Structural Concrete - Hassoun

2.13 Models for Predicting Shrinkage and Creep of Concrete 41
where
t c = concrete age at the beginning of drying (days)
h e = 2A c /u = notional size of member (mm), where A c is the cross section (mm 2 )andu is the
perimeter of the member in contact with the atmosphere (mm)
Creep Calculation. Total stress-dependent strain per unit stress, also called creep compliance or
creep function, can be determined as follows:
where
J(t, t 0 )= 1
E cmt0
+ φ 28(t, t 0 )
E cm28
(2.79)
E cmt0 = modulus of elasticity at age of loading (MPa or psi)
E cm28
= modulus of elasticity at day 28 (MPa or psi)
φ 28 (t, t 0 ) = creep coefficient
E cmt0
√
⎡ ⎛ (28 )⎞⎤ = E cm28
exp ⎢
⎢
0.5S ⎜
⎜
1 − ⎟⎟⎠ ⎥⎥⎦ (2.80)
t
⎣ ⎝
0
where S is the coefficient that depends on cement type and compressive strength and can be determined
from Table 2.17.
√
⎧
f
⎪3,118,310 3 cm28
(in. − lb)
⎪
1450
E cm28
= ⎨ √
(2.81)
⎪ f
⎪21,500 3 cm28
(SI)
⎩ 10
Creep coefficient, φ(t, t 0 ), can be evaluated from the given equation:
where
φ(t, t 0 )=φ 0 β c (t, t 0 ) (2.82)
φ 0 = notional creep coefficient
β(t, t 0 ) = equation describing development of creep with time after loading
φ 0 = φ RH β(f cm28
)β(t 0 ) (2.83)
Table 2.17
Coefficient S as Function of Cement Type and
Compressive Strength
f cm28
Type of Cement S
≤ 60 MPa (8700 psi) Rapidly hardening high strength (RS) 0.20
≤ 60 MPa (8700 psi) Normal or rapidly hardening (N or R) 0.25
≤ 60 MPa (8700 psi) Slow hardening (SL) 0.38
> 60 MPa (8700 psi) All types a 0.20
a Case not considered in CEB MC 90–99.