From: "Saved by Windows Internet Explorer 9" Subject: Latin American Journal of Solids and Structures - Dynamic response of low frequency Profiled Steel Sheet Dry Board with Concrete infill (PSSDBC) floor system under human walking load Date: Mon, 21 May 2012 17:29:19 +0800 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01CD3777.40C09050" X-MimeOLE: Produced By Microsoft MimeOLE V6.0.6002.18463 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01CD3777.40C09050 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252012000100002&lng=pt&nrm=iso =EF=BB=BF
ARTICLES
Dynamic = response of low=20 frequency Profiled Steel Sheet Dry Board with Concrete infill (PSSDBC) = floor=20 system under human walking load
Farhad Abbas Gandomkar*;=20 Wan Hamidon Wan Badaruzzaman; Siti Aminah Osman
Department of Civil & = Structural=20 Engineering, Universiti Kebangsaan Malaysia, Bangi, Selangor =E2=80=93 = Malaysia=20
=20
ABSTRACT
This paper investigates the = dynamic response=20 of a composite structural system known as Profiled Steel Sheet Dry Board = with=20 Concrete infill (PSSDBC) to evaluate its vibration serviceability under = human=20 walking load. For this point, thirteen (13) PSSDBC panels in the = category of Low=20 Frequency Floor (LFF) were developed using Finite Element Method (FEM). = The=20 natural frequencies and mode shapes of the studied panels were = determined based=20 on the developed finite element models. For more realistic evaluation on = dynamic=20 response of the panels, dynamic load models representing human walking = load were=20 considered based on their Fundamental Natural Frequency (FNF), and also = time and=20 space descriptions. The peak accelerations of the panels were determined = and=20 compared to the limiting value proposed by the standard code ISO 2631-2. = Effects=20 of changing thickness of the Profiled Steel Sheet (PSS), Dry Board (DB), = screw=20 spacing, grade of concrete, damping ratio, type of support, and floor = span on=20 the dynamic responses of the PSSDBC panels were assessed. Results = demonstrated=20 that although some factors reduced dynamic response of the PSSDBC system = under=20 human walking load, low frequency PSSDBC floor system could reach high = vibration=20 levels resulting in lack of comfortableness for users.
Keywords: structural = composite floor=20 system, profiled steel sheet dry board, vibration serviceability, human = walking=20 load, dynamic response, human comfort.
=20
1 INTRODUCTION
Serviceability in modern = structures=20 constructed by high strength and lightweight materials is the most = important=20 issue and should be considered in addition to the strength/safety = criteria [6,=20 12]. In case of evaluation of vibration serviceability, generally codes = and=20 standards present two approaches. First is static deflection caused by = nominal=20 live load which is commonly limited to SPAN/360 (A58, 1982) or between = SPAN/180=20 and SPAN/480 in different specifications (ACI 318-77, 1977 and AISC, = 1978), and=20 second is the minimum of DEPTH/SPAN for flexural members depending on = the end=20 restrains (ACI 318-77, 1977) [14]. Ellingwood and Tallin [14] stated = that=20 control of the static deflection is not sufficient to evaluate the = vibration=20 serviceability of floors.
On the other hand, Al-Foqaha et = al. [2]=20 reported a number of researchers (Onysko 1970, 1985, 1988; Polensek = 1970, 1971,=20 1975, 1988; Polensek et al. 1976; Allen 1974, 1990; Allen and Rainer = 1976; Allen=20 and Murray 1993; Murray 1979; Chui 1986; Smith and Chui 1988; = Ebrahimpour and=20 Sack 1989; Ohlsson 1988, 1991; Kalkert et al. 1993; Dolan et al. 1995, = Lenzen=20 1966; Wiss and Parmelee 1974, Filiatrault et al. 1990; Foschi et al. = 1995;=20 Kalkert et al. 1995) have declared that evaluation of the floor = vibration=20 serviceability may not be performed by control of the static deflection = such as=20 SPAN/360 [2]. Wood floor systems were studied based on the finite = element method=20 under dynamic loads induced by human activities. A series of design = curves=20 related to Root-Mean-Square (RMS) acceleration, mass, and FNF were = proposed and=20 compared with the experimental study which concluded in a close = agreement. It=20 was demonstrated that the vibration criteria based on static properties = or FNF=20 are not enough to prevent unwanted vibration of floors [2].
