Post on 13-Aug-2020
ABSTRACT: The excessive vibration in a building due to along-wind and across-wind excitations can affect the health and/or
interrupt the activities of the inhabitants. Perception curves, in terms of mean peak acceleration or standard deviation of
acceleration have been developed and adopted in codes as serviceability criteria for designing buildings. Some of these criteria
do not incorporate the uncertainty in structural properties and wind characteristics. The main purpose of this study is to carry out
a comparison between some of the major serviceability criteria for designing buildings and to estimate the reliability level for
structures designed according to such perception curves, incorporating the uncertainty in structural properties, wind
characteristics, and in the human perception of motion. For the analyses, the probability distribution of the peak acceleration
response proposed by Davenport is adopted, and the random vibration approach is employed to determine the maximum
response of a structure. Results of the analysis indicate that the reliability (the probability that the wind-induced vibration of a
designed structure is not perceived within a service period) associated with structures designed according to different
serviceability criteria is not the same, even if the structures are designed for the same perception level.
KEY WORDS: Wind; Vibration; Acceleration; Perception Curves; Reliability.
1 INTRODUCTION
The design of tall buildings includes the consideration of an
ultimate limit state and a serviceability limit state. Even if the
ultimate limit state is satisfied, tall buildings can experience
excessive vibration under wind loading. This excessive
vibration can deteriorate health of the inhabitants of the
buildings, disrupt the activities or cause discomfort.
Some studies on the acceleration limits for human comfort
levels were carried out in the 70’s by Van Koten, Chen and
Chang [2, 3, 4]. These studies related acceleration levels with
subjective descriptors. From these studies, it is possible to
identify levels of perception of acceleration at about 15 milli-
g. To take into account the excessive vibration during the
design stage, codes and/or standards propose the use of
criteria to limit the excessive wind-induced motion [5, 6, 7].
The criterion proposed by ISO10137 [5] suggests the use of
the mean peak acceleration, as a function of the frequency of
vibration, to limit the discomfort level and disruption of tasks
of inhabitants of buildings. The NBCC [6] also employs the
mean peak acceleration as a perception limit; this criterion is
independent of the frequency of vibration. The AIJ [7]
suggests the use of perception curves with different perception
levels; this criterion is frequency dependent and uses the mean
peak acceleration to limit the wind-induced motion. All these
criteria consider a 1-year return period value of wind speed,
except for the NBCC [6] that considers a 10-year return
period of wind speed.
Figure 1 presents a comparison of the three criteria
described above. All the curves correspond to a 10-year return
period value of the mean wind speed.
Figure 1. Limits of perception.
It is observed in Figure 1 that the perception levels suggested
in ISO10137 [5] and the NBCC [6] depends on the use of the
structure, while the criterion suggested by the AIJ [7]
considers the use of curves associated with different
probability of perception levels.
The serviceability criteria suggested by ISO10137 [5] and the
AIJ [7] is employed to estimate the reliability levels for
Wind-induced vibration: a serviceability study
Adrián Pozos-Estrada1, Isaac F. Lima Castillo
1, Roberto Gómez Martínez
1, J. Alberto Escobar Sánchez
1
1Instituto de Ingeniería, Universidad Nacional Autónoma de México, Circuito Escolar s/n, Ciudad Universitaria, Delegación
Coyoacán, México D.F., C.P. 04510
email: APozosE@iingen.unam.mx, ILimaC@iingen.unam.mx, RGomezM@iingen.unam.mx, JEscobarS@iingen.unam.mx
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014Porto, Portugal, 30 June - 2 July 2014
A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)ISSN: 2311-9020; ISBN: 978-972-752-165-4
1431
structures designed according to such perception curves,
incorporating the uncertainty in structural properties, wind
characteristics, and in the human perception of motion.
