# Determination of Yielded Hinges and Modified Stiffness Matrix

The structural provisions calculated for the i'th step of the thrust analysis are summed with the structural provisions calculated in the previous step and the structural provisions at the end of the i'th step are calculated automatically.

The elements that reach the yield level at the end of each pushing step are automatically determined and the system stiffness matrix is automatically recreated.

In the i th step of the pushover analysis with the ARSA method, the structural responses calculated separately for the ( X ) and ( Y ) earthquake direction, that is, the typical displacement, plastic deformation or internal force values r _{x }^{(i)} and r ^{( i)} calculated as a result of mode coupling after determining the Application of Complete Quadratic Combination (CQC) Rule, it can now be checked whether there is plasticization in the building elements.

Structural equivalents, r _{x }^{(i)} and r _{y }^{(i),} also include axial force and moment diagrams. For this reason, it is checked whether it reaches the yield curve in all plastic hinges defined at the element ends under the effect of additional force and biaxial bending. If the element has reached the yield plane, the system stiffness matrix is reconstructed by keeping the yield moment constant in this region. At the end of the i th thrust step, the plasticizing elements are determined, the necessary changes are made in the system stiffness matrix and the processes are started for the new pushing step.

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