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Carry-over moments: The distributed moments in the ends of members meeting at a joint cause moments in the other ends, which are assumed to be fixed. These induced moments at the other ends are called carry-over moments.
Consider an unloaded prismatic beam fixed at end B , as shown in Figure If a moment M 1 is applied to the left end of the beam, the slope-deflection equations for both ends of the beam can be written as follows:.
Carry-over factor: The ratio of the induced moment to the applied moment is referred to as the carry-over factor. For the beam shown in Figure Distributed factor DF : The distributed factor is a factor used to determine the proportion of the unbalanced moment carried by each of the members meeting at a joint. For the members meeting at joint O of the frame shown in Figure Distributed moments: Upon the release of the imaginary clamp at a joint, the unbalanced moment at that joint causes it to rotate.
The rotation twists the end of the members meeting at the joint, resulting in the development of resisting moments. These resisting moments are called distributed moments. The distributed moments for the members of the frame shown in Figure Sometimes the iteration process in the moment distribution method can be significantly reduced by adjusting the flexural stiffness of some members of the indeterminate structure.
This section considers the influence of a fixed- and a pin-end support on the flexural stiffness of an indeterminate beam. Case 1: A beam hinged at one end and fixed at the other.
Consider a beam hinged at end A and fixed at end B , as shown in Figure Writing the slope-deflection equation for the end A of the member and noting that. By definition, the bending stiffness of a structural member is the moment that must be applied to an end of the member to cause a unit rotation of that end.
By definition, the relative bending stiffness of a member is determined by dividing the bending stiffness of the member by 4E. Applying a moment M at the end A of the simply supported beam shown in Figure Using the modified slope-deflection equation derived in section This established fact can substantially reduce the number of iteration when analyzing beams or frames with a hinged far end using the method of moment distribution.
During the balancing operation, the near end will be balanced just once with no further carrying over of moments from or to its end. The procedure for the analysis of indeterminate beams by the method of moment distribution is briefly summarized as follows:. Using the moment distribution method, determine the end moments and the reactions at the supports of the beam shown in Figure Draw the shearing force and the bending moment diagrams. Shear force and bending moment diagrams.
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