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FIGURE P4.4
Answer:
α
−
α
−
αα
1
k
i
=
where
α
=
1
/
EA
1
+
2
/
EA
2
4.5 Show that the stiffness and flexibility matrices associated with the DOF of the spring
chain shown in Fig. P4.5 are given by
.
.
.
k
1
+
k
2
−
k
2
0
0
.
.
.
.
−
+
−
k
2
k
2
k
3
k
3
.
.
.
.
0
−
k
3
k
3
+
k
4
.
.
.
.
0
0
−
k
4
.
.
.
.
.
k
=
0
0
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
−
k
n
−
1
k
n
+
k
n
−
1
−
k
n
.
.
0
0
0
−
k
n
k
n
α
1
α
α
i
2
··· ···
1
1
k
j
f
=
Symmetric
α
=
i
··· ···
α
j
=
1
α
··············· ···
α
1
2
n
FIGURE P4.5
x
2
2
4.6 Suppose the moment of inertia of a beam element varies as
I
(
x
)
=
I
0
(
1
+
/
)
. Use
the approximate series method to find the stiffness matrix.
Answer:
If the third order Hermitian interpolation polynomials of Fig. 4.8 are
used,
16
.
8
−
7
.
4
−
16
.
8
−
9
.
4
EI
0
4
.
533
7
.
42
.
867
k
i
=
16
.
89
.
4
3
Symmetric
6
.
533
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