SCI P076 Design Guide for Floor Vibrations

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A

Steel Construction

Institute

Publication 4—

inassociationwiththe 4

Construction

_Industry

1

n

Association

11

1 _________ 1 14 ___________________________ 4

1

4 1 44 4 1.1 1411 4,1 4:

(7is

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Although

care

has been taken

to

ensure,

to

the

best

of

our

knowledge, that

all

data

and

information contained herein are

accurate

to

the extent that they relate

to

either matters

of

fact

or

accepted

practice

or

matters

of

opinion

at

the time

of

publication,

the Steel

Construction

Institute assumes no

_{responsibility}

for

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of

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their

use.

Design Guide

on

the Vibration

of

Floors

T.

_{A. Wyatt}

BSc PhD FEng FICE

ISBN: 1 870004

34 5

©

The

Steel Construction Institute 1989

SCI

PUBLICATION 076

The Steel Construction Institute Silwood Park Ascot Berkshire SL5 7QN Telephone 0990 23345 Fax 0990 22944 Telex 846843

Construction Industry Research and Information Association

6 _Storey's Gate London SW1 P 3AU Telephone 01-222 8891

Fax 01-222 1708

FOREWORD

This

_publication

is

intended

to

provide

guidance

for

designers

in an

important

area of

design where

information

is

lacking.

It

has

been prepared

by

Dr

T

A

Wyatt

of

Imperial

College with

assistance

from Dr

A F

Dier

of

the Steel

Construction Institute.

The Guide was drafted in

_conjunction

with the

_support

of

a

_{steering committee}

which

commented

on

and

otherwise

advised

on

the draft

versions.

The

members

of

the

_steering

committee comprised:

Mr

B

Boys British

Steel

Structural Advisory Service

Mr

R

Clark _{Skidmore Owings}

&

Merrill

Mr

E

Dibb-Fuller

_{Building Design}

_Partnersh'ip

Mr

E

Dore

CIRIA

Mr

K

Irish

Vibronoise Limited

Mr

R

Povey

Mitchell

McFarlane

&

Partners

Mr

M

Willford

_{Ove Arup &}

Partners.

The work

_leading

to

this

_publication

has

been funded by

British

Steel

General Steels, and

the Department

of

the

Environment

under

a

CIRIA

research

_{project. Studies are}

continuing

and

future

editions

of

the

_publication

will

be

amended

as

necessary

to

account

for new

results.

The Steel

Construction Institute

will

be

pleased

to

receive any

comments

concerning

this

publication

and

subject area.

How

to

Use

this

Guide

The

Guide is

divided

into seven

Sections

and two

_Appendices

as

shown

on the

_facing

page.

Section 1

is

intended

as

a

broad

introduction

and has been

written

in

such

a

_way

that

it is

suitable

for

copying

to

a

Client

as an

aid

to

preliminary discussions.

The

background

to

the design procedures, which are set out in

Section

7,

is

given

in

Sections

2

to

6

and

a

study

of

these will

be an

aid, although

not

normally necessary,

in

the

application

of

Section

_{7. The design}

_procedures

of

Section

7 are

self

contained

as far

as is

_practical,

although

in

some

cases reference

to

Section

5.2

_may

be

_required.

The

_examples in

Appendix B will be useful for

following

the design

procedures. Explanation

of

terms used

for

describing dynamic behaviour, which

may

not be

familiar

to

the

non-specialist,

will be

found in

Section

_{4.2 where they are highlighted by italic}

_{script. Defmitions essential}

for

the application

of

the design

procedures

are given

in

Section 7.1.

CONTENTS

Page

SUMMARY iv

NOTATION iv

1. INTRODUCTION 1

2. SOURCES

OF

VIBRATION EXCITATION IN BUILDINGS 3

3. HUMAN REACTION TO VIBRATiON 6

3.1 Review

of

Factors 6

3.2 Specifications 7

4. GENERAL CONSIDERATIONS 10

4.1 Structural and Floor _{Configurations} 10

4.2 Introduction

to

Dynamics 11

5. EVALUATION

OF

NATURAL FREQUENCY 16

5.1 _Component and _{System Frequencies} 16

5.2 Practical Evaluation 17

6. FLOOR RESPONSE 20

6.1 Low Frequency Floors 20

6.2 High Frequency Floors 21

7. DESIGN PROCEDURES 25

7.1 Definitions 25

7.2 General Considerations 25

7.3 Procedure

for

_{Checking Floor Susceptibility} 26

7.4 Natural Frequency 26

7.5 Floors

of

_{High Natural Frequency} 27

7.6 Floors

of

_{Low Natural Frequency} 28

7.7 Acceptance Criteria 30

REFERENCES 31

APPENDIX A: CALIBRATION STUDY 32

SUMMARY

This publication presents guidance

for the design

of

floors

in

steel framed

structures

against

unacceptable vibrations caused

by

pedestrian

traffic.

It

has particular relevance to

composite floors

comprising permanent

metal

decking

topped with

concrete.

As

well

as

the design

procedures

set out

in

Section

7,

the Guide contains background

commentary

and

a

general,

non-technical, introduction.

