Structural Concrete - Hassoun

2.13 Models for Predicting Shrinkage and Creep of Concrete 63
Calculation of β(h):
( ) H 4 ( ) 75 4
β(h) =1 − 1.18 = 1 − 1.18 = 0.627
100
100
Calculation of β(t − t c ):
β(t − t c )=
(
t − t c
t − t c + 0.12(V∕S) 2 ) 1∕2
=
(
35 − 8
35 − 8 + 0.12(38) 2 ) 1∕2
= 0.367
ε s (t) =ε shu β(h)β(t − t c )=(843.2 × 10 −6 )(0.627)(0.367) =194 × 10 −6 mm∕mm
Creep Calculation
Calculation of E cmt0 and E cm28
:
J(t, t 0 )= 1
E cmt0
+ φ(t, t 0 )
E cm28
Calculation of φ(t, t 0 ):
t 0 = 28 days ⇒ E cmt0 = E cm28
√
√
E cm28
= 3500 + 4300 f cm28
= 3500 + 4300 45.2 = 32409.3MPa
t 0 = 28 > t c = 8days
(
)
⎡
0.5
0.5 [
φ(t c )= ⎢
t
1 −
0 − t
⎤ (
) 0.5
] 0.5
c ⎥⎥⎦ 28 − 8
= 1 −
= 0.824
⎢
⎣
t 0 − t c + 0.12(V∕S) 2 28 − 8 + 0.12(38) 2
h =
φ 28 (t, t 0 )=φ(t c )
H
100 = 75
100 = 0.75
[ ( ( ) 0.3
t − t0
2
(t − t 0 ) 0.3 + 14
)
( ) 0.5 ( )
7 t −
0.5
t0
+
t 0 t − t 0 + 7
(
) 0.5
+ 2.5(1 − 1.086h 2 t − t
⎤
)
0 ⎥⎥⎦
t − t 0 + 0.12(V∕S) 2
[ ( (35 − 28)
0.3
) ( ) 7 0.5 ( ) 35 − 28 0.5
= 0.824 2
+
(35 − 28) 0.3 + 14 28 35 − 28 + 7
(
) 0.5
]
+ 2.5(1 − 1.086(0.75) 2 35 − 28
)
= 0.636
35 − 28 + 0.12(38) 2
J(t, t 0 )= 1 + φ 28 (t, t 0 ) 1
=
E cmt0 E cm28
32409.3 + 0.636
32409.3 = 50.5 × 10−6 MPa −1
Example 2.11 (SI Units)
Using the CEB 90 model, calculate the shrinkage strain and creep function for the specimen given in
Example 2.8.