Thomas Murray Andres Sanchez Floor Vibrations

8/11/2019 Thomas Murray Andres Sanchez Floor Vibrations

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VIBRATIONS IN FLOOR SYSTEMS OF STEELSTRUCTURES DUE TO HUMAN USE

Presented by

Telmo Andres Sanchez, Ph.D.HDR Engineering, Inc.

Pittsburgh, PA

[email protected]

Developed by

Thomas M. Murray, Ph.D., P.E.

Department of Civil and Environmental Engineering

Virginia Tech

Blacksburg, [email protected]


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Topics

Basic Vibration Terminology

Floor Vibration Fundamentals

Natural Frequency of Steel FramedFloor Systems

Design for Walking Excitation


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Period And Frequency

Period tp


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Natural Frequency

=

wLtIsgE

2f

2/1

4n


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DampingLoss of Mechanical Energy in a

Vibrating System

Critical DampingSmallest Amount of Viscous Damping

Required to Prevent Oscillation of aFree Vibrating System


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Harmonics

P3

1st Harmonic

2nd Harmonic

3rd Harmonic

Footstep = tficosP stepi = 2

f1f step1

=

f2

f step2 =

f3f step3 =

P1

P2


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Acceleration Ratio

Acceleration Of A System, ap

Acceleration Of Gravity, ag

Usually Expressed As %g.

0.5%g is the Human Tolerance

Level for Quite Environments.

Ratio =


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Effective WeightFloor Width

FloorLength

W


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FLOOR VIBRATION

FUNDAMENTALS


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The Power of Resonance

0 1 2

FloorResponse

2 - 3% Damping

Natural frequency, fn

Forcing frequency, f

5 - 7% Damping


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Phenomenon of Resonance

Resonance can also occur when a

multiple of the forcing functionfrequency equals a natural frequency of

the floor. Usually concerned with the first natural

frequency.

Resonance can occur because of walking

dancing, or exercising.


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0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

Frequency (Hz)

Me

asuredAutospectr

um

(Peak,

%g)

Walking

Speed100 bpm

2nd Harmonic3.33 Hz

System Frequency

5 Hz 3rd Harmonic

Response from a Lightly

Damped Floor


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A Tolerance Criterion has two parts: Prediction of the floor response to a

specified excitation. Human response/tolerance

Human Tolerance Criterion


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FloorVibe v2.02Software for Analyzing

Floors for Vibrations

Criteria Based on AISC/CISC Design

Guide 11

SEI

Structural Engineers, Inc.

537 Wisteria DriveRadford, VA 24141

540-731-3330 Fax 540-639-0713

[email protected]

http://www.floorvibe.com

AISC/CISC Design Guide


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_ _ _ _

_ _ _ _

_ _ _ _

_ ___ _

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

PeakAcceleration(%G

ravity)

Frequency (Hz)

Indoor Footbridges,

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

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

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

DG11 Usesthe Modified

ISO Scale for

HumanTolerance


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NATURAL FREQUENCYOF

STEEL FRAMEDFLOOR SYSTEMS


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Fundamental Natural Frequency

Uniformly Loaded SimplySupported Beam

(3.3)

(3.1)

(Hz.)

=

wL4

ItgEs

2

f

2/1

n (Hz.)

/g18.0fn

ItE384 s/wL5 4

=


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Member

Bay

System

Fundamental Frequencies

H/g18.0f zn

)/(g18.0f gbn

)/(g18.0f cgbn


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Loads for Vibration Analysis

LDwItE384 s/wL5 4

D: Actual Load

L: 11 psf for Paper Office

6-8 psf for Electronic Office

6 psf for Residence

0 psf for Malls, Churches, Schools


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Section Properties - Beam/Girder

b (< 0.4 L)

Fully Composite

Effect Width

n = Es/1.35Ec


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Minimum Frequency

To avoid resonance with the firstharmonic of walking, the

minimum frequency must begreater than 3 Hz. e.g.

