231

Wind Loads in City Centres Demonstrated atthe New Commerzbank Building in

Frankfurt/Main

Andreas Berneiser1, Gert König2

SUMMARY

This paper shows the results obtained from full-scale measurements of the windvelocity and its resulting reactions at the new Commerzbank Building inFrankfurt/Main. The wind velocity was measured with propeller anemometers.The propeller anemometers were located on cranes, on the building itself and ontop of a nearby high-rise building. In addition to these measurements we got dataof the 10-minute wind velocity from measurements at the top of a building in aregion of Frankfurt with only low buildings. This enables us to calculate a typicalprofile of mean wind velocity for such inner city regions. Furthermore the strainson 6 mega-columns were measured so that the resultant reactions to the windload could be calculated and correlated with the measured wind velocity. Theresults of these measurements were compared with the results of a wind tunneltest to generalize the outcome for different conditions. Profound knowledge of thecorrelation between wind velocity and building reactions provides numerousopportunities to improve theoretical suppositions and existing standards.

1 Dipl.-Ing., Institut für Massivbau, TU Darmstadt2 Prof. Dr.-Ing. Dr.-Ing. e.h., Institut für Massivbau und Baustofftechnologie, Universität Leipzig

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1 INTRODUCTION

The new European standard Eurocode 1 ([1]), which is coming soon, onlydescribes the wind loads of buildings lower than 200 m. The relevant Germanstandard is not useful to calculate the wind loads of tall buildings either.

We have only little information about the profile of the wind velocity in inner cityregions. The profile of the wind velocity depends on the roughness of thesurrounding area, in urban areas being very high. In the German standard ([2] and[3]) this problem was evaded by using the characteristics of wind over free terrainbased on the power law model of Davenport ([5] - [8]). As a result the calculatedwind loads are much higher than the real loads.

The new Eurocode 1 includes four terrain categories with different roughnessparameters, and in addition there are special wind maps based on different meanwind velocities for different locations. The profile of the mean wind velocity isdescribed with a log law model.

To get more information about the wind velocity in inner city regions windvelocity was measured at different heights during the construction time of the newCommerzbank Building in Frankfurt/Main. These measurements gave us aconsiderable amount of information about the characteristics of the wind in suchan inner city region.

If the wind velocity is known it can be converted into wind loads which result in amoment at the base of the building. Because of the structure of the CommerzbankBuilding it was possible to measure the moment at the base of the whole buildingby using only 30 measuring instruments. These instruments measured thelongitudinal strains at 1st floor level in the six mega-columns, which are the mainstructural elements of the building. Using these strains we were able to calculatehow the forces and the moments at the base of the building correlate with thewind because almost all the wind resistance is provided by the columns incombination with a steel framework in between.

The city of Frankfurt was chosen for these measurements because of its uniquearrangement of high-rise buildings not found in any other town in Germany (seeFig. 1).

Wind Loads in City Centres Demonstrated at theNew Commerzbank Building in Frankfurt/Main

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Fig. 1: Skyline of Frankfurt/Main

The description of the building, the measuring instrumentation and the first resultswere described in [9] and [10]. In this paper the final results are presented.

2 PROFILE OF THE MEAN WIND VELOCITY

2.1 Power law model by Davenport

Davenport’s ([4]) power law model is represented by the following formula:

V(z)=Vref (z / zref )α

where:

V(z) mean wind velocity at height z

Vref mean wind velocity at height zref

zref reference height

z height

α roughness parameter

α = 0.16: open terrain

α = 0.28: suburban areas

α = 0.40: city centres with high rise buildings

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In the German standard Vref is the ten-minutes mean velocity at the heightzref = 10 m.

To compare the wind velocity of different terrain categories it is possible tocalculate the wind velocity at the gradient height and above this height the meanwind velocity is constant. For open terrain zg is 280 m, for suburban areas it is400 m and for city centres it is 520 m. The mean wind velocity at the gradient-height is independent of the roughness of the area.

