Forced Vibration Testing &
Analytical Modeling of a
Four-story Reinforced Concrete
Frame Building
PI’s: J. W. Wallace, E. Taciroglu, J.P. Stewart
Staff: D.H. Whang, Y. Lei, S. Keown, S. Kang
Students: E. Yu, D. Skolnik, W. Elmer
OUTLINE
 Forced Vibration Tests
 Modal Identification
 Finite Element Model Updating
 Conclusions & Outlook
Forced Vibration Tests
BACKGROUND
 Goals of forced vibration tests/studies
 Extract dynamic properties of the structure
experimentally
 Validate the assumptions of analytical model used
to predict structural response
 Evaluate predictive capability of analytical models
 Until now, forced vibration tests have been performed
at low-level response amplitudes
 Two kinds of shakers were used as vibration sources
 Eccentric mass shaker
 Linear shaker
BACKGROUND
 Eccentric Mass Shaker
 Generate harmonic forces through rotation of mass
 Steady state response -> frequency-response curve
 Generally, larger maximum load capacity
 Laborious tests; one frequency at a time
 Linear Shaker
 Arbitrary forcing function (Broadband excitation)
 Transient response : reduce test time / more
computation
 Effective in System Identification
 Simulation of earthquake vibration
OBJECTIVE &OVERVIEW
 Produce a high-quality dataset
- Low noise
155 dB accelerometer, 24-bit AD converter
- High spatial density
Acceleration + Story Displacement + Strain
- Low / high amplitude excitation
~max 200 kip force
Test Building : 4-story RC frame building
• Damage survey
• nees@UCLA equipment
• Instrumentation scheme
• Test procedure
THE BUILDING
 “Four Seasons Building”
 4-Story RC Building with penthouse
 Constructed in 1977
 Damaged by the 1994 Northridge earthquake
 Yellow Tagged (unoccupied, will be demolished)
Western Exterior of the Building
LOCATION
 Located near the intersection of 101 & 405 Freeway, in
Sherman Oaks, California (16 km from UCLA)
UCLA
STRUCTURAL SYSTEM
 Lateral Load: Special Moment Frame (Beams+Columns)
around perimeter
 Gravity Load: Post-tensioned flab slab with drop panels
+ Interior columns
 Foundation: Belled Caissons + Grade beams
 No shear walls
1
1
2
3
4
5
6
2
3
4
5
6
7
N
7
A
PH. EL 59.58' (18.16 m)
RF EL 47.75' (14.55 m)
(3@30'-6")
3' (0.9 m)
3F EL 22.75' (6.93 m)
2F EL 11.25' (3.43 m)
3@9.3 m
4F EL 34.25' (10.44 m)
B
C
GF : EL 0
Section along Lone B
D
9.6 m
5@9.3 m
(31'-6")
(5@30'-6")
Typical Floor Plan
N
STRUCTURAL MEMBERS
 Beam : 24”x30” (Typical), 24”x36” (2nd Floor)
 Column : 24”x24”
Normal weight
concrete (4000 psi)
 Slab : 8-1/2” with 7-1/2” drop panel (typical) ; Lightweight Concrete
(3000 psi)
Slab-Column connection
Interior Columns
Exterior Columns
PREVIOUS STUDIES
• Damage report (Sabol, 1994)
• Previous analytical studies
 Dovitch and Wight, 1994
 Ascheim and Moehle, 1996
