Vibraciones Sistemas Piso

8/13/2019 Vibraciones Sistemas Piso

1/36

Course on Bolted Connections and Floor Vibrations

Puebla, Mexico March 6-8, 2008

Presented by Thomas M. Murray, P.E., PhD Session 7 1

111

FLOOR VIBRATIONSA CRITICAL SERVICEABILITY ISSUE

Presented byThomas M. Murray, Ph.D., P.E.

Department of Civil and Environmental EngineeringVirginia Tech

Blacksburg, [email protected]

222

Todays Topics

FundamentalsWalking Vibrations

Rhythmic VibrationsSensitive EquipmentSpecial Structures

Retrofitting

with War Stories

333

FUNDAMENTALS

444

Each tolerance Criterion has two parts:

Prediction of the floor response to aspecified excitation.

Human response/tolerance

Each criterion has been calibrated using

existing floors.

Tolerance Criteria


2/36




555

Commonly Used Criteria

Modified R-M Scale

Murray Criterion

SJI Technical Digest No. 4/Software

AISC/CISC Design Guide 11FloorVibrations due to Human Activity

6661 5 20

Frequency, Hz

Amp

litude,

in.

NotPerceptible

Slightly

Distinctly

StronglyPerceptible

.001

.01

.10

Amp

litude,

in. Distinctly

.001

.01

.10

Modified Reiher-Meister Scale

Heel Drop

Excitation

777

D > 35Ao

fn

+ 2.5

D = Log Decrement Damping

Ao = Amplitude from Heel-Drop

fn = Fundamental Frequency

Murray Criterion

888

Before 1980s:

Typical Bay

25 ft by 25 ft w/ 7 in. normal weightconcrete

Heavy office loading 15 to 20 psf

Modal Damping 7-8%

Resonance not a significant problem becauseof damping.

Tolerance Criteria


3/36




999

No Resonance

101010

An 00s Office -- Resonance

111111

The Power of Resonance

1

0 1 2

Sinusoidalaccele

rationmass

Sinusoidalforce

2 - 3% Damping

1

fn

f 1

2

Natural frequency, fn

Forcing frequency, f

5 - 7% Damping

121212

Phenomenon of Resonance

Resonance occurs when a multiple of the

forcing function frequency equals a

natural frequency of the floor.

Usually concerned with the first

natural frequency.

Resonance can occur because of walking

dancing, or exercising.


4/36




131313

The Power of Resonance

Why do some walkers cause floor more floormotion than other walkers?

Answer: Their pace is a sub harmonic ofthe floor dominate frequency. That is, a

harmonic of their walking (2 and 3 timestheir walking speed) matches the floordominate frequency.

141414

___

_____

__________

_ _ _ _

___

_____ _

_________

_ _ _ _

___

_____

__________

_ _ _ _

________ __________

_ ___ _

1 3 4 5 8 10 25 40

25

10

5

2.5

1

0.5

0.25

0.1

0.05

Rhythmic Activities

Outdoor Footbridges

Shopping Malls,

Dining and Dancing

Offices,

Residences

ISO Baseline Curve for

RMS Acceleration

Pe

akAcceleration(%G

ravity)

Frequency (Hz)

Indoor Footbridges,

Extended by Allenand Murray (1993). . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

DG11 Uses

the ModifiedISO Scale

Considering

Resonance

151515

Tolerance Criteria

Modified R-M Scale

Murray Criterion SJI Technical Digest No. 4/Software

AISC/CISC Design Guide 11

Floor Vibrations due to Human Activity

161616

FloorVibe v2.02Software for Analyzing

Floors for Vibrations

Criteria Based on AISC/CISC Design

Guide 11

SEI

Structural Engineers, Inc.

