floor vibration induced by human rhythmic activities: design and post-construction validation at tin...
Post on 28-Jul-2015
290 Views
Preview:
DESCRIPTION
TRANSCRIPT
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: wongct@archsd.gov.hk
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
1596
14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University
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.
1597
14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University
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
1598
14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University
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).
1599
14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University
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)
1600
14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University
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.
1601
14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University
Accelerometer no. 1
(a)
(b)
(c)
rms acceleration=0.17%g
peak acceleration=0.28%g
rms acceleration=0.25%g
peak acceleration=0.78%g
rms acceleration=0.38%g
peak acceleration= 1.46%g
Accelerometer no. 2
(a)
(b)
(c)
rms acceleration=0.16%g
peak acceleration=0.3%g
rms acceleration=0.59%g
peak acceleration=1.7%g
rms acceleration=0.43%g
peak acceleration=1.43%g
Accelerometer no. 3
(a)
(b)
(c)
rms acceleration=0.05%g
peak acceleration=0.14%g
rms acceleration=0.41%g
peak acceleration=1.5%g
rms acceleration=0.43%g
peak acceleration=1.53%g
Fig. 4. Measured acceleration-time graphs
(a) by shaker,
(b) by simulated rhythmic load (September 2010),
(c) by simulated rhythmic load (June 2011)
1602
14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University
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
1603
14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University
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
Interaction during Rhythmic Bobbing”, The Structural Engineer, 84(22), 2006, pp. 32-39.
(5) Ellis, B.R. and Ji, T., BRE Digest 426: Response of Structures Subject to Dynamic Crowd
Loads, London: BRE Centre for Structural Engineering, 1997.
(6) Ellis, B.R. and Ji, T., Information Paper 4/02: Loads Generated by Jumping Crowds:
Experimental Assessment, London: BRE Centre for Structural Engineering, 2002.
(7) Ellis, B.R. and Ji, T., BRE Digest 426: Response of Structures Subject to Dynamic Crowd
Loads, London: BRE Centre for Structural Engineering, 2nd
ed., 2004.
(8) Hewitt, M. and Murray, T.M., “Office Fit-Out and Floor Vibrations”, Modern Steel
Construction, April, 2004, pp. 35-8 (available: http://www.arch.virginia.edu, accessed: 23
June 2010).
(9) Hicks, S., NCCI: Vibrations, Ascot: SCI, 2006 (available: http://www.steelbiz.org/,
accessed: 2 June 2009).
1604
14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic University
(10) Ji, T. and Ellis, B.R., “Floor Vibration Induced by Dance-Type Loads: Theory”, The
Structural Engineer, 72(3), 1994, pp.37-44.
(11) Lenzen, K.H., “Vibration of Steel Joist-Concrete Slab Floors”, AISC Engineering Journal,
3(3), 1996, pp. 133-6.
(12) Murray, T.M., “Acceptability Criterion for Occupant-Induced Floor Vibrations”, Sound
and Vibration, November, 1979, pp. 24-30.
(13) Murray, T.M., Allen, D.E. and Ungar, E.E., Steel Design Guide Series 11: Floor Vibrations
due to Human Activity, Chicago: American Institute of Steel Construction, 1997.
(14) Naeim, F., Steel Tips: Design Practice to Prevent Floor Vibrations, California: The
Structural Steel Educational Council, 1991 (available: http://www.johnmartin.com/,
accessed: 23 June 2010).
(15) Pavic, A. and Reynolds, P., “Appendix C: Dynamic Testing of Building Floors”, in Smith,
A.L., Hicks, S.J. and Devine, P.J. (eds.), Design of Floors for Vibration: a New Approach,
Berkshire: SCI, 2009.
(16) Reiher, H. and Meister, F.J., “The Effect of Vibration on People”, Forsch Gebeite
Ingenieurwes, 2(11), 1931, pp. 381–6 [in German].
(17) Reynolds, P. and Pavic, A., “Vibration Performance of a Large Cantilever Grandstand
during an International Football March”, ASCE Journal of Performance of Construction
Facilities, 20(3), 2006, pp. 202-12.
(18) Smith, A.L., Hicks, S.J. and Devine, P.J., Design of Floors for Vibration: a New Approach,
Berkshire: SCI, 2009.
(19) Wiss, J.F. and Parmelee, A., “Human Perception of Transient Vibrations”, ASCE Journal of
Structural Division, 100(ST4), 1974, pp. 773-87.
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.
1605
top related