Civil Engineering Reference
In-Depth Information
f
y
/
f
y
and
E
p
/
E
p
as a function of
f
y
/
f
y
Figure 6.21
E
p
/
E
p
are plotted against
f
y
/
f
y
in Figure 6.21. The test data are closely represented by two
straight lines as follows:
f
y
f
y
f
y
f
y
=
0
.
43
+
0
.
5
(6.83)
f
y
f
y
E
p
E
p
=
3
.
3
−
2
.
5
(6.84)
The plastic modulus
E
p
in Equation (6.84) is the slope of the strain-hardening region of the
bare mild steel bars, and is assumed to be 0.025
E
s
.
A simple bilinear model of the smeared stress-strain relationship of mild steel embedded
in concrete can now be derived. First, substituting
f
y
/
f
y
from Equation (6.72) into (6.83)
and (6.84); and second, inserting
f
o
,
f
y
, and
E
p
from Equations (6.82)-(6.84) into (6.80)
and (6.81) and rounding up the term
f
o
. These two steps result in two simple straight lines
given by:
ε
s
≤
ε
y
f
s
=
E
s
¯
ε
s
when ¯
(6.85)
ε
s
>ε
y
f
s
=
(0
.
91
−
2B)
f
y
+
(0
.
02
+
0
.
25B)
E
s
¯
ε
s
when ¯
(6.86)
where
ε
y
=
f
y
/
f
y
=
E
s
(0
.
93
−
2B)
f
y
(6.87)
f
cr
f
y
1
.
5
31
f
c
(MPa) and
1
ρ
B
=
f
cr
=
0
.
ρ
≥
0
.
15%
(6.88)
