Civil Engineering Reference
In-Depth Information
AE
L
AE
L
0
0
−
0
0
12
EI
L
6
EI
12
EI
L
6
EI
L
0
z
z
0
−
z
z
3
2
3
2
L
6
EI
L
4
EI
L
6
EI
L
2
EI
L
0
z
z
0
−
z
z
2
2
[
]
=
K
m
AE
L
AE
L
−
0
0
0
0
12
EI
L
6
EI
L
12
EI
L
6
EI
L
0
−
z
−
z
0
z
−
z
3
2
3
2
6
EI
L
2
EI
L
6
EI
L
4
EI
L
0
z
z
0
−
z
z
2
2
cos sin
sin os
αα
αα
00 00
00 00
−
0
0 10 00
[]
=
a
0
0
0
cos sin
sin os
αα
αα
0
0
0
0
−
0
0
0 00 01
Members 1, 4, and 5 are already in the global system and do not need
rotation. Selecting the left end as the
i
-end, the rotation is 0°. Tables 5.3
through 5.5 contain the local member stiffness matrices, the rotations
matrices,
a
and
a
T
, and the global member stiffness matrices.
KK
KK
]
=
[
22
21
K
21
12
11
KK
KK
]
=
[
44
42
K
42
24
22
KK
KK
]
=
[
55
53
K
53
35
33
Member 3 is vertical and selecting the bottom end as the
i
-end, the rotation
is 90°. Table 5.6 contains the local member stiffness matrix, the rotations
matrices,
a
and
a
T
, and the global member stiffness matrix.
KK
KK
]
=
[
33
32
K
32
23
22
