EFFECT OF FIT-OUT AND CONSTRUCTION TYPE ON DYNAMIC PROPERTIES OF FLOOR SYSTEMS UNDER HUMAN EXCITATIONS

Transcription

1 EFFECT OF FIT-OUT AND CONSTRUCTION TYPE ON DYNAMIC PROPERTIES OF FLOOR SYSTEMS UNDER HUMAN EXCITATIONS Tuan Nguyen 1, Emad Gad 2, Nicholas Haritos 3, and John Wilson 4 ABSTRACT: This paper investigates the dynamic properties of two long-span building floors with different construction types and fit-out subjected to human excitations. One of case studies pertains to a fully-furnished steel-concrete composite floor whilst the other is a post tensioned concrete floor in its bare condition without fit-outs/services. The natural frequencies, damping ratios, response levels and modal masses of the real floors were determined both experimentally and analytically using a number of physical heel drop and walking tests as well as detailed finite element models. A comparison of the results obtained for the two floors reveals that nonstructural components and furnishings can significantly contribute to the overall damping of the completed composite floor. On the other hand, the higher modal mass and stiffness of the concrete floor with band beams were found to help reduce the response of the floor regardless of the bare floor having lower damping. KEYWORDS: Floor vibrations, human excitations, resonance, damping, modal mass. 1 Department of Civil and Construction Engineering, Swinburne University of Technology. tuannguyen@swin.edu.au 2 Department of Civil and Construction Engineering, Swinburne University of Technology. egad@swin.edu.au 3 Department of Civil and Construction Engineering, Swinburne University of Technology. nharitos@swin.edu.au 4 Department of Civil and Construction Engineering, Swinburne University of Technology. jwilson@swin.edu.au

2 1 INTRODUCTION High strength, efficient structural floor systems such as steel-concrete composite floors and post tensioned floors are being constructed with longer spans to meet the need for larger column-free spaces in buildings. Post tensioned concrete slabs, which can allow large span-to-depth ratio, can also help minimise the structural floor depth hence considerably saving the cost of architectural, mechanical and electrical systems [1]. Whist these long span floor systems can still be robust in terms of ultimate strength, they may be more flexible and susceptible to vibrations induced by various human activities on the floor by building occupants. The main factors affecting the dynamic behaviour of a floor system are the modal mass, stiffness and damping of the floor. Whilst the mass and stiffness can be estimated quite accurately using information about the structural layouts, material properties and expected weight of occupants; evaluation of damping, even by experimental modal analysis, may contain a multitude of errors [2]. Results from dynamic testing of floor systems demonstrated that mass and damping have a significant influence on human-induced floor vibrations [3]. Increasing damping can reduce the vibration magnitude at resonant conditions, attenuate transmission of vibratory energy, enhance sound isolation, and accelerate the decay of free vibration [4]. As the inherent damping of a floor comes from not only structural members but also non-structural elements or architectural components, different floor systems built from the same material may have very different overall levels of damping [5, 6]. Fullheight non-structural partitions have been found to increase not only damping but also stiffness of floors [7]. People themselves may be an additional source of damping as investigations on humanstructure interaction have revealed an increase in damping of occupied structures over ones that are empty, depending on structural configuration, occupant posture and group size [8]. In regard to response to walking excitations, floor systems are categorised into low frequency floors in which resonance may cause severe vibration amplification and high frequency floors where resonance becomes less important compared with transient response. Especially in long-span low-frequency floors, the number of footstep crossing the floors can be sufficient for a steady state motion to occur and hence an increase in the vibration response [9]. The cut-off frequency above which resonant buildup of response is not significant can be taken as four times the expected maximum step frequency [10]. However, Živanovic and Pavic [11] suggested considering both low and high frequency components of response in some circumstances in order to gain a better response prediction. Study has also been made of factors affecting human response to floor vibrations and acceptance criteria for human comfort [12-16]. In this paper, observations from physical heel drop and walking tests performed on a fully furnished steel-concrete composite floor and an unfurnished post tensioned concrete floor are presented. Discussions are made on the effect of construction types and fit-out conditions on the measured modal properties and vibration response of the test floors. The paper also examines various finite element (FE) models for the floors in as-built conditions when tested and in other fit-out and live load conditions. 2 DESCRIPTION OF CASE STUDY FLOORS The framing layouts of the two case study floors are depicted in Figure 1 in which the test bays are shown shaded. Figure 1: Plan view of floor framing details The composite floor (case study floor 1) is composed of a 120 mm lightweight concrete slab supported on secondary beams spanning 12.7 m, which are in turn supported on primary beams spanning 8.7 m. The structural steel beams are I sections 610 mm deep. The floor is utilised as an

