Structural Concrete - Hassoun

2.13 Models for Predicting Shrinkage and Creep of Concrete 29
Creep Calculation. The total load-dependent strain at time t, ε ic (t, t 0 ) of a concrete member
uniaxially loaded at time t 0 with a constant stress σ may be calculated as follows:
where
where
ε ic (t, t 0 )=ε i (t 0 )+ε c (t, t 0 ) (2.13)
ε i (t 0 ) = initial elastic strain at loading
ε c (t, t 0 ) = creep strain at time t ≥ t 0
ε i (t 0 )= σ
E cmt0
(2.14)
ε c (t, t 0 )=
σ
E cmt0
C c (t) (2.15)
E cmt0 = modulus of elasticity at age of loading (MPa) as given in Eq. 2.17
C c (t) = creep coefficient at time t, asgiveninEq.2.19
Usually, the total load-dependent strain is presented with compliance function, also called creep
function, J(t, t 0 ), which represents the total load-dependent strain at time t produced by a unit
constant stress that has been acting since time t 0 .
where
J(t, t 0 )= 1 + C c(t)
(2.16)
E cmt0
{
33(γ) 3∕2√ f ′
E cmt0 =
c(t 0 ) (in. − lb)
0.043(γ) 3∕2√ (2.17)
f c(t ′ 0 ) (SI)
γ = concrete unit weight (kg/m 3 )or(lb/ft 3 )
f c ′(t 0 )=mean concrete compressive strength at age of loading (MPa) or ksi
f c(t ′ t
0 )=f 0
cm28
(2.18)
a + bt 0
where f cm28
is the average 28-day concrete compressive strength (MPa) a and b are constants according
to Table 2.5.
Creep coefficient, C c (t), can be determined as follows:
(t − t
C c (t, t 0 )= 0 ) 0.60
10 +(t − t 0 ) C cuK 0.60 ch K ca K cs (2.19)
Table 2.5
Constants a and b as Function of Cement Type and Curing
Method
Type of Cement Moist-Cured Concrete Steam-Cured Concrete
I a = 4 b = 0.85 a = 1 b = 0.95
III a = 2.30 b = 0.92 a = 0.70 b = 0.98