Direction Dependent Approach to Consider the Wind

Direction Dependent Approach to Consider the Wind-Structure-Interaction in Standards

Mirko Friehe, Jürgen Kuck, Claudia Ziller

Feldmann + Weynand, Aachen, Germany, www.fw-ing.de

1 INTRODUCTION

Meteorological studies are showing that the wind velocities are correlated with the wind direc-tions. The probability that the wind velocity will exceed a certain limit is related to the wind sec-tors and dependent on the considered site. This is demonstrated in the example of the wind ro-sette at the meteorological station Frankfurt Airport in Germany (see Figure 1).

The basic wind values that are used to determine the characteristic wind loads on buildings are usually chosen without consideration of the related wind direction. In most standards only one wind velocity is given for all wind directions.

On the other hand the individual struc-

ture response depends on the onflow direction of the wind due to the influence of the pressure coefficients which are dependent on the angle of attack. That means two different influences of directionality have to be taken into account and their interaction has to be considered.

This paper shows that a direction factor

can be used to adjust the basic wind velocity with the same risk of being exceeded in any wind direction. Based on examples of a terrace near Frankfurt and solar collectors on flat roofs it is demonstrated that taking into ac-count the direction dependency of wind and/or pressure coefficient leads to significant wind load reductions.

Figure 1. Wind rosette, meteorological station Frankfurt Airport In some European standards it is in principle allowed to calculate with direction dependent

wind data which is shown in the following chapter. Some selected procedures and their boundary conditions are introduced.

The wind actions calculated using EN 1991-1-4 are characteristic values, which are deter-

mined either from the basic values of wind velocity or from the velocity pressure. These values are characteristic values having annual probabilities of exceedance of 0.02, which is equivalent to a mean return period of 50 years.

2 EXEMPLARY CALCULATION PROCEDURES IN STANDARDS 2.1 Eurocode EN 1991-1-4 In the Eurocode EN 1991-1-4 the basic wind velocity is calculated as follows:

seasondirbb ccvv ⋅⋅= 0, (1)

with: vb basic wind velocity, defined as a function of wind direction and time of year at 10 m

above ground of terrain category II vb,0 characteristic 10 minutes mean wind velocity, irrespective of wind direction and time of

year, at 10 m above ground level in terrain category II cdir directional factor cseason seasonal factor The directional factor, cdir, for various wind directions may be found in National Annexes. The recommended value is 1.0.

2.2 NBN B03-002-1 In the standard of the Belgisch Insituut voor Normalisitie NBN B03-002-1 the characteristic wind velocity vk [m/s] is given by the following equation (2):

btSk vkkkv ⋅⋅⋅= θ (2)

with: vb basic wind velocity kS factor for the terrain

and surrounding area kt seasonal reduction

factor kθ reduction factor for

the wind direction

Figure 2. Reduction factor kθ for wind direction effects, NBN B03-002-1 The reduction factor kθ (see Figure 2) can be used in situations where special structural responses are correlated with defined wind directions, eg. wind pressure on facades, etc. For global wind ef-fects kθ should be taken as 1.0.

2.3 British Standard BS 6399-2:1997 In the British Standard, Loading for Buildings, Part 2: Code of practice for wind loads, BS 6399-2:1997 the site wind speed Vs for any particular direction should be calculated with (3). The val-ues for the direction factor Sd of the British Standard BS are listed in table 1:

psdabS SSSSVV ⋅⋅⋅⋅= (3)

with: Table 1. Direction factor Sd, BS Vb the basic wind speed dependent on the location,

obtained from a figure in the BS with geograph-ical variations of the basic wind speed

Sa altitude factor, used to adjust the basic wind speed for the altitude of the site above sea level

Sd direction factor Ss seasonal factor for buildings which are ex-

pected to be exposed to the wind for subannual periods

Sp probability factor, used to change the risk of the basic wind speed being exceeded from the stand-ard values

The direction factor Sd can be used to adjust the basic wind speed to produce wind speeds with the same risk of being exceeded in any wind direction. Values for Sd in the BS are given for wind directions in 30° intervals. If the orientation of the building is unknown or ignored, the factor should be taken as 1.0. In addition the British Standard gives external pressure coefficients as a function of the wind direction in Section 3.3 as you can see in the following example (figure 2).

Figure 2. Example of direction dependent pressure coefficients, BS 6399-2:1997, Section 3.3 Directional Pressure Coefficients

2.4 ASCE 7-05 Table 2. Directionality factor Kd from the ASCE

The ASCE uses a directionality factor that takes into account two different effects: on the one hand the reduced probability of maximum winds com-ing from any given direction and on the other hand the reduced probability of the maximum pressure coefficient occurring for any given wind direc-tion. Kd is dependent on the structure type in order to account for the indi-vidual response of different structure shapes.

