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TABLE 4.3
Transfer Matrix for a Beam Element, Part b:
λ =
0,
λ ζη =
0
λ>
0,
λ ζη>
0
1
4
2 ,
5.
λ ζη<
η)
1. λ<
1
4
2
1
4
2
0
2.
ζ = η =
0
3.
η =
0,
ζ =
0
4.
λ ζη =
η)
ζ η =
0
6.
λ ζη>
η)
ζ η
4
1
g
1
g
e 0
(
a 3 C
b 3 D
)
0
ζ
B
(
3 C
+
A
)
(
b 3 D
a 3 C
)
ζη)
e 4 η)
e 2
p
g
b 2
a 2
2 ab
1
g
1
2
e 1
(
a 2 A
+
b 2 B
)
1
A
(
2 A
B
)
(
b 2 B
a 2 A
)
AB
CD
p
g
1
g
1
2
1
2 ab
e 2
(
aC
+
bD
)
B
(
C
+
A
)
(
bD
aC
)
(
aAD
+
bBC
)
2
2
1
g
1
ζ (
C
2
1
g
1
2 ab CD
e 3
(
A
B
)
1
A
)
(
A
B
)
g a
b
A b
a
3
6
1
D
1
ζ (
1
η) (
1
g
C
a
D
b
1
BC
e 4
B
)
C
A
)
(
)
a 2
b 2
2
(
+
)
g a 2 +
b 2
2
2
e 3
g b 2
a 2 +
4
24
p
λ ζη ζ η
1
e 1
1
B
1
a 2 b 2
1
ζ
2
η)
A
1
a 2 b 2
e 5
(
2 A
B
+
2
)
e 3
2
λ ζη
g a 3 +
b 3
e 4
g b 3
a 3 +
5
120
3
6
1
D
a 2 b 2
1
ζ
2
η)
p
C
a 2 b 2
λ ζη ζ η
e 2
e 6
(
3 C
+
A
+
2
)
e 4
2
λ ζη
This case may appear to be of little practical value, but it is retained for later use with dynamics problems.
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