5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 128
© C.G. Daley
" The method of moment distribution is this:
1. Imagine all joints in the structure held so that they
cannot rotate and compute the moments at the ends of
the members for this condition;
2. At each joint distribute the unbalanced fixed-end
moment among the connecting members in proportion to
the constant for each member defined as "stiffness";
3. Multiply the moment distributed to each member at a
joint by the carry-over factor at the end of the member
and set this product at the other end of the member;
4. Distribute these moments just "carried over";
5. Repeat the process until the moments to be carried over
are small enough to be neglected; and
6. Add all moments - fixed-end moments, distributed
moments, moments carried over - at each end of each
member to obtain the true moment at the end."
Description of Method
The moment distribution method is a way to solve
indeterminate structures comprised of beams. The
method works for continuous beams over multiple
supports and for frames. In its basic form it does
not consider joint translation. All joints are only
assumed to rotate, as would occur at a pin or roller
support, or at a frame connection (beams to
column) where sway is prevented. Subsidence of a
support can easily be handled. An extended
version can treat sway of a frame system.
Fixed End Moments – FEM : To start the procedure,
all joint are considered fixed and all fixed-end
moments are calculated. One example of fixed end
moments is shown below for a beam with a central
point force. The moments are expressed as true
moments acting on the supports. This is an
important point. Note that both end moments in
the sketch cause concave downward bending, and
would this have the same sign in a bending
moment diagram. But here they have opposite
true senses (clockwise on left and counterclockwise