2.2 Log law model used in Eurocode 1

The log-law model is based on a logarithmic profile and is defined as:

V(z) = kT ln[ z / z0 ] Vref

where:

V(z) mean wind velocity at height z

Vref mean wind velocity at height zref

z height above ground

kT, zo roughness parameters

In Eurocode 1 the roughness of the surroundings is classified to four categories.The definition of these categories and the values of the roughness parameters areshown in Table 1. For lower heights the wind velocity is constant:

V(z<zmin) = V(zmin)

Terrain category kT z0

[m]zmin

[m]ε

I Rough open sea, etc. 0.17 0.01 2 0.13

II Farmland with boundary hedges, occasionalsmall farm structures, houses or trees

0.19 0.05 4 0.26

III Suburban or industrial areas and permanentforests

0.22 0.3 8 0.37

IV Urban areas in which at least 15% of the surfaceis covered with buildings and their averageheight exceeds 15 m

0.24 1.0 16 0.46

Table 1: Terrain categories and related parameters

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2.3 Measured velocities

The wind velocity was measured at two and three different heights simultaneouslyat the new Commerzbank Building and a nearby high-rise building. The windvelocity was measured in intervals of 2 s. On the basis of this data the ten-minutemean wind velocity was calculated. In addition to these measurements weobtained the mean wind velocity from a weather station located 2 km away fromthe Commerzbank Building in an area with only low buildings.

Fig 2 shows the measured ten-minute mean wind velocities at the heights of 60 m,153 m, 212 m and 261 m. The measurements are compared with the results of thelog law and the power law model for the terrain categories ”suburban” and ”citycentres”. These velocities are related to the velocity at the height of 261 m.

Fig. 3 shows the measured ten-minutes mean velocities at a different time andwithout the values at the height of 212 m.

Fig. 4 shows the measured ten-minutes mean wind velocities at the same heightsas in figure 3, but the measured wind velocities are the highest ones of all themeasurements carried out.

0.00

0.25

0.50

0.75

1.00

1.25

0 50 100 150 200 250 300

Height z [m]

v(z)

/ v(

261m

)

v(261m) = 9.5-12.4 m/s

v(212m) = 9.2-11.3 m/s

v(153m) = 7.3-7.9 m/s

v(60m) = 2.4-3.3 m/s

β = 100° - 125°

Eurocode, Kat. IIIEurocode, Kat IV

Davenport, α = 0.28Davenport, α = 0.40

Fig. 2: Comparison of the measured ten-min. mean velocity over a period of 2 hours with thosecalculated with the power law and the log law model. Date: 16.04.1996.

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0.00

0.25

0.50

0.75

1.00

1.25

0 50 100 150 200 250 300

Height z [m]

v(z)

/ v(

261m

)

v(261m) = 7.3-10.9 m/s

v(153m) = 4.1-7.6 m/s v(60m) = 4.2-4.8 m/s

β = 205° - 230°

Eurocode, Kat. IIIEurocode, Kat. IV

Davenport, α = 0.28Davenport, α = 0.40

Fig. 3: Comparison of the measured ten-min. mean velocity over a period of 3 hours with thosecalculated with the power law and the log law model. Date: 08.06.1996.

0.00

0.25

0.50

0.75

1.00

1.25

0 50 100 150 200 250 300

Height z [m]

v(z)

/ v(

261m

)

v(261m) = 19.6-26.7 m/s

v(153m) = 10.7-15.6 m/s v(60m) = 10.7-15.0 m/s

β = 225° - 235°

Eurocode, Kat. IIIEurocode, Kat. IV

Davenport, α = 0.28Davenport, α = 0.40

Fig. 4: Comparison of the measured ten-min. mean velocity over a period of 3 hours with thosecalculated with the power law and the log law model. Date: 08.06.1996.

From these figures it can be seen that the measured wind velocity is always lowerthan the velocities calculated with the log law profile and the velocities calculatedwith the power law profile for suburban areas. It can also be seen that thevelocities calculated on the basis of Eurocode 1 category III and IV are greaterthan those calculated on the basis of the power law model for the suburban and

Wind Loads in City Centres Demonstrated at theNew Commerzbank Building in Frankfurt/Main

237

urban areas. The profile of the log law model is very flat indicating that thevelocities at the lower heights are too high.

3 TURBULENCE PROPERTY OF THE WIND

3.1 Turbulence intensity

The turbulence intensity Iv is the quotient of the standard deviation σv and themean velocity v. In Eurocode 1 the turbulence intensity depends on the roughnessof the surrounding area and the height z above ground. It is defined as

=

0

v

z

zln

1I

Davenport defines the turbulence intensity by using another roughness parameterK:

α−

⋅⋅=

m10

zK45.2Iv

The roughness parameter K depends on the roughness of the surrounding area andis 0.005 for open terrain, 0.015 for suburban areas and 0.05 for city centres.

Fig. 5 shows the calculated turbulence intensities compared with some measuredturbulence intensities. The turbulence intensities shown were measured duringvery high wind velocity, because at lower velocities the dispersion increases.

