An experimental testing system for fiber reinforced ... experimental testing system for fiber...

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Univ. of Kentucky Center for Applied Energy Research

January 14, 2009

Jeffrey Helm

Stephen Kurtz

Evan O’Brien

Abdul-Rahman Salkini

An experimental testing system for fiber reinforced polymer (FRP)

strengthened concrete panels under uniform pressure loads

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En

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Univ. of Kentucky Center for Applied Energy Research

Jeffrey Helm

Stephen Kurtz

Evan O’Brien

Abdul-Rahman Salkini

An experimental testing system for fiber reinforced polymer (FRP)

strengthened concrete panels under uniform pressure loads

January 14, 2009

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Overview of the presentation

•Motivation for the research

•Concrete panel and FRP configurations

•Loading system

•Digital image correlation basics

•Testing results

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Motivation

Reinforced Concrete

Bridge

Carbon Fiber

Sheet Bonded

With Epoxy

•Determine the design parameters that govern use of fiber reinforced

polymer (FRP) strips for external reinforcement of existing concrete

structures

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Concrete panel specimens

2.1-m

2.1

-m

64-mm

2.1-m x 2.1-m x 64-mm panels

Cylinder strength: 30MPa

9.5-mm coarse rock aggregate

Phase 1

3.42-mm diameter – 75-mm spacing

Yield: 710 MPa

Ultimate: 731 MPa

Elongation: 0.5%

Phase 2

6.35-mm diameter – 150-mm spacing

Yield: 314 MPa

Ultimate: 459 MPa

Elongation: 27.5%

Coated with epoxy bonded sand

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FRP patterns

Phase 1

* *

Phase 2

* Glass fiber strips

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Uniform pressure loading

FRP (tension)

Concrete (compression)

Steel (tension)

Pressure

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Loading system

concrete

panel

pressure bladder

rocker

assembly

stiffening plate

top plate

outer frame

tube

bolt

sleeve

strong floor containment

basin

Maximum pressure = 62 kPa

Distributed load = 278 kN

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Loading system

concrete

panel

pressure bladder

rocker

assembly

stiffening plate

top plate

outer frame

tube

bolt

sleeve

strong floor containment

basin

Maximum pressure = 62 kPa

Distributed load = 278 kN

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DIC in two dimensions

PC with digitizer

Specimen

CCD camera

White light sources

90°

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Measurement basis

Two-dimensional image correlation is based on the ability to accurately

match portions from one image to corresponding locations in a second

image.

Correspondence can be determined to within 0.02 pixels

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Measurement basis

Because the method is computer based we can perform the matching on

a large number of points in the image.

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Displacement example

X img (pixel)

Yim

g(p

ixe

l)

400 600 800

0

200

400

600

800

V (pixel)

120

110

100

90

80

70

60

50

40

Vertical displacements

2.0 pixels/contour

X img (pixel)

Yim

g(p

ixe

l)

400 600 800

0

200

400

600

800

U (pixel)

7.5

5

2.5

0

-2.5

-5

-7.5

-10

-12.5

Horizontal displacements

0.5 pixels/contour

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DIC fundamentals

The image correlation method can be broken into four segments that

answer the following questions:

1. How do you differentiate a positions on the image?

2. How do I get from here to there?

3. How do you work on a scale smaller than a pixel?

4. How do you determine the optimal mapping parameters?

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Patterns and grayscales

From an image, how do you know where you are on the surface?

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Patterns and grayscales

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Mapping from one image to another

C

Q

q

c

uc

vc

Image N

Image 0

Constant displacement mapping:

qx = Qx+uc

qy = Qy+vc

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Mapping from one image to another

C

Q uc

vc

Image N

Image 0

Constant strain mapping:

q

c

qx = Qx + uc + (Qx-Cx)duc/dx + (Qy-Cy)duc/dy

qx = Qx + vc + (Qx-Cx)dvc/dx + (Qy-Cy)dvc/dy

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Mapping from one image to another

C

Q uc

vc

Image N

Image 0

Constant strain mapping:

q

c

qx = Qx + uc + (Qx-Cx)duc/dx + (Qy-Cy)duc/dy

qx = Qx + vc + (Qx-Cx)dvc/dx + (Qy-Cy)dvc/dy

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Working at sub-pixel scales

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Working at sub-pixel scales

0

100

200

0

2

4

6

8

10

0

2

4

6

8

10

0

100

200

0

2

4

6

8

10

0

2

4

6

8

10

Gra

y le

ve

l

Gra

y level

0

100

200

0

2

4

6

8

10

0

2

4

6

8

10

0

100

200

0

2

4

6

8

10

0

2

4

6

8

10

Gra

y level

Gra

y level

Raw image data Bi-linear interpolation

Bi-cubic interpolation Cubic spline interpolation

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Optimizing the mapping parameters

How do we determine the optimal mapping parameters?

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Error functions

common error functions:

(a) i|I’(qi) – I(Qi)| (magnitude of the

intensity differences)

(b) i(I’(qi) – I(Qi))2 (sum of the squares

of intensity differences)

(c) 1 - i(I’(qi) I(Qi))/((i(I’(qi)2)½ (i(I(Qi)

2)½) (normalized cross-

correlation)

error is minimized using a Newton-Raphson based optimization technique

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Extension into 3D Space

PC with digitizer Camera 1

Camera 2

Specimen/grid

location

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Camera parameters

Intrinsic Parameters:

PhD - Pinhole Distance

Cx - Hor. Image Center

Cy - Vert. Image Centerk - Lens Distortion Coef.

