Structural Concrete - Hassoun

2.13 Models for Predicting Shrinkage and Creep of Concrete 39
β H =
{ [
37.5he 1 + (0.012H)
18 ] + 250 ≤ 1500 days (in. − lb)
1.5h e [1 +(0.012H) 18 ]+250 ≤ 1500 days (SI)
(2.69)
2.13.5 CEB MC 90-99 Model
The CEB MC 90-99 is a modification of the CEB 90 and is described in Ref. 17.
Shrinkage Calculation. In this new model, total shrinkage contains an autogenous and drying
shrinkage component. In high-performance concrete, autogenous shrinkage is significant and needs
to be considered in prediction of shrinkage. This new approach was necessary so that shrinkage of
normal as well as high-performance concrete can be predicted with sufficient accuracy [1].
Total shrinkage strain can be calculated using the following equation:
where
ε as (t) = autogenous shrinkage at time t
ε ds (t, t c ) = drying shrinkage at time t
ε s (t, t c )=ε as (t)+ε ds (t, t c ) (2.70)
where
Autogenous shrinkage, ε as (t), should be calculated as follows:
ε as (t) =ε as0 (f cm28
)β as (t) (2.71)
ε cas0 (f cm28
)=notional autogenous shrinkage coefficient according to Eq. 2.72
β as (t) = function to describe the time-development of autogenous shrinkage, from Eq. 2.73
where
Notional autogenous shrinkage coefficient, ε cas0 (f cm ), can be calculated as
⎧ (
)
fcm28 ∕1450 2.5
⎪−α ⎪ as × 10 −6 (in. − lb)
6 + f
ε as0 (f cm28
)=
cm28
∕1450
⎨ (
)
⎪
fcm28 ∕10 2.5
⎪
−α as × 10 −6 (SI)
⎩
6 + f cm28
∕10
α as = coefficient that depends on type of cement
= 800 for slowly hardening cements (SL)
= 700 for normal or rapidly hardening cements (N or R)
= 600 for rapidly hardening high-strength cements (RS)
ε ds0 (f cm28
)=mean compressive strength of concrete at an age of 28 days (MPa or psi)
(2.72)
Function β as (t) should be calculated using the following equation:
β as (t) =1 − exp[−0.2(t) 0.5 ] (2.73)
where t is the age of concrete (days).
Drying shrinkage, ε ds (t, t c ), can be estimated by the equation
ε ds (t, t c )=ε ds0 (f cm28
)β RH (H)β ds (t − t c ) (2.74)