It can be seen that the difference between Eurocode 1 and Davenport is verysmall. The measured values at the height of 261 m are nearly the same as thecalculated ones, but those at the height of 153 m are much higher. One reason forthis is the location of the measurement instrumentation approx. 6 m above the topof a nearby high-rise building, which results in the measurements being slightlyaffected by the flow around the building.

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 50 100 150 200 250 300

Height z [m]

Tu

rbu

len

ce

inte

ns

ity

I vDavenport

Eurocode

Meßwerte

Fig. 5: Comparison of calculated and measured turbulence intensities

3.2 Spectral density

The spectral density describes the distribution of the standard deviation of windvelocity. It shows the intensity of gusts in interdependence with the frequency ofthe gusts.

In Eurocode 1 the product of the spectral density S(n) with the frequency n isdefined as

2v3/5

)z(v)²z(I)x2.101(

x8.6)n(Sn ⋅⋅

⋅+⋅=⋅ ;

)z(v

)z(Lnx i⋅

=

m300300

z300)z(L

300

z300 i

min ≤

⋅=≤

⋅

εε

where:

ε,zmin given in Table 1z height above groundIv(z) turbulence intensity at height zv(z) mean wind velocity at height zn frequency

Wind Loads in City Centres Demonstrated at theNew Commerzbank Building in Frankfurt/Main

239

Davenport provides another definition:

( ) 3/4

2210

²x1

xvK0.4)n(Sn

+⋅⋅⋅=⋅ ;

10v

n1200x

⋅=

where:

K roughness parameter

v10 mean wind velocity at 10 m

Fig. 6 shows the measured spectral density during the storm ”Lilly” in October1996 at 261 m and 153 m. It can be seen that the correlation between themeasured and calculated values at the height of 261 m is very good. At the lowerheight the maximum density of the measured values lies at higher frequency thanthe calculated ones. The chosen values for K are given in the figure. Theseparameters were used to calculate the turbulence intensity on the basis of thedefinition given by Davenport. The turbulence intensity calculated in this way isused to calculate the spectral density for both definitions: Eurocode andDavenport.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.0001 0.001 0.01 0.1 1

Frequency n [Hz]

spec

tral

den

sity

n·

S(n

) [m

²/s²

]

H = 261 mβ = 230°

v10 = 4.7 m/sv261 = 17.3 m/s

K = 0.008

Davenport

Eurocode

0

0.2

0.4

0.6

0.8

1

1.2

0.0001 0.001 0.01 0.1 1

Frequency n [Hz]

spec

tral

den

sity

n·

S(n

) [m

²/s²

]

H = 153 mβ = 230°

v 10 = 3.3 m/sv153 = 9.7 m/s

K = 0.045

Eurocode

Davenport

Fig. 6: Measured spectral densities on October 28 and 29, 1996 compared to those calculatedwith Eurocode and Davenport.

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4 REACTION TO WIND

4.1 Wind tunnel test

To get information about the reaction of the Commerzbank Building to wind, awind tunnel test was carried out.

In this test the pressure on the surface of the building was measured at 270 pointsfor 12 different wind directions. Using these measurements the base moment wascalculated. The profile of the wind simulated in the test was a power law profilewith an exponent α=0.25.

A detailed description of the wind tunnel test is given in [11] and [12].

4.2 Full-scale measurements

The total resistance of the building against wind is provided by six mega-columnscoupled with steel framework. It was thus possible to measure the reaction towind using only 30 instruments. These instruments measured the longitudinalstrains at five points in each column. Using these measurements the reactions ofthe mega-columns and then the base moments from wind load are calculated.

Fig. 7 and Fig. 8 show the east-west and the north-south components of the basemoment calculated on the basis of the wind tunnel test and derived from the full-scale measurements. The moments are related to the wind pressure at 261 m.

It can be seen that the dependence of the base moments on the wind direction isvery strong. This is normal for a building with triangular plan. The differencebetween the direction of the maximum and minimum moments is always 120°.

The values obtained from the full-scale measurements are all similar to or lowerthan the wind tunnel results. This means that the profile of the wind velocity hasan higher exponent α than was predicted for the wind tunnel test. Only for thedirection of 240° to 270° the wind tunnel results and the full-scale measurementshave the same results. In this direction there are many high-rise buildings andmost of them were modelled in the wind tunnel test. The profile of the windvelocity at the building site and in the wind tunnel test also has a different(higher) value for the parameter α for this direction.