537 Wisteria Drive

Radford, VA 24141

540-731-3330 Fax 540-639-0713

[email protected]

http://www.floorvibe.com


5/36




171717

Design Guide 11 Topics

Vibration Fundamentals

Natural Frequency

Design for Walking Excitation

Design for Rhythmic Excitations Design for Sensitive Equipment

Retrofit and Remedies181818

BASIC VIBRATIONTERMINOLOGY

191919

Period And Frequency

Period tp202020

Natural Frequency

====

wL

tIsgE

2f

2/1

4n


6/36




212121

Damping

Loss of Mechanical Energy in aVibrating System

Critical Damping

Smallest Amount of Viscous

Damping Required to PreventOscillation of a Free Vibrating System

222222

Harmonics

1st Harmonic

2nd Harmonic

3rd Harmonic

Footstep

tficosP stepi = 2

f1f step1 =

f2f step2 =

f3f step3 =

P1

P2

P3

232323

0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

Frequency (Hz)

MeasuredAutospectrum(Pe

ak,

%g)

WalkingSpeed100 bpm

2nd Harmonic3.33 Hz

System Frequency5 Hz 3rd Harmonic

Response from a Lightly Damped Floor

242424

Acceleration Ratio

Acceleration Of A System

Acceleration Of Gravity

Usually Expressed As %g.0.5%g is the Human ToleranceLevel for Quiet Environments.


7/36




252525

Period And FrequencyFloor Width

FloorLength

Bg= Girder Panel Width

Bj=

BeamPanel

W

idth

262626

NATURAL FREQUENCYOF

STEEL FRAMEDFLOOR SYSTEMS

272727

Fundamental Natural FrequencyUniformly Loaded Simply

Supported Beam

(3.3)

(3.1)

(Hz.)

==== wL4

ItgEs2f

2/1

n (Hz.)

==== /g18.0fn

(((( ))))ItE384 s/wL5 4====282828

Member

Bay

System

Fundamental Frequencies

(((( ))))H/g18.0f zn ====

)/(g18.0f gbn ++++====

)/(g18.0f cgbn ++++++++====

C B l d C i d Fl Vib i


8/36




292929

D: Actual Load

L: 11 psf for Paper Office

8 psf for Electronic Office6 psf for Residence

0 psf for Malls

Loads for Vibration Analysis

(((( )))) LDwItE384 s/wL5 4 ++++========

303030

Section Properties - Beam/Girder

b (< 0.4 L)

Fully Composite

Effect Width

n = Es/1.35Ec

313131

Deflection Due To Shear

Trusses L/d > 12

Icomp : Fully Composite Moment of Inertia

Ichords : Moment of Inertia Joist ChordsAlone

(3.13)I/I15.01

II

chordscomp

compeff ++++====

323232

Joist Joint Eccentricity

C B lt d C ti d Fl Vib ti


9/36




333333

Deflection Due To ShearOpen Web Joists

Web Shear Deformation

Angle Web Members (6 L/D 24)

C = 0.721 + 0.00725 (L/D)

Cont. Round Rod Web Members (10 L/D 24)

(3.16)

(3.17)

(3.15)

r

ICI chordreff=

]e[10.90C 0.28(L/D)2.8

r ====

343434

Deflection Due To Shear

Open Web Joists

(3.18)

(3.19)

Effective Transformed Moment of Inertia

Icomp = Transformed I using Actual Chord Areas

I

1

I

1I

ompcchord

eff

++++

====

11r==== C

353535

Deflection of Girders SupportingOpen Web Joists

Incomplete Composite Action Becauseof Flexibility of Joists Seats

Ig = Inc + (IgInc )/4 (3.14)

Inc = Non-Composite Mom. of Inertia

Ic = Composite Mom. of Interia

363636

Minimum Frequency

To avoid resonance with the

first harmonic of walking, theminimum frequency must begreater than 3 Hz. e.g.

fn > 3 Hz



10/36




373737

DesignFor

Walking Excitation

383838

_____

___ _

___

______

_ _ _ _

___

_____ _

_________

_ _ _ _

___

_____

__________

_ _ _ _

________ ________

__

_ _ _ _ _

1 3 4 5 8 10 25 40

25

10

5

2.5

1

0.5

0.25

0.1

0.05

Rhythmic Activities

Outdoor Footbridges

Shopping Malls,

Dining and Dancing

Offices,

Residences

PeakAcceleration(%G

ravity)

Frequency (Hz)

Indoor Footbridges,

Extended by Allen

and Murray (1993). . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .


RMS Acceleration

ModifiedISO Scale

393939

Walking Vibrations Criterion

g

a

W

)f35.0exp(P

g

a onop ====

Predicted Tolerance

404040

ap = peak acceleration

ao = acceleration limit

g = acceleration of gravity

fn = fundamental frequency of a beam or joist panel, or acombined panel, as applicable

Po = a constant force equal to 65 lb for floors and 92 lb forfootbridges

= modal damping ratio (0.01 to 0.05)

W = effective weight supported by the beam or joist panel,girder panel, or combined panel, as applicable

= wBL

g

a

W

)f35.0exp(P

g

a onop ====

Walking Vibrations Criterion



11/36




414141

Recommended Values of Parameters in Equation (4.1) and a /g Limitso

Occupancy Constant Force Damping Ratio Acceleration Limitao/g x 100%Po

Offices, Residences, 65 lb 0.02 0.05 * 0.5%

Churches

Shopping Malls 65 lb 0.02 1.5%

Footbridges - Indoor 92 lb 0.01 1.5%

Footbridges - Outdoor 92 lb 0.01 5.0%

Table 4.1

* 0.02 for floors with few non-structural components (ceilings, ducts, partitions,

etc.) as can occur in open work areas and churches,

0.03 for floors with non-structural components and furnishings, but with onlysmall demountable partitions typical of many modular office areas,

0.05 for full height partitions between floors.

Parameters

424242

Use very low live load (6-8 psf) andlow modal damping (2% 2.5%) for

electronic office floor systems.

See Floor Vibration and theElectronic Officein Modern Steel

Construction August 1998

Important

434343

DG11 Damping,

Example Problem Floor

444444

DG11 Damping,

Space: 45 x 130

32LH06 x 45 ft

5 in. Total Depth

2 in. Deck

Normal Wt. Conc.




12/36




454545

DG11 Damping,

Yes, the floor didvibrate and there

were complaints.

DG11 Prediction: = 1.5% 0.70%g

= 2.0% 0.53%g


464646

Equivalent Combined Mode

Panel Weight (W in Eqn. 2.3)

(4.4)

g

a

W

)f35.0exp(P

g

a onop ====

WWW ggj

gj

gj

j

++++

++++

++++

====

474747

Beam and Girder PanelEffective Weights

Beam Panel

Girder Panel

LjBj)S/wj(Wj ====

LgBg)L avg,j/wg(Wg====

484848

Effective Beam Panel Width

Floor Width

Cj = 2.0 For Beams In Most Areas= 1.0 For Beams at a Free Edge

Dj = IJ/S in4/ft

3/2L)Dj/Ds(CjB j4/1

j


13/36




494949

Section Properties - Slab

12

_ _ _ _

de=dc-ddeck /2

A = (12 / n) de

n = Es/1.35 Ec

in4/ ft

fc in ksi

)12/d)(n/12(D 3es====

fwE c5.1c ====

505050

Beam or Joist Panel

Effective Weights

For hot-rolled beams or joistswith extended bottom chords, Wjcan increased 50% if an adjacentspan is greater than 0.7 x the spanconsidered. That is,

Wj = 1.5(wj/S)BjLj

515151

Effective Girder Panel Width

Bg = Cg(Dj/Dg)1/4 Lg 2/3 Floor Length

Cg = 1.6 For Girders Supporting JoistsConnected Only to a Girder Flange

= 1.8 For Girders Supporting BeamsConnected to a Girder Web

Dg = Ig/Lj,avg in4/ft

525252

Bg = Cg(Dj/Dg)1/4 Lg 2/3 Floor Length

Bays A & B

Bg = 59.9 ft

Bays A:

2/3x81 = 54 ft

ap/g=0.46%g

Bay B:

2/3x48.5 =32.3 ft

ap/g=0.61%g



14/36



535353

Constrained Bays

Girder Deflection Reduction Factor forConstrained Bays:

If Lg < Bj, substitute:

(4.5)

for g in Equation (4.4) and in frequency eq.

