dynamic property analysis and development of composite

International Journal of the Physical Sciences Vol. 6(34), pp. 7669 - 7693, 16 December, 2011 Available online at http://www.academicjournals.org/IJPS DOI: 10.5897/IJPS11.676 ISSN 1992 - 1950 ©2011 Academic Journals

Review

Dynamic property analysis and development of composite concrete floor (CCF) and vibration

serviceability: A review

Sinin Hamdan1, Mohammad Nurul Hoque1* and Norsuzailina bt Mohamed Sutan2

1Department of Mechanical and Manufacturing Engineering, University Malaysia Sarawak 94300,

Kota Samarahan, Sarawak, Malaysia. 2Department of Civil Engineering, University Malaysia Sarawak 94300, Kota Samarahan, Sarawak, Malaysia.

Accepted 26 July, 2011

This review article concerns floor vibration, describes the nature of floor vibration and provides options for avoiding it through design, or in the case of existing buildings, reducing or eliminating it through alterations. Excessive floor vibration has become a greater problem as new rhythmic activities, such as aerobics, generators, air conditioners and long-span floor structures have become more common. The current push towards stronger concrete materials and the use of prestressing is resulting in increasing fineness and dynamism of long-span concrete floors in buildings. Although concrete floors have a good vibration serviceability track record, this trend may lead to an increasing number of floors failing their vibration serviceability. There is a current trend towards ever more slender concrete floor structures, which is resulting in more frequent problems with their vibration serviceability. Predictive methods for vibration serviceability must consider not only the structures themselves, but also the non-structural elements which are attached to them, as these may have a significant effect on the dynamic characteristics of the floor structural system. As there has been very little past research in this area, this article describes an investigation into the effects of raised access floors on the vibration serviceability of long-span concrete floors. The development of a new modal testing facility based on electrodynamics shaker excitation, which was capable of producing high quality estimates of the modal properties of full-scale floor structures, is described. This was subsequently utilized to determine the modal properties of three full-scale floor structures, first concrete floor, secondly concrete floor with profiles steel sheet (PSS) and finally concrete floor with PSS and vibration damping compound (VDC) before and after the installation of various configurations of raised access floors. The vibration damping compound (VDC) is used on composite concrete floor (CCF) for getting special performance from floor because vibration damping compound is a water based co-polymer emulsion, with mineral fillers dispersed in a low permeable, polymeric binder. It is solvent free, easy to apply and can be used in most interior and semi-exposed areas. It is designed to reduce noise by damping resonant vibration caused by continuous or impulsive excitation of the substrate to which it is applied. The response of these structures to controlled pedestrian excitation was also measured. Realistic finite element models of all structures were developed and updated using the results from the experimental work. These were subsequently utilized for investigation of the experimentally measured effects of the raised access floors. Reductions in natural frequencies due to the increased mass were, to some extent, offset by the slight increases in stiffness following the installation of the access floors. Modal damping ratios increased for some modes of vibration, but these changes were rather unpredictable: hence they were too unreliable to be used in design. The response of the structures under controlled pedestrian and other excitation was reduced following the installation of various configurations of raised access floors. The reduction appeared to be greater for relatively long access floors (2000 mm) than for relatively width access floors (1200 mm) and height (54 mm). Therefore, it is recommended that the effects of access floors may be included in vibration serviceability analyses by applying a reduction factor to predicted responses calculated by assuming a bare floor. Key words: Rhythmic activities, long-span concrete floor vibration serviceability, profiled steel sheet (PSS), vibration damping compound (VDC), human-induced excitation, natural frequency, whole-body vibration.

7670 Int. J. Phys. Sci. HISTORY OF VIBRATION SERVICEABILITY PROBLEM IN FLOORS Perceptible vibrations annoying the floor occupants, dysfunctional equipment sensitive to vibrations and localised damage are manifestations of the lack of the floor vibration serviceability (Hughes, 1971). There is a long-standing awareness of problems with the vibration serviceability of floors and references to the problem may be found in the literature as far back as the early 19th century. In 1828 Thomas Tredgold, one of the founders of the Institution of Civil Engineers, wrote (Allen and Rainer, 1975): “Girders should always, for long bearings, be made as deep as they can be got; an inch or two taken from the height of a room is of little consequence compared with a ceiling disfigured with cracks, besides the inconvenience of not being able to move on the floor without shaking everything in the room.” In the past, a number of composite steel-concrete and timber floors were found to be too lively under normal everyday dynamic excitations, although they were strong enough and did not deflect excessively. Following complaints by their users, the floors were tested and failed the vibration serviceability design criterion (Murray, 1981; Bachmann et al., 1991a; 1995a). Although not uniquely formulated, this criterion has emerged as a general design require-ment in practically all modern building codes based on limit state design principles. EARLY RESEARCH INTO VIBRATION SERVICEABILITY OF COMPOSITE FLOORS Most of the knowledge about vibration performance of suspended floors in buildings has been gained during this century. However, evidence that floor vibrations were an issue even in the last century exists. Hyde and Lintern (1929) reported that there had been a considerable concern about the damage to roads and buildings due to external vibrations caused by the growing transportation systems. According to them, the problem was not new as in 1901; H. R. A. Mallock had experimentally investigated vibrations caused by the Central London Railway. Prompted by numerous complaints, Mallock investigated the effects of vibration due to passing trains on houses near Hyde Park. One of the first coherent attempts to research the vibration serviceability of floors was performed at the University of Kansas (Lenzen, 1962; Lenzen and Murray, 1969). The work was initiated in *Corresponding author. E-mail: [email protected].

Abbreviations: CCF, Composite concrete floor; PSS, profiles steel sheet; VDC, vibration damping compound; CCF, composite concrete floor; SDOF, single degree of freedom; SCI, Steel Construction Institute; dof, degree-of-freedom; FRF, frequency response function.

1958 by the Steel Joist Institute in the USA which was increasingly concerned with the increase in occurrence of annoying vibrations in composite steel joist - concrete slab floors. This was a direct result of the design of more efficient structural sections possessing adequate static strength, but which were much more lightweight. This research program lasted more than ten years. It included studies into the human perceptibility of vibrations, the development of analytical models of the floors and the development of a design guide. These will be briefly discussed. Human perceptibility of vibrations One of the first papers dealing with the forces caused by human walking was published by Harper (1962). The research described was not related to vibrations of floors but to the abrasion and slipperiness of floor surfaces. For these, the exact level of vertical and horizontal forces transmitted from a foot to the floor surface is of crucial importance. The reported force versus time measure-ments involved several human subjects. All of the traces clearly resemble the characteristic „two peak‟ forcing pattern (Figures 1 and 2) observed by many researchers afterwards (Bachmann et al., 1991a; 1995a). These time-varying force fluctuations are caused by inertial forces developed through the acceleration and deceleration of a human body which rises and falls during walking.

Lenzen (1962) stated that only transient vibrations were a problem for vibration serviceability of floors under human-induced excitation and only if insufficient damping was present to eliminate the vibration within a few cycles of the application of the transient load. In other words, the duration of the vibrations was important. However, at that time, the only existing research into the human perceptibility of vibrations was that which only considered the effects of steady-state vibrations, such as that performed by Reiher and Meister (Wright and Green, 1959) (Figure 3) which had produced perceptibility curves similar to those shown in (Figure 4). Following a number of tests on human perception of vibrations of composite floors, Lenzen (1966) proposed that the Reiher and Meister curves should be scaled by a factor of 10 to take account the transient nature of vibrations caused by impact type loads. This has come to be known as the “Modified Reiher-Meister Scale”. Wheeler (1980; 1982) also investigated pedestrian-induced vibrations in footbridges. After compiling the work of others, he entailed an excellent description of the excitation caused by six different modes of human movements: (1) slow walk, (2) normal walk, (3) brisk walk, (4) fast walk, (5) slow jog, and (6) running. These forcing functions are shown in Figure 2. The speed of walking was determined to be between 0.75 m/s (slow walk) to 1.75 m/s (fast walk).

Hamdan et al. 7671

Figure 1. Typical forcing patterns for running and walking after Galbraith and Barton (1970).

Figure 2. Detailed forcing patterns for various modes of walking, jogging and running after

Wheeler (1982).

Frequency (Hz)

Dis

pla

cem

en

t (”

)

Figure 3. Reiher and Meister scale.

7672 Int. J. Phys. Sci.

Frequency (Hz)

30

0 I”

Dis

pla

cem

ent –

Inch

es

4

8 E

I

Figure 4. Modified Reiher and Meister criteria after

Lenzen (1966).

Analytical models of composite floors To produce design guidelines that could be used by design practitioners, the researchers in Kansas developed formulae that considered the floor to be a single degree of freedom (SDOF) system considering only the fundamental mode of vibration. The stiffness was calculated using simple beam assumptions. Lenzen (1966) stated that: “a more exact method for computing the natural frequency of the floor system was derived in which the stiffness of the slab perpendicular to the joist could be taken into account. Since this refinement made the computations cumbersome, it was not used.” These types of simplifications have persisted ever since this early work and, as will be shown later in this article, have led to many oversimplified guidelines suitable for hand calculation of vibration response of floors.

