
A6.2.4 Wind force coefficients
A6.2.5 Peak external pressure coefficients
A6.2.6 Factor for effect of fluctuating internal
pressures
A6.2.7 Peak wind force coefficient
A6.3.2 Gust effect factor
for roof wind loads
A6.3.1 Gust effect factor
for along-wind loads
6.2 Horizontal wind load
6.3 Roof wind load
6.4 Wind load on
components/cladding
A6.4 Across-wind load
A6.5 Torsional wind load
A6.8 Combination of wind loads
A6.6 Horizontal wind loads on lattice
structural frames
A6.7 Vortex induced vibration
A6.13 1-year-recurrence wind speed
A6.10 Response acceleration
End
Figure 6.1.4
Flow chart for estimation of wind load
– C6-14 –
6.1.3
Recommendations for Loads on Buildings
Buildings for which particular wind load or wind induced vibration need to be taken into
account
(1) Buildings for which horizontal wind loads on structural frames in across-wind and torsional
directions need to be taken into account
Horizontal wind loads on structural frames imply along-wind load, across-wind load and torsional
wind load. Both across-wind load and torsional wind load must be estimated for wind-sensitive
buildings that satisfy Eq.(6.1). Figure 6.1.5 shows the definition of wind direction, 3 component wind
loads and building shape.
Ｂ
Ｄ
along-wind
Ｈ
torsion
across-wind
Figure 6.1.5
wind
Definition of load and wind direction
Both across-wind vibration and torsional vibration are caused mainly by vortices generated in the
building’s wake. These vibrations are not so great for low-rise buildings. However, with an increase in
the aspect ratio caused by the presence of high-rise buildings, a vortex with a strong period uniformly
generated in the vertical direction, and across-wind and torsional wind forces increase. However, with
increase in building height, the natural frequency decreases and approaches the vortex shedding
frequency. As a result, resonance components increase and building responses become large. In
general, responses to across-wind vibration and torsional vibration depending on wind speed increase
more rapidly than responses to along-wind vibration. Under normal conditions, along-wind responses
to low wind speed are larger than across-wind responses. However, across-wind responses to high
wind speed are larger than along-wind responses. The wind speed at which the degrees of along-wind
response and across-wind response change places with each other differs depending on the height,
shape and vibration characteristics of the building. The condition with regard to the aspect ratio of
Eq.(6.1) has been established through investigation of the relationship between the magnitude of
along-wind loads and across-wind loads for flat terrain subcategory II and a basic wind speed of 40m/s
assuming 180kg/m3 building density, f1 = 1 /(0.024 H ) (Hz) natural frequency of the primary mode
and 1% damping ratio for an ordinary building. Therefore, it is desirable to estimate across-wind and
torsional wind loads even for buildings of light weight and small damping to which Eq.(6.1) is not
CHAPTER 6
WIND LOADS – C6-15 –
applicable.
Furthermore, for flat-plane buildings with small torsional stiffness or buildings with large
eccentricity whose translational natural frequency and torsional natural frequency approximate each
other, it is also desirable to estimate the torsional wind loads even where Eq.(6.1) is not applicable to
those buildings.
The discriminating conditional formula shown in this chapter was derived for a building with a
rectangular plane. It is possible to apply Eq.(6.1) to a building with a plane that is slightly different
from rectangular by regarding B and D roughly as projected breadth and a depth. For values of B
and D changed in the vertical direction, the wind force acting on the upper part has a major effect on
the response. Therefore, a representative value for the upper part should used for the computation.
Under normal conditions, a value in the vicinity of 2/3 of the building height is chosen in most cases.
The computation of Eq.(6.1) using a smaller value for the upper part yields a conservative value.
(2) Vortex resonance and aeroelastic instability
It is feared that aeroelastic instabilities such as vortex-induced vibration, galloping and flutter occur
in buildings with low natural frequency and are high in comparison with their breadth and depth, as
well as in slender members. The conditions for estimation of aeroelastic instability in both across-wind
vibration and torsional vibration for building with rectangular planes as well as the conditions for
estimation of vortex-induced vibrations for a building with a circular plane are given based on wind
tunnel test results and the field measurement results 1)-6). The method for estimating the wind load for a
building with a circular plan when vortex-induced vibration occurs is shown in A6.7. It may well be
that vortex-induced vibration and aeroelastic instability will occur in a slender building with a
triangular or an elliptical plan. Therefore, attention must be paid to this.
The first condition required for estimating aeroelastic instability and vortex-induced vibration is the
aspect ratio ( H / BD or H / Dm ). Aeroelastic instability as well as vortex-induced vibration does
not occur easily in buildings with a small aspect ratio. Under this recommendation, the aspect ratio for
estimating both aeroelastic instability and vortex-induced vibration was set to 4 or more and 7 or more,
respectively. The second condition for estimating non-dimensional wind speed is ( U / f BD or
U / fDm ). The occurrence of aeroelastic instability and vortex-induced vibration is dominated by the
non-dimensional wind speed, which is determined by the representative breadth of the building, its
natural frequency and wind speed. The non-dimensional critical wind speed for aeroelastic instability
depends upon the mass damping parameter, which is determined by the side ratio, the turbulence
characteristics of an approaching flow and the mass and damping ratio of a building. Thus, the
non-dimensional critical wind speed with regard to the estimation of aeroelastic instability of a
building with a rectangular plane was provided as the function for those parameters. The
non-dimensional wind speed for vortex-induced vibration of a building with a circular plan is almost
independent of this parameter. Therefore, the value for non-dimensional critical wind speed is fixed.
The non-dimensional wind speed for estimating aeroelastic instability and vortex-induced vibration is
set at 0.83(=1/1.2) times the non-dimensional critical wind speed. This is because it is known that
– C6-16 –
Recommendations for Loads on Buildings
aeroelastic instability or vortex-induced vibration occurs within a period shorter than 10 min, which is
the evaluation time for wind speed prescribed in this recommendation, and that the uncertainty of the
non-dimensional wind speed including errors in experimental values is taken into account.
Furthermore, the damping ratio of a building is required for the computation of the building’s mass
damping parameter. It is thus recommended that the damping ratio of a building be estimated through
reference to “Damping in Buildings” 7).
6.2
6.2.1
Horizontal Wind Loads on Structural Frames
Scope of application
This section describes horizontal wind loads on structural frames in the along-wind direction. The
along-wind load is generally composed of a mean component caused by the mean wind speed, a
quasi-static component caused by relatively low frequency fluctuation and a resonant component
caused by fluctuation in the vicinity of the natural frequency. For many buildings, only the first mode
is taken into account as the resonant component. The procedure described in this section can estimate
the equivalent static wind load producing the maximum structural responses (load effects of stress and
displacement) using the gust effect factor. The equivalent static wind load is also divided into the mean
component, quasi-static component and resonant component. Although the vertical profiles for these
components are different from each other, it is assumed that all profiles similar to that of the mean
component are provided.
6.2.2
Estimation method
Equation (6.4) for horizontal wind loads is derived from a gust effect factor method, which includes
the effect of along-wind dynamic response due to atmospheric turbulence of approaching wind. The
gust effect factor is a magnifying rate of the maximum instantaneous value to the mean building
responses. Davenport, who first proposed the gust effect factor, calculated this factor based on the
displacement at the highest position of a building8). However, in these recommendations the gust effect
factor based on the overturning moment of a base9), which can rationally estimate the design wind load
for a building, was employed. Projected area A is the area projected from the wind direction for the
portion concerned, as shown in Fig.6.2.1, and for wind load at a unit height being taken into account,
projected area A becomes projected breadth B .
CHAPTER 6
Ｂ
WIND LOADS – C6-17 –
Ｄ
ＷD
Ｈ
Ａ
wind
Figure 6.2.1
6.3
6.3.1
Projected area
Roof Wind Load on Structural Frames
Scope of application
Roof wind loads on structural frames should be estimated from load effects of wind forces that act
on roof frames. The properties of wind forces acting on roofs are influenced by the external pressures,
which are affected by the behavior of the separated shear layers from leading edges, and the internal
pressures, which are affected by the building’s permeability. This section describes equations to be
applied to roof frames of buildings with rectangular plan without dominant openings, where the
correlation between fluctuating external pressures and fluctuating internal pressures can be ignored.
A light roof like a hanging roof might generate aerodynamically unstable oscillations. These
oscillations may be generated in roof frames that satisfy the conditions of m / ρL < 3 , U H / f R1 L > 1
and I H < 0.15 , where m is mass per unit area, ρ is air density, L is span length, U H is design
wind speed, f R1 is frequency of first unsymmetrical vibration mode and I H is turbulence intensity
at reference height10),11). In addition, note that large amplitude vibration may occur on large-span roofs
with light weight because the deflection or oscillation-induced wind force due to mean wind pressure
seems to make the stiffness weak. In these cases, wind tunnel tests must be carried out to ensure that
aerodynamic instability such as self-excited oscillation does not occur within the design wind speed.
6.3.2
Procedure for estimating wind loads
The equivalent static wind loads on roofs can be estimated by the gust effect factor method, which
includes the effects of fluctuating external pressures and fluctuating internal pressures for roof
responses. The gust effect factor is only formulated under the condition where beam oscillation is
dominated by the fundamental mode. The equivalent static wind load distribution that produces the
maximum load effect on a roof is not strictly similar to the mean wind pressure distribution. However,
to simplify the procedure, the wind load can be estimated by multiplying the gust effect factor by the
mean wind force distribution.
– C6-18 –
6.4
Recommendations for Loads on Buildings
Wind Loads for Components/Cladding
6.4.1
Scope of application
Wind loads on components/cladding need to be designed for parts of buildings; finishings of roofs
and external walls; bed members such as purlins, furring strips and studs; roof braces; and tie beams
subject to strong effects of intensive wind pressure. These wind loads are also applied to the design of
eaves and canopies.
6.4.2
Procedure for estimating wind loads
Wind loads on components/cladding are derived from the difference between the wind pressures
acting on the external and internal faces of a building, and are calculated from Eq.(6.6). Peak wind
force coefficients Ĉ C corresponding to the peak values of fluctuating net pressures, defined by the
difference between external and internal pressures, are given by Eq.(A6.15) for convenience. For
buildings such as free-standing canopy roofs, where the top and bottom surfaces are both exposed to
wind, the peak wind force coefficients Ĉ C are derived directly from the actual peak values of
pressure differences, as shown in section A6.2.7.
External pressure coefficients provided in the Recommendations correspond to the most critical
positive and negative peak pressures on each part of a building irrespective of wind direction.
Therefore, when the wind loads are calculated by considering the directionality of wind speeds, the
peak pressure or force coefficients for each wind direction are needed, which should be determined
from appropriate wind tunnel experiments or some other method12).
The subject area AC depends on the item to be designed. When designing the finishing of roofs and
external walls, the supported area of the finishing is used, and when designing the supports of the
finishing, the tributary area of the supports is used.
A6.1
A6.1.1
Wind speed and velocity pressure
Velocity pressure
The velocity pressure, which represents the kinetic energy per unit volume of the air flow, is the
basic variable determining the wind loading on a building.. It corresponds to the rise in pressure from
the free stream (atmospheric ambient static pressure) to the stagnation point on the windward face of
the building, and is defined as (1 2)ρU 2 , where U is the wind speed.
It is only necessary to consider the velocity pressure as the basic variable of wind loading when
static effects of the wind are examined. However, it is more appropriate to adopt wind speed as the
basic variable when dynamic wind effects are under discussion. Thus, wind speed is adopted in the
recommendations as the basic variable for calculating wind loading. The design velocity pressure, qH ,
which is based on the design wind speed U H at the reference height H , is defined in Eq.(A6.1).
CHAPTER 6
WIND LOADS – C6-19 –
Air density ρ varies with temperature, ambient pressure and humidity. However, the influence of
humidity is usually neglected. In these recommendations, the air density is taken as ρ = 1.22 (kg/m3),
which corresponds to a temperature of 15°C and an ambient pressure of 1013 hPa.
A6.1.2
Design wind speed
The wind speed at a construction site is a function of its geographical location, orography or
large-scale topographic features (e.g. mountain ranges and peninsulas) as well as the ground surface
conditions (e.g. size and density of obstructions such as buildings and trees), and small-scale
topographic features (e.g. escarpments and hills). The height above ground level is also a factor. Of
these factors, the geographical location and large-scale topographical features are reflected in the
values of basic wind speed U 0 and wind directionality factor K D . The influences of surface
roughness, small-scale topographical features and elevation are reflected in the wind speed profile
factor E H .
Designers are required to decide the wind load level by considering the building’s social importance,
occupancy, economic situation and so on. This is represented by the return period conversion factor
k rW . The basic wind load defined in 2.2 is that corresponding to the 100-year-recurrence wind speed,
which is calculated from Eq.(A6.2) by substituting k rW = 1 . The wind directionality factor K D , a
newly introduced parameter in this version, makes the design more rational by considering the
dependencies of the wind speed, the frequency of occurrence of extreme wind and the aerodynamic
property on wind direction. The wind directionality factor K D is affected by the frequency of
occurrence and the routes of typhoons, climatological factors, large-scale topographic effects and so
on.
If the design ignores wind directionality effects, the design wind speed U H can be calculated by
substituting K D = 1 in Eq.(A6.2).
A6.1.3
Basic wind speed
The basic wind speed U 0 is the major variable in Eq.(A6.2) for calculating the design wind speed.
The wind speed at a construction site is influenced by the occurrence of typhoon and monsoon, the
longitude and latitude of the location and large-scale topographical effects. The basic wind speed
reflects the effects of these factors. The value of the basic wind speed corresponds to the
100-year-recurrence 10-minute-mean wind speed over a flat and open terrain (category II) at an
elevation of 10m. Figure A6.1.1 shows the procedure for making the basic wind speed map. As the
first step of the procedure, data from different metrological stations were adjusted or corrected to
reduce them to a common base considering the directional terrain roughness. Then extreme value
analyses were conducted for mixed wind climates of typhoon winds and non-typhoon winds. For
typhoon winds, a Monte-Carlo simulation based on a typhoon model was also conducted for each
meteorological station in Japan. Although the analysis was conducted with consideration of wind
directionality effect, the basic wind speed was considered as a non-directional value. Instead, the wind
– C6-20 –
Recommendations for Loads on Buildings
directionality effect was reflected by introducing the wind directionality factor, which is defined as the
wind speed ratio for a certain wind direction to the basic wind speed, as defined in A6.1.4.
Records of wind speed and direction
(for all meteorological stations from
1961 to 2000)
Evaluation of terrain category
(considering historical variation)
Reduction to the common base
Extreme value probability
analysis for mixed wind climates
Modeling of typhoon pressure fields
(based on data from 1951 to 1999)
Monte Carlo simulation of typhoon
winds (for 5000 years)
Extraction of independent storm
(including the 2nd higher and less)
Extreme wind probability distribution
due to typhoons
Extreme wind probability distribution
due to non-typhoon winds
Synthesis of extreme value
distributions
Basic wind speed map
Figure A6.1.1
Procedure for making basic wind speed map
1) Data for analysis
Data of wind speed, wind direction and anemometer height from the Japan Meteorological Business
Support Center (Daily observation climate data from 1961-2000, Observation history at metrological
stations) were used for analysis. The daily observation climate data from 1961-1990 and the
Geophysical Review of 1951-1999 by the Japan Meteorological Agency were referred for modeling
the pressure fields and tracks of typhoons, respectively. For homogenization of the wind speed records,
data measured by different types of anemometers were corrected to those of propeller type
anemometers13).
2) Evaluation of directional terrain roughness and homogenization of wind speed
The wind speed records at the meteorological stations were homogenized, that is to say, converted
CHAPTER 6
WIND LOADS – C6-21 –
into data at a height of 10m over terrain category II by utilizing a method for evaluating the terrain
roughness from the pseudo-gust factor (ratio of daily maximum instantaneous wind speed divided by
daily maximum wind speed) and elevation of the measurement point14). The details of the method are
as follows. The pseudo-gust factors were first averaged according to the year and wind direction. Then,
referring to the averaged pseudo-gust factors, a terrain roughness category was identified in which the
same gust-factor was given using the profiles of mean wind speeds (defined in A6.1.5) and turbulence
intensity (defined in A6.1.6). For this calculation, the terrain roughness category was treated as a
continuous variable.
Figure A6.1.2 shows examples of the annual variance of terrain roughness for four dominant wind
directions measured at Fukuoka Meteorological Station, in which the symbols are for the calculated
values and the lines are the results of linear approximation. The value of roughness category was
assumed to be between I and V. This shows that the roughness category changes due to urbanization
and the roughness category varies with wind direction.
Historical changes of the directional terrain roughness were utilized for homogenization of wind
speed records at meteorological stations and calibration of wind speeds near the ground surface in the
Flat terrain categories
V
IV
III
II
I
V
Flat terrain categories
Flat terrain categories
Flat terrain categories
extreme value analysis and the typhoon model.
IV
III
II
I
Figure A6.1.2
V
IV
III
II
I
V
IV
III
II
I
Examples of evaluation for terrain roughness
3) Extreme value analysis in mixed wind climates
The extreme value analysis in mixed wind climates15) was applied to extreme wind data generated
by different wind climates, for instance, typhoons and monsoons. In this method, the extreme wind
records were divided into groups and independently fitted by extreme value distributions, and the
combined distribution was obtained assuming the independency of each extreme distribution.
Based on typhoon track data, the measuring records were divided into typhoon and non-typhoon
winds, that is, if it was within 500 km of the typhoon center, the wind climate was considered as
– C6-22 –
Recommendations for Loads on Buildings
typhoon, and otherwise as non-typhoon. The wind speed data measured in a typhoon area were
analyzed by Monte-Carlo simulation based on a typhoon model to obtain the extreme value
distribution, while those measured in a non-typhoon area were analyzed by the modified Jensen &
Franck method16) in which wind speed data smaller than the highest value were also included as
independent storms for analysis.