==== gj

gg

B

L5.0

B

L

j

g with

545454

Example

555555

S

W24 55

W21 444 SPA @ 7- 6 =30 = L g

W2144

W1422

W18

35

W1422

L=

45

jW18 35

3.502.00

d = 3.50 +e2.00

2= 4.50

SectionW1422

Floor Width = 30 ftFloor Length = 90 ft

Paper Office 565656

Gravity Loads:LL : 11 psf (For Vibration Analysis)

Mech. & Ceiling : 4 psf

Deck Properties:Concrete: wc = 110 pcf fc = 4000 psi

Floor Thickness = 3.50 in. + 2 in. ribs

= 5.50 in.

Slab + Deck Weight = 47 psf



15/36



575757

Beam Properties:

W18 35

A = 10.30 in.2

Ix = 510 in.4

d = 17.70 in.

Girder Properties:

W24 55

A = 16.20 in.2

d = 23.57 in.

Member Properties

Ix = 1350 in.4

585858

Beam Mode Properties

Effective Concrete Slab Width = 7.5 ft < 0.4 Lj= 0.4 x 45 = 18 ft.

n = modular ratio = Es/1.35Ec= 29000 / (1.35 x 2307)

= 9.31

Ij = transformed moment of inertia = 1799 in4

ksi23070.4110fwE5.1

c5.1

c ============

595959

wj = 7.5 (11 + 47 + 4 + 35/7.5) = 500 plf

Equation (3.3)

Beam Mode Properties Cont.

.in885.017991029384

1728455005

EI384

Lw56

4

j

4jj

j ====

========

====

jj

g18.0f

Hz76.3885.0

38618.0 ========

606060

Cj = 2.0

Bj = Cj (Ds/ Dj)1/4Lj

(4.3a)

= 2.0 (9.79 / 240)1/4(45) = 40.4 ft > 2/3 (30) = 20 ft.

Wj = 1.5(wj/S)BjLj (50% Increase)

= 1.5 (500/7.5)(20.0 45) = 90,000 lbs = 90.0 kips

Beam Mode Properties Cont.

Bj = 20 ft.

.ft/.in2405.7/1799S/ID4

jj ============

ft/.in79.9)12/50.4)(31.9/12()12/d()n/12(D433

es ============



16/36



616161

Girder Mode Properties

Eff. Slab Width = 0.4 Lg= 0.4 x 30 x 12

= 144 in. < Lj = 45 x 12 = 540 in.

b = 144

Ig = 4436 in4

626262

wg = Lj (wj/S) + girder weight per unit length

= 45(500/7.5) + 55 = 3055 plf.

(3.3)

Girder Mode Properties Cont.

.in43.044361029384

17283030555

IE384

Lw56

4

g

4gg

g ====

========

.Hz37.5433.0

38618.0g

g18.0fg ========

====

.ft/.in6.9845/4436L/ID4

jgg ============

636363

Cg = 1.8 (Beam Connected To Girder Web)

(4.3b)

= 1.8 (240 / 98.6)1/4 (30) = 67.4 ft > 2/3 (90) = 60

(4.2)

=(3055/45)(60 30) = 122,200 lb = 122 kips

Use

Girder Mode Properties Cont.

L)Dg/Dj(CgB g4/1

g====

LB)L/w(W ggjgg====

646464

Combined Mode Properties

Lg = 30 ft < Bj = 20 ft Do Not Reduce

(3.4)

fn = Fundamental Floor Frequency

)/(g18.0 gj ++++====

Hz08.3)433.0885.0/(38618.0 ====++++====



17/36



656565

Combined Mode Properties Cont.

