Civil Engineering Reference
In-Depth Information
caused by consolidation of clays, occurs over an in
nite period of time. How-
ever, it is reasonable to consider for the analysis of forces that the full settle-
ment occurs between ages
t
0
and
t
1
, with the period (
t
1
,
t
0
) representing the
time necessary for the major part (say 95 per cent) of the consolidation to
occur. With settlement due to consolidation of soil, the transition between
the ascending and descending parts of curve B, Fig. 4.6(b) would be smooth
as shown by the continuous line.
fi
Example 4.5 Two-span continuous beam: settlement of central
support
The continuous concrete beam shown in Fig. 4.6(a) is subjected to a
downwards settlement at B. Find the time variation of the force
F
and
the reaction at the central support. Express
F
in terms of
F
sudden
the
value of the instantaneous reaction when the settlement
δ
is suddenly
introduced. Consider two cases:
(a)
δ
introduced suddenly at
t
0
=
14 days and maintained constant to
t
2
10 000 days.
(b) Settlement introduced gradually from zero at
t
0
=
=
14 days to a value
δ
at
t
1
=
104 days maintained constant thereafter up to
t
2
=
10 000
days.
Use the following creep and aging coe
cients
t
i
t
j
(
tj
,
ti
)
(
tj
,
ti
)
14
14
14
14
23
23
23
23
104
104
104
104
500
2000
10000
104
500
2000
10000
500
2000
10000
1.14
1.79
2.26
2.57
1.01
1.72
2.20
2.55
1.17
1.70
1.96
0.79
0.76
0.76
0.76
0.81
0.80
0.79
The value
t
e
=
23 days is obtained by trial such that Equation (4.9) is
satis
1.077.
Use of Equation (4.10) with
t
0
fi
ed. The ratio
E
c
(
t
1
)/
E
c
(
t
e
)
=
104, 500, 2000, and 10 000
gives the values of
F
(
t
) which are plotted in Fig. 4.7, curve A.
=
14 and
t
=
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