The International Standards = Organization (ISO=20 2631-2) [22] recommended an acceleration limit as a baseline in terms of = RMS for=20 various applications of floors, as illustrated in Fig.=20 1. This Standard proposed a criterion on the basis of the peak = acceleration=20 by multiplication of baseline with 10 for offices, 30 for shopping malls = and=20 indoor footbridges, and 100 for outdoor footbridges.
The American Institute of Steel and = Construction (AISC) [26] has proposed criteria for human comfort which = are the=20 same as the ISO Standard [22], as shown in Fig.=20 1.
Various authors have evaluated the = vibration=20 serviceability of floors under human activities through determination of = their=20 dynamic responses, analysis, and experiment from few years ago [24]. = Sandun de=20 Silva and Thambiratnam [10], da Silve et al. [8], da Silve et al. [9],=20 El-Dardiry and Ji [13], Williams and Waldron [37], Chen [6] determined = dynamic=20 responses of composite floors under human activities to assess their = vibration=20 serviceability. Ellingwood and Tallin [14] mathematically studied the = dynamic=20 response of floors under a pragmatic model instead of the pedestrian = dynamic=20 load. Experimental serviceability criteria were also reported to = minimise the=20 vibration of the floors. Smith and Chui [31] presented a usable method = for=20 designers based on a flow chart to evaluate the dynamic response of = lightweight=20 wood-joist floor by determination of natural frequency and RMS = acceleration of=20 the system under the heel-drop impact load. Howard and Hansen [21] = studied the=20 vibration analysis of waffle floors based on a mathematical method for = several=20 manufacturing buildings which was also verified by finite element and=20 experimental results. Foschi et al. [16] carried out an experimental and = analytical study on the vibration response of wood floors as a = lightweight panel=20 useful in residential and commercial buildings under impact load induced = by=20 users. Occupants were modelled by two simple oscillators, one degree of = freedom=20 and two degrees of freedom. Osborne and Ellis [28] presented a study on = a=20 long-span lightweight LFF (FNF lower than 10 Hz [25]) system by the = analysis of=20 various methods to evaluate the vibration acceptability of the system = through=20 obtaining FNF, damping ratio, and acceleration. Willford et al. [36] = reviewed=20 five methods to predict the response of structures under the footfall = load. The=20 study was performed in two parts; floor and bridge with the FNF lower = than 10=20 Hz, and also floor with the FNF above 10 Hz (HFF). Mello et al. [24] = also=20 studied dynamic analysis of a composite system made of concrete slab and = steel=20 beams. The research on acceptability of studied models was conducted = under four=20 types of dynamic loads which were represented by human walking load, = measurement=20 of peak acceleration of panels, and comparison with limit of codes. The = dynamic=20 response of the mentioned floors was investigated by using FEM as a = modern=20 computational tool for structural analysis.
The PSSDB is a lightweight = composite=20 structural system consisting of the PSS and DB attached together by=20 self-drilling and self-sapping screws, as shown in Fig.=20 2.
Study on using concrete as an = infill material=20 in the PSSDB system uncovered the performance of concrete on increasing = the=20 stiffness of the system [34]. The performance of using concrete in = trough of the=20 PSS of the PSSDB system was revealed experimentally to reduce its = response where=20 the panel is applied under human walking load [17].
It was reported that since the = PSSDB system is=20 slender and flexible in its nature, the natural frequency of the floor = system=20 may be low and becomes perceivable to users [39]. In addition, Gandomkar = et al.=20 [18] showed experimentally and numerically that in practical dimensions = of=20 floors, the FNF of the PSSDBC system is lower than the PSSDB system and = is in=20 the category of LFF. Therefore, the PSSDBC floor panels with usual spans = are=20 exposed to vibrations of human activities, because the FNF of a LFF is = close to=20 frequency range of human activities. Accordingly, a consistent dynamic = analysis=20 of the PSSDBC system with the practical span is advisable to evaluate = the=20 vibration serviceability of the system under human walking=20 activities.
