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1 Available online at Procedia Engineering 14 (2011) The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction Floor Vibration due to Human Rhythmic Activities: Tin Shui Wai Public Library Cum Indoor Recreation Centre W. W. LI, C. T. WONG a, M. K. LEUNG b, S. C. FUNG Architectural Services Deartment, HKSAR Government, China Abstract Nowadays, modern structures have madee good use of f new technology adoting high-strength h and lightweightt materials in building construction. This trend together with increasing needs for oen and large column-free sacess may create excessive floor vibration, esecially if the structures are subjected to rhythmic activities (e.g. sorts events) or other vibrating sources. Excessive vibration causes serviceability roblem such as nuisance n and discomfort to thee users. This aer will resent a roject in Tin Shui Wai, Hong Kong, which consists off an indoor swimming ool off lan size 25m 25m at G/F, a multi-urosee hall of lan size 25m 25m at 2/F and an indoor recreationn centre with ann arena of lan size 44m 42mm at 3/F. Couling with this lightweight steel column-free structural arrangement, theree will be rhythmic activities at both the multi-urose hall and the indoor recreation centre. This aerr will thereforee describe how the human-induced floor vibration roblemm by rhythmic activities on the roject was addressed andd solved in the structural design. This aerr will thereforee review available literatures on the accetable criteria forr floor vibrations subjected to rhythmic activities, and thee methods to calculate the natural frequencyy and the eakk acceleration of a structure. In-situ measurements will alsoo be carried out by the City University of Hong Kong on thee natural frequency and the eak accelerationn of the comleted structure, and this aer will discuss the various tyess of in-situ measurements that can be carried out, and will evaluate the advantages and limitations of these in-situu measurements Published by Elsevier Ltd. Oen access under CC BY-NC-ND license. Selection and/or eer-review under resonsibility of [name organizer] Keywords: Human-Induced Vibration, Lightweight Structures, Methods to Calculate Natural Frequency and Peak Acceleration a Corresonding author: wongct@archsd.gov.hk b Presenter: leungmk@archsd.gov.hk Published by Elsevier Ltd. Oen access under CC BY-NC-ND license. doi: /j.roeng

2 3286 W.W. LI et al. / Procedia Engineering 14 (2011) Proosed develoment The roosed roject is to rovide a ublic library cum indoor recreation centre at the junction of Tin Fuk Road and Ping Ha Road in Tin Shui Wai, Hong Kong (Figure 1(a)) ). The construction workss commenced on site in Aril 2009, and the new ublic library and indoor recreation centre are scheduledd to be oened to the ublic in mid The indoor r recreation centre includes a sorts arena of lan sizee 44m 42m, multi-urose rooms of lan size 25m 25m, and an indoor swimming ool of lan sizee 25m 25m (Figure 1(b)). Both swimming ool and multi-urose rooms underneath the arena require an oen column free sace of aroximately 35m 35m. The adoted relatively lightweight and long san trusses suorting the floor of the arena is suscetible to floor vibration, that may m result in discomfort off and ossible comlaints by the users esecially the fact that the multi-urose rooms and arena may resectively be used to do exercise or laying ball games simultaneously. Hence, detailed comutation off the natural frequency and maximum eak acceleration under rhythmic activitiess is required. Figure 1(a) Location Plan Figure 1(b) Section across the Develoment 2. Accetable Criteria for LightweighT LONG-San Floors The Code of Practice for the Structural Use of Steel 2005 issued by the Buildings Deartment for steell structures states that for lightweight and a long-sann structures where excessive vibration is anticiated,, floor vibration assessment may be necessary; but does not suggest any limits on o the vibration. The Codee of Practice for the Structural Use of Concrete 2004 issued by the Buildings Deartment for reinforced concrete structures states that excessive vibration due to fluctuating loads that may cause discomfort orr alarm to occuants should be avoided, and states that for a floor structure withh the natural frequency lesss than 6 Hz, a dynamic analysis is desirable. In carrying out floor vibration assessment, the resonse of thee floor deends on the ratio of the natural frequencyy of the floor structure to the cyclic frequency of thee excitation. During any rhythmic activity, a erson alies reeated forces to thee floor, ranging from 1.5 to 3 Hz (known as ste frequency ). For grou rhythmic activities, the reetitive forces roduced willl consist not only at the ste frequency, but also at multiles (or called harmonics ) of the ste frequency.. Resonance can thereforee occur at both the ste frequency and its harmonics. That is, if a erson iss alying a force at 2 stess er second (2( Hz), the floor system should be checked for resonance at 2, 4 and

