Civil Engineering Reference
In-Depth Information
f
y
/
f
y
as a function of
ρ
and
f
cr
/
f
y
Figure 6.16
Exact solution:
f
cr
/
f
y
=
2.07/413
=
0.005
f
cr
f
y
1
.
4
n
0
.
4
ρ
7
0
.
4
0075
0
005
1
.
4
=
10
3
0
10
−
3
=
=
.
0
.
290
×
.
601
×
0
.
174
0
.
From Figure 6.15 or Equation (6.71)
f
y
f
y
=
0
.
811
Approximate solution according to Belarbi and Hsu's Equation (6.72):
f
y
f
y
=
4
(0
1
005
1
.
5
)
10
3
)(0
10
−
3
)
1
−
.
=
1
−
4(0
.
133
×
.
353
×
0
.
0075
=
1
−
0
.
188
=
0
.
812
very close to the exact value of 0.811.
Answer:
f
y
=
0.812
f
y
=
0.812(413MPa)
=
335 MPa.
6.1.9.3 Smeared Stress-Strain Curve of Mild Steel After Yield
The smeared stress-strain relationship of mild steel bars embedded in concrete is more difficult
to determine after yielding, because the steel strain at the cracked sections increases rapidly
to reach the strain hardening region of the stress-strain curve. The averaging of the steel
strains and the corresponding steel stresses along the length
L
becomes mathematically more
complex. The integration process involved in the averaging requires numerical integration and
the use of an electronic computer.
In order to simplify the averaging process, two assumptions are made by Tamai
et al
.
(1987).
