Civil Engineering Reference
In-Depth Information
12
EI
L
6
EI
L
12
EI
6
EI
L
y
y
y
y
−
−
10
1
−
10
1
3
2
L
3
2
=−
−
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
z
z
−
3
2
=
K
(4.31)
jj
6
EI
L
4
EI
L
−
z
z
2
If we add the axial stiffness terms that were shown in the previous section,
the entire coplanar X-Y frame stiffness matrix can be found.
AE
L
AE
L
x
x
0
0
−
0
0
12
EI
L
6
EI
L
12
EI
L
6
EI
L
0
z
z
0
−
z
z
∆
x
P
P
M
P
P
M
3
2
3
2
i
ix
∆
6
EI
L
4
EI
L
6
E
I
2
EI
L
iy
iy
0
z
z
0
−
z
z
q
2
2
L
iz
iz
=
AE
L
AE
L
∆
∆
jx
−
x
0
0
x
0
0
jx
jy
jy
12
EI
L
6
EI
L
12
EI
L
6
EI
L
q
0
−
z
−
z
0
z
−
z
jz
jz
3
2
3
2
6
EI
2
EI
L
6
EI
L
4
EI
L
0
z
z
0
−
z
z
L
2
2
(4.32)
4.12
ELAStic MEMbER StiffnESS, 3-D SYStEM
By combining Equations 4.23 and 4.32 and adding the torsional stiffness
terms that are derived in most strength of materials textbooks, we can
construct the elastic member stiffness in the three-dimensional (3-D) sys-
tem Cartesian coordinate system. This will include axial and torsional
stiffness, as well as bending about each orthogonal axes of the member
cross-section.
IG
L
x
M
=
q
ix
ix
