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°*£AU 0? NBS TECHNICAL NOTE 904

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

orrelation of Floor Vibration

to Human Response

QC

100

U5753

no, 904

1976

c.2
NATIONAL BUREAU OF STANDARDS

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1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

- Located at Boulder, Colorado 80302.
James R. Shaver

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

Sponsored by

Office of Policy Development and Research Department of Housing and Urban Development

Washington, D.C. 20410

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Correlation of Floor Vibration

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I ' C-O o to Human Response

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U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

US NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

\\\ Issued May 1976
National Bureau of Standards Technical Note 904

Nat. Bur. Stand. (U.S.), Tech. Note 904, 29 pages (May 1976) CODEN: NBTNAE

Supersedes NBSIR 75-951

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1976

For sale by llie Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.46:904). Price 75 cents (Add 25 percent additional for other than U.S. mailing
TABLE OF CONTENTS

Page

Abstract 1

1. Introduction 1

2

Background 2

3. Approach to Problem 3

4. Data Reduction and Analysis 5

5. Damping 8

6. Human Response to Vibration 9

7. Summary 11

8. References 12

9. Appendix A: Field Test 14

10. Appendix B: Computer Program 15

CORRELATION OF FLOOR VIBRATION

TO HUMAN RESPONSE

James R. Shaver

A new approach to the problem of perceptible floor vibrations

is presented based on the assumption that human activity, which

produces the vibration, and human response to vibration are random variables. Techniques for data reduction are discussed

and a detailed description of one approach is given along with the

associated computer programs. Data from floor vibrations is

compared with current criteria for human response.

Key words: Analysis; experimental; floor systems; human response;

random process; spectral analysis; vibration.

1. INTRODUCTION

Historically, the design of floor systems for serviceability has been

based on limiting the deflection that can occur for a given design load to

prevent structural damage. It was believed by most engineers that this design

procedure indirectly accounted for the effect of human activity on floor

systems which could produce quite perceptible and annoying vibrations for other

human occupants. Research and state-of-the-art studies [1,2,3]— conducted

during the past decade on the various aspects of vibrating floor systems have

increased the awareness of the engineering community to the fact that the traditional

serviceability design procedure does not necessarily lead to floor systems with

satisfactory dynamic characteristics which prevents objectionable vibrations

from the occupant viewpoint when the floor is subjected to human activitv.

Recent efforts [4.5] to study the problem of perceptible floor vibrations

have primarily employed experimental techniques. Results from these studies

have been inconclusive as to what constitutes objectionable floor vibration

from an occupant viewpoint. Questions have been raised about the proper

forcing function to be used in the test to simulate human activity [2,5] and

the lack of information on the human response to this type of vibration [4]

The experimental procedures used have been based on the assumption that both

human activity which produces vibration and occupant response to vibration

of a floor system are deterministic variables. However most scientific studies

which deal with human activity and human response as variables treat them as

a random variable rather than a deterministic one.

- Numbers m brackets refer to literature references
This report describes a new approach to the problem of perceptible floor

vibrations based on the assumption that human activity and human response to

2/ vibration are random variables. Presented is a random varxable methodologybased on physical testing and subsequent analysis of the dynamic response of

floor systems subjected to human activity.

2 . BACKGROUND

In order to understand why both human activity and occupant response

should be characterized as random variables, it is necessary to understand

the difference between a deterministic variable and one that is random. A

deterministic variable is one whose value can be calculated or determined

from knowledge of its behavior at any previous instant in time, while a random variable is one whose instantaneous value cannot be predicted with

complete certainty for any given instant in time. This means that the

instantaneous value for a random variable can only be specified by a probability distribution function which gives the probable fraction of the total

time that the instantaneous value lies within a specified range.

If one considers all the possible parametric variations that can affect

the instantaneous value of the dynamic loading that occurs from human

activities such as walking, running, jumping, it becomes clear that each

activity is, in itself, a random process composed of many variables. For

example, considering footfall or walking since it is the most prevalent

activity that occurs on a floor system, variations in weight, gait, heel-toball of foot contact and foot wear of individuals will all affect the instantaneous value of the dynamic loading that occurs.

It appears, from an examination of the literature, that no definitive

study has been made to determine the statistical data needed for characterization of footfall as a random variable. However, a 1961 English floor

abrasion study [4] made some quantitative measurement of the forces applied

to the floor by walking and does give some insight into the nature of footfall from a static viewpoint. A typical plot of the vertical force component

for a footfall, obtained in this 1967 study, appears in Figure 1. Figure 1 shows two peaks and a trough. As pointed out by the authors, the first and

second peaks will vary in time of occurrence from initial contact and there

is often, although not always, a discontinuity in the curve as it rises to

the first peak. The study also indicated that if the vertical force component was considered in relation to the weight of the person, it appeared

2/—This methodology was developed as part of a larger research effort into the

nature of structural deflection limitations sponsored by the Department of

Housing and Urban Development.
that the trough in the curve is always less than body weight while the

peaks may be either above or below depending on the manner in which the

body trunk is accelerated. Additional information is needed on the duration

of footfall, its frequency content and probability of peak values in order

to describe it as a random dynamic forcing function.

