Structural Concrete - Hassoun

2.13 Models for Predicting Shrinkage and Creep of Concrete 57
[ ( ) 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 )= 437,333 437,333
= = 1.98
(f cm )
1.4
(6556)
1.4
( ) ( )
1 − RH 1 − 75
100
β(RH) = √ ) = 100
√ ) = 0.59
3
3
0.1 0.1
β dc (t 0 )=
γ(t 0 )=
α fcm =
β dc (t, t 0 )=
(
h
4
(
3
4
1
0.1 + t = 1
= 0.475
0.2 0.2 0,adj 0.1 + 32.5
1
1
=
= 0.343
2.3 + √ 3.5
t0,adj
2.3 + √ 3.5
32.5
(
5075
f cm
) 0.5
=
( ) 5075 0.5
= 0.880
6556
β h = 38.1 ⋅ h + 250α fcm ≤ 1500α fcm
= 38.1(3)+250(0.880) ≤ 1500(0.880)
⇒ 334 ≤ 1320
[ ( ) t − t0
β h +(t − t 0 )
] γ(t0 )
φ dc (t, t 0 )=β dc (f cm ) ⋅ β(RH) ⋅ β dc (t 0 ) ⋅ β dc (t, t 0 )
=(1.98)(0.59)(0.475)(0.264) =0.146
φ(t, t 0 )=φ bc (t, t 0 )+φ dc (t, t 0 )
= 0.25 + 0.146 = 0.396
[
] 0.343
(35 − 28)
=
= 0.264
334 +(35 − 28)
1
J(t, t 0 )=
E ci (t 0 ) + φ(t, t 0 )
E ci
1
=
5,156,356 + 0.396
5,156,356 = 0.271 × 10−6 psi −1
Example 2.7 (in.−lb Units)
Using the AASHTO model, calculate the shrinkage strain and creep compliance and coefficient for the
specimen given in Example 2.1.