Notation

a acceleration _amplitude

acceleration

_response

_{(Canadian Code)}

b

floor beam

_spacing

effective width between floor

beams

B

_{parameter for}

effective

width

(Canadian Code)

GB

factor for

determining

natural

frequency

C

Fourier

_{component factor}

C,

effective mass and

lateral

distribution factor for

_{impulsive loading}

C

effective mass and

lateral

distribution factor for

sustained vibration

El

flexural rigidity

(of

composite

section where

appropriate)

f

natural

_frequency

f0 fundamental

system

frequency

f1,

J,

f3

idealised

component

natural

frequencies

of

f0

g

acceleration

due to

gravity

J

impulse

(= force

x

time)

k

stiffness

1,

L

floor beam span

lengths

L

length

of

span

Leff

length

for

establishing

effective

mass

Lm

main beam

span

rn distributed mass

rn _lumped

mass

at

mesh point

'i'

M

effective modal

mass

P

static load

P

force

_amplitude

P1

amplitude

of

fundamental

_{Fourier component}

of

_walking

force

P

weight

of

oscillating

mass

distributed

_loading

R

_{multiplication}

_{factor applied}

to

human reaction

base

curve S

width

for

_{establishing effective mass}

S

weighting factor

t

time

smeared concrete

thickness

5

deflection amplitude

y

deflection

at

mesh point

'i'

y° maximum

value

of

self-weight deflection

y

weighted

average

of

self-weight deflection W

floor bay width

1.

INTRODUCTION

The

main

_purpose

of

this

Guide

is

to

provide

a

practical method

for

assessing

the likely

vibrational behaviour

of

floors

in

steel framed

_buildings.

_{The subject}

of

floor

vibration

is

complex

and

consequently

the Guide

contains

sections

dealing with

the current

'state of

the art',

the

_background

to

the proposed

assessment methods

and

a

commentary so that

the designer may

develop

an

appreciation

of

the

phenomenon

rather than apply the

design method

_by

rote.

Notwithstanding

this

intention,

the design

procedure

set

out in

Section

7 and the

worked examples contained

in

Appendix

B

have been prepared

to

permit

a

conservative

design

assessment

to

be

executed

_by

_{those with only}

a

_{limited knowledge}

of

_{structural dynamics.}

Floor vibration is not

a

new

_phenomenon,

the 'live'

feel

of

timber floors under

_pedestrian

loading

is

well

established.

However,

because

of

_{the increasing trend}

_{towards lighter}

longer span floors

in

all forms

of

construction,

but

most

_notably

in

steelwork,

CIRIA and

SCI

considered

it

an

_opportune

time

to

provide interim

guidance

on this aspect

of

design

pending further

research.

This Guide has

not

therefore

been prepared

in

response

to

any

existing problems

but

rather

it

is

intended

that

its

use

will prevent such

problems

occurring

in

the

future. Vibration

in

forms

of

construction

other than

steelwork

_may

also

require

consideration.

The use

of

structural steelwork

for

_{multi-storey construction}

has

_{increased dramatically}

over the past ten years. Such

increase

is

_largely

due to

the response

of

the

building industry

to

Clients'

demands

for

buildings

that

are fast

to

construct, have

large uninterrupted

floor

areas

and are capable

of

accommodating highly sophisticated air conditioning

and other

services systems. Modern

design and

construction techniques

enable the

_industry

to

satisfy

such

demands

and produce steel framed

structures

which are

competitive

in

terms

of

overall cost.

This trend

towards longer

span lightweight

floor

systems

in

both

steelwork

and

other forms

of

construction,

with their

tendency

to

lower

natural

_frequencies

and less effective natural damping, has created

a

greater

awareness

of

the

_dynamic

nature

of

some types

of

superimposed loadings.

Currently the most popular

form

of

floor

construction

used

in

conjunction

with

multi-storey

steel

frames

is

the

'composite floor'. This

form

of

floor slab

_comprises

_{profiled metal}

_{decking spanning}

between

beams

and

_{topped with insitu concrete.}

Much

of

_{the design}

_guidance

_{given in}

this

publication

is directly related

to

this

form

of

construction.

The

vibration

of

floors can arise from external

sources

such

as

road and rail traffic.

Where

such problems are

anticipated, however,

it

is

preferable

to isolate the building as

a

whole.

This aspect

of

vibration

control

is

not

taken further

in

this Guide, which addresses

floor vibrations caused

_{by internal}

sources.

The most

usual

and

_important

internal source

of

dynamic

excitation

is

pedestrian

traffic.

A

_{person walking}

at

a

_{regular pace applies}

a

periodically

repeated

force

to

the floor which

may cause

a

build up

of

response in the

structural floor.

Other

sources

of

internal

excitation such as vigorous

rhythmic

group

activities

are not

_specifically

covered

in

this

Guide.

However,

where such

activities

are

envisaged

a

robust structure should be

provided which has

adequate ductility,

and special attention should

be

paid

to

the

beam/column connections.

These design

features

are similar

to

those

considered when

preparing good

seismic-resistant designs

and it

is

to

publications dealing

with this

subject

that

the designer's

attention

is

directed.

Human perception

of

vibration

is

in

one sense very

sensitive;

the criterion

is

likely

to

be

set

at

a

low

level.

In

another

sense

it

is

_{very insensitive;}

a

substantial

_quantitative

_change

in

the

_amplitude

of

vibration corresponds

to

a

relatively small qualitative change

in

perception.

If a

person

is

asked

to

express

an opinion on

his

perception

of

vibration

in

two different

rooms

on

_{separate occasions,}

he

will

not

draw

a

distinction

unless the

quantitative difference

is

at

least

a

factor

of

2. There are also

substantial differences

between persons

and

_{there may also}

be

differences

between

nationalities.