3 W.W. LI et al. / Procedia Engineering 14 (2011) Hz, etc. Murray et al (1997) summarised the state of art on the accetable criteria, which should be based on both the natural frequency of the flooring system and the eak acceleration of the flooring system (Table 1), and recommended, similar to the recommendations of the Buildings Deartment, that if the calculated fundamental natural frequency of the flooring system is greater than the minimum natural frequency, then the structure is not suscetible to vibration. However, if the minimum natural frequency is exceeded, the eak acceleration due to vibration shall be calculated. Table 1 Accetable Minimum Required Fundamental Frequency and Acceleration Limits Occuants Minimum Required Fundamental Natural Frequency (Hz) Acceleration Limit (%g) Dancing and Dining Lively Concert or Sorts Event Aerobics only Juming Exercises Shared with Weight Lifting (Source: Adated from Murray et al 1997) Figure 2(a) Original Scheme Figure 2(b) Modified Scheme 3. Schematic Design of the Steel Structures above Swimming Pool and Multi-Purose Rooms The original scheme (Figure 2(a)), which was mainly designed for strength requirements, consisted of one-way structural steel trusses at aroximately 2.7m centre-to-centre and deth of 2m at mid-san with r.c. slabs sanning between these trusses. The to and bottom chords of the trusses would be of size kg/m UC, and the diagonal members at both ends of the trusses consisted of kg/m RSC. All structural steel will be Grade S355JR. However, using the formulae given by Murray et al (1997), the natural frequency of each truss was 2.52Hz (with the comosite action of the reinforced concrete slabs). As these values were far less than 5.9Hz for sorts event and 8.8Hz for aerobics in Table 1, the eak acceleration was then calculated and was found to be 6.8%g, which exceeded the allowable eak acceleration of 5%g for sorts event and 6%g for aerobics. In order to imrove the dynamic behaviour, the original scheme was modified such that the trusses in 2/F and 3/F

4 3288 W.W. LI et al. / Procedia Engineering 14 (2011) would be tied together by steel stanchions of kg/m UB and diagonal members of 2 nos. of kg/m UC to form mega-trusses (Figure 2(b)). The to and bottom chords of the trusses at 3/F would be of size kg/m UC with 2m deth at mid-san, whilst the to and bottom chords of the trusses at 2/F would remain the same size; but the deth would be increased to 2.65m at mid-san. With these modifications, the estimated eak acceleration, using the simlified formulae by Murray et al (1997), was found to be within the accetable limits in Table Detailed Analysis and Design Once the modified structural scheme had been chosen, detailed comuter analysis was then carried out to redict the dynamic behaviour of the structure under rhythmic activities. In order to carry out dynamic analysis to assess the structural behaviour of the floor system, the characteristic of the load should first be evaluated. Unlike that for walking load which consists of two eaks under heel strike and toe off for single footfall, the contact force due to rhythmic activities consists of a single eak as the strike and off occur as a continuous movement, and can therefore be reresented as a series function of semi-sinusoidal ulses exressed as (Ji and Ellis 1994): K G s sin( t / t F ( t) 0, t t T ),0 t t where F(t) is the time varying force, K is the imact factor F max /G s, F max is the eak dynamic load, G s is the weight of a single erson = 0.75kN (Smith et al 2009) although Murray et al (1997) considered that 0.7kN is adequate, t is the time, t is the contact duration, and T is the eriod of juming load. Eqt. (1) can then be modelled by a Fourier series as follows: F( t) G s (1.0 rn n 1 sin(2n f t )) n where f is the juming frequency =1/T (taken as 2.33Hz (Ellis and Ji 2004)), r n is the n th Fourier coefficient, and n is the hase lag. Ellis and Ji (2004) then modified Eqt. (2) to model the load-time history exression for crowd rhythmic activities as follows: F( t) G[1.0 C e rn n 1 sin(2 nf t )] n In Eqt. (3), the term G, which relaces G s in Eqt. (2), 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, adoted G to be 0.2kPa for aerobic or sorts events (i.e erson/m 2 ) and 1.5kPa for social dancing (i.e. 2 ersons/m 2 ). C e is the dynamic crowd effect, which accounts for the fact that the crowd movement will not be erfectly synchronized, and may be taken as 2/3 (Ellis and Ji 1997). Ellis and Ji (2002, 2004), based on his exerimental verification, recommended the values of r n and n for different rhythmic activities given in Table 2, which deend on the contact ratio (= t /T ). (1) (2) (3)

