PI’s: J. W. Wallace, E. Taciroglu , J.P. Stewart Staff: D.H. Whang, Y. Lei, S. Keown, S. Kang

Forced Vibration Testing & Forced Vibration Testing & Analytical Modeling of aAnalytical Modeling of a

Four-story Reinforced Concrete Four-story Reinforced Concrete Frame Building Frame Building

Forced Vibration Testing & Forced Vibration Testing & Analytical Modeling of aAnalytical Modeling of a

Four-story Reinforced Concrete Four-story Reinforced Concrete Frame Building 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

Forced Vibration TestsForced Vibration Tests

Modal IdentificationModal Identification

Finite Element Model Updating Finite Element Model Updating

Conclusions & Outlook Conclusions & Outlook

OUTLINE

Forced Vibration Tests

Goals of forced vibration tests/studiesGoals of forced vibration tests/studies Extract dynamic properties of the structure Extract dynamic properties of the structure

experimentallyexperimentally Validate the assumptions of analyticalValidate the assumptions of analytical model model

used to predict structural responseused to predict structural response Evaluate predictive capability of analyticalEvaluate predictive capability of analytical

modelsmodels

Until now, forced vibration tests have been Until now, forced vibration tests have been performed at performed at low-level response amplitudeslow-level response amplitudes

Two kinds of shakers were used as vibration Two kinds of shakers were used as vibration sourcessources Eccentric mass shaker Eccentric mass shaker Linear shaker Linear shaker

BACKGROUND

Eccentric Mass ShakerEccentric Mass Shaker Generate harmonic forces through rotation of Generate harmonic forces through rotation of

massmass Steady state response -> frequency-response Steady state response -> frequency-response

curvecurve Generally, larger maximum load capacityGenerally, larger maximum load capacity Laborious tests; one frequency at a timeLaborious tests; one frequency at a time

Linear ShakerLinear Shaker Arbitrary forcing function (Broadband Arbitrary forcing function (Broadband

excitation) excitation) Transient response : reduce test time / more Transient response : reduce test time / more

computationcomputation Effective in System IdentificationEffective in System Identification Simulation of earthquake vibrationSimulation of earthquake vibration

BACKGROUND

Produce a high-quality dataset Produce a high-quality dataset

- Low noise - Low noise

155 dB accelerometer, 24-bit AD 155 dB accelerometer, 24-bit AD converterconverter

- High spatial density - High spatial density

Acceleration + Story Displacement + Acceleration + Story Displacement + StrainStrain

- Low / high amplitude excitation- Low / high amplitude excitation

~max 200 kip force~max 200 kip force

Test Building : 4-story RC frame buildingTest Building : 4-story RC frame building

• Damage surveyDamage survey

• nees@UCLA equipmentnees@UCLA equipment

• Instrumentation schemeInstrumentation scheme

• Test procedure Test procedure

OBJECTIVE &OVERVIEW

““Four Seasons Building”Four Seasons Building” 4-Story RC Building with penthouse 4-Story RC Building with penthouse Constructed in 1977Constructed in 1977 Damaged by the 1994 Northridge earthquakeDamaged by the 1994 Northridge earthquake Yellow Tagged (unoccupied, will be demolished)Yellow Tagged (unoccupied, will be demolished)

Western Exterior of the BuildingWestern Exterior of the Building

THE BUILDING

Located near the intersection of 101 & 405 Located near the intersection of 101 & 405 Freeway, in Sherman Oaks, California (16 km Freeway, in Sherman Oaks, California (16 km from UCLA)from UCLA)

UCLAUCLA

LOCATION

Lateral Load: Special Moment Frame Lateral Load: Special Moment Frame (Beams+Columns) around perimeter(Beams+Columns) around perimeter

Gravity Load: Post-tensioned flab slab with drop Gravity Load: Post-tensioned flab slab with drop panels + Interior columnspanels + Interior columns

Foundation: Belled Caissons + Grade beamsFoundation: Belled Caissons + Grade beams No shear wallsNo shear walls

Typical Floor PlanTypical Floor Plan

N

1 2 3 4 5 6

B

D

C

A

7

[email protected] m

(5@30'-6")

3@9.

