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Tall buildings
Wind loading and structural response
Lecture 19 Dr. J.D. Holmes
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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 (" #$$
metres) (%!ule-of-thumb& first mode fre'uency *+h ,ert (h in metres) )
• Sometimes torsional response is significant depending on geometry and
structural system
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Tall buildings
• .mpire State /uilding - full-scale and wind-tunnel studies in #01$&s
2uch stiffer in east-west direction
Y
(N-S
!
("-W
α
#ind
∆ - $ean de%lection (inc&esUh - $ean #ind speed at 1') %eet in $*H (uncorrected
1.)
).
) 1) ') +) ,) ) ) ) /) 9)
0ngle o% attac - degrees
x
x
x
N-S
"-
W x
#$U
1
3 4
h
∆
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Tall buildings
• Commerce Court building5 6oronto5 Canada - #07$&s
8ull-scale and wind-tunnel measurements of local cladding pressures and
overall building response (accelerations)
Studies of local pressure peaks and implications for glass design
9cceleration measurements showed significance of torsional component (twist)
#+3$$ scale aeroelastic model showed good agreement with full scale
) 1 ' + ,
Time (minutes
W i n d
p r e s s u r e
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• :orld 6rade Center ;
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Tall buildings
• 8low around a tall building
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Tall buildings
• >ressure fluctuations on a tall building
(movie by Shimiu Corporation5 6okyo5 ?apan)
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Tall buildings
• >ressure fluctuations on a tall building
(movie by Shimiu Corporation5 6okyo5 ?apan)
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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
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Tall buildings
• S'uare cross section - height+width 3#
)./
).
).,).' ).'
).)
-).' -).'
-$ -$
1./
1.
1.,
1.'1.) 1.)
p2 p2A
p2
stagnation
point ≈ )./&
minimum ma3imum
:indward wall
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Tall buildings
• S'uare cross section - height+width 3#
mean 2p4s 5
-). to -)./
largest minimum 2p 5 -+./
Side wall (wind from left)
-).9
-).9
-).
-).-)./
-)./-).
-).
-).
-'.'-'.,-'.)
-'.)
-1./ -'.'
-'.,
-'.
-'./
-+.'
-+./
-+.,
-+.)
-'./
-'.
-'.,
).
).,
).'
).)
p2 p2A
p2
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Tall buildings
• S'uare cross section - height+width 3#
mean 2p4s 5
-).+ to -).,
largest minimum 2p 5 -1.
Deeward wall
-)., -).,
-).,
-).+
-1.-1.
-1., -1.,
-1.'
-1. -1.
-).1
p2 p2 p2A
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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$)
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Tall buildings
• Elass strength under wind loading
Under wind loading p(t) assume s(t) HIp(t)Jm+n (nonlinear)
ie mth moment of probability density function of C p
[ ] dt t p E K D E mT
K)(LKL$∫ =
p pCp
m
p dC C f C U KT D E )()(KL$
3
3# ∫
∞= ρ
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Tall buildings
• Elass strength under wind loading
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
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Tall buildings
• Elass strength under wind loading
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 +#
$)()#(*$
+= ∫
∞
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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
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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
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Tall buildings
• Overall loading and dynamic response
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
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Tall buildings
• Overall loading and dynamic response
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
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Tall buildings
• Overall loading and dynamic response
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
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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)
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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
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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
);
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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
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Tall buildings
• Mamping
9u4iliary damping
Viscoelastic damper
used on :orld 6rade Center buildings5 .". material
2entreplate
=
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Tall buildings
• Mamping
9u4iliary damping
6uned mass damper
used on CityCorp building5
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Tall buildings
• Mamping
9u4iliary damping
6uned li'uid (sloshing) damper
used on Shin-=okohama hotel5 ?apan
&
'7
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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
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"nd o% Lecture 19
Jo&n Holmes''-,)-+/9 JHolmesAlsu.edu