Development of a design procedure for composite floor vibrations

The ultimate aim of the research at Kansas University was to develop a checking procedure that could readily be used at the design stage to prevent excessive floor vibrations. In order to do this, a simplified forcing function for which the response of the floor could be calculated was required, in addition to the simplified analytical floor system. This aim resulted in the heel-drop test, first mentioned in the literature by Lenzen and Murray (1969). The test is performed by “having a person of average weight with soft-soled shoes rise up on his toes and drop on his heels near the location of the measurement (of the

Time (ms)

Forc

e (

lb)

Figure 5. Idealised Heel-drop forcing function after

Lenzen and Murray (1969).

response)” (CSA, 1989). This was a simple means of applying a more or less standard form of excitation to a real structure, which could be easily simulated analytically using a triangular forcing function (Figure 5). The response to this forcing function was then assumed to be related to the response of the structure to normal walking excitation. The measured or calculated frequen-cies, peak responses and damping values could then be checked against corresponding criteria (Figure 6).

Khan and Williams (1995) published the already mentioned excellent textbook, the first of its kind, describing the state-of-the-art in the design and construction of PT concrete floors. They offered an algorithm, shown in Figure 7, of the steps which are typically performed when designing a post Tensioned (PT) floor in practice. Whereas, the control of cracking is indirectly incorporated in the check of initial and final concrete stresses, and the check of deflections is explicitly shown, the algorithm does not offer a stage in the design when a vibration serviceability check(s) should be performed. Although the textbook contains a discussion of the vibration serviceability problem, clearly indicating that the authors did not neglect it, this omission illustrates that the whole issue is, somehow, a „grey area‟ which practitioners still hesitate to include in everyday design.

The crucial problem in the design stage of in-situ PT concrete floors is how to create a reliable model to perform such vibration serviceability checks. These floors have some unique structural properties which are difficult to model following the procedures which have been established through combined experimental and analytical

Hamdan et al. 7673

Frequency (Hz)

Pe

ak a

cce

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tio

n a

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g

Figure 6. Annoyance criteria for floor vibration after CSA (1989).

research of other types of floors, such as composite steel-concrete or timber floors.

Appendix G of the Canadian standard CSA-S16.1-1974 “Steel Structures for Buildings - Limit States Design” (CSA, 1974) was based upon the research performed at the University of Kansas. Although originally intended to serve as an interim measure (Allen and Rainer, 1976), these guidelines have essentially persisted up to the present day and were still included in the latest revision of the code in 2001. Limitations of the Canadian Standard Association (CSA) guidelines Although widely used and reasonably successful for the design and assessment of composite floors, the CSA guidelines contain a number of limitations. Firstly, the analytical models recommended are based upon the assumption of an SDOF system. As a result, only the fundamental mode of vibration is assumed to contribute to the response of the floor. In reality, higher modes of vibration may also contribute significantly to the response of the floor, and for many forms of floor construction, these higher modes will have frequencies close to that of the fundamental (closely spaced modes of vibration). This limitation was recognized by some of the developers

of the guidelines (Allen and Swallow, 1975), although nothing was proposed to remedy this problem at the time. The „damping ratio‟ used by these guidelines was normally calculated by using the logarithmic decrement of the floor response, which is only theoretically valid for an SDOF system.

This has been a source of great confusion with a very wide variety of damping values being suggested in the existing literature. Commonly quoted damping values of up to 14% for a composite floor with partitions and furniture (Allen, 1974) are now understood to be highly in error, and cannot be taken to represent „modal damping ratios‟ of which they were meant to be (Wyatt, 1989). Realistic modal damping ratios are important as they can be used in frequency and time domain FE analyses for prediction of the response of MDOF systems. The CSA guidelines are only applicable to the particular form of construction for which they were developed, that is, lightweight composite steel-concrete floors (Williams and Waldron, 1994). For other forms of floor construction, such as the typically heavier long-span reinforced or post-tensioned concrete floors considered in this article, the guidelines are simply not suitable. This is because the CSA guidelines related the response measured due to a transient event (that is, a heel-drop) to the likely response of a floor to continuous excitation (that is, walking). Such procedure is only likely to be valid for


Figure 7. The design procedure for PT concrete floors after Khan and Williams (1995).

structures of similar mass and stiffness characteristics. Further research into the vibrations of composite steel-concrete floors North American Research Following the CSA Guidelines Murray (1981) presented the results of heel-drop tests

performed on 91 composite floors which had been rated subjectively as either acceptable or unacceptable. He compared these results with the results of the application of a number of guidelines which were current at that time. He concluded that none of the previous guidelines were reliable and therefore presented yet another empirical formula, which calculated a required amount of damping as a function of natural frequency and peak response. If in the finished structural system this amount of damping was provided, the floor was deemed to be satisfactory.

Hamdan et al. 7675

Figure 8. Overestimation of damping, when using the half-power bandwidth method of estimating

damping for structure with close modes.

However, this guideline was once again based on high damping values estimated from heel-drop tests and its scope of application was limited to composite steel joist-concrete slab floors. It was also limited in that the values for fundamental natural frequency and peak amplitude were assumed to be determined from simple-beam formulae, and no account was taken of higher modes of vibration. Nevertheless, Murray was still advocating its use as late as 1988. Rainer and Pernica (1981) published a paper in which they examined various methods of determining modal damping ratios. In addition to examining damping values estimated from heel impact tests, they performed various shaker tests and calculated damping from the linear spectra of the responses. They concluded that the heel impact test tended to overestimate values of modal damping ratios, probably the first time ever that this problem had been noted by the civil engineering community. However, the calculation of damping from the shaker tests was performed using the „half power bandwidth method‟, which was also likely to be unreliable. This is because it is only theoretically valid for an SDOF system and an overestimation of damping from these tests thus may occur (Figure 8).

The final observation from this work is that there was a very large degree of scatter in the measured values of damping, which is an indication of the fact that damping is a very difficult quantity to measure reliably. An interesting paper by Rainer and Swallow (1986) described a method by which the modal properties (natural frequencies, mode shapes and modal damping ratios) of a structure were obtained from tests using two

shakers. This was, in fact, a testing technique known as operating deflection shapes (ODS) analysis, which is described in more detail in the course of this work. Unfortunately, the values of damping estimated from these tests were again possibly to be inaccurate since they utilized the SDOF half power bandwidth method. An indication of this is apparent through inspection of the damping values corresponding to the various modes of vibration, in which it can be seen that higher damping values were obtained for close modes than for well separated modes. Steel Construction Institute (SCI) Publication 076: Design guide on the vibration of floors In 1989, a Steel Construction Institute (SCI) design guide (Wyatt, 1989) was published. It was primarily aimed at composite floors in offices subjected to pedestrian loading. External forms of excitation, such as traffic, and excitation due to out-of-balance rotating machinery were explicitly excluded from these guidelines. Various methods of calculating natural frequencies were presented and the presence of closely spaced modes of vibration noted. Four methods of computing the fundamental natural frequency of the floor were outlined. These ranged in complexity from estimating the stiffness of the floor using the static deflection at mid-span, to the use of a dynamic analysis computer program (possibly even FE analysis). For assessment of the floor response, two methods were proposed depending on whether the

7676 Int. J. Phys. Sci. floor was classed as a „low frequency floor‟ (fundamental natural frequency lower than 7 Hz) or a „high frequency floor‟ (fundamental natural frequency greater than 7 Hz). The low frequency response was assumed to be mostly due to resonance, and the high frequency response was assumed to be due to a series of impulsive heel impacts, each considered as separate transient events. The suggested damping values of up to 4.5% of critical (for a floor with partitions) were lower than those specified in previous literature, but they are now still considered to be higher than appropriate (ISO, 1992 and the latest version of ISO). Further North American Research in the 1990s and 2000s In the 1990s, there was a general acceptance that walking is a periodic function and that low frequency floors could be excited in resonance by multiples (harmonics) of the pedestrian pacing rate (walking frequency). The already discussed SCI guidelines had presented a means of considering this phenomenon. However, new guidelines were subsequently developed by Allen and Murray which considered the resonance condition. Allen (1990) outlined two modeling techniques for floors subjected to rhythmic loading based upon either an SDOF model or a simple beam model (first mode only). He maintained that: “there are many modes, but for practical problems where resonance is involved, this assumption (fundamental mode only) is generally close enough”. However, more recent research has shown that this is not necessarily true (Eriksson, 1994; Pavic, 1999). Murray and Allen proposed a new criterion in 1993 which was based on acceleration limits from ISO 10137 (ISO, 1992), a time domain loading function based on four harmonics of the pacing frequency, and a response function (structural model) based on the fundamental mode of vibration only. In two papers from the same year (Allen and Murray, 1993; Murray and Allen, 1993), they acknowledged that resonance of long span floors could occur due to walking excitation. The overestimation of damping ratios from heel impact tests was also acknowledged and the authors suggested, in a rather arbitrary manner, that modal damping ratios for calculation of response should be approximately half of those estimated from heel impact tests. Evans (2008) outlined nanotechnology research facility on vibration and noise control design. A nanotechnology research facility was proposed on a large university campus. The facility would incorporate research laboratories and support spaces, clean rooms, faculty and research offices with conference spaces, core and building system spaces. In many circumstances, the vibration amplitude is too low to be harvested efficiently. Hence, researchers have been seeking ways to improve the energy harvesting rate by both mechanical and electrical approaches. A type of