3 m

(3@

30'-

6")

9.6 m

(31'-6")

1 2 3 4 5 6 7

2F EL 11.25' (3.43 m)

3F EL 22.75' (6.93 m)

GF : EL 0

4F EL 34.25' (10.44 m)

RF EL 47.75' (14.55 m)

PH. EL 59.58' (18.16 m)

3' (

0.9

m)

N

Section along Lone BSection along Lone B

STRUCTURAL SYSTEM

Beam : 24”x30” (Typical), 24”x36” (2nd Floor) Column : 24”x24”

Slab : 8-1/2” with 7-1/2” drop panel (typical) ; Lightweight Concrete

(3000 psi)

Interior ColumnsInterior Columns

Slab-Column connectionSlab-Column connection

Exterior ColumnsExterior Columns

Normal weight concrete (4000 psi)

STRUCTURAL MEMBERS

• Damage report (Sabol, 1994)Damage report (Sabol, 1994)

• Previous analytical studies Previous analytical studies Dovitch and Wight, 1994 Dovitch and Wight, 1994 Ascheim and Moehle, 1996 Ascheim and Moehle, 1996 Hueste and Wight, 1998 Hueste and Wight, 1998

• Analytical results were not able to Analytical results were not able to identify the amount of damage observed identify the amount of damage observed in the buildingin the building

• Effects of torsion / vertical response were Effects of torsion / vertical response were significant, orsignificant, or

• Ground motions were more severeGround motions were more severe

PREVIOUS STUDIES

Interior frameInterior frame

• Punching shear failure at slab-column Punching shear failure at slab-column connections around the perimeter of drop connections around the perimeter of drop panelpanel

Column B6 (3Column B6 (3rdrd Floor) Floor) Column B2 (2Column B2 (2ndnd Floor) Floor)

Slab dropped 0.5 ~ 0.75 in. downwardsSlab dropped 0.5 ~ 0.75 in. downwards

OBSERVED DAMAGE

Perimeter Frame Perimeter Frame

• Beam-Column joint crack with concrete Beam-Column joint crack with concrete spallingspalling

• Spalling of cover concrete at beam endSpalling of cover concrete at beam end

• Flexural cracksFlexural cracks

Spalling at beam endSpalling at beam end(Column A7 at 3F level)(Column A7 at 3F level)

Diagonal joint crackDiagonal joint crack(column A4 at 3F level)(column A4 at 3F level)

Flexural cracksFlexural cracks(column B2 at 4(column B2 at 4thth story) story)

OBSERVED DAMAGE

Non-structural MembersNon-structural Members

• Separated from adjacent structural Separated from adjacent structural membersmembers

• No structural contribution during the test No structural contribution during the test was expected, except possibly at the was expected, except possibly at the penthouse levelpenthouse level

Masonry wall at ground floorMasonry wall at ground floorPartition wall at 2Partition wall at 2ndnd story story Penthouse drywallPenthouse drywall

OBSERVED DAMAGE

(B) Slight

(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) N.A.

1 2 3 41 2 3 4 5 6

B

D

C

A

7

(T) Slight

(T) Slight

(B) Slight

(B) Slight (B) Slight

(B) Moderate (B) Slight

(B) Slight (B) Moderate

(T) Slight (T) N.A. (T) N.A.

(T) N.A.

(T) Severe

(B) Moderate (B) Moderate

(T) Slight (T) N.E.

(B) Moderate (B) Severe

(B) Severe (B) Moderate

(B) Moderate (B) Moderate (B) Moderate

(T) N.A. (T) Moderate (T) Severe

N

T : Top faceB : Bottom faceN.A. : Not Accessible(blank) : No Damage

(T) Severe (T) Severe

(T) Severe (T) N. A.


(T) N. A. (T) N. A.


(B) Severe (B) Slight

(B) Severe (B) Moderate (B) N. A.

