Civil Engineering Reference
In-Depth Information
The value
f
11
is the sum of the rotations just to the left and to the right
of section 3, caused by
F
1
1. These rotations can be calculated from
the above curvatures, using Equations (C.6) and (C.7), giving
=
25
6
(2 × 0.2710
f
11
=
+
1 × 0.5995)2 × 10
−9
=
9.513 × 10
−9
(N-m)
−1
.
The age-adjusted
fl
exibility coe
cient
f
12
is the rotation at coordinate
1 due to
F
2
=
1. Using a similar procedure as above gives
25
6
f
12
=
(2 × 0.2710) 10
−9
=
2.258 × 10
−9
(N-m)
−1
.
The de
fl
ection at the centre of AB due to
F
1
=
1 (by Equation (C.8) )
(25)
2
96
(10 × 0.2710
+
0.5995) 10
−9
=
21.55 × 10
−9
m/N-m.
The force
F
2
=
ection at the centre of AB.
Because of symmetry, the two redundants are equal and can be
determined by solving one equation:
1 produces no de
fl
(
f
11
+
f
12
)
∆
F
1
=−∆
D
1
Thus,
4750 × 10
−6
(9.513
−
∆
F
1
= ∆
F
2
=
2.258)10
−9
=−
0.404 × 10
6
N-m.
+
The statically indeterminate bending moment diagram developed
during the period
t
0
to
t
is shown in Fig. 4.10(d).
When considering the bending moment due to prestressing, it is a
common practice to consider the e
ect of the forces of the tendon on
the concrete structure or on the concrete plus the non-prestressed steel
when this steel is present. To determine the bending moment at time
t
,
we calculate
ff
∆
σ
ps
(the prestress loss) in each tendon by Equation (2.48).
The summation
A
ps
∆
σ
ps
y
ps
) performed for all the tendons at any
section gives the change in the bending moment of the released struc-
ture due to the prestress loss; where
A
ps
is the cross-section area of a
Σ
(
−
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