dual-mass vibration energy harvester, where two masses are connected in series with the energy transducer and spring, is proposed and analyzed in this article and the dual-mass vibration energy harvester is proved to be able to harvest more energy than the traditional single degree-of-freedom (dof) one when subjected to harmonic force or base displacement excitations (Xiudong and Lei, 2011; Ma et al., 2010). Vibrations of long-span reinforced and post-tensioned concrete floors There are two general types of floors in buildings: (1) suspended floors, which are supported by other building elements such as beams, columns or walls, and (2) ground floors, also known as slabs on grade, made of concrete and whose surface is supported directly by the ground. Suspended floors are normally considered to be a constitutive part of a building structure, frequently termed the building frame. Excitation induced by walking which causes vibration serviceability problems is in principle an issue only in the case of suspended floors in which annoying vertical vibrations can be developed through bending. Composite floors are made of pre-manufactured concrete, steel or timber elements acting compositely with the concrete slab (or „topping‟) which forms the floor surface. Such forms of construction are typically supported by a system of beams and a building frame which is made of concrete, steel or timber. Floors made entirely of steel, timber or other non-concrete materials do exist, but they are not widely utilised in modern building developments (Pavic, 1999). Historically reinforced concrete floor structures have not been a problem as far as vibration serviceability is concerned, due to a much greater mass and stiffness than their composite counterparts. However, through the use of technologies such as high strength concrete and prestressing, these types of structures are becoming even more slender as designers strive for increased spans and reduced slab thickness (Eriksson, 1994; Pavic, 1999). As a result, problems with the vibration serviceability of such structures may be expected.

Therefore, it is becoming necessary for the designers of such structures to consider vibration serviceability at the design stage. Dynamic behavior of long-span concrete floors Apart from classical textbooks on statics and dynamics of plate systems (Szilard, 1974), a number of papers specifically cover dynamic characteristics of building floors made of concrete. They are typically related to subjects other than problems of human induced and perceived vibrations, such as the isolation of vibrating machinery. Petyt and Mirza (1972) used FE modelling

and performed a parametric study of natural frequencies and mode shapes of column-supported floor slabs (that is, flat plates). Their work was inspired by the increasing need from the construction industry where solid flat slabs made of concrete were becoming popular. In the case of a single floor panel, which was pin-supported at all four corners, the first five natural frequencies, experimentally measured using a small model in a laboratory, were compared with their analytically calculated counterparts. An excellent comparison was obtained justifying the use of the FE technique. However, Petyt and Mirza commented: “… in building construction, if the slab and columns are cast in situ, the joint may be regarded as rigid. Even in the construction of prefabricated panel systems, certain bending rigidity may be introduced if the joints are welded or when additional reinforcement is used and gaps are filled in situ.” When considering pedestrian excitation, vibration problems in long-span concrete floors are more likely to be caused by excitation of resonance than by impulsive excitation caused by individual footfalls (Eriksson, 1994; Wyatt, 1989). Long-span concrete floors typically have greater mass than their composite counterparts, resulting in typically lower natural frequencies (Eriksson, 1994). As such, they are frequently classed as 'low-frequency floors'. Nevertheless, the lack of problems in the past with the vibration serviceability of long span concrete floors has led to a corresponding lack of research interest in the field. Consequently, many of the guidelines which have been reviewed in this article have been aimed at composite floors and therefore have limited applicability to long-span concrete floors. However, two notable works into the vibration of long-span concrete floors are mentioned here. Firstly, in his doctoral thesis, Khan (1996) investigated the reliability of various analytical methods for prediction of the fundamental natural frequencies of floors by comparing the analytical predictions with values obtained from testing. This work was performed with the assumption that controlling the fundamental natural frequency of a floor is the “best way” to ensure satisfactory vibration serviceability performance. This method is questionable. It is now widely recognized (Khan and Williams, 1995; Bachmann et al., 1995; Eriksson, 1996) that vibration serviceability should be accessed through examination of vibration response and that controlling the fundamental natural frequency may result in uneconomic designs for relatively heavy long-span modern concrete floors. This is particularly so when the floors are prestressed. Another observation regarding this thesis is the extremely poor quality of the modal test results. The magnitude and phase of a typical frequency response function measure-ment presented by Khan (1996) is shown in Figure 9.

It is difficult to understand how the reported fundamental frequency of 4.6 Hz and damping ratio of 3.4% were estimated from this measurement and others like it. The second study was conducted by Pavic (1999)

Hamdan et al. 7677 carried out modal testing, FE analysis and FE model correlation and updating of a number of long-span reinforced and prestressed floors. Through these processes, he identified a number of parameters which significantly affect the vibration behavior of prestressed floors which are currently not considered carefully enough in normal civil engineering practice. Probably the most important observation was that in-situ cast columns, which are rigidly connected to the floor which they support, significantly increase the bending stiffness of the floor. This is contrary to normal design practice (Concrete Society, 1994) in which such supports is commonly considered as pin supports. Da Silva (2008) recently pointed out that “some experimental evidence should be considered in the analysis of structures submitted to human induced dynamic excitations. One of the difficulties in analyzing heavily loaded slabs regards how to consider the human mass, since it controls important characteristics of the structural system, such as the fundamental frequency. If this parameter is not properly considered the structure dynamic response can be substantially changed. ” Concrete Society Technical Report No. 43 Pavic‟s work was initiated by the publication of Concrete Society Technical Report No. 43 (Concrete Society, 1994) entitled „Post-tensioned Concrete Floors - Design Handbook‟ in 1994. The aim of this report was to aid the practical day to day design of long-span post-tensioned concrete floors. Appendix G of the report outlines a procedure for checking the vibration serviceability of long-span post-tensioned concrete floors at the design stage. It is of particular importance as it is the most recent and comprehensive design guidance document in the UK covering the vibration of post-tensioned concrete floors. Pavic (1999) presented a deconstruction of the guidelines, illustrating numerous assumptions which were made in order to simplify the vibration serviceability problem for post-tensioned concrete floors. It was found that the guidelines were produced without any experimental verification and they have proven to be unreliable and frequently over conservative for most normal post-tensioned concrete floor structures (Williams and Waldron, 1994; Pavic et al., 1998b; Pavic, 1999). As a direct consequence, the market competitiveness of post-tensioned floors designed using these guidelines have been reduced, resulting in and an immediate requirement for improved design guidelines (Pavic, 1999). Experimental modal analysis (EMA) of floors Experimental modal analysis (also called modal testing) is described by Ewins (1995) as: “… the processes involved


Figure 9. Typical FRF measurement presented by Khan (1996).

involved in testing components or structures with the objective of obtaining a mathematical description of their dynamic or vibration behavior”. This mathematical description normally consists of the natural frequencies, mode shapes and modal damping ratios. Modal testing has traditionally been used by mechanical and aero-nautical engineers to design relatively small structures and components through prototyping. Recently, it has been increasingly used as a means of validating FE models of such structures, hence reducing the number of prototypes required. The application of experimental modal analysis of civil engineering structures is relatively new. The sheer size of civil engineering structures,

combined with technical problems such as very low responses to be measured in the presence of a great deal of environmental noise, means that sensitive instru-mentation and complex signal processing techniques are required (Pavic, 1999). These have not been available until the last few years. Operating deflection shapes (ODS) analysis Olsen (1984) classified structural dynamic excitation techniques into five general types: operating, steady-state, periodic, transient and random. Operating excitation