The human response to vibration involves many variables: vibration

input where intensity, frequency, direction and duration must be considered;

psychological influences in the form of mental state, motivation and experience; and physical influences from sound and sight. Given this multiplicity

of parameters, it is reasonable to classify human response as a random

process

It should be pointed out that the structural floor systems are not

considered to be a random variable. Although there are several types of

floor systems, their dynamic properties can be described deterministically

from an engineering viewpoint. Rather it is the forcing function (human

activity) and the human response to this activity which must be considered

as random processes. This makes the overall problem of human response to

floor vibration induced by human activity a random vibration problem. This

can be stated in functional form as:

F(t) + G(t) -> Y(t) =5> D(t)

where F(t) is the random forcing function, G(t) is the deterministic floor

system characteristics, Y(t) is the random response of the floor system and

D(t) is the random human response to the floor vibration, Y(t)

3. APPROACH TO PROBLEM

The dynamic response of a floor system subjected to human activity

represents a random physical phenomenon which cannot be described by an explicit mathematical relationship because any given observation will

represent only one of the many possible results which might have occurred.

A single time history representation or observation of the random phenomenon

is called a sample function (a sample record when observed over a finite

time interval) . Then the collection of all possible sample functions which

the random phenomenon might have produced is called a random process. From

a given sample function it is possible to estimate statistical parameters

necessary to describe the random process.

Four main types of statistical functions are used to describe the

basic properties of random data: (a) mean square values, (b) probability

density functions, (c) autocorrelation functions, and (d) power spectral

3
density functions. The mean square value furnishes a rudimentary description

of the intensity of the data. The probability density function furnishes

information concerning the properties of the data in the amplitude domain.

The autocorrelation function and the power spectral density function furnish

similar information in the time domain and frequency domain, respectively.

While it is possible to determine the required parameters directly

from the time history under certain simplifying assumptions, the majority

of the techniques used to date perform the analysis in the frequency domain.

Analysis in this domain is usually termed spectral decomposition.

There are three reasons for selecting spectral decomposition over time

history to represent one's data. First, spectral decomposition presents

data in a form that is related to quantities familiar to engineers. Many

physical systems (including the human body) have been modeled with a fair

degree of success in this domain. Most models, for example, consist of a set of simple second order oscillators connected in a manner which simulates

the various components of the particular physical systems. Such a model is

shown in Figure 2. Each oscillator has its own oscillatory or resonant

frequency which, in turn, is dependent upon the size, shape and material

of the component it is simulating. Since each oscillator will be

excited primarily by energy at its resonant frequency, the knowledge of the

frequency content of the response provides the key to the determination of

the system response to impulse or shock, such as that produced by footfall.

Generally, the response of a floor system at resonant frequencies will

predominate in the total response. The second reason for utilizing spectral

decomposition is the independence of each frequency component from all

others. This independence in the frequency domain greatly simplifies

analysis. By comparison, the determination of a response in the time

domain at some instant in time is dependent not only on the value of the

excitation at that time but on all previous values of the excitation.

Third, this type of analysis can be used to describe input data, F(f), re- sponse data, Y(f), or, if the input and response are measured simultaneously,

it can be used to describe the frequency response function, G(f), of the

system as shown in Eq. 3.1. Specifically, given any two of the above

items, the third can be determined.

Y(f) = |G(f) | 2 F(f) (3.1)

The primary approach to obtaining a meaningful dynamic response of a floor system subjected to human activity is to first obtain a time history

and then transform this time history into the frequency domain using Fourier
techniques. In addition, the mean square value and probability density

function should be obtained. It does not appear at this time that the

autocorrelation function or the power spectral density function will provide

any useful information.

4. DATA REDUCTION AND ANALYSIS

Spectral decomposition or analysis using Fourier techniques consists

of decomposing a time history in terms of trigonmetric functions. The

magnitude and phase of each trigonometric term needed to reconstruct the

time history are plotted as a function of frequency. This technique is

simply the evaluation of the finite, Fourier transform of the time history

as expressed by Equation 4.1 where the time history x(t) is multiplied by

the Fourier kernel, a complex exponential containing both the frequency and

time variables, and then integrating this product over the record length;

T/2 ._ - X(f) = / x(t)e : rtdt (4.1)

-T/2

Using Euler's transformation, the kernel may be expanded so that Eq.

4.1 may be rewritten as,

T/2 T/2

X(f) = / x(t) cos 2TTftdt - j / X(t) sin 2iTftdt (4.2)

-T/2 -T/2

This equation shows how spectral analysis can be considered as a decomposition

of the time history in terms of sine and cosine components.