This paper deals with the dynamic = response of=20 the low frequency PSSDBC floor system used as offices and residences = under human=20 walking load. Thirteen PSSDBC panels were considered to reveal effects = of=20 different parameters such as boundary conditions, damping ratio, = thicknesses of=20 the PSS and DB, screw spacing, grade of concrete, and floor span on the = dynamic=20 response of the system. Firstly, natural frequencies and vibration modes = of all=20 panels were obtained. Secondly, dynamic responses of the studied panels = were=20 determined in terms of peak acceleration and also compared to limiting = values=20 proposed by the ISO 2631-2 [22] to show their vibration acceptability.=20
2 HUMAN-INDUCED DYNAMIC=20 LOADS
Vibration of floors under human = rhythmic=20 activities is a very complex problem with respect to mathematical or = physical=20 characterisation of this phenomenon because the properties of dynamic = vibration=20 of these activities are interconnected to the individual body = adversities and=20 the ways which human performs a certain rhythmic activity [24]. A number = of=20 studies tried to evaluate the dynamic loads representing human = activities.=20 According to Mello et al. [24], the first pioneer in determination of = the forces=20 induced by human motion was Otto Fischer, a German mathematician, who = presented=20 his study in 1895. Also, Ohmart presented walking motion forces = graphically in=20 1968. Folz and Foschi [15] idealised the occupants on the floor as = lumped=20 parameter models which are components of discrete masses, springs, and = viscous=20 dashpots with two and eleven degrees of freedom. Racic et al. [29] = reviewed 271=20 references which deal with various experimental and analytical = characterisations=20 of human walking forces and their application in vibration = serviceability design=20 of civil engineering structures when subjected to pedestrian movement = such as=20 footbridges, floors, and staircases. Mello et al. [24] reported that=20 experimental studies were performed by Alves (1997) and Faisca (2003) on = two=20 kinds of concrete platforms; rigid and flexible, when a group of = volunteers=20 acted on them. The aim of their studies was a description of forces = induced by=20 human activities such as soccer and rock, aerobics, and = jumps.
In the current study, dynamic = responses of the=20 studied panels were determined under following four dynamic human = walking loads=20 [24] to evaluate their vibration acceptability.
2.1 First load model =
First load model which represents = people=20 walking is shown in Eq. (1).
Where:
P: individual's weight, = taken as=20 700-800 N;
=CE=B1i: dynamic=20 coefficient for the ith harmonic force component;
i: harmonic multiple of = the step=20 frequency;
fs: step = frequency;=20
t: time in seconds. =
In the first load model, only one = resonant=20 harmonic of the load was considered. The harmonic multiple of the step = frequency=20 was adopted from Tab.=20 1 which depends on the FNF of the panel. For example, if calculated = FNF of a=20 panel is equal to 7.326 Hz (Panel Number (PN) of 9 =3D PN9), according = to Tab.=20 1, only fourth harmonic of the walking loads with step frequency of=20 fs =3D 1.8315 Hz (4 =C3=97 1.8315 Hz =3D 7.326 Hz) = should be used in=20 Eq. (1) to determine the first applied load on the panel. Fig.=20 3 illustrates the first dynamic load model for the panel with FNF = equal to=20 7.326 Hz.
2.2 Second load model =
The second load model that = represents human=20 walking load is presented in Eq. (2).
Where:
P: person' weight; =
=CE=B1i: dynamic=20 coefficient for the harmonic force;
i: harmonic multiple = (i =3D 1,=20 2, 3,... , n);
fs: activity = step frequency=20 (dancing, jumping, aerobics or walking);
t: time;
=CE=A6i: harmonic=20 phase angle.
Unlike the previous load model, = this load was=20 composed of a static parcel and a combination of four time-dependent = repeated=20 loads presented by Fourier series. Four harmonics (see Tab.=20 1) were adopted to produce the second dynamic load model. = Considering a=20 panel the same as the discussed panel in the previous load model with = the FNF=20 equal to 7.326 Hz, the fourth harmonic with a step frequency of 1.8315 = Hz (4 =C3=97=20 1.8315 Hz =3D 7.326 Hz) was the walking load resonant harmonic. Tab.=20 1 shows the dynamic coefficients and phase angles for each harmonic = which =20 were used to produce second dynamic load model, as depicted in Fig.=20 4.
2.3 Third load model =
The mathematical function of the = third load=20 model which represents the human walking load is similar to the second = one,=20 presented in Eq. (2). Similar to the previous load model, the fourth = harmonic=20 with a step frequency of 1.8315 Hz was the resonant harmonic of human = walking=20 load (see Tab. = 1).=20 The third load model is more pragmatic than the last two kinds of the = load=20 models, as the position of this load is changed across the singular = location of=20 the floor system (see Fig.=20 5).
Study of some other parameters = related to the=20 step frequency such as step distance and speed of walking, presented in = Tab.=20 2, is necessary in this kind of load. Also, finite element mesh = should be=20 very refined in the third dynamic load model. The contact time of = application of=20 the dynamic load with floor was calculated from the step distance and = step=20 frequency (see Tab.=20 2).
