Floor Vibration Induced by Human Rhythmic Activities: Design and Post-Construction Validation at Tin Shui Wai Public Library cum Indoor Recreation Centre

14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University

Floor Vibration Induced by Human Rhythmic

Activities: Design and Post-Construction

Validation at Tin Shui Wai Public Library cum

Indoor Recreation Centre

Chi-tong WONG*, Man-kit LEUNG* and Heung-ming CHOW* *Architectural Services Department, Hong Kong SAR Government,

38/F Queensway Government Offices, Hong Kong SAR

E-mail: [email protected]

Abstract

Nowadays, modern structures have made good use of new technology adopting

high-strength and lightweight materials in building construction. This trend

together with increasing needs for open and large column-free spaces may create

excessive floor vibration, especially if the structures are subjected to rhythmic

activities (e.g. sports events) or other vibrating sources. Excessive vibration

causes serviceability problem such as nuisance and discomfort to the users. With

availability of the loading functions, commercial available softwares are now

widely employed to predict the dynamic responses of such structures subjected to

rhythmic activities. However, in-situ full-scale measurements on completed

structures have seldom been carried out in Hong Kong, despite the fact that there

have been so many long-span lightweight structures in Hong Kong. This paper

presents the in-situ measurements on a long-span structural steel structure in Tin

Shui Wai, Hong Kong. Besides using ambient and shaker excitation, 30

participants were asked to jump on the structure to simulate the rhythmic loading in

order to predict the peak acceleration under full service load. This paper

compares these measured results against the calculated ones. The data presented

in this paper therefore makes a significant contribution to the understanding of the

vibration performance of long-span structures subjected to rhythmic activities, thus

providing engineers and researchers with empirical validation on the dynamic

behaviour of lightweight long-span floor systems.

Key words: Human-induced vibration; full-scale vibration test; verification of

responses; damping ratio; peak acceleration

1. Introduction

Occupants in grandstands in stadiums, indoor recreation centres, aerobic dance rooms,

shopping malls, airport terminal corridors, etc. may experience discomfort or nuisance due

to the vibration by human activities. Example of such human activities include: walking,

running, bobbing, and jumping. Among these activities, rhythmic activities where users

sychronise their body movements are critical for sports arena. During any rhythmic

activity, a person applies repeated forces to the floor, ranging from 1.5 to 3 Hz (the ‘step

frequency’). For group rhythmic activities, the repetitive forces produced will consist not

only at the step frequency, but also at multiples (the ‘harmonics’) of the step frequency.

Resonance can therefore occur at both the step frequency and its harmonics. Therefore, in

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carrying out floor vibration assessment, the response of the floor depends on both the

natural frequency of the floor structure and the excitation frequency. Long-span slender

and lightweight structures are especially vulnerable to excessive rhythmic vibration due to

their low natural frequencies which are likely to resonant with the harmonics of rhythmic

excitation. The latest Hong Kong building codes (Code of Practice for the Structural Use

of Steel 2005 and Code of Practice for the Structural Use of Concrete 2004 issued by the

Buildings Department) therefore require floor vibration assessment to be performed for

long-span and lightweight structures. Most designers in Hong Kong carry out such floor

vibration assessment by using commercial softwares using assumed loading functions, and

dynamic properties and parameters for the structure. However, the assumed loading

functions, and properties and parameters are not subsequently validated against in-situ

measurements when the structure is completed. This paper therefore presents a pragmatic

and economical approach to validate dynamic behaviour of lightweight long-span floor

systems.

2. Human Tolerance Criterion and Load Models

Analysis procedures for floor vibration have two components: a human tolerance

criterion and a method to predict the response of the floor system. Although human

tolerance criterion is subjective, extensive studies (e.g. Reiher and Meister 1931; Lenzen

1966; Wiss and Parmelee 1974; Allen and Rainer 1976; Murray 1979) have been carried out

since the mid-1960s. There are two approaches to meet the human tolerance criterion: one

relies on ensuring that the fundamental frequency of the structure is sufficiently higher than

the excitation frequency so that the vibration induced will not be a problem; the other

requires calculation of the peak acceleration of the structure so that occupants will not feel

discomfort. The commonly adopted values for these two approaches are shown in Table 1:

Table 1. Acceptable minimum fundamental frequency and acceleration limits of floor system

