IMCA 1.Diseño Por Vibración 2015

XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.

Del 4 al 7 de marzo de 2015. Mxico D.F.

XIII Simposio Internacional de Estructuras de Acero

Vibration Serviceability- Offices and Quiet Spaces -

Thomas M. Murray, PhD, P.E.Emeritus Professor Virginia Tech


Available Design Guidance AISC/CISC Design Guide 11

SJI Technical Digest 5 2nd Ed.FloorVibe v2.20

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 DriveRadford, VA 24141

540-731-3330 Fax [email protected]://www.floorvibe.com


CRITERIA FOR OFFICES AND QUIET SPACES

- Walking Excitation -


A Tolerance Criterion has two parts: Human response/Tolerance

scale. Prediction of the floor response

to a specified excitation.

Human Tolerance Criteria


ga

W)f35.0exp(P

ga onop

====

Predicted Tolerance

Walking Excitation Criterion


ao = acceleration limitap = peak accelerationg = acceleration of gravityPo = 29 kg (65 lb)fn = fundamental frequency of a beam or joist panel, or

a combined panel as , applicable = 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 applicableFor offices and quiet spaces ao/g = 0.005 or 0.5% of gravity

exp( )0.35op n ofa P ag W g

= = = =



_ _ _ _

_ _ _ _

_ _ _ _

_ ___ _

1 3 4 5 8 10 25 40

25

10

5

2.5

1

0.5

0.25

0.1

0.05

Outdoor Footbridges

Shopping Malls, Dining and Dancing

Offices,Residences

ISO Baseline Curve forRMS Acceleration

P

e

a

k

T

o

l

e

r

a

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c

e

A

c

c

e

l

e

r

a

t

i

o

n

(

%

G

r

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)

Frequency (Hz)

Indoor Footbridges,

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

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

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

Modified ISO Scale for Human Tolerance

ga

W)f35.0exp(P

ga onop

====


Estimating Modal Damping, Structural System 1%Ceiling and Ductwork 1%Electronic Office Build -out 0.5%Paper Office Build-out 1%Churches, Schools, Malls 0% Dry Wall Partitions in Bay 5% to 10%Note: Damping is cumulative.


ga

W)f35.0exp(P

ga onop

====


Electronic OfficeBuild-out Damping 0.5%

Walking Excitation CriterionElectric Office Fit-out

9


Paper Office Fit-out


Paper OfficeBuild-out Damping 1%


pipipipi====

wL4ItgEs

2f2/1

n (Hz.)

==== /g18.0fn

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

Member Natural Frequency

(Hz.)

ga

W)f35.0exp(P

ga onop

====



Member

Bay

System

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

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

Natural Frequencies

==== /g18.0fn

ga

W)f35.0exp(P

ga onop

====



Loads for Vibration Analysis(((( )))) LDwItE384 s/wL5 4 ++++========

D: Structural Framing + Superimposed DL0.2 kPa for Ceiling + Ductwork

L: 0.5 kPa for Paper Office0.35-0.4 kPa for Electronic Office0.25 kPa for Residence0 kPa for Malls, Churches, Schools



Section Properties - Beam/Girder

b (< 0.4 L)

Fully Composite Effective Width n = Es/1.35Ec


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

)/(g18.0f gbn ++++====(((( ))))ItE384 s/wL5 4====

A Frequently Asked Question


Annoying vibrations have displacements less than 1 mm. Thus, the interface shear is negligible, so its acts as fully composite.

A Frequently Asked Question

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


Minimum Frequency

To avoid resonance with the first harmonic of walking, the minimum frequency must be greater than 3 Hz. e.g.

fn > 3 Hz


Effective WeightFloor Width

F

l

o

o

r

L

e

n

g

t

h

W


Equivalent Combined ModePanel Weight

(4.4)

ga

W)f35.0exp(P

ga onop

====

WWW ggj

gj

gjj

++++

++++++++

====


Panel Effective Weights

Beam Panel:

Girder Panel:

LjBj)S/w j(=Wj

LgBg)L avg,j/wg(=Wg


Bj = Beam PanelWidth

Effective Beam Panel Width


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


Section Properties - Slab

12

_ _ _ _

de=dc-ddeck /2

A = (12 / n) de

n = Es/1.35 Ec

in4/ ftfc in ksi

)12/d)(n/12(D 3es ====fwE c5.1c ====


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 span considered. That is,

Wj = 1.5(wj/S)BjLj


Bg = Girder PanelWidth

Effective Girder Panel Width

XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.26


Bg = Cg(Dj/Dg)1/4 Lg 2/3 Floor LengthCg = 1.6 For Girders Supporting Joists

Connected Only to a Girder Flange= 1.8 For Girders Supporting Beams

Connected to a Girder Web

Dg = Ig/Lj,avg in4/ft


Bay Framing

Floor Width = 30 ft Floor Length = 90 ftPaper Office

S

W24 55

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

W

2

1

4

4

W

1

4

2

2

W

1

8

3

5

W

1

4

2

2

L

=

4

5

j

W18 35

3.502.00

d = 3.50 +e2.00

2 = 4.50

Section

W

1

4

2

2


Gravity Loads:LL : 11 psf (For Vibration Analysis)Mech. & Ceiling : 4 psf

Slab Properties:Concrete: wc = 110 pcf fc = 4000 psiFloor Thickness = 3.50 in. + 2 in. ribs

