Moment distribution method

The cross- method is an iterative calculation method of structural analysis (torque distribution method ) to determine the bending moments at the end of the rods of rod constructions and frames. The Stabendmomente are iteratively determined by the moments are gradually distributed to equilibrium. The cross- relaxation method is a method in principle. It is an approximation, but reaches the exact result quite accurately.

In each iteration step, the moment equilibrium is established to only one node, while the other nodes are held non-rotatably. At each step, only the changes of the moments are calculated, written at the nodes and added later. It is applied mainly to staff works with non-movable node in statically indeterminate systems.

A similar method is the Kani method.

Since today, the calculation of statically indeterminate systems primarily electronically, the calculation for Cross has become generally uncommon. For larger systems (eg multi-storey frame over several fields), the calculation is to Cross but very time consuming to obtain a sufficient accuracy of the iteration.

The procedure was in 1930 by the American Civil Hardy Cross (1936? ) (1885 - 1959), professor at the University of Illinois, published in Harvard. It was circa 1935-1960 especially in use. During this period, many buildings were measured with reinforced concrete frame structures with it. Today such static systems are usually solved with computer programs by the FE method.

Hardy Cross method is applied in a similar manner also for flows in pipe networks, for example in complex water distribution networks.