FLOOR VIBRATIONS DUE TO HUMAN ACTIVITIES: …doc.learnwithseu.com/seusessions/2012/09sep/...sept12_2012_vibrati… · 1 FLOOR VIBRATIONS DUE TO HUMAN ACTIVITIES: Tools and Tips for

1

FLOOR VIBRATIONS DUE TO HUMAN ACTIVITIES:

Tools and Tips for Satisfactory Designs

Christopher H. Raebel, Ph.D., P.E., S.E.

Assistant Professor of Civil and Architectural Engineering

Milwaukee School of Engineering

Milwaukee, WI

September 12, 2012 www.LearnWithSEU.com

Presentation Overview

� Introduction

� Floor vibration basics

� Design practices

� Brief Q&A time

� Case study: Kunkle Lounge at Penn State

� Basic computer modeling for vibrations

� Q&A (please ask questions throughout!)

This presentation will focus on steel framed floors, but

many principles may be applied to other framing systems2

About Your Speaker

� Assistant Professor, Civil & Architectural Engr.

� >10 years experience in private practice

� Education:

� B.S. Architectural Engineering, MSOE, 1994

�M.S. Architectural Engineering, Penn State, 2000

� Thesis: “Development of an Experimental Protocol for Floor

Vibration Assessment”

� Ph.D. Civil Engineering, Marquette, 2011

� Dissertation: “A Quantitative Study of Robustness

Characteristics of Steel Framed Structures

� Licensed P.E., S.E.3

2

Why are we talking about this?

� Floor vibrations continue to be common

� “Efficient” designs present new problems

…vibrations!

� Lightweight concrete

� “Stronger” steel

� Design techniques continue to improve based

on new research

4


� Introduction



� Brief Q&A time




5

Floor vibration basics

� Why are vibrations objectionable?

�Our bodies are not comfortable when they’re

vibrating!

� When are vibrations objectionable?

�When our internal organs go into resonance

� This occurs when the floor has a fundamental natural

frequency of approx. 7 Hz.

� Will the floor collapse?

� Strength and serviceability are different things

6

3

What’s a bad floor?

7Experimental floor – Penn State

What’s a bad floor?

8Experimental floor – Penn State

-0.1

-0.075

-0.05

-0.025

0

0.025

0.05

0.075

0.1

0 2 4 6 8 10 12 14

Time (s)


9Recommended peak acceleration for human comfort

(Allen and Murray 1993)

4


� Floors have distributed mass, stiffness

� Modal analysis can be used to determine natural

frequencies and mode shapes

Modal equation of motion

M* = Modal mass matrix

C* = Modal damping matrix

K* = Modal stiffness matrix

F(t) = Forcing function

ΦT = Mode shape vector

= Modal acceleration, velocity and displacement 10

)(***tFYKYCYM

TΦ=++ &&&

YYY ,, &&&


� The following parameters affect vibration:

�Mass

� Stiffness (natural frequency, actually)

�Damping

� In order to improve a floor system, one (or more)

of these must be adjusted

11


� Things that affect vibration in a real system:

�Depth of concrete slab (mass)

� LW vs. NW concrete (mass)

� Steel deck profile (mass)

� Stiffer beams w/ the same spacing (stiffness)

� Spacing beams closer (stiffness)

� Longer/shorter beams and girders (stiffness)

� Full height partitions (damping)

12

5


� Things that DON’T affect vibration:

� Spacing or size of beams if they are “efficiently”

designed

�Composite / non-composite

� Strength of concrete

� Strength of steel

� “Transient” mass (people, desks, etc.)

13


� Introduction



� Brief Q&A time




14

Design references

15

AISC Design Guide 11 SJI Tech. Digest #5

6

Initial assessment

� Who (or what) will object to vibration?

(helps to define appropriate limits)

� Who (or what) causes the vibration?(helps to define the expected dynamic forces)

� What is the expected system response at the

location of those objecting?

16

“Negotiating” design

� Consider the floor plan

� Consider the system

� Consider the framing selection

17

I know you will have problems if...

� The span of the open web steel joists is around

28’-0”

� 0.6C deck with 2 ½” total thickness

� The ballroom floor has a fundamental frequency

of around 3 hertz

� The employee aerobics room is right next to the

office of the VP…

18

7

“System-based” approach

� Slab assumed to continue to adjacent bays

� Mass (weight) and stiffness determined on a

“panel” basis

� We assume fundamental frequency participates

the most (others negligible)

� Assume composite action

� Continuity and cantilevers are considered

19

What about damping?

� Architectural

elements provide

most damping

� Full height partitions?