In order to evaluate this integral by digital techniques, one must

solve the discrete, finite Fourier transform which is given as

X(kAf) = AtV X. e -J2^kAfiAt

(4 _ 3)

i=o

where X. is the digital representation of the time history obtained by

sampling the continuous record at At intervals and the natural frequency

spacing for the complete transform is

Af = -i- (4.4)

NAt

Then kAf is defined by

kAf Nit' k= °' *' 2 '-- N/2 (4 ' 5)

Equation 4.3 may then be rewritten as N-l -i2iTik

X, = At £ X. e N k = 0, 1, 2,..., N/2 (4.6)

K 1 i=o

5
Employing Euler ' s formula again and rewriting, Eq. 4.6 becomes

X

k = A

R

- jB

R k = 0, 1, 2, ..., N/2 (4.7)

where .. , N-l - ., A, = At I X. cos =^i^ (4.7a) k . i N i=o

N-l _ .

,

B. = At Z X. sin fliJS (4.7b) k . l N i=o

A computer program can be written which will evaluate Eq. 4.7 directly.

However, this program would require a rather large amount of running time

particularly when large volumes of data are being analyzed. Although the

most efficient techniques known to date for evaluating Eq. 4.6 are the Fast

Fourier Transform (FFT) methods, they were not used because these methods

are not straight forward in their application and do require some special knowledge and experience for proper utilization.

The evaluation procedure employed to evaluate Eq. 4.7, was first

derived by Goertzel [5] and is believed to be the most efficient of the

pre-FFT methods. The method requires the generation of an auxiliary variable

Q as follows:

Qo =0

Q

i = Vi

Qi = (2 cos ^ ) Q i

_ 1 -Q

i

_ 2 + X -i, i = 2, 3 ,..., N-l (4.8)

Then, A and B in Eqs. 4.7a and 4.7b become

A

k

= At [(cos 2*k,

QN_a

-Q

n_ 2 + X

q

]

B

k

= At (sinM) QN-1 , k=0, 1,..., N-2 (4>9)

This technique was utilized in the spectral analysis of the 40 second walking

record obtained using the test procedure given in Appendix A and required

less than 3 seconds for 12,000 data points on a UNIVAC 1108 with an EXEC 8 system. The computer program is given in Appendix B. It should be remembered that the evaluation of X, by Eqs. 4.8 and 4.9 would require

generally unacceptable amounts of computer running time when extremely

large volumes of data are to be analyzed.
The most useful output from the Fourier spectrum is the modulus. This

modulus is obtained by realizing that the Fourier spectrum can be represented

by a complex expression.

X(f) = |x(f)| e^ 6(f) (4 - 10)

where |x(f) | is the modulus and e

-1 is the phase.

From Eq. 4.7, the expression for the finite Fourier transform, the

modulus is,

ii 2 2 1/2 |Xk

| = (A^ + Bj) L/l

(4.11)

The modulus dimensionally represents a pseudovelocity and it can be

shown [6] that this is identical to the relative velocity of the residual

response for a linear undamped single degree-of -freedom system when the

system response is a pure sinusoid. In general, the two will be in close

agreement for any undamped system with the pseudovelocity lower at low

frequencies and higher at high frequencies than the relative velocity

because of its frequency dependence.

The phase presentation of the spectrum may prove to be useful in

determining damping in the system. Again from Eq. 4.7, the phase angle is

given by

-1 B

k

= tan x ~ (4.12) A

k

Figure 3 is a plot of the modulus of the spectral decomposition of

the 40 second walking record. The values of this modulus are in mq-s which

is a pseudovelocity in feet per second. This graph is also called an energy

density curve in random data analysis. Due to filters in the acceleration

signal conditioning equipment all input above 2 5 Hz has been removed thus

accounting for the low energy content above this value.

The acceleration record was sampled every 160 ms which is

equivalent, because of a difference in record and playback speed of the

analog data tape, to a 10 ms sampling rate in real time. At the 10 ms real

time sampling rate, 1191 samples were taken thus producing a natural frequency

spacing of 0.084 Hz in the Fourier transform. The modulus of the spectral

decomposition has been plotted at every 0.5 Hz.

An examination of Figure 3 indicates that significant amounts of

energy occurs in the range of 15-25 Hz with a pronounced peak at 18 Hz

which is the fundamental frequency for the floor tested. The existence of

7
energy in this range indicates that a vibrating floor system is capable of

inducing a human response to vibration at frequencies other than the

lowest natural frequency of the system. Thus, test procedures which determine

the vibration level only at the fundamental frequency for the floor system

may exclude significant energy levels at other frequencies.

The missing link at this time is a means of transforming the energy

level at these frequencies to a corresponding root-mean-square (rms) acceleration at the same frequency thereby permitting a comparison with the current

human response criteria. However, it is possible to determine the rms acceleration for the record and associate it with the lowest natural frequency

for comparison purposes. This is done in section 6.

