Structural Concrete - Hassoun

2.13 Models for Predicting Shrinkage and Creep of Concrete 67
β c (t, t 0 )=
( ) t − 0.3 t0
(
)
35 − 28 0.3
=
= 0.307
β H + t − t 0 351 + 35 − 28
φ(t, t 0 )=φ 0 β c (t, t 0 )=1.683 × 0.307 = 0.517
J(t, t 0 )= 1 + φ(t, t 0 ) 1
=
E cmt0 E cm28
35,548 + 0.517
35,548 = 42.68 × 10−6 MPa −1
Example 2.13 (SI Units)
Use the fib MC 2010 model to calculate the shrinkage strain and creep function for the specimen given
in Example 2.8.
Solution
Shrinkage Calculation
The equations utilized by the fib MC 2010 shrinkage prediction model are similar to those of the CEB
MC 90-99 model. Refer to Example 2.12 Shrinkage Calculation section for shrinkage prediction.
Creep Calculation
1
J(t, t 0 )=
E ci (t 0 ) + φ(t, t 0 )
E ci
Calculation of E ci (t 0 ) and E ci :
t 0 = 28 days ⇒ E ci (t 0 )=E ci
√
√
f
E ci = 21,500 3 cm28
45.2
10 = 21,500 3 = 35,548 MPa
10
Calculation of φ(t,t 0 ):
β bc (f cm )= 1.8
(f cm ) = 1.8
= 0.125
0.7 (45.2)
0.7
α = 1 for type III cement
[
] α
9
t 0,adj = t 0,T
2 + t + 1 ≥ 0.5 days
1.2 0,T
[
] 1
9
= 28 ⋅
2 + 28 + 1 = 32.5 days≥ 0.5days
1.2
[ ( ) 2
30
β bc (t, t 0 )=ln + 0.035 ⋅ (t − t
t 0 )+1]
0,adj
[ ( ) 30
2
]
= ln
32.5 + 0.035 ⋅ (35 − 28)+1 = 2
φ bc (t, t 0 )=β bc (f cm ) ⋅ β bc (t, t 0 )=(0.125)(2) =0.25
β dc (f cm )= 412 412
= = 1.98
(f cm ) 1.4 (45.2) 1.4
( ) ( )
1 − RH 1 − 75
100
100
β(RH) = √ = √ = 0.59
3 h 3
0.1 ⋅ 0.1 ⋅ 76
100
100