Activities of occupants Minimum fundamental natural frequency of

the structure (Hz)

Peak acceleration

limit (%g)

Dancing and dining 5.4 2

Lively concert or sports event 5.9 5

Aerobics only 8.8 6

(Source: Adapted from Murray et al 1997)

The next step in vibration assessment is to determine the dynamic response of the floor

system. Both the loading from the rhythmic activities and the damping ratio must be

predicted. Numerous studies and experimental validation (e.g. Murray et al 1997; Ellis and

Ji 2002; Ellis 2003; Ellis and Ji 2004; Pan et al 2008) have been carried to determine the

loading functions of various rhythmic activities. The typical load function due to rhythmic

activities is represented by a Fourier series as follow:

)]nt

T

n2sin(

1nnreCG[1.0F(t)

p

(1)

In Eqt (1), Tp is the period of the jumping load, and G is the load density of the crowd. The

value of G has been widely discussed in various literatures (e.g. Bachmann and Ammann

1987; Murray et al 1997), and Smith et al (2009), after reviewing the literatures, suggested

G to be 0.2kPa for aerobic or sports events (i.e. 0.25 person/m2) and 1.5kPa for social

dancing (i.e. 2 persons/m2). Ce is the dynamic crowd effect, which accounts for the fact that

the crowd movement will not be perfectly synchronised, and may be taken as 2/3 (Ellis and

Ji 1997). Ellis and Ji (2002, 2004), based on his experimental verification, recommended

the values of rn and n for different rhythmic activities given in Table 2.

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Table 2. Typical values of rn and n

Activity Coeff. n=1 n=2 n=3 n=4 n=5 n=6

Low impact aerobics rn

n

1.286

- /6

0.164

-5 /6

0.133

- /2

0.036

- /6

0.023

-5 /6

0.032

- /2

High impact aerobics rn

n

1.570

0

0.667

- /2

0.000

0

0.133

- /2

0.000

0

0.057

- /2

(Source: Adapted from Ellis and Ji 2004)

The damping ratio of the floor system has also been discussed in various literatures. The

consensus is that the damping ratio during human-induced vibration should be less than

during that in earthquake; but yet the range of damping ratio has been found to vary from

1% to 20%, depending on the types of partition, the construction material and amplitude of

vibration (Naeim 1991; Hewitt and Murray 2004; Hicks 2006).

3. Design and In-Situ Measurements of Vibration

3.1 Case study: Tin Shui Wai Public Library cum Indoor Recreation Centre

Although the method to predict the response of the floor system have advanced

tremendously with the calibrated load models and availability of commercial softwares,

in-situ measurements and validation against the computed results on completed structures

have seldom been carried out, especially in Hong Kong. A project in Tin Shui Wai, Hong

Kong was therefore selected for in-situ validation of the dynamic responses against the

results from the computer analysis. The project is to provide a public library cum indoor

recreation centre. The construction works commenced on site in April 2009, and the new

public library and indoor recreation centre are scheduled to be opened to the public in

end-2011. The indoor recreation centre includes a sports arena of plan size 44m×42m,

multi-purpose rooms of plan size 25m×25m, and an indoor swimming pool of plan size

25m×25m (Figure 1 and Photo 1). Both swimming pool and multi-purpose rooms

underneath the arena require an open column free space of approximately 35m×35m. The

adopted relatively lightweight and long-span trusses supporting the floor of the arena is

susceptible to floor vibration, that may result in discomfort of and possible complaints by

the users, especially that the multi-purpose rooms and arena may respectively be used to do

exercise or playing ball games simultaneously. Hence, detailed computation of the natural

frequency and maximum peak acceleration under rhythmic activities is required.

