Civil Engineering Reference
In-Depth Information
the change in displacement of the released structure during the time
t
0
to
t
:
74.6
283.4
25.3
25.3
261.3
25.3
25
6
[021]
25
6
[120]
∆
D
1
=
10
−6
+
10
−6
=
4750 × 10
−6
radian.
Use of Equation (C.8) and the curvature values
ψ
(
t
0
) from Table 4.1
gives the instantaneous de
fl
ection at middle of span AB as
41.0
53.2
19.1
(25)
2
96
[1
10
1]
10
−6
=
3.85 × 10
−3
m
=
3.85 mm
(0.152 in).
The change in de
fl
ection of the released structure during the period
t
0
to
t
(using
∆
ψ
values from Table 4.2 and Equation (C.8) ) is
74.6
283.4
25.3
(25)
2
96
[1
10
1]
10
−6
=
19.10 × 10
−3
m
=
19.1 mm
(0.752 in).
1
at coordinate 1; the diagram of the corresponding bending moment
M
u1
i
s
shown in Fig. 4.10(c). Division of the ordinates of this diagram by
E
ref
¯
centroid
at sections 1 to 4 gives the curvatures due to
F
1
For calculation of the age-adjusted
fl
exibility coe
cient, apply
F
1
=
1.
¯
centroid
is
the moment of inertia of the age-adjusted transformed section about an
axis through the centroid:
=
B
2
A
¯
centroid
=
¯
−
The values of the curvatures due to
F
1
=
1, calculated in this fashion
at the four sections considered, are:
{
ψ
u1
}
=
10
−9
{0, 0.2710, 0.5995, 0.2710} m
−1
/N-m.
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