By

Dr Stephen Hicks

HERA Manager Structural Systems

Composite Columns and Innovations in Composite

Floor Construction

Brief Biography

• Heavy Engineering Research Association, NZ (2008 to date) - Manager Structural Systems

• Steel Construction Institute (SCI), UK (1997 to 2008) - Senior Manager

Building Engineering

• Expertise – Steel-concrete Composite Construction – Floor Vibrations – Cold-formed steel structures – Product development – Development of design guidance and Standards – Structural Reliability Methods

• Memberships

– Member of NZS Committee P3404: Steel Structures – Chairman of SA sub-committee BD-090-06: AS5100.6 Bridge

design - steel and composite construction – Board Member and Technical Advisor to National Association of

Steel-framed Housing (NASH) – Chairman of Sustainable Steel Council – Member of European Convention for Constructional Steelwork

Technical Committee 11 “Composite Structures”

– UK representative on CEN Subcommittee 4: Eurocode 4 - Design of Composite Steel and Concrete Structures (CEN/TC250/SC4)

– Member of UK BSI Composite Structures Committee (B/525/4)

Part 1: Human acceptance of vibration

Part 2: Design guidance for floor vibrations

Part 3: Basis of new design guidance

Part 3.1: Steady state response

Part 3.2: Transient response

Part 4: Case studies

Contents

Part 1:

Human Acceptance of Vibration

• Movement of buildings – Worry it is unsafe

• Being disturbed when resting – Sleeping areas such as bedrooms and hospital wards

• Being disturbed whilst concentrating – Sensitive activities such as surgery

• Users vary in sensitivity – Work in terms of ‘low probability of adverse

comment’

Users don’t like:

Human perception of vibration

• Directions of incidence to the human body specified using the basicentric coordinate system

• Base curves are used to define the threshold of human perception

• Acceptability Base curve × Multiplying factor

Information supplied by ISO 10137 and ISO 2631 (identical information given in USA by

ANSI S3.29 and UK by BS6472)

Supportingsurface

y

z

xSupportingsurface

y

x

Supportingsurface

x

z

y

z

Basicentric coordinate system for vibrations influencing humans

• Threshold of human perception defined by ‘base value’ of root-mean-square acceleration

– z-axis vibrations arms

= 5 ×10-3m/s²

– x & y-axis vibrations arms

= 3.57 ×10-3m/s²

ISO 2631 frequency weighting factors for human perception of vibration (asymptotic

approximations)

z-axis x- & y-axis

0.1

1

1 10 100

Frequency (Hz)

We

igh

tin

g fa

cto

r

0.1

1

1 10 100

Frequency (Hz)

We

igh

tin

g fa

cto

r

Human perception

of vibrations

reducing

ISO 10137 Base curves (threshold of human perception of vibrations)

z-axis x- & y-axis

0.001

0.01

0.1

1

1 10 100

Frequency (Hz)

rms a

ccele

rati

on

(m

/s²)

0.001

0.01

0.1

1

1 10 100

Frequency (Hz)

rms a

ccele

rati

on

(m

/s²)

base value divided

by frequency-

weighting

Base curves only

appropriate when

only one floor

frequency is being

excited (not normal

in most practical

floors using steel,

timber or concrete)

ISO 10137 multiplying factors for ‘low probability of adverse comment’

Place Time

Multiplying factors to base curve for 16h day 8h

night

Continuous vibration

Impulsive vibration

excitation with several

occurrences per day

Critical working areas

(e.g., some hospital

operating theatres, some

precision laboratories,

etc.)

