1 Mitigation of Train-Induced Floor Vibrations in Multi-Story Buildings Using a Blocking Floor Ningyu Zhao, Doctoral student, Tufts University Masoud Sanayei, Professor, Tufts University, Dept. of Civil & Env. Engineering James A. Moore, Supervisory Consultant, Acentech Inc. Jeffrey A. Zapfe, Senior Consultant, Acentech Inc. Eric M. Hines, Professor of Practice, Tufts University, Dept. of Civil & Env. Engineering; Associate, LeMessurier Consultants Structures Congress 2010 Saturday May 15 th , 1010
Transcript
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Mitigation of Train-Induced Floor Vibrations in Multi-Story
Buildings Using a Blocking FloorNingyu Zhao, Doctoral student, Tufts University
Masoud Sanayei, Professor, Tufts University, Dept. of Civil & Env. Engineering
James A. Moore, Supervisory Consultant, Acentech Inc.
Jeffrey A. Zapfe, Senior Consultant, Acentech Inc.
Eric M. Hines, Professor of Practice, Tufts University, Dept. of Civil & Env. Engineering; Associate, LeMessurier Consultants
Structures Congress 2010Saturday May 15th, 1010
Importance of this Research
• Vibrations Considerations– Human Comfort– Sensitive Equipment
• Air-rights development• Sources of Measured Excitation
– Running Trains / Subways– Vehicular Traffic
• Simple predictive model for vertical vibration transmission and mitigation
Background• Sanayei et al. (2008) developed a predictive model and
compared it with measurements in collaborations with Acentech Inc. and LeMessurier Consultants – Vibration excitation is from the subway and train stations below– Vibration transmission is from ground into the foundation– Columns are modeled with axial wave propagation (not bending)– Floors slabs are modeled with transverse bending deformations
TD Banknorth Garden, Boston, Massachusetts
Courtesy of TD Banknorth Garden
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Scale Model Testing
• Hughes et al. (2008) confirmed the mathematical model by testing a scale model building at Tufts University– Testing & modeling of structural components such as finite beams,
columns and thin plates.
– Scale model testing & verification between 10 and 5000 Hz (corresponding to full-scale frequencies of 1 to 500 Hz).
– The vibration transmission model was verified with measurements on the scale model
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Current Research• Evaluate feasibility of using “blocking floor” for vibration
transmission mitigation to upper floors
• A “blocking floor” is referred to increasing the thickness of the first floor to reduce vibration transmission to upper floors.
• It is a cost-effective solution to vibration mitigation
• The scale model building is used to evaluate the effectiveness of the blocking floor hypothesis
• Consider the shear softening of thicker blocking floor(s) at higher frequencies
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System Modeling
• Assumptions:‒ System modeled as a vibration
propagating column and bending floor slabs
‒ Axial vibration of column excites bending deformation of the slab at each floor
2[ ]{ } { }col effK M U Fω− =
• Dynamic Equilibrium (Harmonic excitation and response at frequency ω)
• Impedance (Z)– Measure of applied force to resulting velocity
– Finite and infinite system impedances: Resonances & Anti-resonances
– Stiffness controlled at low ω and mass controlled at high ω– Effective mass used in modeling
ikZ i m cω ω= + −
FZV
=
8
2( ) ( )effc km m
i iω ω= + +
m
F
u
k c
Bending Deformation Model of Floor Slabs• Kirchoff plate theory for modeling of thin plates– Only bending deformation considered– No transverse shear and rotary inertia– Input impedance at connection to columns: meff
‒ Floor impedance is proportional to t2: infinite plate theory
• Mindlin plate theory for modeling thick plates (blocking floor)– Accounts for shear deformation and rotary inertia– Shear softening reduces the impedance of slab at the column
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228 8
12(1 )SlabEZ D t t
vρρ= =−
Blocking Floor Impedance of Scale Model Building
Analytical impedances of slabs and columns used in scale model building
• 10 dB is 3 fold increase in impedance
• 20 dB is 10 fold increase in impedance
10
1020logZ Z=
101
102
103
55
60
65
70
75
80
85
90
Frequency (Hz)
Imp
ed
an
ce (
dB
re
:1 N
.S/m
)
Ki rchhoff Pla te 0.75"Ki rchhoff Pla te 1.50"Ki rchhoff Pla te 2.25"Mindl in Pla te 0.75"Mindl in Pla te 1.50"Mindl in Pla te 2.25"1"x1" Alum inum Colum n
Blocking Floor in a 4-story Scale Model Building
0 .75" MDF 1.5" MDF 2.25" MDF
Predicted Velocity Ratios relative to Base Vibration at the shaker using Kirchoff slab model (a) 1st fl., (b) 2nd fl., (c) 3rd fl., (d) 4th fl.
102
103
-20
-10
0
Frequency (Hz)
Ve
l. R
ati
o (
dB
re
:vB
ase
) (a )
102
103
-20
-10
0
Frequency (Hz)
Ve
l. R
ati
o (
dB
re
:vB
ase
) (b )
102
103
-20
-10
0
Frequency (Hz)
Ve
l. R
ati
o (
dB
re
:vB
ase
) (c)
102
103
-20
-10
0
Frequency (Hz)
Ve
l. R
ati
o (
dB
re
:vB
ase
) (d )
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Only the first floor blocking slab thickness has increased. Upper 3 floors are unchanged at 0.75”
1020log i
B
VdB υυ
=
Design of Scale Model Building• Slab-to-column ratios are matched between scale model and typical full-scale
buildings with steel columns (W14x90) and concrete slabs (4.75”)
• Scale-Model– Column: 80/20 Aluminum Model 25-2525– Slab: Medium Density Fiberboard (various thicknesses) – Connection: 8 L-shape brackets (4 above & 4 below) to ensure moment
connection between slab and column (modeled as lumped masses)
– Material properties of MDF were verified by Hughes (2008) & Zhao (2009)
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Scale Model Building
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Instrumentation• Brüel & Kjær Permanent Magnetic
Vibration Exciter Type 4808‒ Connected to the base of center column‒ Drives axially into the column‒ Force Gauge model B&K-8230
• Acceleration measurements:‒ PCB Accelerometer model 352C65‒ Measure vertical vibration at each floor
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Velocity Ratios with 0.75” MDF on 1st Floor• Classical Kirchoff
model with 5% damping
• Good match between model and data
• Model slightly over-predicted vibration attenuation on all floors
