FLOOR VIBRATIONS Questions Concerning Design for ...

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FLOOR VIBRATIONS:

FREQUENTLY ASKED QUESTIONS AND MORE

Presented by Thomas M. Murray, PhD, P.E.

Virginia Tech, Blacksburg, VA January 15,2015

Structural Engineers Association of Texas – Dallas Chapter

Luncheon Meeting

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FLOOR VIBRATIONSFREQUENTLY ASKED QUESTIONS

AND MORE

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

Emeritus ProfessorVirginia Tech, Blacksburg, Virginia

[email protected]

SEAoT DALLAS CHAPTERJanurary 15, 2015

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Presentation is based on AISC/CISC Design Guide 11

and SJI Technical Digest 5 2nd Ed.

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FloorVibe v2.20Software for Analyzing

Floors for Vibrations Criteria Based

on AISC/CISC Design Guide 11

SJI Technical Digest 5

SEIStructural Engineers, Inc.

537 Wisteria Drive

Radford, VA 24141

540-731-3330 Fax 540-639-0713

[email protected]

http://www.floorvibe.com

Questions ConcerningDesign for Walking Excitation

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Frequently Asked Question

What is the power of Resonance?

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The Power of Resonance

0 1 2

Flo

or

Resp

on

se

1 - 3% Damping

Natural frequency, fn

Forcing frequency, f

5 - 7% Damping

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Phenomenon of Resonance

• Resonance occurs when a multiple of the

forcing function frequency equals a

natural frequency of the floor.

• We are usually concerned with the first

natural frequency.

• Resonance can occur because of walking

dancing, or exercising.

Note: Walking step frequency range is

1.6-2.2 Hz (96 to 132 bpm) 6/69

Harmonics

Pα3

1st Harmonic

2nd Harmonic

3rd Harmonic

Footstep = ( )tficosP stepi πα∑= 2

f1f step1•=

f2f step2•=

f3f step3•=

Pα1

Pα2

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Why do some walkers cause more floor motion then other walkers?

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Why do some walkers cause more floor motion then other walkers?

Because their pace is a sub-harmonic of the floor dominant frequency. That is, a harmonic of their walking speed, i.e. 2 or 3 times their walking speed, matches the floor dominant frequency.

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0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

Frequency (Hz)

Measure

d A

uto

spectr

um

(P

eak,

%g)

WalkingSpeed

100 bpm

2nd Harmonic3.33 Hz

System Frequency5 Hz – 3rd Harmonic

Response from a Lightly Damped Floor

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What is new in SJI TD5?

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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

Pea

k A

ccel

erati

on

(%

Gra

vit

y)

Frequency (Hz)

Indoor Footbridges,

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

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

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

DG11 TD5

Use the

Modified

ISO Scale

Considering

Resonance

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DG11 and TD5 Walking Criterion

g

a

W

)f35.0exp(P

g

a onop≤≤≤≤

ββββ

−−−−====

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 a combined panel, as applicable

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

ββββ = 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

g

a

W

)f35.0exp(P

g

a onop≤≤≤≤

ββββ

−−−−====


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• Tolerance Acceleration Limits Updated

Occupancy

Tolerance

Acceleration Limit

ao/g x 100%

Offices, Residences 0.5% – 0.55%

Assembly Areas,

Churches, Schools0.5% – 0.55%

Shopping Malls 1.5%

Indoor Footbridges 1.5%

Outdoor Footbridges 5.0%


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• Improved Approach for Estimating Modal Damping

Structural System 1%

Ceiling and Ductwork 1%

Electronic Office Fit-out 0.5%

Paper Office Fit-out 1%

Churches, Schools, Malls 0%

Dry Wall Partitions in Bay 3% to 5%

Note: Damping is cumulative.


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Fit out Condition:

Electronic Office. Limited number of file cabinets. No full-

height partitions, suspended ceiling and ductwork below.

Estimated Damping:

Floor Structure 1%

Ceiling & Ductwork 0%

Electronic Office 0.5%

Damping 1.5%

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Fit out Condition:

Paper Office. Suspended ceiling or ductwork below. No full

height partitions.

