Structural Concrete - Hassoun

2.13 Models for Predicting Shrinkage and Creep of Concrete 35
Creep Calculation. The creep compliance is composed of two parts: the elastic strain and the
creep strain according to the following equation:
J(t, t 0 )= 1 + φ 28(t, t 0 )
(2.47)
E cmt0 E cm28
where
E cmt0 = modulus of elasticity of concrete at loading (MPa or psi)
E cm28
= modulus of elasticity of concrete at 28 days (MPa or psi)
φ 28 (t, t 0 ) = creep coefficient
E cmt0 =
{ 500,000 + 52,000
√
fcmt0 (in. − lb)
3500 + 4300 √ f cmt0 (SI)
(2.48)
where f cmt0 is the concrete mean compressive strength at loading (MPa or psi), which can be determined
as follows:
t
3∕4
f cmt0 = f 0
cm28
(2.49)
a + bt 3∕4 0
Coefficients a and b are related to the cement type as shown in Table 2.13.
√
E cm28
= 3500 + 4300 f cm28
(2.50)
Creep coefficient, φ(t, t 0 ), can be calculated as shown:
⎧
⎪φ ( ) [ ( ( ) 0.3 ) ( ) t − 0.5 ( )
t0 7 t −
0.5
t0
t
⎪ c 2
+
(t − t 0 ) 0.3 + 14 t 0 t − t 0 + 7
⎪
⎪
⎪
⎪
+2.5 ( ( ) 0.5
1 − 1.086h 2) t − t
⎤
0 ⎥⎥⎦
⎪
t − t 0 + 77(V∕S) 2
φ 28 (t, t 0 )= ⎨ [ ( ( ) 0.3 ) ( )
⎪
t − 0.5 ( )
t0 7 t −
0.5
t0
⎪φ(t c ) 2
+
(t − t 0 ) 0.3 + 14 t 0 t − t 0 + 7
⎪
⎪
⎪
⎪
⎪
⎩
+2.5 ( 1 − 1.086h 2) ( t − t 0
t − t 0 + 0.12(V∕S) 2 ) 0.5
⎤
⎥⎥⎦
(in. − lb)
(SI)
(2.51)
If t 0 = t c then φ(t c )=1 (2.52)
Table 2.13
Coefficient a and b as Function of
Cement Type
Cement Type a b
I 2.8 0.77
II 3.4 0.72
III 1.0 0.92