(B) Slight (T) N. A.(B) Slight

Severe : Big chunk crushed out, Floor level dropped or Reinforcements exposedModerate : Large and developed cracks, small chunk crushed out, or aggregate exposedSlight : long crack around drop panel

RoofRoof 44thth Floor Floor

22ndnd Floor Floor33rdrd Floor Floor

INTERIOR DAMAGE

1 2 3 4 5 6 7

West Perimeter Frame (Line A)West Perimeter Frame (Line A)

East Perimeter Frame (Line D)East Perimeter Frame (Line D) North Perimeter Frame (Line 7)North Perimeter Frame (Line 7)

A B C D

South Perimeter Frame (Line 1 & 2)South Perimeter Frame (Line 1 & 2)

NN EE

NN

Diagonal joint crack

Diagonal joint crack with concrete spalling

Severe concrete crushing (at beam end) /Shear crack

•Building experienced more deformation in N-S direction than E-W direction

EXTERIOR DAMAGE

Two 100-kip capacity eccentric mass shakersTwo 100-kip capacity eccentric mass shakers

15-kip capacity linear shaker15-kip capacity linear shaker

Force-Balanced Accelerometers (FBA)Force-Balanced Accelerometers (FBA)

LVDTs (DC-DC Type)LVDTs (DC-DC Type)

Concrete strain gaugesConcrete strain gauges

24-bit AD converters 24-bit AD converters

Wireless data-logging (Antelope) & Networking Wireless data-logging (Antelope) & Networking system system

National Instrument signal conditioning units National Instrument signal conditioning units (LabView)(LabView)

Mobile Command Center (MCC)Mobile Command Center (MCC)

Power generatorsPower generators

TESTING EQUIPMENT – nees@UCLA

Two 100-kip capacity shakersTwo 100-kip capacity shakers

Generate harmonic forces through rotation of Generate harmonic forces through rotation of massmass

nees@UCLA Eccentric Mass Shaker, MK-15nees@UCLA Eccentric Mass Shaker, MK-15

eccentricitymass

of a basket mass eccentricity e

m

mass

2( ) 2 sin( )eP t m t

ECCENTRIC MASS SHAKER

69 Steel bricks69 Steel bricks

Empty basket Half-full basket

Mass-eccentricity(each basket)

16786 lb-in 56620 lb-in

Limitingfrequency

5.40 Hz 2.95 Hz

Pulse MarkerPulse Marker

• Basket configurations for this studyBasket configurations for this study

• Adjustable basketAdjustable basket

Hydrostone LevelingHydrostone Leveling

ECCENTRIC MASS SHAKER

Produce force through linear motion of a moving massProduce force through linear motion of a moving mass

Moving mass (5 kip/g) + Dynamic Actuator (15 kip, Moving mass (5 kip/g) + Dynamic Actuator (15 kip, ±±15”) + 15”) + Hydraulic system (90 gpm servo-valve, 30 gpm pump, 4 Hydraulic system (90 gpm servo-valve, 30 gpm pump, 4 accumulators) + Controlleraccumulators) + Controller

Digital control : PD, LQG, adaptive ; displacement, accelerationDigital control : PD, LQG, adaptive ; displacement, acceleration Broadband excitation ; white-noise, sine-sweep, earthquake-Broadband excitation ; white-noise, sine-sweep, earthquake-

typetype

Linear ShakerLinear Shaker

Example sine-sweep forcing Example sine-sweep forcing functionfunction

LINEAR SHAKER

Linear Shaker

Eccentric Mass Shaker(South)

N

Eccentric Mass Shaker (North)Reference

Point

37.2 m (122 ft)

9.3 m (30.5 ft)

45°

SHAKER LOCATIONS

Force-balance Force-balance AccelerometerAccelerometer

DCDT (DC-DC type LVDT)DCDT (DC-DC type LVDT)

High performance 24-bit Datalogger High performance 24-bit Datalogger (Kinemetrics, Q330)(Kinemetrics, Q330)

National Instrument National Instrument Signal Conditioning Signal Conditioning Module used for Module used for concrete strain concrete strain gaugesgauges(32 ch X 3 units)(32 ch X 3 units)

