03Lect19TallBld

8/19/2019 03Lect19TallBld

1/30

Tall buildings

Wind loading and structural response

Lecture 19 Dr. J.D. Holmes


2/30

Tall buildings

• Very wind-sensitive in synoptic winds (including hurricanes)

• Stimulated development of boundary-layer wind tunnel

• Usually governed by serviceability response (peak accelerations and

deflections in top floors)

• Cladding pressures can be v high especially at unusual corners and change

of cross section

• !esonant dynamic response for along- and cross-wind very significant (" #$$

metres) (%!ule-of-thumb& first mode fre'uency *+h ,ert (h in metres) )

• Sometimes torsional response is significant depending on geometry and

structural system


3/30

Tall buildings

• .mpire State /uilding - full-scale and wind-tunnel studies in #01$&s

2uch stiffer in east-west direction

Y

(N-S

!

("-W

α

#ind

∆ - $ean de%lection (inc&esUh - $ean #ind speed at 1') %eet in $*H (uncorrected

1.)

).

) 1) ') +) ,) ) ) ) /) 9)

0ngle o% attac - degrees

x

x

x

N-S

"-

W x

#$U

1

3 4

h

∆


4/30

Tall buildings

• Commerce Court building5 6oronto5 Canada - #07$&s

8ull-scale and wind-tunnel measurements of local cladding pressures and

overall building response (accelerations)

Studies of local pressure peaks and implications for glass design

9cceleration measurements showed significance of torsional component (twist)

#+3$$ scale aeroelastic model showed good agreement with full scale

) 1 ' + ,

Time (minutes

W i n d

p r e s s u r e


5/30

• :orld 6rade Center ;


6/30

Tall buildings

• 8low around a tall building


7/30

Tall buildings

• >ressure fluctuations on a tall building

(movie by Shimiu Corporation5 6okyo5 ?apan)


8/30

Tall buildings

• >ressure fluctuations on a tall building

(movie by Shimiu Corporation5 6okyo5 ?apan)


9/30

Tall buildings

• Cladding pressures

8our values of pressure coefficients

3

ha

$ p

U@3

#

p pC

−=

3

ha

$ p

U@3

#

p pACA

−=

3

ha

$ p

U@3

#

p pC

−=

3

ha

3

Cp p

U@3

#

pBC

′==′

Time

Cp (t)

2pA

2p

2 p′

2p


10/30

Tall buildings

• S'uare cross section - height+width 3#

)./

).

).,).' ).'

).)

-).' -).'

-$ -$

1./

1.

1.,

1.'1.) 1.)

p2 p2A

p2

stagnation

point ≈ )./&

minimum ma3imum

:indward wall


11/30

Tall buildings


mean 2p4s 5

-). to -)./

largest minimum 2p 5 -+./

Side wall (wind from left)

-).9

-).9

-).

-).-)./

-)./-).

-).

-).

-'.'-'.,-'.)

-'.)

-1./ -'.'

-'.,

-'.

-'./

-+.'

-+./

-+.,

-+.)

-'./

-'.

-'.,

).

).,

).'

).)

p2 p2A

p2


12/30

Tall buildings


mean 2p4s 5

-).+ to -).,

largest minimum 2p 5 -1.

Deeward wall

-)., -).,

-).,

-).+

-1.-1.

-1., -1.,

-1.'

-1. -1.

-).1

p2 p2 p2A


13/30

Tall buildings

• Elass strength under wind loading

Elass strength is dependent on duration of loading

2icroscopic flaws on tension side grow at a rate dependent on local

stress

[ ] dt t s DnT

∫ = $ )(

9ccumulated damage at constant temperature and humidity

(/rown&s integral)

s(t) is stressF 6 is total time over which it actsF n is a high power (#G to 3$)


