Wind induced response of super-tall buildings with various aerodynamic shapes

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SEMINAR REPORT

on

WIND-INDUCES RESPONSES OF SUPER-TALLBUILDINGS WITH VARIOUS AERODYNAMIC SHAPES.

Submitted in Partial Fulfillment of the Requirements for the Degree of

MASTER OF TECHNOLOGYin

CIVIL ENGINEERING by

NAME : RAHUL BABU

(Roll no ) - 15

DEPARTMENT OF CIVIL ENGINEERING

FEDERAL INSTITUTE OF SCIENCE AND TECHNOLOGY

MOOKANOOR P O, ANGAMALY

YEAR 2015



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CERTIFICATE

Certified that seminar work entitled “WIND-INDUCES RESPONSES OF SUPER-TALL

BUILDINGS WITH VARIOUS AERODYNAMIC SHAPES” is a bonafide work carried out in

the I semester by “RAHUL BABU ” in partial fulfillment for the award of Master of Technology

in Civil Engineering during the academic year 2015 who carried out the seminar work under the

guidance and no part of this work has been submitted earlier for the award of any degree.

Dr. Praseeda K I Mrs. Lidiya P. M

SEMINAR CO_ORDINATOR SEMINAR GUIDE

Mr. Unni Kartha G

HEAD OF THE DEPARTMENT



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ACKNOWLEDGEMENT

First of all, I am grateful to God Almighty, for showering his blessings upon me for

enabling me to complete this seminar work on time. I am deeply indebted to Dr. George Issac

(Principal) for his vital support and encouragement. I wish to express my sincere gratitude to

Mr. Unni Kartha G (HOD, CE) who has been a source of inspiration and for his much needed

motivation. I would also like to extend my heartfelt thanks to my guide Mrs. Lidiya P. M (Asst.

Professor, CE), for his able guidance and useful suggestions without which this seminar would

not have been successful. I am also grateful to all the teaching and non teaching staff for their

valuable assistance. Finally, I am thankful to my parents for their blessings and support, my

friends for their help and encouragement.



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ABSTRACT

Modern tall buildings go higher and higher with the advance in structural

design and high strength materials. As the height and slenderness increase, buildings

suffer from increased flexibility which has negative effects in wind loading. Flexible

structures are affected by vibration under the action of wind which cause building

motion and plays an important role in the structural and architectural design.

Understandably, contemporary tall buildings are much more vulnerable to wind

excitation than their predecessors. Hence different design methods and modifications

are possible in order to ensure the functional performance of flexible stuctures and

control the wind induced motion of tall building. An extremely important and effective

design approach among these methods is Aerodynamic Modification.

Keywords : Super-tall buildings; Wind load; Aerodynamic modification;



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CONTENTS

Chapter No TITLE Page no.

CERTIFICATE ii

ACKNOWLEDGEMENT iii

ABSTRACT iv

LIST OF FIGURES vii

LIST OF TABLES ix

ABBREVIATIONS x

1 INTRODUCTION 1

2 BACKGROUND 2

2.1 Wind Exitation 2

2.1.1 Along Wind motion 3

2.1.2 Across wind motion 3

2.1.3 Vortex-Shedding phenomenon 4

2.2 Aerodynamic modifications against wind excitation 5

2.3 Shaping Strategies 9

3 OUTLINES OF EXPERIMENTS 11

3.1 Test Model 11

3.2 Wind Pressure measurements 15

3.3 Frame model for time history analysis 16

4 RESULTS AND DISCUSSIONS 18

4.1 Variation of peak and normal stresses with wind 18



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direction

4.2 Effect of damping ratio on peak normal stresses 22

4.3 Effect of various loading conditions 26

5 CONCLUSIONS 28

6 REFERENCES 29



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LIST OF FIGURES

Fig no. Description Page no.

1 Wind response direction 2

2 Effect of Vortex shedding on response 4

3 Vortices in different wind speed 5

4 The examples of tapering effect utilization 6

5 The examples of setbacks and sculpted building top utilization 7

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6(a) The Burj Dubai 7

6(b) The Sears Tower 7

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7(a) The Marina City Towers 8

7(b) The Millenium Tower 8

7(c) Toronto City Hall 8

7(d) The U.S Steel Building 8

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8(a) Taipei 9

8(b) The Shanghai World Financial Centre 9

9 Shaping Strategies 10

10 Test Models 14

11 Profiles of mean wind speed and turbulance intensity 16

12 Schematic view of frame model and 3 mode shapes 17

13 Ratio of largest peak tensile stress 19

14 Peak tensile stress for various wind directions 20

15Peak normal stress for various bending moments and axialforces 21

16 Effect of damping ratio on peak tensile stresses 22

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Variation of largest peak compressive stresses with damping

ratio 22



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18 Effect of damping ratio on normal stress 24

19 Effect of damping ratio on bending moments 25



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LIST OF TABLES

Table no Description Page no.

