1. Wind loading and structural response Lecture 19 Dr. J.D. Holmes
Tall buildings

2. Tall buildings
Very wind-sensitive in synoptic winds (including hurricanes)
Stimulated development of boundary-layer wind tunnel
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
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

3. Angle of attack - degrees
Tall buildings
Empire State Building - full-scale and wind-tunnel studies in 1930’s
1.0
0.5
Angle of attack - degrees x
N-S
E-W Y
(N-S) X
(E-W) a
wind
D Mean deflection (inches)
Uh - Mean wind speed at 1250 feet in MPH (uncorrected)
Much stiffer in east-west direction

4. Tall buildings 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 :
Time (minutes)
Wind pressure
Acceleration measurements showed significance of torsional component (twist)
1/200 scale aeroelastic model showed good agreement with full scale

5. Tall buildings World Trade Center – New York 1973-2001
First buildings to be tested in a turbulent boundary-layer flow wind tunnel (mid 1960’s)

6. Tall buildings
Flow around a tall building :

7. Tall buildings Pressure fluctuations on a tall building :
(movie by Shimizu Corporation, Tokyo, Japan)

8. Tall buildings Pressure fluctuations on a tall building :
(movie by Shimizu Corporation, Tokyo, Japan)

9. Tall buildings Cladding pressures :
Time
Cp (t)
Four values of pressure coefficients :

10. Tall buildings Square cross section - height/width =2.1
Windward wall :
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
1.8
1.6
1.4
1.2
1.0
stagnation point  0.8h
minimum maximum

11. Tall buildings Square cross section - height/width =2.1
Side wall (wind from left) :
-0.9
-0.5
-0.6
-0.8
-0.7
-2.2
-2.4
-2.0
-1.8
-2.6
-2.8
-3.2
-3.8
-3.4
-3.0
0.6
0.4
0.2
0.0
mean Cp’s :
-0.6 to -0.8
largest minimum Cp : -3.8

12. Tall buildings Square cross section - height/width =2.1 Leeward wall :
-0.45
-0.4
-0.35
-1.6
-1.4
-1.2
-0.1
mean Cp’s :
-0.35 to -0.45
largest minimum Cp : -1.6

13. Tall buildings 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
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)

14. Tall buildings 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

15. Tall buildings Glass strength under wind loading
Glass testing is usually carried out with a linearly increasing ‘ramp’ load :
time
load
failure
pmax
damage produced by 1-minute ramp load :
pmax is specified load in glass design charts

16. Tall buildings Glass strength under wind loading
writing pmax as Ck. (1/2)aU2 , 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 :
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
Ck is approximately equal to the peak pressure coefficient during the hour of storm winds

17. Tall buildings Glass strength under debris impact
Glazing is vulnerable to damage and failure by roof gravel in the U.S.
ASCE-7 ( ) 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

18. Tall buildings Overall loading and dynamic response cross wind
along wind
Cross-wind vibrations are usually greater than
along-wind vibrations for buildings of heights greater than 100m (330 feet)

19. Tall buildings Overall loading and dynamic response
Standard deviation of deflections at top of a tall building :
along wind
cross wind
Ax and Ay - depend on building shape
kx - 2 to ky to 3.5 (cross-wind)
b - average building density
n1 - first mode frequency  - critical damping ratio

20. Tall buildings Overall loading and dynamic response
Standard deviation of deflections at top of a tall building :
Circular cross section :

21. Tall buildings Overall loading and dynamic response
Deflections at top of a tall building :
Effect of cross section :
Modification of corners are effective in reducing response

22. Tall buildings Torsional loading and response Two 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 10% eccentricity on a square building: doubled mean twist and increased dynamic twist by 40-50%)

23. Tall buildings Torsional loading and response
Mean torque coefficient :
0.2
0.1
f =
depends on ratio between minimum and maximum projected widths of the cross section

24. Tall buildings Interference effects
Surrounding buildings can produce increases or decreases in peak wind loads :
increases
increases
decreases
shows percentage change in peak cross-wind response of building B, due to a similar building A at position (X,Y)

25. Tall buildings Damping
Damping is the mechanism for dissipation of vibration energy
Structural damping (Japanese buildings) :
reinforced concrete
steel frame
n1 = first mode natural frequency xt = amplitude of vibration

26. Tall buildings Damping Auxiliary damping : Viscoelastic damper :
used on World Trade Center buildings, New York

27. Tall buildings Damping Auxiliary damping : Tuned mass damper :
used on CityCorp building, New York (M2=400 ton of concrete)

28. Tall buildings Damping Auxiliary damping :
Tuned liquid (sloshing) damper :
used on Shin-Yokohama hotel, Japan

29. Tall buildings Damping Auxiliary damping :
Tuned liquid column damper :
to be used on Eureka tower building, Melbourne, Australia (under construction)

30. End of Lecture 19 John Holmes 225-405-3789 JHolmes@lsu.edu