is generally not measured and represents the dynamic loading applied to a structure in its operating condition. Since a requirement of EMA is a measurable form of excitation (Ewins, 1995), operating excitation is not suitable. It should be noted; however, that operating excitation is commonly used in civil engineering in „ambient vibration testing‟ in which response only measurements are utilised to obtain unscaled mode shapes, natural frequencies and modal damping ratios. This technique is more common on very large structures (such as large buildings, bridges and dams) for which the measurement of the artificial excitation is impractical. However, mode shapes estimated from ambient vibration testing are „unscaled‟, meaning that it is not possible to relate the response of the structure to the force input. Therefore, it was not utilised in this work and will not be discussed further. The first attempts at experimental modal analysis of civil engineering structures were performed by measuring only the response of the structure due to unmeasured excitation. By examining the ratios of amplitudes of response at various points on the structures and the phase differences between these points, the natural frequencies and so-called mode shapes‟ could be estimated. Since the excitation is not measured in this technique, „it is not theoretically possible to completely decouple multiple modes of vibration and the „mode shapes‟ measured are in fact „operating deflection shapes‟ which contain contributions from all modes of vibration (Spectral Dynamics, 1994). However, near a resonant frequency, for a system with well separated modes of vibration, an operating deflection shape is a close approximation to a mode shape. This form of testing was applied to floor structures by Rainer and Swallow (1986) and by Pernica (1987). A reasonable degree of success was achieved and the testing enabled a fairly accurate assessment of the natural frequencies and mode shapes. However, in both cases, damping ratios were estimated by using the half-power bandwidth method, which, explained previously, possibly resulted in the overestimation of modal damping ratios. ‘True’ experimental modal analysis In modal testing terms, such a plot is actually called a frequency response function (FRF) and is commonly the basis for single- and multi-degree-of-freedom curve fits which are used to determine the modal properties (natural frequencies, mode shapes and modal damping ratios) of structural systems. Osborne and Ellis (1990) reported the results of tests on a composite steel-concrete floor in which they presented a “response spectrum” that were created by: “… converting the measured accelerations to equivalent displacements and then dividing the displacement by the applied force”. They calculated the modal properties of the first two modes of vibration by fitting a “best fit theoretical curve”

Hamdan et al. 7679 to the measured FRF, but they did not state the assumed analytical model for that theoretical curve. One point worthy of comment regarding this work is that the modal damping values were about 1%, which is significantly lower than those values reported quite a number of the literature prior to the 1990s. In his doctoral thesis, Eriksson (1994) considered the problem of the vibration of low frequency floors. He used experimental modal analysis as a tool to determine the modal properties of the structures that he was examining (concrete and composite steel-concrete floors with natural frequencies lower than 8 Hz). Excitation was applied using a custom built impactor for the majority of the tests, although a grounded electrodynamics shaker was used on one occasion. The floor response was measured using accelerometers and both the excitation and response signals were processed by a dual channel spectrum analyzer. Although some success was achieved, the relative crudity of the test equipment and data processing techniques limited the reliability of the experimental data. Caetano and Cunha (1993) described a modal testing facility which they set up for the testing of various sizes of civil engineering structures. The exciters described, in order of applicability to increasing structure sizes, were an instrumented hammer, an electrodynamics shaker and a rotating eccentric mass shaker. In this paper, they also presented a case study of the modal testing applied to a 6.6 m × 6.6 m reinforced concrete roof plate for which they managed to determine its natural frequencies, mode shapes and modal damping ratios. Interestingly, in addition to Single Degree of freedom (SDOF) peak-picking and circle fit modal parameter estimation methods, they also applied an Degree of Freedom (MDOF) parameter estimation algorithm based on the rational fraction polynomial (RFP) method (Richardson and Formenti, 1985). According to the writers, this technique was simpler to apply and provided better quality estimates of modal parameters than the peak-picking method, an observation which would be expected for this more advanced modal parameter estimation technique. Lenzen and Murray (1969) used the impact excitation and amplitude decay method to measure damping on 20 full-scale steel-concrete floors. The estimated damping ratios varied between 3.8 and 15.9%, the average value being 7.9%. These and other similarly obtained damping values were dismissed later as unreliable by Wyatt (1985), Ohlsson (1988a) and Eriksson (1994), due to inappropriate measurement techniques. Similar problems with damping measure-ments can be seen in the papers by Lenzen et al. (1971), Lenzen (1972) and Murray (1975). In the mid-1970s, researchers from Canada worked on new floor vibration serviceability guidelines in the Canadian steel design code published in 1974 (CSA) Standard S16.1-1974 “Steel Structures for Buildings - Limit States Design”). The guidelines were based on Lenzen‟s heel-drop methodology. One of the most comprehensive applications

7680 Int. J. Phys. Sci. of modal testing technology applied to civil engineering structures, in terms of testing and analysis procedures, was performed by Pavic (1999). He successfully tested a number of structures, applied complex MDOF modal parameter estimation techniques and performed quite complex model correlation and „manual‟ model updating to FE models of the same structures. Due to financial constraints, however, the only exciter used in this work was an instrumented impact hammer. Probably because of this, the writer described some difficulties in the testing and modal parameter estimation phases of the work, particularly related to complexity of mode shapes. It is likely that by applying these advanced procedures and methods, using an improved method of excitation such as an electrodynamics shaker, it would be possible to obtain more accurate and consistent modal test data.

PREDICTION AND ASSESSMENT OF VIBRATION SERVICEABILITY Floor vibration is a topic that occupants, depending on their living conditions, can be either very well aware of or totally unfamiliar with. Vibration is an omnipresent form of dynamic motion in which the structure oscillates about an equilibrium position (Meirovitch, 1986). Such motions arise from the interaction between time varying structural disturbances, such as forces or imposed displacements, and inertial properties of the structure (ISO, 1992). Vibrations are a constitutive part of the environment and are unavoidable. In principle, everything vibrates all the time. The problem with vibrations occurs when they become excessive causing annoyance, malfunction of sensitive equipment, damage or structural failure. The human annoyance factor is, however, the most frequent vibration serviceability problem. For example, vibration is regarded as one of the seven main sources of environmental pollution in Japan (Abe et al., 1994). Although the problem of human vibration is, reportedly, very difficult to deal with, design decisions have to be made in contemporary design practice where the vibration SLS has to be considered. An outline of a general state-of-the-art procedure based on the latest international standard ISO 10137 (ISO, 1992) will be presented here. Following the ISO 10137 procedure, the first step towards the assessment of vibration serviceability of floors is to identify and characterise the following three key factors: 1. The vibration source, 2. The transmission path, and 3. The receiver. Each of these parts is of equal importance to the overall vibration serviceability problem and there has been much research work in these separate areas. Integrated methods, which do not consider these three components separately such as the one proposed in the CSA

guidelines, are now considered to be obsolete. This is because inaccuracies in, say, the vibration source modeling have tended to be masked by inaccuracies in, for example, the modeling of the transmission path. As a result, these methods may only be utilized in the manner in which the writers intended, and separate items from them considering vibration source, path and receiver, should not be used in isolation (Wyatt, 1989). It has also been suggested that there is no point in developing accurate models of vibration source when the acceptable limits are so uncertain. Such a philosophy cannot be justified since improvements in all aspects of the vibration serviceability problem are being made through continuing research (Pavic, 1999). The vibration source Vibrations in buildings can have a wide variety of causes. It may vary both in time and in space. These can conveniently be broken down into „external‟ and „internal‟ vibration sources. External vibration sources Vibrations from external sources can be divided into three groups. The first category is low-frequency, below 2 Hz, background vibrations, for example caused by ocean waves. These vibrations have clear seasonal variations and are much stronger during the winter than the summer (Bungum et al., 1971; Ringdal and Bungum, 1977; Bungum et al., 1985; Fyen, 1990). The second category is culturally affected background vibrations, with characteristic frequencies above 2 Hz and clear diurnal variations. These are, for instance, traffic vibrations or vibrations from industry. The third category, involves earthquakes with components of high energy in the (1985) strong wind which in turn may generate ground vibrations, typically having dominant frequencies in the range of 20 to 30 Hz. All the external ground vibrations can be amplified in the structure depending on the dynamic characteristic of the structure and the frequency of the vibration input.

Vibrations due to external sources are normally transmitted to the building through an adjoining medium such as the ground, air or water. ISO 10137 (ISO, 1992) gives the following examples:

(i) Construction, mining or quarry blasting; (ii) Construction activity (pile driving, compaction, excavation, etc.); (iii) Road and rail traffic; (iv) Sonic boom or air blast; (v) Fluid flow (wind or water); (vi) Punching presses or other machinery in nearby buildings; (vii) Impact of ships at nearby wharves.