If the wind load resistance is ex-

Direction ϕ Direction factor Sd

0° North 0.78 30° 0.73 60° 0.73 90° East 0.74 120° 0.73 150° 0.80 180° South 0.85 210° 0.93 240° 1.00 270° West 0.99 300° 0.91 330° 0.82 360° North 0.78

Structure Type

Directionality factor Kd

Buildings Main Wind Force Resisting System 0.85 Components, Claddings 0.85Arched Roofs 0.85Chimneys, Tanks and Similar Structures Square 0.90 Hexagonal 0.95 Round 0.95Solid Signs 0.85Open Signs, Lattice Framework 0.85Trussed Towers Triangular, Square, Rectangular 0.85 All other cross section 0.95

05

101520

‐1,50 0,50 2,50

v [m

/s]

Reduzierte Varianz (Gumbel)

Winkel 0 ‐ 30

05101520

‐1,50 0,50 2,50

v [m

/s]


Winkel 30 ‐ 60

0

5

10

15

‐1,50 0,50 2,50

v [m

/s]


Winkel 60 ‐ 90

0

5

10

15

‐1,50 0,50 2,50

v [m

/s]


Winkel 90 ‐ 120

0

5

10

15

‐1,50 0,50 2,50

v [m

/s]


Winkel 120 ‐ 150

05

101520

‐1,50 0,50 2,50

v [m

/s]


Winkel 150 ‐ 180

0

10

20

30

‐1,50 0,50 2,50

v [m

/s]


Winkel 18 0 ‐ 210

010203040

‐1,50 0,50 2,50

v [m

/s]


Winkel 210 ‐ 240

0

10

20

30

‐1,50 0,50 2,50

v [m

/s]


Winkel 240‐ 270

0

10

20

30

‐1,50 0,50 2,50

v [m

/s]


Winkel 2700 ‐ 300

0

10

20

30

‐1,50 0,50 2,50

v [m

/s]


Winkel 300 ‐ 330

0

5

10

15

‐1,50 0,50 2,50

v [m

/s]


Winkel 330 ‐ 360

actly the same in all directions, a value of 1.0 should be taken. This factor is calibrated with combinations of loads and can only be used in conjunction

with given load combinations; whichever produces the most unfavorable effect in the construc-tion. Table 2 gives the tabulated values of Kd for different structure types.

3 DIRECTION DEPENDENT WIND LOADS FOR A TERRACE NEAR FRANKFURT, GERMANY 3.1 Wind tunnel investigation

In order to show the effects of a direction dependent analysis of wind loads a wind tunnel test of a structure is described in this chapter.

The external net-pressure distribu-tion on the roof of a terrace near Frank-furt, Germany, was investigated. Figure 3 shows a picture of the model in the boundary layer wind tunnel at the RWTH Aachen, Germany.

Figure 3. Wind tunnel model of the terrace

3.2 Results The basic wind data are supplied by the meteorological station at Frankfurt Airport (see Figure 1) for the period of 1979-2009.

Figure 4. Extreme wind value distribution, Frankfurt, Germany

Figure 4 shows the evaluation of the wind data vm(10 m) in [m/s] for Frankfurt in its 12 sec-tions using the extreme value distribution using the Gumble method. These values result in char-acteristic wind velocities for each section with a mean return period of 50 years.

Based upon these measured velocities and the reference wind speed of vref = 22.5 m/s for

Frankfurt from the DIN 1055 it is possible to determine a direction factor kdir (see table 3).

As a result of the wind tunnel tests a representative value of a pressure coefficient depend-ent on the wind direction cp,α is listed in table 3 as well, followed by examples of different ways to calculate the wind pressure WG (case 1 and 2) in [N/m²] for the terrace.

Case 1 eq. (4) is determined using direction dependent wind velocities and pressure coeffi-cients and case 2 eq (5) uses values given in the standards: vref and a comparable pressure coeffi-cient from Eurocode EC1 of cp,EC = -1.1.

The proportion between the gust and the mean wind pressure qG/qm has been chosen accord-

ing to the topography category II of DIN 1055-4.

Table 3. Wind data, direction factor kdir, pressure coefficients and wind pressures, roof of a terrace near Frankfurt Wind Direction

0-30 30-60 60-90 90-120 120-150 150-180 180-210 210-240 240-270 270-300 300-330 330-360N NNO ONO O OSO SSO S SSW WSW W WNW NNW

vm(10m) 13,68 11,75 10,14 9,03 10,22 12,85 20,94 25,17 20,4 18,63 15,83 11,44 kdir 0,61 0,52 0,45 0,40 0,45 0,57 0,93 1,12 0,91 0,83 0,70 0,51 cp,α -0,22 -0,50 -0,53 -0,54 -0,53 -0,27 -0,15 -0,12 -0,24 -0,31 -0,35 -0,17 WG 1 -53,4 -90,3 -71,0 -57,9 -72,3 -59,1 -84,4 -103,1 -129,4 -142,5 -115,2 -29,5 WG 2 -730,9 with:

WG 1 [N/m²] m

GmdirpG q

qvkcW ⋅⋅⋅= 2, 2

1 ρα dependent on kdir and cp,α (4)

WG 2 [N/m²] m

GrefECpG q

qvcW ⋅⋅= 2, 2

2 ρ dependent on vref and cp,EC (5)

Corresponding to the half of the wind pressure, a limitation of the direction factor to kdir = 0.71 is recommended, even if the exact calculated value is less.

