130113 dvase 2013 seminar/breakfastseminarfeb13.pdf · the characteristics of footfall forces ......

25/01/2013

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Air Quality | Wind & Climate | Sound, Vibration & EMI/RFI | Sustainable WaterNovus Environmental Inc. | 150 Research Lane, Suite 105, Guelph, Ontario, Canada N1G 4T2

e-mail [email protected] tel 226.706.8080 fax 226.706.8081

Advanced Approaches to Modeling and Assessment of Floors for Control of Human Activity

Brad Pridham, Ph.D., P.Eng.February 6, 2013

Agenda

• Objectives & Scope

• Fundamentals of structural dynamics

• Forces from footfalls

• Finite Element Modeling

• Vibration criteria

• Numerical assessment

• Application Example

Learning Objectives

• Provide an understanding of: fundamental concepts in structural dynamics

the characteristics of footfall forces

floor vibration criteria

benefits of using advanced methods

• Provide tips on: structural modeling for dynamic response analysis

assessment of as-built floors

Ultra-Low Vibration Environments

• Medical imaging• Microscopy• Micro-surgery

Vibration effects on image quality

Occupant Comfort

• Footfall measurements

measurement

Executive Office

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Crowd Loading - Walking

Video clip downloaded from Youtube URL: http://www.youtube.com/watch?v=eAXVa__XWZ8

Crowd Loading – Jumping/Jouncing

Video clip downloaded from Youtube URL: http://www.youtube.com/watch?v=2CKku4lvNaU

Scope of the Seminar

• Walking activity on floor structures

• Discussion limited to a single walker

• Ultra-low to moderate vibration level environments– Science & Technology

– Health care facilities

– Higher Ed

– Office Environments

Agenda




• Finite Element Modelling




The Simple Oscillator - SDOF

Mass

Stiffness Damping

Applied Force

Frequency

1 cycle per second = 1 Hz

5 cycles per second = 5 Hz

Reduced mass and/or

increased stiffness

-1

0

1

Am

plitu

de

0 1-1

0

1

Time (s)

Am

plitu

de

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Damping

increased damping

-1

0

1

Am

plitu

de

0 1 2 3 4 5 6 7 8 9 10-1

0

1

Time (s)

Am

plitu

de

∙

Resonance:

-1

0

1

F(t)

0 5 10 15 20-10

0

10

By(t)

T ime (s)

Acc

eler

atio

nF

(t)

-10

10

By(t)

0 5 10 15 20

-46

46

By(t)

T ime (s)

Damping and Resonance

5% damping

0.5% damping

Acc

eler

atio

nA

ccel

erat

ion

0.5 1 1.5

10

20

50

Frequency Rat io (r = f p=f n)

By max

(t)=

(F=k

)

Dynamic Amplification Factor - D

1% damping

2.5% damping

5% damping

Dyn

amic

/ St

atic

Frequency Ratio

Steady State Response

Dynamic Amplification Factor

SinusoidNewton’s 1st Law

1

FI(t

)

0 1 2 3 4 5

-50

5

x 10-3

By(t)

T ime (s)

Transient (Impulse) Response

• Unit impulse at t = 0.5 sec

Time (s)

Acc

eler

atio

nF

(t)

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Transient Response

Damped frequency

Newton’s 1st Law Exponentially Decaying Sinusoid

Multi-Degree-of-Freedom (MDOF) Systems

• Mass, stiffness, force and response are distributed spatially

o Matrix formulation

• # of DOFs determines the number of modes of vibration

u1u2

u3

r1

r2

r3Possible DOFs

at node i

mi

Lumped mass

• System is decoupled in to n SDOFs

or nmodes of vibration

After some math….

