Creep in Concrete

7/27/2019 Creep in Concrete

1/29

CREEPINCONCRETE: FORMULATION

TOAPPROXIMATECALCULATION

METHODSFORSTRUCTURALANALYSIS

Ankit Agrawal

PhD Student

Dept. of Civ. & Env. Engr.

Michigan State University

APRIL 2014

ME 940: Project Presentation


2/29

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


3/29

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.)


4/29

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


5/29

Concrete under Constant

Compression


6/29

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

?


7/29

+ Where,

:Applied Stress

:Elastic modulus:Creep strain

: Sum of hygrothermal, chemical and cracking strains

Where,

:Viscoelastic strain

: Viscous strain

Decomposition of Strain in

Components


8/29

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)


9/29

Viscoelastic Component

()

Viscous Component

()

Microscopic Compliance

Functions

1

T

T

t

t


10/29

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


11/29

The Constitutive Relation

Microstress can be eliminated if , 0

The result is:

1() ()

Or

[()]

()

;

()

Similarly, for viscous component

[()]() ()

[()]

()


12/29

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 ,

=> ,

(

)


13/29

l n 1 ; ()

()

4

()

+

; ()

Material Functions


14/29

Simplified Formulations

Load duration much shorter than age for unitconstant load

, 1 ( ) ( ) Load duration much larger than age for unit

constant load

, ()


15/29

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


16/29

Creep functions for different load

times


17/29

Linear Algebraic Methods for the

Calculation of Creep Strain

Effective Modulus Method

Mean StressMethod

Age Adjusted Effective

Modulus Method

EC2 and ACI 209 CommitteeRecommendations


18/29

Effective Modulus Method

1 ,

1(, ) ()1( ,)

(, ) 1( ,)()

:stress-independent inelastic strain


19/29

Age Adjusted Effective Modulus

Method

1 ,

( ,) 1(, ) ()1(,)

, 1 , 1(,)



20/29

Mean Stress Method

1 ,

, 1(,) , , 2



21/29

Graphically


22/29


23/29

Degenerate Kernel Method

, [ 1 ]

=

Approximation of the creep function as a

Dirichlet series

: Multiplicative coefficients : Retardation Times


24/29

EC2 and ACI 209 Committee

Recommendations

EC2

,

=

.3

ACI 209 Committee

, ( ).61 0 ( ).6 (,T)

(,T)=3456


25/29


26/29

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


27/29

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


28/29

Discussion& Suggestions!

Thank You for your time.


29/29

On A Different Note

Documents

Creep in Concrete