Civil Engineering Reference
In-Depth Information
9.2.2 Material Models Developed at UH
9.2.2.1 SteelZ01
The steel module SteelZ01 needed in the CSMM incorporates both the envelope and the
unloading/reloading pattern of uniaxial constitutive relationships of embedded mild steel
(Figure 9.5). The equations for the envelope are given as Equations (9.7)-(9.11). The nonlinear
unloading and reloading paths are described in Equations (9.12)-(9.15).
¯
y
(Stage 1)
f
s
=
E
s
¯
ε
s
,
ε
s
≤
ε
,
(9.7)
f
y
(
0
0
¯
y
(9.8)
ε
s
ε
y
25
B
¯
f
s
=
.
−
2
B
)
+
.
+
.
,
ε
s
>ε
(Stage 2T)
91
02
0
f
cr
f
y
1
.
5
31
f
c
(MPa)
1
ρ
where
B
=
f
cr
=
0
.
and
ρ
≥
0
.
15%
(9.9)
ε
y
=
ε
y
(0
.
−
93
2
B
)
(9.10)
(Stage 2C)
f
s
=−
f
y
(9.11)
1
1
A
−
R
R
−
f
s
−
f
i
f
s
−
f
i
(Stage 3 and Stage 4)
ε
s
−
¯
¯
ε
si
=
+
(9.12)
E
s
f
y
where:
9
k
−
0
.
1
p
A
=
1
.
(9.13)
10
k
−
0
.
2
p
R
=
(9.14)
ε
p
ε
¯
k
p
=
(9.15)
y
ε
p
=
smeared uniaxial plastic strain of rebars
Because the strains are expressed in terms of the stresses in Equation (9.12), iteration
would be needed to calculate a stress based on a given strain. To bypass this iteration, a
multilinear simplification was proposed by Jeng (2002) to approximate the nonlinear curves
using straight-line segments.
In Figure 9.5, the dashed curves are the unloading and reloading paths defined by the
CSMM, and the solid curves are the linear simplifications implemented in SteelZ01. Two
turning points, (
¯
ε
m
1
,
f
m
1
) and (
ε
m
2
,
f
m
2
) in Figure 9.5, are selected as the points at which
ε
m
2
are calculated by substituting
f
m
1
and
f
m
2
into
f
s
of Equation (9.12), respectively. Once the turning points are determined, the stress of the
point on the line segments is a linear function of the strains and stresses of the turning points
f
m
1
=±
0
.
65
f
y
and
f
m
2
=
0, and
ε
m
1
and