Fig. 1. Section across the building Photo 1. Completed building

3.2 Alternative schemes of design

The original scheme (Figure 2(a)), which was mainly designed for strength

requirements, consisted of one-way structural steel trusses at 2.7m centre-to-centre and

depth of 2m at mid-span with r.c. slabs spanning between these trusses. The top and bottom

chords of the trusses would be of size 254 254 167kg/m UC, and the diagonal members at

both ends of the trusses consisted of 254 89 35.74kg/m RSC. All structural steel will be

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Grade S355JR. However, the natural frequency of each truss was 2.52Hz (with the

composite action of the r.c. slabs). As these values were far less than 5.9Hz for sports event

and 8.8Hz for aerobics (Table 1), the peak acceleration was then calculated and was found

to be 6.8%g, which also exceeded the allowable peak acceleration of 5%g for sports event

and 6%g for aerobics (Table 1). In order to improve the dynamic behaviour, the structural

steel trusses in 2/F and 3/F were tied together by steel stanchions of 406×140×46 kg/m UB

and diagonal members of 2 nos. of 406×140×46kg/m UC to form mega-trusses (Figure

2(b)). The top and bottom chords of the trusses at 3/F would be of size 305 305 198kg/m

UC with 2m depth at mid-span, whilst the top and bottom chords of the trusses at 2/F would

be of size 254 254 167kg/m UC with 2.65m depth at mid-span.

Fig. 2(a). Original structural scheme Fig. 2(b). Revised structural scheme

3.3 In-situ measurements

To validate the adopted parameters for the damping ratio, the computed natural

frequency, mode shapes and peak acceleration under rhythmic activities, in-situ

measurements have been carried with the assistance from the CityU Professional Services

Limited of the City University of Hong Kong, when the structures are being constructed and

have been completed in September 2010 and June 2011 respectively. Two types of in-situ

measurements can be carried out: Type 1 and Type 2 (Smith et al 2009). Type 1 tests (e.g.

by ambient excitation, heel-drop and drop-weight hammer) aim at giving the natural

frequencies, whilst Type 2 tests (usually by shaker) can give more detailed information,

including natural frequencies, mode shapes, damping ratio, etc. In the present testing

programme, ambient vibration was used to determine the modal properties and the natural

frequencies under environmental load condition. The acceleration was measured using

Guralp CMG 5T and Kistler 8330B3 accelerometers, which were mounted on base plates

that could be levelled to ensure proper alignment. Data acquisition was performed using NI

9234 and Dewesoft DEWE-43 portable spectrum analysers with 24-bit input channels.

Force vibration test (by using APS 113-AB ELECTRO-SEIS® long-stroke electrodynamic

shaker (Photo 3)) with a payload of 100N was then applied in the order of a few milli-g to

determine accurately the mode shapes, modal properties and the damping ratio under

resonant loading (Au et al 2011). 126 measured locations had been selected to determine

the mode shapes (Au el al 2011), and Figure 3(a) shows the 1st mode. The measurements

on the mode shapes and natural frequencies confirmed that the diagonal members

effectively couple the trusses in 2/F and 3/F (Au el al 2011). About 30 participants

(locations marked on Figure 3(b)) were then asked to simulate the rhythmic loading by

jumping at a step frequency of 2Hz (by a loud metronome beat at 120 beats per minute) for

half a minute to find the peak acceleration under simulated rhythmic load for the 1st mode

(Photos 4 and 5).

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Photo 3. Long-stroke electrodynamic

shaker

Fig. 3(a). 1st mode of vibration

Fig. 3(b). Positions of participants

Photo 4. In-situ test during construction (Sep 10) Photo 5. In-situ test upon completion (Jun 11)

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Besides calibrating the damping ratios using shaker and ambient vibration, the damping

ratio was also calculated with the acceleration response data using the logarithmic

decrement technique. One of the main differences for the floor system in September 2010

and that in June 2011 is that in June 2011, all the finishing work has been completed and all

BS services have been installed. In-situ measurement results of fundamental natural

frequency for the 1st mode are summarised in Table 3. The measured damping ratio from

shaker test is 1.15%, and those using simulated rhythmic jumping are respectively 1.3% in

September 2010 and 1.8% in June 2011.

Table 3. Summary of in-situ measurements

Parameters Shaker test result

(Sep 10)

Ambient test result Actual rhythmic activities

Sep 10 Jun 11 Sep 10 Jun 11

Fundamental natural

frequency (Hz) 6.2 6.2 5.8 6.2 5.8

The measured acceleration-time graphs of three of the accelerometers using shaker and the

rhythmic jumping are shown in Figure 4.