= 5.50 in.Slab + Deck Weight = 47 psf

Loads and Slab Properties


Beam PropertiesW18 35A = 10.30 in.2

Ix = 510 in.4

d = 17.70 in.

W24 55A = 16.20 in.2

d = 23.57 in.

Ix = 1350 in.4

Beam and Girder PropertiesGirder Properties


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

n = modular ratio = Es/1.35Ec= 29,000 / (1.35 x 2,307)= 9.31

Ij = transformed moment of inertia = 1,799 in4

ksi23070.4110f cwEc 5.15.1 ============

Beam Mode Properties


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

.in885.0179910293841728455005

EI384Lw5

6

4

j

4jjj ====

========

========

885.038618.0f j

Bj = Cj (Ds/ Dj)1/4Lj = 40.4 ft > 2/3 (30) = 20 ftWj = 1.5(wj/S)BjLj = 90,000 lbs = 90.0 kips

Beam Mode Properties

3.76 Hz


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 in.

Ig = 4,436 in4


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

Girder Mode Properties

.in43.0=4436102938417283030555

=gIsE384

Lw5= 6

44ggg

========

====

433.038618.0g18.0

ggf

L)Dg/Dj(CgB g4/1g ==== = 67.4 ft > 2/3 (90) = 60 ftLB)L/w(W ggjgg ==== =(3055/45)(60 30) = 122 kips

5.37 Hz


Combined Mode Properties

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

fn = Fundamental Floor Frequency====++++==== )18.0 gj/(g

====

++++++++

++++====

WWW g

gj

gj

gj

j 100 kips

3.08 Hz


= 0.03 from Table 4.1 (Modal Damping Ratio)W = 0.03 100 = 3.0 kips = 3000 lbs

Evaluation

= 0.0074

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

3000)08.335.0exp(65

W)f35.0exp(P

ga nop

========


_ _ _ _

_ _ _ _

_ _ _ _

_ _ __ _

1 3 4 5 8 10 25 40

25

10

5

2.5

1

0.5

0.25

0.1

0.05

Rhythmic ActivitiesOutdoor Footbridges

Shopping Malls, Dining and Dancing

Offices,Residences

P

e

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k

A

c

c

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Frequency (Hz)

Indoor Footbridges,

Extended by Allenand Murray (1993)

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ISO Baseline Curve forRMS Acceleration


Original DesignW18x35 fb = 3.76 hz fn = 3.08 Hz W24x55 fg = 5.37 hz ap/g=0.74%g

Improved DesignIncrease Concrete Thickness 1 in.

W18X35 fb = 3.75 hz fn = 3.04 Hz W24x55 fg = 5.28 hz ap/g=0.65%g


Original DesignW18x35 fb = 3.76 hz fn = 3.08 Hz W24x55 fg = 5.37 hz ap/g=0.74%g

Improved DesignIncrease Girder Size

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


W18x35 fb = 3.76 hz fn = 3.08 Hz W24x55 fg = 5.37 hz ap/g=0.74%g

Improved DesignsIncrease Beam Size

W21x50 fb = 4.84 hz fn = 3.57 Hz W24x55 fg = 5.29 hz ap/g=0.58%gW24x55 fb = 5.22 hz fn = 3.71 Hz W24x55 fg = 5.28 hz ap/g=0.50%g

Original Design


Rule: In design, increase stiffnessof element with lower frequency to improve performance.

If beam frequency is less than the girder frequency, increase the beam frequency to the girder frequency first, then increase both until a satisfactory design is obtained.


Floor Width and Floor Length


Bay FloorWidth

FloorLength

ABCD

A

B

D

C

Floor Width and LengthExample


Bay FloorWidth

FloorLength

A 90 90BCD

Floor Width and LengthExampleA

B

D

C


Bay FloorWidth

FloorLength

A 90 90B 150 90CD


B

D

C


Bay FloorWidth

FloorLength

A 90 90B 150 90C 150 30 (45?)D


B

D

C


Bay FloorWidth

FloorLength

A 90 90B 150 90C 150 30D 30 90


B

D

C


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


Bays A & BBg = 59.9


Bays A & BBg = 59.9 0.5%g

NG

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


Del 4 al 7 de marzo de 2015. Mxico D.F.


5252

Final Thought

Strength is essential but otherwise unimportant.

Hardy Cross


Gracias!!


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