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Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011

Leuven, Belgium, 4-6 July 2011

G. De Roeck, G. Degrande, G. Lombaert, G. Muller (eds.)

ISBN 978-90-760-1931-4

1607

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2 THE WIND LOAD MODEL IN THE TIME DOMAIN

The longitudinal wind load is considered in the followinganalysis neglecting the transverse and vertical wind loadcomponents. The wind speed at level z above the

ground, ( , )v z t , can be written as

( , ) ( ) ( , )v z t v z v z t = + (1)

Where ( , )v z t and ( , )v z t denote the average wind speed and

fluctuating wind speed, respectively. The mean wind speed at

a different level, ( )v z , may be calculated according to the

ASCE7-05 (power law) [1,2]

( ) ( )10

zv z b v= (2)

Where b and are constants that are defined regarding to

exposure categories and v is the basic wind speed (m/s) and inwhich z and ( )v z are the arbitrary height and its

corresponding average wind speed.Since the wind speed is low, the aeroelastic forces arising

out of the interaction between air and the structure are sosmall that they can be neglected. The aerodynamic forces dueto wind turbulence are expressed as follows with no liftingeffect in the present case of vertical cantilever structure. The

fluctuating wind speed ( , )F z t on the structure at levelz can

be written as [3]

2( , )

1( ) ( ) ( , )

2 s

F z t z A z v z t = (3)

Where is the density of air, ( )A z is the orthogonal exposed

wind area at level z and ( )s

z is structural shape factor (or

drag coefficient) of the structure at level z.Substituting Eqs. (1) and (2) into (3) yields

2

1

2

2

( , ) ( ) ( ) ( , )

( ) ( , )

m f

f

F z t C z v C z vv z t

C z v z t

= +

+

(4)

Where2 21

( ) ( ) ( ) ( )2 10

m s

zC z z A z b

= is the coefficient of

mean wind load, which depends on the vertical height of the

selected level (reference height),1( ) ( ) ( )

f sC z z A z b=

( )10

z

and2( ) ( ) ( )

1

2f s

C z z A z= are similarly defined

coefficients for the fluctuating wind load. Benfratello et al.[4],after analyzing the stochastic response of a SDOF structuresubject to wind action, concluded that neglecting the quadraticpressure term of the fluctuating wind speed could not lead toaccurate results. The fluctuating wind speed is simulated as anergodic multivariate stochastic process, and the fast Fouriertransform is needed to estimate the fluctuating wind speed

components acting on the structure [5]. When the mean windspeed ( )v z corresponding to each level z and the time history

of the fluctuating wind speed at all levels, ( , )v z t , are

obtained, the wind load in the structure can be computed.

3 DESIGN OF THE STRUCTURAL MODELS IN THISSTUDY

In this study, five structural models are used for specifyingthe trend of this research that defines as follows:

(1) A 20-storey building in the form of steel momentresisting frame accompanied with RC shear wall (70m height).

(2) A 20-storey building in the form of steel momentresisting frame accompanied with concentricallysteel braced frames (X-braces) (70 m height).

(3) A 30-storey building in the form of steel momentresisting frame accompanied with RC shear wall(105 m height).

(4) A 30-storey building in the form of steel momentresisting frame accompanied with concentrically

steel braced frames (X-braces) (105 m height).(5) A 40-story building in the form of steel complex dual

system of rigid and braced frames in combinationwith outriggers and belt trusses and the brace typesare buckling restrained braces (BRB) (151.2 mheight).

All of tall buildings have a residential application. Thestructural system of the floor is composite of reinforcedconcrete slabs and steel secondary beams. The steel materialused in the sections of the structural members is of ST37 typewith yielding strength of 2400 kg/cm2 and ultimate strengthof 3700 kg/cm2. The compressive strength of concretematerial, f'c, used in the shear walls is 300 kg/cm2. AmericanInstitute of Steel Construction Specifications were used todesign steel members and shear wall respectively [6, 7]. Inorder to calculate earthquake load, the spectrum dynamicmethod was used based on reference Standard No. 2800-05[8].The plans of the structures, lateral load resisting frames, thedirection of the girders, secondary beams and the location ofshear walls and bracings are shown in Figure 1, 2, 3, 4, 5 and6.

