16-.Human-Structure Dynamic Interaction in Civil Engineering Dynamics a Literature Review

8/12/2019 16-.Human-Structure Dynamic Interaction in Civil Engineering Dynamics a Literature Review

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Human-Structure Dynamic Interaction in Civil

Engineering Dynamics: A Literature Review

R. Sachse, A. Pavic and P. Reynolds, Department of Civil and Structural Engineering, University of

Sheffield, Sir Frederick Mappin Building, Sheffield S1 3JD, UK.

Corresponding author:

Regina Sachse

Dept. of Civil and Structural Engineering

University of Sheffield

Sir Frederick Mappin Building

Mappin Street

Sheffield, S1 3JD

E-Mail: [email protected]

Phone: +44 (0) 114 222 5727

Fax: +44 (0) 114 222 5700

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ABSTRACT

This paper reviews more than 130 pieces of essential literature pertinent to the problem of human-

structure dynamic interaction applicable to the design of civil engineering structures. This interaction

typically occurs in slender structures occupied and dynamically excited by humans by walking,

running, jumping and similar activities. The paper firstly reviews the literature dealing with the effects

of structural movement on human-induced dynamic forces. This is the first of two aspects of human-

structure dynamic interaction. The literature dealing with this aspect is found to be quite limited, but

conclusive in stating that structural movement can affect the human-induced dynamic forces

significantly in some cases. The second aspect considered is how human occupants influence the

dynamic properties (mass, stiffness and damping) of the structures they occupy. The body of literature

dealing with this issue is found to be considerably larger. The published literature demonstrates

beyond any doubt that humans present on structures should not be modelled just as additional mass,

which is a common approach in contemporary civil engineering design. Instead, humans present on

structures act as dynamic spring-mass-damper systems interacting with the structure they occupy. The

level of this interaction is difficult to predict and depends on many factors, including the natural

frequency of the empty structure, the posture and type of human activity, and in the case of assemblystructures, relative size of the crowd compared with the size of the structure. One of the reasons for

the existence of more papers in this area is the published biodynamical research into the mass-spring-

damper properties of human bodies applicable to the mechanical and aerospace engineering

disciplines. It should be stressed that results from this research are of limited value to civil

engineering applications. This is because human bodies are, in principle, non-linear with amplitude-

dependent dynamic properties. Levels of vibration utilised when experimentally determining mass-

spring-damper properties of human bodies in biodynamical research are usually considerably higher

than those experienced in civil engineering applications.

KEYWORDS

literature review, human-structure interaction, dynamic occupant models, civil engineering

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1.INTRODUCTION

In civil engineering dynamics, human-induced vibrations are an increasingly important

serviceability and safety issue. In recent years, there has been an increasing number of problems

related to human-induced vibrations of floors, footbridges, assembly structures and stairs. Human-

structure interaction is an important but relatively new consideration when designing slender

structures occupied and dynamically excited by humans (Ellis and Ji, 1997).

Human-structure interaction is a complex, inter-disciplinary and little researched issue. To

summarise the existing knowledge, this paper reviews two key areas of human-structure interaction:

(1) how structural vibrations can influence forces induced by human occupants (section 2) and

(2) how human occupants influence the dynamic properties of civil engineering structures

(section 3).

Focusing more on the latter issue and limiting it to passive sitting or standing people,

biomechanics research and models of the human whole-body are then reviewed (section 4).

Furthermore, investigations analysing and modelling human occupants on civil engineering structures

are presented (section 5). Next, research into the potential of human occupants to absorb vibration

energy is reviewed and, finally, conclusions are presented.

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2.EFFECTS OF HUMAN-STRUCTURE INTERACTION ONHUMAN-INDUCED FORCES

Human occupants can induce dynamic forces on civil engineering structures by various activities

such as walking, jumping, dancing, or hand clapping. Research into quantifying such human-induced

forces has been ongoing for many decades (Tilden, 1913; ASA, 1932; Galbraith and Barton, 1970;

Nilsson, 1976; Matsumoto et al., 1978; Wyatt, 1985).

Since about 1980, experimentally established human-induced force time histories have usually

been approximated by Fourier series. Thereby, the common key assumption is that the human-

induced forces are perfectly periodic. The factors corresponding to each sinusoidal component of this

Fourier series are named dynamic load factors (DLFs) and are reported in a number of publications

(Pernica, 1990; Bachmann et al., 1995; Kerr, 1998). However, assuming human-induced forces as

perfectly periodic is questionable because they are in essence narrow-band (Eriksson, 1994). An

alternative approach is to define human-induced forces as auto-spectral density (ASD) functions

(McConnell, 1995) in the frequency domain (Ohlsson, 1982; Tuan and Saul, 1985; Mouring and

Ellingwood, 1994; Eriksson, 1994).

Dynamic forces induced by crowds are an issue of great concern (Kasperski, 2001), as can be seen

in an increasing number of publications dealing with crowd-induced vibrations. Nevertheless, the

quantification of crowd-induced forces still needs additional research. In particular, the dependency of

the nature and magnitude of induced forces on the size of the active crowd and perceptible motion of

the structure is currently not clear (IStructE, 2001).

Although it has been found that dynamic loads induced by groups of people are higher than those

induced by individuals, the human-induced forces do not increase linearly with the number of people.

This is so even if people are synchronised by a prompt (Ebrahimpour and Sack, 1992; Kasperski and

Niemann, 1993) that can be provided by music, movements of other people, or perceptible

movements of the occupied structure (Fujino et al., 1993; van Staalduinen and Courage, 1994).

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Int estingly, visual and audio contact between people influences and, in principle, improves the

syn

oading, and thus

amplif rom the

oldest

tory

re

perly amusing

themselves, by trying the extent of this motion, produced such an agitation in all its parts, that

important. It can lead to structural vibrations strong enough to disturb people in their movement

(Da nic.

used by this phenomenon, design

proposals by Schulze (1980), Vogel (1983), Slavik (1985), Grundmann and Schneider (1990) and

Gr

little understood phenomenon, was prompted by strong pedestrian-structure

er

chronisation of individuals (Hamam, 1994; Ebrahimpour and Fitts, 1996).