In this load model, the subsequent = scheme was=20 followed: In a panel identical to the panel in the previous load models, = and=20 according to Tab. = 1, the=20 step frequency was equal to 1.8315 Hz when the fourth harmonic was as = the=20 resonant harmonic. Therefore, in accordance with Tab.=20 2, the step distance was equal to 0.666 m (see Fig.=20 5).
The step period which corresponds = with the step=20 distance of 0.666 m is equal to 1/f =3D 1/1.8315 =3D 0.546 s (see = Tab.=20 2). As it is shown in Fig.=20 5, four forces were considered representing one human step, which = each of=20 the forces as P1, P2, P3, and P4 was applied on the floor during = 0.546(contact=20 time)/3 =3D 0.18 s. The dynamic forces of P1, P2, P3, and P4 were not = applied=20 together at the same time. First, the load of P1 was applied on the = floor=20 according to Eq. (2) for 0.18s. At the end of this time period, the load = of P1=20 became zero and the load of P2 was applied for 0.18 s. The other loads = of the=20 first person step, P3 and P4, were applied in the same procedure = described=20 previously. After 0.546 s, the first person step finished and the second = person=20 step started and the load of P1 of the second step was equal to the load = of P4=20 in the first step. According to the mentioned method, the process = continued=20 repeatedly until all the dynamic forces applied along the considered = path (see=20 Fig.=20 12) of the floor.
2.4 Fourth load = model
The fourth dynamic load model = representing=20 human walking load is investigated with the same procedure considered in = the=20 third one. The principal difference between the third and fourth loads = was=20 consideration of the human heel effect in the fourth load which was = ignored in=20 the third load model. The human heel effect was uncovered to be an = effective=20 parameter on the increase of the load by comparing the third and fourth = load=20 models. According to Mello et al. [24], Varelo (2004) proposed the = mathematical=20 functions of the fourth load model as Eqs. (3)-(6).
Fm: maximum = Fourier series=20 value, given by Eq. (4);
fmi: heel-impact = factor;=20
Tp: step period; =
C1: coefficients = given by=20 Eq. (5);
C2: coefficients = given by=20 Eq. (6).
Mello et al. [24] reported that = Varela (2004)=20 and Ohlsson (1982) declared the impact factor varies person-to-person. = In this=20 study, impact factor was adopted equal to 1.12 (fmi = =3D 1.12=20 [24]). Fig.=20 6 shows the dynamic load model of a panel which presented in the = previous=20 load models with the FNF of 7.326 Hz based on Eqs. (3)-(6).
3 DAMPING
Damping of structures used in the = dynamic=20 analysis is the most difficult item to find. Damping is not an exclusive = physical phenomenon in structures dissimilar to mass and stiffness=20 characteristics of a structural system. Therefore, modelling of damping = in=20 structures is not accurate like mass and stiffness and its determination = is=20 entirely possible based on full-scale measurements [19, 23]. The damping = ratios=20 are usually measured from experience or adopted through suggested values = by=20 design guides and cannot be determined through analytical methods [25]. = Sandun=20 de Silva and Thambiratnam [10] had a wide discussion on damping ratios = suggested=20 by some authors such as Osborne and Ellis (1990), Wyatt (1989-SCI-076), = Hewitt=20 et al. (2004), Murray (2000), Elnimeiri and Lyengar (1989), Brownjohn = (2001),=20 and Sachse (2002) which were dependent on application of floors and kind = of=20 partitions built on them. Damping ratios of 1.6%, 3%, 6%, and 12% were = used for=20 a steel-deck composite floor system in their studies.
In order to obtain damping ratios = for floors,=20 applicable design guides present simple guidance which has been = summarised in Tab. = 3=20 [25]. It can be seen that the SCI-P076, SCI-P331, and the AISC [26] have = almost=20 the same values for damping, but according to Middleton and Brownjohn = [25], the=20 Canadian Standards Association (CSA) clearly presents overestimated = damping.=20
A new edition of SCI-P354 [30] = presents=20 critical damping ratios for various floor types which are very similar = to those=20 of SCI-P075 and SCI-P331 but with small differences in content, as = summarised in=20 Tab.=20 4.
Usually damping of the completely = bare floors=20 is not used because the bare floors are mostly utilised during the = construction=20 time and would not be used after the floors are occupied. Therefore, = damping of=20 bare floors is useful to reveal their dynamic response and to evaluate = their=20 vibration acceptability before the building is equipped [30].
