5003 Lectures - Faculty of Engineering and Applied Science

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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
E5003 - Ship Structures I 129 © C.G. Daley on right) and so have opposite signs. And we keep tract of the moments acting from the beam, not the reactions by the support. Moment Distribution factors - α: At each joint where two or more beams connect, each beam provides part of the rotary stiffness. When an external moment is applied to the joint, it rotates as a unit, with each of the connecting beams resisting part of the total moment. The portion of the total is called the moment distribution factor - α. For each beam the moment will be :
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5003 Lectures - Faculty of Engineering and Applied Science

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