4) Typhoon simulation technique
In Japan, typhoons are the dominant wind climates generating strong winds that need to be taken
into account in wind resistant design, due to their high wind speeds and large influence areas. An
average of 28 typhoons occur annually, of which roughly 10% land. Typhoons sometimes do not pass
near metrological stations, so severe wind damage may occur without large wind speeds being
observed. In order to improve the instability of the statistical data (sampling error), a typhoon
simulation method was adopted for evaluating the strong wind caused by typhoons.
Figure A6.1.3 shows a general procedure of this typhoon simulation method. The pressure fields of
typhoons are modeled by several parameters, i.e. central pressure depth, radius to maximum winds,
moving speed, etc. The non-exceedance probability of strong wind in the target area is evaluated by
generating virtual typhoons according to the results of statistical analysis of pressure field parameters.
This Monte-Carlo simulation method is considered in recommendations of other countries. For
example, in the ASCE17) standard, simulation is required as a principle for evaluation of the design
wind speed in hurricane-prone regions. In this standard, the simulation results were adopted as the
value of basic wind speed. In order to improve the accuracy of typhoon simulation18), correlations
between gradient winds and near-ground winds and correlations among parameters of typhoon
pressure fields in each area are considered.
CHAPTER 6
rate of occurrence
initial position
rate of occurrence
central pressure
depth
WIND LOADS – C6-23 –
moving speed and
direction
pressure field
radius of maximum wind
initial position
moving velocity
wind speed field
gradient wind
central pressure depth
correlation of wind speed
and direction based on
observed records
radius of maximum wind
Probability distributions
surface wind
return period r
statistics of
historical typhoons
Figure A6.1.3
General procedure for typhoon simulation
The non-exceedance probability of the annual maximum wind speed caused by a typhoon was
obtained from the typhoon simulation. For strong wind not caused by a typhoon, extreme value
analysis was conducted on data observed from 1961-2000. The results obtained from typhoon and
non-typhoon conditions were combined to evaluate the return period of annual maximum wind speed.
Figure A6.1.4 shows an example of the maximum wind speed evaluated at K city.
– C6-24 –
Recommendations for Loads on Buildings
Figure A6.1.4
Example of maximum wind speed evaluated at K city
5) Map of basic wind speed
The contour line of 100-year-recurrence wind speed was somewhat complicated even though the
data obtained in 4) had been homogenized according to surface roughness, wind direction, etc. This
was assumed to be due to the influences of local topography and structures surrounding the
metrological station and the applicability of the homogenization models. To remove such local effects,
spatial smoothing was conducted.
In addition, the lower limit of wind speed was set to 30m/s. It is difficult to include the effects of
tornado and downburst in the analysis.
6) 100-year-recurrence wind speed in winter
100-year-recurrence wind speed in winter is necessary for combination of wind loads and snow
loads. As for the basic wind speed, 100-year-recurrence wind speed in winter reflects only the effects
of large-scale topography. Figure A6.1.5 is a spatially smoothed wind speed map made for the
100-year-recurrence wind speed at metrological stations during the snow season (from December to
March). The procedure for making this map is the same as that for Fig.A.6.1.1, except that the typhoon
simulation method is not used. Thus, the wind directionality factor should not be used ( K D = 1 ) here.
For return period factor k rW mentioned in A6.1.7, there are small differences in λU among wind
speeds in winter for different meteorological stations. An average value of λU = 1.1 can be applied
for calculating k rW in Eq.(A6.12).
CHAPTER 6
Figure A6.1.5
WIND LOADS – C6-25 –
100-year-recurrence 10-minutes mean wind speed at 10m above ground over a flat
and open terrain in winter (m/s)
– C6-26 –
A6.1.4
Recommendations for Loads on Buildings
Wind directionality factor
Meteorological stations in Japan have approximately 70 years of records at most. However, the
annual average number of typhoon landfalls in Japan is only three, so the number of typhoons
included in the records of a particular site is very limited. When the records are divided into 8 sectors
of azimuth, each sector have very few typhoon data, so sampling error is very large. Thus, typhoon
effect should be considered when wind directionality factor is determined. In these recommendations,
Monte-Carlo simulation for typhoon winds and statistical analysis on the non-typhoon observation
data had been conducted to obtain the wind directionality factor.
There are two types of wind directionality factors. One defines a wind directionality factor that
changes with direction, as shown in BS6399.219) and AS/NZS 1170.220),21), except for the
cyclone-prone regions. The other defines a constant reduction coefficient regardless of wind direction,
as in the ASCE17) standard. For the latter, it is hard to reflect directional design wind speeds in design
practice. In these recommendations, wind directionality factor was defined for each direction as for the
former type, so as to achieve reasonable wind resistant design.
Wind directionality factor was provided on the assumption that the wind load is calculated
according to the following procedure.
(1) Where the aerodynamic shape factors for each wind direction are known from appropriate wind
tunnel experiments, the wind directionality factor K D , which is used to evaluate wind loads on
structural frames and components/cladding for a particular wind direction, shall take the same value as
that for the cardinal direction whose 45 degree sector includes the wind direction. In this case, the
wind tunnel experiments should be conducted for detailed change of directional characteristics for the
aerodynamic shape factors of the structure.
(2) Where the aerodynamic shape factors in A6.2 are used
1) When assessing the wind loads on structural frames, two conditions are considered: whether or not
the aerodynamic shape factors depend on wind direction.
a) Where the aerodynamic shape factors are dependent on wind directions, four wind directions
should be considered that coincide with the principal coordinate axis of the structure. If the wind
direction is within a 22.5 degree sector centered at one of the 8 cardinal directions, the value of the
wind directionality factor K D for this direction should be adopted (Fig.A6.1.6(a)). If the wind
direction is outside the 22.5 degree sector, the larger of the 2 nearest cardinal directions should be
adopted (Fig.A6.1.6(b)). For lattice structures, the effect of inclined wind on the wind force
coefficient can be considered directly, so the same measures as for above rectangular cylinders are
adopted for the 4-leg square plane (8 directions) and 3-leg triangular plane (6 directions).
b) Where the aerodynamic shape factors are independent of wind directions, e.g. a structure that
has a circular sectional plan, the wind directionality factor K D shall take the same value as for the
cardinal direction whose 45 degree sector includes the wind direction.
2) When assessing wind loads on cladding according to the peak wind pressure coefficient in A6.2,
those obtained under the condition of K D = 1 should be used for design because the maximum peak
CHAPTER 6
WIND LOADS – C6-27 –
pressure coefficient of all directions is shown in these recommendations.
The wind directionality factors for the 8 cardinal directions shown in Table A6.1.1 were originally
obtained at 16 directions. When the 16 directional values are converted into 8 cardinal directional ones,
the values are determined to be the maximum of those for the relevant direction and its two
neighboring directions. Therefore, the value for a given direction represents the influence of a 67.5
degree sector centered on that direction. For a building with rectangular horizontal section, the wind
force coefficients for the wind directions normal to the building faces are given by these
recommendations. When the wind direction considered is at an intermediate position between two
cardinal directions shown in the table, the greater value of the two neighboring directions is adopted.
This means that the value considers the influence from a 112.5 degree sector. In addition, considering
the effects of tornado and downburst, which are difficult to take into account, the lower limit of wind
directionality factor is given as 0.85.
wind direction
N
0.9
KD=0.9
NE
0.95
NW
0.85
W
1.0
E
0.85
SW
0.95
S
0.9
SE
0.85
(a) Where the wind direction falls in a 22.5 degree sector as shown in Table A6.1.1
N
0.9
NW
0.85
wind direction
larger value of 0.9 and 0.95
KD = 0.95
NE
0.95
W
1.0
E
0.85
SW
0.95
S
0.9
SE
0.85
(b) Where the wind direction does not fall in a 22.5 degree sector as shown in Table A6.1.1
Figure A6.1.6
Selection of the wind directionality factor (when using the wind force coefficient of
buildings with rectangular horizontal sections defined in these recommendations)
– C6-28 –
Recommendations for Loads on Buildings
Where wind directionality effects are not considered, this corresponds to the condition where the
wind directionality factors equal unity for all directions. This leads a conservative design compared to
the condition when the wind directionality effects are considered.
Whether or not wind directionality effects are considered corresponds to whether or not wind
directionality factors are adopted. As shown in Table A6.1.1, the wind directionality factors are less
than unity, and are defined as values for evaluating 100-year-recurrence wind loads. It is possible to
achieve a more rational design by considering the orientation of the building plan from the viewpoint
of wind directionality factor. In other words, the wind loads are conservative if wind directionality
factor is not considered. However, the amount of this overestimation depends on the orientation of the
building, and not constant for all buildings. When wind directionality effects are considered, because
the wind directionality factor is less than unity, the wind loads will be smaller than those predicted by
conventional method, in which wind directionality is not taken into account. Designers should be
conscious of the fact that safety level decreases when wind directionality factor is utilized.
The wind directionality factors defined in these recommendations are valid only for locations near
major metrological stations. The wind directionality factor defined in Table A6.1.1 can be applied to
construction sites near metrological stations, but they cannot be applied to construction sites far from
metrological stations and influenced by large-scale topography. For these situations, special
consideration should be given, for instance, by not using the wind directionality factors i.e. by setting
KD = 1 .
A6.1.5
Wind speed profile factor
(1) Effects of terrain roughness and topography on wind speed profile
Wind speed near the ground varies with terrain roughness, i.e. buildings, trees, etc., and topography.
The friction force from terrain roughness and the concentration or blockage effects from topography
influence the atmospheric boundary layer from the ground to the gradient height. In the
recommendations, the influence of surface roughness on the wind speed profile over flat terrain is
expressed by E r , while the influence of small-scale topographical features is represented by Eg .
(2) Wind speed profile over flat terrain
Terrain roughness causes a gradual decrease in wind speed toward the ground. The domain than is
influenced by terrain roughness is called the boundary layer, where the wind speed profile changes
with terrain roughness category. The boundary layer depth increases with fetch length, which means
that the wind speed profile extends to a higher elevation downstream. In addition, the boundary layer
tends to develop faster when the terrain is rougher.
For a fully developed boundary layer, the velocity profile can be represented by a power law or a
logarithmic law. The following power law is adopted in the recommendations:
Z
U Z = U Z0 ( )α
Z0
(A6.1.1)
where U Z (m/s) is the mean wind speed at height Z (m), U Z0 (m/s) is the mean wind speed at height
CHAPTER 6
WIND LOADS – C6-29 –
Z 0 , and α is the power law exponent.
It has been realized from many observation data that the power law exponent becomes greater as the
terrain becomes rougher.
However, it is rare for the terrain roughness to be uniform over a long fetch. Roughness conditions
usually vary. When the terrain roughness changes suddenly, a new boundary layer develops according
to the new terrain roughness which gradually propagates with elevation and fetch, such that wind
speeds above this new boundary layer remain unchanged after the roughness change. Thus, the wind
speed profile corresponding to the new roughness condition can not be applied to the high elevation.
This tendency is particularly obvious when the wind flows from the sea to city center, where the
roughness changes suddenly from smooth to rough. After a fetch of approximately 3km (or 40 H ) the
new boundary layer is considered fully developed. Hence, in the recommendations, the roughness
condition in the region of the smaller of 40 H and 3km upstream from the construction site is
considered when the roughness category, shown in Table A6.2 is to be determined.
The influence of terrain roughness becomes smaller at higher elevations. In the recommendations, it
is assumed that the design wind speed at Z G is not influenced by terrain roughness, and is
considered constant for convenience. However, it does not mean that wind speeds at elevations greater
than Z G are really constant. Since the boundary layer depth becomes greater when the terrain
roughness increases, Z G is assumed to increase with terrain category, as shown in Table A6.3.
However, Z G is defined just for the utilization of the power law for different terrain categories,
because the velocity profile is actually unknown in detail at higher elevations. It is different from the
boundary layer depth.
CFD studies on the wind speed profile in urban area show that the wind speed below a certain
height Z b does not follow the power law when the ratio of building plan area to regional area is over
a few percent, as shown in Fig.A6.1.7. The wind speed profile here is complex due to nearby buildings.
For heights below Z b , the wind speed at Z b is usually the maximum, so the wind speeds in this
region are assumed to equal to that at Z b , which is defined in Table A6.3, in order to arrive at a safer
design. For heights above Z b , the power law can approximate the mean wind speed profile.
height
Zb
Figure A6.1.7
Mean wind speed profile in urban area
– C6-30 –
Recommendations for Loads on Buildings
Figure 6.1.8 shows an example of mean wind speed profiles measured in natural wind22), in which
the wind speed profiles measured simultaneously at coastal and inland locations are compared. As
mentioned before, the wind speed near the ground decelerates due to the inland terrain roughness. As a
result, there is great difference between the wind speed profiles in the two locations.
The exposure factor E r of the flat terrain, shown in A6.1.5(2) 2), is defined with the above
considerations included. Figure A6.1.9 shows E r for each terrain category. The exposure factor is the
ratio of wind speed at a given height Z
for each terrain category to the wind speed at 10m over
terrain roughness category II.
Mean wind speed (m/s)
Figure A6.1.8
Example of mean wind speed profiles measured simultaneously at the coast of Tokyo
bay and a suburban residential area 12km away22)
terrain category
Exposure factor E r
Figure A6.1.9
Exposure factor E r
CHAPTER 6
WIND LOADS – C6-31 –
Figure A6.1.10 shows an example of terrain roughness categories.
Terrain category I represents open sea or lake, or unobstructed coastal areas on land.
Terrain category II is defined as terrain with scattered obstructions up to 10m high. Rural areas are
representative. Low rise building areas also belongs to this category, if the building area ratio (total
building plan area divided by regional area) is less than 10.0%.
Terrain category III is characterized be closely spaced obstructions up to 10m high, or by sparsely
spaced medium-rise buildings of 4-9 stories. Suburban residential areas, manufacturing districts, and
wooded fields are typical of this category. The area where the building area ratio is between 10% and
20%, or the building area ratio is larger than 10% while the high-rise building ratio (plan area of
buildings higher than 4 stories divided by total area of buildings) is less than 30% belongs to this
category. The example in Fig.A6.1.10(c) is an area with a building area ratio of 30% and a high-rise
building ratio of 5-20%.
(a) Terrain category I
(b) Terrain category II
(c) Terrain category III
(d) Terrain category IV
(e) Terrain category V
Figure A6.1.10
Example of surface roughness (Photos provided by Kindai Aero Inc.)
– C6-32 –
Recommendations for Loads on Buildings
Terrain category IV is mainly where many 4-9 story buildings stand. Local central cities are typical
of this category. Areas with a building area ratio larger than 20%, and a high-rise building ratio larger
than 30% belong to this category.
In terrain category V, tall buildings of 10 or more stories are close together at a high density. Central
regions of large cities such as Tokyo and Osaka belong to this category.
In an area where the building purpose, floor area ratio and building coverage ratio are the same, the
terrain can usually be considered uniform.
Typically, in the wide area around the construction site,
the terrain roughness is not usually identical. It is common for several terrain categories to co-exist.
When the terrain roughness changes downstream, a new boundary layer gradually develops, and the
developing process depends on whether the change is from smooth to rough or rough to smooth.
Figure A6.1.11 illustrates approximately the development of a new boundary layer with a terrain
roughness change from smooth to rough. When the terrain roughness changes from smooth to rough,
the new boundary layer develops slowly, so the fully developed boundary layer over the new
roughness can not be anticipated if the fetch downstream is not long enough. As a result, a wind speed
profile corresponding to the new roughness category can not be adopted. Thus, if there is a terrain
roughness change from smooth to rough within a distance of the smaller of 40 H and 3km upstream
of the construction site, the terrain category at the upstream region before the roughness change will
be adopted as the terrain category for the construction site.
developing internal
boundary layer
Smooth
Figure A6.1.11
Rough
3 ~ 5km
Developing process of new boundary layer when terrain roughness changes from
smooth to rough
In determining the terrain category for a given wind direction, the upwind area inside a 45 degree
sector within a distance of the smaller of 40 H and 3km of the construction site will be counted.
When there is a terrain roughness change upwind of the construction site, a weighting average of
the wind speed profile on roughness and the fetch distance is conducted in AS/NZS 1170.220) to
determine the exposure factor.
However, in the recommendations, the overall terrain roughness in the upwind sector is adopted as
the terrain category in this direction if there is no sudden roughness change. Generally, the wind load
will be overestimated when a smoother surface roughness category is utilized.
CHAPTER 6
WIND LOADS – C6-33 –
For an urban area centered on a railway station, larger buildings are closely spaced near the station.
Figure A6.1.12 shows an example of how to determine the terrain category if a construction site is
near a railway station, in which the roughness changes from smooth to rough downstream. In this case,
where there is a sudden roughness change within a distance of the smaller of 40 H and 3km upwind
of the construction site, the smoother terrain category upwind before the terrain roughness change will
be selected.
Wind
Category I
Category III
smaller of
40H and 3km
Figure A6.1.12
The terrain roughness
in this wind direction
should be recognized as
category I.
Selection of terrain category (with terrain roughness change from smooth to rough)
If the terrain roughness changes from rough to smooth, the terrain category after the terrain
roughness change is selected. However, if there is a smooth area in a rough area, e.g. a park in a
downtown area, it is sometimes necessary to consider the acceleration of wind speed near the ground
downstream.
Generally, careful consideration should be given in the determination of terrain category, because of
the arbitrariness.
(3) Topography factor
When air flow passes escarpments or ridge-shaped topography as shown in Fig.A6.1.13, the flow is
blocked on the front of the escarpment and the mean wind speed decreases. Then the flow starts to
accelerate uphill, resulting in a mean wind speed larger than that of the flat terrain from the middle of
the upwind slope to the top of the topographic feature. If the upwind slope is not large enough, the
mean wind speed is larger than that over the flat terrain over a long region downstream of the hill top.
However, if the upwind slope is sufficiently steep to establish separation downstream of the hill top,
the wind speed downstream of the hill top near the ground is smaller than that of the flat terrain.
