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

Transcription

1 Wind Loads in City Centres Demonstrated at the New Commerzbank Building in Frankfurt/Main Andreas Berneiser 1, Gert König 2 SUMMARY This paper shows the results obtained from full-scale measurements of the wind velocity and its resulting reactions at the new Commerzbank Building in Frankfurt/Main. The wind velocity was measured with propeller anemometers. The propeller anemometers were located on cranes, on the building itself and on top of a nearby high-rise building. In addition to these measurements we got data of the 10-minute wind velocity from measurements at the top of a building in a region of Frankfurt with only low buildings. This enables us to calculate a typical profile of mean wind velocity for such inner city regions. Furthermore the strains on 6 mega-columns were measured so that the resultant reactions to the wind load could be calculated and correlated with the measured wind velocity. The results of these measurements were compared with the results of a wind tunnel test to generalize the outcome for different conditions. Profound knowledge of the correlation between wind velocity and building reactions provides numerous opportunities to improve theoretical suppositions and existing standards. 1 Dipl.-Ing., Institut für Massivbau, TU Darmstadt 2 Prof. Dr.-Ing. Dr.-Ing. e.h., Institut für Massivbau und Baustofftechnologie, Universität Leipzig 231

2 LACER No. 2, INTRODUCTION The new European standard Eurocode 1 ([1]), which is coming soon, only describes the wind loads of buildings lower than 200 m. The relevant German standard 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 city regions. The profile of the wind velocity depends on the roughness of the surrounding 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 terrain based on the power law model of Davenport ([5] - [8]). As a result the calculated wind loads are much higher than the real loads. The new Eurocode 1 includes four terrain categories with different roughness parameters, and in addition there are special wind maps based on different mean wind velocities for different locations. The profile of the mean wind velocity is described with a log law model. To get more information about the wind velocity in inner city regions wind velocity was measured at different heights during the construction time of the new Commerzbank Building in Frankfurt/Main. These measurements gave us a considerable amount of information about the characteristics of the wind in such an inner city region. If the wind velocity is known it can be converted into wind loads which result in a moment at the base of the building. Because of the structure of the Commerzbank Building it was possible to measure the moment at the base of the whole building by using only 30 measuring instruments. These instruments measured the longitudinal strains at 1 st floor level in the six mega-columns, which are the main structural elements of the building. Using these strains we were able to calculate how the forces and the moments at the base of the building correlate with the wind because almost all the wind resistance is provided by the columns in combination with a steel framework in between. The city of Frankfurt was chosen for these measurements because of its unique arrangement of high-rise buildings not found in any other town in Germany (see Fig. 1). 232

3 Wind Loads in City Centres Demonstrated at the New Commerzbank Building in Frankfurt/Main Fig. 1: Skyline of Frankfurt/Main The description of the building, the measuring instrumentation and the first results were 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)=V ref (z / z ref ) α where: V(z) mean wind velocity at height z V ref mean wind velocity at height z ref z ref 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 233

4 LACER No. 2, 1997 In the German standard V ref is the ten-minutes mean velocity at the height z ref = 10 m. To compare the wind velocity of different terrain categories it is possible to calculate the wind velocity at the gradient height and above this height the mean wind velocity is constant. For open terrain z g is 280 m, for suburban areas it is 400 m and for city centres it is 520 m. The mean wind velocity at the gradientheight 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) = k T ln[ z / z 0 ] V ref where: V(z) mean wind velocity at height z V ref mean wind velocity at height z ref z height above ground k T, z o 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 are shown in Table 1. For lower heights the wind velocity is constant: V(z<z min ) = V(z min ) Terrain category k T z 0 [m] z min [m] I Rough open sea, etc II Farmland with boundary hedges, occasional small farm structures, houses or trees III Suburban or industrial areas and permanent forests IV Urban areas in which at least 15% of the surface is covered with buildings and their average height exceeds 15 m Table 1: Terrain categories and related parameters ε 234

5 2.3 Measured velocities Wind Loads in City Centres Demonstrated at the New Commerzbank Building in Frankfurt/Main The wind velocity was measured at two and three different heights simultaneously at the new Commerzbank Building and a nearby high-rise building. The wind velocity was measured in intervals of 2 s. On the basis of this data the ten-minute mean wind velocity was calculated. In addition to these measurements we obtained the mean wind velocity from a weather station located 2 km away from the 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 the log law and the power law model for the terrain categories suburban and city centres. 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 and without the values at the height of 212 m. Fig. 4 shows the measured ten-minutes mean wind velocities at the same heights as in figure 3, but the measured wind velocities are the highest ones of all the measurements carried out v(z) / v(261m) Eurocode, Kat. III Eurocode, Kat IV Davenport, α = 0.28 Davenport, α = 0.40 v(153m) = m/s v(212m) = m/s v(261m) = m/s 0.25 v(60m) = m/s β = Height z [m] Fig. 2: Comparison of the measured ten-min. mean velocity over a period of 2 hours with those calculated with the power law and the log law model. Date:

6 LACER No. 2, v(z) / v(261m) Eurocode, Kat. III Eurocode, Kat. IV Davenport, α = 0.28 Davenport, α = 0.40 v(60m) = m/s v(153m) = m/s v(261m) = m/s 0.25 β = Height z [m] Fig. 3: Comparison of the measured ten-min. mean velocity over a period of 3 hours with those calculated with the power law and the log law model. Date: v(z) / v(261m) Eurocode, Kat. III Eurocode, Kat. IV Davenport, α = 0.28 Davenport, α = 0.40 v(60m) = m/s v(153m) = m/s v(261m) = m/s 0.25 β = Height z [m] Fig. 4: Comparison of the measured ten-min. mean velocity over a period of 3 hours with those calculated with the power law and the log law model. Date: From these figures it can be seen that the measured wind velocity is always lower than the velocities calculated with the log law profile and the velocities calculated with the power law profile for suburban areas. It can also be seen that the velocities calculated on the basis of Eurocode 1 category III and IV are greater than those calculated on the basis of the power law model for the suburban and 236

7 Wind Loads in City Centres Demonstrated at the New Commerzbank Building in Frankfurt/Main urban areas. The profile of the log law model is very flat indicating that the velocities at the lower heights are too high. 3 TURBULENCE PROPERTY OF THE WIND 3.1 Turbulence intensity The turbulence intensity I v is the quotient of the standard deviation σ v and the mean velocity v. In Eurocode 1 the turbulence intensity depends on the roughness of the surrounding area and the height z above ground. It is defined as I v 1 = ln Davenport defines the turbulence intensity by using another roughness parameter K: I v = 2.45 z z 0 K z 10m The roughness parameter K depends on the roughness of the surrounding area and is for open terrain, for suburban areas and 0.05 for city centres. Fig. 5 shows the calculated turbulence intensities compared with some measured turbulence intensities. The turbulence intensities shown were measured during very high wind velocity, because at lower velocities the dispersion increases. It can be seen that the difference between Eurocode 1 and Davenport is very small. The measured values at the height of 261 m are nearly the same as the calculated ones, but those at the height of 153 m are much higher. One reason for this is the location of the measurement instrumentation approx. 6 m above the top of a nearby high-rise building, which results in the measurements being slightly affected by the flow around the building. α 237

8 LACER No. 2, Davenport Eurocode Meßwerte Turbulence intensity I v Height z [m] Fig. 5: Comparison of calculated and measured turbulence intensities 3.2 Spectral density The spectral density describes the distribution of the standard deviation of wind velocity. It shows the intensity of gusts in interdependence with the frequency of the gusts. In Eurocode 1 the product of the spectral density S(n) with the frequency n is defined as 6.8 x 2 n S(n) = I 5 / 3 v (z)² v(z) ; ( x) ε z min 300 Li (z) = where: z 300 ε,z min given in Table 1 z height above ground I v (z) turbulence intensity at height z v(z) mean wind velocity at height z n frequency ε 300m n Li (z) x = v(z) 238

9 Davenport provides another definition: 2 x n S(n) = 4.0 K v ; 2 10 ( 1+ x² ) 4 / 3 Wind Loads in City Centres Demonstrated at the New Commerzbank Building in Frankfurt/Main 1200 n x = where: K roughness parameter v 10 mean wind velocity at 10 m Fig. 6 shows the measured spectral density during the storm Lilly in October 1996 at 261 m and 153 m. It can be seen that the correlation between the measured and calculated values at the height of 261 m is very good. At the lower height the maximum density of the measured values lies at higher frequency than the calculated ones. The chosen values for K are given in the figure. These parameters were used to calculate the turbulence intensity on the basis of the definition given by Davenport. The turbulence intensity calculated in this way is used to calculate the spectral density for both definitions: Eurocode and Davenport. v 10 spectral density n S(n) [m²/s²] H = 261 m β = 230 v 10 = 4.7 m/s v 261 = 17.3 m/s K = Eurocode spectral density n S(n) [m²/s²] H = 153 m β = 230 v 10 = 3.3 m/s v 153 = 9.7 m/s K = Eurocode Davenport Frequency n [Hz] Davenport Frequency n [Hz] Fig. 6: Measured spectral densities on October 28 and 29, 1996 compared to those calculated with Eurocode and Davenport. 239