1 Effects of various loading conditions on peak compressive stress of SQ model 26

2 Effects of various loading conditions on peak compressive stress of SB model 27

3

Effects of various loading conditions on peak compressive stress of SB+45RT

model 27



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ABBREVIATIONS

1.

CC - Corner Cut

2. TP - Taper

3. SQ - Square

4. CF - Chamfered

5. SB - Setback

6. Hel - Helical

7. CV - Cross-void

8.

RT - Rotation



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1 INTRODUCTION

Super tall buildings are those buildings whose height is more than 300m. As

buildings become higher, wind loads become more important than earthquake loads in

safety design as well as in serviceability design including occupants‟ vibration

perception. Thus many attempts have been made to suppress wind-induced responses

on a building by changing building shapes: so called aerodynamic modification. As

wind forces largely depend on building shape regardless of structural system, studies

on various aerodynamic modifications have been one of the most challenging issues in

wind-resistant design. Aerodynamic modifications include taper, set-back, helical

twist, openings and combinations of them, and a comprehensive study on these

aerodynamic characteristics was recently made. These typical and unconventional

building shapes are a resurrection of an old characteristic, but they have the advantage

of suppressing across-wind responses, which is a major factor in safety and

serviceability design of super- tall buildings. The effectiveness of aerodynamic

modification in reducing wind forces has been widely reported since the late 1980s.

Wind pressure measurements were conducted on super-tall building models,

which showed superior aerodynamic characteristics. Models tested included corner

modifications, taper, setback , helical, cross-void, and combinations of them. Time

history analyses were conducted in the present study using wind pressures. First, time

histories of local wind forces were obtained from the wind pressures, and the time

histories of local wind forces were input at the centre of each floor of the frame model

to investigate the wind load effects. The purpose of the present study was to directly

compare the wind load effects on super-tall buildings with various atypical building

shapes, focusing on peak normal stresses in columns. These comparisons can advise

the structural designers regarding the effectiveness of each aerodynamic

modification and provide them with comprehensive information that can be used in

the preliminary design stage. Also, it would be helpful to evaluate the most effective

structural shape in wind-resistant design of a typical super-tall building.



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2. BACKGROUND

2.1 Wind Excitation

The motion of tall buildings occurs primarily in three modes of action: along

wind, across wind, and torsional modes. For a rectangular building with one face

nearly perpendicular to the mean flow, the motion is measured in the along wind and

across wind directions as well as in the torsional mode. The effects occurring on the

building due to along wind motion, across wind motion, and vortex-shedding

phenomenon of wind is discussed and aerodynamic modifications against these

motions are studied.

Wind approaching a building a complex phenomenon, but the flow pattern

generated around a building is equally complicated by the distortion of the mean flow,

flow separation, the formation of vortices. Large wind pressure fluctuations due to

these effects can occur on the surface of a building. As a result, large aerodynamic

loads are imposed on the structural system and intense localised fluctuating forces act

on the facade of such structures. Under the collective influence of these fluctuating

forces, a building tends to vibrate in rectilinear and torsional modes, as illustrated in

Fig.1. The amplitude of such oscillations is dependent on the nature of the

aerodynamic forces and the dynamic characteristics of the building.

Fig.1: Wind response directions



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2.1.1 Along wind motion

Along wind or simply wind is the term used to refer to drag forces. Under the

action of the wind flow, structures experience aerodynamic forces including the drag

(along wind) force acting in the direction of the mean wind shown in Figure 1. The

structural response induced by the wind drag is commonly referred to as the along

wind response. The along wind motion primarily results from pressure fluctuations on

windward (building‟s frontal face that wind hits) and leeward face (back f ace of the

building).

2.1.2 Across wind motion

The term across wind shown in Figure1 is used to refer to transverse wind.

The across wind response, is a motion in a plane perpendicular to the direction of

wind. In the design of most modern tall buildings, the across wind response often

dominates over the along wind response. Buildings are very sensitive to across wind

motion, and this sensitivity may be particularly apparent as the wind speed increases.

