Civil Engineering Reference
In-Depth Information
The resulting stiffness matrix is shown in Equation 5.3 with only the
affected terms replaced with the new values.
k
0
0 000 0
k
0
0
0
0
11
,
17
,
0
k
0 00 0
k
k
0
0
0
k
22
,
26
,
28
,
212
,
00
3
EI
L
00000
3
EI
L
−
3
EI
L
∆
∆
∆
P
P
P
M
M
M
P
P
P
M
M
M
y
y
y
−
0
0
ix
ix
3
3
2
iy
iy
00 0
k
0 000
0
k
0
0
44
,
410
,
iz
iz
0
0
0 00000 0
0
0
0
q
q
q
ix
iy
ix
iy
0
k
0 00
k
0
k
0
0
0
k
62
,
66
,
68
,
612
,
k
0
0 000 0
k
0
0
0
0
iz
iz
=
71
,
77
,
∆
∆
∆
0
k
0 00 0
k
k
0
0
0
k
jx
jy
jx
jy
82
,
86
,
88
,
812
,
3
EI
L
00000
3
EI
L
3
EI
L
y
y
y
0
0
−
0
0
3
3
2
jz
jz
q
q
q
00 0
k
0 000
0
k
0
0
jx
jx
10 4
,
1010
,
00
3
EI
L
000000
3
EI
L
3
EI
L
jy
jz
jy
jz
y
y
y
−
0
0
2
2
0
k
0 00 0
k
k
0
0
0
k
12 2
,
126
,
12 8
,
1212
,
(5.3)
The member stiffness for releasing ∆
jz
and
q
jy
can be derived in a sim-
ilar manner to ∆
iz
and
q
iy
. The resulting stiffness matrices are shown in
Equations 5.4 and 5.5 with only the affected terms replaced with the new
values.
k
00000 00000
0 0 00 0 0 00
000 000000 000
000
k
11
,
17
,
∆
∆
∆
P
P
P
M
M
M
P
P
P
M
M
M
k
k
k
k
ix
iy
22
,
26
,
28
,
212
,
ix
iy
k
00000
k
0
0
iz
iz
44
,
410
,
q
q
q
EI
L
EI
L
ix
y
y
ix
0000 00000
−
0
iy
iz
iy
iz
0
k
0 00 0
k
k
0 00
k
62
,
66
,
68
,
6
12
=
∆
∆
∆
k
00000 00000
0 0 00 0 0 00
000 0000000 0
k
71
,
77
,
jx
jx
k
k
k
k
82
,
86
,
88
,
812
,
jy
jz
jy
jz
0
000
k
0 0000 00
k
q
q
q
10 4
,
1010
,
jx
jx
EI
L
EI
L
y
y
jy
0000 00000
−
0
jy
jz
jz
0
k
0 00 0
k
k
00 0
k
(5.4)
12 2
,
126
,
12 8
,
1212
,