Gandomkar et al. [18] estimated = damping ratios=20 of bare PSSDBC panels with such characteristics as: width and length of = 795 mm=20 and 2400 mm respectively, and thicknesses of 0.8 mm and 18 mm = respectively for=20 PSS and DB, 200 mm screw spacing, and concrete grade of 30 (C30) where = the=20 panels were located on pin-roller end supports. Damping ratios of 2.90%, = 1.52%,=20 0.83%, and 2.54% were found for the first four vibration modes,=20 respectively.
Osborne and Ellis (1990) stated = that although=20 damping in a floor system can be measured by simple heel impact tests, = various=20 limitations make mostly unknown an exact value for damping of a = steel-deck=20 composite floor. Similarly, according to Dolan et al. [11], Smith and = Chui=20 (1988) reported a wood floor as a component of sheathing and joist which = were=20 connected to each other by glue, had more different damping = characteristics than=20 the same floor where nails are used instead of glue. Therefore, used=20 construction techniques and workmanship in a floor are effective on its = damping=20 ratio.
In this study and in accordance = with the above=20 mentioned literature, the damping ratios were adopted as 1.1%, 3%, and = 4.5% for=20 the studied panels in order to consider different situations of the = floor during=20 the lifetime of its service (see Tab.=20 4).
4 STRUCTURAL MODEL =
Peva45 is available in the local = market by the=20 width of 795 mm and maximum length of 15 m. Also, maximum length and = width of=20 plywood are 2400 mm and 1200 mm, respectively. Therefore, to prepare the = PSSDB=20 panels with practical dimensions with sizes greater than the size of = Peva45 or=20 plywood, some pieces of Peva45 and plywood should be used together. In = the=20 current study, the panels were consisted of four (4) pieces of Peva45 = and eight=20 (8) pieces of plywood. Also, C30 was used in trough of Peva45 as an = infill=20 material. Fig. = 7=20 shows the section of the studied panels. The connection between the two = adjacent=20 Peva45 side by side panels (detail A) was represented by a typical lap = joint=20 idea as shown in Fig.=20 8. Wright and Evans [38] presented the connectivity characteristics = of such=20 joint. As can be seen in Fig.=20 8, nodes I(2) and J(2) are connected to nodes I(3) and J(3) = respectively,=20 assuming complete freedom in the longitudinal and rotational directions = whilst=20 assumed to have complete connection in the vertical and lateral = directions [38].=20
In this study, the PSSDBC control = panel=20 (PN1(see Tab. = 5))=20 adopted 0.8 mm thick Peva45 as PSS, 18 mm thick plywood as DB, DS-FH 432 = self-drilling and self-tapping screws at 200 mm screw spacing as the = connectors,=20 and C30 as an infill material in trough of Peva45. Thirteen (13) PSSDBC = panels=20 have been developed with various supports as shown in Fig.=20 9. The characteristics of these panels are summarised in Tab.=20 5.
The dynamic Young's modulus of = materials was=20 used herein. According to the AISC [26], the dynamic Young's modulus for = steel=20 can be chosen similar to its static value (BS 5950-Part4 [4]), i.e.=20 2.10=C3=97105 MPa for Peva45. Stalnaker and Harris [32] = stated that the=20 property of plywood is mostly isotropic because of its manufacturing = process.=20 Also, Ahmed [1] declared that although dry boards may be found as = isotropic or=20 orthotropic in the nature, they can be modelled as isotropic plates = without any=20 difficulties. Considering isotropic sheeting, the static Young's modulus = of=20 plywood which is available in the local market adopted as 7164 MPa [40] = in this=20 study. However, the dynamic value was chosen 10% greater than the static = value=20 according to Bos and Bos Casagrande [3].
In accordance with BS 8110 [5], = the static=20 Young's modulus of concrete was determined as 24597 MPa and 26567 MPa = for=20 concrete grades of 30 and 35, respectively. da Silva et al. [8] = discussed that=20 according to the AISC [26] in situations where the composite slab is = subjected=20 to dynamic excitations concrete becomes stiffer than the case when is = subjected=20 to pure static loads. This issue [26] suggests a 35% increase in the = dynamic=20 Young's modulus of the conventional concrete in comparison with the = static=20 Young's modulus. Therefore, dynamic modulus of elasticity as 33206 MPa = and 35865=20 MPa were adopted for concrete grades of 30 and 35, = respectively.