5. DAMPING

Damping in floor systems is a very complex quantity yet its measurement

is important since it effects the level and duration of vibration. In

addition, it has been suggested that in the case of a single pulse input

the occupants will perceive motion at a lower threshold if the vibration of

the floor does not decay rapidly. Although the scope of the study did not

permit an investigation into more effective means of determining damping

and relating its effect to human response a brief discussion will be given

because of the significant role damping plays in any dynamic problem.

Structural damping that occurs in floor systems is composed of three

primary components: (1) material damping which is the ability of the

materials themselves to dissipate energy, (2) interlayer slip which is

energy dissipation through friction between the subfloor and joist and (3)

end conditions which may damp motion by inducing support vibration or dissipate energy through friction. Generally, the energy loss from material

damping is small as compared to the amount dissipated by slip and support

effects.

There are six generally accepted mathematical means of representing

damping: (1) logarithmic decrement, (2) amplification factor, (3) quality

factor, (4) equivalent dashpot constant, (5) complex modulus and, (6)

bandwidth. For the simple case of a linear single degree of freedom

system, a relationship can be established between all six definitions, but

for other cases this is no longer necessarily true. When structural damping

is of primary interest any one of the six representations could be used

with some degree of success depending upon the end result desired. Logarithmic decrement or decay rate is the simplest to measure experimentally but

8
is difficult to use in design or analysis. The most useful form of presentation for the designer is specific damping energy, in inch- pounds per

cycle, while for purposes of analysis the equivalent dashpot constant is

most useful.

However, from the viewpoint of the present approach taken in this

methodology and its emphasis on spectral techniques, the use of either the

bandwidth method or quality factor in characterizing the damping of structural

floor systems should lead to a better means cf describing the damping

quality of floors as it relates to human response to vibration. While it

appears feasible at this time to obtain these damping characteristics from

a spectral decomposition, this derivation is beyond the scope of this

report.

6. HUMAN RESPONSE TO VIBRATION

Human body vibration is usually treated as an externally-applied

condition, although it is often self-induced such as during walking or running. The spectrum of human reaction to vibration is extremely wide

encompassing both "pleasant" effects which range from relaxation to stimulation and "unpleasant" effects which span from discomfort to injury. Much

of the information and literature concerning the effects of vibration on man is of a provisional, specialized or contradictory nature. This is

particularly true in the area of human response to floor vibrations where

only in the past decade have attempts been made to quantify this response.

Thus, there does not exist, at this time, a consensus standard for determining whether or not floor vibration induced by human activity is acceptable

from the occupant viewpoint.

This section will present the current state of knowledge on human

reaction to externally applied vertical transient vibration against which

the results of the proposed floor vibration methodology already given might

be compared

The current state of knowledge on human reaction to externally-applied

vertical transient vibration is based on a limited number of studies and

represents a wide range of thresholds. However, as basic as it is, this

knowledge is currently the only information on which to base a judgement of

whether or not a floor is acceptable from a human response viewpoint.

The ISO Guide for the Evaluation of Human Exposure to Whole-Body

Vibration ISO/DIS 2631 [7] provides allowable rms accelerations at different
frequencies for various levels of exposure time. It is primarily intended for

periodic (sinusoidal) vibrations in the frequency range from 1 Hz to 80 Hz but

does cover narrow-band or wide-band vibration within this frequency range.

In the case of either wide- or narrow-band random vibration, the allowable

accelerations are based on the limit given for the center frequency in each

third octave band.

Splittgerber [8] has proposed a standard based on the ISO Guide which

provides vibration and shock limits for occupants of buildings. This

proposed standard differentiates between continuous or intermittent vibration

and impulsive shock excitation during either a day or night environment.

It also contains vibration limits for different types of occupancy such as hospital, residential, office, etc.

A standard acceleration level is specified for each direction of

vibration and then permissable acceleration levels are obtained for the

different types of vibration input, occupant classification, and time

conditions by applying an appropriate weighting factor to the standard.

Figure 4 shows the ISO Guide's standard acceleration curve for vertical

vibrations and Splittgerber ' s permissable acceleration level for intermittent vibration in residences during the daytime hours. This daytime

level is based on minimum complaints from the occupants and was obtained by

applying a weighting factor of two to the standard curve.

Plotted on Figure 4 for purposes of comparison is Lenzen's [9] modification of the original Reiher and Meister work [10] on steady state vibrations

for transient vibration. Lenzen's modification considers transient vibration

as a vibration which may last only a few seconds but is characterized by a buildup to a level which is maintained for several cycles. Realistically,

Lenzen's definition fits the vibration produced by a single footfall or someone jumping with Splittgerber ' s definition fitting the vibration produced

by walking or running. The dashed lines on Figure 4 denote the slightly

perceptible range for Lenzen's modification which is again believed to

represent a minimum complaint level.

