Lecture 12: Moment Distribution Method Eng. 6002 Ship Structures 1 Lecture 12: Moment Distribution Method

Moment Distribution Method The method of moment distribution is a refinement of the classical displacement method presented previously. Instead of solving a matrix equation for the unknown joint rotations, the method of moment distribution uses successive approximations. The method the primary method of analyzing structures that respond primarily in bending until the 1970s, when computer software for structural analysis became generally available.

Steps Compute the moments at the ends of each member in the structure, assuming that all joints which are free to rotate are restrained by a fictitious rotation constant Sum the member end moments at each joint to determine the unbalanced moment which is being restrained by the fictitious rotation constraint. It is not necessary to compute the unbalanced moments at any support joint which has a rotational restraint, since the member and end-moments will be automatically balanced by the reactive moment

Steps Remove the fictitious rotation restraint at each joint in turn, assuming that the other joints are still restrained against rotation, and distribute the unbalanced moment at the joint to the ends of the members which are rigidly attached to the joint In addition, distribute a percentage of the moment along each member to its far joint to keep that joint from rotating. Repeat the distribution process in Step 3 for each joint as many times as necessary until the member end moments are balanced at each joint within an acceptable value. The final member and end moments will correspond to the correct end moments for this structure and loading condition Compute the axial forces and shear forces in the members by using the member equilibrium equations, and compute the reactive forces and reactive moments at the support joints by using the joint equilibrium equations.

Fixed-end moments