Cross procedure
The cross method is an iterative calculation method in structural engineering (moment distribution method ) to determine the bending moments at the end of the bars of bar structures and frames . The member end moments are determined iteratively by gradually distributing the moments up to equilibrium . The cross method is in principle a relaxation method . It is approximate , but achieves the exact result quite precisely.
In each iteration step, the moment equilibrium is established at only one node , while the remaining nodes are kept immovable. In each step, only the changes in the moments are calculated, written to the node and added later. It is mainly applied to frameworks with immovable nodes in statically indeterminate systems.
A similar procedure is the Kani procedure .
Since today the calculation of statically indeterminate systems is mainly done electronically, the calculation according to Cross has become generally unusual. In the case of more extensive systems (e.g. multi-story frames over several fields), the Cross calculation is very time-consuming until the iteration is sufficiently accurate.
The method was published in 1930 (1936?) By the American civil engineer Hardy Cross (1885-1959), professor at the University of Illinois, at Harvard . It was particularly in use from circa 1935 to 1960. During this time, many buildings with reinforced concrete frame structures were measured with it . Today such static systems are mostly solved with computer programs according to the FE method .
The Hardy-Cross method is used in a similar way for flows in pipe networks, for example in complex water distribution networks.
Individual evidence
- ^ Leonard K. Eaton, "Hardy Cross and the 'Moment Distribution Method'", Nexus Network Journal, vol. 3, no. 3 (summer 2001), [1]