Civil Engineering Reference
In-Depth Information
¯
A
=
1483 in
2
;
B
=
28 950 in
3
;
=
874 600 in
4
.
M
}
restrained
in
Equation (2.19) gives the changes in strain in the period
t
0
to
t
:
Substitution of these three values,
E
c
and {
−∆
N
,
−∆
∆
ε
O
(
t
,
t
0
)
=−
716×10
−6
;
∆
ψ
(
t
,
t
0
)
=
12.03 × 10
−6
in
−1
.
Substitution of these two values in Equation (2.17) and addition of
{
∆
σ
restrained
} gives the changes in stress in the period
t
0
to
t
:
{
∆
σ
(
t
,
t
0
)}
top, bot
=
{0.047, 0.485} ksi.
Addition of these two stress values to the stresses determined in step
1 gives the stresses at time
t
:
{
∆
σ
(
t
)}
top, bot
=
{
−
0.506, 0.013} ksi.
The strain and stress distributions at
t
0
and
t
are shown in Fig. 2.15.
Example 2.7 Bridge section: steel box and post-tensioned slab
Figure 2.16 shows the cross-section of a simply supported bridge of
span 144 ft (43.9 m). The deck is made out of precast rectangular seg-
ments assembled in their
nal position, above a structural steel U-
shaped section, by straight longitudinal post-tensioned tendons. Each
precast segment covers the full width of the bridge. In the longitudinal
direction, each segments covers a fraction of the span. At completion
of installation of the precast elements, the structural steel section
carries, without shoring, a uniform load
fi
5.4 kip/ft (79 kN/m), repre-
senting the weight of concrete and structural steel. Shortly after
prestressing, the bridge section is made composite by connecting the
deck slab to the structural steel section. This is achieved by the casting
of concrete to
=
ll holes in the precast deck at the locations of pro-
truding steel studs welded to the top
fi
anges of the structural steel
section. Determine the strain and stress distributions in concrete and
structural steel at the mid-span section at time
t
0
, shortly after prestress-
ing and at time
t
after occurrence of creep, shrinkage and relaxation.
Consider that the post-tensioning and the connection of concrete to
fl
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