Civil Engineering Reference
In-Depth Information
The tensile strain
ε
r
can now be checked:
Equation
15
ε
r
=
0
.
00630
+
0
.
01334
+
0
.
0004
=
0
.
02004
≈
0
.
0200 OK
The angle
α
r
, the shear stress
τ
t
and the shear strain
γ
t
are:
ε
t
−
ε
d
ε
−
ε
d
=
0
.
01335
+
0
.
0002
Equation
16
tan
2
α
r
=
0002
=
2
.
085
0
.
00630
+
0
.
tan
α
r
=
1
.
444
2
◦
4
◦
α
r
=
55
.
2
α
r
=
110
.
Equation 3
τ
t
=
(
−
σ
d
)sin
α
r
cos
α
r
=
(9
.
92)(0
.
821)(0
.
571)
=
4
.
65 MPa
γ
t
2
=
Equation 6
(
ε
r
−
ε
d
)sin
α
r
cos
α
r
=
(0
.
0200
+
0
.
0004)(0
.
821)(0
.
571)
=
0
.
00955
The stresses in the mild steel and prestressing steel can be calculated from the strains using
the stress-strain relationships:
Equation 9
b
f
l
=
413 MPa
Equation 10
b
f
t
=
413 MPa
Equation 11
b
f
p
=
1726 MPa
f
tp
=
Equation 12
a
0
The Mohr circles for stresses on the concrete element, in the steel grid, and on the PC
element, as well as the Mohr circle for strains, are all plotted in Figure 5.19 for the selected
strain of
ε
d
=−
0.0004. In order to plot these Mohr circles, the following additional stresses
are calculated:
ρ
f
+
ρ
p
f
p
=
0
.
012 (413)
+
0
.
003 (1726)
=
10
.
13 MPa
ρ
t
f
t
=
0
.
012 (413)
=
4
.
96 MPa
σ
−
ρ
f
−
ρ
p
f
p
=
3
.
44
−
10
.
13
=−
6
.
69 MPa
σ
t
−
ρ
t
f
t
=
1
.
72
−
4
.
96
=−
3
.
24 MPa
σ
−
σ
t
2
2
σ
+
σ
t
2
2
t
σ
1
=
+
+
τ
3
2
3
.
44
+
1
.
72
.
44
−
1
.
72
=
+
+
4
.
63
2
2
2
=
2
.
58
+
4
.
71
=
7
.
29 MPa
σ
2
=
2
.
58
−
4
.
71
=−
2
.
13 MPa
In addition to the strains
ε
d
=−
0.0002 and
−
0.0004 selected above, calculations were made
for the strains
ε
d
=−
0.0003 and
−
0.0005. The results of all these calculations are recorded
in Table 5.2. Using the
γ
t
values given in Table 5.2, the shear stress vs. shear strain
curve are plotted in Figure 5.20.
τ
t
and