Generally, the synchronisation of people on civil engineering structures can be deliberate or

unintentional. Deliberate synchronisation, as in aerobic classes or cases of vandal l

ication of vibrations has been an important issue for a long time. The following quote f

reference in this review (Stevenson, 1821:243-4) clearly demonstrates this:

It is observed by Mr John Smith, one of the gentlemen above alluded to, that when the original

bridge of Dryburgh was finished, upon the diagonal principle like Fig. 2, it had a gentle vibra

motion, which was sensibly felt in passing along it; the most material defect in its construction

arising from the loose state of the radiating or diagonal chains, which, in proportion to their

lengths, formed segments of catenarian curves of different radii. The motion of these chains we

found so subject to acceleration, that three or four persons, who were very impro

one of the longest of the radiating chains broke near the point of its suspension.

After almost 200 years, Quast (1993) and Kasperski (1996) are still raising the same issue.

However, the unintentional synchronisation of human occupants is now also considered to be

llard et al., 2000) and, therefore, structures can become unserviceable or even unsafe due to pa

The unintentional synchronisation of pedestrians to structural movements is a case of human-

structure interaction. It has been observed on several footbridges as reported by Petersen (1972),

Bachmann (1992), Fujino et al. (1993), Dallard et al. (2000), Curtis (2001), New Civil Engineer

(2001) and Sample (2001). Acknowledging the potential problem ca

undmann et al. (1993) include various means of dealing with it.

Research into the reasons for and the extent of synchronisation between pedestrians and

footbridges has been performed by Schneider (1991) and Fujino et al. (1993). Recently, new researchinto this known, but

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synchronisation during the opening of the Millennium Bridge in London in June 2000 (Parker, 2000;

Fit

lez,

; Minetti et al., 1998; Farley

and Morgenroth, 1999) can probably add valuable knowledge to human-induced forces on civil

eng

ctures were modelled as mass-spring

systems also. More recently, Foschi and Gupta (1987), Folz and Foschi (1991), Foschi et al. (1995)

and Canisius (2000) looked at impactor-structure interaction.

zpatrick, 2001).

It should be realised that human-structure synchronisation is only one aspect of human-structure

interaction influencing human-induced forces. In fact, human-induced forces may depend on the

stiffness of the surface on which people perform (Pimentel, 1997). Indeed, Baumann and Bachmann

(1988) reported DLFs of walking to be up to 10% higher if measured on stiff ground and not on a

flexible 19 m long prestressed beam. Similarly, biomechanical research on jumping identified higher

human-induced forces on stiffer structures (Farley et al., 1998). In this context, it is important to note

that a vast amount of ongoing biomechanical research into human locomotion (Farley and Gonza

1996; Ferris and Farley, 1997; Hoffman et al., 1997; Farley et al., 1998

ineering structures but there is little evidence of cross-fertilisation.

Actually, civil engineers first investigated the interaction of human impactors and flexible

structures more than 20 years ago. In this research, individuals shouldering partition walls (Struck,

1976) or dropping onto planks and boards (Mann, 1979; Struck and Limberger, 1981) were

represented by simple mass-spring models and the flexible stru

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3.EFFECTS OF HUMAN-STRUCTURE INTERACTION ONDYNAMIC PROPERTIES OF CIVIL ENGINEERING

STRUCTURES

Human occupants present on civil engineering structures do not only excite the structure, but can

also simultaneously alter the modal properties of the structure they occupy. Therefore, strictly

speaking, modal properties of the joint human-structure dynamic system should be considered in a

design against human-induced vibrations. However, little reliable information on the properties of

occupied structures or even the modelling of occupants done is available. As a consequence, the

majority of civil engineering design procedures neglect the influence of human occupants on the

dynamics of the vibrating system.

However, when the influence of human occupants on the dynamic properties of civil engineering

structures is considered, occupants are often modelled just as additional mass to the structure. This

model has been widely accepted for a long time (Walley, 1959; Allen and Rainer, 1975; Ohlsson,

1982; Ebrahimpour et al., 1989). It was incorporated into Applied Technology Council (ATC) Design

Guide 1 (Allen et al., 1999) by adding a percentage of the weight of occupants (depending on the

posture of occupants and the natural frequency of the structure). Naturally, such a model leads to a

frequency decrease, as observed by Lenzen (1966) for a group of people occupying a floor.

However, Lenzen (1966) also reported, similarly to Polensek (1975) and Rainer and Pernica

(1981), a significant increase in damping due to human occupants. Based on these and other similar

investigations, such as those by Eyre and Cullington (1985), Manheim and Honeck (1987),

Ebrahimpour et al. (1989), Bishop et al. (1993), Quast (1993), and Pimentel and Waldron (1996), it is

nowadays widely accepted that human occupants add damping to structures they occupy. Moreover,

recent research by Brownjohn (1999; 2001) and Brownjohn and Zheng (2001) showed that an

occupant absorbed significantly more energy than a concrete plank supporting the person. However,

the potentially very beneficial effect of human occupants was included only into Canadian codes

(NRCC, 1985; 1995) and the ATC Design Guide 1 (Allen et al., 1999), which recommend viscous

damping ratios of up to 12% when designing heavily populated structures.

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The observed increases in damping due to human occupation cannot be explained by human

occupants modelled as additional mass only. Nevertheless, this mass-only model is used in the

National Building Code of Canada (NBC) guideline on human-induced vibrations of floors and

footbridges (NRCC, 1995), in the Green Guide (HMSO, 1997) and by Allen et al. (1999). It is also

still employed in the design of structures such as balconies (Gerasch, 1990; Setareh and Hanson,

1992), stadia (Eibl and Rsch, 1990; Harte and Meskouris, 1991; Batista and Magluta, 1993; van

Staalduinen and Courage, 1994; Bennett and Swensson, 1997; Reid et al., 1997) and footbridges

(Beyer et al., 1995; Luza, 1997; Hothan, 1999).

To address this inconsistency, Ohlsson (1982) and Rainer and Pernica (1985) indicated that

damped dynamic models of human occupants could be employed. In 1987, Foschi and Gupta adopted

this approach because damped dynamic models of human occupants can, contrary to the mass-only

model, explain significantly increased damping due to human occupation. However, it is generally

accepted (Ohlsson, 1982; Ebrahimpour et al., 1989) that the mass-only occupant model can accurately

predict frequency changes imposed by human occupants of civil engineering structures.

