CHAPTER 6 WIND LOADS Outline 6.1 General 6.1.1 Scope of ...

CHAPTER 6 WIND LOADS – C6-1 –

CHAPTER 6 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 Procedure A6.5 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 Dispersion of Wind Load References


CHAPTER 6 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.


Notation Notations used in the main text of this chapter are shown here.

Uppercase Letter

A (m2): projected area at height Z

RA (m2): subject area

CA (m2): subject area of components/cladding

0A (m2): whole plane area of one face of lattice structure

FA (m2): projected area of one face of lattice structure

B (m): building breadth

1B (m): building length in span direction

2B (m): building length in ridge direction

0B , HB (m): width of lattice structure in ground and width at height H

DB : background excitation factor for lattice structure

1C , 2C , 3C : parameters determining topography factor gE and IE

DC , RC , XC , YC : wind force coefficients

'LC , '

TC : rms overturning moment coefficient and rms torsional moment coefficient

eC : 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.

gC : overturning moment coefficient in along-wind direction

'gC : rms overturning moment coefficient in along-wind direction

fC : wind force coefficient. For horizontal wind loads, wind force coefficient DC defined in A6.2 with 9.0Z =k shall be used. For roof wind loads, wind force coefficient RC

defined in A6.2 shall be used.

peC : external pressure coefficient

pe1C , pe2C : external pressure coefficients on windward wall and leeward wall

piC : internal pressure coefficient

*piC : factor for effect of fluctuating internal pressure

rC : wind force coefficient at resonance

CC : peak wind force coefficient

peC : peak external pressure coefficient D (m): building depth, building diameter, member diameter

BD (m): building diameter at the base

mD (m): building diameter at height of 3/2H

E : wind speed profile factor

HE : wind speed profile factor at reference height H


IE : topography factor for turbulence intensity

gE : topography factor for wind speed

gIE : topography factor for turbulence intensity

rE : exposure factor for flat terrain categories

DF : along-wind force spectrum factor

F : wind force spectrum factor

DG : gust effect factor for along-wind load

RG : gust effect factor for roof wind load

H (m): reference height

SH (m): height of topography

TI (kgm2): generalized inertial moment of building for torsional vibration

ZI : turbulence intensity at height Z

rZI : turbulence intensity at height Z on flat terrain categories

DK : wind directionality factor

L (m): span of roof beam

SL (m): horizontal distance from topography top to point where height is half topography

height

ZL (m): turbulence scale at height Z

M (kg): total building mass

DM (kg): generalized mass of building for along-wind vibration

LM (kg): generalized mass of building for across-wind vibration

R : factor expressing correlation of wind pressure of windward side and leeward side

DR : resonance factor for along-wind vibration

LR : resonance factor for across-wind vibration

TR : resonance factor for torsional vibration

ReR : resonance factor for roof beam

DS : size effect factor

0U (m/s): basic wind speed

1U (m/s): 1-year-recurrence 10-minute mean wind speed at 10m above ground over flat and

open terrain

1HU (m/s): 1-year-recurrence wind speed

500U (m/s): 500-year-recurrence 10-minute mean wind speed at 10m above ground over

flat and open terrain

HU (m/s): design wind speed *LcrU , *

TcrU : non-dimensional critical wind speed for aeroelastic instability in across-wind and torsional directions

rU (m/s): resonance wind speed *TU : non-dimensional wind speed for calculating torsional wind load


*rU : non-dimensional resonance wind speed

DW (N): along-wind load at height Z

LW (N): across-wind load at height Z

TW (Nm): torsional wind load at height Z

LCW (N): across-wind combination load

RW (N): roof wind load

SCW (N): wind load on components/cladding obtained by simplified method

SfW (N): wind load on structural frames

rW (N): wind load at height Z

SX (m): distance from leading edge of topography to construction site

Z (m): height above ground

bZ , GZ (m): parameters determining exposure factor

Lowercase Letter

Dmaxa , Lmaxa (m/s2), Tmaxa (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

1f (Hz): The smaller of Lf and Tf

Df , Lf , Tf (Hz): natural frequency for first mode in along-wind, across-wind and torsional

directions

Rf (Hz): natural frequency for first mode of roof beam

aDg , aLg , aTg : peak factors for response accelerations in along-wind, across-wind and

torsional directions

Dg , Lg , Tg : peak factors for wind loads in along-wind, across-wind and torsional

directions h (m): eaves height

1k : factor for aspect ratio

2k : factor for surface roughness

3k : factor for end effects

4k : factor for three demensionality

Ck : area reduction factor

rWk : return period conversion factor

Zk : factor for vertical profile for wind pressure coefficients or wind force coefficients l (m): smaller value of H4 and B , minimum value of H4 , 1B and 2B , member

length

a1l (m): smaller value of H and 1B

a2l (m): smaller value of H and 2B


Hq (N/m2): velocity pressure at reference height H

Zq (N/m2): velocity pressure at height Z

r (year): design return period

Rer : 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 , Lδ , Tδ : mass damping parameter for vortex induced vibration, across-wind vibration

and torsional vibration

Dφ , Lφ , Tφ : mode correction factor for vortex induced vibration, across-wind vibration and

torsional vibration

Dζ , Lζ , Tζ : critical damping ratio for first translational and torsional modes

Rζ : critical damping ratio for first mode of roof beam ϕ : solidity

λ : mode correction factor of general wind force

Uλ : 0500 /UU μ : first mode shape in each direction

Dν (Hz): level crossing factor

θ (°): roof angle, angle of attack to member

Sθ (°): inclination of topography ρ (kg/m3): air density

Sρ (kg/m3): building density which is )/( Bm DHDM

LTρ : correlation coefficient between across-wind vibration and torsional vibration

6.1 General 6.1.1 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


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


Figure 6.1.1 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.

Figure 6.1.2 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.

wind load onstructural frames

wind load oncomponents/cladding

horizontal wind load

roof wind load

along-wind load

across-wind load

torsional wind loadwind load

simplifiedproceduresmall-scale building

wind load onstructural frames

wind load oncomponents/cladding

vibration direction vortices wind turbulence

a) fluctuating wind force caused bywind turbulence

vibration direction

b) fluctuating wind force caused by vortex generation in wake of building


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.

Figure 6.1.3 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

lattice type structurehigh-rise buildingdomehouse

qZ

qH

qH qH

ZH

HH


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.


(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.


Figure 6.1.4 Flow chart for estimation of wind load

Start

Outline of building

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

A6.1 Wind speed and velocity pressure

A6.11 Simplified procedure

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

6.2 Horizontal wind load

End

A6.8 Combination of wind loads

Wind tunnel experiment

6.3 Roof wind load 6.4 Wind load on components/cladding

Wind load on components/claddingWind load on structural frames

A6.2.2 External wind pressure coefficientA6.2.3 Internal pressure coefficients A6.2.4 Wind force coefficients

A6.2.1 Procedure for estimating 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

A6.4 Across-wind load A6.5 Torsional wind load

A6.3.2 Gust effect factor for roof wind loads

A6.3.1 Gust effect factor for along-wind loads

A6.6 Horizontal wind loads on lattice structural frames

A6.7 Vortex induced vibration

A6.10 Response acceleration

A6.13 1-year-recurrence wind speed


6.1.3 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.

along-wind

across-windwind

torsion

Ｄ

Ｈ

Ｂ

Figure 6.1.5 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, )024.0/(11 Hf = (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


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 ( BDH / or m/ DH ). 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 ( BDfU / or

m/ fDU ). 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


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 Horizontal Wind Loads on Structural Frames 6.2.1 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 .