2 RESPONSE OF TALL BUILDINGS UNDER WIND
LOADING
2.1 Mean peak acceleration
The action of wind around a structure induces aerodynamic
forces that can cause excessive vibration (acceleration). The
amplitude of vibration depends on the dynamic properties of
the structure. Two types of measures are usually adopted to
study wind-induced vibration, one is the mean peak
acceleration and the other one is the standard deviation of
acceleration. The former is associated with the search for
safety while the latter is associated with physical discomfort
(dizziness for example). These measures are related through
the following expression:
vga aˆ (1)
where a is the mean peak acceleration, a is the r.m.s. of
acceleration for a given wind speed v given by:
000)( fSfv
m
Fva (2)
where 0F is a transformation factor from mean wind speed to
force, m is the mass of the structure (it is considered that the
structure can be modeled as a single-degree-of-freedom
system), f is the natural frequency of the structure in Hz,
0fS is the power spectral density function of turbulent wind
at f0, is the ratio of damping of the structure, and g is a peak
factor defined as:
Tf
Tfg0
0ln2
577.0ln2 (3)
where T is the duration of the application of the wind loading,
in s.
In this study we use the mean peak acceleration as a
measure of wind-induced vibration. The following section
describes how uncertainty in structural properties, wind
characteristics, and the human perception of motion are
considered in this paper.
2.2 Consideration of uncertainty
According to Davenport [1], the probability distribution of the
peak acceleration (response), A , conditioned on a given
mean wind speed v is written as:
)))ln2ˆ(ln2exp(exp(ˆ 00ˆ (v)σT)(fa(v)/σT)(f)a(F aaA (4)
where the mean and standard deviation of A , are given by:
)(ˆ vgm aA (5)
and,
)ln(26/)( 0ˆ TfvaA (6)
If the annual maximum mean wind speed V is modeled as a
Gumbel variable, its probability distribution is given by:
))))/6577.01()(6(exp(exp( vvvvV mvm/(v)F (7)
where v is the coefficient of variation (COV) of v, and mv is
the mean value of v, defined as:
))/6(/11lnln577.01(/ vrTv Tvm (8)
where vT is the maximum wind speed for a given return period
Tr.
According to Burton [8], the probability of perception for a
given peak acceleration is defined by a standard normal
distribution and is written as:
2
1/ˆlnˆˆ c
caaaPP (9)
where c1 and c2 are parameters of the model that depend on
the frequency of vibration.
To take into account the uncertainty in structural properties
(associated with f, , and 0F , we considered that they are
lognormally distributed [9, 10, 11].
By using the total probability theorem and integrating over the
domain of the random variables considered, the unconditional
probability of perception can be written as:
advdFdfddfffFfvfafava
RaPPP DnnfDFVAfPnD
~~~~~~)
~(
~)~(~ˆ~
ˆ 0~~0~~~0
(10)
where 0~
DF , nf~
and ~
represent normalized random
variables (normalized with respect to their mean value) with
probability density functions denoted by 0~~
0 DF FfD
, )~
(~ nf ffn
and ~
~f , respectively; va
R ~ is defined as:
~
),,(
)~,,~
(~~
)~(0
TvfT
vvnfnDv
p
cra
vImSv
mvImfSFmv
g
avR
n
(11)
where acr is a target acceleration that can be used for a design
review; mfn is the mean value of fn, and Iv is the turbulence
intensity of wind.
Equation (10) is used in the following section to estimate
the reliability or probability that the wind-induced vibration of
a designed structure is not perceived within a service period.
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
1432
3 PARAMETRIC ANALYSIS TO ESTIMATE THE
UNCONDITIONAL PROBABLITY OF PERCEPTION
For the parametric analyses, a combination of parameters of
the random variables is employed to estimate the reliability
associated with the criteria suggested by ISO10137 [5] and the
AIJ [7]. Note that the criterion suggested by the NBCC [6] is
not included since it is frequency independent.
3.1 Procedure to estimate the unconditional probability of
perception
The procedure employed to calculate PfP associated with each
of the criteria considered is as follows:
1) From any of the criteria used, select a target value acr,
2) Characterized each probability density function with its
parameters,
3) Using 1) and 2) solve Eq. (10) to determine PfP,
4) Associate the obtained PfP with the target value acr,
5) Repeat Steps 1) to 4) for different values of acr.