In 1988, experiments by Lenzing showed that the mass-only model does not always predict the

natural frequencies of human-occupied structures appropriately. Contrary to his expectations, the

fundamental frequency of a small wooden plate (74 Hz) did not reduce significantly if a person more

than twice as heavy as the structure (32 kg) was on it. Instead, the natural frequency of the structure

increased slightly (Lenzing, 1988). This phenomenon was readily explained by the human occupant

being a dynamic system with mass, stiffness and damping properties which is attached to the empty

plate and with a natural frequency lower than 74 Hz (Lenzing, 1988).

Three years later, in 1991, dynamic response measurements made on the occupied Twickenham

stadium (Ellis and Ji, 1997) also indicated that human occupants of a real-life civil engineering

structure were acting more as a dynamic mass-spring-damper systems than as just additional mass. In

particular, if occupied by spectators, the tested assembly structure clearly showed an additional mode

(Figure 1). Ellis and Ji (1997) hypothesised that this additional mode was caused by human occupants

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adding a degree of freedom (DOF) to the structure. A formal mathematical framework that proves this

hypothesis has recently been developed by Sachse (2002).

Using the response ASDs of three different trusses of Twickenham stadium, Ellis and Ji (1997)

estimated natural frequencies of the empty and the crowd-occupied structure by curve-fitting SDOF

and 2-DOF models respectively. This procedure led to the identification of a fundamental frequency

of the empty structure between 7.24 Hz and 8.55 Hz (Table 1). Under human occupation, the

estimated fundamental natural frequency was 5.13 to 5.44 Hz only and a second natural frequency

from 7.89 to 8.72 Hz, respectively, was identified (Table 1). Interestingly, crowds on another

assembly structure investigated by Ellis and Ji (1997) also reduced the fundamental frequency to

about 5 Hz, although the fundamental frequency of this temporary grandstand was identified as 16 Hz

when empty.

In the UK, civil engineering structures whose natural frequencies are above certain limits are not

req

ever,

f

d

cy

y

particular, Littler measured natural frequencies of a vertical and two horizontal modes of a

retr ing

uired to be designed against human-induced vibrations (BSI, 1996; HMSO, 1997; IStructE, 2001).

These limits are based on the ability of human occupants to induce significant forces at lower

frequencies. In case of vertical modes, BS 6399 (BSI, 1996) specifies 8.4 Hz and the Interim

Guidance (IStructE, 2001) states 6 Hz as limiting natural frequencies of empty structures. How

measurements by Ellis and Ji (1997) demonstrated that crowds can reduce fundamental frequencies o

relatively light empty assembly structures from as high as 16 Hz to about 5 Hz, which is below the

limits of 8.4 and 6 Hz. Therefore, the design approach of frequency limits of empty structures shoul

be re-evaluated particularly in case of assembly structures. Moreover, modelling occupants as

additional mass, which is requested by HMSO (1997), is unlikely to predict such strong frequen

reductions. Actually, to perform a proper design against human-induced forces, it might be necessar

to model individual occupants or the whole crowd as dynamic systems attached to the structure. The

relevance of this proposition is emphasised by measurements on other assembly structures reported by

Littler (1998; 2000).

In

actable grandstand when it was empty and when all 99 places were occupied by sitting or stand

people (Littler, 1998). The data (Table 2) resulting from peak-picking of response ASDs to a small

impact (Littler, 2000) show that the modes of the structure were affected differently by standing or

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sitting human occupants. Moreover, Littler (1998: 125) claimed that damping of the empty and the

two types of occupation varied considerably. Hence, a dynamic occupant model has probably to be

different for standing and sitting crowds. Importantly, the crowd shifted natural frequencies of not

only the vertical, but of the horizontal modes as well and significantly (Table 2). Therefore, dynami

occupant models have to be considered in the design of civil engineering structures against human-

induced vertical and horizontal forces.

c

summary, human occupation of civil engineering structures can lead to increased damping, a

sig

to

e

ecognising this issue, dynamic models of occupants on civil engineering structures are reviewed

in section 5. However, prior to this, biomechanical research of human whole-body vibrations is

bri

In

nificant reduction of fundamental natural frequencies and also to additional natural frequencies,

meaning additional modes of vibration. Such effects need to be accurately predicted to enable safe

and economic design and/or assessment of civil engineering structures against human-induced

vibrations. Therefore, appropriate dynamic models of human occupants have to be used. This is

particularly important in the design of slender assembly structures because they can be subjected

high levels of crowd-induced forces and their dynamic properties can be changed significantly (Tabl

2).

R

efly reviewed in the next section. In particular, limitations of biomechanical human models with

respect to civil engineering applications are presented and discussed.

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4.BIOMECHANICAL MODELS OF THE HUMAN BODY

A number of biomechanical models of individual humans has been developed mainly to be used in

mechanical and aerospace engineering (Griffin, 1990). Some models represent the whole body of an

individual and others model only parts such as hands. The latter models are used to analyse health

related issues and are not of interest here. However, some whole-body biomechanical models of

individuals were developed to predict dynamic properties of human-structure systems such as

occupied vehicle seats (Suggs et al., 1969; Wei and Griffin, 1995; Boileau and Rakheja, 1998). This

is a problem very similar to the influence of human occupants on civil engineering structures.

Therefore, dynamic whole-body models developed in this context are evaluated in this review.

4.1 Whole-Body Biomechanical ModelsBiomechanics researchers usually obtain dynamic characteristics of the whole human body

experimentally by placing a person on a shaking table in laboratory conditions. Thereby, the applied

force and the response of the human-structure system at the driving point are measured. These

experimental data are then used to calculate driving-point frequency response functions (FRFs). TheseFRFs generally relate an acceleration or velocity response to a sinusoidal base excitation with the

frequency fand are, therefore, provided as apparent mass ( )fM or mechanical impedance ( )fI

(Griffin, 1990). By curve-fitting such experimental FRFs, dynamic properties of biodynamic human

models are identified (Wei and Griffin, 1998).

The simplest biodynamic model of the human body is a damped single degree of freedom (SDOF)

system (Figure 2). This type of model can lead to good approximations of experimental and analytical

driving-point FRFs.