Ａ

ＷD

Ｄ

Ｈ

Ｂ

wind

Figure 6.2.1 Projected area

6.3 Roof Wind Load on Structural Frames 6.3.1 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 3/ <Lm ρ , 1/ R1H >LfU and 15.0H <I , where m is mass per unit area, ρ is air density, L is span length, HU is design wind speed, R1f is frequency of first unsymmetrical vibration mode and HI 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.


6.4 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 CC 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 CC 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 Wind speed and velocity pressure

A6.1.1 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 ( ) 221 Uρ , 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, Hq , which is based on the design wind speed HU at the reference height H , is defined in Eq.(A6.1).


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 22.1=ρ (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 0U and wind directionality factor DK . The influences of surface

roughness, small-scale topographical features and elevation are reflected in the wind speed profile factor HE .

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

rWk . 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 1rW =k . The wind directionality factor DK , 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 DK 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 HU can be calculated by substituting 1D =K in Eq.(A6.2).

A6.1.3 Basic wind speed The basic wind speed 0U 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


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)

Modeling of typhoon pressure fields(based on data from 1951 to 1999)

Monte Carlo simulation of typhoonwinds (for 5000 years)

Extreme wind probability distributiondue to typhoons

Extraction of independent storm(including the 2nd higher and less)

Extreme wind probability distributiondue to non-typhoon winds

Synthesis of extreme valuedistributions

Evaluation of terrain category(considering historical variation)

Basic wind speed map

Reduction to the common base

Extreme value probabilityanalysis for mixed wind climates

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


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 extreme value analysis and the typhoon model.

Figure A6.1.2 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

Flat

terr

ain

cate

gorie

s V

IV

III

II I Fl

at te

rrai

n ca

tego

ries V

IV

III

II

I

Flat

terr

ain

cate

gorie

s V

IV

III

II I Fl

at te

rrai

n ca

tego

ries V

IV

III

II

I


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.


moving speed anddirection

radius of maximum wind

wind speed fieldgradient wind

surface wind

central pressuredepth

rate of occurrenceinitial position

Probability distributions

statistics ofhistorical typhoons

return period

pressure field

rate of occurrence

initial position

moving velocity

central pressure depth

radius of maximum wind

correlation of wind speedand direction based onobserved records

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.

r


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 ( 1D =K ) here. For return period factor rWk mentioned in A6.1.7, there are small differences in Uλ among wind speeds in winter for different meteorological stations. An average value of 1.1U =λ can be applied for calculating rWk in Eq.(A6.12).


Figure A6.1.5 100-year-recurrence 10-minutes mean wind speed at 10m above ground over a flat

and open terrain in winter (m/s)


A6.1.4 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 DK , 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 DK 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 DK 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 1D =K should be used for design because the maximum peak


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.

KD=0.9

NW0.85

W1.0

SW0.95

NE0.95

E0.85

SE0.85

S0.9

wind directionN

0.9

(a) Where the wind direction falls in a 22.5 degree sector as shown in Table A6.1.1

N0.9 larger value of 0.9 and 0.95

KD = 0.95NW0.85

W1.0

SW0.95

NE0.95

E0.85

SE0.85

S0.9

wind direction

(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)


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

1D =K .

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 rE , while the influence of small-scale topographical features is represented by gE .

(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:

α)(0

0ZZ ZZUU = (A6.1.1)

where ZU (m/s) is the mean wind speed at height Z (m), 0ZU (m/s) is the mean wind speed at height


0Z , 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 GZ is not influenced by terrain roughness, and is

considered constant for convenience. However, it does not mean that wind speeds at elevations greater than GZ are really constant. Since the boundary layer depth becomes greater when the terrain roughness increases, GZ is assumed to increase with terrain category, as shown in Table A6.3. However, GZ 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 bZ 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 bZ , the wind speed at bZ is usually the maximum, so the wind speeds in this region are assumed to equal to that at bZ , which is defined in Table A6.3, in order to arrive at a safer design. For heights above bZ , the power law can approximate the mean wind speed profile.

Zb

height

Figure A6.1.7 Mean wind speed profile in urban area


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 rE of the flat terrain, shown in A6.1.5(2) 2), is defined with the above considerations included. Figure A6.1.9 shows rE 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)

Exposure factor Er

terrain category

Figure A6.1.9 Exposure factor rE


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.)


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.

Figure A6.1.11 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.

3 ~ 5km Smooth Rough

developing internal boundary layer


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 IIIsmaller of40H and 3km The terrain roughness

in this wind directionshould be recognized ascategory I.

Figure A6.1.12 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.


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)


Figure A6.1.15 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 ss 6.1 HX = downstream of the top of the escarpment at a height s5.1 HZ = .

Calculate the topography factor 1gE and 2gE at 1/ ss =HX and 2 for the inclination

angle of 45 degrees from Eq.(A6.5), and then calculate the topography factor 12gE at

6.1/ ss =HX by linear interpolation according to the following equation:

2g1g12g 6.04.0 EEE += Calculate the topography factor 34gE for the inclination angle of 60 degrees in the same

way as for the inclination angle of 45 degrees. Conduct linear interpolation for topography factors 12gE and 34gE , with respect to the

inclination angle to achieve the topography factor at an inclination angle of 50 degrees and 6.1/ ss =HX from the following equation.

34g12gg 31

32 EEE +=

If the inclination angle is less than 7.5 degrees, the topography effect can be neglected. 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


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 6.1/ ss =HX

A6.1.6 Turbulence intensity and turbulence scale Natural wind speed fluctuates with time. The wind speed )(tU 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 )(tu in the longitudinal direction as well as )(tv and )(tw in the cross wind directions. Usually, the

longitudinal fluctuating wind speed component )(tu is important for design of buildings, so only the characteristics of )(tu 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 )(tw and

)(tv are also sometimes important.


Figure A6.1.17 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 uσ to the mean wind speed U .

UI uσ= (A6.1.2)

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) eq.(A6.8) eq.(A6.8) eq.(A6.8)

Turbulence intensity IrZ Turbulence intensity IrZ Turbulence intensity IrZ Turbulence intensity IrZ Turbulence intensity IrZ

Figure A6.1.18 Observed turbulence intensity27) and recommended value

The turbulence intensity ZI at height Z above the ground, is defined in Eq.(A6.7), in which the turbulence intensity rZI on flat terrain expressed in Eq.(A6.8), and the topography factor gIE , 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.

Terrain category I Terrain category II Terrain category III Terrain category IV Terrain category V


Especially in the separation region, there is an obvious increase in the standard variation of the wind speed fluctuating component )(tu (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 1C , 2C and 3C 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


topography with a height of about 50m23), 24), 25). 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


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 )(tu .