4. Discussion

4.1 Damping ratio

The measured damping ratios of the floor system are in the range of 1.15-1.3% and

1.8% during construction and upon completion respectively, and the increase in the

damping ratio from the construction stage of 1.15-1.3% to completion stage of 1.8% is

unsurprising, and this should be due to the installation of the finishes and services during

the construction, which effectively increases the damping of the floor system. The results

also show that the damping ratio of the long-span structural steel structures is generally in

the low range as compared with the suggested values, e.g. by Naeim (1991), Hewitt and

Murray (2004) and Hicks (2006). It can further be seen that shaker generally gives a

smaller damping ratio than under service load. Although structural damping ratio is usually

assumed to be constant value at design stage, actually damping ratio is a nonlinear

parameter with amplitude-dependent property. Hence, because shaker can only generate

an acceleration of a few milli-g (Figure 4), whilst rhythmic activities can produce a peak

acceleration of over 2%g. Moreover, the participants themselves increase the damping and

mass of the structure (Reynolds and Pavic 2006), and hence the effect of human-structure

interaction is evident (Dougill et al 2006). However, though shaker gives a smaller

damping ratio as compared with that during service load, the difference is not so big that

causes concerns.

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Accelerometer no. 1

(a)

(b)

(c)

rms acceleration=0.17%g

peak acceleration=0.28%g




peak acceleration= 1.46%g

Accelerometer no. 2

(a)

(b)

(c)







Accelerometer no. 3

(a)

(b)

(c)







Fig. 4. Measured acceleration-time graphs

(a) by shaker,

(b) by simulated rhythmic load (September 2010),

(c) by simulated rhythmic load (June 2011)

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4.2 Fundamental natural frequency

The measured fundamental natural frequencies are 6.2Hz and 5.8Hz during and after the

construction works. There is no great difference between the measured values of the

fundamental natural frequency using ambient excitation, rhythmic jumping and forced

vibration by shaker, suggesting that these methods can provide reliable way to measure the

parameter of fundamental natural frequency. The decrease in natural frequency from

construction stage to completion stage is expected, as the mass of the structure increases

with the finishes and services. Compared with the calculated fundamental natural frequency,

it was found that using SAP 2000, its computed value should be 3.97Hz, which is less than

the measured value of 5.8Hz, indicating that the floor system is more stiff than that in the

model. A probable reason is that the joints in the trusses (with fillet welds all round) were

modelled as simple pin connected for strength design, whilst during service load the joints

can take moment and behave with full continuity. By remodelling the joints as continuous

(i.e. rigid joints capable of resisting the forces and moments resulting from the service load),

the computed fundamental frequency using SAP 2000 will be increased from 3.97Hz to

5.45Hz, matching with the measured value of 5.8Hz. Hence, although the joints are

modelled as pin connected in the design for strength requirements, the joints can be

modelled as continuous having capacity to take moment in serviceability analysis.

4.3 Measured acceleration

Shaker can produce a sinusoidal input at resonant frequency, and Figure 4 shows that the

measured accelerations correspond to the input with sinusoidal acceleration-time graphs.

On the other hand, the acceleration-time graphs using simulated rhythmic jumping show

that it is difficult to synchronise the step frequencies among participants. Table 4 shows

the comparison between the measured rms accelerations and the computed rms

accelerations (using SAP 2000) with the simulated rhythmic jumping. The results generally

show good agreement, indicating that the load equation given in Eqt (1) reasonably predicts

the rhythmic loads due to jumping, and that the revised computer model in Section 4.2 (with

joints modelled as continuous) can predict the dynamic responses of the floor structure.

Table 4. rms accelerations for 1st mode of vibration

Accelerometer no. 1 Accelerometer no. 2 Accelerometer no. 3

Measured Calculated Measured Calculated Measured Calculated

0.38% g 0.28% g 0.43% g 0.36% g 0.43% g 0.21% g

4.3 Predicated peak acceleration

The load model, damping ratio and computer model of the floor system have been

validated. In order to predict the dynamic response with full service loads, the following

load functions are then adopted to calculate the peak acceleration:

for the sports arena on 3/F, the design load in Eqt. (2) was adopted:

)]}kPa2

-t

pT

8sin(0.133 )

2t

pT

4sin(0.667t)

pT

2sin([1.570

3

20.2{1.0F(t) (2)

and for the multi-purpose rooms on 2/F, the design load in Eqt. (3) was adopted:

)]kPa6

tpT

8sin(0.036)

2t

pT

6sin(0.133 )

