# How is a progressive-collapse analysis performed in which a column is removed to evaluate dynamic response?

**Answer:** Progressive collapse may be modeled using SAP2000 in the sense that certain members may be removed to study the effect on the structure. Progressive collapse and dynamic effects may be evaluated using time-history analysis as follows:

- Create a model (Model A) which contains the entire structure, including the column to be removed. Analyze this model to obtain the internal forces of the column which will be removed.

- Create another model (Model B) in which the column is removed. Apply the column end forces, obtained during the analysis of Model A, to simulate the presence of the removed column.

- Simulate the removal of the column by running a time-history analysis in which these equivalent column loads are reduced to zero over a short period of time. This is done by applying a ramp time function in which loads opposite to those of the equivalent column loads are scaled from zero to the full value. The duration of this event should match the time in which the column is removed.

Dead load may be applied through either of the following two approaches:

- Apply the dead load together with the equivalent column load in a nonlinear-static load case. Then the time-history load case, in which the column is removed using a time function, should start at the end of this nonlinear-static load case.

- Use a single time-history load case to apply the dead load and the equivalent column load using one time function which gradually ramps these loads to their full values. The column removal load may then be applied through a separate time function which has a later arrival time.

This process enables observation of the dynamic effects which are associated with the removal of a structural member. Note that this is an idealized computational process which will not capture such effect as the impact of material collapsing onto the remaining structure.

# References

- Smilowitz, R. . Weidlinger Associates.

- Agnew, E., Marjanishvili, S. (2006). .
*Structure Magazine*, 24-27.