Figure 1. The structural plan of 20 and 30-storey buildings

with steel braced system

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Figure 2. The structural plan of 20 and 30-storey buildingswith shear wall system

Figure 3. Base Stories Configuration and Structural System of40-storey building

Figure 4. Typical Stories Configuration and Structural Systemof 40-storey building

Figure 5. Mid-Height and Top Stories Configuration andStructural System of 40-storey building (Including Outrigger)

Figure 6. Lateral Load Resisting Frames of 40-storeybuilding

In summary, the first 10 modes of 3 structures are tabulated in

Table 1. Table 1. Modal analysis results

Periods (sec)

Mode 40-storey 30st(X-brace) 20st(X-brace)

1 4.383 2.937 2.23

2 3.773 2.828 2.067

3 2.269 1.664 1.634

4 1.525 0.923 0.651

5 1.322 0.902 0.621

6 0.856 0.535 0.493

7 0.755 0.487 0.326

8 0.677 0.477 0.319

9 0.568 0.322 0.25110 0.54 0.317 0.211


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4 SEISMIC LOAD AND NONLINEAR ANALYSIS

In order to assess the seismic behavior of selected buildings,we have conducted a series of nonlinear time history analysesto compare with time history wind load. The designedstructures have been used by importing into PERFORM-3D[9] software to create a nonlinear model. Buildings were

checked for the following performance level: collapseprevention level using a three dimensional nonlinear step-by-step time history analysis with the program Perform 3D (CSI,2007).

4.1

Collapse prevention step-by-step nonlinear analysis

16 ground motions including 8 rock soil types and 8 Deep soiltypes modified to match the response spectrum according toStandard No. 2800-05, were used to represent the maximumconsidered event (MCE) with a mean recurrence interval of2475 years (2% probability of exceedance in 50 years). Withthis assumption these accelerogroms are selected that distanceof all of 16 accelerograms from fault focus is more than 20

km and all of them are applied to the structures separately in xdirection.5 models were built in Perform 3D (CSI, 2007) to representthe lateral system of the building. The seismic massequivalent to the dead load and its associated rotationalmoment of inertia is assigned at levels above the ground floor.The mass associated to the ground level and below is ignored.The diaphragms above-ground level are modelled as rigiddiaphragms by slaving the horizontal translation degrees offreedom. For 40-storey building, Ground motions are input atthe top of the mat foundation. The foundation is idealized asrigid by providing lateral and vertical supports at the top ofthe foundation. The lateral resistance of the soil surrounding

the subterranean walls is neglected.P-delta effects are considered in the model by the inclusion ofa P-delta column at the centre of mass of the building withan axial load equivalent to the dead load plus the expected liveload. This column is pinned at both ends on each level with itsnodes slaved to the diaphragm defined at each floor.Figure 7 shows a PERFORM frame compound component forthe chord rotation model. The key parts of this model are theFEMA beam components. These are finite length componentswith nonlinear properties. The model has two of thesecomponents for cases where the strengths are different at thetwo ends of element. The PERFORM converts this model tothe model shown in Figure 7. Each FEMA beam component is

actually two components, namely a plastic hinge and anelastic segment.

Figure 7. Basic components for chord rotation model (a) andBeam component with plastic hinges (b)

4.2 Damping

Rayleigh damping is used to run the time history nonlinearanalyses and during applying time history wind load. Todefine the damping curve, the damping is set at 25% ofcritical damping at a period of 02 T1 and at a period of 09

T1, T1 being the fundamental period of the structure. The and values are automatically calculated by Perform 3D(CSI, 2007). Figure 8 shows the resulting damping curve.