Extrinsic Parameters:a - Rotation about Z Axis

b - Rotation about Y Axis

g - Rotation about X Axis

Xo - X Axis Offset

Yo - Y Axis Offset

Zo - Z Axis Offset

Sensor Plane

Pinhole

Optic Axis

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System calibration

Calibrations methods use a

combination of known points

from standards and

correspondence between

cameras to determine each

camera’s parameters.

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Shape Measurement

Surface in

space

Undeformed

Image Cam 1

Undeformed

Image Cam 0

Camera 1

Camera 0

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Displacement Measurement

Undeformed

Image Cam 1

Undeformed

Image Cam 0

Deformed

Image Cam 1

Deformed

Image Cam 0

Surface in

space

Camera 1

Camera 0

Displaced

location

Displacement

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Displacements to strains

Strains determined from

curve fitting local areas

of data

Local areas define a quasi

gage-length for the calculations

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Strain Example

X img (pixel)

Yim

g(p

ixe

l)

400 600 800

0

200

400

600

800

Eyy

0.185

0.16

0.135

0.11

0.085

0.06

0.035

X img (pixel)

Yim

g(p

ixe

l)

400 600 800

0

200

400

600

800

Exy

0.032

0.022

0.012

0.002

-0.008

-0.018

-0.028

-0.038

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Strain example

X img (pixel)

Yim

g(p

ixe

l)

400 600 800

0

200

400

600

800

Exx

-0.01

-0.015

-0.02

-0.025

-0.03

-0.035

-0.04

-0.045

-0.05

-0.055

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Measurement system

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Measurement system

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Panel configurations

.30 m

Local area

Global area

1.98 m

Control panel FRP panel

Local area

Global area

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Surface patterns

global pattern as imaged

from the global camerasglobal and local pattern

as imaged from the local

cameras

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Center point displacement

Center point displacement (mm)

Pre

ssu

re(k

Pa

)

0 50 100

0

5

10

15

20

25

30

35

40

control panel

FRP panel

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Control panel displacement

Animation / Video

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Out-of-plane displacements

X location (mm) -1000

-500

0

500

Y location (m

m)

-1000

-500

0

500

1000

-20

0

20

40

60

80

100

120

140

Wd

isp

lace

me

nt

(mm

)

-20

0

20

40

60

80

100

120

140

X location (mm) -1000

-500

0

500

Y location (m

m)

-1000

-500

0

500

1000

-20

0

20

40

60

80

100

120

140

Wd

isp

lace

me

nt

(mm

)

-20

0

20

40

60

80

100

120

140

Control panel FRP panel

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Initial shape (local area)

X location (mm)

0 200 400 600 800 1000

Ylo

ca

tio

n(m

m)

-1000

-800

-600

-400

-200

0

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Strain progression

Animation / Video

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Failure strains

X location (mm)

0 200 400 600 800 1000

Ylo

ca

tio

n(m

m)

-1000

-800

-600

-400

-200

0

E1

0.04

0.0375

0.035

0.0325

0.03

0.0275

0.025

0.0225

0.02

0.0175

0.015

0.0125

0.01

0.0075

0.005

0.0025

0

X location (mm)S

trip

str

ain

0 200 400 600 800-0.002

0

0.002

0.004

0.006

0.008

0.01 Y = -150 mm strip

Y = -450 mm strip

Y = -750 mm strip

strain map (1st princ. strains) strains along each FRP strip

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Failure modes

Shear-Flexure Failure – Type 1

Shear-Flexure Failure – Type 2

Shear-Flexure Failure – Type 3

*Glass only

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Phase 1 Results

Control phase 1

ultimate = 26.9 kPa

max deflection = 55.6 mm

U/C Disp

1.41 25.5

1.34 37.8

1.48 47.5

U/C Disp

1.0, 55.6

1.41 25.5

1.34 37.8

1.48 47.5

ultimate pressure/control pressure

displacement in mm

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Phase 2 Results

Control phase 1

ultimate = 34.8 kPa

max deflection = 135.1 mm

ultimate pressure/control pressure

displacement in mm

U/C Disp

1.63 77.2

1.05 135.1

1.44 64.6

*

U/C Disp

1.00 135.1

0.96 59.6

1.65 75.5

0.92 125.8

*

Exp

eri

men

tal

stu

dy o

f F

RP

rein

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ed

co

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te p

an

els

Lafa

yett

e C

oll

eg

e D

ep

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f M

ech

an

ical

En

gin

eeri

ng

Conclusions

•Determine the design parameters that govern use of fiber

reinforced polymer (FRP) strips for external reinforcement of

existing concrete structures

Develop a method to apply a uniform distributed pressure load to

large (7ft x 7ft) panels of steel reinforced concrete

Adapt the digital image correlation (DIC) technique to measure

full-field displacements and strains in the panels

Acquire panel failure data for a variety of FRP reinforcement

configurations

Analyze the raw image data to obtain full-field displacements,

strains and crack patterns

•Use the data to develop design criteria for FRP reinforcement of

concrete panels