Mode 1 Mode 2 Mode n

Generalized Coordinates (‘Modal Space’)

Mode n

Generalized Force

Generalized Mass

Modal frequency and damping ,

Mode Shape

• Vector of spatial distribution of motion for mode n

input

mass

response

SDOF

• Results are summed for all modes to arrive at total response

, , ∙ , ∙ SteadyResponse

Response

, , ∙ , ∙ TransientResponse

, ,

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Agenda








• Primary concern for floors are the vertical components of force

Footfall Forces

Right footLeft foot

0 10 20 30 40 50 60 70 80 90 100

11.09

1.27

For

ce /

Wei

ght

% of Stride

Slow cadenceNatural cadenceFast cadence

Footfall Forces – Effect of Cadence

*data normalized to max force for Slow cadence

t0 t1 t2

1

For

ce /

Wei

ght

Time (s)

T0 = t2 - t1

f0 = 1 / T0

Footfall Forces – Time Domain Right footLeft foot

Force Frequency Range

• There are physical limits to our capability to walk comfortably

Reported range: 1.2 Hz – 2.4 Hz72 spm – 144 spm

Practical range: 1.5 Hz – 2 Hz90 spm – 120 spm

Average for the population:

1.87 Hz, 112 spm0

0.1

0.2

0.3

0.4

0.5

Dyn

amic

Loa

d F

acto

r (F

/W)

Frequency (Hz)

Footfall Forces – Frequency Domain

f0 2f0 3f0 4f0

1 2 3 4

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Dynamic Load Factor vs. Pacing Frequency

f0 2f0 3f0 4f00

0.1

0.2

0.3

0.4

0.5

0.6

F /

W

Frequency (Hz)

1

2 3 4

F/ W

• ‘Low-frequency’/Resonant component:

‘Perfect’ Footfall Force Model

∙ ∙ sin 2

0 0.5 1

-0.5

0

0.5

F=W

T ime (s)0 0.5 1

Time (s)

F/ W

What about floors/modes with 4 ∙ ?

• For floors/modes having frequencies above ~10 Hz the force is modeled as an effective impulse

1

FI(t

)

0 1 2 3 4 5

-50

5

x 10-3

By(t)

T ime (s)

Acc

eler

atio

nF

I(t)

‘‘High-frequency’ / Transient Force Model

60 ∙.

. ∙700

0 20 40 60 1.52

2.50

0.005

0.01

f 0 (Hz)f n (Hz)

FIFI

fn (Hz) f0 (Hz)

‘Perfect’ Force Models in the Literature

• AISC DG11• Ungar’s Model• ISO 10137• SCI P354

• Similarity: assume perfect periodicity

• Differences: number of DLFsmagnitude of DLFsexcitation rangestreatment of high frequency modes

‘Perfect’ Force Model

0.5 1 1.5 2 2.5 3 3.5 4

1

F/W

Time (s)

1.8 3.6 5.4 7.2 9 10.80

0.1

0.2

0.3

0.4

0.5

DL

F

Frequency (Hz)

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Probabilistic Force Model

0.5 1 1.5 2 2.5 3 3.5 4

1

F/W

Time (s)

1.8 3.6 5.4 7.2 9 10.80

0.1

0.2

0.3

0.4

0.5

DL

F

Frequency (Hz)

Probabilistic Force Model

• Probability distributions are assigned to:

o Dynamic Load Factors

o Pacing rate: f0

o walker’s stride length

o Pulse amplitude

• Benefits

• LimitationsPDF of the pacing frequency

Agenda







• Field assessment

FEM – Loads & Materials

• Permanent loads are applied as area mass

• Magnitudes should represent actual loads

• Typically apply 30% of LL for modeling

• Distribution is VERY important as it effects the mode shapes.

• Concrete dynamic modulus: 38 Gpa/5500 ksi for NWC 22 Gpa/3200 ksi for LWC

FEM – Profiled Slabs EC

EC

IY

IY

ts

ts

yNA

FEM – Profiled Slabs

• Beams, girders inserted atcorrect elevations

• Slab modeled as equivalentuniform shell

• Orthotropic shell propertiesEC and ECX

EC

IY

ts

yNA

IY

ECXts

12 ,

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FEM – Connections & Boundary Conditions

• Rigid connections on primary framework, but free to move in all 6 DOFs

• Perimeter cladding -> pinned

• Core walls -> fully restrained

• Columns -> pinned at inflection points

• Partitions -> added mass and damping…what about stiffness?