6

5t

pT

4sin(0.164)

6t

pT

2sin([1.286

3

21.5{1.0F(t)

(3)

Although synchronization of the loads in upper and lower floors is unlikely, the analysis has

been carried out with phase difference of 0o, 45o, 90o and 180o between Eqts. (2) and (3) in

order to find the envelope of the peak accelerations. Table 5 summarises the results of the

prediction. A peak acceleration of 4.25%g only occurs when both 2/F and 3/F are being

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occupied for rhythmic activities and they are in synchronised with the other. With the

measured accelerations generally match with the predicated values by the computer model

(Table 4), it is reasonable to conclude that the predicted peak acceleration of 4.25%g under

full service load will be within the acceptable limits.

Table 5. Predicated peak accelerations

Phase lags between 3/F and

2/F rhythmic activities

Maximum Peak acceleration (% g)

2/F (high impact aerobics)

3/F (sports event)

2/F (low impact aerobics)

3/F (sports event)

0o 3.45 4.25

45o 2.72 3.58

90o 2.24 2.22

180o 3.28 3.48

5. Conclusions

Human-induced vibration is becoming more common due to increased structural

slenderness with the use of more high-strength and lightweight materials and the

increasingly demand for long-span column-free floor systems. The load models have

already been well-developed to predict the dynamic response of such structures. In-situ

measurements are now very important in validating the modal parameters in the analysis of

design of the dynamic response of long-span structures. However, rather than using

full-scale service load to test the dynamic response of such structures, this paper provides a

pragmatic and economical testing programme by validating the dynamic properties and

parameters of the structures by ambient vibration and/or shaker, and then using simulated

rhythmic loading by a small group of participants. Once the computer model, modal

parameters and damping ratio have been validated, the dynamic responses of the floor

structure can be predicated with certainty by commercial softwares.

References

(1) Allen, D.E. and Rainer, J.H., “Vibration Criteria for Long-Span Floors”, Canadian Journal

of Civil Engineering, 3(2), 1975, pp. 165-73.

(2) Au, S.K., Ni, Y.C., Zhang, F.L. and Lam, H.F., “Field Measurement and Modal

Identification of a Coupled Floor Slab System”, Presented at the 12th East Asia-Pacific

Conference on Structural Engineering and Construction, Hong Kong SAR, China, 26-28

January 2011.

(3) Bachmann, H. and Ammann, W., Structural Engineering Document 3e: Vibrations in

Structures Induced by Man and Machines, Zürich: International Association for Bridge and

Structural Engineering, 1987.

(4) Dougill, J.W., Wright, J.R., Parkhouse, J.G. and Harrison, R.E., “Human Structure

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(6) Ellis, B.R. and Ji, T., Information Paper 4/02: Loads Generated by Jumping Crowds:

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(10) Ji, T. and Ellis, B.R., “Floor Vibration Induced by Dance-Type Loads: Theory”, The

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(12) Murray, T.M., “Acceptability Criterion for Occupant-Induced Floor Vibrations”, Sound

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(13) Murray, T.M., Allen, D.E. and Ungar, E.E., Steel Design Guide Series 11: Floor Vibrations

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(16) Reiher, H. and Meister, F.J., “The Effect of Vibration on People”, Forsch Gebeite

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(17) Reynolds, P. and Pavic, A., “Vibration Performance of a Large Cantilever Grandstand

during an International Football March”, ASCE Journal of Performance of Construction

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(18) Smith, A.L., Hicks, S.J. and Devine, P.J., Design of Floors for Vibration: a New Approach,

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Acknowledgements

The authors would like to record their thanks to the Director of Architectural Services

for her kind permission of publishing the paper. The authors would also like to record

their thanks to the staff in Division One of the Structural Engineering Branch in the

Architectural Services Department, Hong Kong SAR Government for their help in

preparing the manuscript. The authors also acknowledge the assistance of Professor H.F.

LAM and Professor S.K. AU, both of the Department of Civil and Architectural

Engineering, the City University of Hong Kong, for their assistance in the setup of the

in-situ testing programme and deploying their undergraduate students to simulate the

rhythmic loading.

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Floor Vibration Induced by Human Rhythmic Activities: Design and Post-Construction Validation at Tin Shui Wai Public Library cum Indoor Recreation Centre