However, two peaks were often visible in the apparent mass ( )fM of sitting individuals (Wei and

Griffin, 1998; Mansfield and Griffin, 2000) and generally in the apparent mass of standing people

(Matsumoto, 1996). Therefore, the damped SDOF model (having only one peak in the FRF) was

extended into a two DOF model, which enabled fitting of two peaks in experimental driving-point

FRFs. The additional DOF was either attached to the first DOF (Allen, 1978) as shown in Figure 3a

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or, more often, completely independent of the first DOF (Suggs et al., 1969; Wei and Griffin, 1998)

as indicated in Figure 3b.

Further research showed that adding a non-vibrating mass to a SDOF model (Figure 4a) or a

2-SDOF model (Figure 4b) led to better fits of experimental FRFs. Wei and Griffin (1998: 870)

justified this non-vibrating mass m as presenting the effect of other modes that are above the

frequency range of interest, which is why they contribute only mass.

0Hm

0H

Finally, it is emphasised that models of the human body derived solely from driving-point FRFs

should not be used to predict movements of particular parts of the human body (ISO, 1981). For this

purpose, separately derived and more complex models of the human body are available (ISO, 1987;

Nigam and Malik, 1987; Qassem et al., 1994; Boileau et al., 1996). However, these models are often

unsuitable for describing driving-point FRFs (Boileau and Rakheja, 1998).

4.2 Properties of the Human Body

Most biomechanics research determining whole-body vibrations concentrated on vertical

vibrations of sitting (often male) people. Fewer investigations involved standing humans (Coermann,

1962; Matsumoto, 1996; Matsumoto and Griffin, 1998; 2000) or looked at horizontal vibrations

(Fairley and Griffin, 1990; Holmlund and Lundstrm, 1998; Mansfield and Lundstrm, 1999a;

1999b).

Many publications present experimental driving-point FRFs. However, only a few biodynamic

mo

ach of these models is characterised by its lumped properties of mass ( Hm ), stiffness ( Hk ) and

vis H

dels were fit into the experimental data. Four such whole-body models related to vertical

vibrations of a sitting person are presented in Table 3.

E

cous damping ( c ). They define the natural frequency fand damping ra (Table 3). It is

noteworthy that all ur models feature a heavily damped mode with natural frequencies

tio

fo 1f ranging

from 4.5 to 5.0 Hz and damping ratios ranging from about 20% to about 50% (Table 3).1

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The 2-SDOF models by Suggs et al. (1969) and Wei and Griffin (1998) have an additional DOF

and

al.,

, therefore, a second mode. This second mode accounts for a second broad peak in the frequency

range from 8 Hz to 15 Hz often apparent in driving-point FRFs (Fairley and Griffin, 1989;

Matsumoto, 1996; Matsumoto and Griffin, 1998; Mansfield and Lundstrm, 1999b; Holmlund et

2000; Mansfield and Griffin, 2000). However, the influence of the second mode on the apparent mass

( )fM is rather small. For instance, the apparent mass functions of frequency ( )fM of a SDOF and 2-

F models (both featuring a non-vibrating mass), which are based on the e experimental data

by Wei and Griffin (1998), match closely (Figure 5).

SDO sam

contrast to models based on the same research (Wei and Griffin, 1998), apparent masses ( )In fM

of

ying

major factor influencing the estimated driving-point FRFs is the excitation. Biomechanics

usu p to

esearch has shown that the frequencies corresponding to the peaks of driving-point FRFs

inc ody

models based on different research differ significantly (Figure 5). Also, driving-point FRFs

presented in different publications often differ significantly. This scatter is mainly due to emplo

different individuals (Hinz and Seidel, 1987; Fairley and Griffin, 1989; Mansfield, 1996; Matsumoto,

1996; Wei and Griffin, 1998). Additional variability is introduced by varying test conditions (Boileau

et al., 1998; Holmlund et al., 2000).

A

ally employ sinusoidal, sine sweep, or random excitation with frequencies from below 1 Hz u

about 20 Hz. The vibration levels range from 0.1 to 2.5 m/s2root-mean-square (r.m.s.) accelerations,

which correspond to vibration levels common in vehicles (Mansfield and Griffin, 2000).

R

rease with decreasing vibration levels that have some sort of stiffening effect on a human b

(Hinz and Seidel, 1987; Fairley and Griffin, 1989; Matsumoto and Griffin, 1998; Mansfield and

Griffin, 2000). For example, decreasing r.m.s. accelerations eight times, from 2 to 0.25 m/s2,

increased the frequency of the first peak of ( )fM of vertical vibrations of sitting people by 50%

of the first peak of ( )

, from

4 to 6 Hz (Fairley and Griffin, 1989). Simi atsumoto and Griffin (1998) found the frequencylarly, M

fM increased from 5 to 7 Hz if standing people were subjected to r.m.s.

2

accelerations of 2 and 0.125 m/s respectively.

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The amplitude dependency of driving-point FRFs corresponding to horizontal vibrations is less

clear. Generally, their natural frequencies also tend to increase with decreasing vibration level.

However, some of the modes in the frequency range below 10 Hz were found not to be affected

(Fairley and Griffin, 1990; Holmlund and Lundstrm, 1998; Mansfield and Lundstrm, 1999a).

The previously mentioned research data indicate that driving-point FRFs depend not only on

vibration levels but also on the posture of the person and the direction of the vibrations considered.

The differences between postures prompted the international standard ISO 5982:1981 (ISO, 1981) to

distinguish between vertical driving-point mechanical impedances ( )fI of a person sitting, standing,

or in a supine position. In this context, ISO 5982:1981 defined 2-SDOF (Figure 4) models of seated

or standing individuals (Table 4). Both models have similar properties particularly in the fundamental

mode (Table 4). The apparent masses ( )fM of both models (Figure 6) fit well within the apparent

masses ( )fM of sitting people defined in Table 3 (Figure 5).

Nevertheless, ISO 5982 was heavily criticised because of its limited and inconsistent experimental

background (Griffin, 1990; Holmlund et al., 1995; Matsumoto, 1996; Boileau et al., 1998). Recently,

a revision of ISO 5982 has been published (ISO, 2001). The revised standard includes a single more

complex model of a human body. This model aims to represent not only the driving-point FRFs, but

also the transmission of vibrations to the head of a seated person (ISO, 2001). Until the publication of

ISO 5982 in 2001, the transmission of vibrations to the head of a sitting or standing person could be

evaluated using the 4-DOF model in ISO 7962 (ISO, 1987), which was replaced by ISO 5982 (ISO,

2001).