Use 3% damping

(0.03)

� Use 2% (0.02) for

most other scenarios

20(Tedesco et. al 1999)

Natural frequency of a floor system

21

14K4 JOISTW8x13

12 GA. POUR STOP

PL 3/4 x 10" x 0'-10"

EXIST. FLOOR SLAB

THREADED ROD EPOXY ANCHOR

INTO EXISTING CONC. SLAB

8" DIA. STD. PIPE COLUMN

CONC. SLAB OVER

1.0C22 GALV. FORM DECK

3'-0"

21 2"

Experimental floor – Penn State

An example of how to calculate the natural frequency

8


22

Calculating estimated properties for an open web steel joist

(Hanagan and Murray 1997)

14K4 joist, 26’-0” span, 30 in. center-to-center

• wTL = 251 plf (from SJI load tables using 26’-0”)

•MALL =

•ABOT =

•ATOP =

•ACHORD =

( )( ) ( )( )22

TL251plf 26 ftw L

= =21,209.5 ft-lb =254.5 in-k8 8

( )( ) ( )( )2ALL

ALL

M 254.5in-k= =0.653in14 in.-1in. 30ksid-1 f

2BOT

1.25A =0.816in

2BOT TOP

A +A =1.469in


23

Calculating estimated properties for an open web steel joist (continued)

•

•

( )( ) ( )2BOT

2CHORD

0.653in 14in.-1in.A d-1y =0.5 + =

A 1.469in

=6.28in.

(down from the T.O. joist)

( )( ) ( )( )( ) ( )( )

2 2

CHORD TOP BOT

2 22

4

I = A y-0.5in. + A d-y-0.5 in.

= 0.816in 6.28in.-0.5 in. + 0.653in. 14 in.-6.28in.-0.5 in.

=61.3in


24

Joist mode properties (Murray, Allen and Ungar 1997)

The natural frequency is calculated using composite properties

•

•

•

( )1.5

1.5cC C

E = w f' (ksi) = 145pcf 3ksi =3,024ksi

( )( )S

C

E 29,000ksin= = =7.11.35E 1.35 3,024ksi

(down from the T.O. joist)

( ) ( )

( )

2

c2

30in. 1.5 in.1.469in 1.0in.+6.28in. - 1.5 in.7.1 2

y = =0.76in.30in.1.469in + 1.5in.7.1

(down from the T.O. deck)

9


25

Joist mode properties (continued)

•

•

•

( )

( )( )

24 2

COMP

32

4

I =61.3in + 1.469in 1.0in.+6.28in.-0.76in.

30in. 1.5in.7.1 30in. 1.5in. + + 1.5 in. 0.76in.+

12 7.1 2

=139.2in

2.8-0.28 L/D

t

2.8-0.28 22.3

C =0.90 1-e

=0.90 1-e =0.895

where L/D = 312 in./14 in. = 22.3

For 6 < L/D < 24 and angle webs used

t

1 1= -1= -1=0.1170.895C

γ Parameter used in Ieff calculation


26

Joist mode properties (continued)

•

•

•

•

4EFF

4CHORD COMP

1 1I = = =110inγ 1 0.117 1+ +

I I 61.3in 139.2in

(this is the effective moment of inertia of an OWSJ supported T-beam)

( )j30in.w = 25 psf +6.7plf =69.2plf

12

(25 psf slab load and 6.7 plf from Vulcraft manuals)

( )( )( )( )( )

4 34 3

jj 4

EFFS

in5 69.2plf 26 ft 17285w L ft∆ = = =0.223in.

384E I 384 29,000,000psi 110in

2

jj

in.386.4g sf =0.18 =0.18 =∆ 0.

722

.3in.

49Hz Natural freq. of the joist panel


27

A sidebar: how would it change things if we added an inch of concrete?

Property 2.5 in. slab 3.5 in. slab

0.76 in. below T.O. Deck 0.21 in. above T.O. Deck

ICOMP 139.2 in4 160.6 in4

IEFF 110 in4 123 in4

wj 69.2 plf 99.2 plf

∆j 0.223 in. 0.29 in.

fj 7.49 Hz 6.61 Hz

Cy

10


28

Girder mode properties (Murray, Allen and Ungar 1997)

W8x13 girder, 10’-0” span

• Effective width of slab: 0.2Lg = (0.2)(120 in.) + 6 in. = 30 in.

(the 6 in. is the length of the slab extension past C/L)

• Effective concrete depth: 2 in. (incl. conc. in flutes)

•

( )

( )

2

c2

7.99in. 30in. 2.0in.3.84 in 0.5 in.+2.5 in.+ - 2.0in.2 7.1 2

y = =1.50in.30in.3.84 in + 2.0in.7.1

(down from the effective

concrete depth)


29

Girder mode properties (continued)

•

•

•

( )( )

2

4 2COMP

32

4

7.99in.I =39.6in + 3.84in 0.5 in.+2.5in.+ -1.50in.2

30in. 2.0in.7.1 30in. 2.0in. + + 2.0in. 1.50in.+

12 7.1 2

=211.2in

4 44 4COMP NC

g NC

I -I 211.2in -39.6inI =I + =39.6in + =82.5 in4 4

g69.2plf 27 ftw = +13plf =386.7plf

22.5 ft

(approximating as a uniform load,

and includes slab extension past

centerline of girder)


30

Girder mode properties (continued)

•

•

•

( )( )( )( )( )

4 34 3

jj 4

EFFS

in5 386.7plf 10 ft 17285w L ft∆ = = =0.036in.