10 LACER No. 2, REACTION TO WIND 4.1 Wind tunnel test To get information about the reaction of the Commerzbank Building to wind, a wind tunnel test was carried out. In this test the pressure on the surface of the building was measured at 270 points for 12 different wind directions. Using these measurements the base moment was calculated. The profile of the wind simulated in the test was a power law profile with 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-columns coupled with steel framework. It was thus possible to measure the reaction to wind using only 30 instruments. These instruments measured the longitudinal strains at five points in each column. Using these measurements the reactions of the 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 base moment calculated on the basis of the wind tunnel test and derived from the fullscale 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 is very strong. This is normal for a building with triangular plan. The difference between the direction of the maximum and minimum moments is always 120. The values obtained from the full-scale measurements are all similar to or lower than the wind tunnel results. This means that the profile of the wind velocity has an higher exponent α than was predicted for the wind tunnel test. Only for the direction of 240 to 270 the wind tunnel results and the full-scale measurements have the same results. In this direction there are many high-rise buildings and most of them were modelled in the wind tunnel test. The profile of the wind velocity at the building site and in the wind tunnel test also has a different (higher) value for the parameter α for this direction. 240

11 Wind Loads in City Centres Demonstrated at the New Commerzbank Building in Frankfurt/Main m³ 6 [x 10 / E- W M ref Wind tunnel test Full-scale measurements Direction of the wind β Fig. 7: Base moments around East-West-Axis m³ 6 [x 10 / M ref N- S Wind tunnel test Full-scale measuments Direction of the wind β 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 using Eurocode 1 and Davenport. For Eurocode 1 only the category III and IV and for Davenport all categories were used. 241

12 LACER No. 2, 1997 Source Base moment [MNm] Full-scale measurements 686 Wind tunnel test 825 Davenport, α=0.16 (=German standard) 1585 Davenport, α = Davenport, α = 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 the resulting wind loads are much lower in inner-city regions than in open terrain. In the German standard the definitions by Davenport are used but restricted to the parameters for open terrain. The resulting wind loads are not realistic and much too high. The measurements prove that in city centres like Frankfurt/Main it is permissible 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 but some of the measured wind velocities are higher than predicted with this exponent. The real exponent thus lies between 0.28 and For practical use α=0.28 is suggested. Fig. 2, Fig. 3 and Fig. 4 show that the log law model of Eurocode 1 is very flat indicating that the velocities calculated for lower heights are too high. If the reference velocity is given at a lower height, the velocities at greater heights are too low. This is the reason why the log law model used in the Eurocode 1 is restricted to buildings lower than 200 m. For calculating the wind loads of a high-rise building the power law model of Davenport is suggested. The measurements prove that using parameters like the ones described by Davenport will lead to realistic results. 242

13 Wind Loads in City Centres Demonstrated at the New Commerzbank Building in Frankfurt/Main References [1] CEN Europäisches Komitee für Normung. Eurocode 1. Grundlagen der Tragwerksplanung und Einwirkungen auf Tragwerke. Teil 2.4: Windlasten, [2] Deutsches Institut für Normung. DIN 1055, Teil 4, Ausgabe August [3] Hessisches Ministerium des Innern. Ergänzungserlaß zu DIN 1055, Teil 4, Ausgabe August 1986, Betr. Windlasten bei hohen Hochhäusern im Raum Frankfurt am Main, [5] Davenport, Alan G.. The application if statistical concepts to the wind loading of structures. In: Proceedings of the Institution of Civil Engineers, 19, pages , 1961 [6] Davenport, Alan G.. Spectrum of horizontal gustiness near the ground in strong winds. In: Quarterly Journal of the Royal Meteorology Society, 87, pages , April 1961 [7] Davenport, Alan G.. Note on the distribution of the largest value of a random function with application to gust loading. In: Proceeding of the London Institution of Civil Engineers, 28, pages , 1964 [8] Davenport Alan G.. Gust loading factors. In: Proceedings of the American Society of Civil Engineers, 93, ST 3, pages 11-34, [9] Berneiser, Andreas. Full-scale measurements of wind velocity and reactions at the new Commerzbank building in Frankfurt/Main. In Darmstadt Concrete, 11, pages Institut für Massivbau, TU Darmstadt, [10] Berneiser, Andreas. Full-scale measurements of wind velocity at the new Commerzbank building in Frankfurt/Main. In Leipzig Annual Civil Engeneering Report, 1, pages Institut für Massivbau und Baustofftechnologoe, Universität Leipzig, [11] Winz, Christine and Sonntag, Ralf. Windkanalversuche zum neuen Commerzbank-Hochhaus in Frankfurt/Main. Unpublished, Institut für Massivbau, TU Darmstadt, [12] Sonntag, Ralf.Auswertung von Meßdaten aus Windkanal- und Feldmessungen am neuen Commerzbank-Hochhaus in Frankfurt am Main. Unpublished, Institut für Massivbau, TU Darmstadt,

14 LACER No. 2,