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h1. 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|sap2000:home] 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|kb:Time-history analysis] 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.
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# 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.
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# Simulate the removal of the column by running a time-history analysis wherein which these equivalent column loads are reduced to zero over a short period of time. This is done by applying a ramp [time function|kb:Time function] wherein 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.

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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|kb: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.

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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.

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*Related Email:*
* [5/6/2010 email on progressive collapse capabilities of SAP2000|$1745561]

*Related Incident:*
* 23372: Modeling progressive collapse.
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h1. References

* Smilowitz, R. {new-tab-link:http://www.nibs.org/client/assets/files/mmc/Smilowitz%20paper.pdf}Analytical Tools for Progressive-Collapse Analysis{new-tab-link}. Weidlinger Associates.

* Agnew, E., Marjanishvili, S. (2006). {new-tab-link:http://www.structuremag.org/Archives/2006-4/SF-Dynamic-Analysis-for-Progressive-Collapse.pdf}Dynamic Analysis Procedure for Progressive Collapse{new-tab-link}. _Structure Magazine_, 24-27.