Civil Engineering Reference
In-Depth Information
T
12
EI
L
6
EI
L
12
EI
L
6
EI
L
y
y
y
y
−
−
−
3
2
3
2
T
=
KK
=
=
ij
ji
6
EI
L
2
EI
L
6
EI
L
2
EI
L
y
y
y
y
−
2
2
12
EI
L
6
EI
y
y
−
−
3
2
L
=
K
(4.21)
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
12
EI
L
6
EI
L
12
EI
6
EI
L
y
y
y
y
−
−
−
−
10
1
−
−−
10
1
=−
3
2
3
2
L
K
=
jj
L
6
EI
L
2
EI
L
L
6
EI
L
2
EI
L
y
y
y
y
2
2
12
EI
L
6
EI
L
y
y
3
2
=
K
(4.22)
jj
6
EI
4
EI
L
y
y
2
L
Adding the axial stiffness terms that are derived in most strength of mate-
rials textbooks, the entire coplanar X-Z frame stiffness matrix can be
found.
AE
L
AE
L
AE
L
AE
L
x
P
=
∆
ix
ix
P
=−
x
∆
jx
ix
P
=−
x
∆
ix
jx
P
=
x
∆
jx
jx
