Sequence of nonlinear static load cases

Cyclic pushover analysis can be carried out by performing a sequence of chained pushover analyses. Two key aspects of this approach are provided below:

Each pushover analysis would be pushing the structure in the opposite direction when compared to the push direction for the immediately preceding pushover load case.
Each pushover load case, except for the first one, would be using stiffness at the end of the previous pushover load case.

Time history load case

Another approach is to use a single nonlinear time history load case.

However, using a time history load case requires some special considerations to model that the applied loads should be scaled up (or down) to achieve the desired monitored pushover displacement for each cycle. The time function would consist of linear segments that would apply the loads in one direction and then reverse them in the other direction (with perhaps a constant segment to "hold" the loads before reversing them). The peak positive and negative values of the time function at the end of each cycle would need to be found in for each cycle in the sequence, starting with the first cycle of load application.

Sample time function is shown in the figure below: