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Force Matrix
F
F1x
F2x
0
P
.
k1
0
k1
0
0
k3
0
k3
k1
0
k1 k2
k2
0
k3
k2
k2 k3
d1x
d2x
d3x
d4x
F1x
F2x
0
P
Boundary Conditions:
d1x 0 d2x 0
The boundary conditions reduces the matrix to a 2 by 2 matrix since the first and second
columns and rows are removed.
. k1 k2
k2
k2
k2 k3
d3x
d4x
0
P
d3x
d4x . k1 k2
k2
k2
k2 k3
1 0
P
yields
d3x
d4x . . 1
( ) . k1 k2 . k1 k3 . k2 k3
k2 k3
k2
k2
k1 k2
0
P
yields
positive displacements d3x
d4x
. k2
( ) . k1 k2 . k1 k3 . k2 k3 P
. ( ) k1 k2
( ) . k1 k2 . k1 k3 . k2 k3 P

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