– C6-34 –
Recommendations for Loads on Buildings
Figure A.6.1.13
Change of mean wind speed over an escarpment (thin solid line and thick solid line
are for the mean wind speed over flat terrain and escarpments respectively)
Equation A6.5 for the topography factor is based on the results of wind tunnel experiments of
two-dimensional escarpments and ridge-shaped topography with different slopes23),
24), 25)
. The
experiments were carried out with an approach flow corresponding to terrain category II. The models
corresponded to escarpments and ridge-shaped topography with heights between several tens of meters
to 100m with smooth surfaces. The ratio of the mean wind speed over the escarpments to the
counterpart over flat terrain was obtained from the experiments. The height Z in Eq.(A6.5) is the
height from the local ground surface over the topographic feature. The slope angle is defined with the
aid of the horizontal distance from the top of the topographic feature to the point where the height is
half the topography height.
Although, the wind speed decreases upwind of the escarpment and in the separation region
downstream of steep topography, the topography factor in these regions is defined as 1 in the
recommendations, as shown in Figs.A6.1.14 and A6.1.15, because only acceleration of wind speed is
considered24).
Figure A6.1.14
Wind speed-up ratio over a two-dimensional escarpment with an inclination angle of
60 degrees. The symbols are for the experimental results, and the solid lines are for
Eq.(A6.5)
CHAPTER 6
Figure A6.1.15
WIND LOADS – C6-35 –
Wind speed-up ratio over a two-dimensional ridge-shaped topography with
inclination angle of 30 degrees. The symbols are for the experimental results, and
the solid lines are for Eq.(A6.5)
Tables A6.4 and A6.5 show the values of the parameters in Eq.(A6.5) for the escarpment and
ridge-shaped topography determined from experiment. For a particular location and a particular slope
angle, not shown in these tables, the topography factor can be obtained by linear interpolation. The
following is an example of the procedure for calculating the topography factor of a 50-degree
escarpment, at a location with a distance X s = 1.6 H s downstream of the top of the escarpment at a
height Z = 1.5 H s .
z
Calculate the topography factor Eg1 and E g 2 at X s / H s = 1 and 2 for the inclination
angle of 45 degrees from Eq.(A6.5), and then calculate the topography factor E g12 at
X s / H s = 1.6 by linear interpolation according to the following equation:
Eg12 = 0.4 Eg1 + 0.6 Eg 2
z
Calculate the topography factor Eg 34 for the inclination angle of 60 degrees in the same
z
way as for the inclination angle of 45 degrees.
Conduct linear interpolation for topography factors E g12 and Eg 34 , with respect to the
inclination angle to achieve the topography factor at an inclination angle of 50 degrees
and X s / H s = 1.6 from the following equation.
2
1
Eg12 + Eg34
3
3
If the inclination angle is less than 7.5 degrees, the topography effect can be neglected.
Eg =
The topography factor calculated from Eq.(A6.5) is shown in Figs.A6.1.14 and A6.1.15 by a solid
line. It agrees well with the experimental data at all sections with speedup..
Equation (A6.5) is for the condition in which the air flow passes at right angles to the
two-dimensional escarpments and ridge-shaped topography. However, strict two-dimensional hills do
not exist, and flow does not always pass escarpments and ridge-shaped topography at right angles.
However, even in these conditions, Eq.(A6.5) can be applied if the terrain extends a distance of several
– C6-36 –
Recommendations for Loads on Buildings
times the height of the topographic feature in the traverse direction. In addition, as has been shown in
experimental and CFD studies, the speed-up ratio of two-dimensional topography is greater than that
of three-dimensional topography, and so application of Eq.(A6.5) to three-dimensional topography is
conservative26).
Complex terrain may increase the wind speed in valleys, which is not considered in this equation. In
such cases, it is recommended to investigate the topography factor by wind tunnel or CFD studies
when the construction site is very complex.
Figure A6.1.16
Interpolation procedure for calculating topography factor with inclination angle of
50 degrees and X s / H s = 1.6
A6.1.6
Turbulence intensity and turbulence scale
Natural wind speed fluctuates with time. The wind speed U (t ) at a point, shown in Fig.A6.1.17,
can be separated into a mean wind speed component U and a fluctuating wind speed component
u (t ) in the longitudinal direction as well as v (t ) and w(t ) in the cross wind directions. Usually, the
longitudinal fluctuating wind speed component u (t ) is important for design of buildings, so only the
characteristics of u (t ) are defined in the recommendations. For long-span structures such as bridges
and for tall slender buildings, the vertical and lateral fluctuating wind-speed components w(t ) and
v(t ) are also sometimes important.
CHAPTER 6
Figure A6.1.17
WIND LOADS – C6-37 –
Mean wind and component of turbulence
(1) Turbulence intensity
1) On flat terrain
Wind speed fluctuation can be expressed quantitatively by a statistical approach. Turbulence
intensity I indicates the turbulence level and it is defined in the following equation as the ratio of
standard deviation of the fluctuating component σ u to the mean wind speed U .
I=
σu
(A6.1.2)
U
Turbulence is generated by the friction on the ground and drag on surface obstacles, and is
influenced by the terrain roughness just as is the mean wind speed profile. Figure A6.1.18 shows the
turbulence intensity observed in the natural wind and the recommended values calculated from
Eq.(A6.8).
eq.(A6.8)
eq.(A6.8)
Turbulence intensity IrZ Turbulence intensity IrZ
Terrain category I
Terrain category II
Figure A6.1.18
eq.(A6.8)
eq.(A6.8)
Turbulence intensity IrZ Turbulence intensity IrZ
eq.(A6.8)
Turbulence intensity IrZ
Terrain category III Terrain category IV Terrain category V
Observed turbulence intensity27) and recommended value
The turbulence intensity I Z at height Z
above the ground, is defined in Eq.(A6.7), in which the
turbulence intensity I rZ on flat terrain expressed in Eq.(A6.8), and the topography factor EgI , shown
in Tables A6.6 and A6.7, is considered separately.
2) Topography factor for turbulence intensity
Not only the mean wind speed, but also the wind speed fluctuation is influenced by topography.
– C6-38 –
Recommendations for Loads on Buildings
Especially in the separation region, there is an obvious increase in the standard variation of the wind
speed fluctuating component u (t ) (fluctuating wind speed hereafter) compared to that on flat terrain,
as Figs.A.6.1.19 and A6.1.20 show. Mean and fluctuating wind speed variation are closely related..
The location of the maximum fluctuating wind speed generally corresponds to the location where the
vertical gradient of mean wind speed is maximum. The region where the fluctuating wind speed is
greater than the flat terrain counterpart is generally inside the separation region when the mean wind
speed is smaller than that on flat terrain.
Figure A6.1.19
Topography factor for fluctuating wind speed on an escarpment with inclination
angle of 60 degrees. The symbols are for the experimental results, and the thick
solid lines are for Eq.(A6.10).
Figure A6.1.20
Topography factor for fluctuating wind speed on ridge-shaped topography with
inclination angle of 30 degrees. The symbols are for the experimental results, and
the thick solid lines are for Eq.(A6.10).
In the recommendations, the topography factor for turbulence intensity is defined as the ratio of the
topography factor for fluctuating wind speed to the topography factor for mean wind speed.
Topography factor for fluctuating wind speed is defined in Eq.(A6.10), in which the values of the
parameters besides C1 , C 2 and C3 are identical to those in Eq.(A6.5) for the topography factor for
mean wind speed. Equation (A6.10) is based on the results of wind tunnel experiments on escarpments
and ridge-shaped topography, as for Eq.(A6.5). The experiments were carried out with an approach
flow corresponding to terrain category II. The models corresponded to escarpments and ridge-shaped
CHAPTER 6
topography with a height of about 50m23),
24), 25)
WIND LOADS – C6-39 –
. Topography factors of mean wind speed and
fluctuating speed are defined to be greater than 1 without considering the decrease in mean wind speed
and fluctuating wind speed due to topography effects24). However, when the topography factor for
fluctuating wind speed is smaller than that for mean speed, the topography factor for turbulence
intensity will be smaller than 1.
Fluctuating wind speed near the ground becomes greater on the leeward slope of escarpments or
ridge-shaped topography. In these regions the mean wind speed is smaller, which results in the
maximum instantaneous wind speed being smaller than that for flat terrain in this area, as shown in
Fig.A6.1.21. Because the decrease in mean wind speed is not considered in A6.1.5, the maximum
instantaneous wind speed, and thus the wind load, is possibly overestimated in the separation region if
only the topography factor of fluctuating wind speed is fitted to the experimental data. In order to
reduce this possible overestimation, the actual topography factor for the fluctuating wind speed
(<1)
where the topography factor for mean wind speed is 1, was utilized for the whole region with
deceleration, as shown in Figs.A6.1.19 and A6.1.20. Figure A6.1.21 shows the profile of maximum
instantaneous wind speed as a solid line, calculated by using the topography factors for mean wind
speed and fluctuating wind speed.
Figure A6.1.21
Variation of maximum instantaneous speed over a ridge-shaped topography with an
inclination angle of 30 degrees. The symbols are for the experimental results, and
the solid lines are calculated from the topography factors for mean wind speed and
fluctuating wind speed
For a particular slope and a location of escarpment or ridge-shaped topography, not shown in Tables
A6.6 and A6.7, the topography factor of fluctuating wind speed can be obtained by linear interpolation,
In addition, when the slope of the topographic feature is less than 7.5 degrees, it is not necessary to
consider the topography factor of turbulence intensity because the fluctuating wind speed is almost
uninfluenced by the topography.
Figures A6.1.19 and A6.1.20 show the topography factor of fluctuating wind speed calculated from
Eq.(A6.10) as a solid line. It agrees well with the experimental data at any position and slope on the
escarpment. However, the topography factor for fluctuating wind speed does not match well with
– C6-40 –
Recommendations for Loads on Buildings
Eq.(A6.10) for the ridge-shaped topography because of the complexity of the change of fluctuating
wind speed, but the coincidence is good where the topography factor of mean speed is larger than 1.
Although Eq.(A6.10) is obtained from experiments carried out on a two-dimensional escarpment and
ridge-shaped topography with the oncoming airflow passing at right angles, it can be applied to
topography that extends a long distance in the transverse direction several times the height of the
topography26). However, if the construction site is in a complex terrain, it is necessary to investigate
the topography factor for fluctuating wind speed by wind tunnel or CFD studies.
(2) Power spectral density
Power spectral density reflects the contribution to turbulence energy at each frequency. In the
recommendations, a von Karman type power spectrum, expressed by Eq.(A6.1.3), is employed to
express the power spectral density of fluctuating component of wind speed u (t ) .
Fu ( f ) =
4σ u2 ( L / U )
(A6.1.3)
{1 + 70.8( fL / U ) 2 }5 / 6
where
f : frequency
σ u : standard deviation of fluctuating component of wind speed u (t )
U : mean wind speed
L : turbulence scale
(3) Turbulence scale
Equation (A6.11) is used as the turbulence scale LZ of the wind speed fluctuation u (t ) at height
Z.
Turbulence scale is an important parameter in the power spectrum, expressed in Eq.(A6.1.3). It is
the averaging length scale of the turbulence vortices. Figure A6.1.22 shows an example of a profile of
turbulence scale, which can be expressed in Eq.(A6.11) independently of terrain category.
eq.(A6.11)
Figure A6.1.22
Observation of turbulence scale of wind speed fluctuation u (t )
CHAPTER 6
WIND LOADS – C6-41 –
(4) Co-coherence
Co-coherence of wind speed fluctuation Ru ( f , rz , ry ) is evaluated using Eq.(A6.1.4). It expresses
quantitatively the frequency-dependent spatial correlation of the wind speed fluctuation.
⎡ f k 2r 2 + k 2r 2
z z
y y
Ru ( f , rz , ry ) = exp ⎢−
⎢
U
⎢⎣
⎤
⎥
⎥
⎥⎦
(A6.1.4)
where
f : frequency
rz , ry : distance between 2 points in the vertical and horizontal directions
k z , k y : decaying factors reflecting the degree of spatial correlation of wind speed in the
vertical and horizontal directions
U : mean wind speed averaged at two points
It has been shown by observation that the decay factor is between 5-10.
A6.1.7
Return period conversion factor
Return period conversion factor k rW is defined as the ratio of the r -year-recurrence wind speed
U r to the 100-year-recurrence basic wind speed U 0 . In these recommendations, the maximum wind
speed corresponding to an r -year return period should be estimated using Eq.(A6.1.5), assuming a
Gumbel distribution for annual-maximum wind speeds.
1 ⎧ ⎛ r ⎞⎫
U r = − ln ⎨ln⎜
(A6.1.5)
⎟⎬ + b
a ⎩ ⎝ r − 1 ⎠⎭
where a and b are coefficients. Return period conversion factor krW is calculated approximately in
Eq.(A6.12) by using the parameter λU , which is the ratio of the 500-year-recurrence wind speed
U 500 to the basic wind speed U 0 .
The return period conversion factor estimated from Eq.(A6.12) contains large error when the return
period is not from 100-500 years, e.g., the maximum error is about 5% and 9% when the return period
is 50 and 20 years, respectively.
In addition, the value in A6.13 should be used as the 1-year-recurrence wind speed, in order to
evaluate habitability.
– C6-42 –
Recommendations for Loads on Buildings
A6.2
A6.2.1
Wind force coefficients and wind pressure coefficients
Procedure for estimating wind force coefficients
Wind force coefficients and wind pressure coefficients depend on building shape, building surface
condition, terrain condition and local topography at the construction site. Therefore, they should be
determined from wind tunnel experiments that properly simulate full-scale conditions. However, the
coefficients for buildings with regular shapes can be estimated from the procedure described in this
section. The coefficients are divided into two categories, one for the design of structural frames and
the other for the design of building components/cladding, because the wind effects on structural
frames and components/cladding are quite different from each other.
Wind force coefficients and wind pressure coefficients are generally defined in terms of the velocity
pressure qH evaluated at the reference height H . For lattice structures and members, the wind force
coefficients are defined in terms of the velocity pressure q Z evaluated at the height Z where the
members under consideration are placed.
The aspect ratio H / B is generally large for tall buildings, such as H > 45 m, for example, while
it is generally small, smaller than 1.0 in many cases, for lower buildings. The flow field around a
building changes with the aspect ratio, which results in a significant change in the wind force and
pressure coefficients. Therefore, two different procedures are provided for estimating the wind force
coefficients for buildings with H > 45 m and those with H ≤ 45 m.
The sign of the wind pressure coefficient indicates the direction of the pressure on the surface or
element; positive values indicate pressures acting towards the surface and negative values pressures
acting away from the surface (suction). In the case of curved roofs, the direction of wind pressure
varies with location, as shown in Fig. A6.2.1. The wind forces on buildings and structures are the
vector sum of the forces calculated from the pressures acting on surfaces such as walls and roofs or on
structural elements.
Wind force coefficients C D for estimating horizontal wind loads on structural frames are generally
given by the difference between the wind pressure coefficients, C pe1 and C pe2 , on the windward and
leeward faces, as shown in Eq.(A6.13); the exception is that for buildings with circular sections, where
the resultant wind force coefficients are provided. Similarly, the wind force coefficients C R for
estimating roof wind loads on structural frames are generally given by the difference between the
external and internal pressure coefficients, Cpe and C pi , on the roof, as shown in Eq. (A6.14),
except for open roofs. The wind pressure coefficients are space- and time-averaged values where the
averaging duration is 10 minutes. The averaging area depends on the building shape. The wind force
coefficients C D for estimating horizontal wind loads on lattice structures are given as a function of
the solidity ϕ . The wind force can also be calculated by using the wind force coefficients for
individual members provided in A6.2.4(5).
The peak wind force coefficients Ĉ C for the design of components/cladding are generally given
*
for the
by the difference between the peak external pressure coefficient Ĉpe and the factor C pi
CHAPTER 6
WIND LOADS – C6-43 –
effect of fluctuating internal pressures, except for open roofs, in which the value of Ĉ C is provided.
The values of Ĉpe (and Ĉ C in the open roof case) are determined from the most critical positive
*
for the effect of
and negative peak values irrespective of wind direction. Note that the factor C pi
fluctuating internal pressures is not the actual peak internal pressure coefficient Ĉ pi but an equivalent
value producing the peak wind force coefficient Ĉ C when combined with the peak external pressure
coefficient Ĉpe .
The wind force coefficients and wind pressure coefficients given in this section are all for isolated
buildings and are obtained from the results of wind tunnel experiments. When nearby buildings are
expected to influence the wind forces and pressures, it is necessary to carry out wind tunnel
experiments or other special researches to determine the coefficients12).
Figure A6.2.1
External pressure on a building with a vaulted roof in a wind parallel to the gable
walls
A6.2.2 External pressure coefficient for structural frames
(1) External pressure coefficients Cpe for buildings with rectangular sections and heights greater than
45m
External pressure coefficients on the windward and leeward walls of buildings with rectangular
sections have the following features:
1) External pressure coefficients on windward walls are nearly proportional to the velocity pressure of
the approach flow, except for areas near the top and bottom of the building. In the top and bottom
areas, the external pressure coefficient is almost independent of height.
2) External pressure coefficients on leeward walls are negative and almost independent of height.
Based on these features, the vertical distribution of external pressure coefficients on windward walls
are assumed to be proportional to the factor for vertical profile ( k Z ) provided in Table A6.8, while
those on leeward walls are assumed constant regardless of height. The external pressure coefficients
on leeward walls decrease with increase in side ratio D / B . This feature is related to the behavior of
the separated shear layer from the windward edge and is reflected in the value of C pe2 . The aspect
ratio H / B of high-rise buildings with H > 45 m is in the range from 1 to 8 in most cases. In this
range, the effect of H / B on the wind pressure coefficients is not significant. Therefore, the pressure
– C6-44 –
Recommendations for Loads on Buildings
coefficients are provided independently of H / B .
The external pressure coefficients on roofs are determined from the results of various wind tunnel
experiments20),
28)
as well as on the provisions of international codes and standards. Although
flat-roofed buildings have parapets in many cases, their effect on the pressure coefficients is not
considered here. A reduction factor for external pressure coefficients on roofs with parapets is
provided in Eurocode28).
