VIRGINIA CONCRETE
CONFERENCE
March 3-4, 2011
Presented by:
Teddy Theryo, P.E.
Parsons Brinckerhoff
SEGMENTAL BRIDGE GROUP
1.
2.
3.
4.
5.
Introduction
Understanding of Creep & Shrinkage
Code Development of Creep & Shrinkage
Impact of Creep & Shrinkage on Post-Tensioned
Bridges
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.
Strain
Strain
Creep strain
Instantaneous
strain
Time
Time
TYPICAL CREEP – TIMECURVE
TYPICAL SHRINKAGE – TIMECURVE
Strain
Drying
creep
Basic
creep
Total
creep
Shrinkage
Nominal
elastic strain
t0
Time (t – t0)
Strain - 10
-6
1500
1000
Instantaneous
recovery
Creep recovery
Residual
deformation
500
Strain on application
of load
0
50
100
150
Time since application of load - days
200
1.
2.
3.
4.
5.
Introduction
Understanding of Creep & Shrinkage
Code Development of Creep & Shrinkage
Impact of Creep & Shrinkage on Post-Tensioned
Bridges
Conclusions
Relationship between creep and elastic deformations
cr
=
where:
=
el
E28
cr
= creep strain
el
= elastic strain
= stress
E28 = elastic modules of concrete at age 28 days
= creep factor
3.72
3.5
2.0
2.22
2.00
1.5
1.70
1.44
0
3
Days
3 4 56
0.90
14 21 28 42 56
0.96
7
0.5
1.00
1.0
0.88
2.57
0.91
2.5
0.94
3.03
1.07
3.0
1.20
TOTAL ELASTIC AND CREEP STRAIN
4.0
9 1 1.5 2
Months
DURATION OF LOADING
Years
3
5
t
Mcr(t) = (1 – e - (t)) (MII – MI)
MFinal(t) = MII + (MI – MII) e- (t)
where:
(t) = creep factor at time t
e = Base of Napierian logarithms
= 2.7182
MI = Movement due to permanent loads before
change of statical system
MII = Movement due to the same loads applied on
changed statical system (build on
false-work)
q
Fixed
Fixed
2
qL
MI =
8
MI
½L
½L
Free Cantilever Statical System
2
MII
qL
MII =
12
2
qL
24
Changed Statical System (Midspan Continuous)
MFinal (t)
Mcr (t)
MI
MII
Cantilever Beam
el
(t 0 )
cr
(t
el
(t 0 )
Simple Beam
P
P
Pef
Pef
cr
(t
)
)
Post-Tensioned Beam
P
P
PT Tendon
el
(t0)
P
P
(t )
el (t0)
el
Pef
Pef
1.
2.
3.
4.
5.
Introduction
Understanding of Creep & Shrinkage
Code Development of Creep & Shrinkage
Impact of Creep & Shrinkage on Post-Tensioned
Bridges
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.
2.
3.
4.
5.
Introduction
Understanding of Creep & Shrinkage
Code Development of Creep & Shrinkage
Impact of Creep & Shrinkage on Post-Tensioned
Bridges
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
Bearing &
Expansion Joint
Bearing
In-span Hinge
CL
CL
Mid-span Hinge
In-span Hinge
Expansion Joint
Bearing
Old Generation of Midspan Hinge
(not recommended)
In-Span Hinge
Mid-Span Hinge
Deformation (cm)
2.5
S
5.0
7.5
5.1%
Span Length: 79m (260 feet)
1.8%
C
L EXP. JT. NO. 3
Deck Profile based
on As-Built Dwgs
STA. 65+74
C
L PIER 9
STA. 68+16.59
0.46’
C
L PIER 8
STA. 67+16.50
0.82’
0.36’
Reference
Line
Existing
Deck Profile
BEGIN S.E. TRANSITION
STA. 68+18
C
L EXP. JT. NO. 3
Deck Profile based
on As-Built Dwgs
STA. 67+16.50
0.84’
0.49’
C
L PIER 9
STA. 68+16.59
0.35’
C
L PIER 8
STA. 65+74
Reference
Line
Existing
Deck Profile
Midspan expansion joint
Active hinge member
Typical internal
diaphragm
Hydraulic jack
Active Hinge
(proposed by Jean M. Muller)
C
L Mid-Span
Fixed
Sliding
Expansion Joint
Teflon Surface (typ)
Elastomeric Bearing
Steel Strong Back
Mid-span Hinge with Strong Back
L
L
o
@ TF
creep
L
Point of rotation
V
3’-6”
creep
12’-0”
Abutment
Back Wall
8’-6”
0.079 Degree
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 60Fo in 2010
Abutment 1 = 3-3/4” - 0.5 (3.31) = 2.09” vs 1.75”
Elastomeric Bearing
Abutment 29 = 3-3/8” - 0.5 (3.31) = 1.75” vs 1”
End Span Girder Rotation at Abutment 1
(Varina-Enon Bridge Case Study)
Vertical Displacement (in)
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05 0
200
400
600
800
Distance Along the Bridge (ft)
Camber Diagram of Unit 1 at T =
Abutment
Span 1
Expansion Joint at Abutment
X
CL
Expansion
Joint
Top Plate
Bottom Pot
Ideal/preferred
position at T=
>X
CL Top Plate
creep at T =
Incorrect
position at T=
CL Bottom
Pot
X min.
CL Top Plate
e=
CL Bottom
Pot
creep at T =
Correct bearing &
joint expansion
preset at construction
Over Extended of Bearing Top Plate
Top Abutment
Elevation
Roadway Axis
Girder Axis
GOOD
BAD
A
BAD STRATEGY
Support Axis
A
SECTION A-A
GOOD STRATEGY
Torsional Creep Deformation in Horizontally Curved Bridge
 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