6/52

2u

u })/(8.701{)/(4

)(UfLUL

fF+

=σ

(A6.1.3)

where f : frequency

uσ : standard deviation of fluctuating component of wind speed )(tu

U : mean wind speed

L : turbulence scale (3) Turbulence scale

Equation (A6.11) is used as the turbulence scale ZL of the wind speed fluctuation )(tu 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 )(tu


(4) Co-coherence Co-coherence of wind speed fluctuation ),,( yzu rrfR is evaluated using Eq.(A6.1.4). It expresses

quantitatively the frequency-dependent spatial correlation of the wind speed fluctuation.

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡ +−=

U

rkrkfrrfR

2y

2y

2z

2z

yzu exp),,( (A6.1.4)

where f : frequency

yz , rr : distance between 2 points in the vertical and horizontal directions

yz ,kk : 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 rWk is defined as the ratio of the r -year-recurrence wind speed

rU to the 100-year-recurrence basic wind speed 0U . 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.

br

ra

U +⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛

−−=

1lnln1

r (A6.1.5)

where a and b are coefficients. Return period conversion factor krW is calculated approximately in Eq.(A6.12) by using the parameter Uλ , which is the ratio of the 500-year-recurrence wind speed

500U to the basic wind speed 0U .

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.


A6.2 Wind force coefficients and wind pressure coefficients A6.2.1 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 Hq evaluated at the reference height H . For lattice structures and members, the wind force coefficients are defined in terms of the velocity pressure Zq evaluated at the height Z where the

members under consideration are placed. The aspect ratio BH / is generally large for tall buildings, such as 45>H 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 45>H m and those with 45≤H 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 DC for estimating horizontal wind loads on structural frames are generally given by the difference between the wind pressure coefficients, pe1C and pe2C , 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 RC for

estimating roof wind loads on structural frames are generally given by the difference between the external and internal pressure coefficients, peC and piC , 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 DC 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 CC for the design of components/cladding are generally given by the difference between the peak external pressure coefficient peC and the factor *

piC for the


effect of fluctuating internal pressures, except for open roofs, in which the value of CC is provided. The values of peC (and CC in the open roof case) are determined from the most critical positive and negative peak values irrespective of wind direction. Note that the factor *

piC for the effect of fluctuating internal pressures is not the actual peak internal pressure coefficient piC but an equivalent value producing the peak wind force coefficient CC when combined with the peak external pressure coefficient peC .

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 peC 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 ( Zk ) 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 BD / . This feature is related to the behavior of the separated shear layer from the windward edge and is reflected in the value of pe2C . The aspect

ratio BH / of high-rise buildings with 45>H m is in the range from 1 to 8 in most cases. In this range, the effect of BH / on the wind pressure coefficients is not significant. Therefore, the pressure


coefficients are provided independently of BH / .

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 peC 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 ( HB / , HD / 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 peC 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 1W ), the building shape is represented by the rise/width ratio Bf / and the eaves-height/width ratio Bh / . However, for a wind parallel to the


gable wall (wind direction 2W ) it is represented by the rise/depth ratio Df / and the

eaves-height/depth ratio Dh / . 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 1W , the definition of zones is similar to that for flat, gable and mono-sloped roofs. For wind direction 2W , 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 0/ =Bh and 0/ =Bf or when 0/ =Dh and 0/ =Df ,

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 peC 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 Df / and the eaves-height/span ratio Dh / . The values of peC for five Df / ratios and three Dh / ratios are

provided in Table A6.10. Linear interpolation can be used for values of Df / and Dh / other than shown. Both positive and negative values of peC are provided for zone Ra. The value for 0/ =Dh

and 0/ =Df 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


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 piC 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 DC for buildings with circular sections

Wind force coefficients for cylinders are affected by the Reynolds number, flow condition, aspect ratio DH / , surface roughness of the cylinders, and other factors. Figure A6.2.236) shows the variation of drag coefficient DC on a two dimensional smooth cylinder in a uniform flow with Reynolds

number Re ( ν/UD= , 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 4107 ×≈ UDRe , where U and D are expressed in units of ‘m/s’ and ‘m’, respectively. It is found

from Fig. A6.2.2 that DC 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 DC 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 1k and 2k , respectively37).

The external pressure coefficients peC on roofs are given in Table A6.10 assuming that 0/ =Df

and 1/ =Dh .


Figure A6.2.2 Plots of drag coefficient DC on a two-dimensional cylinder with very smooth

surface as a function of Reynolds number Re 36)

(2) Wind force coefficients RC 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 10<H m. For gable ( 0>θ ο) and troughed roofs ( 0<θ 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

30|| ≤θ 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 DC 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


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 DC 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 DC is provided only for 6.0≤ϕ . 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 FA of the plane to the whole plane area )(0 BhA = 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 DC 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 DC for lattice structures with square and

triangular plan shapes, which consist of angles or circular pipes. The wind force coefficient DC 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 DC 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 DC 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 DC for fences on ground

Wind force coefficients DC 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 DC for 0=ϕ in Table A6.15 is introduced to obtain intermediate values of DC for 2.00 << ϕ . Wind load for a fence can be calculated according to the simplified procedure using DC 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 Zq at height Z of the member under


consideration. The wind load on a component is given by the product of Zq , C , )71( ZI+ and bl ( ϕbl for nets), where ZI 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 peC 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 peC 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 BH / 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 Zk and ZI 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.


(2) Peak external pressure coefficient peC 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 peC for zone Ru in Table A 6.9(1). If no positive value of

peC 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 20≈θ 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 Ck when the subject area CA of components/cladding is greater than 1 m2 (up to 5 m2) 46). 2) Buildings with vaulted roofs

The peak external pressure coefficients peC are determined from the results of wind-tunnel experiments33), focusing on medium-scale buildings in urban areas, in which the 1/ Bh ratio is varied from 0 to 0.7 and the 1/ Bf ratio from 0.1 to 0.4. When the 1/ Bf 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 1/ Bf 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 1/ Bf 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 peC for buildings with circular sections


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 DH / and surface roughness of buildings. The factor 1k considers the effect of aspect ratio, and the factor 2k 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 3k considers this effect47). The values in Table

A6.19 are applicable to buildings with aspect ratios DH / 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 peC for domes with 0/ =Df provided in Table A6.20 can be used.

(4) Peak external pressure coefficients peC 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 )/( Df 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 Df / 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 uHI at the reference height H of the approach flow when 2.0/ ≥Df .

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 CC is represented by Eq.(A.6.15), because the peak external pressure coefficients peC 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 peak external and internal pressures are not induced simultaneously. The factor *

PiC for the effect of 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


external pressure coefficient peC . The value of CC is evaluated from a series of computations for the peak wind force coefficients using wind tunnel data on peC 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.

Fig.A6.2.3 Example of fluctuating external and internal pressures acting on components/cladding A6.2.7 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

Wind force coefficient, wind pressure coefficient

0Time

Cpe ^

Cpi

CC ^ C*

pi wind force coefficient

external pressure coefficient

internal pressure coefficient

peak wind force coefficient

peak external pressure coefficient

peak internal pressure coefficient

CC^

Cpe ^

Cpi


A6.3.1 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.

