Structural Concrete - Hassoun

2.13 Models for Predicting Shrinkage and Creep of Concrete 55
β s1 =
(
35 × 1450
f cm28
) 0.1
=
( ) 35 × 1450 0.1
= 1.23 ≥ 1.0
6556
β s1 = 1.0
[ ( ) H 3
] [ ( ) 75 3
]
β RH =−1.55 1 − =−1.55 1 − =−0.896
100
100
(
) 0.5
t − t
β ds (t − t c )=
c
350 ( h e ∕4 ) 2
+(t − tc )
0.5
⎛
⎞
⎜ 35 − 8 ⎟⎟⎟⎠
= ⎜ ( ) 2
= 0.347
⎜
⎝
350 3
4 +(35 − 8)
ε ds (t, t c )=ε ds0 (f cm28
)β RH (H)β ds (t − t c )
=(511.5 × 10 −6 )(−0.896)(0.347) =−159 × 10 −6 in.∕in.
ε s (t, t c )=ε as (t)+ε ds (t, t c )=(−50.41 × 10 −6 )+(−159 × 10 −6 )=−209 × 10 −6 in.∕in.
Creep Calculation
Calculation of E cmt0 and E cm28
:
J(t, t 0 )= 1
E cmt0
+ φ 28 (t, t 0 )
E cm28
E cm28
Calculation of φ(t, t 0 ):
α 1 =
α 2 =
φ RH =
t 0 = 28 days ⇒ E cmt0 = E cm28
√
√
f
= 3,118,310 3 cm28
6556
1450 = 3,118,310 3 = 5,156,356 psi
1450
[
3.5 × 1450
f cm28
] 0.7
=
[ ] 0.2
3.5 × 1450
=
f cm28
[
1 + 1 − H∕100
0.46 3 √
he ∕100 α 1
[ ] 3.5 × 1450 0.7
= 0.84
6556
[ ] 3.5 × 1450 0.2
= 0.95
6556
] [
α 2 =
5.3
5.3
β(f cm28
)= √ = √ = 2.49
f cm28
∕1450 6556∕1450
[ ]
9
t 0 = t 0.T + 1
2 + t 1.2
0.T
[
= 28
1 + 1 − 75∕100
0.46 3 √
3∕4
0.84
9
2 + 28 1.2 + 1 ]
= 32.5 ≥ 0.5 days
]
0.950 = 1.427