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

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

Angle of attack - degrees Tall buildings Empire State Building - full-scale and wind-tunnel studies in 1930’s 1.0 0.5 0 10 20 30 40 50 60 70 80 90 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

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 : 0 1 2 3 4 5 6 Time (minutes) Wind pressure Acceleration measurements showed significance of torsional component (twist) 1/200 scale aeroelastic model showed good agreement with full scale

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)

Tall buildings Flow around a tall building :

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

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

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

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

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

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

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)

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

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

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

Tall buildings 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

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)

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 2.5 ky - 2.5 to 3.5 (cross-wind) b - average building density n1 - first mode frequency  - critical damping ratio

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

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

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%)

Tall buildings Torsional loading and response Mean torque coefficient : 0.2 0.1 0 0.2 0.4 0.6 0.8 1.0 f = depends on ratio between minimum and maximum projected widths of the cross section

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)

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

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

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

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

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

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