(2) External pressure coefficient Cpe for buildings with rectangular sections and heights less than or
equal to 45m
1) Buildings with flat, gable and mono-sloped roofs
External pressure coefficients are influenced by many factors, such as roof shape, roof angle and
flow condition. The coefficients in this section are estimated from the results of wind tunnel
experiments29), 30), 31) on buildings with rectangular sections and reference heights less than or equal to
45m. The roof shapes under consideration are flat, gable and mono-sloped. When the roof angle is less
than or equal to 10 degrees, the roof can be regarded as a flat roof.
The roof and walls are divided into several zones, and the external pressure coefficients for these
zones are provided in Table A.6.9(1) as a function of building configuration parameters ( B / H , D / H
and θ ). The external pressure coefficient for each zone is estimated from the spatially averaged
pressure over the zone for a range of wind directions, the center of which is normal to the wall. Both
positive and negative values are provided for the external pressure coefficient for zone Ru, because the
pressure coefficient becomes both positive and negative due to a small change in experimental
conditions. It is necessary to combine these values with those for the other zones when the stresses in
the members are calculated.
The net wind forces on windward eaves become very large, because negative pressures act on the
top surface and positive pressures on the bottom surface of the eaves. In this case, the external
pressure coefficient on the bottom surface is approximately equal to that on the windward wall just
bellow the eaves.
2) Buildings with vaulted roofs
The external pressure coefficient for a building with a curved surface generally depends on the
shape and surface roughness of the building, the flow conditions and the Reynolds number. Buildings
with vaulted roofs, however, are immersed in very turbulent flows. Furthermore, such buildings have
walls in most cases and therefore the flow tends to separate at the windward edge. These features
suggest that the external pressure coefficients on vaulted roofs are less sensitive to surface roughness
and the Reynolds number than those on circular cylindrical structures, as shown in A6.2.4(1). The
external pressure coefficients Cpe in Table A6.9(2) are determined from the results of a wind tunnel
eperiment32),
33)
that focuses on medium-scale buildings in urban areas. The effects of surface
roughness are not considered in the experiment.
For a wind normal to the gable wall (wind direction W1 ), the building shape is represented by the
rise/width ratio f / B and the eaves-height/width ratio h / B . However, for a wind parallel to the
CHAPTER 6
WIND LOADS – C6-45 –
gable wall (wind direction W2 ) it is represented by the rise/depth ratio
f / D and the
eaves-height/depth ratio h / D . In both cases, the roof is divided into three zones. However, the zone
definitions vary because of the difference between the flow patterns of the two wind directions. For
wind direction W1 , the definition of zones is similar to that for flat, gable and mono-sloped roofs. For
wind direction W2 , however, the definition is similar to that for spherical domes.
The external pressure coefficient corresponds to the area-averaged value and the design wind load is
assumed constant over each zone. When h / B = 0 and f / B = 0 or when h / D = 0 and f / D = 0 ,
roof level coincides with ground level. The coefficients for these cases, which have no physical
meaning, are provided to make interpolation possible.
The external pressure coefficients on walls are determined in the same way as for buildings with flat,
gable and mono-sloped roofs.
3) Spherical domes
In the same manner as for buildings with vaulted roofs, the external pressure coefficients for
spherical domes are determined from the results of a wind tunnel experiment34). Since the counter lines
of mean pressure coefficients on a spherical dome are almost perpendicular to the wind direction, the
dome surface is divided into four zones (Ra to Rd), as shown in Table A6.10, and the external pressure
coefficient Cpe for each zone is given by spatially averaging the mean external pressure coefficient
over the zone. The building shape is represented by the rise/span ratio
f / D and the
eaves-height/span ratio h / D . The values of Cpe for five f / D ratios and three h / D ratios are
provided in Table A6.10. Linear interpolation can be used for values of f / D and h / D other than
shown. Both positive and negative values of Cpe are provided for zone Ra. The value for h / D = 0
and f / D = 0 are again provided for interpolation.
The wind force coefficients for walls can be obtained from Table A6.12 by substituting h for H .
A6.2.3
Internal pressure coefficients for structural frames
Internal pressures are significantly influenced by the following factors:
a) distribution of external pressures
b) openings and gaps in building envelope
c) internal volume of building
d) openings and gaps in internal partitions
e) operation of air-conditioners
f) distortion of walls and/or roofs
g) air temperature
h) damage to building envelope
In general, buildings have many gaps and openings, such as ventilating openings, etc., in their
envelopes. Air leaks through these gaps and openings due to differences between external and internal
pressures. The internal pressure is determined by applying the mass conservation principle to the air in
the internal volume. For instance, a dominant opening in the windward wall may produce positive
– C6-46 –
Recommendations for Loads on Buildings
internal pressures, whereas one in a side or leeward wall may produce negative internal pressures.
Moreover, the internal pressure fluctuates and its characteristics depend on the relationship between
the size of the openings and the internal volume of the building. In this section, internal pressure
coefficients for buildings without dominant opening are provided based on the results of a series of
computations, in which it is assumed that the internal pressures are significantly influenced by factors
a) and b) mentioned above. That is, the values of Cpi in Table A6.11 are provided based on the
calculations35) of the mean internal pressures for various building configurations, assuming that the
gaps and openings are uniformly distributed over the external walls and the internal pressure is caused
by external pressures acting at the locations of the gaps and openings.
When the influence of other factors is assumed to be significant, it should be taken into account for
evaluating the internal pressure coefficient. For instance, when the internal volume is divided by
airtight partitions, the influence of factor d) is significant. When powerful air-conditioners are in
operation, the influence of factor e) is significant. In buildings with flexible roofs and/or walls, such as
membrane structures, the influence of factor f) is significant. When glass windows on the windward
face are broken by wind-borne debris in strong winds, the internal pressure is suddenly increased by
winds blowing into the building. This often results in failures of roof structures.
In such cases, factor
h) should be considered appropriately.
A6.2.4
Wind force coefficients for design of structural frames
(1) Wind force coefficients C D for buildings with circular sections
Wind force coefficients for cylinders are affected by the Reynolds number, flow condition, aspect
ratio H / D , surface roughness of the cylinders, and other factors. Figure A6.2.236) shows the variation
of drag coefficient C D on a two dimensional smooth cylinder in a uniform flow with Reynolds
number Re ( = UD /ν , where U , D and ν are wind speed, cylinder diameter and kinematic
viscosity coefficient of flow, respectively). For wind, the Reynolds number is approximately given by
Re ≈ 7UD × 10 4 , where U and D are expressed in units of ‘m/s’ and ‘m’, respectively. It is found
from Fig. A6.2.2 that C D changes significantly with Re in the range from 2 × 105 to 5 × 106. The flow
around a cylinder is usually classified into four regimes, i.e. ‘subcritical’, ‘critical’, ‘supercritical’ and
‘transcritical’, as shown in Fig. A6.2.2. Since the Reynolds number of the flow around buildings in
strong winds is in the transcritical regime, the provision of C D in A6.2.4(1) is based on the values of
the drag coefficients in this regime.
The aspect ratio and surface roughness of the cylinder also affect the drag coefficient.
In particular,
the effect of surface roughness is significant in the transcritical regime. In Table A6.12 the effects of
aspect ratio and surface roughness are represented by k1 and k 2 , respectively37).
The external pressure coefficients Cpe on roofs are given in Table A6.10 assuming that f / D = 0
and h / D = 1 .
CHAPTER 6
Figure A6.2.2
WIND LOADS – C6-47 –
Plots of drag coefficient C D on a two-dimensional cylinder with very smooth
surface as a function of Reynolds number Re 36)
(2) Wind force coefficients C R for free roofs with rectangular base
For free roofs where strong wind can flow under the roof, high fluctuating pressures act on both the
top and bottom surfaces. It is reasonable to evaluate the net wind force coefficients directly, not from
the wind pressure coefficients on the top and bottom surfaces, because the correlation between
fluctuating wind pressures on both surfaces is higher than that for enclosed buildings.
The wind force coefficients in Table A6.13 can be used for small-scale buildings, to which the
simplified method (A6.11) is applied, because the coefficients are determined from the results of wind
tunnel experiments on free roofs with H < 10 m. For gable ( θ > 0 ο) and troughed roofs ( θ < 0 ο),
previous studies have shown the most critical peak wind force coefficients on the windward and
leeward areas irrespective of wind direction38). Since the tested roof angle θ is limited to the range of
| θ |≤ 30 ο, the provision is also limited to that range.
The wind force coefficients are regulated for a clear flow case where there are no obstructions under
the roof. The flow pattern around a roof is significantly affected by obstructions under it. If there is
any obstruction whose blockage ratio is larger than approximately 50%, the wind pressure on the
bottom surface may increase significantly, resulting in a significant increase in the net wind force on
the roof. In such a case, it is necessary to evaluate the wind force coefficients from wind tunnel
experiments and so on.
(3) Wind force coefficients C D for lattice structures
The size of individual lattice structure members is generally much smaller than the width of the
structure, and they are arranged symmetrically. Therefore, it is assumed that the only wind force acting
on a plane of the structure is drag. Total drag can be estimated as the summation of the drags on each
member of the structure. Since the flow around a member depends only on the characteristics of the
local flow around it, drag is proportional to the velocity pressure at the height of the member. Based on
these features, the following two methods are often used for estimating the wind force on lattice
– C6-48 –
Recommendations for Loads on Buildings
structures. One is to multiply the wind force coefficient, given as a function of the solidity ϕ of the
plane, by the projected area of the plane. The other method39) is to sum the wind forces on all members,
which is given by the product of the wind force coefficient C D of each member and its projected
area. For any method, the solidity ϕ should be small. In the Recommendations, the former method is
used and the wind force coefficient C D is provided only for ϕ ≤ 0.6 .
The wind force coefficient is represented as a function of the solidity ϕ , the plan of the structure
and the cross section of the member. The solidity ϕ is defined as the ratio of the projected area AF
of the plane to the whole plane area A0 = ( Bh ) of the structure. The value of ϕ is calculated for
each panel of the lattice structure when the wind direction is normal to the plane. In the calculation,
the areas of the leeward lattice members and the appurtenances are not included. The wind forces on
the appurtenances can be estimated from the provision of C D for members (Table A6.16) or from
wind tunnel experiments and they are added to the wind force on the structure.
Table A6.14 provides the wind force coefficients C D for lattice structures with square and
triangular plan shapes, which consist of angles or circular pipes. The wind force coefficient C D for
the triangular shape in plan is the same for the two wind directions shown in the table. When the
members are circular pipes, the wind force coefficients C D for the members are affected by the
Reynolds number. The provisions are based on the value in the subcritical Reynolds number regime. In
strong winds, the value of C D may become smaller than that given in the provisions due to the effect
of the Reynolds number. However, this effect is not considered here.
When the plan of the structure and/or the cross section of the member are different from those in
Table A6.14, the wind loads on the structure can be estimated by using the wind force coefficients of
the members given in Table A6.16 together with the local velocity pressure. However, the solidity ϕ
of the structure is required to be less than 0.6.
(4) Wind force coefficients C D for fences on ground
Wind force coefficients C D for fences on the ground are defined as a function of the solidity ϕ
in the same manner as those for lattice structures. The value of C D for ϕ = 0 in Table A6.15 is
introduced to obtain intermediate values of C D for 0 < ϕ < 0.2 . Wind load for a fence can be
calculated according to the simplified procedure using C D and the projected area A, which is defined
as the whole area multiplied by ϕ .
(5) Wind force coefficients C for components
Wind force coefficients C for components are determined from the results of wind tunnel
experiments40) with two-dimensional models in a smooth flow. The values of C can be applied to
line-like members less than approximately 50cm wide, but should not be applied to ordinary buildings.
In some cases, the value of C in the across-wind direction becomes relatively large when the wind
direction deviates only a little from the normal direction. In such cases, two values of C ( ± 0.6) are
provided in Table A6.16.
Wind force coefficients for components may also be used for calculating the wind loads on lattice
structures, together with the local velocity pressure q Z at height Z of the member under
CHAPTER 6
WIND LOADS – C6-49 –
consideration. The wind load on a component is given by the product of q Z , C , (1 + 7 I Z ) and bl
( blϕ for nets), where I Z is the turbulence intensity at height Z (see Eq.(A6.7)).
A6.2.5
Peak external pressure coefficients for components/cladding
(1) Peak external pressure coefficients Ĉpe for buildings with rectangular sections and heights
greater than 45 m
Peak external pressure coefficients for components/cladding correspond to the most critical positive
and negative peak pressure coefficients irrespective of wind direction. Positive pressures occur on
windward walls, and their characteristics are affected by the vertical profile of the approach flow. On
the other hand, negative pressures (suctions) occur on side and leeward walls, and their characteristics
are not significantly affected by the vertical profile of the approach flow; that is, the vertical
distribution is nearly uniform. Large negative pressures occur near the windward edges of sidewalls
due to flow separation from the edge. The peak external pressure coefficients provided in Table A6.17
are determined from the results of wind tunnel experiments41), 42), 43), 44). These coefficients are given by
the product of the external pressure coefficients influenced by the profile of the mean wind speed and
the gust effect factor influenced by the profile of the turbulence intensity. Therefore, the positive
external peak pressure coefficients are affected by the terrain category. However, negative external
peak pressures are almost independent of terrain category.
For tall buildings with recessed or chamfered corners, the negative peak pressures are influenced by
the size of the recess or chamfer. The values of Ĉ pe for such buildings are also determined from the
results of wind tunnel experiments42), 43). The values in Table A6.17 can also be used for buildings with
more than one recessed or chamfered corner.
Peak external pressure coefficients for roofs are provided only for flat roofs. For diagonal wind
directions, very large suctions are induced near windward corners due to the generation of conical
vortices. However, the large suction zone is limited to a relatively small area45). Therefore, the use of
such large peak pressure coefficients for large components may overestimate the design wind loads. In
order to consider the subject area of components/cladding in zone Rc, an area reduction factor kC for
roofs is introduced.
The provisions are applicable to buildings with aspect ratios H / B less than or equal to 8, because
the values are based on wind tunnel experiments on such buildings.
When a building is constructed on an escarpment or a ridge-shaped topography, the approach wind
is affected by the local topography, and therefore the positive peak pressure coefficients may change
significantly. Since wind speeds near the ground are increased by such local topography, the vertical
distribution of positive peak external pressure coefficients becomes nearly uniform. In such cases,
positive peak external pressures can be calculated by using the values of k Z and I Z at the reference
height H . This simplified method overestimates the wind loads to some degree in most cases.
However, for terrain category I, it may underestimate the positive peak external pressures. In this case,
investigations by wind tunnel experiments are recommended.
– C6-50 –
Recommendations for Loads on Buildings
(2) Peak external pressure coefficient Ĉ pe for buildings with rectangular sections and heights less
than or equal to 45 m
1) Buildings with flat, gable and mono-sloped roofs
For estimating peak pressure coefficients for components/cladding of low-rise buildings, the subject
area is assumed to be 1 m2 as a typical value. Positive peak external pressure coefficients are given as
a function of the turbulence intensity, because the pressures depend significantly on the turbulence of
the approach flow. The positive peak external pressure coefficient on a roof is evaluated by using the
positive external pressure coefficient Cpe for zone Ru in Table A 6.9(1). If no positive value of
Cpe is provided for small roof angles, it is not necessary to evaluate the positive wind pressures.
Negative peak external pressure coefficients in the edge and corner regions are significantly influenced
by vortices related to flow separation at the edge. Negative peak pressure coefficients tend to increase
in magnitude as the turbulence intensity of the approach flow increases. However, the influence of
turbulence on negative peak pressure coefficients is smaller than that on positive peak pressure
coefficients on windward walls. Consequently, the provision of negative peak pressure coefficients is
determined from the values for terrain category IV and are independent of turbulence intensity. High
suctions are induced in the edge and corner regions of walls and roofs, whose widths are affected by
building dimensions such as height and width.
For gable roofs, very high suctions are induced near corners (zone Rb) when the roof angle θ is
less than or equal to 10ο and in the ridge corner (zones Rd and Rg) when θ ≈ 20 ο. For mono-sloped
roofs, very high suctions are induced near the higher eaves corners (zone Rd); the suctions are larger
and the high suction area is wider than that for gable roofs. Consequently, the peak external pressure
coefficient for zone Rd is larger than that for gable roofs. In such high suction zones, the wind load can
be reduced by using the area reduction factor k C when the subject area AC of components/cladding
is greater than 1 m2 (up to 5 m2) 46).
2) Buildings with vaulted roofs
The peak external pressure coefficients Ĉ pe are determined from the results of wind-tunnel
experiments33), focusing on medium-scale buildings in urban areas, in which the h / B1 ratio is varied
from 0 to 0.7 and the f / B1 ratio from 0.1 to 0.4. When the f / B1 ratio is small, the corner and edge
regions of a roof are significantly affected by vortex generation as in the flat roof case. This results in
larger peak suctions in zones Ra and Rd. When the f / B1 ratio is relatively large, large peak suctions
are induced in zone Rd for winds nearly perpendicular to the gable edge and in zone Rc for winds
nearly perpendicular to the eaves.
Taking these wind pressure features into account, the roof is divided into several zones and positive
and negative peak external pressure coefficients are provided for these zones, as shown in Table
A6.18(2). When the f / B1 ratio is lower than 0.1, the roof is subjected to higher suctions similar to
gable and mono-sloped roofs. Therefore, it is not necessary to evaluate the positive peak external
pressure coefficients. The values for walls can be determined from Table A6.18(1).
