...
How
...
is
...
a
...
progressive-collapse
...
analysis
...
performed
...
in
...
which
...
a
...
column
...
is
...
removed
...
to
...
evaluate
...
dynamic
...
response?
...
Answer:
...
Progressive
...
collapse
...
may
...
be
...
modeled
...
using
...
...
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
...
...
...
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
...
...
...
- 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.
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*Related Email:* * [5/6/2010 email on progressive collapse capabilities of SAP2000|$1745561] *Related Incident:* * 23372: Modeling progressive collapse. |
References
- Smilowitz, R. . Weidlinger Associates.
- Agnew, E., Marjanishvili, S. (2006). . Structure Magazine, 24-27.