(4.4)WWW ggj

gj

gj

j

++++

++++++++

====

kips100)122(

433.0885.0

433.0)90(

433.0885.0

885.0====

++++

++++

++++

====

666666

= 0.0074

= 0.03 from Table 4.1 (Modal Damping Ratio)

W = 0.03 100 = 3.0 kips

Evaluation

= 0.74% g > 0.50% g N.G.

3000

)08.335.0exp(65

W

)f35.0exp(P

g

a nop

========

676767

___

___

__ __________

_ _ _ _

________ _

_________

_ _ _ _

________ _____

_____

_ _ _ _

_____

___ _

_________

_ _ _ _ _

1 3 4 5 8 10 25 40

25

10

5

2.5

1

0.5

0.25

0.1

0.05

Rhythmic Activities

Outdoor Footbridges

Shopping Malls,

Dining and Dancing

Offices,

Residences

PeakAccelerat

ion(%G

ravity)

Frequency (Hz)

Indoor Footbridges,

Extended by Allen

and Murray (1993). . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .


RMS Acceleration

686868

Original Design

W18x35 fb = 3.76 hz fn = 3.08 HzW24x55 fg = 5.37 hz ap/g=0.74%g

Improved DesignIncrease Girder Size

W18X35 fb = 3.76 hz fn = 3.33 HzW24x84 fg = 7.17 hz ap/g=0.70%g



18/36



696969

Original Design


Improved Design

Increase Concrete Thickness 1 in.

W18X35 fb = 3.75 hz fn = 3.04 Hz

W24x55 fg = 5.28 hz ap/g=0.65%g

707070


Improved Designs

Increase Beam Size

W21x50 fb = 4.84 hz fn = 3.57 Hz

W24x55 fg = 5.29 hz ap/g=0.58%g


Original Design

717171

Rule: In design, increase stiffnessof element with lowerfrequency to improveperformance.

If beam frequency is less than the girderfrequency, increase the beam frequency tothe girder frequency first, then increase bothuntil a satisfactory design is obtained.

727272

Example: Joist Floor

2 in. slab w/ 1 in. deck

30K8 @ 30 in.

W30x90


P bl M i M h 6 8 2008


19/36



737373

Gravity Loads:

LL: 11 psf

Mech. & Ceiling: 4 psf

Deck Properties:

Concrete: wc = 110 pcf f c = 3,000 psi

Floor Thickness = 1.50 in. + 1 in. ribs

= 2.50 in.

Slab + Deck Weight = 19.3 psf


747474

Joist Properties:

30K8

wt = 13.2 plf

A = 1.633 in.2

Ichords = 339 in.4

D = 30.0 in.

yc = 13.39 in.

Girder Properties:

W30 x 90

A = 26.40 in.2

Ix = 3,620 in.4

d = 29.53 in.


757575

Example: Joist Mode Properties

Effective Concrete Slab Width = 30 in. < 0.4 Lj

Ec = 2,000 ksi n = Es/1.35Ec = 10.74

with

I1

I

1I

compchords

eff

++++

====C

1

r

====

767676


Since 6 Lj/D = 28 x 12/30 = 11.2 24

With Icomp = 609 in.4

250.0180.011

C1

r============

80.0)e1(90.0C 8.2D/jL8.2

r ========

4

compchords

j in420

609

1

339

250.0

1

I1

I

1I ====

++++====

++++

====


P bl M i M h 6 8 2008


20/36



777777


With wj = 99 plf and j = 0.112 in.

= 10.6 Hz

Ds = 0.745 in.4/ft Dj = 168 in.

4/ft

Bj = 14.4 ft < 2/3 (3 20) = 40 ft.Wj = (wj / S) Bj Lj (No continuity)

= (99 / 2.5) (14.4 28) = 16,000 lbs = 16.0 kips

122.0

38618.0

g18.0f

jj ========

787878

Example: Girder Mode Properties

Joist Span = Lj = 28 ft = 336 in.

Girder Span = Lg = 20 ft = 240 in.

Effective Slab Width = 0.4 Lg = 96 in. < Lj

From which

Ic = 7,380 in.