(3) Peak external pressure coefficients Ĉ pe for buildings with circular sections
CHAPTER 6
WIND LOADS – C6-51 –
For buildings with circular sections, the maximum positive peak external pressure coefficient occurs
at the stagnation point on the windward face, whereas the maximum negative peak external pressure
coefficient occurs near the point of maximum negative mean external pressure. The vertical
distribution of positive peak pressure coefficients depends strongly on the mean velocity profile of the
approach flow in the same manner as that for buildings with rectangular sections. On the other hand,
negative peak external pressure coefficients are influenced by the aspect ratios H / D and surface
roughness of buildings. The factor k1 considers the effect of aspect ratio, and the factor k 2 the
effect of surface roughness in the transcritical Reynolds number regime. Negative peak external
pressure coefficients become larger in magnitude near the top of the building because of the flow
separation from the top (i.e. end effect). The factor k 3 considers this effect47). The values in Table
A6.19 are applicable to buildings with aspect ratios H / D less than or equal to 8, because the
provision is based on wind tunnel experiments using such models.
Only negative peak pressures are considered for roofs. The values of Ĉ pe for domes with
f / D = 0 provided in Table A6.20 can be used.
(4) Peak external pressure coefficients Ĉ pe for buildings with circular sections and spherical domes
Peak external pressure coefficients in Table A6.20 are determined from the results of wind tunnel
experiments34). External pressures on domes fluctuate significantly due to the effects of turbulence of
approach flow as well as of vortex generation. Therefore, both positive and negative peak pressure
coefficients are provided. Because the geometry of spherical domes is axisymmetric, they are divided
into three zones (Ra, Rb and Rc) by coaxial circles. When the rise/span ratio ( f / D ) is small, negative
peak external pressures become large in magnitude near the windward edge (zone Ra) due to the flow
separation at the windward edge. On the other hand, when the f / D ratio is large, large positive peak
external pressures are induced near the windward edge due to the direct influence of the approach flow.
Therefore, positive peak external pressure coefficients for zone Ra are provided as a function of the
turbulence intensity I uH at the reference height H of the approach flow when f / D ≥ 0.2 .
A6.2.6
Factor for effect of fluctuating internal pressures
Peak wind force coefficients for components/cladding shall be determined from the maximum
instantaneous values, both positive and negative, of the pressure difference between the exterior and
interior surfaces. However, there are few data on these pressure differences. In the Recommendations,
it is assumed that the peak wind force coefficient Ĉ C is represented by Eq.(A.6.15), because the peak
external pressure coefficients Ĉpe are usually obtained from wind tunnel experiments and a large
amount of data is available.
Figure A6.2.3 shows a schematic illustration of fluctuating external and internal pressures. The
frequency of internal pressure fluctuations is lower than that of external pressure fluctuations, and the
*
for the effect of
peak external and internal pressures are not induced simultaneously. The factor C Pi
fluctuating internal pressures in Eq.(A6.15) does not represent the peak internal pressure coefficient
itself but an equivalent value that provides the actual peak wind force when combined with the peak
– C6-52 –
Recommendations for Loads on Buildings
external pressure coefficient Ĉpe . The value of Ĉ C is evaluated from a series of computations for
the peak wind force coefficients using wind tunnel data on Ĉpe for various building configurations.
The following assumptions are made in the computations48):
1) Gaps and openings in the external walls are uniformly distributed, and the internal pressures are
generated from the external pressures at the locations of the gaps and openings.
2) The fluctuating internal and external pressures are independent of each other.
When the building has intentionally designed openings or when glass windows on the windward
face are broken by flying debris, the size of the openings may be very large compared with ordinary
gaps and openings. The values in Table A6.21 cannot be used for such cases. It is necessary to estimate
the peak wind force coefficients appropriately by using the data on the external and internal pressures
obtained from wind tunnel experiments49). Some international codes and standards20),
50)
provide
internal pressure coefficients for buildings with dominant openings.
Wind force coefficient, wind pressure coefficient
^
CC
C*pi
^
C
wind force coefficient
pe
external pressure coefficient
internal pressure coefficient
0
Time
^
C
C
^
C
peak wind force coefficient
pe
peak external pressure coefficient
Cpi
peak internal pressure coefficient
Cpi
Fig.A6.2.3
A6.2.7
Example of fluctuating external and internal pressures acting on components/cladding
Peak wind force coefficient for components/cladding
For free roofs, it is necessary to directly evaluate the net wind force represented by the pressure
difference between the top and bottom surfaces. Regulation of peak wind force coefficients is based on
previous wind tunnel experiments for the most critical peak wind forces irrespective of wind
direction38). When the roof angle is relatively large, large peak wind forces are induced along the roof
edges as well as along the ridge, because large suctions are induced by conical vortices on either the
top or bottom surface of the roof. The roof is divided into two zones (Ra and Rb), and positive and
negative peak wind force coefficients are provided for each zone as a function of roof angle θ . Larger
net wind forces are induced in zone Rb.
When any obstruction whose blockage ratio is larger than approximately 50% is placed under the
roof, it is necessary to evaluate the peak wind force coefficients from an appropriate wind tunnel
experiment and so on.
A6.3
Gust Effect Factors
CHAPTER 6
A6.3.1
WIND LOADS – C6-53 –
Gust effect factor for along-wind loads on structural frames
(1) Fundamental consideration
In this recommendation, gust effect factor is based on overturning moment as described by the
following equation.
M
M
+ g Dσ MD
g σ
= 1 + D MD
GD = Dmax = Dmax
MD
MD
MD
(A6.3.1)
where M Dmax , M D , σ MD are maximum value, mean value and rms of overturning moment at the
base of the building, respectively. M Dmax and σ MD involve load effect due to the dynamic
response of the building. If σ MD is expressed as composition of background component σ MDQ and
resonance component σ MDR , Eq.(A6.3.1) becomes as follows.
2
2
GD = 1 + g D σ MDQ
+ σ MDR
M D ≈1 + g D
σ MDQ
MD
1 + φ D2
πf D S MD ( f D )
2
4ζ Dσ MDQ
(A6.3.2)
where S MD ( f D ) is power spectrum density of overturning moment at natural frequency for the first
mode f D and φ D is the mode correction factor. σ MDR is considered for only the first mode
vibration, and σ MDR is inertia force by vibration as described in the following equation.
H
H
0
0
σ MDR = ∫ σ a ( Z )m( Z ) ZdZ = σ a ( H ) ∫ μ ( Z )m( Z ) ZdZ
(A6.3.3)
where σ a ( Z ) , m( Z ) and μ ( Z ) are rms of acceleration at height Z , mass per unit height and
vibration mode, respectively.
The parameters of Eq.(A6.3.2) are expressed by aerodynamic force coefficients as follows.
M D = q H BH 2 C MD
(A6.3.4)
σ MDQ = qH BH 2C ' MD
(A6.3.5)
f D S MD ( f D )
2
σ MDQ
=
f D* S CMD ( f D* )
C '2MD
(A6.3.6)
'
is rms overturning moment coefficient and
where C MD is overturning moment coefficient, C MD
S CMD ( f D* ) is power spectrum of overturning moment coefficient at non-dimensional frequency f D* .
If these equations are taken into consideration, Eq.(A6.3.2) becomes as follows.
GD ≈ 1 + g D
C ' MD
C MD
1 + φ D2
πf D* S CMD ( f D* )
4ζ D C ' 2MD
(A6.3.7)
Additionally, in this formula non-dimensional frequency is defined by turbulence scale,
f D* = f D LH /U H , but, in the wind tunnel test breadth of the building it is used usually f D* = f D B /U H .
(2) Model of wind force
The model of wind force is based on the assumption that wind velocity fluctuation is directly
changed into the wind pressure on the wall of the building51). In this model, mean wind velocity,
turbulence intensity, power spectrum of wind velocity and co-coherence are described by Eqs.(A6.8),
(A6.11), (A6.1.3), (A6.1.4), respectively. Additionally, wind force coefficient is expressed by a
– C6-54 –
Recommendations for Loads on Buildings
difference of the wind pressure coefficient of the windward side and the wind pressure coefficient
(constant) of a lee side as described by the following equation.
⎛Z⎞
CD = CPA ⎜ ⎟
⎝H⎠
2α
− CPB
(A6.3.8)
'
and S CMD ( f D* ) are expressed using the parameter of the recommendation equations as
C MD , C MD
follows.
C MD = C H Cg
(A6.3.9)
'
C MD
= C H Cg'
(A6.3.10)
f D* S CMD ( f D* ) = C ' 2MD FD
(A6.3.11)
where C H is wind force coefficient at the top of the building, Cg is a factor relevant to overturning
moment in the along-wind direction, Cg' is a factor relevant to rms overturning moment in the
along-wind direction and FD is a spectrum factor of windward force. Spectrum factor of wind
velocity F , size reduction factor S D , factor R expressing correlation of wind pressure of a
windward side and a leeward side R are considered for FD .
Characteristics of overturning moment expressed by Eqs.(A6.3.9)−(A6.3.11) are shown in
Fig.A6.3.1 in comparison with those obtained from wind tunnel tests. The recommendation values of
overturning moment and rms overturning moment are slightly greater than the test values, and the
1.0
category
terrain
地表面粗度区分
0.5
II
III
IV
0.0
0
1
2
3
side ratio D/B
(a) mean overturning moment
coefficient
Figure A6.3.1
1.5
10 -2
1.0
10 -3
fSCMD(f)
1.5
recommendation value/test value
recommendation value/test value
spectrum is mostly in agreement with the test values.
category
terrain
地表面粗度区分
0.5
10 -4
II
III
IV
0.0
0
1
2
3
side ratio D/B
(b) rms overturning moment
coefficient
10 -5 -3
10
test
実験値
recommendation
指針値
10 -2
10 -1
10 0
fB/UH
(c) power spectrum density of
over turning moment
Along-wind force in comparison with those obtained from wind tunnel tests
( H / BD = 4 )52)
(3) Fluctuating component of overturning moment
When the vibration mode is μ = Z / H , the relation between spectrum of overturning moment due
to the wind force S MD ( f ) and spectrum of overturning moment due to the load effect by vibration
'
S MD
( f ) is expressed by the following equation.
CHAPTER 6
WIND LOADS – C6-55 –
2
S 'MD ( f ) = χ m ( f ) S MD ( f )
where χ m ( f )
(A6.3.12)
2
is mechanical admittance as expressed by the following equation.
1
χm ( f ) =
2
1 − ( f / f D ) 2 + 4ζ D2 ( f / f D ) 2
2
{
}
(A6.3.13)
2
is the integral of
The variance of overturning moment due to the load effect by vibration σ MD
2
and resonance component
Eq.(A6.3.12), and the variance consists of back ground component σ MDQ
2
as expressed by the following equation.
σ MDR
∞
2
2
2
σ MD
= ∫ S ' MD ( f )df ≈ σ MDQ
+ σ MDR
0
=
∞
∞
∫0 S MD ( f )df + S MD ( f D )∫0
2
2
+
χ m ( f ) df = σ MDQ
πf D S MD ( f D )
4ζ D
(A6.3.14)
In this equation, resonance component is estimated approximately as a response to white noise
S MD ( f D ) .
Therefore, overturning moment for maximum load effect is expressed by following equation.
2
2
M Dmax = M D + g D σ MDQ
+ σ MDR
(A6.3.15)
where g D is called peak factor, and is the ratio of maximum fluctuating component to standard
deviation. This is expressed by the following equation, based on the theory of stationary stochastic
process.
g D = 2 ln(ν DT ) +
0.577
2 ln(ν DT )
≈ 2 ln(ν DT ) + 1.2
(A6.3.16)
where T is time for evaluation and ν D is level crossing rate calculated from power spectrum density
as in the following equation.
∞
νD =
∫0
f 2 S ' MD ( f )df
∞
∫0 S 'MD ( f )df
≈ fD
RD
1 + RD
(A6.3.17)
Additionally, in some foreign wind loading standards, M Dmax is expressed by the following formula.
In this equation, the background component and the resonance component are distinguished.
2
2
M Dmax = M D + g Q2 σ MDQ
+ g R2 σ MDR
(A6.3.18)
where g Q is peak factor of background component (=3.4) and g R is peak factor of resonance
component calculated from Eq.(A6.3.16) as ν D = f D .
(4) Vertical distribution of equivalent static wind load
In the gust effect factor method, the vertical distribution of wind load is given by mean wind load
multiplied by gust effect factor. This wind load is an approximate value based on the assumption that
vibration mode is close to mean wind load distribution and the building has uniform density. Actually,
the mean, background and resonance components of wind load distribution are different. The mean
component is expressed by Eq.(A6.3.8), and the resonance component is expressed by Eq.(A6.3.3).
Therefore, if the vertical distribution of building mass is remarkably uneven, the resonance component
should be estimated carefully. In that case, the distribution of resonance component for the
– C6-56 –
Recommendations for Loads on Buildings
fundamental vibration mode could be estimated from the following equation.
2
2
WD = W D + WDQ
+ WDR
(A6.3.19)
where
W D = qH CD A
WDQ = g DQ q H C D
C'g
Cg
A
WDR = a Dmax μ ( Z )m( Z )
A
B
where
WD , WDQ , WDR (N): mean, background and resonance component of wind load, respectively
a Dmax (m/s2): maximum acceleration at top of building as defined in A6.10.2
g DQ : peak factor of background component
In this recommendation, it is assumed that the background component has a similar distribution to
mean component. The following methods may also be used.
1) Shear force or overturning moment at a certain building height may be obtained from the integral of
pressure on area over the height20).
2) Load distribution can be defined by LRC formula53).
(5) Example of calculation of gust effect factor
Figure A6.3.2 shows the variation of gust effect factor by terrain category and building height for
H / B = 4 , D / B = 1 and U 0 = 35 m/s. The gust effect factors become large with terrain category
and building height.
gust effect factor G D
3.8
3.4
A6.3.2
V
IV
III
II
I
3.2
3.0
2.8
2.6
2.4
2.2
2.0
Figure A6.3.2
category
3.6
0
0
50
50
100
100
150
150
200
200
height of building (m)
250
250
300
300
Variation of gust effect factor with terrain category and building height
Gust effect factor for roof wind loads on structural frames
Gust effect factor for roof wind loads on structural frames is influenced by external pressure and
internal pressure. It can be assumed that there is no correlation between fluctuation of external
pressure and fluctuation of internal pressure for a building without dominant openings. Furthermore,
CHAPTER 6
WIND LOADS – C6-57 –
Helmholtz resonance, the phenomenon of varying internal pressure at a specific frequency by external
pressure, can be disregarded. Fluctuating internal pressure coefficient is derived from the theory for
buildings with uniform openings54). Therefore, external pressure fluctuation, which is slower than
response time of internal pressure, is transmitted as internal pressure, and it is assumed that quicker
pressure fluctuation is not transmitted as internal pressure. Furthermore, fluctuating internal pressures
act on all parts of a roof simultaneously for more safety. Generally, response time of internal pressure
is long enough, compared with the natural period for the first mode of the roof structure. Therefore,
resonance of the roof structure for internal pressure can be disregarded. Under these conditions, gust
effect factor for roof wind loads is given by the following equation.
GR = 1 ±
2 2
2 2 2
g Re
rRe (1 + RRe ) + g Ri
rRi rc
(A6.3.21)
1 − rc
where g Re and g Ri are peak factors for generalized external pressure and generalized internal
pressure, and these value are g Re = 3.5 , g Ri = 3 from the results of test and measurement. rRe and
rRi are the generalized fluctuating external and internal pressures divided by the generalized mean
wind pressure coefficient. rc is the generalized mean internal pressure divided by the generalized
mean external pressure coefficient. RRe is resonance factor, which is calculated from the
non-dimensional power spectrum density at the frequency of the first mode of the roof and the critical
wind load
damping ratio.
ïó
â³
èd
０
（－）
（＋）
時間
time
Figure A6.3.3
Fluctuation of roof wind loads when wind force coefficient is small
An equation of gust effect factor is expressed for two cases of internal pressure coefficient,
C pi = −0.4 and C pi = 0 , given by Table A6.11. If wind force coefficient is small, roof wind loads act
in the upward direction and in the downward direction as shown in Fig.A6.3.3. When combinations
with other loads are considered, downward wind load can be dominant even if the absolute value is
small. Therefore, downward wind load can be calculated. In Eq.(A6.17), G R for “+”corresponds to
load in the same direction as given by wind load coefficient, and G R for “−“ is opposite. The above is
the same for Eq.(A6.18) and Eq.(A6.19). However, wind force coefficients are given as positive or
negative in A6.2.2, and gust effect factor should be calculated from Eq.(A6.17) with “+”. Furthermore,
the equation, f R ≈ 0.57
δ ( δ is deformation at center due to weight), can approximately evaluate
the natural frequency for the first mode of the roof beam, and the document55) is useful for estimating
– C6-58 –
Recommendations for Loads on Buildings
the critical damping ratio, ζ R .
(1) Case for C pi = −0.4
Roof wind loads can be calculated for roof beams parallel to the wind direction and for roof beams
normal to the wind direction.
If external pressure coefficient Cpe is −0.4 over the whole subject area as center beam shown in
Fig.A6.3.4(a), the wind force coefficient becomes C R = 0 . In this case, roof wind loads can be
calculated from Eq.(A6.18), which is the product C R G R of wind force coefficient C R and gust
effect factor G R . However, when the wind force coefficient becomes partially C R = 0 as shown in
Fig.A6.3.4(b), the wind loads can be calculated from Eq.(A6.17).
(a) beams normal to the wind direction
Figure A6.3.4
(b) beams parallel to the wind direction
Relation between wind force coefficient and external or internal pressure coefficient
(for C pi = −0.4 )
(2) For C pi = 0
Wind force coefficient is equal to external pressure coefficient for C pi = 0 . In this case, gust effect
factor can be calculated from Eq.(A6.19). The equation considers the mean and fluctuating
components of external pressure, and the fluctuating component of internal pressure.
A6.4
A6.4.1
Across-wind Vibration and Resulting Wind Load
Scope of applications
The procedure described in this section applies to the equivalent static wind load with consideration
of across-wind forced vibration at a design wind speed lower than the non-dimensional critical wind
speed for vortex-induced vibration or aeroelastic instability. For a design wind speed expressed by
CHAPTER 6
WIND LOADS – C6-59 –
U H /( f L BD ) > 10 , aeroelastic instability may well occur and wind load will need to be calculated
from the wind force and the response in wind tunnel tests.