Also plotted in Figure 4 is Splittgerber ' s rms acceleration limit for

daytime impulsive shock in residences which he characterizes as a rapid

buildup to a peak followed by decay. It is comparable to Lenzen's definition

for transient vibration. This acceleration limit was obtained by weighting

the standard curve by sixteen. As can be seen from Figure 4 there is good

agreement between these two criteria for f > 8 Hz with a divergence of the

two below this frequency. No definite conclusion can be drawn at this time

on the reason for this divergence in the low frequency range.

10
Plotted as a triangle on Figure 4 is the peak rms acceleration of 0.95

mg as determined from the 40 second continuous walking test record. This value

was obtained using analog techniques with the time constant of the rms meter

and scan rate of the data adjusted so that the uncertainty is less

than 2% and is the peak rms value associated with maximum acceleration.

Since the major energy component in the frequency spectrum occurs at 18 Hz,

in accordance with the ISO Guide, this rms value is plotted at a frequency

of 16 Hz as this is the center frequency for the third octave band in which

18 Hz falls.

A reinterpretation of this rms acceleration with regard to frequency

and type of excitation was also made in order to compare the results with

Lenzen's criteria. Lenzen's criteria would consider it to be a single

pulse at the predominate floor frequency which in this case is 18 Hz. The

maximum rms acceleration is found from the expression:

A = -i- A . rms /=— peak

and is 1.2 mg . This value is plotted as a circle on the figure.

From the figure it can be seen that the treatment of the walking

record as an intermittent vibration gives a resulting rms acceleration

slightly below the standard curve and well below the minimum complaint

level. Treating the data as being comparable to single footfall or an impulsive shock which is the case for the plot of the peak rms acceleration

it is obvious that the results are not realistic.

An interview with the occupants of the rlwpll.ina where the test data were obtained indicated that the vibrations produced by walking were not considered

annoying although at times they were perceptible. It is interesting to

note that a deaf couple living in this housing project used floor vibrations

(which are, in this case, quite low) as a means of sensing the presence of someone in the room.

7 . SUMMARY

In this report a new approach to the treatment of perceptible floor

vibrations is presented based on the concept that human activity and human

response to this activity are random variables. The reasons for choosing

the random process approach to this floor vibration problem are given along

with an overview of the method in functional form. A description of the

random process and the statistical functions used to treat random data is

presented.

11
Spectral analysis is chosen over time, history, as the method for

analyzing floor vibration data. A computationally efficient procedure for

obtaining the Fourier spectrum is given along with the associated computer

software

The current state of knowledge on human reaction to externally applied

vertical transient vibration is discussed. One record of human activity

obtained in a field test is analyzed using the techniques presented in this

report and the results compared with a proposed standard for vibration and

shock limits for occupants of buildings.

8 . REFERENCES

1. Lenzen, K.H., "Vibration of Steel Joist-Concrete Slabs Floor System - Final Report," Studies in Engineering Mechanics , No. 16, Center for

Research in Engineering Science, the Univ. of Kansas, Lawrence, Kansas,

August, 1962.

2. Onysko, D.M., "Performance of Wood-Joist Floor Systems - A Literature

Review," Forest Products Laboratory, Information Report OP-X-24,

Ottawa, Ontario, Canada, January, 197 0.

3. Glamabos, T.V., Gould, P.L., Ravindra, M.R., Suryoutomo , H., Crist,

R.A., "Structural Deflections - A Literature and State-of-the-Art

Survey," Building Science Series 47, National Bureau of Standards,

Washington, D.C., October, 1973.

4. Harper, F.C., Warlow, W.J., Clarke, B.L., "The Forces Applied to the

Floor by the Foot in Walking," National Building Studies, Research

Paper 32, Building Research Station, Watford, England, January, 1961.

5. Geortzel, G., "An Algorithm for the Evaluation of Finite Trigonmetric

Series," American Mathematical Monthly , Vol. 65, No. 1, January, 1958,

pp. 34-35.

6. Rubin, S., "Concepts in Shock Data Analysis," Shock and Vibration Handbook

(Harris, CM., Crede, C.E., Eds.) Vol.2, Ch . 23, McGraw-Hill Book Co.,

New York, 1961.

7. International Organization for Standardization, "Guide for the Evaluation

of Human Exposure to Whole-Body Vibration," Draft International Standard

ISO/DIS 2631, May, 1972.

12
8. Splittgerber , H., "Vibration and Shock Limits for Occupants of Buildings,"

ISO/TC 108/SC4/WG2, Draft document, June, 1973.

9. Lenzen, K.H., Dorsett, L.P., "Effect of the Variation of Structural

Parameters on the Vibrational Characteristics of Steel Joist-Concrete

Slab Floor Systems and Suggested Designs," Studies in Eng. Mech. No.

32 , Univ. of Kansas, Lawrence, Kansas, August 1968.

10. Reihler, H. , Meister, F.J., "The Sensitivity of Humans to Vibrations,"

Forsc auf den Gebiere des Ingenieureuesens , Vol. 2, No. 11, November,

1931.

