78 — Build 134 — February/March 2013

Departments/ResearchBy Paul Carpenter and Peter Cenek, Opus International Consultants, and Richard Flay, Department of Mechanical Engineering, University of Auckland

MONITORING THE WIND-INDUCED motion of five tall buildings in New Zealand has been undertaken over several years as part of a research programme to develop an improved methodology for building design.

This aims to ensure that wind-induced motion of new tall buildings remains within acceptable limits and prevent building occupants from experiencing motion sickness.

Building motion can be reduced at the design stage by increasing the building density and stiffness and by avoiding slender designs. However, this conflicts with the aims of designing lightweight flexible buildings to achieve earthquake resistance.

Limits set in standard

ISO standard 10137:2007 provides guidance for limits on horizontal accelerations and human response to wind-induced motions in buildings. The ISO limits in the frequency range 1–2 Hz are annual maximum horizontal accelerations of 6 milli-g for offices and 4 milli-g for residences. The limits increase for frequencies below

Wind-induced motion of tall buildingsThe wind-induced motion performance of several buildings has been

monitored, helping to produce an equation for use at the design stage to predict the potential for excessive motion.

1 Hz and above 2 Hz due to the way that people notice and respond to vibrations.

Some buildings exceed the limits

Some tall buildings in New Zealand substantially exceed these accelera-tion limits, and that partly prompted the research. These buildings were avoided, as the aim was to investigate the motion of representa-tive modern tall buildings. Those selected ranged between 10 m and 28 storeys in height. Four are in Wellington, and one is in Auckland.

Design analysis procedures for wind-induced building motion have previously been largely based on the results of wind tunnel testing. Getting monitoring data from real buildings provided an opportunity for a much-improved understanding of building motion.

Motion measured in five buildings

One building had predicted annual maxi mum accelerations at the centre of the top floor of 9 milli-g, exceeding the ISO limit of 7.5 milli-g for this building by about 20%.

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Build 134 — February/March 2013 — 79

The accelerations due to torsion at the top corners of this building were also unusually large, resulting in combined accelerations at the corners of up to 15 milli-g.

Building occupants at these corners would be very likely to feel uncomfortable due to this motion.

The measured X, Y and torsion frequencies for this building were all similar (0.65 Hz), indicating that the building experiences coupled mode response. Coupled modes should be avoided in building design, where possible, to avoid excessive wind-induced motion.

The other four monitored buildings all experienced wind-induced motions within the ISO limits.

Wind speed and building motion relationship

Determining the relationship between wind speed and building motion was an important aspect of the research and was measured for three of the five buildings.

The average exponent of the power-law fit for the three buildings was measured to be 3.05, with a range of ±5%, i.e. the building motion is approximately proportional to wind speed cubed.

This relationship is not intuitive, as wind forces on structures are typically proportional to wind speed squared. The reason for the approximately cubic relationship is that, as wind speed increases, the building experiences larger and more powerful wind turbulence or gusts at frequencies that coincide with the sway frequencies of the building.

It should be noted that the analysis procedure provided in the loading standard AS/NZS 1170.2 does not properly account for this effect and therefore underestimates the effects of changes in wind speeds.

Figure 1: The largest measured displacement at the centre of the top floor of Building E.

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6 Predicting building motion

A reasonable prediction of building motion at the design stage is:

wherea = peak resultant acceleration (m/s2)Vdes, 1-year = 1-year design wind speed at the roof of the building (m/s),

which may be calculated using the loading standard AS/NZS 1170.2f = fundamental frequency (Hz)m0 = building mass per unit height over the top one-third of the

structure (kg/m).This equation has been derived by examining building motion and

wind tunnel measurements from the current research and previous studies. It is a refined version of a similar equation in use for many years. Note that this equation does not account for:

● coupled mode effects – consequently, it underestimated the motion for the building that has coupled mode response

● effects due to building shape and the influence of adjacent build-ings, which can be substantial.

For the study buildings it provided a better prediction than the method in AS/NZS 1170.2.

Going hypothetical

It is instructive to apply this predictive equation to a hypothetical slender tall lightweight apartment building 100 m tall with:

f = 0.4 HzVdes, 1-year = 40 m/sρb = 200 kg/m3 (building density)A = 400 m2 (plan area)m0 = 80,000 kg/m

The predicted acceleration is 22 milli-g – nearly four times the limit acceleration for this building of 6.1 milli-g from ISO 10137. The wind-induced motion of this building would clearly be very unsettling for the occupants of the upper floors.

Note that the frequencies that have been used in the calculation are the actual 1st mode frequencies for each building. The measured frequencies are typically 20–30% higher than those estimated in structural design calculations. Be aware that use of the design calcula-tion frequencies is likely to calculate somewhat higher accelerations.

Accuracy is critical

The measured wind-induced accelerations are approximately proportional to the cube of the wind speed. Accurate wind speed estimates are critical for design predictions of wind-induced building motion. A simple predictive equation provides a reasonable indication in the design stage of potential excessive wind-induced motion. Note The research is a collaborative programme involving Opus, University

of Auckland and GNS and has been funded by the Building Research Levy.

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