4

(Full Composite)

797979

Example: Girder Mode Properties

To account for the effect of joist seats

Ig = Inc + (Ic Inc)/4

= 3620 + (7,380 3,620)/4 = 4,560 in4

With wg = 1,200 plf , g = 0.033 in.

And

Hz19.50.0333860.18

g0.18fg ============

808080

Example: Combined Mode Properties

Lg = 20 ft > Bj = 14.7 ft Do Not Reduce g

Hz9.29 0.033)386/(0.1120.18==== ++++====

kips18.9(27.6)0.0330.112

0.033(16.3)0.0330.112

0.112W ====++++

++++++++

====

Combined Mode Panel Weight:

)gjg/(0.18nf ++++====


Puebla Mexico March 6 8 2008


21/36



818181

Example: Walking Evaluation

0050.00044.0)900,18)(03.0(

)29.935.0exp(65


22/36



858585

Fit out Condition:

Office plan. Cubicles and no full height partitions with no

suspended ceiling or ductwork below.

Estimated actual

Dead Load:

Estimated actual

Live Load:

EstimatedDamping:

868686

Fit out Condition:

Office library. Full-height bookcases in heavily loaded room.

Suspended ceiling and ductwork attached below the slab.

Estimated actual

Dead Load:

Estimated actual

Live Load:

EstimatedDamping:

878787

DG11 Floor Width and Length

888888

Bay Building

Width

Building

Length

A

B

C

D

Floor Width and

Length Example

90 ft30 ft

30 ft150 ft

90 ft150 ft

90 ft90 ft

A

B

D

C


Puebla Mexico March 6-8 2008


23/36

Puebla, Mexico March 6 8, 2008


898989

Complex Framing

909090

DG11 Accuracy

Evaluated with 86 Bays with Field Measurements

25 Floors with Hot-Rolled Beams

30 Floors with Joists and Hot-Rolled Beams

28 Floors with Joists and Joist-Girders

5 Floors with Castellated Beams

Predicted and Measured Frequencies Compared

Predicted Tolerance Compared to SubjectiveEvaluation

919191

DG11 Frequency Accuracy

Type ofFraming

Hot-RolledBeams

AndGirders

Avg.

(Std. Dev.)

Joists w/Hot-Rolled

Girders

Avg.

(Std. Dev.)

Joist w/Joist-

Girders

Avg.

(Std. Dev.)

Cast.Beams w/Hot-Rolled

GirdersAvg.

(Std. Dev.)

Over-All

Avg.

(Std. Dev.)

fbeam/ fm1.034

(0.176)1.059

(0.252)1.003

(0.225)1.058

(0.078)1.031

(0.216)

fbay/ fm0.797

(0.132)0.896

(0.195)0.759

(0.166)0.858

(0.090)0.822

(0.173)

fm = measured frequency

929292

DG11 Frequency Accuracy

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16

Predicted fn, Hz

MeasuredBayfmeas.,

Hz

H-R

J/H-R

J/J-G

C/H-R

Measured Bay Frequency vs. Predicted Bay Frequency

Stiffer thanpredicted

Less stiff thanpredicted




24/36

Puebla, Mexico March 6 8, 2008


939393

DG 11 Criterion Accuracy

Evaluation of Floors Based on Final Occupancy.

Damping and live loading estimates based onoffice occupancy: paper or electronic.

Floor systems separated by framing type.

The limiting acceleration for DG11 is a peakacceleration of 0.50%.

Subjective evaluations from occupants andmeasurement team.