13
9. APPENDIX A Field Test Procedure

The physical test procedure to be used must be designed for field

application. Because of this requirement, the instrumentation must be

simple and require a minimum of set-up time with little inconvenience to

the occupants where the test is being made. A transducer which has the

required sensitivity and response time and measures acceleration is preferred

since it directly measures the quantity generally considered by most to be

related to human response. Velocity transducers may also satisfy the above

requirements but the subsequent differentiation needed to produce acceleration

is often difficult to achieve without loss of information. Displacement

transducers are difficult to satisfactorily employ in the field for this

type of test, due to physical restraints of installation and reference

datum. In addition, these transducers generally do not have the proper

time response. Transformation of the displacement data to acceleration

would also result in a considerable amount of lost information.

A displacement transducer was used in addition to an accelerometer in

the field test.

Description of Test Site

The site selected for application of this methodology was a single

family attached house (townhouse) with a wood-joist floor system located in

Gaithersburg, Maryland. The house was occupied at the time of the test and

furnished as shown in Figure 5. The floor system was typical of that found

in many houses and consists of 2 x 8 wood joists spaced 16 in on center

overlaid with 1/2-in plywood, The joists have a clear span of 12 feet 10

inches with diagonal bridging at mid-span. A synthetic wood floor tile is

attached to the plywood subfloor by an adhesive. The floor construction is

shown in Figures 6 and 7,

Floor response measurements were obtained from both an accelerometer

and linear variable differential transformer (LVDT) . The range of the

accelerometer is from 10 mg to 0.001 mg. Figure 6 shows the location of

this instrumentation. The LVDT was positively attached to the joist at

mid-point of the clear span and the accelerometer set on the floor directly

above the LVDT. Output from the LVDT and accelerometer were recorded as. analog signals. While the frequency response of the electronic equipment

was adequate to reproduce the time histories, the signal conditioning

equipment for the accelerometer has a cut-off frequency of 25 Hz. This is

generally considered satisfactory for most wood-joist floor systems.

14
Test Procedure

A series of tests were made using two procedures: (1) human activity

represented by a 170-lb man walking in a normal traffic pattern, and (2)

dropping a 25-lb bag from several heights. The first procedure is typical

of a minimum human activity on a floor system while the second one has been

used in the past as a method to assess the adequacy of floor systems from a vibrational viewpoint.

During the activity test, the walker utilized a path which was considered

typical of the traffic patterns in that room. This path was followed for

approximately 4 seconds.

The bag was dropped from heights of 7, 6, 5 and 4 inches. Several

tests were made for drop heights greater than 7 in and, in each instance,

the accelerometer raised from the floor in a rebound action.

Test Results

The walking test is the most significant data obtained since it is

representative of the human activity that most frequency occurs on floor

systems. In addition, it is a minimum type of activity as compared to

running, jumping, etc. The accelerometer is a representative measure of

the human response as its output is that which is preceived by a human

standing or sitting in an unpadded chair at the location of the transducer.

A typical segment of this record is given in Figure 8 .

10. APPENDIX B Computer Program

The computer program developed to perform the spectral decomposition

of a digitized time history is presented. The main program acquires a channel of digitized data, called data counts, from tape and then converts

this to data in engineering units. The program assumes that the data is

going to be either a record of displacement measurements or acceleration and

makes the conversion upon being given the appropriate conversion factor and

displacement or acceleration identification. Following the conversion, the

data is made available to a subroutine which, using the Fourier techniques

described in section 4.0, performs the spectral decomposition. The program

is written in Fortran V and is operational on a UNIVAC 1108 system equipped

with Exec 8 . Only minor modification needs to be made to the main program

for operation on any computer with a Fortran V compiler assuming the input

data tape is compatible with the one for which the program was written.

However, the subroutine can be used, without any modification, on a system

with a Fortran V compiler.

15
COMPUTER PROGRAM FOR FLOOR VIBRATION ANALYSIS

DIMeNs»ON IHEADU2), IjIMEjq), 1MUXTM2), IGA1NU21, CNVFC(12),

I IBUT( 120(30) , XU2000), TlME(l2000), IDCDU2). I0P<12)

DIMENSTON REL VEC ( AOnO ) , EMG VEC f 6000 ) , FREQ16000)

EQUIVAt ENCE ( I HEAD ( J ) , ID J , ( ! HEAD ( 2 ) . 1 RUN ) ,

(

l HEAD ( 3 )

,

NSCPRC) ,

1 (!HCAD(H),NRCPFL),(!HEAn(5),NSM!N),<lHEA0(6),NSSEC),

I

( I HEAD (7) .NgMsEc) , ( I HEAD ( 8 ) , I T ! ME ( 1 ) ) , ( I HEAD ( 9 > , 1 1 1 ME ( 2 ) »

,

1 ( I HE AD ( 10) , I TIME (3) j ,( I HEAD ( 11) ,!TIME(<4) 1 , ( I HE AD (.12) .NCHSNJ

C*****READ PROGRAM AND ChAnNEL C

RDS •••«•••***•••••*«••••*•••****• •***• READ(5,60o1 NDCH, tPSDFC

600 FORMAT? I5.EJ2.M, 15)

DO 5 !! i NDCH

5 READ(5,600) IDCD(!», CN VEC t I ) • I OP < I ) NDCHRD

c »read ht a ding record a n d ch a wnel nos. with gain** **** ***•••«»

CALL NTran(7,2, 12, iHFAD.L.2?)