Wind induced instabilities of modern tower-like structures with excess slenderness,

flexibility and lightly-damped (insufficient mechanical preventions against side sway

such as use of tuned mass dampers) features could cause considerably larger across

wind responses. Besides, while the maximum lateral wind loading and deflection are

usually observed in the along wind direction, the maximum acceleration of a building

loading to possible human perception of motion or even discomfort may occur in

across wind direction.

The well-known expression of Strouhal gives the frequency N at which

vortices are shed from the side of the building, causing oscillatory across-wind forces

at this frequency.

Eq. (1)

where, S = Strouhal number, U = wind speed, b = building width.

The Strouhal number is a constant with a value typically in the range 0.1 to

0.3. For a square cross-section it is around 0.14 and for a rough circular cylinder it is

about 0.20. When N matches one of the natural frequencies Nr of the building,



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resonance occurs which results in amplified crosswind response, as illustrated in

Figure 2. From Equation 1 this will happen when the wind speed is given by

U= Eq. (2)

Fig.2: Effect of Vortex Shedding on Response

The peak response in Figure 2 can be moved to the right on this plot if the

building natural frequency is increased and if it can be moved far enough to the right

the wind speed where the peak occurs will be high enough that it is not a concern.

This is the traditional approach of adding stiffness but this approach can become

extremely expensive if the peak has to be moved a long way to the right. However,

the height of the peak is sensitive to the building shape and, with astute aerodynamicshaping, the peak can be substantially reduced or even eliminated. There are many

examples of slender structures that are susceptible to dynamic motion perpendicular

to the direction of the wind. Tall chimneys, street lighting standards, towers and

cables frequently exhibit this form of oscillation which can be very significant

especially if the structural damping is small.

2.1.3 Vortex-shedding phenomenon

When a building is subjected to a wind flow, the originally parallel wind

stream lines are displaced on both transverse sides of the building shown in Figure 3.

and the forces produced on these sides are called vortices. At low wind speeds, the

vortices are shed symmetrically (at the same instant) on either transverse side of the

building shown in Figure 3a. and building does not vibrate in the across wind

direction. On the other hand, at higher wind speeds, the vortices are shed alternately

first from one and then from the other side. When this occurs, there is an impulse both

in the along wind and across wind directions. The across wind impulses are, however,



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applied alternatively to the left and then to the right. This kind of shedding which

causes structural vibrations in the flow and the across wind direct ion is called „vortex-

shedding‟. This phenomenon of alternate shedding of vortices for a rectangular tall

building is shown schematically in Figure 3b.

(a) (b)

Fig.3: Vortices in different wind speed conditions: (a) vortices in low speed of wind

(there is no vibration in the across wind direction); (b) vortices in high speed of wind

– vortex-shedding phenomenon (there is vibration in the across wind direction).

2.2 Aerodynamic Modifications against Wind Excitation

Many studies show that from the wind engineer‟s point of view, aerodynamic

modifications of tall building‟s form and cross-sectional shape are very effective

design dimensions to be considered to control wind excitation and many of the most

elegant and notable buildings utilize these approaches. The aerodynamic

modifications of tall buildings against wind excitation are classified into two:

1. Major architectural modifications: Modifications having effect on the architectural

concept such as tapering, setbacks, sculptured building tops, varying the shape,

openings.

2. Minor architectural modifications: Modifications having no effect on architectural

concept such as corner modifications and orientation of building in relation to the

most frequent strong wind direction.

Some examples are: The John Hancock Centre (Chicago, 1969), Chase Tower

(Chicago, 1969) and the Transamerica Pyramid (San Francisco, 1972) shown in



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Figure 4. are the examples of the „tapering‟ effect utilization by creating smaller

surface areas at higher levels and reducing the upper level plans, and thus mitigating

the wind load. The Jin Mao Building (Shanghai, 1998) and the Petronas Towers

(Kuala Lumpur, 1998) shown in Figure 5. use „setbacks‟ to slightly taper the building

shape, and „sculptured building tops‟ highlighting the height of the structure, but also

serving for the practical aerodynamic purposes such as reduction in the wind response

of the building . The more sculptured a building‟s top, the better it can minimize the

along wind and across wind responses.

Fig.4: The examples of tapering effect utilization;

(a)

The John Hancock Center, (b) Chase Tower, (c) The Transamerica Pyramid



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Fig.5. The examples of setbacks and sculptured building top utilization;

(a) The Jin Mao Building, (b) The Petronas Towers

Fig.6: (a) The Burj Khalifa (b) the Sears Tower (Chicago, 1974).

