Structural Concrete - Hassoun

48 Chapter 2 Properties of Reinforced Concrete
The modulus of elasticity at 28 days should be calculated as follows:
where
{ √
33000ω
1.5
c f
′
c
E c =
√
0.043ω 1.5
c f
′
c
(in. − lb)
(SI)
ω c = concrete unit weight (kip/ft 3 )orkg/m 3
f c ′ = specified concrete compressive strength at 28 days (ksi or MPa)
(2.120)
Example 2.1 (in.−lb Units)
Calculate the shrinkage strain and creep compliance and coefficient for the concrete specimen given
below. Use the ACI 209R-92 model.
Given factors:
Humidity = 75%
h e = 2V/S = 2A c /u = 3in.
f cm28
= 6556psi
w = 345 lb/yd 3
w/c = 0.46
a/c = 3.73
t = 35 days
t 0 = 28 days
t c = 8days
γ = 146 lb/ft 3
Cement type III
Moist-cured concrete
Solution
Shrinkage Calculation
ε sh (t, t c )=
t − t c
f +(t − t c ) K ss K sh ε shu
ε shu = 780 × 10 −6 in.∕in.
According to Table 2.4, f = 35
V
S = 1.5in.
( ) V
K ss = 1.23 − 0.152 = 1.23 − 0.152(1.5) =1.002
S
For H = 75%,
K sh = 1.40 − 0.01H = 1.40 − 0.01(75) =0.65
t − t
ε sh (t, t c )= c
f +(t − t c ) K ss K sh ε shu
35 − 8
=
35 +(35 − 8) (1.002)(0.65)(780 × 10−6 )= 222.3 × 10 −6 in.∕in.