384E I 384 29,000,000psi 82.5in

2

gg

in.386.4g sf =0.18 =0.18 =∆ 0.

103

86in.

.6Hz Natural freq. of the joist panel

Combined mode properties (includes joists and girders)

2

ggj

in.386.4g sf =0.18 =0.18 =∆ +∆ 0.223in.+.036in.

6.95Hz

11

It’s halftime!

31

Do you have any questions

on the material so far?


� Introduction


� Current design practices

� Brief Q&A time




32

Case study: Kunkle Lounge

33

� Pre-engineered frame

� Second and third

floors hung from

frame

� Interior support by

steel rods from beams

� Exterior support

directly to columns

� VERY bouncy floor

12


34


35

Experimental analysis hardware

36

Proof-mass actuator Accelerometer

13

Acceleration response

37

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 1 2 3 4 5 6 7 8

Accele

rati

on

(g

)

Time (sec)

Frequencies and mode shapes

38

Mode 1: 7.08 Hz

ζ = 3.24%Mode 2: 7.63 Hz

ζ = 1.02%Mode 3: 8.96 Hz

ζ = 1.59%Mode 4: 10.66 Hz

ζ = 0.50%

(Excitation centered on the floor)

Frequencies and mode shapes

39

Mode 1: 7.09 Hz Mode 2: 7.62 Hz Mode 3: 8.96 Hz Mode 4: 10.66 Hz

(Excitation offset from center)

14

Results from Kunkle floor testing

� Clearly the floor is not within allowable limits per

DG #11

� Several natural frequencies within the “danger

zone”

� Active control tried to minimize vibration

� Proof-mass actuator used

� Floor was noticeably “stiffer” when actuator tuned to

the floor’s vibration

40


� Introduction



� Brief Q&A time




41

Computer analysis

42

� Packages with

vibration capabilities

� SAP 2000 / ETABS

�RISA

�Others…

� Basic modeling

using available

packages

� Advanced modeling

using FE packages

15

Computer analysis

43

-0.1

-0.075

-0.05

-0.025

0

0.025

0.05

0.075

0.1

0 2 4 6 8 10 12 14

Time (s)

Computer analysis

� Model slab using

“plate” elements

� Model beams and

girders using shape

database

� Superimpose DL and

11 psf LL

44

Deflected shapes from

RISA-3D

Computer analysis

45

059

069

005

001

27'-0"

11'-0"

2'-6" C/C JOISTS

TYPICAL PLATE ELEMENTS

2'-2"

1'-3"

14K4 JOISTS

W8X13

W8X13

Example floor plan

16

46

MODE 1

7.48 Hz

MODE 2

9.41 Hz

MODE 4

23.3 Hz

MODE 1

7.01 Hz

MODE 2

8.87 Hz

MODE 3

19.36 Hz

F.E. HEEL DROP

Computer model expectations

� Expect the computer model to be stiffer than the

actual floor

� Expect a few modes to develop that don’t really

exist

� Expect that modes may “switch”

47


� Introduction



� Brief Q&A time




48

17

References and acknowledgments

49

Funding for this research provided (in part) by the National Science Foundation, grant no. CMS 9900099

Allen, D.E. and Murray, T.M. (1993). Design Criterion for Vibrations Due to Walking, AISC Engineering Journal, 4th Qtr., pp.117-129.

Hanagan, L.M. (2003). Floor Vibration Serviceability: Tips and Tools for Negotiating a Successful Design, Proceedings of the North American Steel Construction Conference, Baltimore, MD.

Hanagan, L.M., Raebel, C.H. and Marsh, E. (2000). Modeling for Controller Design on a Steel Floor System, Proceedings of the 18th International Modal Analysis Conference, San Antonio, TX.

Hanagan, L.M. and Murray, T.M. (1997). Serviceability Considerations for Floor and Roof Systems, In “Steel Design Handbook: LRFD Method,” Edited by A.R. Tamboli, p.9-1 – 9-41.

References and acknowledgments

50

Raebel, C.H. (2000). Development of an Experimental Protocol for

Floor Vibration Assessment, M.S. Thesis, The Pennsylvania State

University, University Park, PA.

Murray, T.M., Allen, D.E. and Ungar, E.E. (1997). Floor Vibrations Due

to Human Activity, AISC Design Guide #11, American Institute of Steel

Construction, Chicago, IL.

Tedesco, J.W., et. al. (1999). Structural Dynamics: Theory and

Application, Addison Wesley Longman, Menlo Park, CA.

FLOOR VIBRATIONS DUE TO HUMAN ACTIVITIES:

Tools and Tips for Satisfactory Designs

Christopher H. Raebel, Ph.D., P.E., S.E.

Assistant Professor of Civil and Architectural Engineering

Milwaukee School of Engineering

Milwaukee, WI

September 12, 2012 www.LearnWithSEU.com

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FLOOR VIBRATIONS DUE TO HUMAN ACTIVITIES: …doc.learnwithseu.com/seusessions/2012/09sep/...sept12_2012_vibrati… · 1 FLOOR VIBRATIONS DUE TO HUMAN ACTIVITIES: Tools and Tips for