While reducing the plan areas at the upper level by „varying the shape‟ of the

building along its height, minimizes the wind forces by causing the wind to behave

differently, preventing it becoming organized as in the Burj Khalifa Tower (UAE,

2008) shown in Figure 6(a). The Sears Tower (Chicago, 1974) is also a good example

for this effect shown in Figure 6(b). It is a well-known fact that the shape of structures

has a considerable effect on maintaining the lateral resistance. If the form of a tall

building is limited to rectangular prisms, from geometrical point of view, this form is

rather susceptible to lateral drift. Other building shapes such as cylindrical, elliptical,

crescent, triangular and like, are not as vulnerable to lateral force action as a

rectangular prism. Since these shapes have inherent strength in their geometrical

form, they provide higher structural efficiency or allow greater building height at

lower cost. Building codes permit a reduction of the wind pressure design loads for

circular or elliptical buildings by 20 to 40% of the usual values for comparably sized

rectangular buildings. Hence, in many of the most famous buildings, these

aerodynamically favourable forms are preferred. The Marina City Towers (Chicago,1964) shown in Figure 7(a) with its cylindrical form, the Millennium Tower (Tokyo,



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2009) shown in Figure 7(b) with tapered circular plan, Toronto City Hall (Toronto,

1965) shown in Figure 7(c) with its crescent form, and the U.S. Steel Building

(Pittsburgh, 1970) shown in Figure 7(d) with its triangular plan are among these

buildings.

Fig.7.(a). The Marina City Towers (Chicago, 1964), (b) The Millennium Tower

(Tokyo, 2009), (c) Toronto City Hall (Toronto, 1965), (d) The U.S. Steel Building

(Pittsburgh, 1970).

Some modifications on cross-sectional shape such as slotted, chamfered,

rounded corners, and corner cuts on a rectangular building can have significant

effects on both along wind and across wind responses of the building to wind as in

Taipei 101 (Taipei, 2005) shown in Figure 8(a). Corner modifications in Taipei 101

provide 25% reduction in base moment when compared to the original square section.

Chamfers of the order of 10% of the building width, makes 40% reduction in the

along wind response, and 30% reduction in the across wind response when compared

to the rectangular cross sectional shape without corner cuts. Excessive rounding of

corners of the cross section, approaching a circular shape in the cross section, and

cylindrical form in the building, significantly improve the response against wind.

Addition of openings completely through the building, particularly near the top, is

another very useful way of improving the aerodynamic response of that structure

against wind by reducing the effect of vortex shedding forces which cause across

wind motion. The Shanghai World Financial Centre (Shanghai, 2008) shown in

Figure 8(b) is a good example for this modification.



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Fig 8.(a) Taipei 101 (Taipei, 2005),(b) The Shanghai World Financial Center

(Shanghai, 2008).

2.3 Shaping Strategies

Softened Corners: - Square or rectangular shapes are very common for

buildings and experience relatively strong vortex shedding forces. However, it

is found that if the corners can be “softened” through chamfering, rounding or

stepping them inwards, the excitation forces can be substantially reduced. The

softening should extend about 10% of the building width in from the corner.

The corners on Taipei 101 where stepped in order to reduce crosswind respond

and drag, resulting in a 25% reduction in base moment.

Tapering and Setbacks: - As indicated in Equation 1, at a given wind speed,

the vortex shedding frequency varies depending on the Strouhal number S and

width b. If the width b can be varied up the height of the building, through

tapering or setbacks, then the vortices will try to shed at different frequencies

at different heights. They become “confused” and incoherent, which can

dramatically reduce the associated fluctuating forces. Burj Dubai shown in

Figure 6(a), is a classic example of this strategy.



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Fig 9: Shaping strategies

Varying Cross-Section Shape: - A similar effect can be achieved by varying

the cross-section shape with height, e.g. going from square to round. In this

case the Strouhal number S varies with height, which again, in accordance

with Equation 1 causes the shedding frequency to be different at different

heights. This again results in “confused” vortices.

Spoilers: - One can also reduce vortex shedding by adding spoilers to the

outside of the building. The most well known form of spoilers is the spiral

Scruton strake used on circular chimneystacks. Architecturally and practically,

the Scruton strake leaves something to be desired for circular buildings, but

other types of spoiler could be used that might be more acceptable, such as

vertical fins at intervals up the height.

Porosity or Openings: - Another approach is to allow air to bleed through the

building via openings or porous sections. The formation of the vortices

becomes weakened and disrupted by the flow of air through the structure.