The stiffness of screws which are = connections=20 between Peva45 and plywood and also between Peva45 and concrete was = obtained by=20 push-out tests. The stiffness of shear connectors is needed in the = finite=20 element analysis. Nordin et al. [27] performed a study to identify the = stiffness=20 of screws between Peva45-Cemboard, Cemboard-Timber, and Peva45-Plywood. = It was=20 found that the shear connection stiffness between Peva45 and plywood was = 610=20 N/mm [27]. This value was represented instead of the connections between = I(1)=20 and J(1) respectively to I(2) and J(2) (Fig.=20 8). The connection between Peva45 and concrete as an infill in = trough of=20 Peva45 is also a partial interaction problem. Gandomkar et al. [18] = focused on=20 finding the connection stiffness between Peva45 and concrete with = different=20 grades of C25, C30, and C35 by push-out tests where covering was chosen = as=20 plywood. The shear stiffness of this connection was obtained as 386 = kN/mm and=20 417.60 kN/mm respectively for C30 and C35 where spacing between the = springs was=20 considered as 200 mm. The density of Peva45 and plywood was adopted as = 7850=20 kg/m3 and 600 kg/m3, respectively. Also, the = density of=20 concrete was determined as 2273 kg/m3 in the laboratory [18]. =
5 COMPUTATIONAL = MODEL
The FEM presents a more accurate = dynamic=20 response especially for structures with involved geometry. Using this = method is=20 increased because it can reduce the cost of computing functions [25]. = The=20 logical estimation on vibration of composite floors under walking load = is a=20 complicated work because of complexity in geometry of structures, = variety of=20 material properties in different structural components, and the nature = of=20 walking load as a continuous and transient load. It has been known that = using=20 FEM can cover and solve the mentioned tasks foremost [6]. Therefore, the = FEM was=20 used in this study to evaluate the dynamic response of the PSSDBC panels = under=20 the dynamic human walking load.
Developed finite element models = were simulated=20 by the use of refined mesh in the ANSYS program [33]. In the studied = system, the=20 PSS and DB were made of SHELL281 element as a suitable element for = analysing=20 thin to moderately-thick shell structures. In addition, the = self-drilling and=20 self-tapping screws were represented by COMBIN14 element as connection = between=20 Peva45 and plywood and also between concrete and Peva45. Moreover, = SOLID65=20 element was adopted for modelling of concrete in the computational = models.=20
For more clarification, Fig.=20 10 shows the procedure of modelling Peva45, concrete, and plywood in = the=20 simulation for one bay of the studied system. The connection between = elements of=20 Peva45 and concrete [20], plywood and concrete, and also Peva45 and = plywood in=20 the simulation is performed by using spring element (COMBIN14) in three=20 directions (X, Y, and Z). In this case and according to Fig.=20 10, nodes of D2 and D10 were respectively connected to nodes of P2 = and P10=20 which stiffness of springs was adopted as 610 N/mm [27] in X and Y = directions=20 (see section 4) and 105 N/mm in Z (vertical) direction (see = Fig.=20 10). Nodes of CT3, CB4, CB5, CB7, CB8, CT9, and D6 were connected to = nodes=20 of P3, P4, P5, P7, P8, P9, and CT6 respectively in the same procedure as = mentioned above with 1 N/mm [20] stiffness of springs for all directions = (X, Y,=20 and Z). Node of CM6 was connected to node of P6 by 386 KN/mm stiffness = of=20 springs in X and Y directions (see section 5) and 106 N/mm in = Z=20 direction, when C30 is used in the PSSDBC system.
6 DYNAMIC ANALYSIS OF THE = STUDIED=20 PANELS
To determine the dynamic responses = of the=20 PSSDBC composite panels, a linear time-domain analysis was performed = [7]. The=20 dynamic responses of the studied panels were obtained from a vast = parametric=20 analysis performed using finite element ANSYS program [33]. The results = were=20 natural frequencies, displacements, velocities, and accelerations. =
The main goal of this study was to = evaluate=20 vibration serviceability of the PSSDBC composite panels. For this = purpose, the=20 maximum acceleration of the panels was determined under the four dynamic = load=20 models described previously. Then, the obtained accelerations were = compared to=20 the proposed peak acceleration limit by the ISO [22].
6.1 Natural frequencies and = mode vibrations=20 of studied panels
Gandomkar et al. [18] conducted a = wide=20 experimental and numerical investigation on the natural frequencies of = the=20 PSSDBC system. The numerical study performed by FEM presented accurate = results=20 compared to the corresponding experimental results. In the current = study,=20 developed finite element models which were verified in the literature = [18] were=20 used to obtain the natural frequencies of the studied panels, as = tabulated in Tab.=20 6.
