Civil Engineering Reference
In-Depth Information
1
(
)
(
)
SSL
−
∆
+
S LS
−
θ
M
M
2
1
iz
2
3
iy
D
jy
COF
=
=
i
→
j
1
−
S
∆θ
+
S
iy
2
iz
3
iy
D
When only the rotational deformation is considered, the following is the
COF:
SL S
S
−
COF
=
2
3
i
→
j
3
The distribution factor (DF) used in the moment distribution method is the
ratio of the rotational stiffness of a member to the sum of the rotational
stiffness of all members at the joint. The rotational stiffness is the moment
at a joint due to the rotation at a joint. This is the term Kii
ii
for rotation and
moment only.
S
D
K
=
3
Miy,
q
iy
The DF for a member at a joint can be written as follows:
S
D
S
D
−
3
DF
=
∑
3
We could find the deflection and rotation at the
j-
end using the same
method. Alternatively, since the stiffness matrix is symmetric we can find
the forces at the
i-
i-end due to motions at the
j-
i-end directly.
T
S S
SSLSLS D
−
−
−
SSSL
SS
−
=
1
1
T
1
2
1
2
1
=
KK
D
=
ij
ji
−
LS
−
2
1
2
3
2
2
3
∆
θ
P
M
=
−
SSSL
SSLS
−
−
1
jz
iz
1
2
1
D
iy
2
2
3
jy
=
FK
i
d
ij
We can use the transmission matrix equation again to find the forces at the
j-
end of the member.