The parameters used to estimate the reliability are
summarized in Table 1.
Table 1. Summary of parameters used in the analysis.
Parameter Value Parameter Value
T 3600s COV of 0~
DF 0.125
0.01 COV of nf~
0.175
0f 0.1-1.0 Hz COV of ~
0.275
vT 30 m/s COV of v See plots
3.2 Unconditional probability of perception associated
with ISO10137 (2007)
For the analyses, the mean peak acceleration curves for
residences and offices (see Fig. 1) are considered. The
procedure described in Section 3.1 is applied and the results of
the analysis are presented in Figure 2, for two different values
of v.
1.0
50.0
0.1 1
Me
an
pe
ak a
cce
lera
tio
n (
mill
i-g
)
f (Hz)
v=0.15
ISO10137 (2007)
CALCULATED
Pfp=0.95
Pfp=0.55Pfp=0.67
Pfp=0.75
Offices
Pfp=0.84
Residences
a)
1.0
50.0
0.1 1
Me
an
pe
ak a
cce
lera
tio
n (
mill
i-g
)
f (Hz)
v=0.30
ISO10137 (2007)
CALCULATED
Pfp=0.60
Pfp=0.25
Pfp=0.50
Pfp=0.54Pfp=0.40
Offices
Residences
b)
Figure 2. ISO10137 (2007) perception curves and calculated
curves for different Pfp values: a) v = 0.15; b) v = 0.30.
It is observed in Figure 2 that Pfp is very sensitive to the
uncertainty in wind speed. Another important observation is
that forv = 0.15, the curve for residences suggested by [5]
could be associated approximately with a Pfp value equal to
0.67, whereas that for offices could be associated with a Pfp
value equal to 0.84. For v = 0.30, the values of Pfp for
residences and offices are equal to 0.40 and 0.54, respectively.
3.3 Unconditional probability of perception associated
with AIJ (2004)
For the analyses, the H-90 and the H-10 curves (90% and 10%
of perception level) are considered. The results obtained are
presented in Figure 3.
1.0
50.0
0.1 1
Me
an
pe
ak a
cce
lera
tio
n (
mill
i-g
)
f (Hz)
v=0.15
AIJ (2004)
CALCULATED
Pfp=0.90
Pfp=0.12
Pfp=0.16
Pfp=0.47
Pfp=0.67
H-90
H-10
a)
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
1433
1.0
50.0
0.1 1
Mea
n p
ea
k a
ccele
ration
(m
illi-
g)
f (Hz)
v=0.30
AIJ (2004)
CALCULATED
Pfp=0.53
Pfp=0.095
Pfp=0.15
Pfp=0.30
Pfp=0.40
H-90
H-10
b)
Figure 3. AIJ (2004) H-90 and H-10 curves and calculated
curves for different Pfp values: a) v = 0.15; b) v = 0.30.
Similar conclusions to those drawn from Figure 2 are
applicable to Figure 3, except that the H-90 and H-10 could be
associated approximately with a Pfp value equal to 0.67 and
0.12 for v = 0.15, respectively. These Pfp values are
approximately equal to 0.40 and 0.095 for v = 0.30.
3.4 Comparison of results
Table 2 presents a summary of the results obtained from the
parametric study.
Table 2. Summary of results
Code or standard AIJ (2004)
Pfp
ISO10137 (2007)
Pfp
Residences (v=0.15) - 0.67
Offices (v=0.15) - 0.84
Residences (v=0.30) - 0.40
Offices (v=0.30) - 0.54
H-10 (v=0.15) 0.12 -
H-90 (v=0.15) 0.67 -
H-10 (v=0.30) 0.09 -
H-90 (v=0.30) 0.40 -
It is observed in Table 2 that the impact of v on Pfp is very
significant. This observation is important since the wind
climate (v) of a particular site could affect the value Pfp
associated with a particular criterion, although some
researchers have proposed the use of serviceability factors that
can be used for design checking; these factors were calibrated
to take into account a range of v values [12]. When using the
criterion proposed by ISO10137 [5], Pfp for residences is
smaller than that for offices, as expected. With respect to the
H-90 curve, it is observed that it is associated with values of
Pfp within 0.40 to 0.67 for the parameters considered; these
values are smaller than the original 90% of perception level.