 Hueste and Wight, 1998
• Analytical results were not able to
identify the amount of damage observed
in the building
• Effects of torsion / vertical response were
significant, or
• Ground motions were more severe
OBSERVED DAMAGE
 Interior frame
•
Punching shear failure at slab-column connections
around the perimeter of drop panel
Column B6 (3rd Floor)
Column B2 (2nd Floor)
Slab dropped 0.5 ~ 0.75 in. downwards
OBSERVED DAMAGE
 Perimeter Frame
•
Beam-Column joint crack with concrete spalling
•
Spalling of cover concrete at beam end
•
Flexural cracks
Spalling at beam end
(Column A7 at 3F level)
Diagonal joint crack
(column A4 at 3F level)
Flexural cracks
(column B2 at 4th story)
OBSERVED DAMAGE
 Non-structural Members
•
Separated from adjacent structural members
•
No structural contribution during the test was
expected, except possibly at the penthouse level
Masonry wall at ground floor
Partition wall at 2nd story
Penthouse drywall
INTERIOR DAMAGE
1
2
3
4
5
6
7
A
(T) N.A.
(T) N.A.
(T) N.A.
(T) N.A.
(T) N.A.
(T) N.A.
(T) N.A.
(T) N.A.
(T) Slight
(T) Slight
(B) Slight
(B) Moderate
(T) N.A.
(T) Slight
(B) Slight
(B) Moderate
(T) N.A.
(B) Slight
(B) Slight
(T) N.A.
(B) Slight
(B) Slight
B
C
D
Roof
(T) N.A.
(T) N.A.
(T) Moderate
(B) Moderate (B) Moderate (B) Moderate (B) Moderate
(T) Severe
(B) Severe
4th Floor
N
(T) Slight
(B) Moderate (B) Moderate
3rd Floor
(T) Severe
(T) Severe
(T) Severe
(B) Slight
(B) Slight
(T) N. A.
(B) Severe
(B) Severe
(B) Moderate
(B) N. A.
(B) Slight
(B) Slight
(T) Severe
(T) N. A.
(T) N. A.
(B) Severe
(B) Slight
(T) N.E.
(B) Moderate
T : Top face
B : Bottom face
N.A. : Not Accessible
(blank) : No Damage
(B) Slight
(T) N. A.
(B) Slight
2nd Floor
Severe : Big chunk crushed out, Floor level dropped or Reinforcements exposed
Moderate : Large and developed cracks, small chunk crushed out, or aggregate exposed
Slight : long crack around drop panel
EXTERIOR DAMAGE
N
1
2
3
4
E
5
6
West Perimeter Frame (Line A)
East Perimeter Frame (Line D)
7
A
B
C
D
South Perimeter Frame (Line 1 & 2)
North Perimeter Frame (Line 7)
Diagonal joint crack
Diagonal joint crack with concrete spalling
N
Severe concrete crushing (at beam end) /Shear crack
• Building experienced more deformation in
N-S direction than E-W direction
TESTING EQUIPMENT – nees@UCLA
 Two 100-kip capacity eccentric mass shakers
 15-kip capacity linear shaker
 Force-Balanced Accelerometers (FBA)
 LVDTs (DC-DC Type)
 Concrete strain gauges
 24-bit AD converters
 Wireless data-logging (Antelope) & Networking system
 National Instrument signal conditioning units (LabView)
 Mobile Command Center (MCC)
 Power generators
ECCENTRIC MASS SHAKER
 Two 100-kip capacity shakers
 Generate harmonic forces through rotation of mass
mass
eccentricity
mass