In summary, when utilising the results of biomechanics research of whole-body dynamic models

in civil engineering, several important issues must be borne in mind. Firstly, the human body is a very

complex non-linear dynamic system that has properties that differ between different people (inter-

subject variability) and between individuals themselves (intra-subject variability) (ISO, 1981; Griffin,

1990). Secondly, vertical vibrations of the whole-body of sitting or standing people are dominated by

a heavily damped mode. This mode has a natural frequency between 4 and 6 Hz and its damping ratio

is quoted with values ranging from 20% up to 50%. Thirdly, and most importantly, the properties of

the human body strongly depend on the magnitude of vibration. However, vibration levels usually

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encountered in civil engineering are considerably smaller than those employed by biomechanics to

derive dynamic human models (Griffin, 1990). Therefore, it is essential to verify and, possibly, refine

biomechanical models before they are adopted to model human occupants of civil engineering

structures. Furthermore, all biomechanical models known to the writers represent single individuals

only. However, modelling groups of occupants is essential in modelling the dynamic behaviour of

assembly structures, which is a point of particular concern in civil engineering design.

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5.DYNAMIC MODELS OF HUMANS IN CIVIL ENGINEERING

Current design guidelines assess the vibration serviceability of civil engineering structures based

on their vibration response (ISO, 1989; BSI, 1992; ISO, 1992). However, as previously mentioned,

correct prediction of structural responses to human-induced vibrations requires detailed knowledge of

the dynamic properties of the joint human-structure system. With this in mind, civil engineers

increasingly investigate the effects of human occupants and attempt to model human occupants as

dynamic systems. Such research, which should lead to dynamic models of human occupants

appropriate for use in civil engineering, is reviewed in sections 5.1 and 5.2.

5.1 Experimental InvestigationsThe influence of human occupants on civil engineering structures is a complex issue and the

current state-of-the-art is such that this influence cannot be, according to Littler (1998),

mathematically predicted. However, the 1990s saw several attempts to quantify the influence of one

or two sitting or standing occupants on the dynamic behaviour of well-defined structures under

laboratory conditions.

5.1.1 Experiments by Ellis and JiInspired by the already mentioned measurements at Twickenham stadium (see section 3), Ellis and

Ji performed laboratory experiments on a simply-supported concrete beam. This particular research

was published widely (Ellis et al., 1994a; Ellis et al., 1994b; Ji and Ellis, 1994; Ji, 1995; Ji and Ellis,

1995; Ellis and Ji, 1997; Ji and Ellis, 1997; Ji and Ellis, 1999). The most informative papers are Ji

(1995), Ellis and Ji (1997) and Ji and Ellis (1999).

Ellis and Ji quantified the influence of four different individuals (a, b, c and d) on a high-

frequency (18.68 Hz) structure (Table 5). The laboratory experiments demonstrated that a single

occupant can increase the natural frequency and damping of a high-frequency (18.68 Hz) structure

(Figure 7). The research indicated that the influence of a human occupant depends on the individual

test subject (Table 5). Additionally, it confirmed the dependence of the influence of an occupant on

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his/her posture (Table 5) found by Littler (2000) (Table 2) and fits well with the biomechanical

research (Griffin, 1990).

Unfortunately, Ellis and Ji did not estimate damping and the ASDs given in Figure 7 were

reported without quantifying the response magnitude. Therefore, the effect of an occupant on the

response of the light beam structure employed cannot be evaluated.

Finally, Ellis and Ji (1997) claimed that moving people are a dynamic load only because neither a

jumping occupant nor an occupant walking on the spot changed the estimated natural frequency of the

beam. This statement contradicts the finding of Pimentel (1997: 201) that:

the natural frequencies of the structure during walking remained somewhere between those

obtained from pedestrians standing still (after jumping tests) and without pedestrians (following

walking tests).

Pimentel (1997) came to his conclusion observing the reduction of natural frequencies of 2.3 Hz,

3.6 Hz and 4.7 Hz of a footbridge. Instead of such a real-life structure, Ellis and Ji (1997) employed a

small beam with a non-typical high natural frequency, whose fundamental frequency was actually

increased by a stationary human occupant (Table 5). These differences might have led to the

apparently contradictory findings and further experimental investigations are required. They should

quantify the effect of moving occupants not only on natural frequencies but also on damping of the

occupied structure. Such an analysis might reveal that structures occupied by moving (walking or

jumping) occupants could be modelled as time dependent non-linear systems, as proposed by

Ebrahimpour and Sack (1992).

5.1.2 Experiments by Hothan (1999)Hothan (1999) analysed the influence of a static mass or a standing person on two similar beam-

like steel structures. The first structure was 5 m long and weighted 236 kg. It was set up with seven

different spans ranging from 4.8 to 2 m. The second structure was 4 m long and had a mass of 226 kg.

It had six spans ranging from 3.9 to 2 m.

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This phenomenon is particularly pronounced for structures with fundamental frequencies above 6 Hz

(Figure 8). It peaks with a difference of 2.7 Hz in experiment 12, where the empty structure had a

natural frequency of 9.78 Hz (Table 6).

Hence, modelling the human occupant as a mass only would significantly overestimate the

fundamental frequency 1f . This conclusion is in line with observations by Eibl and Rsch (1990)

made on a full-scale stadium. The two authors computed analytically a frequency reduction of a

beam-like structure from 3.9 Hz to 3.44 Hz due to the presence of 28 human occupants. However, the

experimentally estimated fundamental frequency was 2.91 Hz, noticeably lower than the predicted

3.44 Hz.

Figure 8 shows that a human occupant can reduce the fundamental natural frequency of a three

times heavier structure from above 9 Hz to below 6 Hz. In fact, the human occupant reduced natural

frequencies from above 6 Hz to between 4 and 5 Hz (experiments 10, 11 and 12 in Table 6 and Figure

8). This phenomenon corresponds to measurements by Ellis and Ji (1997) on Twickenham stadium

(Table 1) and another grandstand with a fundamental frequency of 16 Hz (section 3).

Similar to measurements at Twickenham stadium (Figure 1), Hothan identified additional modes

in the response spectra of the human-occupied structure. In particular, he noted second heavily

damped modes with natural frequencies of 6.6 Hz or 7.6 Hz in experiments 6 and 9 respectively

(Hothan 1999).

