14th Asia Pacific Vibration Conference, 5-8 December 2011, The Hong Kong Polytechnic UniversityFloor 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 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 Dancing and dining Lively concert or sports event Aerobics only Minimum fundamental natural frequency of the structure (Hz) 5.4 5.9 8.8 (Source: Adapted from Murray et al 1997) Peak acceleration limit (%g) 2 5 6 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: 2 n (1) t )] F(t) G[1.0 C r sin( e n n 1 Tp n 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 Activity Low impact aerobics High impact aerobics Coeff. rn n n n=1 1.286 - /6 1.570 0 n=2 0.164 -5 /6 0.667 - /2 n=3 0.133 - /2 0.000 0 n=4 0.036 - /6 0.133 - /2 n=5 0.023 -5 /6 0.000 0 n=6 0.032 - /2 0.057 - /2 rn n (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 Fundamental natural frequency (Hz) Shaker test result (Sep 10) 6.2 Ambient test result Sep 10 6.2 Jun 11 5.8 Actual rhythmic activities Sep 10 6.2 Jun 11 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) rms acceleration=0.17%g peak acceleration=0.28%g (b) rms acceleration=0.25%g peak acceleration=0.78%g (c) rms acceleration=0.38%g peak acceleration= 1.46%g Accelerometer no. 2 (a) rms acceleration=0.16%g peak acceleration=0.3%g (b) rms acceleration=0.59%g peak acceleration=1.7%g (c) rms acceleration=0.43%g peak acceleration=1.43%g Accelerometer no. 3 (a) rms acceleration=0.05%g peak acceleration=0.14%g (b) rms acceleration=0.41%g peak acceleration=1.5%g (c) 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 Measured 0.38% g Calculated 0.28% g Accelerometer no. 2 Measured 0.43% g Calculated 0.36% g Accelerometer no. 3 Measured 0.43% g Calculated 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: F(t) 0.2{1.0 2 2 4 [1.570 sin( t) 0.667 sin( t 3 Tp Tp 2 ) 0.133 sin( 8 t - )]}kPa Tp 2 (2) and for the multi-purpose rooms on 2/F, the design load in Eqt. (3) was adopted: F(t) 1.5{1.0 2 2 4 5 6 8 [1.286 sin( t ) 0.164 sin( t ) 0.133 sin( t ) 0.036 sin( t )]kPa 3 Tp 6 Tp 6 Tp 2 Tp 6 (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 Maximum Peak acceleration (% g) Phase lags between 3/F and 2/F rhythmic activities 0o 45o 90o 180o 2/F (high impact aerobics) 3/F (sports event) 3.45 2.72 2.24 3.28 2/F (low impact aerobics) 3/F (sports event) 4.25 3.58 2.22 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) (2) Allen, D.E. and Rainer, J.H., “Vibration Criteria for Long-Span Floors”, Canadian Journal of Civil Engineering, 3(2), 1975, pp. 165-73. 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. 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. 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. Ellis, B.R. and Ji, T., BRE Digest 426: Response of Structures Subject to Dynamic Crowd Loads, London: BRE Centre for Structural Engineering, 1997. Ellis, B.R. and Ji, T., Information Paper 4/02: Loads Generated by Jumping Crowds: Experimental Assessment, London: BRE Centre for Structural Engineering, 2002. 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. 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). Hicks, S., NCCI: Vibrations, Ascot: SCI, 2006 (available: http://www.steelbiz.org/, accessed: 2 June 2009). (3) (4) (5) (6) (7) (8) (9) 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. 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