Problems with vibrations caused by external sources are generally best treated by isolating the building as a whole (Wyatt and Dier, 1989). However, this is beyond the scope of this article and will not be discussed further. Internal vibration sources Internal vibration sources consist of ventilation systems, diesel units, elevators, fork-lifts, cranes, the transport and setting down of heavy loads and masses, objects falling on the floor and other occasional impacts and blows and, last but not least, vibrations caused by walking people (Bjarni and Christian, 2000). Beforehand, to predict the vibration level on the laboratory floors in the new facility generated by the above-listed vibration sources was quite complicated. First, there are many uncertainties and scatter in the load amplitude and frequency content of the sources, and second, the transmitted waves are affected by a number of random reflections, refraction, structural behaviour and attenuation within the complex path they pass through. ISO 10137 also quotes the following examples for internal vibration sources: (i) Human excitation; (ii) Rotating and reciprocating machinery; (iii) mpact machinery (punches, presses, etc.); (iv) Moving machinery (trolleys, lift trucks, elevators, conveyors, overhead cranes, etc.); (v) Construction or demolition activity in adjoining parts of the building. Mechanical excitation is generally tackled at the source by the reduction of out-of-balance or through the use of vibration-isolation mountings for the machine (Wyatt, 1989). Moreover, excitation due to construction or demolition activities tends to be temporary and case specific. Eriksson (1994; 1996) suggested that the owner should specify the intended use of a structure at the design stage so that reasonable dynamic service actions can be considered. He suggested a set of “service action classes” as follows: A1. Light domestic type activity; A2. Intermittent pedestrian traffic (for example, office corridor); A3. Public pedestrian traffic and light machine installations; A4. Crowded open space or mall areas without vehicle traffic; A5. Open space areas with vehicle traffic and pedestrians; A6. Medium machine installations and vehicle traffic; A7. Dance halls and gymnasia; A8. Assembly areas for concerts or sports events; A9. Heavy machine installations and vehicle traffic: A10. Various construction activities within the building.

Hamdan et al. 7681 For the types of buildings considered in this article, service action class A2 is obviously applicable. The loading case suggested for this class by Eriksson (1996) was “one person treading in place”. He also suggested a return period for application of this forcing function which is important if vibrations are to be assessed using a “vibration dose” approach. The transmission path Simplified structural models for vibration analysis In the context of a vibration serviceability analysis or assessment, the transmission path is defined as the path through which vibration energy is transferred from the vibration source to the receiver. Structural components transmitting vibrations could be foundations, columns, walls and floors, whereas non-structural paths may be access floors, removable partitions, cladding, etc. Physical properties of the transmission path, such as stiffness, mass or damping, modify the vibration excitation at the source into a structural response „felt‟ at the position of the receiver. It is interesting to note here that Reynolds (2000), who carried out the only in-depth investigation of vibration performance of long-span floors supplied with access (also known as „raised‟ or „false‟) floors, found that they add very little damping and stiffness to bare long-span concrete floors. For vibrations in buildings, the transmission path is most frequently assumed to comprise the building structure itself. However, ISO 10137 (ISO, 1992) gives the following more comprehensive range of examples of transmission path: (i) Ground, air, or water; (ii) Structural components (foundations, floors, columns, walls, etc.); (iii) Non-structural components (pipes, partitions, etc.). Since external sources of vibration will not be considered in this article, consideration of the transmission path will be restricted to elements that exist within buildings, that is, structural components and non-structural elements which are attached to the building structure. Literature describing the modeling of structural components and systems will be reviewed here. State-of-the-art dynamic analysis of structures Without doubt, the current state-of-the-art in the analytical determination of the modal properties of structures is through the use of FE analysis. Unlike most simplified methods of determining the dynamic properties of structures, the use of FE analysis facilitates easy calcu-lation of modes of vibration higher than the fundamental.

7682 Int. J. Phys. Sci. It also allows the multi-mode response of a floor structure to be calculated for highly complex loading scenarios, of which the spatially and temporally varying walking load is a prime example.

Dynamics of concrete floor

Apart from classical textbooks on statics and dynamics of plate systems (Szilard, 1974), a number of papers specifically cover dynamic characteristics of building floors made of concrete. They are typically related to subjects other than problems of human induced and perceived vibrations, such as the isolation of vibrating machinery. The importance of accurate modelling when checking the vibration performance of floors was also demonstrated by Heins and Yoo (1975). They concluded that a properly restrained equivalent grillage was a much better mathematical representation of the floor structure than a single beam-like element(s), typically advocated in the codes of practice. Petyt and Mirza (1972) used FE modelling and performed a parametric study of natural frequencies and mode shapes of column-supported floor slabs (that is flat plates). Their work was inspired by the increasing need from the construction industry where solid flat slabs made of concrete were becoming popular. In the case of a single floor panel, which was pin-supported at all four corners, the first five natural frequencies, experimentally measured using a small model in a laboratory, were compared with their analytically calculated counterparts. An excellent comparison was obtained justifying the use of the FE technique. However, Petyt and Mirza commented: “… in building construction, if the slab and columns are cast in situ, the joint may be regarded as rigid. Even in the construction of prefabricated panel systems, certain bending rigidity may be introduced if the joints are welded or when additional reinforcement is used and gaps are filled in situ.”

Caetano and Cunha (1993) presented a very advanced method for estimating the modal properties (natural frequencies, mode shapes and modal damping ratios) of a relatively small (6.6 m square, weighting approximately 15 t) but full-scale reinforced concrete roof slab having closely spaced modes of vibration. This powerful method, adopted from the more advanced mechanical and aero-space engineering disciplines, is based on state-of-the-art modal testing technology (Ewins, 1995; Maia et al., 1997) and it consists of:

1, MDOF vibration parameter estimation using the measured FRFs, 2. FE modelling prior to the full-scale testing 3. FRF measurements using a manually operated instrumented sledge-hammer and 4. FE model correlation with the experimental data gathered after modal testing.

The receiver

The receiver is defined in ISO 10137 (ISO, 1992) as the “person, structure or equipment subjected to vibrations”. The persons are, obviously, the human occupants of the building whereas the objects can be either vibrating structural or non-structural elements (windows, walls, beams, slabs, etc.) or contents of the building such as instruments or machinery. An amount of vibration passed to the receiver should be evaluated in accordance to certain established criteria. This evaluation is the core problem of the vibration serviceability assessment. Vibrations typically cause annoyance to occupants long before reaching levels at which structural damage can occur (Wyatt, 1989). Damage to or malfunctioning of sensitive equipment (for example, high precision optical and micro-assembly equipment) is also considered to be a problem (Ungar and White, 1979; Ohlsson, 1988). However, items of equipment typically encountered in office buildings (for example, personal computers, photocopiers, etc.) are generally robust enough not to be affected by low level vibrations up to the levels which are likely to cause annoyance to occupants (Waller, 1969). Therefore, for the purposes of this research, the limiting vibration response of offices will be assumed to be dictated by the annoyance threshold of the human occupants. As to the floors, two types of vibration serviceability assessment exist: (1) the evaluation by calculation during the floor design stage, and (2) the evaluation by vibration measurement of already built full-scale floor structures (ISO, 1992; Griffin, 1996). In both cases, the state-of-the-art assessment approach, based on a proper characterisation of the vibration source, transmission path and receiver, is required. The difference between the calculation and the measurement based assessments comes, naturally, from the way that the response at the receiver is obtained. In the case of the former, it is obtained by mathematical modelling of the structure and performing its (analytical) vibration response calculations for the given vibration excitation. In the case of the latter, the response is obtained by measurements on a real-life floor structure under the specified excitation.

The main problem being whether or not to treat the vibration serviceability requirements as mandatory is in the building standards and codes of practice. The relevant American Society of Civil Engineers (ASCE) Committee 7 was, according to Ellingwood (1996), deeply divided over this issue. As a result, the limited floor vibration serviceability provisions given for the first time by the ASCE (1995) are non-mandatory. Similar provision exists in ISO 10137 (1992), the four Annexes of which contain the most valuable practical information as to the problem of vibration serviceability. The Annexes are still “for information only”. Consequently, the research community should provide designers with appropriate procedures to deal with all serviceability limit states, including floor vibrations (Ellingwood, 1996).

To conclude, the main idea of the state-of-the-art procedures which are mentioned so far and are, in general, accepted worldwide, is to provide the common framework not only for future designs but also for research (ISO, 1992).

Human perception of vibrations Tilly et al. (1984) also investigated walking excitation in conjunction with the vibration serviceability of footbridges. It was reported that 95% of people walk normally with a pacing rate of 1.5 to 2.5 steps per second. Also, it was suggested that, being periodic and non-sinusoidal, walking forcing functions have higher harmonics in addition to the fundamental. Frequencies of these are integer multiplies of the fundamental walking frequency (1.5 to 2.5 Hz) and, in principle, have the potential to excite the fundamental or other vibration resonances in footbridges. However, it was also found that humans are not as perfect exciters as, say, machines, able to maintain the pacing frequency which excites the footbridge resonance spot-on. This is especially so in the case of lightly damped structures. In such structures, due to the narrowness of peaks around resonances in the FRF modulus function, and due to large response amplification at resonance, only a slight off-resonance (or near-resonance) excitation may result in a tremendous reduction in the response. This important aspect was clearly confirmed by Matsumoto et al. (1978) and, to some extent, by Tuan and Saul (1985) and Saul and Tuan (1986). Tuan and Saul (1986) reported that movements of an individual or a group of people could not be precisely duplicated in repeated experiments even when a timing device was used. Prior to embarking on a summary of the available literature into the subject of human perception of vibrations, it is necessary to highlight the difference between local vibration and whole-body vibration. Griffin (1996) defined them as follows: “Whole-body vibration occurs when the body is supported on a surface which is vibrating. Local vibration occurs when one or more limbs (or the head) are in contact with a vibrating surface.”