Human

reaction

activity

being

performed. Response

to

vibrations

is

_{often affected by other stimuli}

_(sight

and

_{sound). Although}

floor

vibration

_{may induce}

a

sense

of

insecurity

in

some people, it

must

be

stressed

that

_perception

of

floor

vibration

does

not

_{imply any lack}

of

structural safety.

Once constructed,

it

is

_very

difficult

to

_modify

an

existing

floor

to

reduce

its

susceptibility

to

_{vibration, since only}

_{major changes}

to

the mass,

stiffness

or

damping

of

the

floor system

will produce any

perceptible reduction

in

vibration

_{by people}

_{regularly trafficking}

the

floor.

It

is

therefore important

that the levels

of

acceptable vibration

be

established

at

the conceptual

stage

having

regard

to

the

anticipated

usage

of

the

floors.

The Client

must be

involved in this

decision, since

_{the selected design target}

level

for

_{vibrational response}

will usually have

a

significant bearing

on both the cost

and

overall

floor

construction

depth

for

the

project.

The question is

frequently

raised

of

the

tolerance

of

modem

computer equipment

to

ambient

vibration.

The

_steering

_{group for this study has been}

unable

to

fmd any firm

evidence

of

actual problems

resulting from floor

vibration. Manufacturers commonly

state that their

_equipment

is tolerant

of

the levels

of

_{vibrations acceptable}

_in

_a

_good

office environment. Consultation with

a

prominent manufacturer

has

confirmed

that

vibrations within

_{the range tolerable}

for

_{human occupancy would}

cause

no

problem

to

computer equipment.

In

_{conclusion, therefore,}

_it

is

intended

that the

_publication

of

this Guide will aid

both designers

and

Clients

in

setting sensible

targets

for

acceptable

levels

of

vibration

which

can then

be

incorporated

into the design

of

the

floor structure

to

produce

economic, usage-related, buildings.

2.

SOURCES OF VIBRATION EXCITATION

IN

BUILDINGS

There

are

a

number

of

distinct

_possible

causes

of

dynamic

excitation

of

floors.

The

important characteristics

of

these excitations

vary

to

the extent that quite

different check procedures

may

be

appropriate depending

on

which potential cause

is

most

important.

The obvious, almost

universal, excitation

is the effect

of

walking on the

floor. The geometry

of

the

human

body walking is (to

a

first

approximation)

a

straight-leg motion

that necessarily causes the main body mass

to rise

and

fall

with

_every

_pace

_(see

Figure 2.1). This rise

and

fall

is

typically about

50

mm, peak

to

peak,

but

is sensitive to

the angle

of

the leg

at

full

stretch,

and

thus

to

the extent

to

_{which the walker is forcing}

the

pace. One

is

not

aware

of

this

movement,

because the brain

identifies

_{the resulting}

acceleration signals

as

correlated

with

_walking

and

_disregards

them;

it is,

however, interesting

to note that these

accelerations

are around 3

m/s2,

which is roughly 30

times

the value that

would

be

_acceptable

as

_{the resonant response}

of

a

floor, and

100

times

the

value that would

_commonly

be

set

as

a

limit

to

sustained vibrations.

The

_annoyance

caused

_by

floor

vibrations

is

_{essentially psychological, and}

_{is very}

_susceptible

to

expectation

or

familiarity;

it

is none the

less

a

real

problem.

Direction of walk

Rise and fall of

-——f main body mass

________ Legs at mid-stride (broken lines)

The vertical accelerations

of

_{the body mass are}

_{necessarily associated}

with

reactions on

the floor, and they will be

closely periodic,

at

the pace

frequency.

The

fluctuation

can be

resolved as

a

series

of

_{sinusoidal components}

_(i.e.

a

Fourier

_series)

and

it

is

found that the

fundamental

_{term agrees fairly well with the}

_{simple visualisation}

of

_Figure

_{2.1, giving}

a

force

_amplitude

between

100

N

and 300

_{N. Walking}

_pace

_frequency

_{can vary between}

1.4

Hz and 2.5 Hz, and the

force amplitude tends

to

increase

_{rather severely with}

_increasing frequency. However,

walking pace

indoors

is

most commonly

towards

the lower end of

this

_range,

around

1.6

Hz. The

British Standard

for

bridges"

suggests 180

N

force amplitude

for

checking

footbridge

designs2.

A

typical example

of

the contact

force

from

a

single

footfall

is

shown as the light

solid

curve in Figure 2.2(a).

Unless

the floor structure is

_{exceptionally sensitive}

to

the

_precise

location

of

_{the load (i.e.}

if

one

_pace-length

makes

a

_major

difference),

the

dynamic

excitation

is

_given

_by

the sum

of

the

concurrent

_{walker's foot forces, which takes the}

form

shown

as the

_{heavy solid}

_{curve in Figure 2.2(a). The basic pace}

_frequency

is

_clearly

represented

but the

second

Fourier

component, representing

excitation

at

twice the pace

frequency,

is also

important.

The third

component

is

smaller,

and

succeeding components

can

_generally

be

_ignored,

_{except that there is}

a

significant impulsive

effect

of

very

short

duration as the foot

contacts

the

_ground.

The first three Fourier

_components

are shown in

Figure

2.2(b),

and the degree

of

approximation given

by the

summation

of

these three

components

is

indicated

on Figure 2.2(a). This example is taken

from

the work of

Ohlsson3.

The

_magnitude

of

the

second

Fourier

_{component varies with}

the

_walking

_pace

in

a

similar

way

to

the basic

component. Unfortunately, however,

these higher

frequency effects,

especially the contact

impulse, vary considerably

between persons. The average

values

of

Legs at point

of footfall (Solid lines)

'',,

;''-.'

