Civil Engineering Reference
In-Depth Information
their
flexural stiffness
(stiffness factor). Then, the member-end moments
are carried over to their far ends by the carryover factor. The process is
repeated and continues until the amount of moment being distributed
becomes significantly small.
Many factors are used with the moment-distribution method. The first
is the
member stiffness factor
and is the amount of moment required to
rotate the end of a beam 1 radian. This is actually the definition of stiff-
ness, force due to unit motion. The far end of the beam that is rotating is
fixed. We will derive this expression in the next section on elastic member
stiffness.
=
4
EI
L
K
The
joint stiffness factor
is the sum of all the member stiffness factors for
the members connected at a joint.
KK
T
=Σ
The
distribution factor
for each member-end at a joint is the member stiff-
ness factor divided by the joint stiffness factor.
K
K
K
D
==
Σ
K
F
T
If a member is connected to a support and not to other members, the dis-
tribution factor is dependent on the support type. If the support is fixed
against rotation, then
D
F
=
1. If the support is free to rotate, then
D
F
=
0.
The
member relative stiffness factor
is used when a continuous beam
or frame is made from the same material when calculating the distribution
factor. This can be used in place of the member stiffness factor for calcu-
lation of the other factors.
I
L
K
R
=
The final factor is the
carry-over factor
, which represents the fraction of a
moment that is carried over from one end of a member to the other. If the
member is prismatic, then the ratio of the far end moment to the near end
moment of a member is one-half (½).
