IMCA 1.Diseño Por Vibración 2015
description
Transcript of IMCA 1.Diseño Por Vibración 2015
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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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
CRITERIA FOR OFFICES AND QUIET SPACES
- Walking Excitation -
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
A Tolerance Criterion has two parts: Human response/Tolerance
scale. Prediction of the floor response
to a specified excitation.
Human Tolerance Criteria
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
ga
W)f35.0exp(P
ga onop
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Predicted Tolerance
Walking Excitation Criterion
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
= = = =
Walking Excitation Criterion
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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Outdoor Footbridges
Shopping Malls, Dining and Dancing
Offices,Residences
ISO Baseline Curve forRMS Acceleration
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Frequency (Hz)
Indoor Footbridges,
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Modified ISO Scale for Human Tolerance
ga
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ga onop
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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.
Walking Excitation Criterion
ga
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ga onop
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Electronic OfficeBuild-out Damping 0.5%
Walking Excitation CriterionElectric Office Fit-out
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Paper Office Fit-out
Walking Excitation Criterion
Paper OfficeBuild-out Damping 1%
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
pipipipi====
wL4ItgEs
2f2/1
n (Hz.)
==== /g18.0fn
(((( ))))ItE384 s/wL5 4====
Member Natural Frequency
(Hz.)
ga
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Walking Excitation Criterion
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Member
Bay
System
)/(g18.0f gbn ++++====
)/(g18.0f cgbn ++++++++====
Natural Frequencies
==== /g18.0fn
ga
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ga onop
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Walking Excitation Criterion
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
Walking Excitation Criterion
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Section Properties - Beam/Girder
b (< 0.4 L)
Fully Composite Effective Width n = Es/1.35Ec
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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?
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Effective WeightFloor Width
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Equivalent Combined ModePanel Weight
(4.4)
ga
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ga onop
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WWW ggj
gj
gjj
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++++++++
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Panel Effective Weights
Beam Panel:
Girder Panel:
LjBj)S/w j(=Wj
LgBg)L avg,j/wg(=Wg
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bj = Beam PanelWidth
Effective Beam Panel Width
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Section Properties - Slab
12
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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 ====
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bg = Girder PanelWidth
Effective Girder Panel Width
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.26
Effective Girder Panel Width
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Effective Girder Panel Width
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bay Framing
Floor Width = 30 ft Floor Length = 90 ftPaper Office
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W24 55
W21 444 SPA @ 7- 6 =30= L g
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W18 35
3.502.00
d = 3.50 +e2.00
2 = 4.50
Section
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
wj = 7.5 (11 + 47 + 4 + 35/7.5) = 500 plf
.in885.0179910293841728455005
EI384Lw5
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4jjj ====
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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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
wg = 45(500/7.5) + 55 = 3055 plf.
Girder Mode Properties
.in43.0=4436102938417283030555
=gIsE384
Lw5= 6
44ggg
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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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
= 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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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1 3 4 5 8 10 25 40
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Rhythmic ActivitiesOutdoor Footbridges
Shopping Malls, Dining and Dancing
Offices,Residences
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Frequency (Hz)
Indoor Footbridges,
Extended by Allenand Murray (1993)
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ISO Baseline Curve forRMS Acceleration
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
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.
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Floor Width and Floor Length
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bay FloorWidth
FloorLength
ABCD
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D
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Floor Width and LengthExample
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bay FloorWidth
FloorLength
A 90 90BCD
Floor Width and LengthExampleA
B
D
C
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bay FloorWidth
FloorLength
A 90 90B 150 90CD
Floor Width and LengthExampleA
B
D
C
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bay FloorWidth
FloorLength
A 90 90B 150 90C 150 30 (45?)D
Floor Width and LengthExampleA
B
D
C
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bay FloorWidth
FloorLength
A 90 90B 150 90C 150 30D 30 90
Floor Width and LengthExampleA
B
D
C
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bg = Cg(Dj/Dg)1/4 Lg 2/3 Floor Length
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bays A & BBg = 59.9
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bays A & BBg = 59.9
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Bays A & BBg = 59.9 0.5%g
NG
Bg = Cg(Dj/Dg)1/4 Lg 2/3 Floor Length
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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
5252
Final Thought
Strength is essential but otherwise unimportant.
Hardy Cross
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XIII Simposio Internacional de Estructuras de Acero. Marzo 4 a 7, 2015. Mxico D.F.
Gracias!!
XIII Simposio Internacional de Estructuras de Acero