5.1.3 Experiments by Brownjohn (1999; 2001)Brownjohn (1999; 2001) investigated the influence of different postures of the same human

occupant on FRFs of a prestressed simply-supported concrete plank having a mass of 1200 kg and

spanning 6 m. He obtained FRFs of the empty and several cases of human occupation using linear

chirp excitation over a frequency range from 2 to 20 Hz. The experimental data collected (Table 7 and

Figure 9) confirm that the posture of a human occupant determines his/her influence on the occupied

structure (Tables 2 and 5).

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relatively low natural frequencies. However, it is opposite to the frequency increases observed by

Lenzing (1988) and Ji (1995) on structures with high fundamental frequencies (74 Hz and 18.68 Hz).

This fact can be explained by modelling humans as an additional dynamic system (Falati 1999).

Finally, it is noted that Falati (1999) reported larger frequency decreases for a static mass than for

occupant(s) on the structure (Table 8). This is inconsistent with experiments by Hothan (1999) and

Brownjohn (1999) (sections 5.1.2 and 5.1.3). However, this discrepancy might be explained by the

smaller mass of occupants in comparison to the mass of the structure in experiments by Falati (1999).

5.2 Dynamic Models of Stationary Human OccupantsTo predict mathematically the influence of (stationary) human occupants on civil engineering

structures, a limited number of dynamic models of human occupants are available. These can be

divided into damped and undamped models. The undamped models can be separated further into

discrete and continuous models. Models corresponding to each of the three groups (undamped

discrete, undamped continuous and damped) are reviewed here.

5.2.1 Undamped Discrete ModelsThree undamped SDOF models of human occupants were found in the literature (Table 9). All

three models are for standing occupants and are characterised by a mass m assumed to be equal to

the total mass of the person . However, the models have different stiffnesses and, therefore,

different natural frequencies

H

Tm

H

Hk

f .

Lenzing (1988) defined the stiffness by 50 kN/m probably based on research of Struck and

Limberger (1981) into human impact.

Hk

Hothan (1999) (section 5.1.2) specified the SDOF human model by a natural frequency Hf of

6 Hz because this value was quoted by Schneider (1991) as possibly corresponding to an upper body

movement. Using the resulting undamped SDOF model (Table 9), Hothan computed natural

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frequencies of a finite element (FE) human-structure model. The fundamental frequencies of this

human-structure model match his experimental data closely (Figure 10).

The third undamped SDOF model of a standing occupant listed in Table 9 was presented by

Williams et al. (1999). The numerical background of this model is not clear.

Also, Williams et al. (1999) extended this undamped SDOF model (Table 9) to an undamped 13-

DOF model, which was probably based on a model proposed by Nigam and Malik (1987). It is not

clear from the article how this was done or what the parameters of the MDOF model are.

5.2.2 Undamped Continuous ModelsAs previously mentioned, the undamped SDOF models (Figure 11a) presented by Lenzing (1988),

Hothan (1999) and Williams et al. (1999) (Table 9) all have a lumped mass assumed to be equal

to the total mass m of the human occupant. Although this might be a valid simplification, the mass

of a SDOF model (Figures 2 and 11a) of a continuous structure such as the human body is different

from the total mass of the structure (Ji 2000: 185). Therefore, Ji (1995) and Falati (1999) developed

and analysed continuous models of the standing human body to estimate the mass of SDOF

models of standing people.

Hm

T

Hm

Ji (1995) employed a continuous bar with two segments of different masses and stiffnesses (Figure

11b). He assumed that the stiffness k ranges from 0.5 k to 2 k . Based on this assumption, he

concluded that the mass of an undamped SDOF system (Figure 11a) representing one of the first

four modes of a standing human ranges from 1/2 m to 2/3 m .

H 1H 1H

Hm

T T

A significantly lower value m = m /3 was derived by Falati (1999) by employing a uniform

continuous model of a standing man (Figure 11c).

H T

Both Ji (1995) and Falati (1999) then used the theoretically derived lumped mass m to estimate

the stiffness k of an undamped SDOF human model (Figure 11a). Thereby, both researchers

simplified both the human occupant and the occupied structure as undamped SDOF systems. Thus,

H

H

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the human-structure system is an undamped 2-DOF system, whereby the human DOF is connected to

the grounded structural DOF. This undamped human-structure model can be defined uniquely by:

(1) the natural frequency of the empty structure ( Sf ),

(2) one of the two natural frequencies of the undamped 2-DOF human-structure system (

or ) and

( )UM1f

( )UM2f

(3) the lumped masses of the structure ( m ) and the human occupant ( m ).S H

Knowing these parameters, the natural frequency of the DOF representing the human occupant

( Hf ) can be estimated using Equation (1) (Randall and Peng, 1995) whereby expf is the measured

natural frequency of the structure and stands for or .( )UM

1f ( )UM

2f

( )2exp

S

H2S

2exp

2S

2exp2

H

fm

m1f

ffff

+

= (1)

Applying this theory, Ji (1995) concluded that the natural frequency of a standing person ranges

from 10 to 12 Hz. Falati (1999) computed a similar frequency of 10.43 Hz, which was based on the

seemingly mistyped natural frequency of the occupied structure of 7.76 Hz (Table 8).

It is noted that the same procedure of assuming an undamped 2-DOF human-structure system was

employed by Randall et al. (1997), who used a structure with a fundamental frequency of about

40 Hz. However, in contrast to Ji (1995) and Falati (1999), Randall et al. (1997) probably assumed

the total mass of the human occupant to be m = m . They determined the natural frequenciesH T Hf of

113 individual standing occupants to range from 9 to 16 Hz.

To summarise, Ji (1995), Randall et al. (1997) and Falati (1999) identified similar natural

frequencies Hf of undamped SDOF models of standing people. Interestingly, the identified natural

frequencies cover a range (9 to 16 Hz) significantly higher than commonly reported in biomechanics.

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5.2.3 Damped ModelsBiomechanical research established that the human body is heavily damped. This was recognised

by civil engineers and led to the development and use of some damped SDOF models of human

occupants (Figures 2 and 4b).