Figure 8. Rayleigh damping as defined in Perform 3D

5 SIMULATION OF THE FLUCTUATING WINDLOAD

The highest frequency of interest of the fluctuating windcomponent is taken as 4 rad/s and the size of fast Fourier

transform is 1024. The time step of data is 0.78 s. Theroughness length z0 is taken as 0.7 m, and the exponentialdecay coefficient Cz is taken as 10 [3] for calculating the windpower spectrum; for the coherence function between the windspeeds at two different levels. The vertical wind profile isassumed to follow the ASCE7-05. The basic wind speedaccording to the ASCE7-05 was selected 47 and 76 m/s, andthe angle between the wind direction and the positivedirection of the x-axis is assumed to be 0 degrees. Thequantity of basic wind speed deliberately was selected highquantity for comparison with nonlinear analysis due to theselected ground motions were used to represent the MCE. Thedensity of air is taken as 1.226 kg/m3 in the wind load

calculation. The fluctuating wind speed is simulated as anergodic multivariate stochastic process. The mentioned inputinformation and other vital information are tabulated in table2.

Table 2. Time history wind design parameters

Basic wind speed (V) 47 and 76 m/s

Time step of data 0.78

Occupancy category II

Surface roughness B

Exposure type B

Enclosure classification Enclosed

Cut off frequency (Wu) 4 rad/s

Roughness length (Z0) 0.7

Exponential decay coefficient (Cz) 10

Von Karman constant (K) 0.4

Structural shape factor (s) 1.3

Density of air 1.226 kg/m3

These above information are input data for the programwritten for simulation of ergodic multivariate stochasticprocess by using the spectral representation method werewritten by Shinozuka and Deodatis [10].

In this study, to evaluate the role of duration of time historywind load in tall buildings, 60 sec and 3600 sec intervals areselected for assessing this goal and sequently time history


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wind load in form of these two duration is applied to thestructures.The time history along-wind load will be imposed at thelocation of perimeter beam-column joints (major joint of eachfloor) while considering the area that assume for those joints(i.e., it worth nothing to mention that contribution of corner

joints shall be half of the interior ones). According to abovedescription, method of applying dynamic along-wind load ineach story in form of time history is shown in figure 8.

Figure 8. Procedure of applying time history along-wind loadalong the height on exterior side of tall building

6 ANALYSIS RESULTS

Finally, One group of analyses are performed by simulatingfluctuation wind speed under dynamic time history wind load

and its counterpart, nonlinear dynamic earthquake load due toexcitation from the ground motion earthquake accelerograms.This study has focused on Three prominent structuraldemands such as the peak inter story drift (which is a failureindex), maximum story displacement and peak story shearwas evaluated and the results of wind.Figures 923 represent the behaviour of buildings under timehistory along-wind load derived from two basic wind speeds(47 m/s and 76 m/s) for duration of 60 sec and 3600 sec. Also,these figures show the behaviour of buildings under the MCErecords in form of theirs Averages (Mean) and mean plusstandard deviation (Mean+) separately for 8 deep soil types

and 8 rock soil types.

0

2

4

6

8

10

12

14

16

18

20

0 0.003 0.006 0.009 0.012

Story

Drift(ratio)

20story-Bracing system Rock Soil(Mean)

Deep Soil(Mean)

Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

wind load-Vb=76m-

s-t=3600

wind load-Vb=76m-

s-t=60

Figure 9. Peak story drifts for 20-story (bracing system)

0

2

4

6

8

10

12

14

16

18

20

0 0.002 0.004 0.006 0.008 0.01

Story

Drift(Ratio)

20 story-shear wall System

Deep Soil(Mean)

Rock Soil(Mean)

Wind Load-Vb=76m-

s-t=3600

Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=76m-s-

t=60

wind load-Vb=47m-s-

t=3600

wind load-Vb=47m-s-

t=60

Figure 10. Peak story drifts for 20-story (shear wall system)