D

MDD

D

MDDDmax

D

DmaxD 1

M

g

M

gM

M

MG σσ+=

+== (A6.3.1)

where DmaxM , DM , MDσ are maximum value, mean value and rms of overturning moment at the base of the building, respectively. DmaxM and MDσ involve load effect due to the dynamic response of the building. If MDσ is expressed as composition of background component MDQσ and resonance component MDRσ , Eq.(A6.3.1) becomes as follows.

2MDQD

DMDD2D

D

MDQDD

2MDR

2MDQDD 4

)(111σζ

πφσ

σσ fSf

MgMgG ++≈++= (A6.3.2)

where )( DMD fS is power spectrum density of overturning moment at natural frequency for the first mode Df and Dφ is the mode correction factor. MDRσ is considered for only the first mode vibration, and MDRσ is inertia force by vibration as described in the following equation.

ZdZZmZHZdZZmZHH

)()()()()(0a0 aMDR ∫∫ == μσσσ (A6.3.3)

where )(a Zσ , )(Zm and )(Zμ 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.

MD2

HD CBHqM = (A6.3.4)

MD2

HMDQ 'CBHq=σ (A6.3.5)

2MD

*DCMD

*D

2MDQ

DMDD

')()(

CfSffSf

=σ

(A6.3.6)

where MDC is overturning moment coefficient, 'MDC is rms overturning moment coefficient and

)( *DCMD fS is power spectrum of overturning moment coefficient at non-dimensional frequency *

Df . If these equations are taken into consideration, Eq.(A6.3.2) becomes as follows.

2MDD

*DCMD

*D2

DMD

MDDD '4

)(1'

1C

fSfCC

gGζ

πφ++≈ (A6.3.7)

Additionally, in this formula non-dimensional frequency is defined by turbulence scale,

HHD*D /ULff = , but, in the wind tunnel test breadth of the building it is used usually HD

*D /UBff = .

(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


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.

PB

2

PAD CHZCC −⎟⎠⎞

⎜⎝⎛=

α

(A6.3.8)

MDC , 'MDC and )( *

DCMD fS are expressed using the parameter of the recommendation equations as

follows.

gHMD CCC = (A6.3.9) 'gH

'MD CCC = (A6.3.10)

D2MD

*DCMD

*D ')( FCfSf = (A6.3.11)

where HC is wind force coefficient at the top of the building, gC is a factor relevant to overturning moment in the along-wind direction, '

gC is a factor relevant to rms overturning moment in the along-wind direction and DF is a spectrum factor of windward force. Spectrum factor of wind velocity F , size reduction factor DS , factor R expressing correlation of wind pressure of a windward side and a leeward side R are considered for DF .

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 spectrum is mostly in agreement with the test values.

Figure A6.3.1 Along-wind force in comparison with those obtained from wind tunnel tests

( 4/ =BDH )52)

(3) Fluctuating component of overturning moment

When the vibration mode is HZ /=μ , the relation between spectrum of overturning moment due to the wind force )(MD fS and spectrum of overturning moment due to the load effect by vibration

)('MD fS is expressed by the following equation.

0.0

0.5

1.0

1.5

0 1 2 3

　II　III　IV

地表面粗度区分

0.0

0.5

1.0

1.5

0 1 2 3

　II　III　IV

地表面粗度区分

reco

mm

enda

tion

valu

e/te

st v

alue

10-5

10-4

10-3

10-2

10-3 10-2 10-1 100

実験値指針値

side ratio D/B side ratio D/B

test recommendation

(a) mean overturning momentcoefficient

(b) rms overturning momentcoefficient

(c) power spectrum density ofover turning moment

fB/UH reco

mm

enda

tion

valu

e/te

st v

alue

category category

fSC

MD(f)

terrain terrain


)()()(' MD2

mMD fSffS χ= (A6.3.12)

where 2m )( fχ is mechanical admittance as expressed by the following equation.

{ } 2D

2D

22D

2m

)/(4)/(1

1)(ffff

fζ

χ+−

= (A6.3.13)

The variance of overturning moment due to the load effect by vibration 2MDσ is the integral of

Eq.(A6.3.12), and the variance consists of back ground component 2MDQσ and resonance component

2MDRσ as expressed by the following equation.

2MDR

2MDQ0 MD

2MD )(' σσσ +≈= ∫

∞dffS

D

DMDD2MDQ0

2mDMD0 MD 4

)()()()(ζ

πσχ fSfdfffSdffS +=+= ∫∫∞∞

(A6.3.14)

In this equation, resonance component is estimated approximately as a response to white noise )( DMD fS .

Therefore, overturning moment for maximum load effect is expressed by following equation. 2MDR

2MDQDDDmax σσ ++= gMM (A6.3.15)

where Dg 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.

2.1)ln(2)ln(2

577.0)ln(2 DD

DD +≈+= TT

Tg νν

ν (A6.3.16)

where T is time for evaluation and Dν is level crossing rate calculated from power spectrum density

as in the following equation.

D

DD

0 MD

0 MD2

D 1)('

)('

RRf

dffS

dffSf

+≈=

∫∫

∞

∞

ν (A6.3.17)

Additionally, in some foreign wind loading standards, DmaxM is expressed by the following formula.

In this equation, the background component and the resonance component are distinguished. 2MDR

2R

2MDQ

2QDDmax σσ ggMM ++= (A6.3.18)

where Qg is peak factor of background component (=3.4) and Rg is peak factor of resonance

component calculated from Eq.(A6.3.16) as DD f=ν .

(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


fundamental vibration mode could be estimated from the following equation. 2

DR2

DQDD WWWW ++= (A6.3.19)

where

ACqW DHD =

ACC

CqgWg

g'DHDQDQ =

BAZmZaW )()(DmaxDR μ=

where

DW , DQW , DRW (N): mean, background and resonance component of wind load, respectively

Dmaxa (m/s2): maximum acceleration at top of building as defined in A6.10.2

DQg : 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 4/ =BH , 1/ =BD and 350 =U m/s. The gust effect factors become large with terrain category

and building height.

Figure A6.3.2 Variation of gust effect factor with terrain category and building height A6.3.2 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,

2.02.22.42.62.83.03.23.43.63.8

0 50 100 150 200 250 300

VIVIIIII I

category

0 50 100 150 200 250 300height of building (m)

gust

eff

ect f

acto

r G

D


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.

c

2c

2Ri

2RiRe

2Re

2Re

R 1)1(

1r

rrgRrgG

−++

±= (A6.3.21)

where Reg and Rig are peak factors for generalized external pressure and generalized internal pressure, and these value are 5.3Re =g , 3Ri =g from the results of test and measurement. Rer and

Rir are the generalized fluctuating external and internal pressures divided by the generalized mean wind pressure coefficient. cr is the generalized mean internal pressure divided by the generalized mean external pressure coefficient. ReR 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 damping ratio.

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,

4.0pi −=C and 0pi =C , 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), RG for “+”corresponds to

load in the same direction as given by wind load coefficient, and RG 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, δ57.0R ≈f (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

時間

（－）

（＋）

０ïóâ³èdw

ind

load

time


the critical damping ratio, Rζ . (1) Case for 4.0pi −=C

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 peC is −0.4 over the whole subject area as center beam shown in Fig.A6.3.4(a), the wind force coefficient becomes 0R =C . In this case, roof wind loads can be calculated from Eq.(A6.18), which is the product RRGC of wind force coefficient RC and gust effect factor RG . However, when the wind force coefficient becomes partially 0R =C as shown in Fig.A6.3.4(b), the wind loads can be calculated from Eq.(A6.17).