Strain GaugeStrain Gauge

Synchronization using GPS timeSynchronization using GPS time

SENSORS & DATALOGGERS

Q330WAP

Yagi Antenna

WAPAntelope server

Mobile Command Center

Wireless Communication

WiredSensors

Wireless

DC : Data Concentration Point

WAP : Wireless Access Point

DC

Data ConcentrationPoint (DC)

Wireless Access Point (WAP)

WIRELESS DATA ACQUISITION

Power for the shakersPower for the shakers

Battery box/portable powerBattery box/portable powerPower for DAQPower for DAQ

POWER GENERATORS

• AccelerationAccelerationForce-balance type Force-balance type AccelerometerAccelerometer

• StrainStrainStrain gauges placed Strain gauges placed at top and bottom of at top and bottom of floor slabs and 3 faces floor slabs and 3 faces of columnsof columns

• InterstoryInterstory DisplacementDisplacement

DCDTs measure DCDTs measure displacement from displacement from bottom of one column bottom of one column to top of the to top of the consecutive columnconsecutive column

197 Total channels197 Total channels• 16 tri-axial + 27 uniaxial accelerometers16 tri-axial + 27 uniaxial accelerometers• 26 DCDT’s26 DCDT’s• 96 Strain gauges96 Strain gauges

INSTRUMENTATION

Vertical AccelerometerNS Accelerometer EW Accelerometer Column with strain gauge

LVDT

3u1

3v1

3u2

3v2

3u3

3v3

3u4

3v4

1 2 3 4 5 6 71u1

1v1

1w5

1w1

1w4

1v4

1w3

1v3

1w8

1w7

1w6

1u2

1v2

1w2

LVDT-NS1

LVDT-NS2LVDT-EW

Rv1

Ru1Ru4

Rv4

Rv3

Ru3

Rv2

Ru2

Pu1

N LVDT-NS2

LVDT-NS1

LVDT-EWPv1 Pv2

N

521 43 76

Rw1 Rw4

Rw3Rw2

3w1 3w4

3w33w2

Roof / Roof / Penthouse Penthouse

33rdrd floor level floor level

Ground floorGround floor Elevation (A-A)Elevation (A-A)

A A

Roof Roof LevelLevel

3F Level3F Level

GroundGround

INSTRUMENTATION PLAN

8"

8"

8"

4" 12"

24"

12"

Curtain Wall

Column Strain GaugesColumn Strain Gauges

• 3 faces for curvature 3 faces for curvature calculation in both calculation in both directionsdirections

• Along A2 & B2 Along A2 & B2 column from ground column from ground floor to roof floor floor to roof floor

• Below and above the Below and above the floor slab levelfloor slab level

S1S2S3

S4

S5

S6

S8 S10

S7 S90.25L

L=30'-6"

60"60"

42"

1 2 3

B

A

0.25L

0.25L

0.25L Floor Slab Strain Floor Slab Strain Gauges Gauges

• Top and bottom Top and bottom faces of 3faces of 3rdrd & 4 & 4thth floor floor slabslab

INSTRUMENTATION PLAN

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

TESTING SEQUENCE

Eccentric Mass Shaker Test

VIDEO CLIPS

Modal Identification

TESTING & DATA ACQUISITION

vc

Nu2 u3

v3

u4

v4

v2

u1

v1

ucrc

x

y

21 3 4 5 6 7

B

A

D

C

• 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

1k k k

k k k

X X u

y X u

A B

C D

2

Re 2

sign Re

i i

i i i

i i i

f

f

C C

u: input force applied with linear shaker

y: output measured floor responses


Stability Tolerances

• f ≤ 1.5%

• ≤ 5%

• MAC ≥ 98%

Stability Plot

EW NS Tor

2

( , )T

A B

T TA A B B

MAC A B


EW NS Tor

Frequencies and Damping Ratios

For Amb

Mode Forced

f (Hz) (%)Ambient

f (Hz) (%)Ambient /

Forced

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 - - - -

Ks1 Ks2

Ambient vibration > linear shaker test > EMS testAmbient vibration > linear shaker test > EMS test

=> Stiffness degradation of structural member => Stiffness degradation of structural member

(contribution of nonstructural elements is negligible ; damage (contribution of nonstructural elements is negligible ; damage survey)survey)

3 ~ 4% frequency drop in ambient vibration after EMS test3 ~ 4% frequency drop in ambient vibration after EMS test

due to the high amplitude vibrations during Half-full basket due to the high amplitude vibrations during Half-full basket testingtesting

=> degradation of (cladding / Foundation & soil / structural => degradation of (cladding / Foundation & soil / structural member) ??member) ??

