Civil Engineering Reference
In-Depth Information
Table 4.6
Displacement Correspondence
Global
Element 1
Element 2
1
1
0
2
2
0
3
3
0
4
4
1
5
5
2
6
6
3
7
0
4
8
0
5
9
0
6
Table 4.7
System Stiffness Matrix
1,250
.
4
0
−
12,504
1,250
.
4
0
−
12,504
0
0
0
−
500,000
0
500,000
0
0
0
0
0
0
−
12,504
0
166,720
12,504
0
833,360
0
0
0
1,250
.
4
0
12,504
501,250
.
4
0
12,504
−
500,000
0
0
[
K
]
=
0
−
500,000
0
0
501,250
.
4
12,504
0
−
1,250
.
4
12,504
−
12,504
0
83,360
12,504
12,504
333,440
0
−
12,504
83,360
0
0
0
−
500,000
0
0
500,000
0
0
0
0
0
0
−
1,250
.
4
−
12,504
0
1,250
.
4
−
12,504
0
0
0
0
12,504
83,360
0
−
12,504
166,720
Using the system stiffness matrix, the assembled system equations are
U
1
U
2
U
3
U
4
U
5
U
6
U
7
U
8
U
9
R
X
1
R
Y
1
M
R
1
0
−
100
−
333
.
3
R
X
3
R
Y
3
−
100
M
R
3
+
333
.
3
[
K
]
=
where we denote the forces at nodes 1 and 3 as reaction components, owing to the dis-
placement constraints
U
1
=
U
2
=
U
3
=
U
7
=
U
8
=
U
9
=
0
. Taking the constraints into
account, the equations to be solved for the active displacements are then
=
501,250
.
4
0
12,504
U
4
U
5
U
6
0
−
100
−
16
.
7
0
501,250
.
4
12,504
12,504
12,504
333,440