He also quotes three principal possibilities for whole-body vibration to occur: sitting on a vibrating seat, standing on a vibrating floor, or lying on a vibrating bed. Therefore, references relating to whole-body vibration are pertinent to this research. One of the first studies into the human perception of whole-body vibrations was published by Reiher and Meister in 1931 (Wright and Green, 1959). They subjected ten people of varying ages to sinusoidal excitation at various frequencies and amplitudes. The subjects were then required to rate the vibration as just perceptible, definitely perceptible, annoying, unpleasant and exceedingly unpleasant. This which showed enabled them to compile the graph shown in (Figure 10), that the perception threshold was dependent dependent on vibration velocity between 5 and 60 Hz

Hamdan et al. 7683

Frequency (Hz)

Domains of various strengths of sensations for standing persons subject to vertical vibration

Dis

pla

cem

ent

amp

litu

de

- In

ches

Figure 10. Continuous sinusoidal vibration rating after Reiher and Meister (1993).

(Griffin, 1996).

In 1948, Goldman produced an excellent report that summarized the results of a number of previous research efforts, including the work by Reiher and Meister. He recognized a number of problems concerning the measurement of human vibrations that are still encountered by researchers today. The first of these was that researchers tend to use different experimental conditions (such as position of subject, direction of motion, frequency range and duration of exposure) which were not always clearly outlined in their publications. Such uncertainties bring the repeatability of presented results into question and this was the reason for Griffin (1996) to state that: “… the full and careful reporting of research studies is vital to the subsequent interpretation and application of the findings”. Another problem reported by Goldman (1948) was that there was no consistency in terminology used by different researchers. For example,


Table 1. Some source of inter- and intra-subject variability.

Inter-subject variability Intra-subject variability

Body dynamics Body dynamics

Body dimensions Body posture

Body masses Age

Body posture Health

Age Experience and training

Gender Attitude and motivation

Health Sensitivity and susceptibility

Experience and training

Attitude and motivation

Sensitivity and susceptibility

the interpretation of the difference between „definitely perceptible‟ and „annoying‟ (used by Reiher and Meister) is almost certain to vary for different subjects. In addition, the works examined by Goldman were intended for different fields of application, hence complicating the interpretation of the results. For example, vibrations that would be acceptable for, passengers in an aircraft for instance are likely to be completely unacceptable for building structures. Goldman also recognised a significant limitation of the experimental work performed then. This came in the form of the vibration to which subjects were exposed to, which was a single frequency sinusoidal motion. In normal situations, humans are rarely exposed to such vibrations and it is more normal for „real‟ vibration to exhibit complex multi-frequency characteristics. Due to the inherent difficulties in studying the effects of complex vibrations, single frequency techniques were the sole method used up until the 1960‟s (Griffin, 1996). In recognition of the complex nature of vibrations to which humans are exposed, a number of methods have been developed which allow the effects of complex vibration to be assessed. These can be broadly divided into two classifications (Griffin, 1996): (i) Rating methods are methods in which only the worst component of vibration is assessed. (ii) Weighting methods are methods in which the complex vibration is weighted according to differences in human response to vibrations at different frequencies. The frequency weighted complex vibration is then summed in some manner (for example, RMS) resulting in a single quantity that may be used for assessment. Weighting methods are now widely considered to be more appropriate than rating methods (Griffin, 1996). Variability of human perception to vibrations Previous studies into the human response to vibration have determined that there is a massive variability in

quantities determined for the magnitude of the threshold of perception of vibration, and for the magnitudes of the various comfort criteria. This has been noticed for different individuals (inter-subject variability) and for the same individual at different times (intra-subject variability). Table 1, reproduced from Griffin (1996), illustrates the large number of factors that may affect how a person perceives vibrations. The modern vibration assessment guidelines, therefore, tend to acknowledge the relatively recent research findings. They accept that perception thresholds are likely to govern the acceptability of floors as regards their vibration performance. Nevertheless, floor vibration could be acceptable for levels of vibrations higher than the perception threshold. Perceptible vibrations which are acceptable, therefore, cover a band of human responses which vary from the vibration perception thresholds to certain upper vibration sensation limits. Many, mostly environmental factors influence these sensation limits in a way which is extremely difficult to predict (ISO, 1992; Bolton, 1994; Eriksson, 1994; Griffin, 1996). As a result of the very large differences in results which may be expected, it is necessary that any specified criteria for perceptibility or comfort limits are based on the responses of a large number of people followed by a proper statistical analysis (Griffin, 1996). However, it is only in recent years that such statistical analyses have been regularly performed and criteria such as the highly referenced Reiher and Meister 1931, in which no such statistical analysis was performed, must be viewed with caution. Human response to building vibrations One of the first laboratory studies into human vibration was carried out by Reiher and Meister. In 1931 they published a paper entitled “The Sensitiveness of the Human Body to Vibrations” in which the effects of sinusoidal whole-body vibrations were investigated. This research, which, according to the secondary sources,

Hamdan et al. 7685

Figure 11. The Reiher and Meister (unmodified) scale after Wright and Green (1959).

had a great impact on the scientific community, recommended bounds for “imperceptible”, “just perceptible”, “clearly perceptible”, “annoying”, “unpleasant” and “painful” vibrations as a function of harmonic displacements and frequency (Figure 11). In many environments, humans are willing to tolerate, and indeed expect the presence of vibrations. For example, certain vibrations in ships can be associated with the engines and, paradoxically, the cessation of such vibrations can cause alarm to passengers (Guignard, 1971). However, most occupants of buildings do not expect the structures to be able to move and are therefore willing to tolerate little or no vibration at all. In fact, Steffens (1974) stated that people in buildings will “tend to overestimate the magnitudes of vibratory movements”. It is therefore clear that much of the concern of occupants of buildings that vibrate, who typically are ignorant of structural engineering, is caused by fear of collapse, even though there is little chance of this actually happening.

Parsons and Griffin (1988) reported that “if the vibration exceeds the perception threshold, the disturbance produced by the vibration may become more dependent on vibration frequency”. This implies that there is a certain range of frequencies which causes building occupants to worry about building collapse. Guignard‟s (1971) observation that “high frequencies are not as a rule associated with major structural responses indicative of possible danger” points out that low frequencies are the most important in terms of building vibration serviceability. The duration of vibrations is also important for floor vibration serviceability assessment. This is clear from the early work performed by Lenzen (1966), who has already mentioned proposed, that the Reiher and

Meister‟s 1931 criteria should be multiplied by a factor of 10 to take into account the transient nature of floor vibrations. However, more state-of-the-art approach proposed by Eriksson (1994) is to determine the number of vibration events in accordance with the dynamic service action classes listed previously, and use a vibration dose approach such as that specified in ISO 2631 (ISO, 1997). Current relevant codes of practice and guidelines There are numerous codes of practice around the world which are concerned with the assessment of whole-body vibrations. In order to quantify whole-body vibration and its effects, a relevant dynamic motion descriptor has to be chosen. Displacement, velocity, acceleration or „jerk‟ (first derivative of acceleration) could be selected. Typically, accelerations are selected due to the ease of instrumentation (Griffin, 1996). In addition, body posture, type of vibration (periodic, random, or transient) and its frequency content, magnitudes and duration have to be known. The body posture may be defined using a coordinate system as shown in (Figure 12) (ISO, 1985).

A frequency analysis of an acceleration time history, measured or calculated over a certain period of time, provides all necessary information to describe the whole body vibration. Many of the more important ones were outlined by Griffin (1996) and will not be covered here. However, the following codes of practice have been adopted for the assessment of vibration serviceability performance of floors in this research: 1. ISO 2631: 1997 Mechanical vibration and shock.


Figure 12. Body postures and standardised coordinate systems for assessing vibration after BSI

(1992).

Evaluation of human exposure to whole-body vibration - Part 1: General requirements (ISO, 1997), and 2. BS 6472:1992 Guide to evaluation of human exposure to vibration in buildings (1 Hz to 80 Hz) (BSI, 1992). ISO 2631:1997 gives recommendations for the measurement of whole-body vibrations, which are, of course, applicable to the measurement of vibrations on floors. In order to perform a vibration serviceability assessment, it recommends that the following procedure is followed: Vibration responses are measured at the point of entry to the body.

A basic evaluation of weighted root-mean-square acceleration should be performed (using the frequency weighting curves specified in the code), and If the basic evaluation can possibly underestimate the effects of vibration (high crest factors, occasional shocks, transient vibration), the running RMS and/or the vibration dose value methods of evaluation should be applied. Whilst ISO 2631:1997 specifies methods for measurement and evaluation of whole-body vibrations, it does not specify any limits to be applied in accordance with these evaluations. For this purpose, it is necessary to utilise BS 6472:1992 which is the relevant UK code of practice which specifies vibration serviceability limits for building floors.