Figure A6.3.4 Relation between wind force coefficient and external or internal pressure coefficient

(for 4.0pi −=C )

(2) For 0pi =C

Wind force coefficient is equal to external pressure coefficient for 0pi =C . 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 Across-wind Vibration and Resulting Wind Load

A6.4.1 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

(a) beams normal to the wind direction (b) beams parallel to the wind direction


10)/( LH >BDfU , 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 5~2.0/ =BD ) from which

many experimental data have been obtained. Moreover, by taking into account the fact that

experimental data for buildings with an aspect ratio BDH / 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 Lφ 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


values used in Eq.(A6.20) need to be set to 06.0'L =C , 1=m , 9.01 =κ , BUf /15.0 H1S = ,

2.01 =β . These parameter values are in the transcritical critical region of Reynolds number ( 6H ≥DU (m2/s)).

A6.5 Torsional Vibration and Resulting Wind Load

A6.5.1 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

10)/( TH >BDfU , 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 5~2.0/ =BD ) and aspect ratio

BDH / 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 Tφ 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.


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 2=β , and vibration

modes higher than the fundamental one are neglected. β

μ ⎟⎠⎞

⎜⎝⎛=

HZ (A6.6.1)

According to the above assumptions, the peak response Zmax,x at height Z is given as a function

of the generalized stiffness K of the fundamental mode by:


( )DDH0DH

Dmax, 195.0

2 RBIK

HBCqgx Z +

++=

βαμ (A6.6.2)

However, the mean response ZX at height Z is given by:

μβαβα ⎟⎟⎠

⎞⎜⎜⎝

⎛++

−−

++=

2221H00DH

ZBBB

KHCqX (A6.6.3)

where Hq , HI are the velocity pressure and the turbulence intensity, respectively, at H height, and α is the exponent of the power law in the wind speed profile. Dg , DR and DB 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 Definition of 0B , HB , H

A6.7 Vortex Induced Vibration

A6.7.1 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


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 rC , 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, 3mr <DU is the subcritical region, 63 mr <≤ DU is critical region and mr6 DU≤ is super/trance critical Reynolds number region. Ls ζρ in Table A6.23 depends on the amplitude at the resonant condition. 5Ls <ζρ corresponds with the large amplitude, and 5Ls ≥ζρ corresponds with the small amplitude.

A6.7.3 Vortex induced vibration and resulting wind load on building components with circular 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 Combination of Wind Loads A6.8.1 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.


A6.8.2 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.

A6.8.3 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, xM , yM , 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 ycM , which should be combined with maximum x-direction overturning moment xmaxM , is defined by the following equation using mean y-direction overturning moment yM and maximum fluctuating component of y-direction overturning moment ymaxm .

( )122ymaxyyc −++= ρmMM (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, 0=ρ

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 LTρ , shown in Table A6.25, is defined

by calculation based on wind tunnel tests.

LTρ is calculated by a statistical analysis method61) under the conditions that the critical damping

Figure A6.8.1 Windward load and combined load for across wind direction

Figure A6.8.2 Relation between side ratio (D/B) and combination factor γ

wind

plan of building

quasi-static wind load


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.

Figure A6.8.3 Schema of load combination in consideration of response correlation

A6.8.4 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 Mode Shape Correction Factor A6.9.1 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 HZ=μ 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 ( )2/ HZ=μ 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 ( )βμ HZ /= .

A6.9.2 Procedure

The mode shape correction factor is specified by Eq.(A6.32). This corrects the gust effect factor for

xM

yM

ycM

0yM )122(maxy −+ ρmρmaxym

)221(maxy ρ−−m

point A

maxyM

maxxM

yM

xM

maxym

maxxm

considered point ofcombination load


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 βσ of the generalized wind force

for its first vibration mode to 1σ for the reference vibration mode shape (the power index of a first vibration mode 1=β for a conventional building and 2=β for a lattice structure).

1σσ

λ β= (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.

( ) ( )⎪⎩

⎪⎨

⎧

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−

=structurelattice 4.123.05.04.016.0

buildingalconvention 1.01.1

0

HD ββ

β

φBB (A6.9.2)

( )1

L 73.027.0−

⎟⎠⎞

⎜⎝⎛+=

β

βφHZ (A6.9.3)


( )1

T 73.027.0−

⎟⎠⎞

⎜⎝⎛+=

β

βφHZ (A6.9.4)

In addition, the generalized mass DM , LM and the generalized inertial moment TI of a

building can be calculated according to Eqs.(A6.9.5) and (A6.9.5), respectively.

( ) dZHZmM

H β2

0 ZLD ∫ ⎟⎠⎞

⎜⎝⎛= (A6.9.5)

dZHZII

H β2

0 ZT ∫ ⎟⎠⎞

⎜⎝⎛= (A6.9.6)

where Zm and ZI are the mass and the inertial moment at height Z , respectively.

A6.10 Response Acceleration A6.10.1 Scope of application

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.

A6.10.2 Maximum along-wind response acceleration Rms of generalized response acceleration aDσ is given by the following equation.

∫∞

=0 2

g

2m4

g2aD

)()2)(( df

Kf

ffSχ

πσ (A6.10.1)

where aDσ is rms of generalized acceleration, )(g fS is power spectrum density of generalized wind force, 2

m )( fχ is mechanical admittance as described in Eq.(6.3.13), f is frequency and gK is generalized stiffness as described in the following equation.

2DDg )2( fMK π= (A6.10.2)

where DM is generalized mass. Because the resonant component is dominant in acceleration, )(g fS can be substituted by white noise having power spectrum density at natural frequency Df , as

described in the following equation.

D

D2gHHDg )'()(

fFCBHCqfS λ= (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.


D

DgHHaD '

MR

CBHCq λσ = (A6.10.4)

Furthermore, aDσ 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 Dν for calculating peak factor is approximated by the natural frequency Df .

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

daa Tmaxdmax = (A6.10.5)

A6.11 Simplified Procedure A6.11.1 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 DK

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

eC 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

gE .

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


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

4/ =BDH 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 BD12 in the x-direction and BD6 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).

6 x

y

12 BD

6 BD

4 2

2

4

1.0

1.1 1.1

1.2

1.0

0.8

6x

y

12 BD

6 BD

4 2

2

4

1.0

1.1

1.1

1.2

1.2

1.3

1.1

1.2

1.3

1.3

(a) Terrain category II, along-wind direction (b) Terrain category II, across-wind direction

1.2

1.2 1.1

0.86x

y

12 BD

6 BD

4 2

2

4

1.0

1.2

1.2

1.2

1.1

1.0

1.1

1.4

1.01.01.1

1.2

(c) Terrain category IV, across-wind direction

Figure A6.12.1 Contours of response ratios63), 64)


A6.13 1-Year-Recurrence Wind Speed 1-year-recurrence wind speed 1HU 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 1U 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 maxa is approximated as a function of wind speed U shown in Eq.(A6.13.1), the return period maxat for maximum acceleration maxa 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).

