Civil Engineering Reference
In-Depth Information
From statics equilibrium, the forces at the
i
i-end transmitted to the
j
-end
plus the forces at the j-end are equal to zero. The forces at the
j
-end due to
motions at the
i
-end are denoted as stiffness matrix [
K
ji
].
[]
[
+
=
TK K
0
ii
ji
=−
[]
[]
K
T K
ji
ii
12
I
L
E
6
EI
L
12
EI
L
6
EI
z
z
z
z
10
1
−
10
1
3
2
3
L
2
K
=−
−
=
ji
L
6
EI
L
4
EI
L
L
−
6
EI
L
4
EI
L
z
z
z
z
2
2
12
EI
L
6
EI
L
−
z
−
z
3
2
K
=
(4.29)
ji
6
EI
L
2
EI
z
z
2
L
For a prismatic member it can be shown that the stiffness matrix is sym-
metrical about the main diagonal. This results in stiffness [
K
ij
] being equal
to the transpose of [
K
ji
], where the forces at the
j
-end due to motions at the
i
-end are denoted as stiffness matrix [
K
ji
].
T
12
EI
L
6
EI
L
12
EI
L
6
EI
L
z
z
z
z
−
−
−
3
2
3
2
T
=
KK
=
=
ij
ji
6
EI
L
2
EI
L
6
EI
L
2
EI
L
z
z
−
z
z
2
2
12
EI
L
6
EI
y
y
−
3
2
L
=
K
(4.30)
ij
6
EI
L
2
EI
L
y
y
−
2
From statics equilibrium, the forces at the
i
i-end transmitted to the
j
-end
plus the forces at the
j
-end are equal to zero. The forces at the
j
-end due to
motions at the
j
-end are denoted as stiffness matrix [
K
jj
].
[]
+
=
TK K
0
ij
jj
=−
[]
K
T K
jj
ij