3 office whose tenants were complaining about the annoying footfall induced vibrations that they clearly perceived. The test floor bay has two long corridors which are perpendicular to each other as indicated by the arrows in Figure 1(a), and the distance from the intersection of these corridors to the closest work station is just about 1 m. The floor was fully furnished with demountable partitions, furniture, a suspended ceiling system below, and false floor panels above the concrete slab. The office fit out of the first case study floor can be seen in Figure 2(a). The second case study floor is comprised of 180 mm post tensioned concrete slabs formed on metal formwork and spanning 10.2 m between concrete band beams which are 2400 mm wide and mm deep. The floor was in an almost bare condition without fittings and services when tested, as depicted in Figure 2(b). Of the two test bays shaded in Figure 1(b), the Western bay was the main focus of the heel drop and walking measurements. Figure 2: Floor fit-out and heel drop testing 3 HEEL DROP TEST AND ESTIMATION OF MODAL PROPERTIES A standard heel drop impact is created by an 86-kg person rising onto their toes with their heels about 63 mm off the floor and suddenly dropping their heels to the floor [17]. It is common practice to perform output-only (i.e. unreferenced) heel drop tests where only the floor response is measured. A simple heel drop test which normally requires only one or a few measurement points can be used to provide a reasonable estimate of the natural frequencies and damping ratios of the floor. On the other hand, by allowing measurement of the heel impact force using load cells simultaneously with the floor response, an instrumented heel drop test would provide more robust estimates of the modal properties of the floor [18]. Figure 2 shows heel drop testing in progress on the two case study floors where heel impacts were applied at locations close to the centre of the test bays. Dytran seismic accelerometers of 5 V/g sensitivity were used to record the response at some test points around the centre of the forced bays. A notebook PC that controlled a National Instruments data acquisition system was used at the test site of the first case study floor, allowing real-time observation of the floor response. In the second case study floor, a Data Physics data acquisition system was utilised. A sampling rate of 128 Hz was used for both floors. Figures 3(a) and 4(a) show the frequency response spectrum averaged from a large number (> 20) of repeat heel drop tests performed on each floor. The sharp peaks in the response spectrum indicated a fundamental frequency of about 6.2 Hz and 7.6 Hz for the composite floor and prestressed concrete floor respectively. Another lively mode at 9.1 Hz for the second case study floor was also observed in Figure 4(a). As building floors are generally MDOF systems, it is likely that multi-mode responses of the test floors were captured. In order to estimate the damping ratio of an equivalent SDOF system corresponding to the fundamental mode, a one-third octave bandpass filter having the floor fundamental frequency as the central frequency was first applied to the measured acceleration time histories. The frequency limits used in this filtering were taken as Hz for the first case study floor (6.2 Hz) and Hz for the second one (7.6 Hz). Subsequently an analysis using the Random Decrement technique was performed to acquire an averaged acceleration time history for each floor as shown in Figures 3(b) and 4(b). Generally speaking, the Random Decrement method has the effect of eliminating the impulse response due to an initial velocity and the random response component, leaving the free-decay response due an