";

/

z

C.) 0

'300

E C 200 100 0 —100 -200 N 300 200 100 0 —100 -200

(b) Fourier components of reaction on floor Figure 2.2 Typical walking excitation

the

Fourier

coefficients

_reported

_by

_Rainer,

Pernica and

len4

from

a

_{Canadian study}

directed

to

_footbridge

_loading

are

shown

in

_{Figure 2.3. The contact}

_impulse

is

_typically

about

3

Ns

(Newton seconds).

It

is,

of

course,

possible

for more than one person

to

walk

in

unison,

but

such

_augmented

excitation

is

not

normally

regarded as

sufficiently common

to

be

_{taken as the design check case}

_against

comfort

criteria.

Much larger

impulsive

loading can arise

in

the

so-called

'heel

_drop'.

A

person

standing

on

tip-toe who returns

heavily

onto

his

heels can deliver

an

impulse

of

typically 70

Ns, within

a

duration

of

some 0.04

s.

Although

such action can occur

in an

office or

residence, for example when

reaching

for

something

on

a

high

shelf,

it

is

probably

of

greater

significance

as

a

standard design-check

(or

practical measurement)

input5,

which

will give useful

guidance

on

sensitivity

to

impulsive

loadings from

any cause,

including walking.

One pace, period 0.6 s

(a) Footfall force and reaction on floor

Amplitude (N)

,0

/

\

N _{(presuming body} 0.6 400 mass is 67 kg)

/1

0:.

/

2 Frequency (Hz)

Figure 2.3 Fourier component amplitudes for regular walking

Running-step frequencies

can rise

to

higher values, but

do

not commonly exceed 3

Hz.

The fundamental Fourier

component

of

the force exerted on the floor

is

of

the order

of

the

body weight (i.e.

perhaps

three times the

corresponding component

in

walking),

with

a

period

of

zero force while both feet are off the

ground.

The

'free

_{flight' phase}

of

_{body motion becomes even more}

_important

when

_rhythmical

activities,

_{such as dancing}

or

aerobic exercises,

are

considered.

_{The body leaving the}

ground,

with

no

way

of

accelerating

the

return

to keep

up

with

_{the 'beat', imposes}

a

clear

upper bound on the

combination

of

_impulse

and

_frequency

that can

be

developed6,

and

for this reason the

_frequency

will

not

_{significantly exceed}

the value

_quoted

for

_running.

Unfortunately, however,

such

activities clearly

offer the

likelihood

of

a

_{large number of}

persons acting

in

unison,

and the

structural effects

are

_{potentially severe. Useful}

quantitative guidance

can

be

found

in

_{the National Building Code}

_of

Canada.

Mechanical excitation

is also

_possible.

The

_{classic example}

is

_{out-of-balance rotating}

machinery.

There is little to

be

said about such

excitation;

it

is

generally strongly preferable

to

tackle such

problems

at

source rather than

in

the

structure,

by

reduction

of

the

out-of-balance

or

_by

_{vibration-isolation mountings}

for

the

machine. Impulsive

or

transient

mechanical excitation

is

more

_{commonly external}

to

the

building,

possible

causes being road or

rail traffic,

or

(in

special

cases)

heavy

machinery

or

use

of

explosives.

Where this effect

is

likely

to be

severe,

vibration isolation

at

_{building foundation}

level

is

generally preferable

to

using control

measures

at

specific floors, especially

because user

reaction would

be

_dependent

on the

interaction

of

vibration

_{(including high}

_frequencies)

and

acoustic effects.

The

same

comment that the solution does

not

really lie

in

the hands

of

the floor designer

applies

to

the

_{occasional within-building impulsive mechanical}

_{loads, such}

_as

_{problems arising}

from

_operation

of

the

lifts.

In

this

_preliminary

_survey

it

_{is also pertinent}

to

point

out

that similar

_problems

can arise

from

vehicle

movement

in

_car-parking

areas

within

a

building, and again the

preferable remedy

is

to

tackle the problem

at

source by

3.

HUMAN REACTION

TO

VIBRATION

3.1

Review

of

Factors

Given

_large

_amplitudes

of

oscillation

at

_frequencies

in

the range

2

Hz to 20 Hz there

_may

be

significant strains within

the

human

_body,

_{possibly including resonance}

of

_specific organs, giving

rise

to

acute discomfort, serious impairment

of

ability

to

perform mechanical

tasks,

and

even

_{injury. These}

_{problems have been}

_{studied extensively}

in

relation

to

tasks

involved

in

national defence,

such as piloting

high-performance aircraft,

and also

for

the

establishment

of

criteria

for

working conditions

in

onerous industrial situations.

It

is

immediately clear that

there is

a

very

wide

range between

the

amplitudes

of

motion

associated with

such

criteria

and the

threshold

of

perception;

this

range is

typically

one

hundred

times the

threshold.

The

criteria appropriate

to

residential

or

office environments

are

associated with intermediate levels

of

vibration

at

_{which purely}

physiological

effects take second

place

to

psychological factors.

The

_importance

of

psychological factors makes

it

difficult

to

quantify

human

reaction

at

these levels. Any

experiment

in

which the

subjects

are

aware

that their reaction

is

under

test is

_{clearly subject}

to doubt. There are also

wide variations

between

individuals,

a

range

of

_{amplitude exceeding}

a

factor

of

2

exists between the

_top

and bottom

5%

of

the

population

for any

given reaction.

