Structural Concrete - Hassoun

34 Chapter 2 Properties of Reinforced Concrete
Shrinkage Calculation. Parameters required for calculation of shrinkage strain using the GL
2000 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 shrinkage strain can be calculated using the following equation:
where
ε s (t) =ε shu β(h)β(t − t c ) (2.43)
ε shu = ultimate shrinkage strain according to Eq. 2.44
β(h) = correction term for effect of humidity according to Eq. 2.45
β(t − t c ) = correction term for effect of time of drying according to Eq. 2.46
Ultimate shrinkage strain should be calculated from the following equation:
⎧ ( ) 1∕2
⎪ 4350
(900) K
× 10 −6 (in. − lb)
⎪ f
ε shu =
cm28
⎨ ( ) 1∕2
⎪ 30
(900)K × 10
⎪
−6 (SI)
f
⎩
cm28
where
K = shrinkage constant, which depends on cement type as shown in Table 2.12
f cm28
= mean 28-day concrete compressive strength (MPa) or psi
(2.44)
Shrinkage constant K can be determined from Table 2.12.
Correction term for effect of humidity, β(h), should be calculated as shown:
( ) H 4
β(h) =1 − 1.18
(2.45)
100
where H is the relative humidity (%).
Correction term for effect of time, β(t − t c ), should be determined as follows:
(
)
⎧
1∕2
t − t
⎪
c
(in. − lb)
⎪ t − t
β(t − t c )=
c + 77(V∕S) 2
⎨(
) 1∕2
(2.46)
⎪ t − t c
⎪
(SI)
⎩ t − t c + 0.12(V∕S) 2
where
t = age of concrete after casting (days)
t c = age of concrete at the beginning of shrinkage (days)
V/S = volume-to-surface area ratio (mm or in.)
Table 2.12
Shrinkage Constant K as
Function of Cement Type
Type of Cement
I 1.00
II 0.75
III 1.15
K