VIRGINIA CONCRETE CONFERENCE

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25 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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VIRGINIA CONCRETE
CONFERENCE

March 3
-
4, 2011

Presented by:


Teddy Theryo, P.E.


Parsons Brinckerhoff


SEGMENTAL BRIDGE GROUP

1.
Introduction

2.
Understanding of Creep & Shrinkage

3.
Code Development of Creep & Shrinkage

4.
Impact of Creep & Shrinkage on Post
-
Tensioned
Bridges

5.
Conclusions


Definitions



Creep

is time dependent deformations of concrete
under permanent loads (self weight), PT forces and
permanent displacement



Shrinkage

is shortening of concrete due to drying and
is independent of applied loads


Factors Affecting Creep



Concrete mix proportion


Cement properties


Curing conditions


Size and shape of members


Environment


Age at loading


Stress level


Factors Affecting Shrinkage



Concrete mix proportion


Cement properties


Aggregate properties


Curing conditions


Size and shape of members


Environment



In structural concrete creep and shrinkage strains are
coexist and occur together.



The rate of both creep and shrinkage decrease with time.


Theoretically the creep and shrinkage are considered
diminished at 10,000 days (27 years) after construction.


For practical purposes the ending time of 4,000 days (11
years) is also commonly used in creep and shrinkage
calculations .


Mathematically the non linear shape of creep and
shrinkage has been assumed as hyperbolic, exponential or
logarithmic.


S

t

r

a

i

n

S

t

r

a

i

n

Time

Time

Creep strain

Instantaneous

strain

TYPICAL CREEP


TIMECURVE

TYPICAL SHRINKAGE


TIMECURVE

Drying

creep

Basic

creep

Total

creep

Shrinkage

Nominal

elastic strain

Time (t


t )

0

t

0

S

t

r

a

i

n

0

50

100

150

200

Instantaneous

recovery

Creep recovery

Residual

deformation

500

1000

1500

Strain on application

of load

Time since application of load
-

days

S

t

r

a

i

n



-



1

0

-

6

1.
Introduction

2.
Understanding of Creep & Shrinkage

3.
Code Development of Creep & Shrinkage

4.
Impact of Creep & Shrinkage on Post
-
Tensioned
Bridges

5.
Conclusions


Relationship between creep and elastic deformations


cr

=


el

=

E
28



where:


cr

= creep strain


el

= elastic strain


= stress

E
28
= elastic modules of concrete at age 28 days


= creep factor

4.0

3.5

3.0

2.5

2.0

1.5

3.72

3.03

2.57

2.22

2.00

1.70

1.44

1.0

0.5

0

3

7

14

21

28

42

56

3

4

5

6

9

1

1.5

2

3

5

Days

Months

Years

1

.

2

0

1

.

0

7

1

.

0

0

0

.

9

6

0

.

9

1

0

.

9

4

0

.

9

0

0

.

8

8

t

DURATION OF LOADING

T

O

T

A

L



E

L

A

S

T

I

C



A

N

D



C

R

E

E

P



S

T

R

A

I

N

M
cr
(t)
=

(1


e
-


(t)
) (M
II



M
I
)

M
Final
(t)
= M
II

+ (M
I



M
II
) e
-

(t)


where: (t) = creep factor at time t



e = Base of
Napierian

logarithms




= 2.7182



M
I

= Movement due to permanent loads before



change of
statical

system



M
II

= Movement due to the same loads applied on



changed
statical

system (build on



false
-
work)

Free Cantilever Statical System

Changed Statical System (Midspan Continuous)

M

Final (t)

½L

½L

M

I

M =

I

Fixed

Fixed

q

qL

2

8

M

II

M =

II



qL

2

12

qL

2

24

M

II



M

I

M

cr (t)



el


(t )

0

cr


(t )

P

P

P

ef

P

ef

Cantilever Beam

Simple Beam

el


(

)

t

0

cr


(t )

P

Post
-
Tensioned Beam

P

P

P

P

ef

P

ef

el


(t )

0

el


(t )

0

el


(t )