IF ( L+| .LT. ) GO TO 90

CALL N'»'RANI7,2,NCH«;N^IMUXT,L.22)

IF < L+l ,LT. ) f,0.T0 90

CALL NTrAn<7,2,NCH S n, IGAIN.L ,2?)

IF ( L*| ,LT. ) GO TO 90

C*****WRITE READING AND cHaNNEL NOS. WITH G A I N* • *•••*•••••*•••• • •*•*••*•

WRITE< A, 601) ID, IrUN, NSCPRC, NRCPFL , NSMIN, NSSEC, NSMSEC ,

1 ( ITI M E( I ) , I«l ,<4 ) , NCHSN

601 FORMAT' lHl • • » * X , »SlTE ID . 15 / 15X, 'RUN NO.t, 15 / 15X t

1 'STAMS / RECORD = *. 15/ I5X, 'RECORDS / FILE »', 15 /

1 1 5X7 'SCAN INTERVAL MN» • , I H , 3X , • SC« * , I *• , 3X ,

« MS« • , H /

1 15X^ 'TIME *' , l3,» ' • ,12, •

:

,T2,» : • ,12 / 15X,

1 »N*. CHANNELS SCA N *', I * // ) WRlTE(A,602) (IMUX T ( J) ,IGAIN( J) , J-1.NCH5N ) 602 FORMAT? | 5 X, CHANNEL', 13. 2X, ,GA!N«, I 3 ) C*****READ A»'D WRITE CHANNEL OF DATA COUNTS* ***••*•*••»•*•••** »***«*••

500 CALL NTran(7,2, 120nO, IBUF,u,22)

IF ( L*l .LT. 1 GO TO 90

NDCHRD * NDCHRD + 7 NDTPCH * NSCPRC • NRc p FL

WRITER, 6o3> IMUXT(NDCHRD) , ( IBUFU), I I . NDTPCH ) 603 FORMAT' 1 H 1 . * X , VHaNNEL', 13, 1517 / ( 15X, 1517 ) > C***»*IF DATA is DlSPLACpMFNT ( CODE * 1 ) REMOVE OFFSET* •••••*•« ••**•

IF j I^CD(NOCHRD) '.E0. ) GO TO 100

DO 10 Tal, NDTPCH

10 !B0>( I » > IBUF( I ) „ JBUF( 1 ) C*****CDNVER ,; lON FROM DATA COUNT TO ENGINEERING UN I TS»« •••**••*•*•*•« •*•

100 DO 20 T«l , NDTPCH

20 X(I) » ( 10 • IBUF(I) ) / ( 20<4fl • IGAIN(NDCHRD) * CNVFC < NDCHRD ) ) C«****FILL TTME ARRAY********« »»** ****»****************»*******»*»*»

DELTAT 3 ( NSMIN * 6n + NSSFC + NSMSEC * 0.001 ) * TPSDFC

TIME( 11 0.

DO 30 1=2, NDTPCH

30 TIME(H = T!ME«I-1> DELTaT

C*****WRITE CoNvERtED DAtA*«»»«»**«»*«*»»*»«**»»»»*»»»»«*»*»**»**»**»«* # IF ( I^CD(NDCHRD) .EO. ) GO TO 200

WRITE* * ,6Q<4» IMUXTjNDCHRO)

60<4 FORMAT' I H 1 , 1 X , VHaNnEL', 13, « IS DISPLACEMENT IN INCHES* ) GO TO >00

200 WRITE(*,6o5) I MUX TNDCHRD ) 605 FORMAT' lHl, « X , VH A NNEL', 13, • IS ACCELERATION IN MG» ) 300 WRITE(6,606) (TIME(I)i X(I), 1*1, NDTPCH)

606 FORMAT' IOC F*.3, E 1 2 • 1 ) ) c ***** S pe: c tral analysis ( c ode » 1 I************************************

IF ( I"P(NDCHRD) ,f0. 1 GO TO 400

CALL F*URTR(X,NDTPcH"DELTAT,EMGVEC,RELVEC,FREQ)

MOO IF ( NDCHRD - NDCH 1 5oO

CALL NTRANJ7.10)

GO TO '05

90 WRITE(A,607)

607 FORMAT '» ***»**• L =*,ll,' •*•***••)

205 STOP

END 16
SUBROUTINE FOR SPECTRAL DECOMPOSITION

SUBROUTINE FOURTRIx.N.DELTATiEMGvEC.RFlVFCtFREQ)