5 W.W. LI et al. / Procedia Engineering 14 (2011) Table 2 Tyical values of r n and n Activity Coeff. n=1 n=2 n=3 n=4 n=5 n=6 Low imact aerobics High imact aerobics 2/3 1/2 r n n - /6 r n n 0 (Source: Adated from Ellis and Ji 2004) / / / With these recommendations, for the sorts arena (which was taken conservatively as that due to high imact aerobics) the design load in Eqt. (4) was adoted: 2 2 t 4 t 8 t F ( t) 0.2{1.0 [1.570 sin( ) sin( ) sin( )]}kpa (4) 3 T T 2 T 2 and for the multi-urose rooms, both high imact and low imact aerobics would be likely, and both the design loads in Eqts. (4) and (5) were adoted and were alied in turn. In Eqt. (5), a conservative value of G of 1.5kPa (i.e. 2 ersons/m 2 ) was used, although in reality it is difficult to house 2 ersons/m 2 even in low imact aerobics: 2 2 t 4 t 5 6 t 8 t F( t) 1.5{1.0 [1.286 sin( ) sin( ) sin( ) sin( )] kpa 3 T 6 T 6 T 2 T 6 The corresonding load-time history grahs over one-cycle are shown in Figures 3(a) and (b) resectively. Once the load-time history was found, it was used to analyze the dynamic resonse of the modified structural scheme due to the dynamic load, and to calculate the fundamental natural frequency, eak acceleration and mode shae of vibration of the flooring system by SAP2000. The comuter model of the floor structure is shown in Figure 4. The uer floor (which is intended to be used for sorts events) was loaded with the load in Eqt. (4), whilst the lower floor (which is intended to be used as multi-urose activities) with the loads in Eqts. (4) and (5) in turn. The eaks in Eqts. (4) and (5) occur at different time. Although synchronization of the loads in uer and lower floors is unlikely, the analysis has been carried out with hase difference of 0 o, 45 o, 90 o and 180 o between Eqts. (4) and (5) in order to find the maximum ossible eak accelerations. There would be full-height artitions enclosing the lower floor multi-urose rooms. Additional bracings would also be installed into these artitions to imrove the dynamic behavior of the modified structural scheme. A daming ratio of 4% was therefore adoted for the uer and lower floors (Hewitt and Murray 2004; Naeim 1991). Full comosite action between the steel I-beams and the reinforced concrete slabs was assumed, and a value of dynamic modulus of elasticity of 38MPa was adoted for the reinforced concrete slabs (Smith et al 2009). After analyzing the model, the fundamental natural frequency, mode shae of vibration (Figure 5) and the calculated eak acceleration (Table 3) of the floor structure were obtained. The natural frequency of this modified scheme has been increased to 3.97Hz, and the eak accelerations vary from 2.22%g to 4.25%g deending on the synchronization of the loads in the uer and lower floors. The maximum eak acceleration of 4.25%g (which still meets the accetable criterion in Table 1) only occurs when both 2/F and 3/F are being occuied for rhythmic activities and they are in synchronized with the other. (5)

6 3290 W.W. LI et al. / Procedia Engineering 14 (2011) (a) sorts event and high imact aerobics a (b) low imact aerobics Figure 3 Load-time history over one cycle Figure 4 Comuter Model for Dynamic Analysis Table 3 Calculated Peak Accelerations Phase lags between 3/F and 2/F rhythmic activities 0 o 45 o 90 o 180 o Maximum Peakk acceleration (% g) with different rhythmic activities at 2/F 2 (high imact aerobics) 2/FF (low imact aerobics) 3/F (sorts event) 3/F (sorts event)

