Civil Engineering Reference
In-Depth Information
=−
[]
K
T K
jj
ij
S S LS
SL SSLSLS
D
−
−
−−
10
1
−
SSSL
SSLS
−
1
1
1
1
2
1
2
1
=
K
=
jj
2
L
−
D
−
−
2
+
2
2
3
1
2
1
2
3
P
M
∆
q
S S LS
SL SSLSLS
−
1
jz
jz
1
1
2
=
2
D
−
−
2
+
jy
jy
1
2
1
2
3
F
=
K
jj
d
j
The COF from the
j-
end to the
i-
i-end is as follows considering the defor-
mations at the
j-
end:
1
(
)
S
∆
+
S LS
−
q
M
M
2
jz
2
3
jy
D
iy
COF
→
=
=
j
i
1
(
)
(
)
2
jy
SL S
−
∆
+
SLSL
−
2
+
S
q
1
2
jz
1
2
3
jy
D
When only the rotational deformation is considered the following is the
COF:
SL S
SL SL S
−
2
3
COF
→
=
j
2
−
2
+
1
2
3
The DF is a ratio of the rotational stiffness of a member to the sum of the
rotational stiffness of all members at the joint.
Rotational stiffness, the stiffness due to rotation at point A:
2
SL SL S
D
−
2
+
K
=
1
2
3
q
The DF for a member at a joint can be written as follows:
2
SL SL S
D
SL SL S
D
−
2
+
1
2
33
−
DF
=
2
−
2
+
∑
1
2
3