14/30

Tall buildings


Under wind loading p(t) assume s(t) HIp(t)Jm+n (nonlinear)

ie mth moment of probability density function of C p

[ ] dt t p E K D E mT

K)(LKL$∫ =

p pCp

m

p dC C f C U KT D E )()(KL$

3

3# ∫

∞= ρ


15/30

Tall buildings


Elass testing is usually carried out with a linearly increasing %ramp& load

damage produced by #-minute ramp load

m)(#

*$pH

*$

tH M

m

ma4

m*$

$

ma4

+=

= ∫ dt p

time

load %ailure

pma3

pma4 is specified load in glass design charts


16/30

Tall buildings


Ck is appro4imately e'ual to the peak pressure coefficient during the hour

of storm winds

Ck e'uivalent glass design pressure coefficient - gives pressure which

produces same damage in # hour of wind loading as that produced by a #-

minute ramp load

=

+

∫ ∞

p pCp

m

p

m

m

k

dC C f C m

C )(U@

3

#)1*$$(H

)#(

U@3

#

*$H

$

3

a

3

a

writing pma4 as Ck (#+3)ρa U3 5 where Ck is an e'uivalent glass design pressure coefficient5 and e'uating damage in ramp load test to that in #

hour (1*$$ sec) of wind

m

p pCp

m

pk dC C f C mC +#

$)()#(*$

+= ∫

∞


17/30

Tall buildings

• Elass strength under debris impact

Elaing is vulnerable to damage and failure by roof gravel in the US

9SC.-7 (*G01) re'uires glaing above #N1 m above ground level5 and

over 03m above gravel source5 to be protected

Eravel acts like a sphere or cube ; will only go up if there is a vertical

wind velocity component


18/30

Cross-wind vibrations are usually greater thanalong-wind vibrations for buildings of heights greater than

#$$m (11$ feet)

along wind

cross wind

Tall buildings

• Overall loading and dynamic response


19/30

Tall buildings


along wind

Standard deviation of deflections at top of a tall building

P

#

bn

U

@

@9

h

Bk4

#

h

b

a4

4

=

P

#

bn

U

@

@9

h

Bky

#

h

b

ay

y

= cross wind

94 and 9y - depend on building shapek 4 - 3 to 3G k y - 3G to 1G (cross-wind)

ρ b - average building density

n# - first mode fre'uency η - critical damping ratio


20/30

Tall buildings


Standard deviation of deflections at top of a tall building

Circular cross section 1)

1

'

1))

'

1)-1

' + 1) 1

#ind X

Y

3

cross #ind

1))) 3 de%lection&eig&t

σ6&

σ3&

1


21/30

Tall buildings


Meflections at top of a tall building

.ffect of cross section

* e a 1 d e % l e c t i o n

& e i g & t

)

.))1

.))'

.))+

.)),

+) ) 1)) )) 1)))

7eturn period86ears

D i r e c t i o n o % m o t i o n

2odification of corners are effective in reducing response


22/30

Tall buildings

• 6orsional loading and response

6wo mechanisms

• applied moments from aerodynamic forces produced by non-uniform

pressure distributions or non-symmetric cross-sections

• structural eccentricity between elastic center and geometric center

(a #$Q eccentricity on a s'uare building doubled mean twist and increased

dynamic twist by $-G$Q)


23/30

Tall buildings

• 6orsional loading and response

2ean tor'ue coefficient

depends on ratio between minimum and ma4imum proRected widths of

the cross section

).'

).1

) ).' )., ). )./ 1.)

% 3

ma4

min

bb


24/30

Tall buildings

• nterference effects

Surrounding buildings can produce increases or decreases in peak wind

loads

shows percentage change in peak cross-wind response of building /5 due to

a similar building 9 at position (T5=)

1)b /b b ,b 'b -'bb

:uilding :

Wind direction

(X,Y)

:uilding 0

V

b

'b

+b

,b

);


25/30

Tall buildings

• Mamping

Mamping is the mechanism for dissipation of vibration energy

Structural damping (?apanese buildings)

$$#N$7$$#$ ## − +≅ h x

n t η

$$30$$$$#1$ ## +

+≅h

xn t η

reinforced concrete

steel frame

n# first mode natural fre'uency 4t amplitude of vibration


26/30

Tall buildings

• Mamping

9u4iliary damping

Viscoelastic damper

used on :orld 6rade Center buildings5 .". material

2entreplate

=


27/30

Tall buildings

• Mamping

9u4iliary damping

6uned mass damper

used on CityCorp building5


28/30

Tall buildings

• Mamping

9u4iliary damping

6uned li'uid (sloshing) damper

used on Shin-=okohama hotel5 ?apan

&

'7


29/30

Tall buildings

• Mamping

9u4iliary damping

6uned li'uid column damper

to be used on .ureka tower building5 2elbourne5 9ustralia (under

construction)

!

!

=lo#

0

@ri%ice


30/30

"nd o% Lecture 19

Jo&n Holmes''-,)-+/9 JHolmesAlsu.edu

03Lect19TallBld

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