Structural Concrete - Hassoun

36 Chapter 2 Properties of Reinforced Concrete
(
)
⎡
0.5
0.5
If t 0 > t c then φ(t c )= ⎢
t
1 −
0 − t
⎤
c ⎥⎥⎦
⎢
⎣
t 0 − t c + 77(V∕S) 2
(
)
⎡
0.5
0.5
If t 0 > t c then φ(t c )= ⎢
t
1 −
0 − t
⎤
c ⎥⎥⎦
⎢
⎣
t 0 − t c + 0.12(V∕S) 2
h =
H
100
(in. − lb)
(SI)
(2.53)
where H is the relative humidity (%).
2.13.4 CEB 90 Model
The CEB 90 model was developed by Muller and Hillsdorf [16].
Shrinkage Calculation. Parameters required for calculation of shrinkage strain using the CEB 90
model are mean 28-day concrete compressive strength f cm28
, relative humidity H, age of concrete
at the beginning of shrinkage t c , type of cement, and specimen shape.
The strain due to shrinkage may be calculated from the following equation:
ε s (t, t c )=ε cs0 β s (t − t c ) (2.54)
where
ε cs0 = notional shrinkage coefficient according to Eq. 2.55
β s (t, t c ) = coefficient describing development of shrinkage with time according to Eq. 2.58
where
Notional shrinkage coefficient is
ε cs0 = ε s (f cm28
)β RH (2.55)
ε s (f cm28
)=concrete strength factor on shrinkage according to Eq. 2.56
β RH = relative humidity factor on notional shrinkage coefficient according to Table 2.14
Concrete strength factor on shrinkage, ε s (f cm28
), can be calculated as
⎧[
⎪ 160 + 10 ( ) ( β
⎪
sc 9 − f )]
cm 28
× 10 −6 (in. − lb)
1450
ε s (f cm28
)= ⎨[
⎪
⎪
160 + 10 ( ) (
β sc 9 − f )]
cm 28
× 10 −6 (SI)
10
⎩
(2.56)
Table 2.14
Humidity
Determination of Coefficient β RH
β RH
40% ≤ H < 99% −1.55 × β arh
H ≥ 99% 0.25