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Estimated Damping:

Floor Structure 1%

Ceiling & Ductwork 1%

Paper Office 1%

Damping 3%


How accurate are the AISC DG11 and SJI TD5 procedures?

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How accurate is the DG11 procedure?

FramingNo. of

Bays

AgreementDG11

Procedure

PercentAgreement

Hot-Rolled Framing 50 48 of 50 96%

Joists w/ Hot-Rolled Girders

27 26 of 27 96%

Joists w/ Joist Girders 22 22 of 22 100%

Castellated Beams 6 6 of 6 100%

ALL 105 102 of 105 97%

Data from a study being conducted at the University

of Kentucky by Dr. Brad Davis.20/69

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No recommendations are given in DG11 for public areas like airport terminals, lobbies, etc. What do you recommend?

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No recommendations are given in DG11 for public areas like airport terminals, lobbies, etc. What do you recommend?

1.0%g based on personal experience of spending many hours sitting at airline departure gates. (Recommendation will be included in AISC DG11 2nd Ed.)

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Why is the full composite moment of inertia used in the frequency calculations even when the beam, joist or girder is non-composite?

)/(g18.0f gbn ∆∆∆∆++++∆∆∆∆====

(((( ))))ItE384 s/wL5 4====∆∆∆∆

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Why is the full composite moment of inertia used in the frequency calculations even when the beam or girder is non-composite?

Annoying vibrations have displacements

of 0.001-0.010 in. Thus, the interface

shear is negligible, so its acts as fully

composite for vibration analyses. 24/69

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Does camber affect beam or girder frequency? Prestressing?

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(((( ))))ItE384 s/wL5 4====∆∆∆∆

ππππ====

wL4

ItgEs2

f

2/1

n

∆∆∆∆==== /g18.0fn

Does camber affect beam or girder frequency?

No! Classical frequency equation:

∆ is not part of equation.

Substituting

Results in

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Is there a lower frequency limit?

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Is there a lower frequency limit?

To avoid resonance with the first harmonic of walking and rogue or vandal jumping, the minimum frequency should be greater than 3 Hz, e.g.

fn > 3 Hz

(Required in the British building code.)

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How do I determine floor width and floor length when calculating effective panel weights, Wb and Wg?

g

a

W

)f35.0exp(P

g

a onop≤≤≤≤

ββββ

−−−−====

W

WWW ggj

gj

gj

j

∆∆∆∆++++∆∆∆∆

∆∆∆∆++++

∆∆∆∆++++∆∆∆∆

∆∆∆∆====

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Beam Panel Width

Bj = Beam Panel

Width

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

≤≤≤≤ 2/3 Floor Width

Beam Panel:

LB)s/w(W jjjj ====

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Effective Girder Panel Width

Bg = Girder Panel

Width

Bg = Cg(Dj/Dg)1/4 Lg

≤≤≤≤ 2/3 Floor Length

Girder Panel:

Wg = (wg/Lj,avg)BgLg)

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Bay Floor

Width

Floor

Length

A

B

C

D

Floor Width and

Length Example

A

BD

C

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Bay Floor

Width

Floor

Length

A 90 90

B

C

D

Floor Width and

Length Example

A

BD

C

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Bay Floor

Width

Floor

Length

A 90 90

B 150 90

C

D

Floor Width and

Length Example

A

BD

C

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Bay Floor

Width

Floor

Length

A 90 90

B 150 90

C 150 30 (45?)

D

Floor Width and

Length Example

A

BD

C

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Bay Floor

Width

Floor

Length

A 90 90

B 150 90

C 150 30 (45?)

D 30 90

Floor Width and

Length Example

A

BD

C

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

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Bays A & BBg = 59.9’<2/3 Floor L

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Bays A:

Floor Length = 81’e.g. (32.5’ + 16” + 32.5’)

Bg=2/3x81 = 54’ < 59.9’

ap/g=0.46%g < 0.5%

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Bays A: Bg = 54’ap/g=0.46%g < 0.5%

OKBay B:Floor Length = 48.5’e.g. (32.5’ + 16’)2/3x48.5 =32.3’ < 59.9’

ap/g=0.61%g > 0.5%gNG

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How do I modify a design that does not satisfy the criterion?

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How do I modify a design that does not satisfy the criterion?

