WIND ISSUES IN THE DESIGN OF TALL BUILDINGS

Transcription

1 WIND ISSUES IN THE DESIGN OF TALL BUILDINGS Peter A. Irwin RWDI Los Angeles Tall Building Structural Design Council May 7, 010

2 Wind Issues for Structural Design Structural integrity under ultimate loads Deflections under service loads Building motions and occupant comfort Uncertainties in building structural properties (stiffness, damping) Uncertainties in wind loading Uncertainties in wind climate Codes and standards Computational Fluid Dynamics

3 Relationship between importance of wind and height Importance of wind loads Building height

4 Vortex shedding Shedding frequency N is given by N = S U b S = Strouhal number U = wind speed b = building width Directions of fluctuating force wind

5 Peak response due to vortex excitation Magnitude of peak response 1 density damping

6 Vortex excitation on a tapered spire Mode 1

7 Vortex excitation on a tapered spire Mode

8 Shape strategies to reduce excitation Softened corners Tapering and setbacks Varying cross-section shape Spoilers Porosity or openings

9 Taper effect - Petronas towers

10 Taipei 101 corner softening Original Modified 5% REDUCTION IN BASE MOMENT

11 Shape effect, Taipei 101 wind tunnel tests

12 Burj Khalifa 88 m Set backs, changing cross-section, orientation Completed Building Early 1:500 scale wind tunnel tests

13 Shanghai Center 63 m Twisting and tapering

14 151 storey tower in Korea Creation of bleed slots at edges to suppress vortex shedding Full scale rendering 1:500 wind tunnel model

15 Use of corner slots to bleed air through corners on a tall building Plan view without slots Plan view with slots Crosswind motion Base moments reduced by 60% Wind Wind

16 With vortex excitation 10 yr 50 yr 700 yr Without vortex excitation (a) (b) With vortex excitation 50 yr 700 yr Without vortex excitation (c) (d)

17 Reliability considerations for flexible buildings where where Expression for load factor λ w λ W = 1 K w e α β V w Vw β = K w = = α = Coefficient of variation of wind load Reliability index Bias factor Combination factor

18 First order, second moment reliability analysis for rigid buildings Code analysis method V w = ( Vqi + Van ) λ W = 1/ = ( ) 1/ 1 α β ( ) K w e V w = e = 0.36 = 1.56 Wind tunnel method V w = ( ) 1/ 1 ) = 0. λ W = 1.0 e ( = 1.54 Both the coefficient of variation and bias factor are smaller in the wind tunnel method. Load factor ends up at about the same.

19 Reliability of flexible buildings with monotonic response Wind load varies as power law Rigid building V = + w V = + w Flexible building W U n 1/ ( Vqi Van ) 1/ ( Vqi + Van Vdyn ) V dyn n damp V ς + ( n ) V f + ( n ) VV Damping term Frequency term Velocity sensitivity term

20 V w V w Required load factors for flexible buildings with monotonic response Rigid building 1/ ( V + V ) = = qi an Typical flexible building = ( Vqi + Van + Vdyn ) λ W 1/ λ W ( (0.75 = e = = (0. Highly flexible building e (0.75 ) + 1/ ) ) = 0. = ) = / = 0.49 V w = ( Vqi + Van + Vdyn ) 1/ = ( ) 1/ = 0.31 λ W = e ( ) = 1.84 Note:- Wind tunnel method is assumed in all cases.

21 Wind loads determined directly at ultimate return period by wind tunnel method Building Required type n n damp Load Factor Actual Load Factor Ratio 1.64 n Rigid Flexible Very Flexible Slightly conservative

22 Consequence of vortex shedding on reliability assessment Nakheel Tower Low ratio of 1000 year to 50 year loads Uncertainty in loads is mostly dictated by uncertainty in this peak Need to carefully assess uncertainty in peak vortex shedding response since the normal assumption that uncertainty in wind speed governs is no longer valid. Damping and frequency uncertainties become important.

