vibraciones sistemas piso
TRANSCRIPT
-
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
-
8/13/2019 Vibraciones Sistemas Piso
2/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 2
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
-
8/13/2019 Vibraciones Sistemas Piso
3/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 3
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.
-
8/13/2019 Vibraciones Sistemas Piso
4/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 4
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
http://www.floorvibe.com
-
8/13/2019 Vibraciones Sistemas Piso
5/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 5
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
-
8/13/2019 Vibraciones Sistemas Piso
6/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 6
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.
-
8/13/2019 Vibraciones Sistemas Piso
7/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 7
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
-
8/13/2019 Vibraciones Sistemas Piso
8/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 8
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
-
8/13/2019 Vibraciones Sistemas Piso
9/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 9
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
Course on Bolted Connections and Floor Vibrations
-
8/13/2019 Vibraciones Sistemas Piso
10/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 10
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). . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .
ISO Baseline Curve for
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
Course on Bolted Connections and Floor Vibrations
-
8/13/2019 Vibraciones Sistemas Piso
11/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 11
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.
Example Problem Floor
Course on Bolted Connections and Floor Vibrations
-
8/13/2019 Vibraciones Sistemas Piso
12/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 12
454545
DG11 Damping,
Yes, the floor didvibrate and there
were complaints.
DG11 Prediction: = 1.5% 0.70%g
= 2.0% 0.53%g
Example Problem Floor
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
-
8/13/2019 Vibraciones Sistemas Piso
13/36
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 13
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
Course on Bolted Connections and Floor Vibrations
-
8/13/2019 Vibraciones Sistemas Piso
14/36
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 14
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
Course on Bolted Connections and Floor Vibrations
-
8/13/2019 Vibraciones Sistemas Piso
15/36
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 15
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 ============
Course on Bolted Connections and Floor Vibrations
-
8/13/2019 Vibraciones Sistemas Piso
16/36
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 16
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 ====++++====
Course on Bolted Connections and Floor Vibrations
-
8/13/2019 Vibraciones Sistemas Piso
17/36
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 17
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). . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .
ISO Baseline Curve for
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
Course on Bolted Connections and Floor Vibrations
-
8/13/2019 Vibraciones Sistemas Piso
18/36
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 18
696969
Original Design
W18x35 fb = 3.76 hz fn = 3.08 HzW24x55 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
707070
W18x35 fb = 3.76 hz fn = 3.08 HzW24x55 fg = 5.37 hz ap/g=0.74%g
Improved Designs
Increase Beam Size
W21x50 fb = 4.84 hz fn = 3.57 Hz
W24x55 fg = 5.29 hz ap/g=0.58%g
W24x55 fb = 5.22 hz fn = 3.71 HzW24x55 fg = 5.28 hz ap/g=0.50%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
Course on Bolted Connections and Floor Vibrations
P bl M i M h 6 8 2008
-
8/13/2019 Vibraciones Sistemas Piso
19/36
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 19
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
Example: Joist Floor
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.
Example: Joist Floor
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
Example: Joist Mode Properties
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 ====
++++====
++++
====
Course on Bolted Connections and Floor Vibrations
P bl M i M h 6 8 2008
-
8/13/2019 Vibraciones Sistemas Piso
20/36
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 20
777777
Example: Joist Mode Properties
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 ++++====
Course on Bolted Connections and Floor Vibrations
Puebla Mexico March 6 8 2008
-
8/13/2019 Vibraciones Sistemas Piso
21/36
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 21
818181
Example: Walking Evaluation
0050.00044.0)900,18)(03.0(
)29.935.0exp(65
-
8/13/2019 Vibraciones Sistemas Piso
22/36
Puebla, Mexico March 6-8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 22
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
Course on Bolted Connections and Floor Vibrations
Puebla Mexico March 6-8 2008
-
8/13/2019 Vibraciones Sistemas Piso
23/36
Puebla, Mexico March 6 8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 23
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
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
24/36
Puebla, Mexico March 6 8, 2008
Presented by Thomas M. Murray, P.E., PhD Session 7 24
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
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
25/36
, ,
Presented by Thomas M. Murray, P.E., PhD Session 7 25
979797 989898
Aerobics
999999
Balcony Video
100100100
10 Story Special Purpose Building
Large Ballroom Floor
Auditorium Balcony
Case Studies
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
26/36
Presented by Thomas M. Murray, P.E., PhD Session 7 26
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
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
27/36
Presented by Thomas M. Murray, P.E., PhD Session 7 27
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 ++++++++====
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
28/36
Presented by Thomas M. Murray, P.E., PhD Session 7 28
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)
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
29/36
Presented by Thomas M. Murray, P.E., PhD Session 7 29
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
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
30/36
Presented by Thomas M. Murray, P.E., PhD Session 7 30
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
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
31/36
Presented by Thomas M. Murray, P.E., PhD Session 7 31
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
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
32/36
Presented by Thomas M. Murray, P.E., PhD Session 7 32
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
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
33/36
Presented by Thomas M. Murray, P.E., PhD Session 7 33
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
Queen Post Hanger Stiffening
Course on Bolted Connections and Floor Vibrations
Puebla, Mexico March 6-8, 2008
-
8/13/2019 Vibraciones Sistemas Piso
34/36
Presented by Thomas M. Murray, P.E., PhD Session 7 34
133133133
Queen Post Hanger Stiffening
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
-
8/13/2019 Vibraciones Sistemas Piso
35/36
Presented by Thomas M. Murray, P.E., PhD Session 7 35
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
-
8/13/2019 Vibraciones Sistemas Piso
36/36
Presented by Thomas M. Murray, P.E., PhD Session 7 36
141141141 142142142
The Hanging Graduate Student Solution
143143143
Final Thought
Strength is essential but otherwise
unimportant.
Hardy Cross