949494

DG11 Criterion AccuracyHo t- Ro ll ed B ea ms a nd G ir der s J ois ts a nd H ot -Ro ll ed Gi rd er s J ois ts a nd J oi st -Gi rd er s

Subjective

Response

DG11

peak/g (%)

Subjective

Response

(Complaints)

DG11

peak/g (%)

Subjective

Response

DG11

peak/g (%)

None

Many

Many

Many

Some

Some

Some

None

None

None

None

Some

Some

Many

Many

Many

None

None

None

0.34

1.08

0.71

0.71

0.80

0.80

0.94

0.50

0.42

0.46

0.31

0.40

0.56

0.43

0.59

0.75

0.38

0.37

0.38

X

X

None

Some

Some

None

None

None

Many

Some

None

Some

Many

Many

Many

None

None

0.42

0.45

0.62

0.29

0.35

0.35

0.74

0.89

0.50

0.73

0.61

0.73

0.73

0.47

0.57

X

X

None

Many

Some

Many

Many

Many

Some

None

None

None

None

None

None

Some

Some

Some

Some

0.53

0.6

1.08

0.95

1.12

0.77

0.54

0.48

0.48

0.54

0.21

0.21

0.22

0.97

0.97

0.68

0.54

X

X

959595

DG11 Criterion Accuracy

Framing

Agreement

Design Guide

11

Agreement

Modified R-M

Agreement

Murray

Criterion

Hot-Rolled

Framing 89% 47% 68%

Joists w/ Hot-

Rolled

Girders

87% 47% 67%

Joists w/ Joist

Girders88% 65% 71%

969696

Design

ForRhythmic Excitation




25/36

, ,


979797 989898

Aerobics

999999

Balcony Video

100100100

10 Story Special Purpose Building

Large Ballroom Floor

Auditorium Balcony

Case Studies




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101101101

Rhythmic Vibrations

10

R

9

8

7

6

5

43

2

Office Personnel Complaining

Dance Studios

Fundamental Frequency of10th Floor was 4 Hz.

102102102

Rhythmic Vibrations

Sec.

Acceleration Measurementsmade on 10th Floor

103103103

Large Ballroom Floor

>150 ft

>150 ft

Wt. of Bay 4,000,000 lbs

Fundamental Frequency

2.46 Hz (~150 BPM)

Tested with 42 people (~7500 lb) jumping at 120-144BPM). Equivalent to 150 people dancing

104104104

10% of gravity




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105105105

Concert Hall Balcony

106106106

Center - 1st Row, 0.2V, Steve Hoffman Bounce

7/28/99 - B169

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 0.5 1 1.5 2 2.5 3 3.5 4

Time (s)

Acceleration(g)

5% of gravity caused by one person.

107107107

Center - 1st Row, 0.2V, Steve Hoffman Bounce, FRF

7/28/99 - B170

3

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 5 10 15 20 25

Frequency (Hz)

Amplitud

e

Hz. Resonance

108108108

b, g and c are beam, girder and columndeflections due to supported weight

Natural Frequency forRhythmic Excitation

Column deflections may be important foraerobic excitations.

)/(g18.0f cgbn ++++++++====




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109109109

Three Methods of Evaluation

Minimum Required Frequency

Evaluation using Frequency

Evaluation using Acceleration

110110110

Typical Required Frequencies

Floor Wt. Req'd Freq.Activities (psf) (Hz)

Dancing and Dining 100 6.450 8.1

Lively Concert or 100 5.9Sports Event 50 6.4

Aerobics Only 100 8.850 9.2

Aerobics and 100 9.2Weight Lifting 50 10.6

111111111

(5.1)

fn = Natural Frequency of Floor

if = Multiple of Step Frequency, i = 1, 2, 3,

k = Depends on Activity: 1.3, 1.7 or 2.0

iwp = Effective Weight of Participants, psf

ao/g = Acceleration Limit

wt = Effective Weight Supported, psf

Evaluation Using Frequency

wt

wpi

)g/a( o

k1iffn

++++

112112112

Evaluation Using Acceleration

++++

====

f

f2 n2

1f

fn2

2

w/w3.1

g

a

stepstep

tpip

(2.4)

[[[[ ]]]] aa 5.1pa omax5.1/1==== (1.5 Power Rule)




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113113113

Rhythmic Vibrations

====

g18.0nf

Thus for a given fn, is constant.

Ex. For fn

= 5 Hz,

= 0.5 in for any span!!