The effects of non-structural elements on the vibration characteristics of floors Serviceability concerns are a growing issue for many designers, modern design specifications, coupled with today‟s stronger steel, aloe for lighter sections when strength is the governing factor. However, in most offices-especially today‟s electronic offices-vibration require-ments are often more important. All practical office floor structures are likely to contain one or more non-structural elements such as partition walls (part- or full-height), access floors, suspended ceilings, electrical and mechanical services and finishes. However, while its has been recognized for a long time that such non-structural elements can significantly affect the vibration performance of a floor structure, quantification of this phenomenon has been quite arbitrary and supported with very little systematic research in the past. The use of non-structural elements in the analysis of vibration serviceability It is interesting to discuss whether the effects of non-structural elements should be utilised in designing vibration serviceability analyses. Indeed, whilst Ohlsson (1988) stated that partitions and other non-structural components can make the difference between acceptable

and unacceptable vibration response, he also stressed that: “… it is the author's opinion that the serviceability limit state design should not rely upon „non load-bearing‟ components (…) [as they] may be removed any day by the user.” However, the writers disagree with this opinion. While partition walls may be removed at any time, it is unlikely that other non-structural elements such as services, suspended ceilings and access floors would be completely and permanently removed during the useable life of a building. Therefore, it is perfectly reasonable to make an appropriate allowance for the effects of these elements when performing a vibration serviceability analysis during design. Furthermore, Allen and Murray (1993) stated that "the damping ratio depends primarily on non-structural components and furnishings". Therefore, to base vibration serviceability analyses on damping values measured from bare structures is likely to lead to gross overestimation of structural responses. This opinion is shared by Fahy and Westcott (1978) who stated that "vibration tests on incomplete, unoccupied buildings and isolated components are of little practical value". Nevertheless, it is also the opinion of the writers that it is important to understand the effects of non-structural elements in greater detail before including them in vibration serviceability analyses. Quantification of the effects of non-structural elements In the early work on the vibration serviceability of composite floor structures performed at the University of Kansas (Lenzen, 1962; 1966; Lenzen and Murray, 1969), measurements of damping of real structures using the heel-impact method led to the conclusion that non-structural elements increased damping significantly. Subsequent papers published from research in Canada indicated that realistic damping ratios for composite floors were 3% of critical for a bare floor, 6% for a finished floor and 12% for a finished floor with partitions (Allen, 1974; Allen and Rainer, 1975; 1976). Although it is now recog-nized that these damping values were inappropriately estimated and are much higher than properly estimated modal damping ratios, these measurements clearly indicated the possibility for a significant effect of non-structural elements on the damping of floor structures. In the early work on the vibration serviceability of composite floor structures performed at the University of Kansas (Lenzen, 1962; 1966; Lenzen and Murray, 1969), measurements of damping of real structures using the heel-impact method led to the conclusion that non-structural elements increased damping significantly. Irwin‟s (1978) work remedied this to some extent as it served as the basis for the revised version of ISO 2631 published in1985 (Wyatt, 1989; Wyatt and Dier, 1989). The paper generally covers the aspects of human response to motions of large structures such as buildings,

Hamdan et al. 7687 off-shore platforms and bridges. As the main reason for people to be particularly sensitive to low-level vibrations in large static objects, Irwin singles out the lack of expectation. Users of large objects of infrastructure simply do not expect them to move and, if the movement is perceived, then annoyance may arise. This is probably the reason for Wyatt (1989) to point out that human reactions to low-level vibrations in buildings are more psychological than physiological phenomena. Deter-mination of more realistic changes in modal damping ratios caused by the installation of access floors is one of the aims of the work presented here. It has also been suggested that some non-structural elements, such as access floors, suspended ceilings and services, may increase the stiffness of floor structures, although only to a limited extent (Osborne and Ellis, 1990; Eriksson, 1994). Partitions, however, can significantly increase the stiffness of floors and even act as supports for low-level vibrations (Pernica, 1987). Quantification of the effects of non-structural elements In the recent work on the vibration serviceability of composite floor structured at the many Universities like University of Kansas, floor vibration in steel buildings increasingly is a condition of consideration for structural engineers, architects, owners and users. The difference between acceptable floors is in the architectural features. In office buildings, these features can vary over the life of the structure (Linda, 2003). The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way (Chen Wei-min and SUN 2005). Structural designers have long been trying to develop minimum cost solutions, as well as to increase the construction speed. This procedure has produced slender structural solutions, modifying the ultimate and serviceability limit is the states that govern their structural behavior (Jose and Pedro, 2008). Assuming that the material properties vary in a power law manner within the thickness of the plate, the governing differential equations are derived. In archi-tectural engineering, for instance, reinforced-concrete slabs with one or two way joists are used for floor systems in buildings (Rahbar and Rostami, 2009). The effects of access floors There are only a handful of papers in the literature which described the possibly beneficial effects of access floors with respect to floor vibrations. Williams and Waldron (1994) presented the results of tests carried out on 14

7688 Int. J. Phys. Sci. structures, 4 of which contained access floors. They concluded that floors with access floors were quite heavily damped in comparison with floors without access floors. However, on further examination of some of the work on which Williams and Waldron based their paper (Caverson, 1992), it was determined that the damping values were estimated using the half-power bandwidth method, and it is possible that these larger damping values were caused by the likely presence of modes of vibration of the floors close to the fundamental. Osborne and Ellis (1990) presented the results from vibration tests on a composite steel-concrete floor before and after the addition of an access floor. They did not detect significant changes in modal properties of the floor following the addition of the access floor, but they did report that the perception of floor vibrations due to footfall loading was considerably reduced, although they did not elaborate on this. Rainer and Pernica (1981) presented data which demonstrated an increase in damping of a composite floor sample following the addition of a suspended ceiling. They speculated that this was caused by friction between the ceiling panels and the supporting T-sections. Bearing in mind the construction of most access floors, and the fact that access floors are significantly heavier than suspended ceilings, it is reasonable to expect that access floors may also exhibit this damping mechanism, possibly to a greater extent than suspended ceilings. However, there is currently no evidence to support this speculation. A paper by Williams and Falati (1999) describes a series of tests which were performed on a small slab strip constructed at the University of Oxford, some of which concerned the effects of an access floor system on the dynamic properties of the slab. The slab strip was 5.1 m long by 1.0 m wide by 135 mm deep and two configurations of access floors were considered. Firstly, a single row of 7 panels 600 mm × 600 mm pedestals was bonded to the slab. Secondly, two rows of 7 panels were installed on the slab with the panels screwed down at all interior corners and left loose around the perimeter of the slab, in order to simulate a detail which is sometimes used in normal construction. The finished floor height (that is, distance between the surface of the slab and the top surface of the access floor) was not given. In these tests, it was determined that the first configuration resulted in a reduction in natural frequency from the slab‟s bare state of 1.3% and a modest increase in damping of 9.1%. The second configuration resulted in a reduction of natural frequency by 5.0% and a significant increase in damping of 63.6%. The authors concluded, therefore, that access floors may be designed and utilised in such as way as to increase the damping of floor systems and hence improve their vibration serviceability performance. However, it is important to note the limitations of this work. Firstly, the half-power bandwidth and logarithmic decrement methods were utilised to determine the modal damping ratios. These methods have been shown typically to overestimate

damping. However, because the modes of vibration were well separated for this particular structure, it is unlikely that the damping estimates were adversely affected. A more important limitation is that the slab on which the access floors were tested was very small compared to what might be expected in practice, while the access floors were the same size as would be used in practice. This may have led to an overestimation of the effects of the access floors to a degree which is not possible to quantify. So, while these tests clearly indicate a possible benefit of using access floors, the magnitude of the benefit remains uncertain. Current acceptability criteria There are many procedures available to determine the acceptability of a floor in terms of human perception. Current methods of predicting the acceptance of floors vary according to the material used in the construction of the floor. Lightweight wood floors and metal framed floors have been studied extensively over the past 20 years, in many different countries. Several acceptability criteria have been developed for such floor systems based on the static deflection of the floors. The intent of this work is to determine whether it is reasonable or not to apply these criteria to Composite Concrete Floor. Ohlsson’s criterion A design procedure to limit annoying vibration caused by people in motion is presented in detail in a design guide published by the Swedish Council for Building Research (Ohlsson, 1988). The guide is developed from years of research by Professor Sven Ohlsson at the Chalmers University of Technology. The majority of Ohlsson‟s research involved timber floors. The guide includes a description of “springiness” and vibration problems, the development of the proposed dynamic expressions (Ohlsson, 1982), and the design procedure and design

examples for various floor systems.

x

yxn

D

D

B

Ln

B

Ln

gL

Df

4

4

2

2

421

2

(1)

Where fn = natural frequency in the nth normal mode g = unit weight Dx = plate flexural stiffness in the x-direction (parallel to the joists) = EIx/S Dy = plate flexural stiffness in the y-direction (perpendicular to the joists) = Et3/12 E = modulus of elasticity

Hamdan et al. 7689

Imp

uls

e ve

loci

ty r

esp

on

se (m

/s/N

s)

Forc

e (N

)

Time (s)

Impulse velocity response versus time

Force versus Time

Figure 13. Idealised impulse and resulting vibration velocity for a typical

floor after Ohlsson (1988).