3 EXPERIMENTAL STUDY

3.1 Test Model

The test models used for the pressure measurements are given below. The

width B of the square (SQ) model is 0.05 m, which is used as the representative

width in this work, and the height H is 0.4 m, giving an aspect ratio H/B of 8. The

geometric scale of the wind tunnel tests is 1/1000, so the height of the super-tall



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buildings is 400 m in full scale. The total volumes of the super-tall buildings are set

to be the same: about 106 m3 in full scale.

Single Modification Models

Square (SQ)

Width=0.05m

Height=0.4 m

Aspect ratio= 8

Chamfered(CF)

Modification length = 0.1 times building

width

Corner-cut (CC)

Modification length = 0.1 times building

Taper(TP)

Taper ratio = 10%



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width Area ratio of top to bottom floor= 1/6

Setback(SB)

4 layer setback with area ratio of roof floor to

base floor=1/6

90 Helical (90Hel)



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180 helical (180Hel) Cross-void (CV)

Void size=5H/24

Multiple modification models

CC + 180Hel TP + 180Hel



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CC + TP + 180Hel CC + TP + 360Hel

SB + 45RT

Setback model with 45◦

rotation

Fig.10:Test models

Eight different single modification models were used. For corner

modifications, chamfered (CF) and corner- cut (CC) were focused on, and the



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modification length was set at 0.1B, where B is the building width. This modification

length was determined considering the previous result which showed that the

optimistic modification length is 0.1B. For the tapered model (TP), although models

with larger tapering ratios show better aerodynamic characteristics, a taper ratio of

about 10% was used considering practicality. Taper ratio is defined as (base width-

roof width)/height*100, and the taper ratio of the John Hancock Center on its long

side is about 9.1%. The taper ratio of 10% roughly corresponds to an area ratio of the

top floor to the bottom floor of 1/6. A 4-layer setback (SB) is used, and the area ratio

of the roof floor to the base floor is also set at 1/6. Two helical models were used,

whose helical angles between roof floor and base floor were 90◦(90Hel) and

180◦(180Hel). A cross-void model whose void was provided at the top-center was

used. The void size was set at 5H/24.

Five multiple modification models were also used, which combined the above

aerodynamic modifications, i.e. corner cut (CC), taper (TP), setback (SB), and two

helical angles (90Hel and 180Hel). Multiple modification models included corner-cut

+ 180 helical (CC + 180Hel), taper + 180 helical (TP + 180Hel), corner-cut + taper

+180 helical (CC+ TP+ 180Hel), and corner-cut+taper+180 helical (CC+TP+

360Hel). Besides, the effects of rotation of each portion of setback shape on load

effect characteristics were also examined (SB+45RT).

3.2 Wind Pressure Measurements

Wind tunnel experiments were performed in a closed-circuit boundary-layer

wind tunnel whose working section was 1.8 m high by 2.0 m wide. Fig 11 shows the

condition of the approaching turbulent boundary layer flow with a power -law index of

0.27, which represents an urban area flow. The wind speed and turbulence intensity at

the top of the model were about UH ≈11.8 m/s and Iu,H ≈ 0.09% respectively.

The fluctuating wind pressures of each pressure tap were measured and

recorded simultaneously using a vinyl tube 80 cm long through a multi-channel

pressure transducer. The sampling frequency was 1 kHz with a low- pass filter of 500

Hz. The total number of data was 32,768. The fluctuating wind pressures were revised

considering the transfer function of the vinyl tube. There were about 20 measurement

points on one level on four surfaces, and the measurement points were instrumented at

10 levels, giving about 200 measurement points. The local wind force coefficients



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were obtained for the structural axes by considering the dynamic velocity at model

height qH and the building width of the square model B regardless of building shape.

Fig.11: Profiles of mean wind speed U/UH and turbulence intensity Iu.

3.3 Frame model for time history analyses

The frame model for the time history analyses and the fir st three mode shapes are

shown in Fig 12. Building dimensions (B*D*H) are 50*50*400 in common, and all

beams were assumed to be rigid shown in Fig 11(a). Square tube columns were used

and column sizes were adjusted such that the first translational natural period becomesabout H/50 assuming steel buildings. Local wind force coefficients were converted

into full-scale local wind forces, and input at the center of each floor. A design wind

speed of 70 m/s was used, corresponding to a 500 year return period wind speed in

Tokyo. In the frame model, no eccentricities were considered, and dead and live

loads were not applied, so that only the effects of various building shapes on load

effect were evaluated. For mode shapes, as no eccentricities were considered, there

was no coupled motion, as shown in Fig 12(b). The frame model was designed

approximately as bending type.