me of a basket  mass  eccentricity
nees@UCLA Eccentric Mass Shaker, MK-15
P(t )  2me 2 sin(t )
ECCENTRIC MASS SHAKER
• Adjustable basket
Pulse Marker
69 Steel bricks
Hydrostone Leveling
• Basket configurations for this study
Empty basket
Half-full basket
Mass-eccentricity
(each basket)
16786 lb-in
56620 lb-in
Limiting
frequency
5.40 Hz
2.95 Hz
LINEAR SHAKER
 Produce force through linear motion of a moving mass
 Moving mass (5 kip/g) + Dynamic Actuator (15 kip, ±15”) + Hydraulic
system (90 gpm servo-valve, 30 gpm pump, 4 accumulators) +
Controller
 Digital control : PD, LQG, adaptive ; displacement, acceleration
 Broadband excitation ; white-noise, sine-sweep, earthquake-type
Linear Shaker
Example sine-sweep forcing function
SHAKER LOCATIONS
37.2 m (122 ft)
Eccentric
Mass
Shaker
(South)
Linear
Shaker
Reference
Point
N
Eccentric
Mass
Shaker
(North)
9.3 m (30.5 ft)
SENSORS & DATALOGGERS
Force-balance
Accelerometer
High performance 24-bit Datalogger
(Kinemetrics, Q330)
Synchronization using GPS time
DCDT (DC-DC type LVDT)
Strain Gauge
National Instrument
Signal Conditioning
Module used for
concrete strain
gauges
(32 ch X 3 units)
WIRELESS DATA ACQUISITION
DC : Data Concentration Point
Data
Concentration
Point (DC)
WAP : Wireless Access Point
Yagi Antenna
Wireless
Communication
DC
Sensors
WAP
Wireless
Q330
Wireless Access
Point (WAP)
Wired
WAP
Antelope
server
Mobile
Command Center
POWER GENERATORS
Power for the shakers
Power for DAQ
Battery box/portable power
INSTRUMENTATION
• Acceleration
Force-balance type
Accelerometer
• Strain
Strain gauges placed at
top and bottom of floor
slabs and 3 faces of
columns
• Interstory
Displacement
DCDTs measure
displacement from
 197 Total channels
• 16 tri-axial + 27 uniaxial accelerometers bottom of one column to
top of the consecutive
• 26 DCDT’s
column
• 96 Strain gauges
INSTRUMENTATION PLAN
NS Accelerometer
Vertical Accelerometer
EW Accelerometer
1
Rv4
Rv1
Rw1 Ru1
Rw4
Pu1
Pv1
Column with strain gauge
2
3v1
Ru4
A
5
6
LVDT-NS1
3v4
3w1 3u1
A
3w4 3u4
3v2
Ru2
N
Ru3
3w2
3v3
LVDT-NS2
3u2
3u3
3w3
3rd floor level
Roof / Penthouse
1v2
LVDT-NS1
1u1
1w2
1w5
1u2
1
2
3
4
5
1v3
1w3
Ground floor
Ground
LVDT-EW
LVDT-NS2
1w8
7
3F Level
1w7
1v4
6
Roof Level
1w6
1w4
7
LVDT-EW
Rv3
Rw3
Rw2
1w1
4
Pv2
Rv2
1v1
3
LVDT
Elevation (A-A)
N
INSTRUMENTATION PLAN
 Column Strain Gauges
• 3 faces for curvature
calculation in both
directions
8"
• Along A2 & B2 column
from ground floor to roof
floor
12"
8"
4"
8"
• Below and above the
floor slab level
 Floor Slab Strain Gauges
12"
Curtain Wall
24"
1
2
3
A
0.25L
S8 S10
• Top and bottom faces of
3rd & 4th floor slab
S5 0.25L
42"
L=30'-6"
S4 0.25L
S7 S9
B
S6
60" 60"
S3 0.25L
S2
S1
TESTING SEQUENCE
Date
Test
6/22/04
E-W translational excitation with empty basket – Run1
7/2/04
Ambient vibration measurement – Run1
7/13/04
E-W translational excitation with empty basket – Run2
Torsional excitation with empty basket – Run1
7/14/04
E-W translational excitation with half-full basket – Run1
Torsional excitation with half-full basket – Run1
7/19/04
E-W translational excitation with half-full basket – Run2
Torsional excitation with half-full basket – Run2
Ambient vibration measurement – Run2
Linear shaker sinesweep / whitenoise – Run1
7/22/04
N-S translational excitation with half-full basket – Run1
7/28/04
N-S translational excitation with empty basket – Run1
Linear shaker seismic simulation test
8/2/04
N-S translational excitation with empty basket – Run2
Linear shaker sinesweep / whitenoise – Run2
8/3/04
Ambient vibration measurement – Run3
E-W translational excitation with empty basket – Run3
VIDEO CLIPS
Eccentric Mass Shaker Test
Modal Identification
TESTING & DATA ACQUISITION
• Identification and updating
performed with data from the linear
shaker white noise excitation
• Data recorded with four tri-axial
accelerometers used derive three
story responses
SYSTEM IDENTIFICATION
N4SID (Numerical Algorithm for Subspace State Space System Identification)
• Discrete time domain method uses measured data directly
• Makes projections of certain subspaces generated from the input/output
observations to estimate state sequence using linear algebra tools such as
QRD and SVD.
• Identifies system matrices from estimated states based on a linear least
squares solution
• Can be applied to systems subjected to known or unknown excitation
• Well implemented in MATLAB’s System Identification Toolbox
u: input force applied
with linear shaker
y: output measured
floor responses
X k 1  A X k  Buk
yk  C X k  Duk
fi  i 2
 i  Re  i  2 fi
i  C i  sign  Re  C i  
SYSTEM IDENTIFICATION
Stability Plot
Stability Tolerances
• Df ≤ 1.5%
• D ≤ 5%
• MAC ≥ 98%
MAC ( A, B) 

