Civil Engineering Reference
In-Depth Information
Figure 6.7
Propped cantilever, Example 6.1: (a) cantilever loaded at time
t
0
; (b)
member end forces developed between time
t
1
and
t
2
due to the
introduction of support
B
at
t
1
.
increase in de
ection at
B
due to creep. Determine the change in the end
forces at
A
and
B
between time
t
1
and a later time
t
2
. Given data:
fl
φ
(
t
1
,
t
0
)
=
0.9;
φ
(
t
2
,
t
0
)
=
2.6;
φ
(
t
2
,
t
1
)
=
2.45;
χ
(
t
2
,
t
1
)
=
0.8. Ignore the di
ff
erence
between
E
c
(
t
0
) and
E
c
(
t
1
).
The computer program PLANEF is used here, but the results can be
checked by hand computation as discussed in Chapter 5. Table 6.1
shows the input data and the results of Computer run 1, analyzing the
immediate e
ect of the load introduced at time
t
0
. Each of
E
c
(
t
0
),
q
and
l
are considered equal to unity; the support conditions are those of a
cantilever encastré at
A
and free at
B
(Fig. 6.7(a) ); the end forces for a
totally
ff
fi
xed beam subjected to uniform load are entered as the load
input:
{
A
r
(
t
0
)}
=
{0,
−
0.5
ql
,
−
0.0833
ql
2
, 0,
−
0.5
ql
, 0.0833
ql
2
}
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