fn > 3 Hz


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DESIGN FOR

WALKING EXCITATION


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Walking Vibrations Criterion

g

a

W

)f35.0exp(P

g

a onop

=

Predicted Tolerance


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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 or 1% to 5%)

W = effective weight supported by the beam or joist panel,

girder panel, or combined panel, as applicable

g

a

W

)f35.0exp(P

g

a onop

=

Walking Vibrations Criterion


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_ _ _ _

_ _ _ _

_ _ _ _

_ _ __ _

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(%

Gravity)

Frequency (Hz)

Indoor Footbridges,

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

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

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

ISO Baseline Curve for

RMS Acceleration

Modified

ISO Scale


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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 only

small demountable partitions typical of many modular office areas,

0.05 for full height partitions between floors.

Parameters


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Equivalent Combined ModePanel Weight (W in Eqn. 2.3)

(4.4)

g

a

W

)f35.0exp(P

g

a onop

=

WWW ggj

gj

gj

j

=


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Beam and Girder Panel

Effective Weights

Beam Panel:

Girder Panel:

LjBj)S/wj(=Wj

LgBg)L avg,j/wg(=Wg


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Beam Panel Width

Bj = Beam PanelWidth


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Effective Beam Panel Width

Floor Width

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

(Balcony)

Dj = Ij/S (in4/ft)

3/2L)Dj/Ds(CjB j4/1j 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/.in240 4=5.7/1799=S/Ij=Djft/

.in79.9 4

=)12/50.4 3

)(31.9/12(=)12

/d( 3

e)n/12(=D

s


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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


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

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

(3.3)

Girder Mode Properties Cont.

.in43.0=44361029384

17283030555

=gIsE384

Lw5

= 6

44gg

g

.Hz37.5=433.0

386

18.0=

g

18.0=f gg

.ft/.in6.98 4=45/4436=Lj/Ig=Dg


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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=


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Combined Mode Properties

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

fn = Fundamental Floor Frequency

)+18.0= /(g gj

Hz08.3=)433.0+885.0/(38618.0=


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Combined Mode Properties Cont.

W

W

g

gj

gj

gj

j

++

+=W

kips100=

)122(433.0+885.0

433.0+)90(

433.0+885.0

885.0=


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1 3 4 5 8 10 25 40

10

5

2.5

1

0.5

0.25

0.1

0.05

Rhythmic ActivitiesOutdoor Footbridges

Shopping Malls,Dining and Dancing

Offices,

Residences

PeakAcce

leration(%G

ravity)

Frequency (Hz)

Indoor Footbridges,

Extended by Allen

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

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

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

ISO Baseline Curve forRMS Acceleration

Original Design


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Original Design

W18x35 fb = 3.76 hz f n = 3.08 Hz

W24x55 fg = 5.37 hz ap/g=0.74%g

Improved Design

Increase Concrete Thickness 1 in.

W18X35 fb = 3.75 hz f n = 3.04 Hz

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

Original Design


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Original Design

W18x35 fb = 3.76 hz f n = 3.08 Hz

W24x55 fg = 5.37 hz ap/g=0.74%g

Improved Design

Increase Girder Size

W18X35 fb = 3.76 hz f n = 3.33 Hz

W24x84 fg = 7.17 hz ap/g=0.70%g

Original Design


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W18x35 fb = 3.76 hz f n = 3.08 Hz

W24x55 fg = 5.37 hz ap/g=0.74%g

Improved Designs

Increase Beam Size

W21x50 fb = 4.84 hz f n = 3.57 Hz

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

W24x55 fb = 5.22 hz f n = 3.71 Hz

W24x55 fg = 5.28 hz ap/g=0.50%g

Original Design


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Rule: In design, increase stiffnessof element with lower

frequency to improve

performance.

If beam frequency is less than the girderfrequency, increase the beam frequency to

the girder frequency first, then increase bothuntil a satisfactory design is obtained.

Final Thought


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Final Thought

Strength is essential but otherwiseunimportant.

Hardy Cross


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Thank You!!

Thomas Murray Andres Sanchez Floor Vibrations

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