Civil Engineering Reference
In-Depth Information
A system of forces representing the prestress loss is applied on the
released structure in Fig. 4.5(h) and the corresponding bending
moment is shown in Fig. 4.5(i). The displacement at coordinate 1 due to
prestress loss is
1
(
E
c
)
AD
I
c
D
1
(
E
c
)
DC
I
c
C
(
∆
D
1
)
prestress loss
=
M
i
M
u1
d
l
+
M
i
M
u1
d
l
A
D
where
M
i
is the bending moment shown in part (i) of Fig. 4.5.
The values of the two integrals in this equation are separately
indicated in the following:
1
0.45
E
c
(
t
0
)
−0.06 × 10
−3
ql
3
1
0.34
E
c
(
t
0
)
+
(
∆
D
1
)
prestress loss
=
I
c
2.4×10
−3
ql
3
I
c
ql
3
E
c
(
t
0
)
I
c
= 7.0×10
−3
ql
3
E
c
(
t
0
)
I
c
=
34.7 × 10
−3
ql
3
E
c
(
t
0
)
I
c
7.0)10
−3
∆
D
1
=
(27.7
+
.
The age-adjusted
fl
exibility coe
cient
1
(
E
c
)
AD
I
c
D
A
M
2
u1
d
l
1
(
E
c
)
DC
I
c
C
D
M
u1
d
l
2.51
l
E
c
(
t
0
)
I
c
f
11
=
+
=
.
Substitution in Equation (4.5) and solving for the redundant value,
34.7
2.51
×10
−3
ql
2
∆
F
1
=−
=−
13.8 × 10
−3
ql
2
.
The bending moment diagram at time
t
2
shown in Fig. 4.5(j) is
obtained by superposition of
F
1
times
M
u1
,
M
c
,
M
e
and
M
i
. The two
broken curves shown in Fig. 4.5(j) are approximate bending moment
diagrams obtained as follows: (a) considering the construction stages
but ignoring creep; (b) ignoring the construction stages and creep; thus
applying the dead load and 0.85 the prestress forces directly on a
continuous beam.
Figure 4.5(j) indicates that the bending moment diagram for a
structure built in stages is gradually modi
∆
fi
ed by creep to approach the
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