EW NS Tor
AT B 
T
A

2
  A B T  B

SYSTEM IDENTIFICATION
Frequencies and Damping Ratios
For
Amb
Mode
Forced
f (Hz)  (%)
Ambient
f (Hz)  (%)
1 EW
0.88
5.6
1.09
3.4
1.24
0.61
2 NS
0.94
6.9
1.25
3.1
1.33
0.45
3 Tor
1.26
6.0
1.55
2.1
1.23
0.35
4 EW
2.73
5.6
3.23
3.0
1.18
0.54
5 NS
2.94
7.7
3.63
3.1
1.23
0.40
6 Tor
3.44
6.1
4.16
2.1
1.21
0.34
7 Mix
4.54
13.5
-
-
-
-
EW NS Tor
Ambient /
Forced
DISCUSSION
 Ambient vibration > linear shaker test > EMS test
=> Stiffness degradation of structural member
(contribution of nonstructural elements is negligible ; damage survey)
 3 ~ 4% frequency drop in ambient vibration after EMS test
due to the high amplitude vibrations during Half-full basket testing
=> degradation of (cladding / Foundation & soil / structural member) ??
 Larger frequency drop in N-S
direction => effect of damage
Ks1 Ks2
Finite Element Model
Updating
FINITE ELEMENT MODELING
Modeling Assumptions
• Lumped Mass
• Rigid Diaphragms
• Classical Damping
From Core Tests
• rn =140pcf, rl = 115pcf
• Ecn = 4028ksi, Ecl = 2517ksi
Effective Stiffness (FEMA 356 ,
Paulay&Priestley, “Effective
Beam Method”)
• Columns: 0.5EcnIg
• Beams: 0.42EcnIg
• Slabs: 0.4EclIg
N
FINITE ELEMENT MODELING
Natural Frequencies (Hz)
Mode
FE
SID
FE / SID
1 EW
0.92
0.88
1.05
2 NS
1.12
0.94
1.19
3 Tor
1.35
1.26
1.07
4 EW
2.6
2.73
0.95
5 NS
2.94
2.94
1.00
6 Tor
3.53
3.44
1.03
EW NS Tor
FINITE ELEMENT MODELING
FRF - NS direction
MODEL UPDATING
Sensitivity-Based Updating Procedure using Frequency
Response Function (FRF) and Modal Frequencies
M x(t )  C x(t )  K x(t )  L f (t )
  2 M  iC  K  x( )  L f ( )
B( )    2 M  iC  K 
H( )  x( ) / f ( )
B( )H( )  L
K  2M
Parameter Vector
Error residuals
p  [ p1 , p2 ,
MODEL UPDATING
T
, pk ]
ε F  L  B(p,  )H( )
Non-linear functions of p
ε M  Ω  (p)
Linearize with a first-order Taylor series expansion
 B(p,  )

F  
H( )  Dp  L  B(p 0 ,  )H( )

p


p  p0

M

 (p)


 Dp  Ω  (p 0 )