The results of Tab.=20 6 illustrate that increasing the thickness of plywood and Peva45 = decreased=20 and increased the FNF of the system, respectively. Therefore, it can be = seen=20 that the obtained results reveal the effect of the mass and stiffness of = Peva45=20 and plywood on the FNF of the system.
It was also shown that the decrease = of the=20 screw spacing enhances the FNF of the panel, because the panel will be = stiffer=20 [35].
The increase of the concrete grade = can improve=20 the FNF of the PSSDBC panel, but not significantly. Control of sliding = parallel=20 with the strong direction of the PSS and using four-sided support = instead of=20 two-sided support (perpendicular to the strong direction of the PSS) can = considerably increase the FNF of the system. It is clear that change in = the=20 panel span can also change the FNF of the panel. The FNF of the panels = had two=20 properties. First, all were smaller than 10 Hz; therefore, the category = of the=20 studied panels was LFF. Second, all were greater than 3 Hz, as a minimum = limitation of FNF for floors proposed by the SCI - P354 [30].
First six vibration modes of the = PN9 which=20 were obtained by the finite element model are illustrated in Fig.=20 11.
6.2 Peak acceleration of = studied panels=20
The peak accelerations of the = panels were=20 determined by the dynamic analysis of the developed finite element = models.=20 Person walking across the panel was considered in the third and fourth = dynamic=20 load models. Therefore, the paths of walking should be defined. The peak = accelerations of all models were determined for path 1 (see Fig.=20 12) under three different support models (see Fig.=20 9). Also, the peak accelerations of PN2, PN7, and PN10 were obtained = where=20 person used path 2 (see Fig.=20 12) for walking. Tab.=20 7 indicates the peak accelerations of the PSSDBC panels under the = four=20 previously described loads. This table also presents the limit of peak=20 acceleration recommended by the ISO 2631-2 [22] for residences and = offices (see=20 Fig. = 1).=20
According to Tab.=20 7, the peak accelerations of the studied panels were evaluated under = the=20 second load model which uncovered to be greater than those corresponding = evaluated peak accelerations under the first load model. This point = revealed=20 that considering four harmonics in the dynamic load is a very important = issue in=20 the dynamic responses of the floor and showed a significant effect on = the=20 increase of the peak acceleration. As it is obvious from Tab.=20 7, when the third and fourth load models were applied on the studied = panels,=20 the peak accelerations were higher than those of the applied first and = second=20 load models. This fact was highlighted when the position of the dynamic = load=20 changed across the individual direction, the dynamic response of the = panels=20 increased. Mello et al. [24] also focused on this point and stated that = this is=20 a substantial increase in the structure. The peak acceleration of the = panels=20 under the fourth load model was assessed higher than those under the = third load=20 model. On the other hand, the scheme of loading on the panels in the = third and=20 fourth load models was the same as each other. Therefore, this increase = should=20 be caused by the heel impact factor (fmi =3D 1.12) = used in the=20 fourth load model.
In accordance with the design = criteria=20 proposed by the ISO 2631-2 [22] and also based on the peak accelerations = of the=20 panels produced by the first load model, all the studied panels did not = have any=20 problems regarding the human comfort. By comparing the results of PN1, = PN8, and=20 PN9, an interaction was revealed between the dynamic load model with = different=20 parameters such as support conditions and dynamic characteristics of the = panels=20 which made an unknown phenomenon in the dynamic response of the panels. = It=20 should be noted that the harmonic of the resonant in PN1 was the third = harmonic;=20 therefore, the dynamic coefficient of the load is 0.1. However, the = fourth=20 harmonic is the resonant harmonic in PN8 and PN9, accordingly, the = dynamic=20 coefficient is 0.05. By investigation of the results of the second load = model,=20 all studied panels did not show any problems related to the human = comfort. On=20 the other hand, by comparing the peak accelerations of the dynamic = analysis of=20 the panels under the third and fourth load models and recommendations of = the ISO=20 2631-2 [22], it was uncovered that all panels were not comfortable for = human=20 under these loads.