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B× D× H =50m×50m×400 m

1st mode 2nd mode 3rd mode

Fig.12: Schematic view of frame model and first three mode shapes (a) Framemodel,(b) first three mode shapes.



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4 RESULTS AND DISCUSSION

4.1 Variations of Peak Normal Stresses with Wind Direction

The variations of peak tensile stresses with wind direction for two single

modification models (square (SQ) and setback (SB)) and two multiple modification

models (CC+TP+360Hel and SB+45RT) are shown in Fig 13. For SQ, the largest

peak tensile stress was observed for wind directions of 0◦ and 90◦.The peak tensile

stresses of Col. 1 were generally large and those of Col.4 were generally small in the

ranges between 0◦ and 90◦. Col. 3, which was on the windward side, showed a large

peak tensile stress, but the peak tensile stresses decreased with increasing wind

directions because Col.3 was located on the leeward side for large wind directions.The opposite trend was found for Col. 2. One thing to be noted is that when the wind

direction ranged from 0◦ to about 20◦, the peak tensile stresses in Col.3 were larger

than those in Col.1. This seems to be because, for these wind directions, as the

separated shear layer approached the side surface of Col.1 and Col.2, relatively large

peak tensile stresses occurred at Col.3. Similarly, relatively large peak tensile stresses

were found in Col.2 for wind directions from 70◦ to 85◦. Similar discussions can be

made for SB, although the peak normal stresses were smaller than those for SQ for the

considered wind directions. For the multiple modification models, the peak tensile

stresses in Col.1 were the largest for the considered wind directions, and the

variations with wind direction for Col. 1 and Col.4 were small compared with those

for SQ and SB. One more difference was that there were no stress reversals between

Col. 1 and Col. 3, and between Col. 1 and Col. 2 with wind direction. The variations

of peak tensile stresses of the two helical models (90Hel and 180Hel) showed a quite

similar tendency to the multiple modifications models, showing less variation of peak

tensile stresses in Col.1 and Col.4 and not showing stress reversal for specific wind

directions.

The largest peak tensile stresses were selected for the considered wind

directions, and the ratios of stress for each model to that of SQ were calculated and

shown in Fig 13. The largest peak tensile stress in SQ was about 11kN/cm 2. The

largest peak tensile stresses for the multiple modification models were generally

smaller than those for the single modification models, and the largest peak tensilestresses for the single modification models were less than 90% of that of SQ, and



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those for the multiple modification models were about 70 – 80%. The smallest value

was found for the CC + TP + 360Hel model. The corner modification models (CF

and CC) showed similar values, and it was found that setback was quite effective in

reducing peak normal stresses in columns, showing superior characteristics to taper

and helical shapes. The effects of corner cut and taper seemed to be negligible when

they were added to the 180Hel model, showing similar values to the 180Hel model.

Increasing helical angle resulted in smaller peak tensile stresses for single and

multiple modification models but, as pointed out by, the helical angle effect is small

when the helical angle is larger than 180◦. The ratios of peak tensile stresses of SB

and SB + 45RT were similar, showing that the effect of rotation of each setback

portion on peak normal stresses in the columns was very small.

Fig 13: Ratio of largest peak tensile stresses (The largest peak tensile stresses of SQ

is about 11 kN/cm2)

To examine the contributions of two bending moments (MY and MX) and

axial force (NZ) to peak normal stresses, peak normal stresses were evaluated

separately and the variations of peak normal stresses with MX, MY and NZ are

shown in Fig 14 for the square model (SQ) for a damping ratio of 1%. Peak normal

stresses by bending moments were relatively small and showed less variation with

wind direction and column position. But significant variations with wind direction and

column position were found for axial force, and it was found that the peak normal

stresses were greatly affected by axial force. The contributions of bending

moments were approximately 20% when the wind directions were 0◦ and 90◦, and

they increased when the wind directions were between 0◦ and 90◦ because the peak



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normal stresses decreased for these wind directions, as shown in Fig 13(a). Similar

trends were found for the other models.

Fig 14: Peak tensile stresses for various wind directions for damping ratio of 1%(unit: kN/cm2). (a) SQ, (b) SB, (c) CC + TP + 360Hel, (d) SB+ 45RT.



