Civil Engineering Reference
In-Depth Information
Figure 6.14
Stress-strain curve of mild steel
6.1.9.2 Smeared Yield Stress of Mild Steel
f
y
Inserting ¯
1
ε
1
=
f
s
/
E
s
from Equation (6.62) into (6.55) and, in turn, substituting
σ
=
σ
c
from
Equation (6.55) into Equation (6.65) gives:
E
s
ε
cr
f
s
0
.
4
f
cr
ρ
f
so
−
f
s
=
(6.69)
Equation (6.69) states that the difference between the steel stress at the crack
f
so
and the
smeared steel stress
f
s
, i.e.
f
so
−
f
s
, depends on the parameter on the right-hand side of the
equation.
Yielding of a reinforced concrete panel occurs when the steel stress at the cracked section
reaches the yield plateau, i.e.
f
so
=
f
y
. At the same time, the smeared steel stress reaches a
level which we shall call the 'smeared yield stress of steel' (
f
y
), i.e.
f
s
f
y
. Substituting
=
f
y
f
so
=
f
y
and
f
s
=
into Equation (6.69), dividing by
f
y
, then multiplying both sides of the
equation by (
f
y
/
f
y
)
0
.
4
, result in:
f
y
f
y
0
.
4
f
y
f
y
1
.
4
E
s
ε
cr
f
y
0
.
4
f
cr
ρ
−
=
(6.70)
f
y
Using the relationships
ε
cr
=
f
cr
/
E
c
and the modulus ratio
n
=
E
s
/
E
c
, Equation (6.70)
becomes
f
y
f
y
0
.
4
f
y
f
y
1
.
4
f
cr
f
y
1
.
4
n
0
.
4
ρ
−
=
(6.71)