Increase stiffness of the element with the lower frequency to improve performance.

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W18 × 35

3.50”2.00”

d = 3.50 +2.00

2= 4.50”

Section

W24 × 55

e

S

W21 × 444 SPA @ 7´- 6´ =30´= L´ g

W21 ×

44

W14 ×

22

W18 ×

35

W14 ×

22

L =

45´

j

W14 ×

22

Floor Width = 30 ft Floor Length = 90 ft

Paper Office

Example: Bay D of previous example.

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Original Design

W18x35 fb = 3.76 hz fn = 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 fn = 3.04 Hz W24x55 fg = 5.28 hz ap/g=0.65%g

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Original Design


Improved Design

Increase Girder Size

W18X35 fb = 3.76 hz fn = 3.33 Hz W24x84 fg = 7.17 hz ap/g=0.70%g

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Improved Designs

Increase Beam Size



Original Design

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Question ConcerningDesign for Rhythmic Excitation

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I am designing a floor in a health club that will be used for aerobics. Why are my required members so large?

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I am designing a floor in a health club that will be used for aerobics. Why are my required members so large?

Resonance with the first, second and third harmonics of the activity must be avoided.

fstep = 1.5 Hz to 2.5 Hz (90 bpm to 150 bpm)

i = 1, 2, 3 which means fn > 7.5 Hz


( )tfiπ2cosPα=Footstep stepi∑

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Floor VibrationsFrequently Asked Questions

andMore

(as in current research)

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Long Span (> 25 ft)eck Floors

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• Single 30 ft by 30 ft bay constructed and

tested at the Virginia Tech .

• Supported only at the perimeter with

W21x44 girders an W14x22 beams.

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• If the deck is supported by beams, it will probably be a low frequency floor (fn < 9-10 Hz) and provisions in DG11 or TD5 can be used.

• If the deck is supported by walls, it will probably be a high frequency floor (fn > 9-10 Hz) and further analysis will not be necessary.

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• Low Frequency Floor: Provisions in DG11 or TD5 can be used.

• Analyze assuming 1 ft width of slab is equivalent to a beam.

1 ft

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• Low Frequency Floor Analysis Model

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Analysis of Slender Stairs

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• Loading is much more severe than walking on floors: Much faster. More synchronization.

• If linear or near linear model as a beam.

Linear Near Linear


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How do I evaluate a slender stair design?

• Frequency:

L = Stringer Length

• Predicted Acceleration:

• Tolerance Acceleration:

1.7 to 4.6%g

ππππ====

wL4

ItgEs2

f

2/1

n

2cos (1 exp( ))100p oR Qa a

g W g= ≤= ≤= ≤= ≤

α φ −α φ −α φ −α φ − − β− β− β− β

ββββ


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• ReferencesDavis, B. and Murray, T.M. (2009). “Slender

Monumental Stair Vibration Serviceability.” J.

Architectural Engineering, 15(4), 111–121.

Davis, B. and Avci, O. (2015 In Press) “Simplified

Vibration Serviceability Evaluation for Slender

Monumental Stairs.” Journal of Structural

Engineering.


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Alternate Bay Framing

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Advantages:

• Eliminates back-to-back connections– Improved speed of erection

• Shallower Girder Depth– Added space for MEP Systems

– Lower floor-to-floor height

• Improved Vibration Performance

– Improved occupant satisfaction


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Disadvantages:

• May be Added Tonnage

– Minor increase in overall weight

• Increased Amount of Deck Closure Strips

– Increased material and labor

• Odd Shear Stud Layout at Girders

– Potential for improper layout

• Coordination of Deck Layout


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Disadvantages:

• Better with Bays with Aspect Ratios Close to

1:1

• Current AISC DG11 Procedures Over

Predict Vibration Response


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Modified DG11 Analysis Procedure:

• fn =min (beam and girder frequencies)

• Floor Width = Girder Span

• Floor Length = Beam Span + ∑1/2 Adjacent

Beam Spans


g

a

W

)f35.0exp(P

g

a onop≤≤≤≤

ββββ

−−−−====

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Combined

Mode

Panel:


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Strength is essential but otherwise

unimportant.

Hardy Cross

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Thank

You!!

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