Civil Engineering Reference
In-Depth Information
Figure 6.18
Belarbi's stress distribution along a reinforcing bar after cracking
6.1.9.4 Bilinear Model for Smeared Stress-Strain Curve
As shown in Figure 6.19(a) and (b), the shape of the average stress-strain curve of mild steel
resembles two straight lines. These two straight lines will have a slope of
E
s
before yielding
and a slope of
E
p
after yielding, as illustrated in Figure 6.20. The plastic modulus
E
p
after
yielding is only a small fraction of the elastic modulus
E
s
before yielding. The stress level
at which the two straight lines intersect is designated as the smeared yield stress
f
y
.The
equations of these two lines are then given as follows:
f
y
f
s
=
E
s
¯
ε
s
when
f
s
≤
(6.80)
f
o
+
E
p
¯
f
y
f
s
=
ε
s
when
f
s
>
(6.81)
where
f
o
is the vertical intercept of the post-yield straight line. This vertical intercept
f
o
can
be calculated by
E
p
E
s
−
f
o
=
f
y
(6.82)
E
s
It should be noted that
f
y
is quite different from
f
y
. The symbol
f
y
is the smeared yield
stress of the bilinear model shown in Figure 6.20, while the symbol
f
y
is the smeared yield
stress derived from the theoretical model explained in Section 6.1.9.2. The smeared yield stress
f
y
and the plastic modulus
E
p
are determined to best approximate the smeared yield stress
f
y
(Section 6.1.9.2) as well as the post-yield smeared stress-strain curve (Section 6.1.9.3). The
lower the
f
y
, the lower the
f
y
, and the higher the
E
p
. The nondimensional ratios
f
y
/
f
y
and