0

5

10

15

20

25

30

0 0.002 0.004 0.006 0.008 0.01

Story

Drift(ratio)

30 story-Bracing system

Deep soil(Mean)

Rock Soil(Mean)

Mean+ (Deep soil)

Mean+ (rock soil)

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

wind load-Vb=76m-

s-t=3600

wind load-Vb=76m-

s-t=60

Figure 11. Peak story drifts for 30-story (bracing system)

0

5

10

15

20

25

30

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Story

Drift(ratio)

30 story-Shear wall system

Deep soil(Mean)

Rock soil(Mean)

Wind Load-V=76m-

s-t=3600

Mean+ (Deep soil)

Mean+ (Rock Soil)

wind load-Vb=76m-

s-t=60

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

Figure 12. Peak story drifts for 30-story (shear wall system)

According to figures, In 20-story and 30-story buildings,

peak of story drift and displacements along the height due todeep soil types are more than ones in rock soil types and in

peak story shear along the height, thats vice versa. With


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-5

0

5

10

15

20

25

30

35

0 0.003 0.006 0.009 0.012 0.015 0.018 0.021

Story

Drift(ratio)

40 story

Deep soil(Mean)

Rock soil(Mean)

wind load-

Vb=47m-s-t=3600wind load-

Vb=47m-s-t=60

wind load-

Vb=76m-s-t=3600

Deep soil(Mean+)

Rock soil(Mean+)

wind load-

Vb=76m-s-t=60

Figure 13. Peak story drifts for 40-story

0

2

4

6

8

10

12

14

16

18

20

0 0.1 0.2 0.3 0.4 0.5

Story

Displacement(m)


Deep Soil(Mean)

Rock Soil(Mean)

Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

wind load-Vb=76m-

s-t=3600

Wind load-Vb=76m-

s-t=60

Figure 14. Peak displacements for 20-story (bracing system)

0

2

4

6

8

10

12

14

16

18

20

0 0.1 0.2 0.3 0.4

Story

Displacement(m)

20 story- Shear wall System

Deep soil(Mean)

Rock Soil(Mean)

Wind Load-V=76m-

s-t=3600Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=76m-

s-t=60

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

Figure 15. Peak displacements for 20-story (shearwall system)

0

5

10

15

20

25

30

0 0.1 0.2 0.3 0.4 0.5 0.6

Story

Displacement(m)


Deep Soil(Mean)

Rock Soil(Mean)

Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

wind load-Vb=76m-

s-t=3600

wind load-Vb=76m-

s-t=60

Figure 16. Peak displacements for 30-story (bracing system)

0

5

10

15

20

25

30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

story

Displacement(m)

30 story-shear wall system

Deep soil(Mean)

Rock soil(Mean)

Wind Load-V=76m-

s-t=3600

Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=76m-

s-t=60

wind load-Vb=47m-s-t=3600

wind load-vb=47m-

s-t=60

Figure 17. Peak displacements for 30-story (shearwall system)

-5

0

5

10

15

20

25

30

35

0 0.2 0.4 0.6 0.8 1 1.2

Story

Displacement(m)

40 story Deep Soil(Mean)

Rock Soil(Mean)

Rock soil(Mean+)

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

wind load-Vb=76m-

s-t=3600

Deep soil(Mean+)

Wind load-Vb=76m-

s-t=60

Figure 18. Peak displacements for 40-story (outrigger system)

increasing height, responses related to peak story shear in the

two types of soil converge to each other and even in higher

stories, peak story shear due to deep soils ground motions

become dominant (thats obvious in 40-story building).