( )Ufa =max (A6.13.1)

( )maxamaxa 1

1aF

t≤−

= (A6.13.2)

( ) ( ){ }∑=

−≤=≤16

1max

1Umaxa

iii afFpaF (A6.13.3)

where ( )maxa aF ≤ : probability that maximum acceleration does not exceed maxa

ip : occurrence frequency for wind direction i

( ){ }max1

U afF i−≤ : probability that the wind speed does not exceed the wind speed that the

maximum acceleration is equal to maxa for wind direction i The occurrence frequency at each wind direction ip , parameters ia and ib 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 ia and ib should be used for the return period less than 1

year. ( ) ( ){ }[ ]iiii bUaUF −−−=≤ expexpU (A6.13.4)

where

iU (m/s): 10-minute mean wind speed at 10m above ground over a flat and open terrain for

wind direction i

ii ba , : parameters estimated based on the daily maximum speed for wind direction i


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 parameters ia , ib and occurrence frequency ip for each wind direction at 30 cities

Asahikawa Sapporo Aomori Akita Sendai ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%)

NNE 0.58 4.26 3.3 1.58 3.59 0.4 1.22 3.57 4.6 0.73 4.79 0.4 0.82 4.40 1.7NE 0.52 4.32 0.8 1.23 3.76 0.5 0.82 4.03 4.0 0.56 5.88 0.1 0.61 3.72 1.1

ENE 0.54 3.63 0.2 1.30 3.80 1.6 0.76 5.84 3.7 0.73 3.17 0.2 0.56 5.86 0.8E 1.45 2.28 0.7 0.94 4.93 4.0 0.90 5.46 7.9 0.63 4.77 0.3 0.66 5.09 0.7

ESE 1.05 2.74 0.7 0.72 5.52 6.2 0.60 6.09 1.1 0.65 6.57 7.2 0.74 4.97 0.8SE 0.76 4.44 6.4 0.59 7.49 8.1 0.64 7.71 0.7 0.63 6.25 17.0 1.14 3.89 16.7

SSE 0.55 5.61 17.1 0.47 8.86 13.5 0.58 4.61 0.5 1.25 4.70 0.2 0.76 4.58 13.3S 0.54 4.34 3.9 0.43 7.94 3.2 1.58 2.79 0.2 0.72 6.27 0.1 0.75 4.66 6.4

SSW 0.48 6.37 3.3 0.45 7.31 1.8 0.54 5.27 2.8 0.38 8.91 2.2 0.87 5.06 1.8SW 0.59 6.72 1.2 0.44 7.96 2.1 0.47 6.47 12.6 0.46 7.44 9.9 0.77 5.55 0.9

WSW 0.49 7.58 10.1 0.47 8.41 3.9 0.48 7.56 10.2 0.38 6.98 12.5 0.46 8.02 1.6W 0.63 6.45 17.6 0.53 8.53 5.1 0.50 9.11 14.0 0.36 7.91 17.7 0.42 8.75 7.7

WNW 0.65 5.80 19.4 0.45 9.28 5.2 0.55 8.43 15.7 0.37 9.68 11.9 0.39 9.42 16.9NW 0.68 4.78 8.8 0.46 8.63 19.5 0.66 6.00 8.6 0.45 9.56 9.2 0.43 8.62 10.1

NNW 0.86 5.66 4.7 0.59 7.05 23.3 1.00 4.20 6.7 0.60 7.87 3.8 0.56 5.44 7.9N 0.83 4.92 1.8 0.83 4.78 1.6 0.84 3.49 6.7 0.75 5.86 7.3 0.75 5.17 11.6

Niigata Kanazawa Utsunomiya Maebashi Tokyo ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%)

NNE 1.07 4.61 14.4 0.76 5.11 5.8 0.70 4.47 18.5 0.28 9.56 0.1 0.87 5.46 4.2NE 1.78 3.66 6.6 0.81 5.38 3.0 0.88 4.43 8.8 －－ 0.0 1.04 5.43 6.2

ENE 0.85 3.72 0.3 0.99 5.02 10.5 1.01 4.52 2.3 1.20 4.78 0.1 1.05 5.58 6.6E 1.24 4.17 0.2 0.93 4.62 9.9 1.13 3.81 3.5 0.71 4.32 1.4 1.10 5.47 3.3

ESE 0.64 7.39 0.2 0.87 3.56 0.9 1.37 3.85 7.1 0.81 5.19 22.7 1.22 5.67 3.6SE 0.69 8.05 6.6 1.35 3.32 1.2 1.33 3.76 9.2 0.99 4.83 8.7 1.37 6.02 1.9

SSE 0.98 5.69 4.4 2.15 3.26 1.6 1.00 4.26 9.1 1.21 3.84 2.0 0.94 4.99 0.3S 1.65 4.38 1.7 0.17 4.11 0.5 0.78 4.68 6.0 1.17 3.76 1.2 0.83 6.53 20.2

SSW 1.19 4.78 3.0 0.42 7.62 8.2 0.75 4.48 6.4 0.57 2.88 0.3 0.56 7.61 2.0SW 0.45 6.84 3.2 0.43 9.16 8.5 0.81 4.12 2.8 0.49 3.30 0.3 0.53 7.80 9.8

WSW 0.40 8.65 14.4 0.45 8.65 9.7 0.68 4.79 1.5 0.50 4.65 1.3 0.64 5.84 0.4W 0.44 7.29 18.8 0.36 7.49 12.1 0.59 6.99 2.2 0.44 6.78 1.5 0.45 7.83 0.2

WNW 0.38 8.39 7.7 0.37 6.62 9.1 0.53 7.17 3.1 0.34 6.86 3.5 0.50 7.23 0.2NW 0.48 8.40 6.9 0.44 5.36 7.4 0.47 5.14 1.6 0.45 6.82 26.0 0.45 8.28 4.9

NNW 0.52 7.43 6.7 0.38 5.82 3.7 0.50 5.67 3.6 0.47 8.43 26.7 0.47 7.37 25.8N 0.66 5.56 4.9 0.66 4.89 7.9 0.58 4.49 14.3 0.51 11.0 4.2 0.64 5.85 10.4

Chiba Yokohama Shizuoka Hamamatsu Nagoya ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%)

NNE 0.73 6.38 6.2 0.58 7.52 1.8 0.83 4.75 2.9 0.80 4.59 0.4 1.10 3.61 1.6NE 0.89 6.10 6.1 0.81 6.50 0.1 0.77 5.74 9.5 1.25 3.20 3.0 1.80 2.92 0.7

ENE 0.97 5.46 6.7 0.64 7.58 1.4 0.94 5.74 23.7 0.56 6.29 7.1 2.25 2.29 0.8E 1.02 4.85 2.5 1.04 5.62 9.1 0.88 5.51 1.8 0.59 6.69 7.8 2.46 3.82 0.1

ESE 1.41 4.08 6.9 1.19 5.00 1.9 0.80 4.50 1.8 0.74 6.59 2.5 0.47 6.21 0.4SE 1.27 4.26 9.9 0.71 5.81 0.9 0.75 3.95 1.3 1.03 5.35 5.5 0.47 6.03 3.8