DIMENSION RECFOR(3,, REL VEc ( 60Q0 ) , EMG VEC < 6000 ) , FREQ<6000>,

1 X(»2000)

L N - I M N / 2 00 100 K a 0,M

OMEGA 6.2831853 • < / N CS0ME6 » COS(OMEGA)

SNOMEG SINIOMEGAJ

C*»*«* EVALU*TE RECURRSIoN FORMULA ••* * •«»•••••••••«

RECFORf 1 ) * X(N)

RECF0Rf2> X( N-l ) RECF0RI3) X( N-2 ) * 2 . CS0ME6 • RECF0R(2) - RECFOR(l)

DO 200 I « 3,L

RECFORf I ) « RECF0R(2»

RECF0R»2) * RECF0R,3)

200 RECF0R(3) * X( N-I ) 2. • CSOMEG • RECF0R(2) - RECFOR(l)

C****« COMPUTE REAL AND IMAGINARY VECTORS ••••••*••»•«••••••*••**•*•

FREO(K> » K / f N « OELTAT ) EMGVECfK) REcF0R(3l * SNOMEG • DELTAT

100 RELVECfK) * < X(0) RECF0R(3) * CSOMEG - RECF0R(2) > * DELTAT

C*«»*t COMPUTE ABSOLUTE vAlUE ••**•••••*•*••*•••**••••••*••*•••*•<

DO 300 K=O.M

300 X(K) SORT( RELVEc«K»»*? EMGVEC(K>»»2 ) WRITEC*,201> < FREg(HT), RE L VEC(k), EMGVEC ( K ) , X ( K> , K»0,M ) 201 F0RMATf|Hj, H X , «4F)6.8 / ( 5X, 4F16.8 / ) ) RETURN

END

17
!20

(533.8)

105

(4670)

90

(400.3)

75 r (333.6)

uT 60

o (266.9)

O

45 r (200.2)

30

(133.4)

15

(66.7)

Figure 1 VERTICAL LOAD FROM FOOTFALL [f|

18
F(t)

M,

K,

M, M.

K l±J C

2

C3M >K

3

S"

Figure 2 ENGINEERING VIBRATION MODEL

19
z

00

o

ro

CVJ

>-

o z

CM M UJ

_L a

>- >

O

z

LJ UJ

l£> o Z

LLi UJ

cr CO

L_

4) O O)

s-^'srnnaow u3iunoj

20
io-' I

rms.g

Id3

LENZEN'S

PERCEPTIBLE

RANGE

SPLITTGERBER

MINIMUM COMPLAINT

LEVEL

1

10

f,Hz

20

/

SPLITTGERBER

IMPULSIVE SHOCK

SO

STANDARD CURVE

50 100

Figure 4 HUMAN RESPONSE THRESHOLDS

TRANSIENT VERTICAL VIBRATION

21
N"

/y.

m

22
I

I I

I

i

I I

!

1 I

I

I

I

I

I

I I 'II

J-2x8 JOISTS

r i !6inO.C. Z^i

!

' .

r a-^ i

i

I LVDT S^ I ACCELEROMETER

I

I

I I

i

I

lzlzizlzl -l-lrr

K

PARTITION

^SUPPORT BEAM

DOWN

Figure 6 FLOOR PLAN OF TEST FLOOR

23
EhD

Cm

EhD

O

EhH

i. FIGURE 7 TEST FLOOR UNDERSIDE

24
1ft*

-

J----J- — —

l ---

— -: —

-. f V,

> c*

i

-

-

V

!• V

3P»

:

; ^

j

/

-

fv 1

..._.!. 1^3

!

i - ! -- - .j

i •

i

- -'-• f

i

co

Oj

OSw —

wW

CJo 4 w

:| 4—

- ^T

-H- -l" -- ~

i

\ _-__ - jf"

>

E1

I : i] : Jf | j

CO J.

Ifc

fcc

2

rt

p.

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1 _| .. c i s

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<:

ftCOQ
TH6S-1.4A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN-9042. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Correlation of Floor Vibration to Human Response

5. Publication Date May 1976

6. Performing Organization Code 461.01

7. AUTHOR(S)

James R. Shaver

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4618381

11. Contract/Grant No.

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Office of Policy Development and Research

Department of Housing and Urban Development

Washington, DC 20410

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code Samp as 17

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary ot most significant information. If document includes a significant

bibliography or literature survey, mention it here.) A new approach to the problem of perceptible floor vibrations is presented predicated

on the realization that human activity and human response to this activity are random variables. Techniques for data reduction are discussed and a detailed

description of one approach is given along with the associated computer program.

Data from floor vibrations is compared with current criteria for human response

to vibration.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Analysis; experimental; floor systems; human response;

random process; spectral analysis; vibration.

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