FEM – Dynamic Analysis

• Eigenvalue analysis of the FEM produces:o Mode frequencies

o Mode shapes

o Lumped masses

• For response analysis retain modes up to at least twice the fundamental frequency

• More modes may be required depending on criteria for specific equipment etc. (i.e., high frequency sensitivities)

Agenda








Generic Criteria – Human Comfort

1 4 8 80

0.05

0.1

0.5

RM

S A

ccel

erat

ion

(%g)

Frequency (Hz)

1 4 8 80

0.05

0.1

0.5

RM

S A

ccel

erat

ion

(%g)

Frequency (Hz)

Generic Criteria – Human Comfort

• 1x, ISO-OpOperating theathers

• 2x, ISO-ResResidences

• 4x, ISO-OfficeOffices

• 8x, ISO-WorkshopWorkshops

8

4

2

1

Generic Criteria – Response Factors

• Steps:

1) filter time series

2) calculate sliding 1-sec RMS

3) divide RMS by 0.05%g

,

0.05%g10

010

110

20.1

1

Wei

ghtin

g F

acto

r

Frequency (Hz)

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-5

0

5

x 10-3

By(t)

(g)

0.005

0.01

0.015

0.02

0 1 2 3 4 5

-5

0

5

x 10-3

By wt(

t)(g

)

T ime (s)1 10 100

0.005

0.01

0.015

0.02

Frequency (Hz)

Response Factors - Example

• f0 = 2 Hz; fn = 12 Hz; β = 1.3%

un-weighted

weighted

Acc

eler

atio

nA

ccel

erat

ion

Response Factors - Example

• f0 = 2 Hz; fn = 12 Hz; β = 1.3%

-0.01

-0.005

0

0.005

0.01

By wt(

t)(g

)

Running 1s RMS

0 1 2 3 4 5 6 7 8 9 100123456

Time (s)

RA

ccel

erat

ion

RGeneric Criteria – Equipment & Procedures

• Conversion to RMS velocity

1 4 8 80

0.05

0.1

0.5

RM

S A

ccel

erat

ion

(%g)

Frequency (Hz)1 4 8 80

4000

RM

S V

eloc

ity (i

n/s)

Frequency (Hz)

2

Generic Criteria – Equipment & Procedures

• 1/2x, Class ALow res microscopy

• 1/4x, Class BCT scanners

• 1/8x, Class CHigh res microscopy

• 1/16x – 1/32x, Class D/EMRI, SEM, NMR 1 4 8 80

125

250

500

1000

2000

4000

RM

S V

eloc

ity (i

n/s)

Frequency (Hz)

1

12

14

18

116

132

A

B

C

D

E

ISO-Op

Additional Comments

• Manufacturer’s criteria should always be used when available

• Data processing should be consistent with criteria

• End User requirements are very important in Sci-Tech and Health Care facilities

Agenda








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Numerical Assessment Methodology

1. Construct FEM

2. Extract the modal parameters (frequencies, lumped masses, mode shapes)

3. Select damping ratio, input & response locations

4. Compute floor responses

5. Compare against criteria

6. Establish mitigation, if required

Selecting the Damping Ratio

• ISO 10137, SCI P354

Floor Condition βdesign

Steel joist/concrete slab, bare floor 1.3%

Composite steel beam with shear connectors, bare floor 1.1%

Prestressed concrete, precast, bare floor 1.3%

Reinforced concrete, monolithic, bare floor 1.5%

Fully fit-out and furnished floors 2 – 3%

Floors where partitions interrupt relevant modes 4 – 5%

Single Point Method

Response location

Force location

,

,

FEM Mode Shape

Fit-Out Floor

Single Point Method

• Select worst-case locations on the floor

• Typically maximum mode shape locations or locations of sensitive equipment

, , ∙ , ∙ SteadyResponse

, , ∙ , ∙ TransientResponse

, ,

Single Point Method

• Benefits: Easy to implement in a spreadsheet

Fast calculations

Conservative – walking ‘on-the-spot’ to steady state

• Limitations: Moving loads are not considered

Difficult to visualize response of entire floor

Results cannot easily be processed into specific formats

Full Time Domain Simulation

• In reality, the forces are varying in both time and space!