Along-wind vibration is caused by turbulence in natural wind, but across-wind vibration is caused
by wind turbulence as well as by the vortex in the wake of the building. Although there are many study
examples with regard to the behavior of a vortex in the wake of a building, unclear points remain.
Furthermore, since the behavior is greatly affected by building shape, it is difficult on the whole to
theoretically estimate across-wind vibrations in the same manner as for along-wind vibrations. With
consideration of the first mode, an estimation equation for across-wind load has been derived from
data of across-wind fluctuating overturning moment obtained from wind tunnel tests. Subjects for this
estimation equation are structures with rectangular planes (side ratio D / B = 0.2 ~ 5 ) from which
many experimental data have been obtained. Moreover, by taking into account the fact that
experimental data for buildings with an aspect ratio H / BD exceeding 6 are insufficient, and that
aeroelastic instability easily occurs in these buildings, the scope of application is limited to aspect
ratios of 6 or less.
Furthermore, data of across-wind fluctuating overturning moment for buildings with plane shapes
other than rectangular planes can be obtained from wind tunnel tests. Where it is unnecessary to
consider aeroelastic instability, across-wind wind loads can be calculated using the method indicated
in the recommendations.
A6.4.2
Procedure
(1) Concept of wind load estimation
Since a fundamental mode usually predominates in across-wind vibration, across-wind loads are
calculated using the spectral modal method considering only to the first translational mode, in the
same manner as for along-wind loads. For the non-resonance component, the profile of fluctuating
across-wind force is set to be vertically uniform and the magnitude of the fluctuating wind force is
decided to agree with the fluctuating overturning moment. The resonance component estimates the
inertia force due to vibration and the vertical profile is determined using φ L in Eq.(A6.33) so as to be
proportioned to the first translational mode.
It is recommended that the critical damping ratio be estimated with reference to “Damping in
buildings” 7).
(2) Modeling of overturning moment
The overturning moment varies with building shape and wind characteristics, but in the subjective
scope the breadth-depth ratio has the greatest effect on the overturning moment: the effects of other
parameters are slight. Therefore, in the recommendations, the fluctuating overturning moment is set as
a function of only the breadth-depth ratio of a building based on wind tunnel test data 52, 56).
(3) Buildings with circular planes
Across-wind responses of buildings with plane shapes other than rectangular planes can be
estimated with the same concept. This section details buildings with circular planes. The parameter
– C6-60 –
Recommendations for Loads on Buildings
values used in Eq.(A6.20) need to be set to C L' = 0.06 , m = 1 , κ 1 = 0.9 , f S1 = 0.15U H / B ,
β1 = 0.2 . These parameter values are in the transcritical critical region of Reynolds number
( U H D ≥ 6 (m2/s)).
A6.5
A6.5.1
Torsional Vibration and Resulting Wind Load
Scope of application
The procedure described in this section applies to the equivalent static wind load with consideration
of torsional vibration with a design wind speed lower than the non-dimensional critical wind speed for
vortex-induced vibration or aeroelastic instability. For the design wind speed expressed by
U H /( f T BD ) > 10 , aeroelastic instability may well occur and the wind load needs to be calculated
from the wind force or the response in wind tunnel tests.
Torsional vibration is caused by asymmetric wind pressure distribution on the windward face, side
faces and leeward face. This is due to both wind turbulence and the vortex in the building’s wake. The
torsional moment induced wind force is subject to the effects of building shape and wind behavior.
Therefore, the method for assessing the torsional wind load is derived from the fluctuating torsional
moment data obtained from wind tunnel tests as for the across-wind direction. Subjects for this
estimation equation are buildings with rectangular planes (side ratio D / B = 0.2 ~ 5 ) and aspect ratio
H / BD of 6 or less, from which many experiment data have been obtained.
Furthermore, data of torsional moment for buildings with plane shapes other than rectangular planes
can be obtained by carrying out wind tunnel tests. Where aeroelastic instability does not need to be
considered, torsional wind loads can be calculated using the method indicated in the
recommendations.
A6.5.2
Estimation equation
(1) Concept of wind load estimation
Since the effects of pressure acting on both sides on the torsional moment are complex, it is difficult
to formulate the power spectral density as a simple algebraic function. However, it is relatively easy to
collect experimental data of the response angle acceleration. Therefore, the equation for computing the
torsional wind load is based on the estimate of the response angle acceleration56). With regard to the
non-resonant component, the profile of fluctuating torsional moment is set as vertically uniform and
the magnitude of the fluctuating torsional moment is decided to agree with the fluctuating torsional
moment at the base of the building. The resonant component estimates the inertia force due to
vibration and the vertical profile is determined using φ T in Eq.(A6.34) so as to be proportioned to the
first translational mode. Buildings with an eccentric factor (eccentric distance / radius of rotation) of
0.2 or less for which any effect of eccentricity can be ignored are subject to the formulation of the
estimation equation. The wind load on a building for which the eccentricity cannot be ignored needs to
be calculated by carrying out wind tunnel tests.
CHAPTER 6
WIND LOADS – C6-61 –
It is recommended that the critical damping ratio be estimated with reference to “Damping in
buildings” 7).
(2) Modeling of torsional moment
The torsional moment varies according to building shape and wind characteristics, but in respect of
buildings in the subjective scope the breadth-depth ratio exerts the greatest effect on the torsional
moment and the effects of other parameters are slight. Therefore, in the recommendations, the
fluctuating torsional moment is set as a function of only the breadth-depth ratio of a building based on
wind tunnel test data 52, 56).
A6.6
Horizontal Wind Loads on Lattice Structural Frames
A6.6.1
Scope of application
This procedure has been prepared for estimating horizontal wind loads on lattice structures built
directly on the ground, and whose members all have small enough sections in comparison with the
width of the structure for the flow field around a member to be dominated by the local wind speed.
The procedure for estimating wind loads on lattice structures is basically the same as that described for
horizontal wind loads on buildings in Section 6.2, and can be applied to lattice structures of varying
widths and solidity ratios in the vertical direction. In addition, the effects of accessory ladders are
considered by the evaluation of wind force coefficients of those obtained from wind tunnel tests and so
on.
A6.6.2
Procedure for estimating wind loads
Horizontal wind loads are estimated by a gust effect factor method57). The wind loads are calculated
from the local design velocity pressure because lattice structures often have varying widths and
solidity ratios in the vertical direction.
The projected area in Eq.(A6.22) is the total projected area of all elements on one face normal to the
wind. The area per panel is usually calculated.
A6.6.3
Gust effect factor
In deriving Eq.(A6.23), it is assumed as follow:
i)
Solidity ratios in the vertical direction are uniform, that is to say, wind force coefficients
of each panel are uniform.
ii)
A fundamental mode shape can be given by Eq.(A6.6.1) where β = 2 , and vibration
modes higher than the fundamental one are neglected.
β
⎛Z⎞
(A6.6.1)
⎟
⎝H⎠
According to the above assumptions, the peak response x max,Z at height Z is given as a function
μ =⎜
of the generalized stiffness K of the fundamental mode by:
– C6-62 –
Recommendations for Loads on Buildings
x max,Z = g D
q H C D HB0
2I H μ
K
0.95 + α + β
BD (1 + RD )
(A6.6.2)
However, the mean response X Z at height Z is given by:
XZ =
where qH , I H
⎛
B0
B − BH ⎞
⎜⎜
⎟⎟ μ
(A6.6.3)
− 0
⎝ 1 + 2α + β 2 + 2α + β ⎠
are the velocity pressure and the turbulence intensity, respectively, at H height, and
qH CD H
K
α is the exponent of the power law in the wind speed profile. g D , RD and BD are the peak
factor, the resonance factor and the back ground excitation factor, respectively.
Gust effect factor is given by Eq.(A.6.23).
Figure A6.6.1
A6.7
A6.7.1
Definition of B0 , BH , H
Vortex Induced Vibration
Scope of application
This section describes vortex-induced vibration, which can occur in tall slender buildings, chimneys,
and structural components with circular sections.
A6.7.2
Vortex induced vibration and resulting wind load on buildings with circular sections
Shear layers separated from windward corners of both sides of buildings roll up alternately to shed
into wake and form Karman vortex streets behind the buildings. According to the alternate shedding,
the periodic fluctuating wind loads act on the buildings in the across-wind direction. When the natural
frequency of the building coincides with the vortex shedding frequency, the vibration of the building
can be resonant with the periodic fluctuating wind loads, causing the building to vibrate at large
amplitude in the across-wind direction. This is vortex-induced vibration, which is a problem for many
structures, particularly chimneys.
The critical wind speed of the resonance is larger than the design wind speed for most buildings, so
these phenomena are not normally important. However, as the critical wind speed is smaller than
CHAPTER 6
WIND LOADS – C6-63 –
design wind speed for very slender buildings with small natural frequency and damping like steel
chimneys, tall buildings and building components, the effect of vortex induced vibration should be
checked carefully in the wind resistance design stage.
A lot of research has been done on vortex-induced vibration and a number of methods have been
developed in the past decade for estimating vibration amplitude and its equivalent static wind loads,
particularly for structures with circular sections. The equivalent wind loads described in the
recommendation are based on the spectral modal method in which the Strouhal number of vortex
shedding is 0.2, and the power spectrum of the fluctuating wind loads depends on the vibration
amplitude6) and the Reynolds number.
The effects of structural density, damping and Reynolds number are included in the resonant wind
force coefficient C r , which is shown in Table A6.2.3 for three categories of Reynolds number region
and for two types of structures with various density and damping. The rows in the table show the
effect of Reynolds number, that is, U r Dm < 3 is the subcritical region, 3 ≤ U r Dm < 6 is critical
region and 6 ≤ U r Dm is super/trance critical Reynolds number region. ρ s ζ L in Table A6.23
depends on the amplitude at the resonant condition. ρ s ζ L < 5 corresponds with the large
amplitude, and ρ s ζ L ≥ 5 corresponds with the small amplitude.
Vortex induced vibration and resulting wind load on building components with circular
A6.7.3
sections
Occurrence of vortex induced vibration of building components with circular section can be
checked by Eq.(A6.26). Most design wind speeds for components like members of truss towers are
larger than the critical wind speed, so the effect of vortex induced vibration should be checked
carefully. In particular, the vibration amplitude can be very large for components like steel pipes
whose mass and damping are small. The equivalent wind loads described in Eq.(A6.27) are introduced
in the sub-critical Reynolds number region based on wind tunnel tests59). The equation is applicable for
various boundary conditions at the ends of components.
A6.8
A6.8.1
Combination of Wind Loads
Scope of applications
This section defines the combination of horizontal wind loads and roof wind loads on structural
frames. These wind loads are evaluated separately, but this does not mean that each wind load acts on
the building independently. However, maximum wind loads do not occur at the same time. Therefore,
if they are applied to the building at the same time, the combination of wind loads overestimates actual
loads. This section shows the formula for combination of wind loads considering correlations of wind
force and response. The formula is divided in two ways: for buildings not satisfying the conditions of
Eq.(6.1) and for buildings satisfying the conditions of Eq.(6.1). Combination of horizontal wind loads
and roof wind loads is also described.
– C6-64 –
A6.8.2
Recommendations for Loads on Buildings
Combination of horizontal wind loads for buildings not satisfying the conditions of Eq.(6.1)
Buildings not satisfying the conditions of Eq.(6.1) have a small resonance component. For such
cases, it is considered that wind load of γ times of the windward loads act in the across-wind
direction, as shown in figure 6.8.1. γ tends to increase with building height according to the stress
analysis for buildings with rectangular columns using wind load from wind tunnel tests. Therefore, an
approximate equation of γ
60)
for an 80m-high building is defined as per the recommendation.
wind
quasi-static
wind load
plan of building
Figure A6.8.1
A6.8.3
Windward load and combined
load for across wind direction
Figure A6.8.2
Relation between side ratio
(D/B) and combination factor γ
Combination of horizontal wind loads for buildings satisfying the conditions of Eq.(6.1)
Buildings satisfying the conditions of Eq.(6.1) have a large resonance component. For such cases, it
is assumed that response probability is expressed by a normal distribution. If the overturning moments
in two directions, M x , M y , are expressed by a 2-dimensional normal distribution, the equivalence
line of probability becomes an eliptical line using correlation coefficient of response, ρ , as shown in
Figure A6.8.3. Every point on the eliptical line (solid line) can be considered as a load combination,
but it is not practical to consider a lot of them. Therefore, load combinations can be defined as the
apexes of an octagon enveloping the oval. In other words, y-direction overturning moment M yc ,
which should be combined with maximum x-direction overturning moment M xmax , is defined by the
following equation using mean y-direction overturning moment M y and maximum fluctuating
component of y-direction overturning moment mymax .
M yc = M y + m ymax
(
)
2 + 2ρ −1
(A6.8.1)
Table A6.24 shows the combination of loads according to the upper equation considering following
characteristics of along-wind, across-wind and torsional wind loads.
・Co-coherence (correlation coefficient for each frequency) is negligible between along-wind force
and across-wind force, and between along-wind force and torsional wind force. Therefore, ρ = 0
as co-coherence of response is negligible.
・Because the co-coherence between across-wind force and torsional wind force is not zero, the
absolute value of the correlation coefficient of response ρ LT , shown in Table A6.25, is defined
by calculation based on wind tunnel tests.
ρ LT is calculated by a statistical analysis method61) under the conditions that the critical damping
CHAPTER 6
WIND LOADS – C6-65 –
ratios for across-wind vibration and torsional vibration are 0.02, and the building has no coupling
vibration mode. Therefore, if the critical damping ratio differs greatly from 0.02 or the building’s
vibration mode is significantly coupled, it is necessary to carry out special research.
My
mx max
point A
M y max
my max
M yc
considered point of
combination load
M y0
my max ρ
My
m y max ( 2 + 2 ρ − 1)
my max (1 − 2 − 2 ρ )
Mx
Mx
Figure A6.8.3
A6.8.4
M x max
Schema of load combination in consideration of response correlation
Combination of horizontal wind loads and roof wind loads
Combination of horizontal wind loads and roof wind loads can be considered theoretically as in
A6.8.2 or A6.8.3. However, because the relation between horizontal wind loads and roof wind loads is
not well enough understood, it is defined that horizontal wind loads and roof wind loads act at the
same time.
A6.9
A6.9.1
Mode Shape Correction Factor
Scope of application
The mode shape correction factor can be used in calculating the gust effect factor, the across-wind
load and the torsional wind load for a conventional building, as described in A.6.3.1, A6.4.2 and
A6.5.2, respectively, if the first translation mode shape function is different from μ = Z H and the
vertical distribution of mass per height of a building over the ground is not regarded as almost constant.
The mode shape correction factor can be used in calculating the gust effect factor for a lattice structure,
as described in A.6.3.3, if the first mode shape function is different from μ = (Z / H )2 and the mass
per height of a lattice structure is not regarded as almost constant.
The mode shape correction factor can be applied with β ranging from 0.2 to 4 for a conventional
building, and with β ranging from 1 to 3.5 for a lattice structure when the mode shape function can
be approximated by the function μ = (Z / H )β .
A6.9.2
Procedure
The mode shape correction factor is specified by Eq.(A6.32). This corrects the gust effect factor for
– C6-66 –
Recommendations for Loads on Buildings
an along-wind load on a building according to its vibration mode.
The vibration mode shape correction factors for the resonance components of across-wind load and
torsional wind load are specified by Eqs.(A6.33) and (A.6.34), respectively.
λ given by Eq.(A6.35) is the ratio of the resonance component σ β of the generalized wind force
for its first vibration mode to σ 1 for the reference vibration mode shape (the power index of a first
vibration mode β = 1 for a conventional building and β = 2 for a lattice structure).
λ=
σβ
σ1
(A6.9.1)
The values of λ for a conventional building in Eq.(A6.35) are approximations that fit the results62)
obtained from a wind tunnel test for rectangular cross section buildings, in which the power index
indicating the vibration mode shape β between 0.2 and 4 are taken into consideration.
The mode shape correction factor φ can be derived by multiplying the correct factor of the
generalized wind force by the correct factor of the generalized mass or the generalized inertial moment
of the building.
The vertical distributions of the along-wind load are taken into consideration by the vertical
distribution of the mean wind load, but the resonance component of the across-wind load or the
torsional wind load is proportional to the vibration mode, because the mean load is not considered in
the recommendation. As a result, the mode shape correction factor of the across-wind load or the
torsional wind load involves a variable for height.
The mode shape correction factor for a lattice structure is derived from the buffeting theory. This is
to deal with the lattices of varying widths in the vertical direction.
The mode shape correction factor can be set to 1 if the vibration mode shape agrees with the
reference vibration mode shape and the vertical distribution of mass per unit height of a building over
the ground is regarded as almost constant. If the vibration mode shape agrees with the reference
vibration mode shape and the vertical distribution of mass per unit height can not be regarded as
constant, the mode shape correction factor can be replaced by the ratio of the generalized mass or the
generalized inertia moment of a building to that with a uniform mass distribution in the vertical
direction. Furthermore, if the vertical distribution of mass per unit height of a building over the ground
is regarded as almost constant, the mode shape correction factors for the along-wind load, the
across-wind load and the torsional wind load can be simplified by Eqs.(A6.9.2), (A6.9.3) and (A6.9.4),
respectively.
⎧1.1 − 0.1β
⎪
⎫⎪
⎧⎪⎛
φD = ⎨
⎞
BH
⎪(0.16 β + 0.4)⎨⎪⎜⎜ 0.5 B − 0.3 ⎟⎟(β − 2) + 1.4⎬⎪
0
⎠
⎭
⎩⎝
⎩
⎛Z⎞
⎟
⎝H⎠
φ L = (0.27 β + 0.73)⎜
conventional building
lattice structure
(A6.9.2)
β −1
(A6.9.3)
CHAPTER 6
WIND LOADS – C6-67 –
β −1
⎛Z⎞
(A6.9.4)
⎟
⎝H⎠
In addition, the generalized mass M D , M L and the generalized inertial moment I T of a
φ T = (0.27 β + 0.73)⎜
building can be calculated according to Eqs.(A6.9.5) and (A6.9.5), respectively.