Larger frequency drop in Larger frequency drop in N-S direction => effect of N-S direction => effect of damagedamage

DISCUSSION

Finite Element Model Updating

FINITE ELEMENT MODELING

Modeling Assumptions

• Lumped Mass

• Rigid Diaphragms

• Classical Damping

From Core Tests

• n =140pcf, l = 115pcf

• Ecn = 4028ksi, Ecl = 2517ksi

Effective Stiffness (FEMA 356 , FEMA 356 , Paulay&Priestley, “Effective Paulay&Priestley, “Effective Beam Method”Beam Method”)

• Columns: 0.5EcnIg

• Beams: 0.42EcnIg

• Slabs: 0.4EclIg

N


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

Natural Frequencies (Hz)

EW NS Tor


FRF - NS direction

2( )

H( ) x( ) / ( )

i

f

B M C K

MODEL UPDATING

x( ) x( ) x( ) ( )t t t L f t M C K

2 x( ) ( )i L f M C K

( )H( ) L B

2 K M

Sensitivity-Based Updating Procedure using Frequency Response Function (FRF) and Modal Frequencies

MODEL UPDATING1 2p [ , , , ]T

kp p p

0

0

0

p p

0

p p

(p, )H( ) L (p , )H( )

(p)Ω (p )

F

M

pp

pp

BB

Error residuals

dp

dF F F

M M M

C

C

ε L (p, )H( )

ε Ω (p)

F

M

B

Parameter Vector

Non-linear functions of p

Linearize with a first-order Taylor series expansion

MODEL UPDATING

0p p p plb ub

2

pMin p d W C W

lim1 cor(C ,C ) , if cor(C ,C ) i j i j i jp p c

such that

and

Objective Function

MODEL UPDATING

Parameter(s) associated with Bounds Initial Values

Mass of 2F

85 % - 115 %

65.0 (kips sec2/ft)

Mass of 3F & 4F 64.7 (kips sec2/ft)

Mass of RF 62.1 (kips sec2/ft)

Mass of PH 50 % - 150 % 7.6 (kips sec2/ft)

Radius of gyration of 2F & 3F

75 % - 135 %

64.2 (ft)

Radius of gyration of 4F 64.0 (ft)

Radius of gyration of RF 57.5 (ft)

Radius of gyration of PH 26.7 (ft)

Column Stiffness at 2F - RF

35 % - 150 %

0.5Ecn Ig

Column Stiffness at PH0.75Ecn Ig, (NS)

2.5Ecn Ig (EW)

Slab Stiffness at 2F - RF 0.4Ecl Ig,

Slab Stiffness at PH0.6Ecl Ig (NS)

2.0Ecl Ig (EW)

Beam Stiffness at 2F - RF 0.42Ecn Ig

Damping ratios 2.5 % - 20 % 5 %

Dimensionless Parameters

• 10 Mass

• 52 Stiffness

• 9 Damping

MODEL UPDATINGRatios 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

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

Natural Frequencies (Hz)

EW NS Tor

MODEL UPDATING

FRF - NS direction

MODEL UPDATING

2nd Floor

3rd Floor

4th Floor

Roof

Penthouse

Predicted and Measured NS response to 0.5 - 5 Hz linear shaker sine sweep

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- FRF-sensitivity 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

PI’s: J. W. Wallace, E. Taciroglu , J.P. Stewart Staff: D.H. Whang, Y. Lei, S. Keown, S. Kang

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Transcript of PI’s: J. W. Wallace, E. Taciroglu , J.P. Stewart Staff: D.H. Whang, Y. Lei, S. Keown, S. Kang