Reaction

at

these levels may

be

influenced

_by

a

number

of

factors.

At

the lower end

of

the

frequency

range, reaction is

strongly

linked

to

a

feeling

of

insecurity,

based on

instinctive association

of

_{perceptible motion}

in

a

'solid'

_{building structure}

with an

_expectation

of

structural inadequacy

or

failure.

_{At the higher end}

of

the

_frequency

_{range, reaction is}

strongly

linked

to

associated

noise levels.

Ohlsson3 has reported

a

case

study

in

which

office workers

had

_{mutually agreed}

that hard

shoes would

not be

worn, and found

this

highly

beneficial. Measurement

showed that the

difference

in

vibration

was

quite insufficient

to

account

for the

difference

_{in reaction, which was}

attributed

to the

elimination

of

noise that the

_{occupant would associate}

with

vibration.

The floor in

question

falls

seriously

short

of

the

acceptance criteria

put

forward

in

this Guide. Because

of

the wide range

to be

covered,

it

is

usual

to

plot

contours indicating human

reaction on twin

_{logarithmic scales}

of

frequency

and

amplitude

of

response;

the

response

can be

_expressed

in

terms

of

either

_{displacement, velocity}

or

acceleration.

If

_amplitude

of

acceleration

is

taken as the

ordinate,

a

constant value

of

displacement

plots

as

a

straight line

of

slope

+2.

A

line

of

slope —1 _corresponds

to

a

constant value

of

the rate

of

_change

of

acceleration.

It

is

rational to assume that

human

reaction would

be

related

to the

former

at

very high

frequencies,

since the body mass will

not

follow

the floor

motion

and

the

perception

will

be

of

strain

in the legs and

spine.

At

the other extreme

of

very low frequency, human

reaction

would

be

related

to

the rate

of

adjustment

of

the

inertia forces

on the body, and thus reaction

contours

_{should plot}

to

the

_{slope of—i.}

It

is

therefore

apparent that the

contours

will have

a

trough

shape.

The most

_important

_range

of

floor

_frequencies

covers the band where the

reaction contours

are changing

from slope

zero

_{(acceleration criterion)}

_to

_slope

+

1 _(velocity

criterion).

Typical broad

qualitative contours

of

reaction

to

sustained

uniform

vibration

are shown in

_{Figure 3.1.}

A

margin

of

at

least

a

factor

of

2 is

required before

an

observer would change

his

_{qualitative description}

of

reaction,

in

addition

to the

_variability

between

observers.

It

is

even more difficult

to

extend

the

criteria

to

_{non-steady vibrations.}

For

continuous

random

oscillation (i.e.

a

continuously modulated harmonic motion)

it

is usual

to

quote

criteria

in

terms

of

the

_{root-mean-square}

value

of

the

motion.

It

is

not

clear, however, how

far this

is

a

uniform criterion

over

different

rates

of

modulation,

or

over

oscillations in

bursts that are

_separated

_by

intervals

of

_quiescence.

It

is

_certainly

not

a

_good

criterion for occasional occurrences

of

oscillation,

especially where the

oscillation

is

initiated sharply

and

damped

out

rapidly.

The rapidity

of

decay

is

widely recognised

as

having

a

major

effect;

doubling

the effective decay rate may raise the

level

of

a

given reaction

contour

10

//

Quickly tiring

/

1.0 strongly perceptible — tiring over long periods C Clearly perceptible —

disacting

0.1 Perceptible 0.01

.:

Barely

perceptible/

Frequency (Hz) (log scale)

Figure 3.1 Qualitative description

of

human reaction _{to sustained steady} oscillation

It

_{has been suggested}

above

that

noise directly associated

with the oscillation

is

an

adverse

factor. However,

for

high-quality environments (residential

or

office) where an

occupant

will resent

intrusion

on

his

mental concentration,

it

may

be

that the

appropriate vibration

limit

_{would actually}

be

higher where there is

substantial

ambient noise

from

other

causes.

3.2 Specifications

As

noted

above, studies

of

human reaction have tended

to

focus on

relatively severe circumstances,

and this is reflected

in

the balance

of

published specifications.

For

example, several specifications

can

be

consulted about

severe industrial working

conditions,

but

there is

_very

little

available

with

a

track record

of

_{satisfactory application}

to

assessment

of

floors

in

office or

residential accommodation.

The

_{Canadian Specification} CAN3—S 16.1

Steel Structures

for

Buildings8 does,

however,

include

a

_{very useful Appendix entitled 'Guide for floor vibrations', although}

this

is

not

a

mandatory

part

of

the Code. The

proposed annoyance

criteria for floor vibrations are

shown

in

_Figure

3.2.

_{The labelling}

of

these curves need

_{interpretation:}

the curves

labelled

'walking vibration' are

to be

used

for

assessing

the response

to

heel drop impulse, and the

curve labelled

'continuous

vibration'

is

to be

used

for

the

assessment

of

the

motion

caused by

a

person walking across the

floor.

For

example,

in the latter case,

a

floor of

span

14

m

and

_frequency

6

Hz

crossed

_by

a

_person

_walking

at

2

paces

per

second

(so that

there was

_significant

_response

to

the third

harmonic

in the pace

excitation)

would

show

sustained response

over about ten paces

or 30

cycles.

The

interpretation

of

'average peak'

in

such

a

case is left open; the

average

over the worst 20 cycles might

be

reasonable.

The three curves in Figure 3.2

labelled

_{'walking vibration' are}

_specifically

linked

in

the

Canadian

Code8

with

_{the 'heel drop'}

_impact

test. The

_{Canadian Specification suggests}

6%

of

critical damping

for

_{typically-furnished floors}

without

_partitions.