The results on the path 1 also = demonstrated=20 that change of the characteristics of the PSSDBC system changes its = dynamic=20 response. By the increase of the thickness of plywood from 18 mm to 25 = mm and=20 Peva45 from 0.8 mm to 1.0 mm, peak accelerations of the four load models = were=20 decreased by an average value of 11.52% and 17.06%, respectively. = Furthermore,=20 the reduction of the screw spacing from 200 mm to 100 mm decreased the = peak=20 acceleration of the four load models by an average value of 7.35%. The = grade of=20 concrete did not have a considerable effect on the dynamic response of = the=20 PSSDBC panel, as by changing C30 to C35 the peak acceleration of the = panel only=20 reduced by 2.98%. The results also indicated that change of the damping = ratios=20 from 1.1% to 3% and 4.5% can respectively decrease the peak = accelerations of the=20 PSSDBC panels by 14.94% and 26.38% for the panel with the support type = of I (see=20 Tab. = 5=20 and Fig.=20 9) and respectively 13.63% and 24.36% for that with the support type = of III=20 (see Tab.=20 5 and Fig.=20 9). By comparing PN1 with PN12 and PN13 it was shown that the length = of the=20 panels had a direct effect on the peak acceleration of the panels, where = the=20 response enhanced and reduced respectively for the increase and decrease = of the=20 length of panels for all four load models. However, these results are = not=20 addressable, as according to results of Ref. 24, the peak accelerations = are not=20 attributed to the length of the panels.
By comparing results of PN1 and = PN8, it is=20 obvious that control of sliding in support decreased the peak = acceleration of=20 the panel for the first load model. It may be due to the significant = increase of=20 the FNF of the panel, therefore, the dynamic coefficient changed from = 0.1 to=20 0.05. On the other hand, as stated in the first load model only one = harmonic=20 considered depending on the FNF, the dynamic load applied on PN1 was = higher than=20 that on PN8. According to the results illustrated in Tab.=20 7, the mentioned issue was not shown to be effective when four = harmonics=20 considered in the dynamic load models (load models of II, III, and IV), = even for=20 PN9. The reason was about the complexity in the dynamic responses of the = panels=20 under interaction between supports and other substantial characteristics = of=20 structures.
Comparing peak accelerations of = path 1 and=20 path 2 in the panels shows different phenomena. The response of path 1 = was=20 greater than that of path 2 when only two sides of panels were = supported. On the=20 other hand, the response of path 2 was greater than that of path 1 when = all four=20 sides of panels were supported. The panels were not also comfortable for = users,=20 where walking performed across path 2.
7 FINAL REMARKS
This paper investigated the = dynamic response=20 of the PSSDBC low frequency floor panels under human walking load to = evaluate=20 the vibration serviceability of the system. Four dynamic load models = were used=20 while the third and fourth load models were more pragmatic having two=20 properties; changing load according to the individual position, and = generating=20 time function corresponding to the nature of human walking load. The = effect of=20 human heel impact was also considered in the fourth load model. =
The dynamic responses of the = studied PSSDBC=20 panels were obtained in terms of the peak acceleration and compared to = the=20 proposed limiting value by the ISO 2631-2 [22] where the panels used as=20 residences and offices. The studied panels were showed to be comfortable = when=20 the first and second dynamic load models applied on them. The position = of loads=20 was changed across the individual directions when the third and fourth = dynamic=20 load models applied on the panels. For these two types of loads, two = paths were=20 selected to show the effect of direction of walking on the response of = the=20 panels. The peak accelerations of the studied panels under the third and = fourth=20 dynamic load models were determined higher than those of the first and = second=20 loads and also limiting value of the ISO 2631-2 [22]. Therefore, all = panels were=20 uncomfortable for users when the third and fourth load models applied on = them.=20 These results uncovered the fact that changing the position of the load = is an=20 effective item in the increase of the response of the panels. =
Increasing the thickness of the = PSS and DB and=20 decreasing screw spacing significantly reduced the peak acceleration of = the=20 system. However, change of the concrete grade did not show a pronounced = effect=20 on changing the response of the PSSDBC system. Enhancement of the = damping ratio=20 of the PSSDBC system can considerably reduce the peak acceleration of = the=20 system. These results can be useful to help designers reduce the = response of the=20 floor by furniture and types of partitions (see Tab.=20 4).
The increase and decrease of the = length of the=20 studied panels enhanced and reduced the peak acceleration of the panels, = respectively.
Acknowledgment Authors = extremely=20 appreciate the help of Mr. Alireza Bahrami, who contributed in some = parts of=20 this study.
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Received 10 May 2011;
In =
revised form=20
03 Jan 2012
*=20 Author email: farhad.abbas.gandomkar@g= mail.com=20
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