7 W.W. LI et al. / Procedia Engineering 14 (2011) Figure 5 Mode shae of the floor structure showing first harmonicc forcing frequency 5. In-situ Measurement To validate the adoted arameter for the daming ratio, and the comuted natural frequency, modee shaes and eak acceleration under rhythmic activities, in-situ measurements will be carried with thee assistance from the CityU Professional Services Limited of the City University of Hong Kong on sitee when the structures are comleted in Setember There are two tyes of in-situ measurements: Tyee 1 and Tye 2 (IStructE 2008). Tye 1 tests aim at giving the natural frequency, whilst Tye 2 tests can give more detailed information, including natural frequencies, mode shaes, daming ratio, etc. Ambientt excitation, heel-dro and dro-weight hammer are tyical Tye 1 tests. IStructE (2008) suggests that thee more comrehensive Tye 2 tests can be erformed by the use of shakers. In the scheduled testing rogramme, ambient vibration test will be used to determine the modal roerties under thee environmental load condition. Force vibration test will then be alied to determine accurately the modall roerties and the daming ratio under resonant loading. About 30 articiants will thenn be asked to simulate the rhythmic loading to find the eak acceleration under service load. Similar strategy wass suggested by Pavic and Reynolds (2009)( in their recent ublication. The findings of the in-situ measurement will be comared againstt the comutedd values, and results will bee ublished in n due course. 6. Conclusions The modified structural scheme formed by tying the 2/F and 3/F trusses as mega trusses has increased the natural frequency from 2.52Hz to t 3.97Hz. The calculated natural frequency is still below 6Hzz required by the Code of Practice for the Structural Use of Concrete However, the erformance and dynamic resonse of the structure can c now be simulated with detailed structural s analysis. It wass calculated that, the structure in this roject though using high-strength and lightweight materials to coee

8 3292 W.W. LI et al. / Procedia Engineering 14 (2011) with the long san requirements, can still meet the acceleration limits in Table 1. The calculated results will be validated later by in-situ measurements. The roject is indeed a challenge to structural engineers who can now make use of state of art technology and the availability of commercial structural analysis software for dynamic analysis to satisfy the ever changing demands from the clients and the innovative ideas of nowadays architects. Acknowledgments The authors would like to record their thanks to the Director of Architectural Services for her kind ermission of ublishing the aer. The authors would also like to record their thanks to the staff in Division One of the Structural Engineering Branch in the Architectural Services Deartment, Hong Kong SAR Government for their hel in rearing the manuscrit. References [1] Bachmann, H. and Ammann, W., Structural Engineering Document 3e: Vibrations in Structures Induced by Man and Machines (Z?rich: International Association for Bridge and Structural Engineering); 1987 [2] Ellis, B.R. and Ji, T., BRE Digest 426: Resonse of Structures Subject to Dynamic Crowd Loads (London: BRE Centre for Structural Engineering); [3] Ellis, B.R. and Ji, T., Information Paer 4/02: Loads Generated by Juming Crowds: Exerimental Assessment (London: BRE Centre for Structural Engineering); [4] Ellis, B.R. and Ji, T., BRE Digest 426: Resonse of Structures Subject to Dynamic Crowd Loads (London: BRE Centre for Structural Engineering, 2nd ed.); [5] Hewitt, M. and Murray, T.M., "Office Fit-Out and Floor Vibrations", Modern Steel Construction, Aril; 2004, (available: htt:// accessed: 23 June 2010). [6] IStructE, Dynamic Performance Requirements for Permanent Grandstands Subject to Crowd Action (London: IStructE); [7] Ji, T. and Ellis, B.R., "Floor Vibration Induced by Dance-Tye Loads: Theory", The Structural Engineer, 72(3); 1994, (available: htt:// floor-theory.df, accessed: 23 June 2010). [8] 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); [9] Naeim, F., Steel Tis: Design Practice to Prevent Floor Vibrations (California: The Structural Steel Educational Council) (available: htt:// accessed: 23 June 2010); [10] Pavic, A. and Reynolds, P., "Aendix 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 Aroach (Berkshire: SCI); [11] Smith, A.L., Hicks, S.J. and Devine, P.J., Design of Floors for Vibration: a New Aroach (Berkshire: SCI); 2009.