The

_sensitivity

to

the level

of

damping reflects

the greatly

reduced annoyance caused

by an

impulsive

event

100 : I 1 I 50

/

,

- •

,

-

,"

Criteria _{for waiking} 20 —

Walking vibration

,

— vibrations:

— — — _{acceleration determined} (12% damping) ,- by heel impact test 10 Walking vibration c_ • _{(6% damping)} Co -

,

- 2 — _{Walking vibration}

/

— — Criterionfor 1.0 (3% damping) continuous vibration 0 Continuous vibration a0 _I_t,,_r • _{(10 to 30} cycles) 0.1 I 11111 I 1 2 4 6 10 20 Frequency (Hz)

Figure 3.2 Annoyance criteria for floor vibrations (residential, school and office occupancies)

this

test

to

assessing

the

sensitivity

of

the floor

to

walking

excitation,

where damping

has

a

different

action.

In

_{this case higher damping}

_primarily

causes

a

reduction

of

the

dynamic magnifier

at

resonance.

_{The more rapid decay once the source}

_of

excitation

has

moved

off

_{the span}

is

_only

of

secondary significance.

As

noted later

in

Section 4.2,

the

effective decay rate from the

impulsive

event is

very commonly enhanced

by

a

lateral

dispersion

of

the energy

of

oscillation.

_{This may}

_legitimately

be

included

in

the

effective

damping value

for

identifying

the

acceptable

level

of

initial response

to

impulsive

excitation, and

is

presumably

so

included

in the

Canadian Specification.

The

_energy

dispersion effect is

not

equally effective

under

repeated-pace excitation.

Care

is

therefore recommended

in

the use

of

these

curves.

_Impulse

_{response criteria}

_{which give}

similar values

have also been presented by

_Murray;

some

discussion

of

his

_proposals

_{is given in}

Section 6.2

The Supplement

to

_{the National Building}

Code

_of

Canada°

_postulates

limits

for

human tolerance

in

cases

of

_group

activities,

_namely

an

_{acceleration amplitude}

of

O.02g

for

dancing

and

dining, or

O.05g

for lively

concert

or

sports

events.

For

these

activities, the

check

is

applied

to

the

consideration

of

the

_{fundamental-frequency}

excitation

_component

only. The

response considered

is

thus

at

frequencies

up to

3

Hz, and floor

resonance

to

high frequency

components

is

not

taken into

account.

A

_{second-component excitation,}

thus giving

an

excitation

_frequency

_{up to}

6

Hz,

is

given for 'jumping exercises'.

The most relevant United

_{Kingdom specification}

is BS 6472 Evaluation

_of

human exposure

to

vibration

in

buildings (1

Hz

to 80

Hz)9. This is

strongly

linked

to

the

International

Standard ISO 2631 Guide

to

the

evaluation

_of

_{human exposure}

to

whole

body

vibration°>,

which is in

turn to

some

extent

a

descendant

of

German

_{specifications}

originally drawn

up

for

industrial working conditions. However,

it

incorporates a substantial

recent

review

in the broader

context, including

the work

of Irwin".

BS

6472

defmes

a

base curve

of

acceleration

as

a

function

of

frequency, with multipliers

to

define

the

_acceptable

level as

a

function

of

building

function and the

nature

of

the

excitation.

The

base curve

is

identical

in

shape

to

the lines

of

Figure

3.2

(for

_{frequencies exceeding}

4

Hz), with

numerical values one-tenth

of

the

Canadian

curve for

sustained oscillation.

acceleration,

rather than the peak (or 'average peak').

For

a

response which is

dominated

by

a

single hannonic excitation

component

the r.m.s. value

is

l//

times the peak,

and

the

Canadian

curve

is

thus

_equivalent

in

this case

to 7

units (or 'Curve

7' in

the

notation

of

BS

_{6472) according}

to

the

British Standard.

BS

_{6472 gives}

(inter alia)

values

for the

_multiplying

factor

to

apply

to

the

base

curve for

the

assessment

of

continuous vibration,

as shown

in

Table

3.1.

Table _{3.1 Multiplying factors} to apply to the base curve Environment Reaction level A* Reaction level B

Offices 4 8

Residential — _{day 2 to 4 4 to 8}

Residential — _{night 1.4 3}

*

_{See text for explanation}

_of

_{'reaction level'}

The values

in

column

A

_{are postulated as 'magnitudes below which the}

_probability

of

adverse comment

is

low', and

it is

postulated

that the values

in

column B 'may result in

adverse comment'.

A

note is added

to

the effect that tolerance

in

residential

accommodation

is

_{strongly influenced}

_{by 'social and cultural factors,}

_{psychological}

attitudes and the

_expected

_degree

of

intrusion'.

It

will

be

seen that the levels B and

A

for

_{offices correspond}

_roughly

to

the

Canadian recommendation (Figure

3.2),

and to

one-half that

level, respectively.

However,

there

is

a

strong implication

that the term

'continuous

vibration'

is

to be

interpreted

rigorously

in

BS

6472. These values

are

_{thus reasonably applicable}

_only

to

_very

_heavily

trafficked

floors with

_{walkers continually}

_{present. In such}

cases occasional

_peaks

due

to

concurrent

excitation

_{by more than one}

_person

_{can probably}

be

traded

off

against the

number

of

_people

not

_moving

_regularly

or at

resonant-pace frequency.