Wind Loads in City Centres Demonstrated at theNew Commerzbank Building in Frankfurt/Main

241

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0° 90° 180° 270° 360°

Direction of the wind β

ME-W

/ref

[x10

6

m³

Wind tunnel test

Full-scale measurements

Fig. 7: Base moments around East-West-Axis

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0° 90° 180° 270° 360°

Direction of the wind β

MN-S

/ref

[x10

6

m³

Wind tunnel test

Full-scale measuments

Fig. 8: Base moments around North-South-Axis

4.3 Comparison between calculated and measured reactions

In addition to the measurements the reaction to wind was calculated usingEurocode 1 and Davenport. For Eurocode 1 only the category III and IV and forDavenport all categories were used.

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Source Base moment[MNm]

Full-scale measurements 686

Wind tunnel test 825

Davenport, α=0.16 (=German standard) 1585

Davenport, α = 0.28 1120

Davenport, α = 0.40 727

Eurocode 1, Cat. III 1239

Eurocode 1, Cat. IV 956

Table 2: Calculated and measured base moments

5 CONCLUSIONS

All results of the measurements show that the profile of the wind velocity and theresulting wind loads are much lower in inner-city regions than in open terrain. Inthe German standard the definitions by Davenport are used but restricted to theparameters for open terrain. The resulting wind loads are not realistic and muchtoo high. The measurements prove that in city centres like Frankfurt/Main it ispermissible to use an exponent of α=0.28 without lowering the safety standards.Most measured data would correlate to calculations with an exponent of 0.40 butsome of the measured wind velocities are higher than predicted with thisexponent. The real exponent thus lies between 0.28 and 0.40. For practical useα=0.28 is suggested.

Fig. 2, Fig. 3 and Fig. 4 show that the log law model of Eurocode 1 is very flatindicating that the velocities calculated for lower heights are too high. If thereference velocity is given at a lower height, the velocities at greater heights aretoo low. This is the reason why the log law model used in the Eurocode 1 isrestricted to buildings lower than 200 m.

For calculating the wind loads of a high-rise building the power law model ofDavenport is suggested. The measurements prove that using parameters like theones described by Davenport will lead to realistic results.

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References

[1] CEN Europäisches Komitee für Normung. Eurocode 1. Grundlagen derTragwerksplanung und Einwirkungen auf Tragwerke. Teil 2.4:Windlasten, 1994.

[2] Deutsches Institut für Normung. DIN 1055, Teil 4, Ausgabe August 1986.

[3] Hessisches Ministerium des Innern. Ergänzungserlaß zu DIN 1055, Teil 4,Ausgabe August 1986, Betr. Windlasten bei hohen Hochhäusern im RaumFrankfurt am Main, 1987.

[5] Davenport, Alan G.. The application if statistical concepts to the windloading of structures. In: Proceedings of the Institution of Civil Engineers,19, pages 449-473, 1961

[6] Davenport, Alan G.. Spectrum of horizontal gustiness near the ground instrong winds. In: Quarterly Journal of the Royal Meteorology Society, 87,pages 194-221, April 1961

[7] Davenport, Alan G.. Note on the distribution of the largest value of arandom function with application to gust loading. In: Proceeding of theLondon Institution of Civil Engineers, 28, pages 187-196, 1964

[8] Davenport Alan G.. Gust loading factors. In: Proceedings of the AmericanSociety of Civil Engineers, 93, ST 3, pages 11-34, 1967.

[9] Berneiser, Andreas. Full-scale measurements of wind velocity andreactions at the new Commerzbank building in Frankfurt/Main. InDarmstadt Concrete, 11, pages 209-219. Institut für Massivbau, TUDarmstadt, 1996.

[10] Berneiser, Andreas. Full-scale measurements of wind velocity at the newCommerzbank building in Frankfurt/Main. In Leipzig Annual CivilEngeneering Report, 1, pages 303-318. Institut für Massivbau undBaustofftechnologoe, Universität Leipzig, 1996.

[11] Winz, Christine and Sonntag, Ralf. Windkanalversuche zum neuenCommerzbank-Hochhaus in Frankfurt/Main. Unpublished, Institut fürMassivbau, TU Darmstadt, 1997.

[12] Sonntag, Ralf.Auswertung von Meßdaten aus Windkanal- undFeldmessungen am neuen Commerzbank-Hochhaus in Frankfurt am Main.Unpublished, Institut für Massivbau, TU Darmstadt, 1997.

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