PT Tendon

1.
Introduction

2.
Understanding of Creep & Shrinkage

3.
Code Development of Creep & Shrinkage

4.
Impact of Creep & Shrinkage on Post
-
Tensioned
Bridges

5.
Conclusions


CEB
-
FIP 1970 Model Code

CEB
-
FIP 1978 Model Code

CEB
-
FIP 1990 Model Code

FIB 2010 Draft Model Code

ACI
-
209

BP3


1.
Introduction

2.
Understanding of Creep & Shrinkage

3.
Code Development of Creep & Shrinkage

4.
Impact of Creep & Shrinkage on Post
-
Tensioned
Bridges

5.
Conclusions


There are two major impacts of creep and shrinkage
on structural concrete



Deformations (simply supported and indeterminate
structures)


Redistribution of stresses / forces on indeterminate
structure, including support reactions

C

L

C

L

In
-
span Hinge

In
-
span Hinge

Mid
-
span Hinge

Bearing &
Expansion Joint

Bearing

Expansion Joint

Bearing

Old Generation of
Midspan

Hing
e

(not

recommended)

M

i

d

-

S

p

a

n



H

i

n

g

e

I

n

-

S

p

a

n



H

i

n

g

e

5.1%

S

1.8%

2.5

5.0

7.5

D

e

f

o

r

m

a

t

i

o

n



(

c

m

)

Span Length: 79m (260 feet)

Deck Profile based

on As
-
Built Dwgs

Existing

Deck Profile

Reference

Line

C EXP. JT. NO. 3

L

STA. 67+16.50

C PIER 9

L

STA. 68+16.59

BEGIN S.E. TRANSITION

STA. 68+18

C PIER 8

L

STA. 65+74

0.36’

0.46’

0

.

8

2



Deck Profile based

on As
-
Built
Dwgs

Existing

Deck Profile

Line

C EXP. JT. NO. 3

L

STA. 67+16.50

C PIER 9

L

STA. 68+16.59

C PIER 8

L

STA. 65+74

0.49’

0.35’

0

.

8

4



Reference

Active Hinge

(proposed by Jean M. Muller)

Active hinge member

Midspan expansion joint

Typical internal

diaphragm

Hydraulic jack

Sliding

Expansion Joint

C

L Mid
-
Span

Steel Strong Back

Fixed

Elastomeric Bearing

Teflon Surface (typ)

Mid
-
span Hinge with Strong Back

-

0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0

200

400

600

800

Distance Along the Bridge (ft)

V

e

r

t

i

c

a

l



D

i

s

p

l

a

c

e

m

e

n

t



(

i

n

)

L

L

@ TF

o

creep

0.079 Degree

8’
-
6”

3’
-
6”

12’
-
0”

L

creep = 0.079 x 3.5 x 12 = 3.31”

Assuming 50% of the creep had been corrected

camber during segment casting.

L

available gap at 60F in 2010

o

Abutment 1 = 3
-
3/4”
-

0.5 (3.31) = 2.09” vs 1.75”

Abutment 29 = 3
-
3/8”
-

0.5 (3.31) = 1.75” vs 1”

Point of rotation

creep

V

Abutment

Back Wall

Camber Diagram of Unit 1 at T =

End Span Girder Rotation at Abutment 1

(Varina
-
Enon Bridge Case Study)

Elastomeric Bearing

Expansion Joint at Abutment

Abutment

Span 1

X

C

L

Top Plate

Bottom Pot

>X

C

L

Top Plate

X min.

C

L

C

L

Bottom

Pot

C

L

Bottom

Pot

creep at T =

Top Plate

creep at T =

e =

Ideal/preferred

position at T=

Incorrect

position at T=

Correct bearing &

joint expansion

preset at construction

Expansion

Joint

Over Extended of Bearing Top Plate

Torsional

Creep Deformation

i
n Horizontally

Curved

Bridge

A

A

GOOD

BAD

Roadway Axis

Girder Axis

S

u

p

p

o

r

t



A

x

i

s

SECTION A
-
A

BAD STRATEGY

GOOD STRATEGY

Top Abutment

Elevation


Introduction


Understanding of Creep & Shrinkage


Code Development of Creep & Shrinkage


Impact of Creep & Shrinkage on Post
-
Tensioned
Bridges


Conclusions


In order to avoid the negative impacts of long
-
term
creep and shrinkage:


1.
Good understanding of creep and shrinkage behaviors

2.
Accurate estimation of creep and shrinkage on structural
concrete design

3.
Proper counter measures of long
-
term creep and
shrinkage effects

4.
Implement simple structural details