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

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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.

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