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0

2

4

6

8

10

12

14

16

18

20

0 1000 2000 3000 4000

Story

Peak Story Shear(Ton)

20 story-Bracing systemDeep Soil(Mean)

Rock Soil(Mean)

Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

wind load-Vb=76m-

s-t=3600

wind load-Vb=76m-

s-t=60

Figure 19. Peak story shear for 20-story (bracing system)

0

2

4

6

8

10

12

14

16

18

20

0 2000 4000 6000 8000

Story

Peak Story shear(Ton)

20 story-Shear wall system

Deep Soil(Mean)

Rock Soil(Mean)

Wind Load-V=76m-

s-t=3600

Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=76m-

s-t=60

wind load-Vb=47m-

s-t=3600

wind load-vb=47m-

s-t=60

Figure20. Peak story shear for 20-story (shear wall system)

0

5

10

15

20

25

30

0 1000 2000 3000 4000 5000 6000

Story

Peak story Shear(Ton)

30 story-Bracing SystemDeep soil(Mean)

Rock soil(Mean)

Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

wind load-Vb=76m-

s-t=3600

Wind load-

Vb=76m-s-t=60

Figure 21. Peak story shear for 30-story (bracing system)

Regarding to analytical results, among 5 tall buildings thatsubjected to dynamic wind load, just 40-story building underdynamic time history wind load with basic wind speed 76 m/sand wind duration 3600 sec entered in nonlinear phase. Incomparison with seismic load in all responses,growth rate of

dynamic wind forces more increases with increasing height oftall buildings. With comparing average quantity of responses

0

5

10

15

20

25

30

0 3000 6000 9000 12000 15000

story

Peak Story Shear(Ton)

30 story-shear wallDeep soil(Mean)

Rock soil(Mean)

Wind Load-V=76m-

s-t=3600

Mean+ (Deep soil)

Mean+ (Rock soil)

wind load-Vb=76m-

s-t=60

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

Figure 22. Peak story shear for 30-story (shear wall system)

-5

0

5

10

15

20

25

30

35

0 2000 4000 6000 8000

Story

Peak Story shear(Ton)

40 story

Deep Soil(Mean)

Rock Soil(Mean)

wind load-Vb=47m-

s-t=3600

wind load-Vb=47m-

s-t=60

wind load-Vb=76m-

s-t=3600

Deep soil(Mean+)

Rock soil(Mean+)

wind load-Vb=76m-

s-t=60

Figure 23. Peak story shear for 40-story (outrigger system)

(mean) due to deep soil types and rock soil types with extremedynamic wind load in this study (basic wind speed 76m/s andwind duration 3600 m/s), it is obvious that peak ofdisplacement and drift of models along the height are sensitiveparameters to dynamic wind load, because as it is observedresponses stem from applying extreme dynamic load onstructures get closer to responses due to rock soil types withincreasing height and finally, in 40-story building, peak

displacements due to extreme wind load became more thanaverage quantity of responses (mean) due to rock soil types.According to figure 14, 15, 16, 17 that included peakdisplacements derived from dynamic wind and seismic load,separately, the structures with bracing system are moreflexible that ones with shear wall system.In these figures, it is obvious that with increasing basic windspeed and height, difference of wind duration will be moreeffective in comparison with lower basic wind speed (47m/s).On the other hand, at the same basic wind speed, withdecreasing wind duration, because of being neighbor of gustwind speed to wind speed, participation of gust in mean windspeed is increasing and vice versa. Therefore, this is an

acceptable reason for this fact that with increasing windduration mean wind speed decrease (Durst 1960).


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6.1 Evaluation and comparison of frequency domain of

dynamic wind load and seismic load

Figure 24, 25 show power spectral density of dynamic timehistory wind load calculated regarding to basic wind speed76m/s at 5 levels and PSD of earthquake force in 40st floordue to 8 deep soil ground motions for 40-story building,

respectively. Figure 24 indicate that in lower frequencydomain, dynamic wind load increase with respect toincreasing in height and also in frequency domain higher than0.01 Hz, variability or fluctuation of dynamic wind loadincreases. Gradually dynamic wind forces diminish infrequency domain higher than 0.1 Hz.