SSE 0.68 4.96 3.8 0.76 5.48 7.5 0.92 4.96 6.1 0.80 5.06 6.7 0.51 6.54 13.5S 0.77 4.62 2.2 0.63 5.85 4.2 0.81 5.46 17.6 0.93 4.93 2.5 1.16 4.85 11.0

SSW 0.35 9.90 4.8 0.40 9.60 5.8 0.50 6.50 4.1 0.67 5.94 0.6 1.26 4.67 2.0SW 0.45 7.69 13.4 0.38 8.74 15.8 0.42 8.63 12.4 0.58 5.77 3.2 1.14 4.78 1.1

WSW 0.74 4.95 8.8 0.40 8.42 3.4 0.57 9.01 4.0 0.68 6.00 13.8 0.88 3.81 1.3W 0.59 4.84 0.7 0.48 8.68 0.2 0.51 10.1 5.3 0.66 7.30 16.7 0.59 5.61 1.4

WNW 0.42 8.33 0.6 0.65 8.27 0.3 0.39 7.05 3.8 0.49 9.15 23.6 0.70 6.49 18.8NW 0.46 7.68 7.0 0.36 8.39 0.5 0.55 4.96 1.8 0.39 8.27 5.9 0.53 7.29 19.0

NNW 0.48 6.26 15.1 0.32 6.95 2.5 1.28 4.07 2.9 0.55 4.18 0.5 0.50 5.49 16.2N 0.61 5.46 5.3 0.46 7.21 44.5 0.59 3.81 1.0 1.69 4.88 0.2 0.89 4.10 8.3


Table A6.13.1(continued) parameters ia , ib and occurrence frequency ip for each wind direction at 30 cities

Kyoto Osaka Kobe Wakayama Okayama ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%)

NNE 0.75 4.05 5.6 0.88 4.24 17.6 0.57 6.22 1.4 0.82 5.92 8.9 0.47 5.61 4.2NE 0.73 4.01 5.1 0.72 5.23 4.4 0.32 5.41 1.2 1.28 4.44 5.3 0.89 3.61 2.3

ENE 0.93 4.97 6.1 0.56 5.95 4.4 0.48 6.50 12.1 1.90 3.99 10.3 1.13 4.17 7.6E 0.85 5.15 6.6 0.63 5.80 1.7 0.59 5.67 3.3 1.63 4.19 1.4 0.67 5.30 5.2

ESE 0.78 4.80 3.9 0.89 4.80 1.3 1.01 4.06 0.5 0.29 4.96 0.3 0.56 5.13 4.3SE 0.84 4.64 1.5 0.57 5.16 0.5 1.71 3.33 0.7 0.64 7.04 0.5 0.73 4.27 7.9

SSE 0.95 4.06 3.3 0.68 4.96 0.5 0.95 3.56 0.3 0.39 8.26 1.0 1.26 3.72 1.8S 0.92 4.99 8.9 0.51 6.42 0.5 1.56 3.84 1.6 0.35 7.97 5.3 1.35 3.43 5.3

SSW 0.80 5.76 10.3 0.31 7.86 1.8 0.60 5.27 6.9 0.43 7.32 9.0 1.01 4.37 5.7SW 0.58 6.03 2.5 0.64 5.75 14.4 1.05 5.54 5.9 0.94 4.71 10.7 0.60 5.24 14.1

WSW 0.72 6.56 4.6 0.80 5.57 19.0 0.65 5.89 13.7 0.61 4.44 9.0 0.62 5.34 6.0W 0.69 6.83 3.8 0.46 6.47 12.7 0.50 7.15 11.8 0.38 6.58 4.0 0.45 7.01 5.9

WNW 0.61 6.74 4.7 0.39 6.80 1.9 0.51 7.17 7.2 0.54 8.19 5.3 0.40 8.07 5.8NW 0.58 7.53 3.1 0.63 6.32 3.6 0.72 5.91 3.9 0.61 6.99 7.7 0.58 6.09 6.5

NNW 0.85 6.55 10.0 0.77 6.66 7.4 0.56 6.72 13.2 0.77 5.48 9.3 0.62 5.24 8.6N 0.75 5.49 20.0 0.77 5.73 8.3 0.72 5.78 16.3 0.80 5.61 12.0 0.51 5.60 8.8

Matsue Hiroshima Takamatsu Kochi Matsuyama ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%)

NNE 0.72 5.15 1.6 1.26 4.40 31.5 1.29 3.65 2.5 0.82 7.11 6.7 0.91 6.61 3.4NE 0.64 5.77 8.2 0.58 5.18 0.9 0.79 3.39 1.2 1.04 6.95 1.0 0.74 6.15 2.6

ENE 0.59 6.07 7.1 0.42 7.43 0.3 1.17 3.90 12.7 0.96 4.78 2.4 0.96 4.74 3.6E 0.78 5.25 10.0 1.48 5.93 0.4 1.10 3.86 9.8 0.75 3.85 4.2 1.57 3.26 4.5

ESE 1.35 3.90 8.0 0.68 5.19 0.5 0.70 4.24 6.2 0.57 4.99 6.9 0.91 3.50 4.7SE 0.61 5.22 1.7 1.39 5.13 0.2 0.87 3.71 2.2 1.38 4.02 21.7 0.87 4.45 2.7

SSE 0.45 5.62 0.5 0.23 5.84 0.6 0.93 3.88 0.2 1.93 4.19 6.0 0.47 6.18 2.6S 0.68 5.75 0.2 0.49 4.66 5.7 0.77 2.89 0.4 1.11 4.50 8.5 0.42 6.40 2.0

SSW 0.40 8.19 1.8 0.84 5.28 8.2 0.69 5.39 0.6 0.71 5.18 2.4 0.89 4.59 2.1SW 0.55 6.61 1.5 1.05 4.60 10.8 0.61 4.48 3.2 0.80 6.32 1.2 0.79 5.48 2.2

WSW 0.45 6.91 12.1 0.67 5.11 0.5 0.57 6.10 13.0 0.78 4.55 4.0 0.91 5.31 6.8W 0.41 7.72 28.3 0.69 7.13 3.3 0.57 6.90 19.4 0.55 4.62 19.9 0.66 5.92 20.7

WNW 0.42 7.10 5.9 0.64 7.44 3.2 0.49 7.19 5.6 0.55 4.30 7.2 0.66 5.99 20.1NW 0.59 5.91 8.6 0.70 6.54 0.9 0.50 6.53 2.9 0.59 7.03 1.7 0.99 5.09 13.0

NNW 0.67 5.93 3.4 0.79 6.65 3.7 0.87 4.32 11.4 0.56 7.08 1.4 0.92 5.04 6.6N 0.64 6.08 1.1 0.99 4.54 29.3 0.98 4.41 8.7 0.66 7.22 4.8 0.69 6.99 2.4

Fukuoka Oita Kumamoto Kagoshima Naha ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%) ai bi pi(%)

NNE 0.67 5.37 3.2 0.78 4.67 8.7 1.52 3.06 1.5 0.56 5.50 9.7 0.54 4.98 11.2NE 0.95 5.61 1.6 0.95 4.27 7.3 0.56 5.42 2.1 0.52 6.03 7.0 0.63 5.75 2.6

