![]() ![]() Once we release the node, the node must rotate until it is in equilibrium. These moments do not have to be in equilibrium prior to the unlocking because they are consider to be transferred not to the node, but to some external rotational support. Unbalanced loads are possible because the node was previously fixed, so one member connected to that node may be applying a fixed end moment to the node and another member connected to that node may be applying a different fixed end moment or none at all. This rotation is caused by whatever unbalanced moment there is on the node prior to the unlocking. The act of unlocking the node allows that node to rotate freely. Then, for each node in turn, one at a time, we can unlock the node and then lock it up again (e). Those external loads on the members cause a moment at each fixed end, which we can calculate (d). Then, we apply all of the external loads on the structure (c). This effectively causes the ends of all the members to be fixed. To picture the moment distribution method conceptually, imagine that at the start of our analysis, before we even add any external loads to the structure, we grab hold of all of the nodes and prevent them from rotating (b). Parts of this figure, referenced by part letter will be referenced in the description below. The generalized moment distribution method procedure is illustrated in Figure 10.2. We will see this process in detail through the use of an example is a later section. Then by locking and unlocking each joint in succession, the internal moments at the joints are slowly distributed and balanced until each joint reaches a final equilibrium condition. So this method amounts to first assuming each joint is fixed for rotation (locked). Transactions of the American Society of Civil Engineers, Vol. (1949) Analysis of Continuous Frames by Distributing Fixed-End Moments. The method of moment distribution is this: (a) Imagine all joints in the structure held so that they cannot rotate and compute the moments at the ends of the member for this condition (b) at each joint distribute the unbalanced fixed-end moment among the connecting members in proportion to the constant for each member defined as "stiffness" (c) multiply the moment distributed to each member at a joint by the carry-over factor at that end of the member and set this product at the other end of the member (d) distribute these moments just "carried over" (e) repeat the process until the moments to be carried over are small enough to be neglected and (f) 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 Cross, H. In his own words, Hardy Cross summarizes the moment-distribution method as follows: ![]()
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