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FIGURE P5.55
Frame response.
5.56 Perform a flexibility method analysis of the beam shown in Fig. P5.56.
FIGURE P5.56
A continuous beam.
5.57 Repeat Problem 5.56 with the rigid support at node
b
replaced by a spring of
constant
k
.
5.58 Repeat Problem 5.56, but let the support at node
b
settle
b
.
5.59 Use the force method to solve the beam problem of Example 5.8 with the internal
moments at
b
and
c
chosen as the two redundants.
Hint:
Use
v
i
R
=
f
i
p
i
R
, where
f
i
is from Chapter 4. Set up unassembled matrices
f
and
p
T
[
M
a
=
M
b
M
b
M
c
M
c
M
d
=
0]
T
. Choose
M
b
and
M
c
=
0
as redundants.
M
c
]
T
and
P
x
=
[
M
b
M
c
]
T
[
M
b
M
c
]
T
In
p
=
b
0
P
+
b
1
P
x
,
P
=
[
M
b
.
Setting
P
x
=
=
0]
T
[0
is equivalent to adding hinges at
b
and
c
.
Then
001000
000010
T
b
0
=
01
T
1000
0001
−
b
1
=
−
10
5.60 Solve the continuous beam problem of Example 5.8 using the reactions at
a
and
d
as
redundants.
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