p

p  p0 



  F   CF 
 dF 
     Dp   
 M  CM 
d M 
MODEL UPDATING
Objective Function
Min
p
WC Dp  W d
2
such that
plb  p0  Dp  pub
and
pi  p j  1  cor(Ci , C j ) ,
if cor(Ci , C j )  clim
MODEL UPDATING
Parameter(s) associated with
Bounds
65.0 (kips sec2/ft)
Mass of 2F
Mass of 3F & 4F
85 % - 115 %
Mass of RF
Mass of PH
50 % - 150 %
Radius of gyration of 2F & 3F
Radius of gyration of 4F
Radius of gyration of RF
Initial Values
64.7 (kips sec2/ft)
62.1 (kips sec2/ft)
Dimensionless
Parameters
7.6 (kips sec2/ft)
• 10 Mass
64.2 (ft)
75 % - 135 %
64.0 (ft)
57.5 (ft)
Radius of gyration of PH
26.7 (ft)
Column Stiffness at 2F - RF
0.5Ecn Ig
Column Stiffness at PH
0.75Ecn Ig, (NS)
2.5Ecn Ig (EW)
Slab Stiffness at 2F - RF
35 % - 150 %
0.4Ecl Ig,
Slab Stiffness at PH
0.6Ecl Ig (NS)
2.0Ecl Ig (EW)
Beam Stiffness at 2F - RF
0.42Ecn Ig
Damping ratios
2.5 % - 20 %
5%
• 52 Stiffness
• 9 Damping
MODEL UPDATING
Ratios of Initial Mass
2F
3F
4F
RF
PH
Translational Mass
94%
97%
104%
105%
97%
Radius of gyration
102%
104%
97%
102%
104%
Stiffness Factors
2F
3F
4F
RF
PH
NS Interior, North & South Frame Columns
0.40
0.48
0.32
0.45
0.73
NS of East Frame Columns
0.36
0.41
0.22
0.49
-
NS of West Frame Columns
0.45
0.39
0.26
0.46
-
EW of Interior, East & West Frame Columns
0.46
0.62
0.49
0.42
2.20
EW of North Frame Columns
0.49
0.52
0.59
0.49
-
EW of South Frame Columns
0.52
0.56
0.34
0.46
-
East Frame Girders
0.45
0.23
0.38
0.41
-
West Frame Girders
0.42
0.17
0.39
0.40
-
South Frame Girders
0.49
0.32
0.36
0.39
-
North Frame Girders
0.43
0.57
0.43
0.42
-
Slab NS
0.43
0.19
0.36
0.40
0.58
Slab EW
0.44
0.36
0.35
0.37
1.86
Damping
Ratios
7th
8th
9th
10th
11th
12th
13th
14th
15th
9.6%
15.9%
7.3%
15.5%
2.5%
8.8%
8.8%
5.4%
13.5%
MODEL UPDATING
Ratios of Initial Mass
2F
3F
4F
RF
PH
Translational Mass
94%
97%
104%
105%
97%
Radius of gyration
102%
104%
97%
102%
104%
Stiffness Factors
2F
3F
4F
RF
PH
NS Interior, North & South Frame Columns
0.40
0.48
0.32
0.45
0.73
NS of East Frame Columns
0.36
0.41
0.22
0.49
-
NS of West Frame Columns
0.45
0.39
0.26
0.46
-
EW of Interior, East & West Frame Columns
0.46
0.62
0.49
0.42
2.20
EW of North Frame Columns
0.49
0.52
0.59
0.49
-
EW of South Frame Columns
0.52
0.56
0.34
0.46
-
East Frame Girders
0.45
0.23
0.38
0.41
-
West Frame Girders
0.42
0.17
0.39
0.40
-
South Frame Girders
0.49
0.32
0.36
0.39
-
North Frame Girders
0.43
0.57
0.43
0.42
-
Slab NS
0.43
0.19
0.36
0.40
0.58
Slab EW
0.44
0.36
0.35
0.37
1.86
Damping
Ratios
7th
8th
9th
10th
11th
12th
13th
14th
15th
9.6%
15.9%
7.3%
15.5%
2.5%
8.8%
8.8%
5.4%
13.5%
MODEL UPDATING
Natural Frequencies (Hz)
Mode
Initial
Updated
SID
1 EW
0.92
0.90
0.88
2 NS
1.12
0.97
0.94
3 Tor
1.35
1.25
1.26
4 EW
2.6
2.72
2.73
5 NS
2.94
2.93
2.94
6 Tor
3.53
3.44
3.44
EW NS Tor
MODEL UPDATING
FRF - NS direction
MODEL UPDATING
Predicted and Measured NS response to 0.5 - 5 Hz linear shaker sine sweep
Penthouse
Roof
4th Floor
3rd Floor
2nd Floor
Conclusions & Outlook
CONCLUSIONS
• Identified modal properties of the first seven modes
using N4SID
• Frequencies identified from ambient vibrations
represent a stiffer structure than that identified from
white noise excitation
• FE model is updated using a modal- FRFsensitivity based method
• Frequencies, mode shapes, and FRF of the
updated model compare well with those identified
• Predicted acceleration response of the updated
model compares quite well with the measured data