M D (L ) =
A6.10
∫0
⎛Z⎞
mZ ⎜ ⎟
⎝H⎠
2β
(A6.9.5)
dZ
2β
⎛Z⎞
I Z ⎜ ⎟ dZ
0
⎝H⎠
and I Z are the mass and the inertial moment at height Z , respectively.
IT =
where m Z
H
∫
H
(A6.9.6)
Response Acceleration
Scope of application
A6.10.1
This section defines the maximum along-wind response acceleration for ordinary buildings, the
maximum across-wind response acceleration for buildings with rectangular plan satisfying the
conditions of A6.4.1 and the maximum torsional response acceleration for buildings with rectangular
plan satisfying the conditions of A6.5.1.
Each formula considers only the first vibration mode. If a building has a large dynamic response in
higher modes or partial vibration, other special research should be carried out.
Maximum along-wind response acceleration
A6.10.2
Rms of generalized response acceleration σ aD is given by the following equation.
∞
2
σ aD
= ∫ S g ( f )(2πf ) 4
0
χm ( f )
2
K g2
df
(A6.10.1)
where σ aD is rms of generalized acceleration, S g ( f ) is power spectrum density of generalized
wind force, χ m ( f ) 2 is mechanical admittance as described in Eq.(6.3.13), f is frequency and K g
is generalized stiffness as described in the following equation.
K g = M D (2πf D ) 2
(A6.10.2)
where M D is generalized mass. Because the resonant component is dominant in acceleration,
S g ( f ) can be substituted by white noise having power spectrum density at natural frequency f D , as
described in the following equation.
S g ( f D ) = (qH BHCH C 'g λ ) 2
FD
fD
(A6.10.3)
where FD is along-wind force spectrum factor, as shown in A6.3.1.
If Eqs.(A6.10.2) and (A6.10.3) are incorporated in Eq.(A6.10.1), the equation become the
following.
– C6-68 –
Recommendations for Loads on Buildings
σ aD = qH BHCH C 'g λ
RD
MD
(A6.10.4)
Furthermore, σ aD is multiplied by the peak factor in the recommended equation for the
acceleration at the top of the building. Because the resonant component is dominant in acceleration,
level crossing rate ν D for calculating peak factor is approximated by the natural frequency f D .
A6.10.3
Maximum across-wind response acceleration
The equation consists of coefficients according to across-wind direction as a development in the
along-wind direction, A6.10.2.
A6.10.4
Maximum torsional response acceleration
admax = aTmax d
A6.11
A6.11.1
(A6.10.5)
Simplified Procedure
Scope of application
A simplified procedure is used for estimating wind load for small buildings. This procedure can be
applied to buildings that have regular shapes and structural systems, such as detached houses. The
reference height and the projected breadth shall be less than 15m and 30m, respectively.
A.6.11.2
Procedure
The simplified procedures are derived from the results of calculation for buildings with reference
heights of 5 - 15m and projected breadths of 5 - 30m, assuming that the wind directionality factor K D
is 1.0 and the terrain category is III. Therefore, this procedure can be applied to terrain categories IV
and V with some overestimates in wind loads. For terrain categories less than III, the exposure factor
C e is introduced. When wind speed is expected to increase due to local topography, the wind loads
shall be increased appropriately, for example, by multiplying by the square of the topography factor
Eg .
A6.12
Effects of Neighboring Tall Buildings
When groups of two or more tall buildings are constructed in proximity, the fluid flow through the
group may be significantly deformed and have a much more complex nature than is usually
acknowledged, resulting in enhanced dynamic pressures and motions especially on neighboring
downstream structures. Therefore, study of mutual interference among closely-located tall buildings is
an important problems not only in wind resistant structure design but even in minimizing wind-motion
discomfort to building occupants. Wake-induced oscillation in the downstream structure is considered
to be affected by interference from upstream buildings of various sizes placed in various locations and
WIND LOADS – C6-69 –
CHAPTER 6
also by the turbulence of incident flows.
Figure A6.12.163), 64) shows contours of the increase or decrease ratios for the maximum along/across
wind responses of the downstream building exposed to interference from an upstream building at
various locations to those of an isolated building where the maximum responses including mean
deflection are estimated at near the design wind speeds of 40～60m/s by a modal-spectrum method
(1,2). The contours are illustrated for an identical pair of square tall buildings with aspect ratio
H / BD = 4 where two coordinate axes are normalized by the non-dimensional distance using the
reference building breadth
BD .
The response ratios in the across-wind direction are usually larger than those in the along-wind
direction. Interfering positions producing response ratio contours higher than 1.2 are generally
restricted to regions of 12 BD in the x-direction and 6 BD in the y-direction, whereas interfering
positions higher than 1.1 exceed the regions indicated in the figure.
When the flat terrain subcategories increase from Category II to Category IV, the dynamic responses
of the downstream building are relatively independent of mutual interference effect. This is closely
related to the fact that when turbulence is added to an incident flow, shedding vortices from an
upstream building and the alternately deformed wake surrounding the vortices are not clearly formed
in the wake owing to increased entrainment and diffusive action, and the production of additional
turbulence by the introduction of the upstream building is unlikely because of the sufficiently high
turbulence in the incident flow (3) 65).
y
y
6 BD
6 BD
1.1
4
1.1
1.1
x
1.0
6
1.0
4
4
1.2
1.2
12 BD
1.3
0.8
1.1
1.2
y
6 BD
4
1.4
1.2
1.1
2
1.2
1.0
12
6
1.1
BD
1.0
1.1
1.0
6
4
2 0.8
(c) Terrain category IV, across-wind direction
Figure A6.12.1
4
2 1.3
(b) Terrain category II, across-wind direction
1.2
1.0
1.1
1.2
BD
1.2
1.2
2
1.0
1.1
x
12
(a) Terrain category II, along-wind direction
x
1.3
2
2
1.2
Contours of response ratios63), 64)
– C6-70 –
A6.13
Recommendations for Loads on Buildings
1-Year-Recurrence Wind Speed
1-year-recurrence wind speed U 1H is used to calculate the acceleration of wind response for the
evaluation of the habitability, defined in Eq.(A6.41).
Figure A6.5 is smoothing of the wind speed map based on the 1-year-recurrence wind speed at the
metrological offices, from which the wind speed U 1 at any locations can be estimated. The
1-year-recurrence wind speeds at the metrological offices are established based on the daily-maximum
wind speed data regardless of wind directions collected from 1991 to 2000. On the other hand, because
the wind response characteristic is not the same for the wind direction, the wind speed, which becomes
the same acceleration is also different for the wind direction. Therefore, if the wind direction
characteristic, that is, the frequency of exceedance of each wind speed can be understood, a reasonable
design becomes possible. This wind direction characteristic in the range of the wind speed to evaluate
the habitability is generally clarified.
When the maximum acceleration a max is approximated as a function of wind speed U shown in
for maximum acceleration a max
Eq.(A6.13.1), the return period t a max
is calculated by
Eq.(A6.13.2). The probability at the right side of Eq.(A6.13.2) is expressed as the total sum of the
occurrence probability of the wind speed in every 16 azimuths shown in Eq.(A6.13.3).
a max = f (U )
1
t a max =
1 − Fa (≤ amax )
Fa (≤ amax ) = ∑ pi FU {≤
16
}
f i −1 (amax )
(A6.13.1)
(A6.13.2)
(A6.13.3)
i =1
where
Fa (≤ a max ) : probability that maximum acceleration does not exceed a max
pi : occurrence frequency for wind direction i
{
}
FU ≤ f i −1 (a max ) : probability that the wind speed does not exceed the wind speed that the
maximum acceleration is equal to a max for wind direction i
The occurrence frequency at each wind direction pi , parameters ai and bi in Eq.(A6.13.4),
which are the parameters to calculate the right side of Eq.(A6.13.3), are shown in Table A6.13.1.
These parameters are estimated based on the daily maximum wind speed at 30 cities, with the least
square method applied for the data at Naha where typhoon is dominant, and the Gumbel’s moment
method for other cities. These parameters ai and bi should be used for the return period less than 1
year.
FU (≤ U i ) = exp[− exp{− ai (U i − bi )}]
(A6.13.4)
where
U i (m/s): 10-minute mean wind speed at 10m above ground over a flat and open terrain for
wind direction i
ai , bi : parameters estimated based on the daily maximum speed for wind direction i
CHAPTER 6
WIND LOADS – C6-71 –
In addition, the wind direction factor in A6.1.4 should be used for 100-year-recurrence wind
speed, and it is not possible to use it here.
Table A6.13.1
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW
SW
WSW
W
WNW
NW
NNW
N
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW
SW
WSW
W
WNW
NW
NNW
N
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW
SW
WSW
W
WNW
NW
NNW
N
parameters ai , bi and occurrence frequency p i for each wind direction at 30 cities
Asahikawa
bi
pi(%)
4.26
3.3
4.32
0.8
3.63
0.2
2.28
0.7
2.74
0.7
4.44
6.4
5.61
17.1
4.34
3.9
6.37
3.3
6.72
1.2
7.58
10.1
6.45
17.6
5.80
19.4
4.78
8.8
5.66
4.7
4.92
1.8
Niigata
ai
bi
pi(%)
1.07
4.61
14.4
1.78
3.66
6.6
0.85
3.72
0.3
1.24
4.17
0.2
0.64
7.39
0.2
0.69
8.05
6.6
0.98
5.69
4.4
1.65
4.38
1.7
1.19
4.78
3.0
0.45
6.84
3.2
0.40
8.65
14.4
0.44
7.29
18.8
0.38
8.39
7.7
0.48
8.40
6.9
0.52
7.43
6.7
0.66
5.56
4.9
Chiba
ai
bi
pi(%)
0.73
6.38
6.2
0.89
6.10
6.1
0.97
5.46
6.7
1.02
4.85
2.5
1.41
4.08
6.9
1.27
4.26
9.9
0.68
4.96
3.8
0.77
4.62
2.2
0.35
9.90
4.8
0.45
7.69
13.4
0.74
4.95
8.8
0.59
4.84
0.7
0.42
8.33
0.6
0.46
7.68
7.0
0.48
6.26
15.1
0.61
5.46
5.3
ai
0.58
0.52
0.54
1.45
1.05
0.76
0.55
0.54
0.48
0.59
0.49
0.63
0.65
0.68
0.86
0.83
Sapporo
bi
pi(%)
3.59
0.4
3.76
0.5
3.80
1.6
4.93
4.0
5.52
6.2
7.49
8.1
8.86
13.5
7.94
3.2
7.31
1.8
7.96
2.1
8.41
3.9
8.53
5.1
9.28
5.2
8.63
19.5
7.05
23.3
4.78
1.6
Kanazawa
ai
bi
pi(%)
0.76
5.11
5.8
0.81
5.38
3.0
0.99
5.02
10.5
0.93
4.62
9.9
0.87
3.56
0.9
1.35
3.32
1.2
2.15
3.26
1.6
0.17
4.11
0.5
0.42
7.62
8.2
0.43
9.16
8.5
0.45
8.65
9.7
0.36
7.49
12.1
0.37
6.62
9.1
0.44
5.36
7.4
0.38
5.82
3.7
0.66
4.89
7.9
Yokohama
ai
bi
pi(%)
0.58
7.52
1.8
0.81
6.50
0.1
0.64
7.58
1.4
1.04
5.62
9.1
1.19
5.00
1.9
0.71
5.81
0.9
0.76
5.48
7.5
0.63
5.85
4.2
0.40
9.60
5.8
0.38
8.74
15.8
0.40
8.42
3.4
0.48
8.68
0.2
0.65
8.27
0.3
0.36
8.39
0.5
0.32
6.95
2.5
0.46
7.21
44.5
ai
1.58
1.23
1.30
0.94
0.72
0.59
0.47
0.43
0.45
0.44
0.47
0.53
0.45
0.46
0.59
0.83
Aomori
ai
bi
pi(%)
1.22
3.57
4.6
0.82
4.03
4.0
0.76
5.84
3.7
0.90
5.46
7.9
0.60
6.09
1.1
0.64
7.71
0.7
0.58
4.61
0.5
1.58
2.79
0.2
0.54
5.27
2.8
0.47
6.47
12.6
0.48
7.56
10.2
0.50
9.11
14.0
0.55
8.43
15.7
0.66
6.00
8.6
1.00
4.20
6.7
0.84
3.49
6.7
Utsunomiya
ai
bi
pi(%)
0.70
4.47
18.5
0.88
4.43
8.8
1.01
4.52
2.3
1.13
3.81
3.5
1.37
3.85
7.1
1.33
3.76
9.2
1.00
4.26
9.1
0.78
4.68
6.0
0.75
4.48
6.4
0.81
4.12
2.8
0.68
4.79
1.5
0.59
6.99
2.2
0.53
7.17
3.1
0.47
5.14
1.6
0.50
5.67
3.6
0.58
4.49
14.3
Shizuoka
ai
bi
pi(%)
0.83
4.75
2.9
0.77
5.74
9.5
0.94
5.74
23.7
0.88
5.51
1.8
0.80
4.50
1.8
0.75
3.95
1.3
0.92
4.96
6.1
0.81
5.46
17.6
0.50
6.50
4.1
0.42
8.63
12.4
0.57
9.01
4.0
0.51
10.1
5.3
0.39
7.05
3.8
0.55
4.96
1.8
1.28
4.07
2.9
0.59
3.81
1.0
Akita
bi
pi(%)
4.79
0.4
5.88
0.1
3.17
0.2
4.77
0.3
6.57
7.2
6.25
17.0
4.70
0.2
6.27
0.1
8.91
2.2
7.44
9.9
6.98
12.5
7.91
17.7
9.68
11.9
9.56
9.2
7.87
3.8
5.86
7.3
Maebashi
ai
bi
pi(%)
0.28
9.56
0.1
－
－
0.0
1.20
4.78
0.1
0.71
4.32
1.4
0.81
5.19
22.7
0.99
4.83
8.7
1.21
3.84
2.0
1.17
3.76
1.2
0.57
2.88
0.3
0.49
3.30
0.3
0.50
4.65
1.3
0.44
6.78
1.5
0.34
6.86
3.5
0.45
6.82
26.0
0.47
8.43
26.7
0.51
11.0
4.2
Hamamatsu
ai
bi
pi(%)
0.80
4.59
0.4
1.25
3.20
3.0
0.56
6.29
7.1
0.59
6.69
7.8
0.74
6.59
2.5
1.03
5.35
5.5
0.80
5.06
6.7
0.93
4.93
2.5
0.67
5.94
0.6
0.58
5.77
3.2
0.68
6.00
13.8
0.66
7.30
16.7
0.49
9.15
23.6
0.39
8.27
5.9
0.55
4.18
0.5
1.69
4.88
0.2
ai
0.73
0.56
0.73
0.63
0.65
0.63
1.25
0.72
0.38
0.46
0.38
0.36
0.37
0.45
0.60
0.75
ai
0.82
0.61
0.56
0.66
0.74
1.14
0.76
0.75
0.87
0.77
0.46
0.42
0.39
0.43
0.56
0.75
ai
0.87
1.04
1.05
1.10
1.22
1.37
0.94
0.83
0.56
0.53
0.64
0.45
0.50
0.45
0.47
0.64
ai
1.10
1.80
2.25
2.46
0.47
0.47
0.51
1.16
1.26
1.14
0.88
0.59
0.70
0.53
0.50
0.89
Sendai
bi
pi(%)
4.40
1.7
3.72
1.1
5.86
0.8
5.09
0.7
4.97
0.8
3.89
16.7
4.58
13.3
4.66
6.4
5.06
1.8
5.55
0.9
8.02
1.6
8.75
7.7
9.42
16.9
8.62
10.1
5.44
7.9
5.17
11.6
Tokyo
bi
pi(%)
5.46
4.2
5.43
6.2
5.58
6.6
5.47
3.3
5.67
3.6
6.02
1.9
4.99
0.3
6.53
20.2
7.61
2.0
7.80
9.8
5.84
0.4
7.83
0.2
7.23
0.2
8.28
4.9
7.37
25.8
5.85
10.4
Nagoya
bi
pi(%)
3.61
1.6
2.92
0.7
2.29
0.8
3.82
0.1
6.21
0.4
6.03
3.8
6.54
13.5
4.85
11.0
4.67
2.0
4.78
1.1
3.81
1.3
5.61
1.4
6.49
18.8
7.29
19.0
5.49
16.2
4.10
8.3
– C6-72 –
Recommendations for Loads on Buildings
Table A6.13.1(continued)
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW
SW
WSW
W
WNW
NW
NNW
N
ai
0.75
0.73
0.93
0.85
0.78
0.84
0.95
0.92
0.80
0.58
0.72
0.69
0.61
0.58
0.85
0.75
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW
SW
WSW
W
WNW
NW
NNW
N
ai
0.72
0.64
0.59
0.78
1.35
0.61
0.45
0.68
0.40
0.55
0.45
0.41
0.42
0.59
0.67
0.64
Kyoto
bi
pi(%)
4.05
5.6
4.01
5.1
4.97
6.1
5.15
6.6
4.80
3.9
4.64
1.5
4.06
3.3
4.99
8.9
5.76
10.3
6.03
2.5
6.56
4.6
6.83
3.8
6.74
4.7
7.53
3.1
6.55
10.0
5.49
20.0
Matsue
bi
pi(%)
5.15
1.6
5.77
8.2
6.07
7.1
5.25
10.0
3.90
8.0
5.22
1.7
5.62
0.5
5.75
0.2
8.19
1.8
6.61
1.5
6.91
12.1
7.72
28.3
7.10
5.9
5.91
8.6
5.93
3.4
6.08
1.1
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW
SW
WSW
W
WNW
NW
NNW
N
ai
0.67
0.95
0.87
1.18
1.03
0.77
0.40
0.37
0.63
0.65
0.62
0.55
0.56
0.63
0.63
0.69
Fukuoka
bi
pi(%)
5.37
3.2
5.61
1.6
5.82
0.5
5.42
0.2
5.01
0.7
5.41
9.7
7.33
4.5
7.29
2.2
8.48
3.1
6.43
0.7
8.56
0.6
7.92
3.1
8.60
6.3
6.15
3.1
5.84 31.7
5.82 28.8
parameters ai , bi and occurrence frequency p i for each wind
direction at 30 cities
Osaka
bi
pi(%)
4.24
17.6
5.23
4.4
5.95
4.4
5.80
1.7
4.80
1.3
5.16
0.5
4.96
0.5
6.42
0.5
7.86
1.8
5.75
14.4
5.57
19.0
6.47
12.7
6.80
1.9
6.32
3.6
6.66
7.4
5.73
8.3
Hiroshima
ai
bi
pi(%)
1.26
4.40
31.5
0.58
5.18
0.9
0.42
7.43
0.3
1.48
5.93
0.4
0.68
5.19
0.5
1.39
5.13
0.2
0.23
5.84
0.6
0.49
4.66
5.7
0.84
5.28
8.2
1.05
4.60
10.8
0.67
5.11
0.5
0.69
7.13
3.3
0.64
7.44
3.2
0.70
6.54
0.9
0.79
6.65
3.7
0.99
4.54
29.3
ai
0.88
0.72
0.56
0.63
0.89
0.57
0.68
0.51
0.31
0.64
0.80
0.46
0.39
0.63
0.77
0.77
ai
0.78
0.95
1.54
0.80
0.47
0.37
0.60
0.97
0.52
0.56
0.56
0.57
0.63
0.65
0.71
1.62
Oita
bi
4.67
4.27
3.91
3.71
5.92
5.99
5.39
3.42
4.11
6.41
6.86
8.41
8.08
7.36
6.66
3.64
pi(%)
8.7
7.3
11.3
3.3
0.6
2.1
6.4
7.9
4.1
2.0
2.6
7.1
2.7
10.3
17.8
5.8
Kobe
bi
pi(%)
6.22
1.4
5.41
1.2
6.50
12.1
5.67
3.3
4.06
0.5
3.33