23 Reynolds number effects Originate from viscosity of air Can cause changes in flow patterns on a small scale model relative to full scale Not a concern on sharp edged structures Can be a concern on curved shape buildings Is lessened by high turbulence and surface roughness

24 Effect of Reynolds number on pressure coefficient around a circular cylinder U θ b θ degrees C p Reynolds number R e = Ub ν Kinematic viscosity of air Sub-critical Re < 10 5 Transcritical Re >

25 1:50 Scale Model of Upper Portion of Burj Khalifa High Reynolds Number Tests, Re ~ x10 6 Note: Full scale Re~7x10 7

26 Comparison of Mean Pressure Coefficients at Low and High Reynolds Number - Burj Dubai Pressure Taps

27 High Reynolds number tests on Shanghai Center Example of Mean Pressure Coefficients Pressure tap count

28 Damping and dynamic response beyond the elastic limit ζ = eff 1 δe π E 1/ F F 1 k 1 k η = ( x x x1) / 1 x 1 x ζ eff = k 1 k 1 η + η 1 k1 k1 π k 1 + η + η k 1

29 Effect of stiffness reductions and inelastic deflections on effective viscous damping ratio ζ = eff 1 δe π E 1/ k /k 1 =0.5 Example: For 0% deflection beyond elastic limit effective increment in damping ratio = This would be additive to the damping ratio below the elastic limit which is typically assumed to be 0.01 to 0.0. k /k 1 =0.75 ( x x x 1) / 1

30 Damping and inelastic response research Non-linear time domain analysis of structures under realistic wind loading will allow us to evaluate whether more efficient structures can be developed. How feasible is it to load the structure beyond its elastic limit and how far can one go with this? Can we learn how to keep the structure stable and robust after going plastic. What can be learnt from earthquake engineering? More full scale monitoring needed at representative deflections.

31 Building motions and criteria Problem is complex due to variability amongst people What return period should be used? What quantity best encapsulates comfort: acceleration; jerk; something in between; angular velocity; noises combined with motion, etc? Designers have to make decisions and move on. What is the actual experience using traditional approaches?

32 Table 1: Table 1: Building Motion Criteria. Historical review of 19 buildings wind tunnel tested by RWDI in the 1980s and 1990s. Building Number Building Height (m) First Order Modes Frequencies (Hz) f x f y f tor Assumed Damping Ratio (% of critical) 1* * * * * * For these buildings, wind tunnel studies predicted peak resultant accelerations above the milli-g range.

33 Summary of computed frequencies of 19 buildings Building Height, H ( m ) fx fy f = 33/H Fitting Curve

34 Summary of Predicted and Improved Acceleration Responses 30 Acceleration ( milli - g ) Building # milli-g range accelerations Above milli-g range accelerations Reduced acceleration responses using SDS

35 Buildings with Supplemental Damping System Building Number Building Name and Location SDS Type Installed 10-Year Peak Resultant Acceleration ( milli g ) Without SDS With SDS 1 Park Tower, Chicago, IL TMD Random House, New York, NY Wall Centre, Vancouver, BC Bloomberg Tower, New York, NY TLCD TLCD TMD Trump World Tower, New York, NY TMD

36 Park Tower, Random House and Wall Center with Damping Systems Chicago New York Vancouver

37 Trump world Tower and Bloomberg Center with Damping Systems New York New York

38 Chicago Spire Very Long period Higher Mode Effects

39 Higher modes can affect response ~ questions re frequency dependent motion criteria such as ISO comfort criteria Height, m nd harmonic 1st harmonic Mode deflection shape

40 Chicago spire - motion and deflection control through use of damping system.

41 Assessing building motions. ISO Criteria for single frequency Moving room simulations of multiple frequencies Peak acceleration, milli-g Residential Commercial Frequency, Hz

42 Meso-scale Modelling of June 1988 Event

43 Thank you