FLOOR VIBRATIONS Questions Concerning Design for ...
-
Upload
khangminh22 -
Category
Documents
-
view
0 -
download
0
Transcript of FLOOR VIBRATIONS Questions Concerning Design for ...
1
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
11
FLOOR VIBRATIONSFREQUENTLY ASKED QUESTIONS
AND MORE
Presented byThomas M. Murray, Ph.D., P.E.
Emeritus ProfessorVirginia Tech, Blacksburg, Virginia
SEAoT DALLAS CHAPTERJanurary 15, 2015
1/69
Presentation is based on AISC/CISC Design Guide 11
and SJI Technical Digest 5 2nd Ed.
2/69
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
http://www.floorvibe.com
Questions ConcerningDesign for Walking Excitation
3/69
Frequently Asked Question
What is the power of Resonance?
4/69
2
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
The Power of Resonance
0 1 2
Flo
or
Resp
on
se
1 - 3% Damping
Natural frequency, fn
Forcing frequency, f
5 - 7% Damping
5/69
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
7/69
Frequently Asked Question
Why do some walkers cause more floor motion then other walkers?
8/69
3
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
Frequently Asked Question
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.
9/69
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
10/69
Frequently Asked Question
What is new in SJI TD5?
11/69
_ _ _ _
_ _ _ _
_ _ _ _
_ ___ _
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
12/69
4
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
DG11 and TD5 Walking Criterion
g
a
W
)f35.0exp(P
g
a onop≤≤≤≤
ββββ
−−−−====
Predicted ≤≤≤≤ Tolerance
13/69
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
−−−−====
DG11 and TD5 Walking Criterion
14/69
• 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%
DG11 and TD5 Walking Criterion
15/69
• 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.
DG11 and TD5 Walking Criterion
16/69
5
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
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%
17/69
Fit out Condition:
Paper Office. Suspended ceiling or ductwork below. No full
height partitions.
18/69
Estimated Damping:
Floor Structure 1%
Ceiling & Ductwork 1%
Paper Office 1%
Damping 3%
Frequently Asked Question
How accurate are the AISC DG11 and SJI TD5 procedures?
19/69
Frequently Asked Question
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
6
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
Frequently Asked Question
No recommendations are given in DG11 for public areas like airport terminals, lobbies, etc. What do you recommend?
21/69
Frequently Asked Question
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.)
22/69
Frequently Asked Question
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====∆∆∆∆
23/69
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?
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
7
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
Frequently Asked Question
Does camber affect beam or girder frequency? Prestressing?
25/69
Frequently Asked Question
(((( ))))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
26/69
Frequently Asked Question
Is there a lower frequency limit?
27/69
Frequently Asked Question
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.)
28/69
8
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
Frequently Asked Question
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
∆∆∆∆++++∆∆∆∆
∆∆∆∆++++
∆∆∆∆++++∆∆∆∆
∆∆∆∆====
29/69 303030
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 ====
30/69
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)
31/69
Bay Floor
Width
Floor
Length
A
B
C
D
Floor Width and
Length Example
A
BD
C
32/69
9
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
Bay Floor
Width
Floor
Length
A 90 90
B
C
D
Floor Width and
Length Example
A
BD
C
33/69
Bay Floor
Width
Floor
Length
A 90 90
B 150 90
C
D
Floor Width and
Length Example
A
BD
C
34/69
Bay Floor
Width
Floor
Length
A 90 90
B 150 90
C 150 30 (45?)
D
Floor Width and
Length Example
A
BD
C
35/69
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
36/69
10
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
Bg = Cg(Dj/Dg)1/4 Lg ≤≤≤≤ 2/3 × Floor Length
37/69
Bg = Cg(Dj/Dg)1/4 Lg ≤≤≤≤ 2/3 × Floor Length
Bays A & BBg = 59.9’<2/3 Floor L
38/69
Bg = Cg(Dj/Dg)1/4 Lg ≤≤≤≤ 2/3 × Floor Length
Bays A & BBg = 59.9’<2/3 Floor L
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%
39/69
Bg = Cg(Dj/Dg)1/4 Lg ≤≤≤≤ 2/3 × Floor Length
Bays A & BBg = 59.9’<2/3 Floor L
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
40/69
11
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
Frequently Asked Question
How do I modify a design that does not satisfy the criterion?
41/69
Frequently Asked Question
How do I modify a design that does not satisfy the criterion?
Increase stiffness of the element with the lower frequency to improve performance.
42/69
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.
43/69
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
44/69
12
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
Original Design
W18x35 fb = 3.76 hz fn = 3.08 Hz W24x55 fg = 5.37 hz ap/g=0.74%g
Improved Design
Increase Girder Size
W18X35 fb = 3.76 hz fn = 3.33 Hz W24x84 fg = 7.17 hz ap/g=0.70%g
45/69
W18x35 fb = 3.76 hz fn = 3.08 Hz W24x55 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 Hz W24x55 fg = 5.28 hz ap/g=0.50%g
Original Design
46/69
Question ConcerningDesign for Rhythmic Excitation
47/69
Frequently Asked Question
I am designing a floor in a health club that will be used for aerobics. Why are my required members so large?
48/69
13
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
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
Frequently Asked Question
( )tfiπ2cosPα=Footstep stepi∑
49/69
Floor VibrationsFrequently Asked Questions
andMore
(as in current research)
50/69
Long Span (> 25 ft)eck Floors
51/69
Long Span (> 25 ft)eck Floors
• 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.
52/69
14
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
Long Span (> 25 ft)eck Floors
• 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.
53/69
Long Span (> 25 ft)eck Floors
• 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
54/69
Long Span (> 25 ft)eck Floors
• Low Frequency Floor Analysis Model
55/69
Analysis of Slender Stairs
56/69
15
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
• 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
Analysis of Slender Stairs
57/69
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
Analysis of Slender Stairs
58/69
• 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.
Analysis of Slender Stairs
59/69
Alternate Bay Framing
60/69
16
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
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
Alternate Bay Framing
61/69
Alternate Bay Framing
62/69
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
Alternate Bay Framing
63/69
Alternate Bay Framing
64/69
17
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
Disadvantages:
• Better with Bays with Aspect Ratios Close to
1:1
• Current AISC DG11 Procedures Over
Predict Vibration Response
Alternate Bay Framing
65/69
Modified DG11 Analysis Procedure:
• fn =min (beam and girder frequencies)
• Floor Width = Girder Span
• Floor Length = Beam Span + ∑1/2 Adjacent
Beam Spans
Alternate Bay Framing
g
a
W
)f35.0exp(P
g
a onop≤≤≤≤
ββββ
−−−−====
66/69
Combined
Mode
Panel:
Alternate Bay Framing
67/69
Strength is essential but otherwise
unimportant.
Hardy Cross
68/69