creep in concrete
TRANSCRIPT
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CREEPINCONCRETE: FORMULATION
TOAPPROXIMATECALCULATION
METHODSFORSTRUCTURALANALYSIS
Ankit Agrawal
PhD Student
Dept. of Civ. & Env. Engr.
Michigan State University
APRIL 2014
ME 940: Project Presentation
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Why study Creep in
Concrete? Final strain may be several times initial elastic strain Critical in pre-stressed concrete
Control deflections in segmental concrete bridge constructionand service stages
Various code recommendations are still controversial
Various code recommendations are still controversial
May lead to collapse in extreme cases (Koror-BabeldaobBridge, Palau, 1996)
Before After
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Creep and Shrinkage in
Concrete: an intricate
phenomenon
Un-hydrated cement cores
Inner C-S-H product
Outer C-S-H project is
yellow
Water-filled space
(Courtesy of K. van
Breugel.)
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Complying with Thermodynamic
Restrictions
Dealing with changing and with timeExperimental data sensitive to
scatter and might not lead to non-
decreasing positive creep
compliance function
Complicating Factors in
Mathematical Modeling
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Concrete under Constant
Compression
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Factors Influencing Creep in
Concrete
Internal Factors
External Factors
Aggregate (Concentration +
Stiffness)
Inversely proportional
Water/cement ratio, Aggregate
permeability, Aggregate creep
Directly proportional
Aggregate grading and
distribution, Cement ?
Cross-section, Stress
intensity
Directly proportional
Size, Shape, Time (age of
loading and load history),
Environmental factorsambient humidit
?
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+ Where,
:Applied Stress
:Elastic modulus:Creep strain
: Sum of hygrothermal, chemical and cracking strains
Where,
:Viscoelastic strain
: Viscous strain
Decomposition of Strain in
Components
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N-Kelvin Voigt Models in series
Shrinkage+Thermal
+Cracking
Creep
Viscoelastic
Viscous
(flow)
Role of Solidification in Creep
(,)
Elastic
v(t)
h(t)
dv(t)
dh(t)
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Viscoelastic Component
()
Viscous Component
()
Microscopic Compliance
Functions
1
T
T
t
t
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Volume fractions v and f associated withviscoelastic and viscous strains respectively
Stress equilibrium in terms of Microstress
, ()
Stress-strain relation for viscoelastic part
( ) ,
Assumed to be non aging and viscoelastic
Key Ideas and
Assumptions
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The Constitutive Relation
Microstress can be eliminated if , 0
The result is:
1() ()
Or
[()]
()
;
()
Similarly, for viscous component
[()]() ()
[()]
()
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Under a Constant Stress
Under a constant stress applied at a age T , ,
, () 1() The Compliance function, representing strain at
time t by a unit constant stress applied at age T
, 1 ,
=> ,
(
)
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l n 1 ; ()
()
4
()
+
; ()
Material Functions
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Simplified Formulations
Load duration much shorter than age for unitconstant load
, 1 ( ) ( ) Load duration much larger than age for unit
constant load
, ()
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A General Summary
The Creep Function
, 1() , Specific Creep Function , Aging Function ;
Power law:
Exponential Law: Load Duration Function ;
Power law: ( )Logarithmic Law: log 1
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Creep functions for different load
times
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Linear Algebraic Methods for the
Calculation of Creep Strain
Effective Modulus Method
Mean StressMethod
Age Adjusted Effective
Modulus Method
EC2 and ACI 209 CommitteeRecommendations
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Effective Modulus Method
1 ,
1(, ) ()1( ,)
(, ) 1( ,)()
:stress-independent inelastic strain
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Age Adjusted Effective Modulus
Method
1 ,
( ,) 1(, ) ()1(,)
, 1 , 1(,)
:stress-independent inelastic strain
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Mean Stress Method
1 ,
, 1(,) , , 2
:stress-independent inelastic strain
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Graphically
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Degenerate Kernel Method
, [ 1 ]
=
Approximation of the creep function as a
Dirichlet series
: Multiplicative coefficients : Retardation Times
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EC2 and ACI 209 Committee
Recommendations
EC2
,
=
.3
ACI 209 Committee
, ( ).61 0 ( ).6 (,T)
(,T)=3456
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Conclusions
Separatingthe phenomenon of aging or
solidificationfrom creep leads to a more
justifiable constitutive model
Degenerate kernel methodseems to bemore useful for determining complete strain
history
Linear methodsare more useful fordetermining creep at a particular time
Code methodscan provide a reasonable
estimateof creep for structural design
purposes
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Bibliography
WEB http://ciks.cbt.nist.gov/garbocz/AmCeram/node19.htm
http://en.wikipedia.org/wiki/Koror%E2%80%93Babeldaob_Bridge
Buyukozturk, O. Mechanics and Design of Concrete Structures. Lectrure notes, Spring 2004,MIT.
ARTICLES Bazant Z.P. and Prasannan S., Solidification theory for
concrete creep I: Formulation, Journal of EngineeringMechanics, ASCE, Vol. 115 (8), August 1989, pp. 1691-1703.
Veglianti, D. and Sgambi, L. Approximate methods foranalysis of viscoelastic behavior of concrete structures.OnlinePublication.(https://www.academia.edu/1906077/Approximate_methods_for_analysis_of_viscoelastic_behavior_of_concrete_stru
ctures)
http://ciks.cbt.nist.gov/garbocz/AmCeram/node19.htmhttp://en.wikipedia.org/wiki/Koror%E2%80%93Babeldaob_Bridgehttp://en.wikipedia.org/wiki/Koror%E2%80%93Babeldaob_Bridgehttp://en.wikipedia.org/wiki/Koror%E2%80%93Babeldaob_Bridgehttp://ciks.cbt.nist.gov/garbocz/AmCeram/node19.htm -
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Discussion& Suggestions!
Thank You for your time.
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On A Different Note