4 initial displacement only [19, 20]. The popular logarithmic decrement method [21] was then applied to these average response time histories to obtain the damping ratios. The equivalent viscous damping ratio corresponding to the fundamental mode was found to be 3.0% for the fully furnished composite floor and 1.1% for the bare prestressed concrete floor. Whilst the fundamental frequency of the concrete floor (7.6 Hz) is greater than that of the composite floor (6.2 Hz), both floors can be classified as lowfrequency floors with natural frequencies less than 9 10 Hz according to current floor vibration guidelines [22-24]. When evaluating the response of low-frequency floors to walking excitation, it is necessary to consider the possibility of the resonant condition which would occur when a harmonic of footstep frequencies matches a floor natural frequency. The modal damping of the fully furnished composite floor was found to be about 2.7 times that of the prestressed concrete floor in its bare condition. This would imply a considerable contribution from non-structural elements to the overall damping level of the furnished floor. Moreover, since there are fewer cracks in the prestressed concrete floor, this may have an effect of increasing floor stiffness on one hand, whilst simultaneously lowering the structural damping on the other. The measured damping of the test floors appears to compare well with current design guides that normally recommend a damping ratio of 2.0% 3.0% for furnished composite floors with typical fit-out [22-24] and 1.3% for bare floors of prestressed concrete construction [16]. Figure 3: Case study floor 1: response to heel drop Figure 4: Case study floor 2: response to heel drop 4 WALKING TEST A number of repeat walking tests were performed on each test floor by a person weighing about 80 kg walking along the walking paths indicated by the arrows shown in Figure 1. The selected walking paths were critical because they passed through the mid points of the investigated bays which were predicted by FE models to be the locations of large modal displacements. The test subject attempted to maintain his pacing rates in the range of approximately Hz and Hz for the first and second floors respectively. These step frequency ranges would ensure a relatively close match between the third and fourth harmonic of a footfall frequency with the fundamental frequency of the first floor (6.2 Hz) and second floor (7.6 Hz) correspondingly. The response time histories at some test points close to the centre of the floor bays of interest were recorded at a sampling rate of 128 Hz by Dytran seismic accelerometers with a sensitivity of 5 V/g. The same data acquisition systems were used as for the heel drop tests. High pass filtering with a cut-off frequency of about twice the fundamental frequency of the test floors (12 Hz and 15 Hz cut-off for the first and second floors respectively) was applied to the measured acceleration time histories. Figure 5 depicts typical filtered acceleration time traces with a peak acceleration of 0.61% g and 0.32% g obtained for the first and second floors correspondingly. The histograms of Figure 6 show the frequency of occurrence of peak acceleration ranges observed from a number of repeat walking tests. The peak acceleration measured on the first floor was found to exceed 0.5% g in most tests and

5 could reach a maximum of 0.67% g. The vibration level of the first floor can be considered to be unacceptable as 0.5% g is suggested to be the acceleration threshold for human comfort in an office environment [22]. Consequently, an innovative multi tuned mass damper system was then developed and installed on the first floor to mitigate the floor vibration to a tolerable level [25, 26]. On the other hand, vibration levels of the second floor were found to be only 60% of that of the first floor, with the maximum and average values of peak acceleration being 0.41% g and 0.28% g respectively. It should be noted that the walking force can be considered as a combination of multi harmonic components of footstep frequency and the dynamic load factor of walking decreases with increasing harmonic number [22-24]. Compared with the composite floor with steel beams (the first floor), the post tensioned floor with concrete band beams (the second floor) has higher fundamental frequency and would be more likely to experience resonant condition at the fourth harmonic of walking rather than the third harmonic. Another important factor that would influence the response levels of the two floors is the great disparity in their modal masses, as investigated in the following FE analyses. Figure 5: Typical response traces to walking Figure 6: Histogram of peak response to walking 5 FE ANALYSIS OF FLOORS IN AS- BUILT CONDITIONS WHEN TESTED FE models of the test floors were created in which the slabs and band beams were modelled by shell elements, and the steel beams by frame elements. The top faces of the slab and beam elements were placed on the same level using an offset technique, to better simulate the geometry and hence stiffness of the real floor systems. The concrete dynamic modulus of elasticity was taken as 1.35 times the nominal modulus of elasticity specified in structural standards, as per the AISC DG11 [22]. It should be noted that the first case study floor was constructed of 30 MPa lightweight concrete whilst 40 MPa normal-weight concrete was used in the second floor. Apart from the structural self weight and superimposed deal load, a representative live load of about 10% 20% of the nominal live load can be included to the mass source used in dynamic analysis, as suggested by current floor vibration design guides [22, 27]. The calibrated FE model of the fully furnished composite floor (case study floor 1) used a superimposed dead load of 1.2 kpa and representative live load of 0.5 kpa. For the FE model of the bare concrete floor (case study floor 2), an additional gravity load of 0.3 kpa was added to the structural self weight to approximate the total mass of the floor in its as-built condition when tested. FE modal analysis revealed a fundamental frequency of 6.22 and 7.53 Hz for the composite

