Kani method
The Kani method by Gaspar Kani (born October 16, 1910 in Franztal near Semlin (today the city of Belgrade ) in Serbia ; † September 29, 1968 in Lake Simcoe , Ontario , Canada ) is an iterative moment compensation method in structural engineering for the calculation of multi-storey frames with predominant stress from bending moments . It is a hand calculation method for highly statically indeterminate systems to determine the associated bearing and cutting reactions .
The iterative calculation according to Kani is based on the Gauss-Seidel iteration method . The moment compensation is carried out iteratively at the nodes of the bar structure. Usually the moments are entered in a system sketch at the nodes. It is similar to the Cross method by Hardy Cross from 1930. The Kani method takes into account the displaceability of the framework in a particularly simple form. Both methods can now only be found in textbooks; Computer programs are used today for practical calculation.
The advantages of the method are based on the fact that, despite the complexity of the calculation, only the four basic arithmetic operations are required. Furthermore, a single calculation error only affects the duration of the iteration, but not the result of the calculation. Haunches can be easily taken into account in the calculation.
The invoice process essentially consists of the following steps:
- Definition of the full clamping torques for each node (frame corner); these can be found in the relevant tables.
- The stiffnesses of the connected frame bars are determined for each node ; The rotation factors are determined from these values
- For each floor of the frame, the displacement factors are determined from the same stiffnesses.
- Starting at the node with the greatest full clamping torque, the torsion components are calculated, with the torsion components of the neighboring nodes being included in the calculation. The computation proceeds from node to node.
- The displacements of the floors are determined in a similar way.
- After the rotation and displacement components have converged to the desired accuracy, the iteration is ended.
- The final billing is done by adding the full clamping torques, the rotation and displacement components of each node and each floor, whereby the rotation components of the neighboring nodes and the displacement components of the neighboring floors are included in the calculation.
Gaspar Kani published his method in 1949. He used it to calculate the first German prestressed concrete bridge that was built for the railroad near Heilbronn .
literature
- Gaspar Kani: The calculation of multi-storey frames . Wittwer, Stuttgart 1956.