Civil Engineering Reference
In-Depth Information
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
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
E
I
2
EI
L
6
EI
L
4
EI
L
0
z
z
0
−
z
z
2
2
L
cos sin
sin os
a
a
00 00
00 00
−
a
a
0
0 10 00
[]
=
0
0
0
cos sin
sin os
a
a
0
0
0
0
−
a
a
0
0
0 00 01
Members 1 and 3 have the same orientation. Selecting the bottom end as
the
i
i-end, the rotation is 90°. Table 4.3 contains the local member stiffness
matrix, the rotation matrices,
a
and
a
T
, and the global member stiffness
matrix.
KK
KK
KK
KK
KK
]
=
=
[
]
=
[
11
12
44
43
12
43
21
22
34
33
Member 2 is already in the global system and does not need rotation.
Selecting the left end as the
i
-end, the rotation is 0°. Table 4.4 contains
the local member stiffness matrix, the rotation matrices,
a
and
a
T
, and the
global member stiffness matrix.
KK
KK
]
=
[
22
23
K
23
32
33