To the best of the writers knowledge, Foschi and Gupta (1987) were the first to use a damped

dynamic human model. This was done to predict the vibration response of wooden floors to heel-drop

excitation. (A heel-drop is defined by a man weighing about 170 lb (77 kg) rocking up on the balls of

his feet, lifting his heels about 2.5 in. (6.4 cm) off the floor, then relaxing, allowing his heels to

impact the floor (Allen, 1974)). This, and subsequent research by Folz and Foschi (1991) and Foschi

et al. (1995) into response time histories to assess the serviceability of floors led to damped SDOF

models characterised by an assumed lumped mass m equal the total mass of the impactor, a

viscous dashpot = 1.25 kNs/m and a stiffness = 40 kN/m (Foschi et al., 1995). This model

resulted from a comparison of experimental displacement response time histories to heel-drop and

computed responses of a human-structure model to a SDOF human model impacting the floor with a

certain velocity. However, the lumped mass was assumed, the actual excitation history was apparently

unknown, and presented analytical and experimental response time histories (Foschi et al., 1995) do

not fit very closely. Nevertheless, this damped SDOF impactor model was adopted by Al-Foqahaa

(1997) to propose a design criterion for the vibration serviceability of wooden floors.

H

Hk

Tm

Hc

Falati (1999) added a viscous dashpot to his undamped SDOF model ( Hf = 10.43 Hz, m = m /3)

presented above and thus developed a damped SDOF model (Figure 2a) of a standing (not impacting)

person (Table 10). To determine the damping ratio of the damped SDOF human model, Falati

computed responses of the structural DOF of damped 2-DOF human-structure models and compared

them to experimental time histories. For this purpose, Falati probably used decaying vibrations caused

by a heel-drop. He identified the damping ratio to be within a range from 45% to 55% (Falati,

1999) and employed the median value of 50% to define a model of a standing person (Table 10).

H T

H

H

Another damped SDOF model of a human occupant was used by Brownjohn (1999) to predict the

influence of a standing human occupant on his test structure. For this purpose, he defined a damped

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SDOF model assuming the lumped mass m to be the total mass m of the human occupant (Table

10). Brownjohn also choose the stiffness k and the viscous damping c to lead to a natural

frequency

H

H

T

H

Hf and a damping ratio corresponding to the fundamental mode of a 4-DOF human

model given by ISO 7962 (ISO, 1987). However, it is noteworthy that this ISO 7962 model serves

only for estimating the transmission of vibrations to the head of sitting or standing people. It is, in

contrast to the 2-DOF models of ISO 5982 (see section 4.2), not aimed at modelling the influence of

human occupants on the dynamic behaviour of occupied structures.

H

Nevertheless, the natural frequencies and damping ratios of the fundamental mode of a damped 2-

DOF human-structure model were 2.93 Hz and 2.0%. Thus, they correspond to the experimentally

determined properties of the beam-like test structure occupied by an erect standing or a seated person

(Table 7).

Brownjohn (2001) fitted a damped SDOF model into the apparent mass of a single person with a

total mass of 47 kg standing on a test structure. He obtained the best SDOF circle-fit for Hf = 5.8 Hz,

= 38% and a lumped mass m = 60 kg, thus exceeding the weight of the occupant. Thus,

Brownjohn found the natural frequency

H H

Hf of a SDOF model of single standing person to be

significantly higher than the 4.9 Hz of his first human model (Brownjohn, 1999).

To determine the variability of the natural frequencies of standing humans, Zheng and Brownjohn

(2001) estimated natural frequencies Hf of 30 standing individuals. For this purpose, they used a 4 m

long reinforced simply-supported concrete plank that had a fundamental natural frequency of 12.8 Hz.

Probably employing sinusoidal shaker excitation, Zheng and Brownjohn estimated natural frequencies

and damping ratios of the empty structure and of the structure with each of the 30 test subjects

standing at midspan.

Zheng and Brownjohn (2001) used these experimental natural frequencies and damping ratios to

compute the natural frequencies Hf and the damping ratios of damped SDOF models of individual

occupants. This calculation also used the modal mass of the fundamental mode of the empty structure,

which was probably calculated from the spatial properties of the structure. Additionally, it required

H

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the lumped mass of the SDOF occupant model to be known. Similar to most other researchers, Zheng

and Brownjohn set this mass m to be equal the total mass of the occupant.H

Zheng and Brownjohn (2001) concluded that Hf and of the test subjects are about 5.24 Hz and

= 39%, respectively. Thus, the identified natural frequencies

H

H Hf match biomechanical research

(Tables 3 and 4) more closely than the significantly higher Hf identified by Ji (1995), Randall et al.

(1997) and Falati (1999). However, similarly to Randall et al. (1997), Zheng and Brownjohn found no

clear dependency of Hf on the total mass m , the height, or the mass/height ratio of individuals.T

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7.CONCLUSIONS

Human-structure interaction is an important aspect of human-induced vibrations. Nevertheless, its

multiple effects are little researched and understood. However, this issue has to be well understood to

successfully design slender structures occupied and dynamically excited by humans, in particular

assembly structures.

Broadly speaking, human-structure and dynamic interaction covers two aspects: (1) how structural

movement affects human induced dynamic forces, and (2) how humans change dynamic properties of

structures they occupy. The literature dealing with the first aspect was found to be quite limited.

However, the literature reviewed was quite conclusive in stating that structural movement can affect

the forces - significantly in some cases.

To predict accurately the influence of human occupants on dynamic properties of structures they

occupy, dynamic human occupant models are required. Biomechanical human whole-body models are

only of limited value because the properties of the human body depend on the level of vibration and

significantly lower levels of vibration are encountered in civil engineering than used to derive the

reviewed biomechanical human models. Furthermore, in civil engineering, the effect of groups of

occupants is of primary importance for vibration design although occupant models themselves could,

via absorbed energy for example, also be used to assess serviceability.

So far, several SDOF models of single people standing on civil engineering structures have been

proposed. However, all these SDOF occupant models are based on more or less unwarranted

assumptions in respect to damping and/or the lumped mass of the occupant model. Furthermore, the

experimental data presented in the literature and used to derive the properties of human occupant

models were often incomplete and unreliable. Therefore, there is an urgent need for further research

into modelling human occupants of civil engineering structures, particularly groups, which should

employ sophisticated techniques yielding more reliable experimental data.

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ACKNOWLEDGEMENT

The research presented in this paper has been conducted as part of an EPSRC funded project titled

Dynamic Crowd Loading on Flexible Stadium Structures, grant reference GR/N38201, whose support

is gratefully acknowledged.

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Table 3. Characteristics of biomechanical models of a sitting human subjected to vertical vibrations.