Day 1 1

Night 1

1

Residential (e.g. flats,

homes, hospitals)

Day 2 to 4 30 to 90

Night 1.4 1,4 to 20

Quiet office, open plan Day 2 60 to 128

Night 2 60 to 128

General office (e.g.

schools, offices)

Day 4 60 to 128

Night 4 60 to 128

Workshops Day 8 90 to 128

Night 8 90 to 128

ISO 10137 Building vibration curves

z-axis x- & y-axis

0.001

0.01

0.1

1

1 10 100

Frequency (Hz)

rms a

ccele

rati

on

(m

/s²)

0.001

0.01

0.1

1

1 10 100

Frequency (Hz)

rms a

ccele

rati

on

(m

/s²)

Curve 1

Curve 4

Curve 8

Part 2:

Design guidance for floor vibrations

General design guidance (UK)

SCI P 076 AD 253, 254 & 256

AISC/CISC DG11

General design guidance (USA & Canada)

Floor vibration research and development for steel-framed floors

• 1997 – 1999 UK Department of Environment, Transport and the Regions (DETR) Partners in Innovation project “Design guidance & interpretation of Cardington composite frame tests”

• 2001-2004 EC project through the European Coal and Steel Community (ECSC) entitled “Generalisation of criteria for floor vibrations for industrial, office, residential and public building and gymnastic halls”

• 2004 – 2005 UK Department of Trade and Industry (DTI) Partners in Innovation project “Holistic Assessment of the vibration sensitivity of lightweight floor for various use patterns”

• 2003 – 2006 EC project for through the Research Fund for Coal and Steel (RFCS) entitled "High quality acoustic and vibration performance of lightweight steel constructions“

• 2007-2008 EC project through RFCS entitled "Human-induced vibration of steel structures

Multi-Input Multi-Output (MIMO) modal testing of operating theatre

Walking tests

Summary of work between 1997 and 2008

• In situ vibration tests on a wide variety of steel-framed composite floors undertaken in UK, France, Germany, Netherlands, Luxembourg, Finland and Sweden (including long-span beams, standard UB’s and UC’s, slim floors beams and light steel frame floors)

• Tests undertaken on floors within different environments (offices, hospitals, retail, residential, dance-floors, gymnasium)

• Comparison of test data with existing design guidance showed that, although floor frequencies compared favourably with predictions, the predicted floor response was very variable (particularly AISC/CISC DG11)

• Finite element models of tested floors constructed to understand in situ behaviour

• To enable comparisons to be made with ISO 10137: – General method for evaluating floor response from finite element model outputs

developed

– Simplified methods (conservative), which are amenable to hand calculations (one approach based on FE models using general method)

New design guide on the vibration of steel-framed floors

SCI P354

• General approach using the results from computer models (can actually be applied to any floor, stairs, etc. made from any material) – Based on a modal

superposition approach

• Simplified (conservative) approach using hand calculations - for walking activities only! – Based on FE models of

composite floors with regular grids

Simplified design guidance (walking only) developed from

partners on EC projects

JRC-ECCS Publication ArcelorMittal

Design guide for vibrations on concrete floors

• Modal superposition method (very similar to SCI P354)

• Simplified and approximate method (for hand calculations)

Concrete Centre CCIP-016 (2006)

Part 3:

Basis of new design guidance

SCI P354 – Design of Floors for Vibration

Multiplying factors

• Multiplying factors in ISO 10137 don’t cover all environments within buildings

• Supplementary multiplying factors recommended in SCI P354 (based on measured floor performance together with historical evidence)

Assessments cf. measurements on 103 LSF residential floors in Finland

0

20

40

60

80

100

120

8 13 18 23 28 33

Fundamental frequency [Hz]

ISO

fa

cto

r

accepted

not accepted

Multiplying factor = 16 for

vibrations within dwellings

Place Multiplying factor

Office 8

Shopping mall 4

Dealing floor 4

Stairs – Light use (e.g. offices) 32

Stairs – Heavy use (e.g. public buildings,

stadia)

24

vibrations within residential dwellings 16

Recommended multiplying factors to supplement ISO 10137 based on excitation from a single person

Damping

• For design, it is recommended that the following damping values may be assumed: – = 1.1%

• for bare unfurnished floors.

– = 3.0% • for floors in normal use.

– = 4.5% • for a floor with partitions, where the designer is

confident that partitions will be appropriately located to interrupt the relevant modes of vibration.

• Floor loading should be taken as expected loading, i.e. what will be present in service.