Similar observations can be drawn from the H-10 curve. It is
also interesting to note that the Pfp values associated with
ISO10137 [5] for residences are similar to those from the H-
90 curve proposed by the AIJ [7]. This can be explained by
noting that the limits of perception (see Figure 1) from both
curves are very similar.
4 FINAL COMMENTS
A comparison between some of the major serviceability
criteria for designing buildings and to estimate the reliability
level for structures designed according to such perception
curves, incorporating the uncertainty in structural properties,
wind characteristics, and in the human perception of motion
was carried out. For the analyses, the probability distribution
of the peak acceleration response, and the random vibration
approach was employed. The analyses results indicate that the
unconditional probability of perception associated with
structures designed according to different serviceability
criteria is not the same, even if the structures are designed for
the same perception level.
Other conclusions that can be drawn from the results are:
Pfp is very sensitive to the COV of wind speed.
When considering uncertainty in structural
properties, wind characteristics, and the human
perception of motion, the Pfp values calculated for
each criterion are different than the probability of
perception associated with each criterion.
ACKNOWLEDGMENTS
The financial support received from the Institute of
Engineering of UNAM, the National Council on Science and
Technology (CONACYT), and from the Graduate School of
Engineering at UNAM are gratefully acknowledged.
REFERENCES
[1] Davenport, A. G. Note on the distribution of the largest value of a random function with application to gust loading. Proceedings of the
Institution of Civil Engineers, Paper No. 6739, Vol. 28, pp. 187– 196,
1964. [2] Van Koten, H. The Comparison of Measured and Calculated
Amplitudes of some Buildings, and determination of damping effect on
Buildings. Proceedings of the third international conference on wind effects on buildings and structures, Tokyo, Japan, pp. 825 – 840, 1971.
[3] Chen. P. W., and Robertson, L. E. Human Perception Thresholds of
Horizontal Motion. Journal of the Structural Division, ASCE, Vol. 98, pp. 1681 – 1695, 1972.
[4] Chang, F. K. Human Response to Motion in Tall Buildings. Journal of
the Structural Division, ASCE, Vol. 99, pp. 1259 – 1272, 1973. [5] ISO10137-2007 International Organization for Standardization. Bases
for design of structures —Serviceability of buildings and walkways
against vibrations. ISO 10137:2007(E), International Organization for Standardization, Geneva, Switzerland. 2007.
[6] NBCC. National Building Code of Canada, Part 4 Structural Design,
Commentary 1, Wind Load Effects. 2005. [7] Architectural Institute of Japan Recommendations. Guidelines for the
evaluation of habitability to building vibration. AIJES-V001-2004,
Tokyo, Japan. 2004. [8] Burton, M.D. Effects of low frequency wind-induced building motion
on occupant comfort. PhD. Thesis, Civil Engineering Department, The
Hong Kong University of Science and Technology, Hong Kong, 2006.
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
1434
[9] Davenport, A.G. A comparison of seismic and windstorm hazards. In Proceedings of the 6th Environmental Specialty Conference of the
Canadian Society for Civil Engineering, 7–10 June 2000, London, Ont.
Canadian Society for Civil Engineering, Montréal, Que. pp. 504–509, 2000.
[10] Kareem, A. Reliability Analysis of Wind Sensitive Structures. J. Wind
Engineering and Industrial Aerodynamics, Vol. 33, pp. 495 – 514, 1990.
[11] Haviland, R. Evaluation of seismic safety of buildings. M.Sc. Thesis
supervised by J.M. Biggs, E.H. Venmarcke, Massachusetts Institute of Technology, 1976.
[12] A. Pozos-Estrada, H.P. Hong and J. K. Galsworthy. Serviceability
Design Factors for Design of Wind-Sensitive Structures. Canadian Journal of Civil Engineering, Vol. 37(5), pp. 728 – 738, 2010.
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
1435