6 floor and prestressed concrete floor respectively. The corresponding mode shapes of vibration are shown in Figure 7 with antinodes located around the centre area of the test bays. The modal mass associated with the fundamental mode of the prestressed concrete floor was found to be more than twice that of the composite floor (44500 kg versus kg). Although the prestressed concrete floor with band beams was in its bare condition when tested, its larger structural members resulted in its gravity load being about 1.4 times larger than that of the fully furnished composite floor (6.3 kpa versus 4.5 kpa). In order to estimate the floor response to walking, time history analysis was performed on the floor models in which the walking excitation was modelled as a concentrated force applied at the centre of the floor bays of interest. The walking force function F(t) had the form of a Fourier series: ( if t φ ) F( t) = P αi cos 2π p + i u (1) in which the walker s weight P was taken as 800 N; the dynamic load factor α i can be taken as 0.5, 0.2, 0.1 and 0.05 for the first, second, third and fourth harmonic components, respectively, of the footstep frequency f p [22]. Phase angles φ i can be taken as 0 for the first harmonic and π/2 for the others [28]. The floor mode shape value u corresponding to various footstep locations along the walking path was incorporated into the forcing function, to take into account the moving characteristic of the walking force. The measured damping ratios (3% for the furnished composite floor and 1.1% for the bare prestressed concrete floor) were used in the FE time history analysis. The worst case response at resonance can be estimated assuming a theoretical resonant pacing rate f p of 2.06 Hz for the first floor and 1.88 Hz for the second floor. The third harmonic of the 2.06 Hz pacing rate and the fourth harmonic of the 1.88 Hz pacing rate coincide with the FE-predicted fundamental frequency of the first and second case study floors respectively. Figure 8 shows the floor response obtained from time history analysis, from which a peak acceleration of 0.73% g and 0.43% g was found for the composite floor and prestressed concrete floor correspondingly. In other words, the response level of the bare concrete floor was predicted to be about 57% of that of the furnished composite floor. Some key analysis results for the two floors are summarised in Table 1 in which w is the gravity load (including structural self weight) used in dynamic analysis, ζ is the damping ratio measured from the heel drop tests; f n, m n and a p are the FEpredicted fundamental frequency, modal mass and peak acceleration, respectively. Table 1: FE results for test floors w (kpa) ζ (Hz) m n (kg) a p (g) Floor % % Floor % % Figure 7: Mode shapes most critical to test bays Figure 8: FE-predicted floor response at resonance f n

7 The natural frequencies and response levels obtained from the proposed FE models compare well with measurements. The modal masses, which were not measured using simple heel drop tests, can be estimated using the FE models. It can be inferred from the experimental findings and FE results that the higher modal mass, stiffness and frequency of the concrete floor with band beams would help lessen the vibration level, in spite of the bare concrete floor having lower damping than the fully furnished composite floor. 6 FE ANALYSIS OF FLOORS IN OTHER FIT-OUT AND LIVE LOAD LEVELS Although current guidelines suggest using a representative live load when evaluating the dynamic performance of floors, it would also be instructive to investigate the floors under their full live load condition. This is because the latter scenario would reduce the floor natural frequencies when increasing the modal masses. An additional FE model of the composite floor was analysed in which the live load was taken as 3.0 kpa, a typical live load value suggested for office floors. The likely effect of increasing floor occupants on the floor overall damping was not considered here. Other parameters including the floor stiffness, superimposed dead load, and damping value were assumed to be the same as those used earlier. Under the 3 kpa live load level, the total gravity load of the floor increased to 7.0 kpa, the fundamental frequency of the first floor decreased to 4.97 Hz and its corresponding modal mass increased to kg. The modal mass of the fully furnished composite floor with full live load condition is still much less than that of the second concrete floor in its bare condition. A time history analysis of the floor subjected to walking at a 1.66 Hz pacing rate, one third of the new fundamental frequency, predicted a peak acceleration of 0.52% g which still exceeds the acceptable limit of 0.5% g. As the resonant pacing rate of 1.66 Hz can be considered relatively slow, the floor response was also checked with another step frequency of 2.3 Hz for a fast walk [28]. It was found that this fast pacing rate did not increase the vibration level more than for the 1.66 Hz pacing rate. It in fact resulted in a peak floor acceleration of 0.33% g, lower than that due to the resonant slow walk. In general, for the first case study floor, the full live load scenario (3.0 kpa) was found to be less critical than the representative live load condition (0.5 kpa). Regarding the prestressed concrete floor, which was tested in its bare condition, two additional scenarios were investigated as summarised in Table 2. Scenario (i) is for the bare condition whilst scenarios (ii) and (iii) are for a furnished floor with 0.5 kpa live load and 3.0 kpa live load respectively. As can be seen, there was an increase in the total gravity load w and predicted modal mass m n, and a decrease in the predicted fundamental frequency f n when superimposed dead load and live load were included in the FE models. The damping ratio ζ of the furnished prestressed concrete floor can be expected to be in the range of %, depending upon the extent and nature of the fittings. Table 2: Floor 2: loading and modal properties Fit-out and live load levels (i) (ii) (iii) w (kpa) f n (Hz) m n (kg) % % % ζ (measured) (expected) (expected) A number of time history analyses were performed to evaluate the worst case response when a harmonic of walking if p matched the floor fundamental frequency f n. A damping ratio of 1.1% was used for analysis of the floor in its bare condition and 2% for the furnished condition, either with 0.5 kpa or 3 kpa live load. The critical step frequencies selected for the three live load scenarios (i)-(iii) were different because of the variation in the floor fundamental frequency. Figure 9 shows the resultant peak floor acceleration obtained for different resonant pacing rates which can be grouped into slow-to-normal walks (f p = Hz) and normal-to-fast walks (f p = Hz). Compared with the bare condition, there was a significant reduction in floor response in the furnished condition, under slow-to-normal pacing rates. Under quite fast pacing rates, however, the bare floor (i) and the furnished floor with 0.5 kpa live load (ii) appeared to have similar response levels. Moreover, the response level of the prestressed concrete floor can be further reduced when full live load was present instead of representative live load, similar to the composite floor case study. For all the investigated levels of damping and live load, the prestressed concrete floor was found to be considerably less lively than the composite floor.

