5003 Lectures - Faculty of Engineering and Applied Science

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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.
E5003 - Ship Structures I 133 © C.G. Daley Steps 10: Solve for the other reactions and beam responses. Once the end moments on a beam are known, the vertical reactions can be found from static equilibrium. Remember that the end moments found in the MDM are moments acting "on" the supports. Moment reactions "from" the supports are opposite to these. Once the vertical reactions are found, all other responses (distribution of shear, bending, slope
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5003 Lectures - Faculty of Engineering and Applied Science

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