5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 132
© C.G. Daley
Step 4: Find fixed-end moments:
In this step, we find the fixed end moments for
each beam end. In the example at left, we have 3
beams connected in a frame. The top two have
loads and so have fixed-end moments. The vertical
beam (the column) is unloaded so its FEM are
zero.
Steps 5, 6, 7, 8, 9: Perform iterative calculation to
correct end moments. The fixed-end moments
found in step 4 are the first estimate of the
solution. The moments are in equilibrium with the
external loads, with the only problem being that
some of the joints are incorrectly fixed, when they
should be free to rotate. We will set up a
calculation table that will allow us to add a
correcting moment to each joint. We will perform
the corrections iteratively and the solution will
converge to the correct answer.
The table with the solution is shown on the next
page. With two beam, there are 4 end and so there
are 4 columns in the table. The first row contains
the moment distribution factors. The second
contains a note describing the target moment (this
is an extra feature normally not included). The
third row contains the fixed end moments. The
fourth row shows the total correction (later
ignored), with the fifth row dividing the correction
among the beam ends. The sixth row adds the
carry-over moments from the neighboring ends.
And then the seventh row add the third, fifth and
sixth row terms to get a new estimate for the end
moments.
The whole process is repeated until the solution is
sufficiently converged.