Model Spatial properties Modal Properties

Coermann (1962) a):

Damped SDOF model

Hm = 86.2 kg (86200 dyne s2/cm)

Hk = 85.25 kN/m (85.25 dyne/cm)

Hc = 1.72 kNs/m (1.72106dyne s/cm)

1f = 5.0 Hz

1 = 32%

1Hm = 36.3 kg (80 lb)

1Hk = 28.45 kN/m (1952 lb/ft)

1Hc = 474 Ns/m (32.5 lb s/ft)

1f = 4.5 Hz

1 = 23%Suggs et al. (1969) b):

2-SDOF model2Hm = 12.5 kg (27.6 lb)

2Hk = 15.03 kN/m (1030 lb/ft)

2Hc = 271 Ns/m (18.6 lb s/ft)

2f = 5.5 Hz

2 = 31%

0Hm = 4.1 kg -

Wei and Griffin (1998) c):

SDOF model

with non-vibrating mass

1Hm = 46.7 kg

1Hk = 44.115 kN/m

1= 1.522 kNs/mHc

1f = 4.9 Hz

1 = 53%

0Hm = 5.6 kg -

1Hm = 36.2 kg

1Hk = 35.007 kN/m

1Hc = 815 Ns/m

1f = 4.9 Hz

1 = 36%

Wei and Griffin (1998) c):

2-SDOF model

with non-vibrating mass2Hm = 8.9 kg

2Hk = 33.254 kN/m

2Hc = 484 Ns/m

2f = 9.7 Hz

2 = 44%

Imperial units were converted into metric units employing Beranek (1988: appendix B3).

a)Based on the mechanical impedances ( )fI of eight men.

b)Based on the mechanical impedances ( )fI of 11 men.

c)Based on the apparent masses ( )fM of 60 people.

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Table 4. Characteristics of human models specified in ISO 5982 (ISO, 1981).

Model Spatial properties Modal Properties

1Hm = 69 kg

1Hk = 68 kN/m

1Hc = 1.54 kNs/m

1f = 5.0 Hz

1 = 36%ISO 5982 (ISO 1981):

2-SDOF modelof the seated human body 2H

m = 6 kg

2Hk = 24 kN/m

2Hc = 0.19 kNs/m

2f = 10.1 Hz

2 = 25%

1Hm = 62 kg

1Hk = 62 kN/m

1Hc = 1.46 kNs/m

1f = 5.0 Hz

1 = 37%ISO 5982 (ISO 1981):

2-SDOF model

of the standing human body 2Hm = 13 kg

2Hk = 80 kN/m

2Hc = 0.93 kNs/m

2f = 12.5 Hz

2 = 46%

Table 5. Influence of a single human occupant on natural frequencies of a beam (Ji, 1995; Ji and Ellis,

1999).

Configuration

Naturalfrequency

[Hz]

empty beam 18.68

one sitting human occupant (a) 19.04

one standing human occupant (a) 20.02

one standing human occupant (b) 20.51

one standing human occupant (c) 20.51

one standing human occupant (d) 21.00

mass of 45 kg (100 lb) on the beam 15.75

mass of 91 kg (200 lb) on the beam 13.92

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Table 6. Influence of a single human occupant or an equivalent mass on natural frequencies 1f and

damping ratios 1a)of steel structures (Hothan, 1999: appendix 3).

Emptystructure

Human occupantEquiv.mass

No.1f

[Hz]1

[%]1f

[Hz]1

[-]1f

[Hz]1

[-]

1 1.98 0.4% 1.51 1.0% 1.53 0.5%

2 2.27 0.3% 1.71 0.8% 1.72 0.3%

3 2.82 0.2% 2.05 1.0% 2.08 0.3%

4 3.49 0.1% 2.47 1.5% 2.55 0.2%

5 4.06 N/A 2.98 N/A 3.10 0.1%

6 4.12 N/A 3.31 2.5% 3.43 N/A

7 3.63 N/A 3.39 N/A 3.43 N/A

8 4.62 0.1% 3.36 2.2% 3.51 0.1%

9 5.75 0.1% 3.91 N/A 4.27 0.1%10 6.36 0.1% 4.23 N/A 4.68 0.1%

11 8.00 0.2% 4.72 7.2% 5.80 0.1%

12 9.78 0.03% 4.73 13.6% 7.46 0.1%

13 9.84 0.03% N/A N/A 8.39 0.03%a)Hothan (1999) provided logarithmic damping decrements that were evaluated and converted into

damping ratios using

1 2 (Chopra, 1995).

Table 7. Influence of a single human occupant (80 kg) or an equivalent mass on the natural frequencyand damping ratio of a beam-like structure (Brownjohn, 1999).

Configuration

Naturalfrequency

[Hz]

Dampingratio

[-]

empty beam 3.16 0.8%

erect standing occupant 2.87 2.0%

occupant standing with bent knees 2.86 6.0%

occupant standing with very bentknees

3.10 9.2%

sitting occupant 2.82 2.8%

equivalent mass 2.95 1.1%

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Table 8. Influence of human occupation or a mass on the natural frequency and damping ratio of aslab (Falati, 1999: 170).

Configuration

Naturalfrequency

[Hz]

Dampingratio

[-]

empty structure (without two screed

layers)

8.02 1.10%

one human occupant (75 kg) 7.76a) 3.84%

equivalent mass of one man (75 kg) 7.68 1.45%

empty structure with two screedlayers

10.15 1.25%

one human occupant 9.96 3.11%

two human occupants 9.96 3.46%

equivalent mass of one occupant 9.93 1.28%

equivalent mass of two occupants 9.81 1.28%a) This value was mistyped by Falati and should read 7.79 Hz.

Table 9. Characteristics of undamped SDOF models of a standing human occupant (Lenzing, 1988;Hothan, 1999; Williams et al., 1999).

Human Model Spatial propertiesModal

Properties

Lenzing (1988)Hm = m (76 kg)T

Hk = 50 kN/mHf = 4.1 Hz

Hothan (1999)Hm = m (80 kg)T

Hk = 113.7 kN/mHf = 6 Hz

Williams et al.(1999)H

m = m (75 kg)T

Hk = 66 kN/mHf = 4.7 Hz

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16-.Human-Structure Dynamic Interaction in Civil Engineering Dynamics a Literature Review