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Fig.15: Peak normal stresses for various bending moments and axial forces for SQ

wind damping ratio of 1%. (a) Peak normal stresses by bending moment MY, (b)

Peak normal stresses by bending moment MX, (c) Peak normal stresses by axial force



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4.2 Effects of damping ratios on peak normal stresses

In the wind-resistant design of super-tall buildings, a damping ratio of 1% is

recommended for safety design, and 70 – 80% of that damping ratio is recommended

for serviceability design including habitability check. The results shown before were

for the damping ratio of 1%.

Fig 16: Effects of damping ratios on peak tensile stresses for square and 180 helical

models (Q.S. means quasi-static). (a) SQ (wind direction of 0◦), (b) 180Hel (wind

direction of 30◦)

Fig 17: Variations of largest peak compressive stresses with damping ratio(Q.S.

means quasi-static)



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But examination of the effects of damping ratio on wind load effect is an

issue of interest, and variations of peak compressive stresses with damping ratio are

shown in Fig 16 for the SQ and 180 Hel models for the wind directions where the

largest peak normal stresses occur. Q.S. shown in Fig 16 indicates quasi- static

condition. As expected, peak compressive stresses decrease with increasing damping

ratios, approaching the quasi-static value. Decreasing ratios of peak compressive

stress also decrease with increasing damping ratios. But there are clear

discrepancies in trend for the SQ and 180Hel models. For the SQ model, the

differences among peak compressive stresses in columns are large for extremely

small damping ratios, even for columns located on the windward side (Col. 1 and

Col. 3) or leeward side (Col. 2 and Col. 4). As the damping ratios increase, these

differences for Col.1 and Col. 3 or Col. 2 and Col. 4 decrease, and when the

damping ratio is larger than approximately 3%, the difference is negligible. For the

180Hel model, the differences among peak compressive stresses in columns

remains for large damping ratios, and decreasing ratios of peak compressive stresses

with damping ratio are not significant compared with those for SQ. For the column

on the windward side, i.e. Col.1, the peak compressive stresses are negative when

the damping ratio is larger than about 3%, which means that tensile forces are

applied to Col. 1 at all time instants for these damping ratios.

Fig 17 shows the variations of the largest peak compressive stresses with

damping ratios of the square (SQ), corner cut (CC),180 helical (180Hel), and CC +

180Hel models. The largest peak compressive stresses were defined as the largest

value for considered wind directions. The largest peak compressive stresses for SQ

is the largest, and those for 180 Hel are the smallest. As mentioned before, the

effect of corner cut is negligible, and when the damping ratio is less than 1%,

corner cut has a negative effect on peak normal stresses, giving larger peak

compressive stresses for CC + 180Hel than for 180Hel.

The effects of damping ratio on phase-plane trajectories are shown in Fig 18

for square (SQ) and cross void (CV) models for wind directions of 0◦ and 85◦,

respectively. When the damping ratios are relatively small, the shapes of the

envelopes are elliptic or parallelogram, but as the damping ratio increases, decreases

of bending moments in the across-wind direction (MX for SQ and MY for CV) are



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significant, and the shapes of the envelopes change to semi-circular or semi-elliptic.

The decreases of bending moments in the along-wind direction are not so

noticeable, and the mean value of along-wind bending moments is almost the same.

The envelopes of phase-plane trajectories in quasi-static conditions are similar to

those of the phase-plane trajectory of along- and across-wind forces. Fig 18 shows

time histories of normal stresses by bending moments (MX and MY) for the square

model (SQ) for wind direction 0° for different damping ratios. Fig 18(a) shows the

time histories with MX, which corresponds to across-wind direction. As damping

ratios increase, a decrease in the resonant component is clearly observed. Some

differences are admitted for the time histories with bending moments MY (Fig

18 (b)), which correspond to the along-wind direction, but the differences are not

significant compared with those in the across-wind direction.

Fig 18(a): Effect of damping ratio on Normal stress by MX for square (SQ) for wind

direction 0◦.

Fig.18(b): Effect of damping ratio normal stress by MY for square (SQ) for wind

direction 0◦.



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The effects of damping ratio on phase-plane trajectories are shown in Fig 18

for square (SQ) and cross void (CV) models for wind directions of 0° and 85°,

respectively. When the damping ratios are relatively small, the shapes of the

envelopes are elliptic or parallelogram, but as the damping ratio increases, decreases

of bending moments in the across-wind direction (MX for SQ and MY for CV) are

significant, and the shapes of the envelopes change to semi-circular or semi-elliptic.