BS

6472 offers

the

_suggestion

that

intermittent vibration

can

be

equated

to an

equivalent continuous

level by the

root-mean-quad, i.e.:

T 114

aeq

=

(J

a4(t)&)

where

a(t) is the value

of

acceleration

at

time

t.

The root-mean-quad

of

a

_{sinusoidal vibration modulating}

as

a

person walks

across

a

floor

taking six

seconds,

repeated once

_per

minute,

is

about

one-third

of

the peak

amplitude.

As

this

root-mean-quad

is used in

substitution

for

the

root-mean-square

value

of

continuous

oscillation,

which would

be

1 times

the peak

_amplitude,

a

floor

_subject

to

a

_person

walking

at

the resonant

frequency

once

per

minute could reasonably

be

permitted

to

show

peak response

of

twice the peak value

acceptable

for

continuous oscillation.

BS

6472 notes

_{that there may}

be

locations

where

it

is

_necessary

to

restrict vibrations

to

the

level

of

the

base curve

_(factor

_1).

'Some

_{hospital operating}

theatres'

and

'some

_precision

laboratories' are put forward as

examples.

4.

GENERAL

CONSIDERATIONS

4.1

Structural and

_{Floor Configurations}

The

_following

discussion

of

_{steel flooring}

_{configurations}

is

presented

to

indicate

the

terminology

used in

discussion

of

floor

vibrations

and

the

_{approximate parameter ranges;}

it

is

not

intended

to

_{constitute guidance}

on the

selection

of

the

_parameters.

The essential objective

of

flooring

is

to

provide

a

flat

load-carrying surface.

The floor

slab

construction is

_generally

either

_{steel-concrete composite,}

timber or

concrete,

and

_usually

carries

some form

of

_fmishing

or

furnishing

(carpeting

and

underlays, hardwood surfacing

or

similar,

and,

in

the case

of

concrete

slabs,

a

screed).

There is little

evidence

that

finishes

have much effect on

_{vibration problems,}

_except

_through

_{the resulting}

increase

of

mass.

There is

_possibly

a

_{marginal increase}

in

_damping

and

a

_marginal

_cushioning

of

_impulsive

loads by

appropriate fmishes,

but

a

finish soft enough

to

have

a

marked

_{cushioning action}

will

be too

soft

to

have much

structural

_{damping action.}

_However,

the

acoustic

and

_walking

comfort factors

of

_{various fmishes are likely}

to

interact

in

_{the expressed}

_opinion

of

users

relating

to

the

vibration environment

as discussed

in

Section 3.1.

Timber floors are certainly

susceptible

to

vibration problems,

which have been studied in

both Canada8

and

Swederi3.

It

_{will be shown that higher mass}

is

generally favourable,

and in this

_{respect timber floors are}

_inherently

more

at

risk than concrete

floors.

Nevertheless,

in

view

of the

current

balance

of

the market

in

the

_U.K.,

attention will be

focused

in this

Guide on concrete

_floors,

_but

_{with emphasis}

_{on recent design}

_trends

leading

to

a

reduction

of

the mass

_per

unit area. In

_particular,

there

is

increasing use of

permanent

steel

formwork (profiled decking

of

various

_{configurations)}

and

of

_lightweight

concrete,

often

in

conjunction

with each

other.

The density

of

lightweight

concrete

_commonly

_adopted

in

the

U.K.

is

around 1800

_kg/m3;

lower

values

are not

uncommon

in

North

America.

A

composite

slab

comprising

a

70 mm

continuous thickness

of

lightweight concrete

on

60 mm steel

decking

may

thus

have

a

mass

of

about

_{220 kg/m2,}

_excluding

finishes.

It

_{may be noted here that}

references

to

floor

thicknesses

in

the

_{U.K. generally}

refer

to

_{the total slab depth;}

a

'smeared'

_{thickness equal}

to

(mass

of

concrete

_per

unit

area)/(concrete density)

is

often

used in North

American literature, including

design

guides.

Such

a

slab is typically

supported

on floor

beams (commonly called

'joists' in

North

_America)

_at

about 3

m

spacing.

The

short-term

modulus

of

_elasticity

should

be

used for all

_{dynamic calculations, and}

current

_{specifications}

_{and design guides tend}

_to

_{present rather}

conservative

(low)

values, bearing

in

mind the

influence

of

the age

of

the concrete

and

the area

participating

in

the

critical

circumstances.

For

normal

_density

concrete

the

_{dynamic modulus}

of

_elasticity

can

be taken as 38

kN/mm2,

and for lightweight

concrete

at

around 1800

_kg/rn3

the

_dynamic

modulus can

be

taken as 22 kN/mm.

A

stiffness

_parameter

of

the

_{form El1/L4}

can

be

considered

as an

aid

to

the

_appreciation

of

the

_importance

of

slab

_stiffness,

in

which El1

is

the

flexural rigidity

per

unit width. For the

application

of

the design

guidance

in

Section

7,

the rigidity may

be

computed

from a

smeared

thickness

of

concrete with

_decking

_{as appropriate (see design example No}

1 in

Appendix

B).

The

actual

stiffness under

distributed

load would

be

obtained by

multiplying

the stiffness

parameter

by

a

coefficient

_depending

on

support conditions

and

load

_{distribution. Considering}

_{the span between adjacent}

floor

_{beams, so that the}

effective

span

L,,

is

set

equal

to

the beam

spacing

b, this

parameter

is

commonly

in

the

range

30—100 kN/m3. On

the other

_{hand, considering}

the

_ability

of

the slab

to

support

load

over

the full bay width,

Le

=

W,

this

_parameter

_{very rarely}

exceeds 1 kN/m3

and for wide

bays continuous

over

_(say)

8 floor

beams

it

will

be

less

than

0.01 kN/m3.