8 Figure 9: Floor 2: predicted peak acceleration 7 CONCLUDING REMARKS This paper has highlighted the effect of construction type and fit-out on the modal properties and footfall response of two building floors. A number of physical heel drop and walking tests were performed to determine the fundamental frequency, damping ratio and acceleration response of the floors. Whilst higher damping was observed in the fully furnished composite floor, a noticeably lower response level was found in the prestressed concrete floor in its bare condition when tested. The modal masses were predicted using FE models which also validated the natural frequencies and response levels obtained from the experiments. Both the modal mass and stiffness of the prestressed concrete floor with band beams were greater than those of the composite floor. As the increase in mass was more than offset by the increase in stiffness, the fundamental frequency of the prestressed concrete floor was still higher than that of the composite floor. The dynamic behaviour of the case study floors under full live load condition was also evaluated using FE models by way of a sensitivity analysis. This analysis revealed that response predictions considering a representative live load would be more critical than when utilising the full live load. The measured and FE-predicted vibration levels were checked against vibration limits recommended for human comfort in office environments. The composite floor was found to be unacceptable whilst the prestressed concrete floor appeared to be acceptable in all fit-out and live load conditions. REFERENCES [1] Henin E. E.: Efficient precast/prestressed floor system for building construction. PhD thesis, University of Nebraska - Lincoln, [2] Reynolds P., Pavic A., and Waldron P.: Modal testing, FE analysis and FE model correlation of a 600 tonne post-tensioned concrete floor. In: 23rd International Seminar on Modal Analysis ISMA, , 1998 [3] Haritos N., Gad E. F., and Wilson J. L.: Evaluating the Dynamic Characteristics of Floor Systems using Dynamic Testing. In: ACAM2005 conference, Melbourne, Australia, , [4] E. E. Ungar. Damping of Panels. In L. L. Beranek, editor, Noise and Vibration Control, pages , McGraw-Hill, New York, [5] Murray T.: Design to prevent floor vibrations. Engineering Journal AISC, 1975(Third quarter):82-87, [6] Hewitt C., Murray T.: Office Fit-Out and Floor Vibrations. Modern Steel Construction, 2004(April):35-38, [7] Middleton C., Pavic, A.: The Dynamic Stiffening Effects of Non-Structural Partitions in Building Floors. In: 31st IMAC, A Conference on Structural Dynamics, Springer, , [8] Salyards K. A., Noss N. C.: Experimental Results from a Laboratory Test Program to Examine Human-Structure Interaction. In: 31st IMAC, A Conference on Structural Dynamics, Springer, , [9] Nguyen T. H., Gad E. F., Wilson J. L., and Haritos N.: Improving a current method for predicting walking-induced floor vibration. Steel and Composite Structures, 13(2): , [10] Willford M., Young P., and Field C.: Predicting footfall-induced vibration, Part 1. In: Proceedings of the Institution of Civil Engineers-Structures and Buildings, 160(2):65-72, [11] Živanovic S., Pavic A.: Probabilistic Modeling of Walking Excitation for Building Floors. Journal of Performance of Constructed Facilities, 23: , [12] Smith J.: Vibration of Structures: Applications in civil engineering design. Chapman & Hall, London & New York, 1988 [13] Pernica G., Allen D.: Floor vibration measurements in a shopping centre. Canadian Journal of Civil Engineering, 9(2): , [14] Wyatt T.: Design guide on the vibration of floors. SCI Publication 076, Steel Construction Institute Ascot, UK, 1989.

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