Small-Amplitude Vibration Tests of a Full-Scale RC Flat-Plate Structure By: Luis Arboleda MSCE Thesis

Small-Amplitude Vibration Small-Amplitude Vibration Tests of a Full-Scale RC Tests of a Full-Scale RC

Flat-Plate StructureFlat-Plate Structure By: Luis ArboledaBy: Luis Arboleda

MSCE ThesisMSCE Thesis

Problem DefinitionProblem Definition

Interior frame

Exterior frame

E-W

N-S

HypothesisHypothesis

““The natural frequencies and lateral The natural frequencies and lateral stiffness of stiffness of

a 3D RC flat-plate structure can be a 3D RC flat-plate structure can be estimated estimated

using a conventional 2D frame using a conventional 2D frame analysis”analysis”

L22L

SpecimenSpecimen

30'

7"30'

50'

20'

18"

Literature ReviewLiterature Review

Pecknold (1975) 0.55-0.85 0.35-0.60

Allen and Darvall (1977) 0.65 0.45

Banchik (1987) 0.50 0.65

Hwang and Moehle (1993) 0.15-0.40 0.20-0.65

αInteriorExterior

Test SetupTest Setup

N

Plan ViewElevation View

1155

0 500 1000-0.02

0.02

Dis

p. 3

le

vel (

in)

1090 1100 1110 1120 1130Time (sec)

0

rd

Typical ResultTypical Resultrd

Displacement (in)

Loa

d 3

le

vel (

kips

)

LVDTDIAL GAGE

0 0.005 0.01 0.015 0.02 0.025

0

0.6

1.2

1.8

Test ResultsTest Results

PropertyPropertyTesting DirectionTesting Direction

N-SN-S E-WE-W

f (Hz)f (Hz) 2.092.09 1.981.98

k (kips/in)k (kips/in) 8686 7979

f and k for Ef and k for Ecc= 3800 ksi= 3800 ksi

AssumptiAssumptionon PropertyProperty

Testing DirectionTesting Direction

N-SN-S E-WE-W

KirchoffKirchoffff11 (Hz) (Hz) 1.581.58 1.561.56


Mindlin Mindlin ReissnerReissner

ff11 (Hz) (Hz) 1.741.74 1.701.70


2.09 1.98

86 79

2.09 1.98

86 79

1.20 1.16

1.34 1.30

1.32 1.27

1.69 1.58

f K / M

Variables to Calculate kVariables to Calculate k

Check as-built dimensions

Width

Length

Depth

EcEc ?0.9%

0.5%

0.5%

77




N-SN-S E-WE-W




ff11 (Hz) (Hz) 1.941.94 1.891.89


2.09 1.98

86 79

2.09 1.98

86 79

1.08 1.05

1.09 1.05

1.19 1.14

1.36 1.27

f K / M

1.321.321.201.20




N-SN-S E-WE-W




ff11 (Hz) (Hz) 2.142.14 2.082.08


2.09 1.98

86 79

2.09 1.98

86 79

0.98 0.95

0.90 0.87

1.08 1.04

1.12 1.05

f K / M

1.191.191.081.08

αα for E for Ecc= 4700 ksi= 4700 ksi


N-SN-S E-WE-W

ff11 (Hz) (Hz) 2.052.05 1.951.95


2.09 1.98

86 79

0.5

αExterior FramesInterior Frames

2D Frame Analysis

αα for E for Ecc= 5700 ksi= 5700 ksi


N-SN-S E-WE-W

ff11 (Hz) (Hz) 2.002.00 1.901.90


2.09 1.98

86 79

0.3

αExterior FramesInterior Frames

2D Frame Analysis

Is it plausible thatEc is larger than

3800 ksi?

Pauw (1960)Pauw (1960)

2.0

0.5

1.0

1.5

Str

ess

(ksi

)

Strain0.00050.00040.00030.00020 0.0001

Ec of the Flat-Plate Ec of the Flat-Plate StructureStructure

Ecmean= 4000 ksi

66

EC,ASTM= 3950 ksi

CYLINDER C-3

Could Could Ec be Larger than be Larger than EC,ASTM??

S3S2S1

C3C2C1

C

C,ASTME

E

cf '/

00.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.5

1

1.5

2

2.5

More CylindersMore Cylinders

3322

S-3S-2S-1C-3C-2C-1

G1-3G1-7G1-14G1-28G2-3G2-7G2-14G2-28

f '/c

C,ASTME

2.5

2

1.5

1

0.5

00.450.40.350.30.250.20.150.10.050

EC

Small StressesSmall Stresses

2.0

0.5

1.0

1.5

Str

ess

(ksi

)

Strain0.00050.00040.00030.00020 0.0001

Free-Vibration TestsFree-Vibration Tests

2 2 4

4

4 f L mE

I

15 Tests, 6L, 15 Tests, 6L,

9M9M

L= 80 in or 40 in

A'

A

Midpoint

Hammer

Accelerometer

D= 2 in

A-A'

Free-Vibration Test Free-Vibration Test ResultsResults

TestTest ffMEANMEAN (Hz) (Hz) Ec (ksi)Ec (ksi)1-L-17.41-L-17.4

2-L-17.42-L-17.4

3-L-17.43-L-17.440.340.3 42504250

1-L-251-L-25

2-L-252-L-25

3-L-253-L-2532.932.9 42004200

1-M-8.61-M-8.6

2-M-8.62-M-8.6

3-M-8.63-M-8.6175175 46504650

1-M-151-M-15

2-M-152-M-15

3-M-153-M-15117117 42504250

1-M-01-M-0

2-M-02-M-0

3-M-03-M-07878 47504750

Stresses in the Pull-Release Stresses in the Pull-Release TestTest

S3S2S1C3C2C1

G1-3G1-7G1-14G1-28G2-3G2-7G2-14G2-28

Free-Vibration Tests

f '/c

C

C,ASTME

E

2.5

2

1.5

1

0.5

00.450.40.350.30.250.20.150.10.050

ConclusionsConclusions

- The secant modulus of concrete can be larger than 1.25× EC,ACI (or 1.2 × EC,ASTM) for σ< fC’/15.

- α= 1/2 can be used to model a 3D flat-plate structure using 2D frame analyses. (It was obtained assuming EC= 1.25 ×

EC,ACI).

Documents

Small-Amplitude Vibration Tests of a Full-Scale RC Flat-Plate Structure By: Luis Arboleda MSCE Thesis