• Benefits: Full walking paths are considered

All force models can be used

Results can be processed in any format

Visualization

• Drawbacks: Complex implementation and computationally intensive

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Example: Response Contours

Path B

Example: MRI Criteria Evaluation

0 1 2 3-1.5

-1

-0.5

0

0.5

1

1.5x 10

-3

Time (s)

Acc

eler

atio

n (m

/s2 )

0 20 40 60 80 10010

-7

10-6

10-5

10-4

10-3

Frequency (Hz)

Acc

eler

atio

n (m

/s2 )

Agenda








Building Re-Use: Bare Floor

Final Fit-Out: Executive Office Suite

L2 Office Suite

L1 Servery

Full-height partition

25/01/2013

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Modal Testing and Model Correlation

Modal Testing of Bare Floor

• 12 x 4 = 48 point test grid

Impact point

Measurement point

A

A1

B 6

5

4

3

2

4

8

12

16

3

20

7

24

11

28

32

15

2

36

19

6

40

23

10

27

44

14

1

31

48

18

5

35

22

9

39

Mode 1, 7.08 Hz

26

13

43

30

17

34

47

21

38

25

42

29

33

46

37

41

45

A

A1

B 6

5

4

3

2

4

8

12

16

3

20

7

24

11

28

32

15

2

36

19

6

40

23

10

27

44

14

1

31

48

18

5

35

22

9

39

Mode 2, 7.26 Hz

26

13

43

30

17

34

47

21

38

25

42

29

33

46

37

41

45

A

A1

B 6

5

4

3

2

4

8

12

16

3

20

7

24

11

28

32

15

2

36

19

6

40

23

10

27

44

14

1

31

48

18

5

35

22

9

39

Mode 1, 7.01 Hz

26

13

43

30

17

34

47

21

38

25

42

29

33

46

37

41

45

A

A1

B 6

5

4

3

2

4

8

12

16

3

20

7

24

11

28

32

15

2

36

19

6

40

23

10

27

44

14

1

31

48

18

5

35

22

9

39

Mode 2, 7.24 Hz

26

13

43

30

17

34

47

21

38

25

42

29

33

46

37

41

45

Measured

FEM

= 1.9% = 0.7% Footfall Testing of Bare Floor

• Test pacing rates: 1.4, 1.6, 1.8, 2.0 Hz87, 96, 109, 120 spm

Measurement point

Path A

Path B

0 2 4 6 8 10 12-0.44

-0.22

0

0.22

0.44

Time

Acc

eler

atio

n (m

/s2 )

Running 1s RMS

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

Time

Res

pons

e F

acto

r -

R

ISO Office Criterion

Maximum Response

• 120 spm, Path A

215 216 214 219 222 220 2230

5

10

15

20

Room - Measurement/Prediction Location

Res

pons

e F

acto

r - R

Walking Path B, 96 spm

Measured

Model

215 216 214 219 222 220 2230

5

10

15

20


Res

pons

e F

acto

r - R


Force Model Validation – Probabilistic Model

215 216 214 219 222 220 2230

5

10

15

20


Res

pons

e F

acto

r - R

Walking Path A, 96 spm

Measured

Model

215 216 214 219 222 220 2230

5

10

15

20


Res

pons

e F

acto

r - R


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215 216 214 219 222 220 2230

5

10

15

20

25

30


Res

pons

e F

acto

r - R


Measured

Model

215 216 214 219 222 220 2230

5

10

15

20

25

30


Res

pons

e F

acto

r - R


Force Model Validation – Probabilistic Model

215 216 214 219 222 220 2230

5

10

15

20

25

30


Res

pons

e F

acto

r - R


Measured

Model

215 216 214 219 222 220 2230

5

10

15

20

25

30


Res

pons

e F

acto

r - R


Force Model Comparisons

Predicted vs. Measured

0

1

2

3

4

5

6

7

8

216 223 220 222

R F

acto

r


Max Measured Predicted

Summary – Key Takeaways

1. MDOF systems ‘de-couple’ in to SDOF modes of vibration

2. Two components of footfall forcei. Low-frequency, resonant

ii. High-frequency, transient

3. Forces contain ‘harmonics’ that are multiples of the pacing frequency

4. Probabilistic force model best-reflects reality

Summary – Key Takeaways

5. Most connections can be modeled as rigid for FEM (small strains)

6. Magnitude and distribution of mass in FEM is important due to the effect on mode shapes

7. Generic vibration criteria are derived from the ISO Base Curve for perceptibility

8. Full time domain simulations of response provide the most comprehensive assessment of response

130113 dvase 2013 seminar/breakfastseminarfeb13.pdf · the characteristics of footfall forces ......

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