The decreases of bending moments in the along-wind direction are not so noticeable,

and the mean value of along-wind bending moments is almost the same. The

envelopes of phase-plane trajectories in quasi-static conditions are similar to those of

the phase-plane trajectory of along- and across- wind forces .

Fig.19: Effect of damping ratio on bending moments for square (SQ) and cross

void model (CV). (a) SQ when damping ratio is 0.3% (left),1% (center), and quasi-

static (right) when wind direction of 0◦, (b) CV when damping ratio is 0.3% (left),

1% (center), and quasi-static (right)when wind direction of 85◦.



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4.3 Effects of Various Loading Conditions

For the wind directions where the largest peak normal stresses occurred, the

effects of various loading conditions were examined. Loading conditions included (i)

ALL loads (Fx+ Fy + Mz), (ii) Fx only, (iii) Fy only, (iv) Mz only, (v) Fx and Fy

(Fx + Fy), (vi) Fx and Mz (Fx+ Mz), and (vii) Fy and Mz (Fy + Mz), i.e. 7 cases in

total. The results are summarized in Tables 1 - 3 for the square model (SQ, wind

direction 0◦), setback model (SB, wind direction 85◦), and SB +45RT (wind direction

40◦). For SQ, the peak compressive stress in Col. 4 when Fx and Fy (Fx + Fy) are

applied is almost the same as that for the ALL loading condition. Under the (Fx +

Mz) loading condition, thestresses are slightly larger than those under the Fx only

loading condition, and under the (Fy + Mz) loading condition, they are slightly larger

than those under the Fy only loading condition. The results for the Mz only loading

condition are very small, and can thus be ignored only when there are no

eccentricities. For SB, the peak compressive stress under the Fy only loading

condition is larger than that under the Fx only loading condition for wind direction

85◦. For this wind direction, Fy roughly corresponds to along-wind force. Thus,

the trends are very similar to those for SQ, i.e. for Col. 3, the (Fx + Fy) loading

condition gives almost the same results as the ALL loading condition, and (Fy + Mz) gives slightly larger results than the Fy only loading condition. Also, the

results for the Mz only loading condition are negligible. For Col. 4 of SB + 45RT,

when the wind direction is 40◦, the contributions of the Fx only and the Fy only

loading conditions are similar.

Table 1. Effects of various loading conditions on peak compressive stress of square

model (SQ) for ζ = 1% (wind direction of θ = 0◦, kN/cm2)



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Table 2 Effects of various loading conditions on peak compressive stress of setback

model (SB) for ζ = 1% (wind direction of θ=85◦, kN/cm2)

Table 3 Effects of various loading conditions on peak compressive stress of SB +

45RT model for ζ = 1% (wind direction of θ=40◦, kN/cm2)

5 CONCLUSIONS

Using wind pressures applied to 13 super-tall building models with atypical

building shapes, time history analyses were conducted. Test models included 8 single

modification models, and 5 multiple modification models. The primary purpose was

to directly compare the peak normal stresses in columns of super-tall buildings.

Comparison and discussion led to the following concluding remarks.

The peak normal stresses for the square model were the largest among all the

models tested. The CC + TP + 360Hel model showed the smallest peak normal

stresses among the models tested, and the setback model showed the smallest peaknormal stresses among the single modification models tested. The peak normal



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stresses of the two helical models and the multiple-modification models showed less

variation with wind direction. Also, it was found that the effects of corner-cut and

taper seemed to be negligible when they were added to the 180Hel model.

The peak normal stresses under bending moments Mx and My were almost

the same for the considered wind directions, and the contributions of bending

moments to total peak normal stresses were about 20% of the total. Most of the peak

normal stresses were affected by axial force. This was because the frame model

used in the present study was designed as bending type.

As the damping ratio increases, the peak normal stress decreases and

approaches the quasi-static value. The increase in bending moment for the across-

wind direction became significant as the damping ratios decreased, and the sensitivity

of the peak normal stresses for the helical and multiple modification models to

damping ratio as well as wind directions was smaller than for the other models. The

effects of damping ratio are also clearly seen in the time histories of normal stresses.

From the analyses for the various loading conditions, it was found that the

contribution of bending moment in the along-wind direction was larger than those of

the other loading conditions and that of torsional moment was almost negligible.

6 REFERENCES

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[2] Ankit Mahajan, Puneet Sharma, Er. Ismit Pal Singh “Wind Effects on Isolated Buildings with Different Sizes through CFD Simulation” IOSR Journal of

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