• Generally dead loads plus a maximum of 10% of partitions and live loads.

Floor loading

Load-time function (for walking at 2.0 Hz), into the first three

harmonic components

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 0.5 1 1.5

% o

f p

ers

on

's w

eig

ht

Time (sec)

Decomposition of the load-time function, into the first three

harmonic components

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5

Fo

urie

r co

effic

ien

t (%

of

pe

rso

n's

w

eig

ht)

Time (sec)

First harmonic

Second harmonic

Third harmonic

Fourier coefficients for walking activities after Rainer et al.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6 7 8 9 10

Frequency (Hz)

Fo

uri

er

co

eff

icie

nt,

n

Harmonic, n

1

2

3

4

Fourier coefficients for synchronized crowd movement

after Ellis & Ji

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10

Fo

urie

r co

effic

ien

t

Frequency (Hz)

High impact aerobics

Normal jumping

High jumping

Activity frequency

= 1.5 to 2.8 Hz

Floor type

• For excitation from walking

– ‘Low frequency floor’ has a fundamental natural frequency, f1 < 10 Hz

– ‘High frequency floor’ has a fundamental natural frequency, f1 > 10 Hz

• For other excitations

–Depends on highest harmonic

Type of response vs Floor type

• Low frequency floors –Steady-state response (at harmonics of

excitation frequency).

–Transient response (as higher modes may dominate the response).

• High frequency floors –Transient response (at frequencies of

the floor).

Part 3:

Basis of new design guidance

3.1 - Steady-state response

Steady-state response

Steady-state response

• When a cyclic force (e.g. a walking activity) is applied to a structure, it will begin to vibrate.

• If the cyclic force is applied continuously the motion of the structure will reach a steady-state (constant amplitude and frequency); this condition is known as resonance.

• Resonance can occur even if the frequency of the floor is above a minimum design value (due to components of the walking activity exciting the floor).

• These components from the walking activity occur because the force versus time graph is made up of many different sine curves.

e,n is the mode shape amplitude, from the unity or mass normalised FE output, at the point on the floor where the excitation force Fh is applied

r,n is the mode shape amplitude, from the unity or mass normalised FE output, at the point where the response is to be calculated

Fh is the excitation force for the hth harmonic, where Fh = hQ. [N]

Mn is the modal mass of mode n (equal to 1 kg if the mode shapes are mass normalised) [kg]

Dn,h is the dynamic magnification factor Wh is the appropriate code-defined weighting factor for human

perception of vibrations, which is a function of the frequency of the harmonic under consideration hfp.

hhn,

n

hnr,ne,hn,r,e,peak,w, WD

M

Fa

Steady-state response per mode/harmonic

Excitation force

h is the Fourier coefficient of the hth harmonic Q is the static force exerted by an ‘average person’

(normally taken as 76 kg × 9.81 m/s² = 746 N).

Harmonic Excitation

Frequency range

hfp (Hz)

Design value of

coefficient

h

Phase

angle

h

1 1.8 to 2.2 0.436(hfp – 0.95) 0

2 3.6 to 4.4 0.006(hfp + 12.3) -/2

3 5.4 to 6.6 0.007(hfp + 5.2)

4 7.2 to 8.8 0.007(hfp + 2.0) /2

~0.4

~0.1

~0.1

~0.1

QF hh

Dynamic magnification factor

h is the number of the hth harmonic

n is the frequency ratio (taken as fp/fn)

is the damping ratio

fp is the frequency corresponding to the first harmonic of the activity

fn is the frequency of the mode under consideration

2222

22

,

21 nn

nhn

hh

hD

• Square-root sum of squares (steady-state):

H

h

N

n

WDM

Fa

1

2

1

hhn,

n

hnr,ne,re,rms,w,

2

1

Total steady-state root-mean-square acceleration

0

2

4

6

8

10

12

14

16

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5

Frequency (Hz)

Re

sp

on

se

First Harmonic

Second Harmonic

Third Harmonic

Fourth Harmonic

Total

Typical steady-

state response

versus pace

frequency

Part 3:

Basis of new design guidance

3.2 – Transient response

Transient response

Transient response

• For the case when a structure possess a sufficiently high frequency, so that it is out of the range of the first four harmonic components of the pace frequency (where most of the excitation energy is concentrated i.e., 1 + 2 + 3 + 4 0.7), the floor will exhibit a transient response.

