Tall Buildings - Wind Engineering - Lecture Slides, Slides of Environmental Law and Policy

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• 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
• Resonant dynamic response for along- and cross-wind very significant (> 100 metres)

(‘Rule-of-thumb’ first mode frequency : 46/h Hertz (h in metres) )

• Sometimes torsional response is significant depending on geometry and structural system

• Commerce Court building, Toronto, Canada - 1970’s

Full-scale and wind-tunnel measurements of local cladding pressures and overall building response (accelerations)

Studies of local pressure peaks and implications for glass design :

Acceleration measurements showed significance of torsional component (twist)

1/200 scale aeroelastic model showed good agreement with full scale

0 1 2 3 4 5 6 Time (minutes)

Wind pressure

• World Trade Center – New York 1973-
• First buildings to be tested in a turbulent boundary-layer flow wind tunnel (mid 1960’s)

• Pressure fluctuations on a tall building :

(movie by Shimizu Corporation, Tokyo, Japan)

• Pressure fluctuations on a tall building :

(movie by Shimizu Corporation, Tokyo, Japan)

• Square cross section - height/width =2.

0.2 0.4 0.

-0.2 -0. -0.4 -0.

1.0 1.2 1.

Cp Cp Cˆp



stagnation point  0.8h

minimum maximum

Windward wall :

mean Cp’s :

Cp Cp Cˆp

• • Square cross section - height/width =2.
• -0.6 to -0. - largest minimum Cp : -3. - -0. Side wall (wind from left) : - -0. - -0. - -0.8 -0. - -0.8 -0. - -0. - -0. - -2.4 -2. - - 2. - -2. - -1.8 -2. - -2. - -2. - -2. - -3. - -3. - -3. - -3. - -2. - -2. - -2. - 0. - 0. - 0. - 0.

• Glass strength under wind loading

Glass strength is dependent on duration of loading :

Microscopic flaws on tension side grow at a rate dependent on local stress

D  s t  dt

T n  (^)  0 ( )

Accumulated damage at constant temperature and humidity

(Brown’s integral) :

s(t) is stress; T is total time over which it acts; n is a high power (15 to 20)

• Glass strength under wind loading

Under wind loading p(t) : assume s(t) = K[p(t)]m/n^ (nonlinear)

i.e. mth moment of probability density function of Cp

E D K E  p t  dt

T m { }  0 { ( ) }

Cp p p

m E { D } KT ( U ) 0 Cp f ( C ) dC 2 2

1 

  

• Glass strength under wind loading

Ck is approximately equal to the peak pressure coefficient during the hour of storm winds

Ck = equivalent glass design pressure coefficient - gives pressure which produces same damage in 1 hour of wind loading as that produced by a 1- minute ramp load



 





 

  

  

  

 

  





 Cp p p

m p

m

m k C f C dC m

C ρ U ( ) 2

1 K( 3600 ) ( 1 )

ρ U 2

1 K. 60..

2 a

2 a

writing pmax as Ck. (1/2)aU^2 , where Ck is an equivalent glass design pressure coefficient, and equating damage in ramp load test to that in 1 hour (3600 sec.) of wind :

m Cp p p

m Ck m Cp f C dC

1 / 60 ( 1 ) 0 ( )     ^  



• Glass strength under debris impact

Glazing is vulnerable to damage and failure by roof gravel in the U.S.

ASCE-7 (6.5.9.3) requires glazing above 18.3 m above ground level, and over 9.2m above gravel source, to be protected

Gravel acts like a sphere or cube – will only go up if there is a vertical wind velocity component

• Overall loading and dynamic response

along wind

Standard deviation of deflections at top of a tall building :

η

1 n b

U ρ

ρ A h

σ

kx

1

h b

a x

x  

  

  

  

 

η

1 n b

U ρ

ρ A h

σ

ky

1

h b

a y

y  

  

  

  

  cross wind

Ax and Ay - depend on building shape

kx - 2 to 2.5 ky - 2.5 to 3.5 (cross-wind)

b - average building density

n 1 - first mode frequency  - critical damping ratio

• Overall loading and dynamic response

Standard deviation of deflections at top of a tall building :

Circular cross section : 101

5

2

100

5

2

10 - 1

(^52 3 5 7 10 )

X wind

Y

x

cross wind

1000 x deflectionheight

sy h

shx

1