Civil Engineering Reference
In-Depth Information
The envelopes of the ConcreteL01 model in tension and compression are similar to those
of the concrete constitutive model in CSMM for reinforced concrete. Only the compression
envelope prior to the peak stress is changed in this module to keep the initial slope of the
compressive stress-strain envelope lower than 2
f
c
ε
0
. The equations defining the envelopes
are expressed as below.
c
1
E
c
¯
Stage UC :
σ
=
ε
1
+
σ
ci
,
ε
1
≤
¯
(¯
ε
cx
−
ε
ci
)
¯
(9.18)
c
1
E
c
(¯
Stage T1 :
σ
=
ε
1
+
ε
ci
−
¯
ε
cx
)
¯
,
(¯
ε
cx
−
ε
ci
)
¯
<
¯
ε
1
≤
(
ε
cr
−
ε
ci
)
¯
(9.19)
f
cr
ε
cr
¯
0
.
5
c
1
σ
=
,
ε
1
>
ε
cr
−
ε
ci
)
Stage T2 :
¯
(
¯
(9.20)
ε
1
+
ε
ci
¯
3875
f
c
(MPa)
31
f
c
(MPa)
E
c
=
,
f
cr
=
0
.
,ε
cr
=
0
.
00008
2
¯
2
¯
kDf
c
ε
0
ε
2
ζε
0
ε
2
ζε
0
ε
2
ζε
0
≤
¯
c
2
f
c
Stage C1 :
σ
=
D
ζ
−
≤
ε
2
,
¯
1
(9.21)
⎡
2
⎤
⎦
,
¯
ε
2
ζε
0
−
1
ε
2
ζε
0
>
¯
⎣
1
c
2
f
c
σ
=
ζ
−
4
ζ
−
Stage C2 :
D
1
(9.22)
1
f
f
c
f
(¯
ζ
=
ε
1
)
f
(
β
)
W
p
≤
0
.
9
(9.23)
f
f
c
=
8
f
c
≤
5
.
9(
f
c
in MPa)
0
.
(9.24)
1
f
(¯
ε
1
)
=
√
1
(9.25)
+
400¯
ε
1
|
β
|
24
◦
f
(
β
)
=
1
−
(9.26)
+
|
β
|
(0
.
09
|
β
| −
1)
W
p
=
1
.
15
(9.27)
6
2
tan
−
1
γ
12
1
β
=
(9.28)
(
ε
1
−
ε
2
)
where:
where
σ
c
1
=
smeared (average) concrete stress in the 1
−
direction
c
σ
2
=
smeared (average) concrete stress in the 2
−
direction
σ
ci
=
initial compressive stress in concrete due to prestress force
¯
ε
1
=
uniaxial smeared (average) principal strain in the 1
−
direction