• In this case, the response is dominated by a train of impulses, which correspond to the heel impacts. As a consequence, successive peaks and decays typify the overall dynamic response of a floor of this type.

Transient response

e,n is the mode shape amplitude, from the unity or mass normalised FE output, at the point on the floor where the impulse force FI is applied

r,n is the mode shape amplitude, from the unity or mass normalised FE output, at the point where the response is to be calculated

FI is the excitation force [Ns] Mn is the modal mass of mode n (equal to 1 if the mode shapes

are mass normalised) [kg] Wn is the appropriate code-defined weighting factor for human

perception of vibrations, which depends on the direction of the vibrations on the human body using the basicentric coordinate system and the frequency of the mode under consideration fn.

nI W

M

Ffa

n

nr,ne,

2

nnr,e,peak,w, 1π2

Transient excitation force

fp is the pace frequency

fn is the frequency of the mode under consideration

Q is the static force exerted by an ‘average person’ (normally taken as 76 kg 9.81 m/s² = 746 N)

70060

3.1

43.1Q

f

fF

n

p

I

Total transient acceleration

• Superposition of modal responses:

• Calculate root-mean-square (rms)

n22

n

n

I

1

nr,ne,2

n

1

nr,e,w,,ew,

n12sin12

)()(

WetfM

Ff

tata

tfN

n

N

n

r

πππ

p1

0

2re,w,prmsw,

f

dttafa

Typical transient response versus pace frequency

0

0.5

1

1.5

2

2.5

3

3.5

4

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5

Frequency (Hz)

Response

Evaluation of Response factors

• For z-axis vibration:

For x- and y-axis vibration:

005.0

rmsw,aR

00357.0

,rmswaR

If R Multiplying factor from ISO 10137 or SCI P354, floor is acceptable

Contour plots on floor plan

• Assessment at every point over the floor area can show hotspots of response factors and help with architectural layouts

Excitation and response points (useful for sensitive areas)

+

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Pre

dic

ted

re

sp

on

se

Measured response

Floor H1

Floor H2

Floor H3

Floor H4

Floor H5

Part 4:

Case studies

Framing layout of St Richards Hospital UK Slimflor floor

48% saving on steel

weight!

Verification of predictions through testing on floor

Measured mode shape

R = 0.29

Worst-case acceleration-time trace measured in operating theatre

Project Bay size

(m)

Overall

slab

depth

(mm)

Beam depth

Sec/Pri (mm)

f0

(Hz)

R

Hospital 1

(bare)

11.3×7.2 300 625/571

Cellular beam

9.01 0.25

(2.70)

Hospital 1

(finished)

11.3×7.2 300 625/571

Cellular beam

6.38 0.34

(0.70)

Hospital 2 15×7.5 175 457×152UB/70

0 Cellular beam

4.88 0.58

(4.76)

St Richards

Hospital

5.9×5.5 335+80

screed

300ASB153/- 9.5 0.29

(1.10)

Sunderland

Royal Infirmary

6.8×5.7 337 300ASB185/- 9.6 0.54

(1.16)

Measurements taken on steel-framed floors in operating theatre areas

General approach now implemented within commercial

software such as Oasys GSA

One Shelley Street, Sydney, Australia

Icon Hotel, Dubai, UAE

Conclusions

• Acceptance criteria for vibrations in buildings given in ISO 10137 and ISO 2631.

• New design guidance based 11-years of research conducted in UK and Europe.

• New design guidance based on actual measured performance of floors as opposed to subjective assessments.

• Application of general method of design has been simplified through incorporation within software

• Methodology has been in use within the UK since 2004 and is now being used internationally.