0.7
3.56
0.3
3.84
1.6
5.27
6.9
5.54
5.9
5.89
13.7
7.15
11.8
7.17
7.2
5.91
3.9
6.72
13.2
5.78
16.3
Takamatsu
ai
bi
pi(%)
1.29
3.65
2.5
0.79
3.39
1.2
1.17
3.90
12.7
1.10
3.86
9.8
0.70
4.24
6.2
0.87
3.71
2.2
0.93
3.88
0.2
0.77
2.89
0.4
0.69
5.39
0.6
0.61
4.48
3.2
0.57
6.10
13.0
0.57
6.90
19.4
0.49
7.19
5.6
0.50
6.53
2.9
0.87
4.32
11.4
0.98
4.41
8.7
ai
0.57
0.32
0.48
0.59
1.01
1.71
0.95
1.56
0.60
1.05
0.65
0.50
0.51
0.72
0.56
0.72
Kumamoto
ai
bi
pi(%)
1.52 3.06
1.5
0.56 5.42
2.1
0.60 6.28
3.7
0.50 6.42
2.9
0.59 5.74
2.5
0.34 3.88
1.2
0.72 3.69
1.5
0.38 3.71
3.3
0.57 5.09
6.0
0.83 5.15 17.7
0.65 6.35
9.8
0.52 5.52
4.9
0.52 6.14
7.6
0.64 5.23 18.5
0.70 4.89 13.8
0.77 4.86
3.0
Wakayama
bi
pi(%)
5.92
8.9
4.44
5.3
3.99
10.3
4.19
1.4
4.96
0.3
7.04
0.5
8.26
1.0
7.97
5.3
7.32
9.0
4.71
10.7
4.44
9.0
6.58
4.0
8.19
5.3
6.99
7.7
5.48
9.3
5.61
12.0
Kochi
ai
bi
pi(%)
0.82
7.11
6.7
1.04
6.95
1.0
0.96
4.78
2.4
0.75
3.85
4.2
0.57
4.99
6.9
1.38
4.02
21.7
1.93
4.19
6.0
1.11
4.50
8.5
0.71
5.18
2.4
0.80
6.32
1.2
0.78
4.55
4.0
0.55
4.62
19.9
0.55
4.30
7.2
0.59
7.03
1.7
0.56
7.08
1.4
0.66
7.22
4.8
ai
0.82
1.28
1.90
1.63
0.29
0.64
0.39
0.35
0.43
0.94
0.61
0.38
0.54
0.61
0.77
0.80
Kagoshima
ai
bi
pi(%)
0.56 5.50
9.7
0.52 6.03
7.0
0.36 5.95
0.9
0.42 6.55
0.9
0.31 5.67
1.7
0.46 5.17
5.0
0.50 4.48
7.5
0.43 4.28
4.7
0.57 6.88
0.9
0.39 7.90
2.0
0.52 7.37
4.0
1.03 5.41 11.6
0.67 6.23 18.1
0.56 7.25
8.5
0.71 5.52 13.2
0.75 5.23
4.3
ai
0.91
0.74
0.96
1.57
0.91
0.87
0.47
0.42
0.89
0.79
0.91
0.66
0.66
0.99
0.92
0.69
Okayama
bi
5.61
3.61
4.17
5.30
5.13
4.27
3.72
3.43
4.37
5.24
5.34
7.01
8.07
6.09
5.24
5.60
Matsuyama
bi
6.61
6.15
4.74
3.26
3.50
4.45
6.18
6.40
4.59
5.48
5.31
5.92
5.99
5.09
5.04
6.99
ai
0.54
0.63
0.79
0.30
0.43
0.20
0.20
0.20
0.39
0.16
0.09
0.39
0.46
0.22
0.52
0.72
Naha
bi
4.98
5.75
6.17
-0.27
3.63
-4.53
3.93
-1.73
2.01
-9.17
-25.88
5.35
4.52
-5.84
7.13
7.89
ai
0.47
0.89
1.13
0.67
0.56
0.73
1.26
1.35
1.01
0.60
0.62
0.45
0.40
0.58
0.62
0.51
pi(%)
4.2
2.3
7.6
5.2
4.3
7.9
1.8
5.3
5.7
14.1
6.0
5.9
5.8
6.5
8.6
8.8
pi(%)
3.4
2.6
3.6
4.5
4.7
2.7
2.6
2.0
2.1
2.2
6.8
20.7
20.1
13.0
6.6
2.4
pi(%)
11.2
2.6
7.2
8.9
8.6
6.7
4.1
5.2
9.8
4.4
2.5
1.1
1.3
1.9
7.3
17.2
CHAPTER 6
Appendix 6.6
WIND LOADS – C6-73 –
Dispersion of Wind Load
1. Factors influencing wind loads
The horizontal wind load for structural frames is obtained from Eq.(6.4), and the roof wind load for
structural frames is based on this equation.
WD = q H C D G D A
(6.4)
where qH is velocity pressure, C D is wind force coefficient, G D is gust effect factor for
along-wind load and A is projected area at height Z .
The wind load for components/cladding is obtained form Eq.(6.6).
W = q Cˆ A
C
H
C C
(6.6)
where qH is velocity pressure, ĈC is peak wind force coefficient and AC is subject area.
The velocity pressure qH is expressed as Eq.(Appendix 6.6.1) form Eq.(A6.1) and Eq.(A6.2)．
1
1
ρU H2 = ρ (U 0 K D EH k rW ) 2
(Appendix 6.6.1)
2
2
where ρ is air density, U H is design wind speed, U 0 is basic wind speed, K D is wind
qH =
directionality factor, E H is wind speed profile factor at the reference height H and k rW is return
period conversion factor.
The factors influencing dispersion of horizontal wind load for structural frames WD and wind load
for components/cladding WC are air density ρ , basic wind speed U 0 , wind directionality factor
K D , wind speed profile factor E H at reference height H according to the surface roughness,
return period conversion factor k rW , wind force coefficient C D and gust effect factor G D or peak
wind force coefficient Ĉ C .
The gust effect factor G D is influenced by design wind speed U H , turbulence intensity I H ,
turbulence scale LH , reference height H , building breadth B , building natural frequency f D ,
building critical damping ratio ζ D and so on. The dispersion of these factors must be evaluated when
estimating the wind load on the frame for limit state design.
2. Dispersion of each factor
(1) Air density ρ
The air density ρ varies with temperature, atmospheric pressure and humidity, but the influence of
humidity can usually be ignored. In these recommendations, ρ = 1.22 (kg/m3) at 15℃ and 1013hPa
can be used. The difference between this value and that for the range of 0℃, 1013hPa to 25℃, 960hPa
is within 10%.
(2) Basic wind speed U 0 and return period conversion factor k rW
For allowable stress design, the wind load can be obtained from Eq.(6.4) or Eq.(6.6) and
Eq.(Appendix 6.6.1) based on basic wind speed U 0 , wind directionality factor K D , wind speed
profile factor E and return period conversion factor k rW . For limit state design, however, the
maximum wind speed occurs during the building’s service life T years ( T -year maximum value)
and its coefficient of variation is required. These recommendations provide maps for
– C6-74 –
Recommendations for Loads on Buildings
100-year-recurrence basic wind speed U 0 and 500-year-recurrence wind speed U 500 based on the
annual maximum wind speed approximated by a Gumbel distribution. The mean value and the
standard deviation of the T -year maximum value can be obtained from these values based on the
method described in chapter 2. A calculated example for the mean value, the standard deviation and
the coefficient of variation of 50-year maximum values is shown in appendix Table 6.6.1. The
difference between U 500 and U 0 is 4m/s and the coefficient of variation is about 0.08 to 0.11 in
most areas other than the Okinawa Islands.
Appendix Table 6.6.1
Mean value, standard deviation and coefficient of variation for 50-year
maximum values of wind speed
city
U 0 (m/s)
U 500 (m/s)
Sapporo
Aomori
Sendai
Niigata
Tokyo
Nagoya
Osaka
Hiroshima
Kochi
Fukuoka
Kagoshima
30.5
31.0
30.5
37.0
36.0
32.5
34.5
30.0
39.0
33.5
42.0
34.5
35.0
34.5
41.0
40.0
36.5
38.5
34.0
43.0
37.5
46.0
50-year maximum value
standard deviation
mean (m/s)
(m/s)
30.2
3.2
30.7
3.2
30.2
3.2
36.7
3.2
35.7
3.2
32.2
3.2
34.2
3.2
29.7
3.2
38.7
3.2
33.2
3.2
41.7
3.2
coefficient of
variation
0.11
0.10
0.11
0.09
0.09
0.10
0.09
0.11
0.08
0.10
0.08
(3) Wind directionality factor
The wind directionality factor is decided in order to make the load effect using the wind
directionality factor equivalent to the load effect considering the wind direction. When the wind
directionality factor is considered, the standard deviation of the design wind speed is about 1m/s to
2m/s and its coefficient of variation is about 0.03 to 0.05 for each wind direction. However,
considering phenomena such as down-bursts, which cannot be caught enough, its lower limit of 0.85
and pitch of 0.05 are adopted. Furthermore, considering various uncertain parts, the maximum wind
directionality factor for adjacent wind directions is employed.
(4) Wind speed profile factor
Five flat terrain subcategories and wind speed profile factor E H corresponding to these flat terrain
subcategories are prescribed based on the observed data and the results calculated from computational
fluid dynamics. It is difficult to estimate differences between the actual values and the prescribed
values in consideration of the condition for the flat terrain subcategories of used data. When the flat
terrain subcategories entrusted to designer's judgment varies by one classification, the value of wind
CHAPTER 6
WIND LOADS – C6-75 –
speed profile factor E H deviates 25% at H = 5 m, 15% at H = 100 m and 10% at H = 200 m, and
the coefficients of variation can be estimated as half their values as follows;
0.13 at H = 5 m
0.08 at H = 100 m
0.05 at H = 200 m
(5) Wind force coefficient, wind pressure coefficient
The case for a rectangular plan building is introduced here as an example for wind force coefficients
of horizontal wind load for structural frames of a building whose reference height is greater than 45m.
Wind tunnel test results obtained from reference papers and so on vary with aspect ratio and side ratio
of the building, and the wind force coefficients shown in Table A6.8 are their mean. For the vertical
distribution of wind force coefficient, test values at heights from 0.2 H to 0.9 H are mostly within
the range of ±10% of these recommendation values. For the overturning moment coefficient at the
building base, most test results are within the range of ±20% of these recommendation values. If a
building has a corner recess, the wind force coefficient generally takes a safe value66). Therefore, if
these recommendations are adopted for such a building, its design is generally safe.
Horizontal wind force coefficients for structural frames of a rectangular plan building whose
reference height is 45m or less are influenced not only by building shape but also by many other
parameters such as wind characteristics. The values shown in Table A6.9(1) are simplified so that they
represent the results under various conditions. Therefore, their values are 10-30% greater than actual
ones, and 50% greater in some parts. They exceed 30% in part Lb when the roof slope is 30° or less,
but about 10-20% in parts WU and La . Furthermore, they may exceed 30% in part RLb when the
roof slope is less than 30° but about 10-20% in part RU on negative pressure parts and positive
pressure parts.
For the external pressure coefficient C pe , to calculate the roof wind load on structural frames
around the leading edge of the eave, for example, for B / H ≥ 6 and D / H > 1 , the spatial mean
value of the test results deviates within the range of ±30% of these recommendation values of -1.0.
The positive and negative peak external pressure coefficients of the roof wind load for
components/claddings are determined from the maximum and minimum peak external pressures on
each part of the building for all wind directions. These values vary with wind profile, wind tunnel test
condition (such as sampling frequency, measuring position), side ratio and size reduction rate of the
test model and so on. Their coefficients of variation are about 0.2.
(6) Gust effect factor G D
The parameters that influence the gust effect factor G D of the horizontal wind load for structural
frames, excluding the height and the width of the building, are the natural frequency f D of the first
translational mode in the along-wind direction, the critical damping ratio ζ D of the first translational
mode in along-wind direction, the design wind speed U H , turbulence scale LH , turbulence intensity
I H and the exponent of the power law α in the wind speed profile. The influence of these
parameters on the gust effect factor varies with the flat terrain subcategory, the assumed building
– C6-76 –
Recommendations for Loads on Buildings
shape and so on. Here, the reference height H = 80 m, the width B = 40 m, the natural frequency for
the first translational mode f D = 0.5 Hz, the critical damping ratio for the first translational mode
ζ D = 2 %, the basic wind speed U 0 = 39 m/s and the flat terrain subcategory III are assumed. The
increase of the gust effect factor ΔGD when each parameter is increased by 1% individually is shown
in appendix Table 6.6.2.
Appendix Table 6.6.2
Increase of gust effect factor ΔGD when value of each parameter is
increased by 1% individually
parameter
increase of gust effect factor ΔGD
natural frequency f D
−0.29%
critical damping ratio ζ D
−0.16%
design wind speed U H
0.34%
turbulence intensity I H
0.55%
turbulence scale LH
−0.07%
exponent of power law α
0.02%
For example, if the coefficient of variation of the critical damping ratio is 20%, that for the gust
effect factor caused by the critical damping ratio is estimated as 0.16×0.20=0.032.
Although the gust effect factor of the roof wind load for structural frames is influenced by various
parameters, the difference between the maximum loading effect for roof structural frames obtained
from these recommendations and the wind tunnel test results is within 15% and mostly around 30%.
(7) Natural frequency and critical damping ratio of first mode
“Damping in Buildings”7) proposed an estimation formula for the natural frequency and the critical
damping ratio of the first mode. When the dispersion of the values calculated from these proposed
formula is evaluated as the coefficient of variation of the difference between these recommendation
values and the field measurement values, the coefficient of variation of the natural frequency for the
first mode is about 0.1-0.5 for reinforced concrete structures, steel reinforced concrete structures and
steel structures, and that of the critical damping ratio for the first mode is about 0.2 for reinforced
concrete structure and steel reinforced concrete structures, about 0.3 for steel structures.
(8) Turbulence intensity I H
Fig.A6.1.17 compares the turbulence intensities of these recommendations and field measurements.
The coefficient of variation of the difference between these values can be estimated as about 0.2 for
flat terrain subcategory III where many field measurement data have been obtained.
(9) Turbulence scale LH
Fig.A6.1.21 compares the turbulence scales of these recommendations and field measurements. The
coefficient of variation of the difference between these values can be estimated as about 0.5.
CHAPTER 6
WIND LOADS – C6-77 –
3. Coefficient of variation of wind load
The coefficient of variation of horizontal wind load for structural frames and of wind load for
components/claddings can be obtained from Eq.(Appendix 6.6.2) or Eq.(Appendix 6.6.3).
Horizontal wind load for structural frames: VWD = Vρ2 + 4VU2H + VC2D + VG2D
Wind load for components/cladding
: VWC = Vρ2 + 4VU2H + VĈ2
C
(Appendix 6.6.2)
(Appendix6.6.3)
where
VWD : coefficient of variation of horizontal wind load for structural frames WD
VWC : coefficient of variation of wind load for components/cladding WC
Vρ : coefficient of variation of air density ρ
VU H : coefficient of variation of design wind speed U H
VCD : coefficient of variation of wind force coefficient C D
VG D : coefficient of variation of gust effect factor G D
VĈ : coefficient of variation of peak wind force coefficient ĈC
C
When a building with reference height H = 80 m, width B = 40 m, natural frequency for first
translational mode f D = 0.5 Hz, and critical damping ratio for first translational mode ζ D = 2 % is
constructed in a region of flat terrain subcategory III in each city of appendix Table 6.6.1, the
coefficient of variation VWD can be estimated as around 0.3 to 0.33 for wind load on structural frames
and the coefficient of variation VWC can be estimated as around 0.32 to 0.35 for wind load on
components/claddings.
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Recommendations for Loads on Buildings
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Recommendations for Loads on Buildings
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CHAPTER 6
WIND LOADS – C6-81 –
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