ENE 0.87 5.82 0.5 1.54 3.91 11.3 0.60 6.28 3.7 0.36 5.95 0.9 0.79 6.17 7.2E 1.18 5.42 0.2 0.80 3.71 3.3 0.50 6.42 2.9 0.42 6.55 0.9 0.30 -0.27 8.9

ESE 1.03 5.01 0.7 0.47 5.92 0.6 0.59 5.74 2.5 0.31 5.67 1.7 0.43 3.63 8.6SE 0.77 5.41 9.7 0.37 5.99 2.1 0.34 3.88 1.2 0.46 5.17 5.0 0.20 -4.53 6.7

SSE 0.40 7.33 4.5 0.60 5.39 6.4 0.72 3.69 1.5 0.50 4.48 7.5 0.20 3.93 4.1S 0.37 7.29 2.2 0.97 3.42 7.9 0.38 3.71 3.3 0.43 4.28 4.7 0.20 -1.73 5.2

SSW 0.63 8.48 3.1 0.52 4.11 4.1 0.57 5.09 6.0 0.57 6.88 0.9 0.39 2.01 9.8SW 0.65 6.43 0.7 0.56 6.41 2.0 0.83 5.15 17.7 0.39 7.90 2.0 0.16 -9.17 4.4

WSW 0.62 8.56 0.6 0.56 6.86 2.6 0.65 6.35 9.8 0.52 7.37 4.0 0.09 -25.88 2.5W 0.55 7.92 3.1 0.57 8.41 7.1 0.52 5.52 4.9 1.03 5.41 11.6 0.39 5.35 1.1

WNW 0.56 8.60 6.3 0.63 8.08 2.7 0.52 6.14 7.6 0.67 6.23 18.1 0.46 4.52 1.3NW 0.63 6.15 3.1 0.65 7.36 10.3 0.64 5.23 18.5 0.56 7.25 8.5 0.22 -5.84 1.9

NNW 0.63 5.84 31.7 0.71 6.66 17.8 0.70 4.89 13.8 0.71 5.52 13.2 0.52 7.13 7.3N 0.69 5.82 28.8 1.62 3.64 5.8 0.77 4.86 3.0 0.75 5.23 4.3 0.72 7.89 17.2


Appendix 6.6 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. AGCqW DDHD = (6.4)

where Hq is velocity pressure, DC is wind force coefficient, DG 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).

CCHCˆ ACqW = (6.6)

where Hq is velocity pressure, CC is peak wind force coefficient and CA is subject area.

The velocity pressure Hq is expressed as Eq.(Appendix 6.6.1) form Eq.(A6.1) and Eq.(A6.2)．

2rWHD0

2HH )(

21

21 kEKUUq ρρ == (Appendix 6.6.1)

where ρ is air density, HU is design wind speed, 0U is basic wind speed, DK is wind directionality factor, HE is wind speed profile factor at the reference height H and rWk is return

period conversion factor. The factors influencing dispersion of horizontal wind load for structural frames WD and wind load

for components/cladding CW are air density ρ , basic wind speed 0U , wind directionality factor

DK , wind speed profile factor HE at reference height H according to the surface roughness, return period conversion factor rWk , wind force coefficient DC and gust effect factor DG or peak

wind force coefficient CC . The gust effect factor DG is influenced by design wind speed HU , turbulence intensity HI ,

turbulence scale HL , reference height H , building breadth B , building natural frequency Df , building critical damping ratio Dζ 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, 22.1=ρ (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 0U and return period conversion factor rWk

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 0U , wind directionality factor DK , wind speed profile factor E and return period conversion factor rWk . 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


100-year-recurrence basic wind speed 0U and 500-year-recurrence wind speed 500U 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 500U and 0U 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 0U (m/s) 500U (m/s) 50-year maximum value

coefficient ofvariation mean (m/s)

standard deviation (m/s)

Sapporo 30.5 34.5 30.2 3.2 0.11 Aomori 31.0 35.0 30.7 3.2 0.10 Sendai 30.5 34.5 30.2 3.2 0.11 Niigata 37.0 41.0 36.7 3.2 0.09 Tokyo 36.0 40.0 35.7 3.2 0.09

Nagoya 32.5 36.5 32.2 3.2 0.10 Osaka 34.5 38.5 34.2 3.2 0.09

Hiroshima 30.0 34.0 29.7 3.2 0.11 Kochi 39.0 43.0 38.7 3.2 0.08

Fukuoka 33.5 37.5 33.2 3.2 0.10 Kagoshima 42.0 46.0 41.7 3.2 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 HE 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


speed profile factor HE deviates 25% at 5=H m, 15% at 100=H m and 10% at 200=H m, and

the coefficients of variation can be estimated as half their values as follows; 0.13 at 5=H m 0.08 at 100=H m 0.05 at 200=H 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 H2.0 to H9.0 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 bL when the roof slope is 30° or less, but about 10-20% in parts UW and aL . Furthermore, they may exceed 30% in part LbR 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 peC , to calculate the roof wind load on structural frames

around the leading edge of the eave, for example, for 6/ ≥HB and 1/ >HD , 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 DG

The parameters that influence the gust effect factor DG of the horizontal wind load for structural

frames, excluding the height and the width of the building, are the natural frequency Df of the first translational mode in the along-wind direction, the critical damping ratio Dζ of the first translational mode in along-wind direction, the design wind speed HU , turbulence scale HL , turbulence intensity

HI 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


shape and so on. Here, the reference height 80=H m, the width 40=B m, the natural frequency for the first translational mode 5.0D =f Hz, the critical damping ratio for the first translational mode

2D =ζ %, the basic wind speed 390 =U m/s and the flat terrain subcategory III are assumed. The increase of the gust effect factor DGΔ 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 DGΔ when value of each parameter is

increased by 1% individually

parameter increase of gust effect factor DGΔ natural frequency Df −0.29%

critical damping ratio Dζ −0.16% design wind speed HU 0.34% turbulence intensity HI 0.55%

turbulence scale HL −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 HI

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 HL

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.


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: 2G

2C

2U

2ρW DDHD

4 VVVVV +++= (Appendix 6.6.2)

Wind load for components/cladding : 2C

2U

2ρW CHC

4 VVVV ++= (Appendix6.6.3)

where

DWV : coefficient of variation of horizontal wind load for structural frames DW

CWV : coefficient of variation of wind load for components/cladding CW

ρV : coefficient of variation of air density ρ

HUV : coefficient of variation of design wind speed HU

DCV : coefficient of variation of wind force coefficient DC

DGV : coefficient of variation of gust effect factor DG

CCV : coefficient of variation of peak wind force coefficient CC

When a building with reference height 80=H m, width 40=B m, natural frequency for first

translational mode 5.0D =f Hz, and critical damping ratio for first translational mode 2D =ζ % is

constructed in a region of flat terrain subcategory III in each city of appendix Table 6.6.1, the coefficient of variation

DWV can be estimated as around 0.3 to 0.33 for wind load on structural frames and the coefficient of variation

CWV can be estimated as around 0.32 to 0.35 for wind load on

components/claddings.

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CHAPTER 6 WIND LOADS Outline 6.1 General 6.1.1 Scope of ...

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