114114114

Chapter VI

Design ForSensitive Equipment

115115115

Sensitive Equipment

Manufacturers Requirements:Generally in Terms of Velocity

Requirements are Usually Very Strict.Short Span, Very Stiff Floor Systems

are Required

116116116

Sensitive Equipment Criteria

U

V

f vn

p

(6.5)

b = Floor Flexibility, in/lb

fn = Natural Frequency of Floor

V = Specified Limiting Velocity

UV = Parameter Depending on Walking Speed




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117117117

Walking Speed Parameter

Slow Walking 50 steps/minute

Uv = 1,500 lb-Hz2

Intermediate Walking 75 steps/minute

Uv = 5,500 lb-Hz2

Fast Walking 100 steps/minute

Uv = 25,000 lb-Hz2

U

V

f vn

p

118118118

Typical Specified Velocities

Operating Rooms 8,000

400 Microscopes 2,000

Eye Surgery 1,000

30,000 Microscopes 500

Electron Microscopes 250

Microelectronics Manufacturing 130

in / sec

119119119

Special

Structures

120120120

Be careful when designing foot-bridges and crossovers

Very low damping

Low frequency Position of girders

Lateral Vibrations




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121121121

Footbridges

)damping%1(01.0

.)acceltolerance%(5gpa

with11DGfrom

W

)nf35.0(exp92

g

pa

toequivalentis

Hz3)W/180ln(86.2nf

====

====

====

Guide requirement:

122122122

Footbridges

Typical bridges satisfy fn > 2.86 ln (180/W)

but not fn > 3 Hz.

Requirement is equivalent to one personwalking.

123123123

Footbridges

Recommendation:

Where n = number of walkers on bridge.

But the real problem is rouge or vandaljumping. A small group can easilyexcite a footbridge if its naturalfrequency is less than 6-7 Hz.

g%g

aoW

)f. nexp(n

g

ap75

35092====

====

124124124

Troubled Bridge

Over Water

Troubled Bridge

Over Water




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125 126126126

127127127

Evaluationand

Remedial Measures

128128128

Remedial Methods

Reduce Excitation

Relocation of Source

Damping

StiffeningIncrease Natural FrequencyStiffen Components With Greatest

Dynamic Flexibility (i) Passive or Active Control




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129129129

Methods To Stiffen Floors

Additional Columns

AddedPosts

DampingElement

130130130

Methods To Stiffen Floors

Steel RodCover Plate

Cover Plates and Bottom Chord ReinforcingGenerally do not Work

131131131

Queen Post Hanger Stiffening

HVAC

Added Queen Post Hanger

132132132





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133133133


134134134

Stiffening Of Girders SupportingCantilevered Beams and Joist Seats

CantileveredBeam orJoist Seat

Girder

Stiffener

135135135

Pendulum TMD

Large Mass ~ 2% Mass RatioFrictionless Bearings

Coil Spring

Air Dashpot Damping

136136136

Pendulum TMD

Course on Bolted Connections and Floor VibrationsPuebla, Mexico March 6-8, 2008


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137137137

5th Floor - Response to Walking

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0

Time, seconds

Acceleration,

g's

Floor Acceleration w/o TMD

5th Floor - Response to Walking

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0

Time, seconds

Acceler

ation,

g's

Floor Acceleration with TMD

Without TMD

With TMD

Walking

138138138

Response to Walking

Results

5th Floor Response to Walking

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0 1 2 3 4 5 6 7 8 9 10

Frequency, Hz.

Velocity,

in/sec0-pk

Floor Velocity w/o TMD

Floor Velocity with TMD

5.25 Hz. , 0.01523 ips 0-pk

5.25 Hz. , 0.00756 ips 0-pk

50% Reduction

139139139 140140140

Course on Bolted Connections and Floor VibrationsPuebla, Mexico March 6-8, 2008


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141141141 142142142

The Hanging Graduate Student Solution

143143143

Final Thought

Strength is essential but otherwise

unimportant.

Hardy Cross

Vibraciones Sistemas Piso

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Transcript of Vibraciones Sistemas Piso