4 DIRECTION DEPENDENT WIND LOADS FOR SOLAR COLLECTORS ON FLAT ROOFS 4.1 Model and wind tunnel The use of solar panel technology has recently increased in both domestic and industrial applica-tions. For the industrial use new low-ballast mounting systems for flat roofs were developed. Those systems can be easily laid on the roof, without damaging and penetration of the roof. They are fixed using ballast – the volume of ballast is amongst others dependent on the wind loads of the system.

In the current situation the wind loads of those solar collector systems that have to be ap-plied to determine the necessary ballast volume are not regulated in the standards. Using the val-ues in e.g. the DIN 1055 for flat roofs lead to uneconomical results and often means the death of a project, because the additional ballast can often not be carried by existing buildings.

Figure 5. Wind tunnel model of the solar collectors Therefore a wind tunnel investigation was performed with a model of the roof and the solar

systems in a scale of 1:100. Figure 5 and 6 are showing pictures of the used models.

4.2 Wind Loads Figure 6 shows the normalized wind pressure WSolar of the solar collectors on the flat roof of the building. In this figure the results are given for all wind directions, i.e. the maximum measured pressure coefficients cp considering all onflow directions is multiplied by the same dynamic wind pressure for all wind directions. Hence, the evaluation of the wind loads is performed in the con-servative and classical way; the influences of directionality have not been taken into account.

Figure 6. Normalized wind pressure for all wind directions In order to consider the interaction of both effects that are dependent on the wind direction

the wind pressure can be determined as shown in figure 7. The structural response i.e. the meas-

ured maximum pressure coefficients cp, are evaluated in relation to the directionality of the wind. As recommended in the literature and due to reliability the reduction of the direction dependent wind velocity is limited to 71% in this evaluation.

For the example of a building in Hannover, Germany, it is possible to calculate the realistic

wind pressure which result in reliable values for the ballast that is used to fix the mounting sys-tem on flat roofs.

Also the wind data for Hannover is evaluated using the extreme value distribution of the Gumble method. The values are representing characteristic values having annual probabilities of exceedance of 0.02 (see figure 4).

Figure 7. Normalized wind pressure for the direction dependent evaluation In the current situation the wind loads of those solar collector systems that have to be ap-

plied to determine the necessary ballast volume are not regulated in the standards. Using the val-ues in e.g. the DIN 1055-4 for flat roofs will lead to uneconomical results and often means the death of a project.

5 CONCLUSION

The wind pressures for the terrace in table 3 and the results for the solar collectors on a flat roof in figure 7 are showing that the consideration of direction factor for the wind and the direction dependent pressure coefficients leads to a significant load reduction due to the fact that the wind velocities are not correlated with the maximum structural response. Both, the meteorological, aerodynamical and the structural response have to be considered in order to apply realistic wind effects without reducing the reliability.

It is quite clear that the maximum values of the pressure coefficients are strongly dependent

on the individual shape of the building and thus show different dependencies on the onflow angle of the wind. A general solution does not exist for all kinds of buildings. But for some standard-ized shapes tables with direction dependent cp-values should be helpful for an economic design. This procedure is already performed in the British Standard.

As proposed in the Belgian Standard NBN, even in situations where no wind tunnel tests were performed and no direction dependent pressure coefficients for the global structure are available it should be considered that special structural responses are correlated with defined wind directions by using a direction dependent wind factor.

6 REFERENCES

Eurocode EN 1991-1-4:Eurocode 1. Actions on structures – Part 1-4: General actions, Wind actions; July 2005 NBN B 03-002-1:Windbelasting op Bouwwerken, Algemeen, Winddruk op een Wand en gezamenlijke windeffek-

ten op bouwwerken, Belgisch Instituut voor Normalisatie, Brussel, 1988 British Standard BS 6399-2:1997: Loading for buildings, Part 2: Code of practice for wind loads. ASCE Standard 7-07: Minimum Design Loads for Buildings and Other Structures. ASCE/SEI 7-05 DIN 1055-4: Action on structures Part 4: Wind loads, March 2005 Niemann, H.-J.; Hölscher, N. 2004. Erfassung des Windrichtungseinflusses auf die Windlasteffekte an Tragwerken.

Stahlbau (73) Heft 4, 249-253. Kasperski, M. 2007. Design wind loads for a low-rise Building taking into account directional effects. Journal of

Wind Engineering and Industrial Aerodynamics 95, 1125 - 1144. Feldmann+Weynand. 2009 - 2011. Wind Tunnel Investigations. Internal Reports.

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Direction Dependent Approach to Consider the Wind