Magnitude of these fluctuations in wind force with respectto figure 24 can be computed by introducing a parametercalled RMS (Root Mean Square). Indeed by calculating thearea that is under the diagram of related to each story, RMS

1.00E-02

1.00E+00

1.00E+02

1.00E+04

1.00E+06

1.00E+08

1.00E+10

1.00E+12

1.00E+14

1.00E+16

0.0001 0.001 0.01 0.1 1PowerSpectralDensity(N2/Hz)

Frequency(Hz)

5st Floor

15st Floor

25st Floor

35st Floor

40st Floor

Figure 24. PSD of dynamic wind force for 40-story buildingalong the height

Figure 25. PSD of produced earthquake force in 40th floordue to 8 deep soil ground motions in 40-story building

can be acquired and according to the calculated RMS,quantity of RMS in each of 5 levels increases with increasingin height. In other words, this description means that averageof absolute fluctuations of dynamic wind forces increase withincreasing in height of tall buildings.Figure 25 in comparison with figure 24 indicates that

earthquake forces in higher frequency domain reach to theirpeak of magnitude and finally, being neighbor of peak offrequency content in earthquake force to the modes of 5models is a significant reason for dominating the responsesderived (3 prominent structural parameter that are discussed inthis study) due to seismic load in comparison with dynamicwind force.

7

CONCLUSION

Among these 3 parameters that were evaluated in relation todynamic wind load, Peak drift and displacement are twoimportant parameters for comfort criteria that affect humanperception to motion in the low frequency range of 0-1 Hz

encountered in tall buildings.Being close peak of frequency content of earthquake forces

along in stories to fundamental modes of models can bereasonable proof for dominating earthquake force againstdynamic wind forces and also this concept causes stimulatingand resonating higher modes of tall buildings.

According to figure 14, 15, 16, 17 that included peakdisplacements derived from dynamic wind and seismic load,separately, the structures with bracing system are moreflexible that ones with shear wall system.

With this assumption that mass of all stories are equal,according to F=M.ag (M is mass of each story, ag isacceleration of ground motion measured by accelerograms

and F is earthquake force applied to each story), time historyearthquake forces applied to each story (figure 25) areuniform quantity along the height whereas not only dynamicwind force in not constant along the height but also it becomeslarger and more intense with increasing height.

REFERENCES

[1] Simiu E, Scanlan RH. Wind effects on structures. 3rd ed. New York:Wiley; 1996.

[2] ASCE (American Society of Civil Engineers). 2006. ASCE 7-05,Minimum Design Loads for Buildings and Other Structures, IncludingSupplement No. 1. ASCE: Reston, VA.

[3] Liu H. Wind engineeringA handbook for structural engineers.Englewood Cliffs, NJ; 1991.

[4]

Benfratello S, Falsone G, Muscolino G. Influence on the quadratic termin the along-wind stochastic response of SDOF of structures.Engineering Structures 1996;18(8):68595.

[5] Deodatis G. Simulation of ergodic multivariate stochastic processes.Journal of Engineering Mechanics 1996;22(8):77887.

[6] American Institute for Steel Construction (AISC), (2005). "Specificationfor Structural Steel Buildings, ANSI/AISC 360-05", Chicago (IL):American Institute for Steel Construction.

[7] American Concrete Institute, Building Code Requirements ForStructural Concrete (ACI 318-05).

[8] Building and Housing Research Center, (2007). "Iranian Code ofPractice for Seismic Resistant Design of Buildings [Standard No.2800,3th Edition] ", Tehran, Iran.

[9] CSI (Computers & Structures, Inc.). 2007. Perform 3D Version 4.0.3.Nonlinear Analysis and Performance Assessment of 3D Structures. CSI:Berkeley, CA.

[10] Shinozuka, M., and Deodatis, G. (1991). Simulation of stochasticprocesses by spectral representation. Appl. Mech., Rev., 44(4), 191-204.


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MS08-1096