The

_{corresponding}

stiffness parameter

EI/bL4

for the floor

beams

_{is typically}

in

the

_range 1—10 kN/m3.

The relative

stiffness

of

slab and floor beams

indicated

_{by these}

_parameters

has the

effect

that under

a

_{global distributed}

_loading

the slab

deflection

between beams

is

relatively small.

The slab is

also sufficient

_to

_give

_significant

resistance

to

differential deflection

of

concept that the

dominant

_{load path}

is

via the floor beams

as

a

'one-way'

span.

The net

result

in

terms

of

dynamic

action

is

that the floor behaves broadly as

a

strongly

orthotropic

plate

(see Section

4.2) and

a

strip containing

one

or

two floor

beams

can be

considered

as

the

dominant structural

unit when

_considering

_walking

excitation.

Precast 'Omnia type'

planks, 50—65

mm in

thickness

with

an

insitu concrete topping

and supplementaiy continuity reinforcement,

will

behave

in

a

similar

manner

to

a

metal decking

composite floor

system considered above. However,

greater

caution

must

be exercised

when

_assessing

the

_continuity

and

_stiffening

effects

of

other

forms

of

_precast

floor

construction. Where hollow-cored

_{precast units are required}

to

mobilise

the

composite action

of

the

supporting

beams, then the ends

of

the units

should

be

'notched'

and

_{supplementary}

_tying

reinforcement

used

in

_conjunction

with an

insitu concrete

topping

should

be

provided.

The

implementation

of

these

measures

will,

in

addition,

have

a

stiffening

effect

on

the floor slab such that the floor system will tend

to

act as an

orthotropic

plate.

Conversely,

if

'dry

construction'

_{precast flooring}

is

used, without such

measures

_being

_implemented,

then the

_supporting

beams should

not be

considered

to

act

compositely with

the slab

nor

should

the slabs be

assumed

to

assist

in

reducing

any differential deflection

between beams

or in

distributing

any

local effects.

This form of

construction

_{therefore, through}

Ick

_of

_{stiffness, contributes}

_{only by virtue}

_of

_its

mass to

the

vibration characteristics

of

the floor as

a

whole.

For very long

spans,

or

where

very high

standards

are

_sought,

_{the floor system}

_may

comprise beams

of

comparable stiffness

in

the two

orthogonal

directions, constituting

an

effective 'two-way' span,

and

thus

a

_nearly

_{isotropic dynamic system. Subject}

to the

above limitation

on deflection

of

the slab between beams, this mobilises the whole

floor

in

_{resisting dynamic excitation,}

and

is

thus

_a

_very

_{favourable configuration.}

The floor beams

themselves

_{will very}

often

be

_supported

_by

_{main beams, which form part}

of

the principal

structural framing

of

_{the building. The resulting}

additional deflection

under

a

_global

_{distributed loading}

_{may be}

_comparable

to

the floor beam

deflection

between main

beams.

It

should

be

noted

that

the

deflection

and

stress

levels

tolerable

in

_dynamic

_response

are

low, typical

stress amplitudes

being less than

1%

of

the

static

_design

stress,

so that

conventional

_design

_provisions

for

_{simple supports}

will

not

generally

in

practice

act as

such

in

dynamic situations.

Large floor areas may

thus

act as

if

_{structurally continuous.}

The greater

effective structural continuity,

under

_{dynamic loading,}

has the effect

that column stiffness commonly contributes significant

end

restraint,

even where the beam

connections

are

of

a

form

that

would normally

be

regarded as

permitting rotation. Column

stiffness

is

particularly

likely

to be

significant

in

high-rise

buildings.

An adequate

analysis

can

_commonly

be

achieved

_{by the}

_{'substitute-frame' procedure.}

Cantilever

forms

of

construction

are

_{relatively uncommon. Although}

the

methods presented

in

Section

5 for

evaluating

natural

frequencies

are

broadly applicable

to

cantilever

_{construction,}

this

form

_gives

a

rather

ineffective mobilisation

of

mass

if

dynamic

excitation

is

applied near the free

end,

and the evaluation

of

response

presented

in

Section 6 may be

non-conservative. Specialist advice should

be taken

if

a

reliable

estimate

is

required.

4.2

Introduction

to

Dynamics

The classic

text-book model

of

a

_dynamic

_{system, shown}

in

_Figure

4.1,

is

characterised

by

a

mass,

a

spring stiffness, and

a

damper.

For

mathematical convenience,

the damper is

usually imagined

to

develop

a

force

opposing

the

direction

of

movement

in

proportion to

the

_velocity.

_Except

in

_{very rare}

cases

where some

identifiable

_{damper has been}

fitted

to

tackle

a

_{specific oscillation}

_{problem, real}

floors

do

not

incorporate

such

elements,

but

nevertheless

there will

be

some

_ways

in

which

_energy

is

dissipated

in

the event of

oscillation.

This

is

usually

by

friction which commonly

depends

heavily on

non-structural components

such

as

partitions.

It

also depends

on

structural behaviour

differing

from the

designer's model, such as

nominally non-moment-resisting connections

that

actually develop considerable

frictional

resistance. Human occupants

also add

damping, although

a

high density

of

occupation would

be

necessary

to

have any

substantial

effect

on

a

floor