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k3ex
0
0
0
0
0
0
0
0
0
0
k3
k3
0
0
k3
k3
Add matrices
K k1ex k2ex k3ex
yields
= K
4 10⁶
4 10⁶
0
0
4 10⁶
8 10⁶
4 10⁶
0
0
4 10⁶
8 10⁶
4 10⁶
0
0
4 10⁶
4 10⁶
Force Matrix
F
F1x
4000
10000
F4x
.
. 4 10⁶
. 4 10⁶
0
0
. 4 10⁶
. 8 10⁶
. 4 10⁶
0
0
. 4 10⁶
. 8 10⁶
. 4 10⁶
0
0
. 4 10⁶
. 4 10⁶
d1x
d2x
d3x
d4x
F1x
4000
10000
F4x
Boundary Conditions
d1x 0 d4x 0
Therefore the stiffness matrix reduces to 2 by 2 since the first and second columns and rows
are removed
. . 8 10⁶
. 4 10⁶
. 4 10⁶
. 8 10⁶
d2x
d3x
4000
10000
d2x
d3x . . 8 10⁶
. 4 10⁶
. 4 10⁶
. 8 10⁶
1 4000
10000
yields
Negative displacements = d2x
d3x
1.66667 10⁴
0.00133

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