Ix = transformed moment of inertia S = joist spacing t = plate thickness L = span length of floor n = modal number B = width of floor The moment of inertia used in Ohlsson‟s design guide does not have to take into account composite behavior between the joists and flooring. For floors with Dy/Dx < 0.01, Equation 1 can be simplified to:

42 gL

Df x

n

(2) Deflection due to a concentrated load applied at the most flexible point on the floor is limited under the first check. When the value of Dy/Dx is low (<0.01), a point load is assumed to be carried by the joist directly under the load. The deflection of this single joist in a floor system is to be limited to 0.059 in. (1.5 mm) under the action of a 225 lb (1.0 kN) static concentrated load. Deflection of the joist is calculated from:

x

pEI

PL

48

3

(3)

Where

ðp = vertical displacement P = applied load L = joist length E = modulus of elasticity of joist Ix = moment of inertia of joist

A more accurate method of computing the deflection (that is, computer modeling of the floor system) may be used if desired. The second requirement is a check on the response to an impulse load of 1.0 N-s. The impulse velocity response, h‟max, is “the initial vertical vibration velocity due to an idealized vertical force impulse (Ohlsson, 1988). A better understanding of this parameter can be seen in Figure 13.

Australian criterion The Australian Standard Domestic Metal Framing Code (1993) was developed for residential steel framed construction and uses much of the criterion proposed by Ohlsson (1988). The dynamic serviceability requirements provided in this Code are limited to floors with a lowest natural frequency greater than 8 Hz. This frequency is calculated using Equation 1 with n equal to 1 and a uniformly distributed live load of 6.26 lb/ft2 (0.3 kPa). Two

7690 Int. J. Phys. Sci. requirements are be used to assess the dynamic performance of a steel framed floor system. The first requires that under the application of a static concentrated load of 225 lb (1.0 kN) anywhere on the floor, the floor deflection shall not exceed 0.0787 in. (2.0 mm). The Code suggests that this requirement will most likely govern the design of short open floors. However, the range of span lengths that correspond to short open floors is not specified in the Code. The midspan deflection of a floor joist is determined from the following equation

bb

d

IE

LP

48

3

Where

δ= midspan deflection of a single joist Pd = effective applied load = kd P P = 225 lb (1.0 kN) Onysko’s criterion Onysko‟s criterion is based on the results of an extensive field study conducted in the1970‟s in Canada (Onysko, 1985). The survey involved the assessment of perceived acceptability of 646 floors in five cities of all types of wood construction. Great care was taken to obtain the subjective evaluation of the suitability of the floor from the homeowner, not the vibration performance. The judgment of acceptability was based on the everyday experiences of the homeowners and not on a specific excitation of the floor

s

joist

K

PL

EI

PLx

PLPLEI

2

48

1

4848 3

33

Where EIjoist = apparent bending stiffness of the joist calculated at the trial span P = 225 lb (1.0 kN) L = trial span ∆ = deflection of a single joist EI = published stiffness of floor joist Ks = shear deflection coefficient Johnson’s criterion Johnson (1994) developed a design criterion for timber floors based on the results of 86 in-situ floors under construction. The original goal was to apply Murray‟s

criterion (Murray, 1991) for steel/concrete floor systems to timber floors. Instead, Johnson proposed that the fundamental frequency be greater than 15 Hz for a floor supporting only its own weight. Typically, the fundamental frequency is calculated from a single joist in the floor system. However, if a girder is contributing to the response of the floor, the system frequency is taken as the fundamental frequency. The fundamental frequency of a single joist is calculated from:

357.1

WL

gEIf

Where f = fundamental bending frequency g = acceleration due to gravity E = modulus of elasticity I = moment of inertia of joist alone W = self weight of the floor L = span length Composite action is ignored in the calculation of the moment of inertia. The conclusion that effective sheathing width is negligible resulted from numerous static deflection tests performed on laboratory built floors (Johnson, 1994). If girder effects cannot be ignored, Dunkerley‟s equation is used to calculate the fundamental frequency of the floor system. In simplified form:

girderjoist

girderjoist

systemff

fff

22.

Where fsystem is the fundamental frequency of the floor system, fjoist is the fundamental frequency of a joist and fgirder is the fundamental frequency of a girder. The 15 Hz criterion applies only to floors supporting their own weight and is intended to be used in the design stage to determine whether a floor system will be rated acceptable in terms of vibration level from human footfalls (Shue, 1995). Classification of the published literature Since the 1930s, the number of papers related to various aspects of human vibration has been growing rapidly, particularly because of the rapid development of trans-portation where problems due to higher level of vibration imposed on humans are more pronounced. Pavic (1999) classified the published papers into the following groups: Group 1: Literature mainly covering determination and modelling of dynamic forces caused by walking (vibration

source characterisation). Apart from office floors, such excitation is important when analysing more various specialised pedestrian structures such as footbridges and stairs. Group 2: Literature covering research into dynamic properties of floors as structural systems (vibration path characterisation) without taking into detail the vibration source or its receiver‟s response. Group 3: Literature covering the area of the receiver‟s response to vibrations without taking into detail the vibration source or its path (vibration receiver chara-cterisation). Typically, the role of the receiver is taken either by humans (Griffin, 1996) or sensitive equipment (Unger and White, 1979; Shioya and Maebayashi, 1988), the former being much more publicised than the latter. Publications into general human response to vibrations are pertinent to many areas such as defence, transportation, health and safety. For example, the review by Griffin alone (1996) contains more than one thousand references on human vibration. However, many of these are not relevant to the problem of low-level floor vibrations in quiet building occupancies. Compared to other applications, human response to building vibrations is under-represented in this group. Group 4: Literature covering vibration performance of floors in relatively quiet environments where all three key factors, the vibration source, path and receiver, are considered together. This integrated (or „packaged‟) approach can frequently be encountered when dealing with vibration serviceability of any type of floors in buildings (Wyatt, 1989; Eriksson, 1996). Consequently, majority of papers which specifically cover floor vibration serviceability belong to this group.

Group 5: Literature covering vibration performance of a wider range of structures, mainly under dynamic loads induced by groups of people. These publications typically deal with footbridges (Leonard, 1966; Smith, 1969; Blanchard et al., 1977; Campbell et al., 1979; Wheeler, 1980; 1982; Tilly et al., 1984), grandstands, gymnasia, dance floors (Allen et al., 1985; Rainer and Swallow, 1986; Allen, 1990a, b) and other types of structures where, generally, greater levels of vibration occur.

Group 6: State-of-the-art reviews or proceedings of specialised conferences published from time to time, where literature from all the above mentioned groups is included (Steffens, 1952; 1965; 1974; BRS, 1955; 1983; Galambos et al., 1973; Bachmann et al., 1991a; 1995a; NRCC, 1988; IABSE, 1993; Xiudong and Lei, 2011; Ma et al., 2010).

The literature classified as Group 4 and 5, which consider all key elements of vibration serviceability including the

Hamdan et al. 7691 possibility of annoying floor vibration, is the most relevant topic of this review. Most recent various papers are published on this topic (Thomas, 1998; Allen et al., 1998; Linda, 2003; Anthony, 2003; Chen Wei-min et al., 2006; da Silva et al., 2008; Jafari et al., 2009). SUMMARY The background reviews have presented an overview of relevant past research work which has been performed in the area of floor vibration serviceability prediction and assessment. In general, it is clear that, simplified techniques for prediction and assessment of floor vibration serviceability tend to be inadequate. Therefore a more rigorous treatment of the problem through modern experimental and analytical techniques has been applied. Nevertheless, there has been very little work on the quantification of this phenomenon. The few results which have been presented have tended to be conflicting and inconclusive. Consequently, there is a need for the effects of access floors to be investigated and quantified in such a way as to facilitate their inclusion in calculations aimed at predicting floor vibration serviceability. The background reviews have demonstrated that the problem of vibration serviceability of long-span concrete floors in buildings is complex and interdisciplinary in nature. Current state-of-the-art suggests that it is prudent to rationalise it into three key components comprising the characterisation of: (1) the floor vibration sources, (2) the floor structural dynamic properties, and (3) the receiver‟s response. Of these, the last is, from an engineering point of view, probably the most complex when humans are specified as the vibration receivers.

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