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# RE: Progressive Collapse Design

• To: seaint(--nospam--at)seaint.org
• Subject: RE: Progressive Collapse Design
• From: "Michael Valley" <mtv(--nospam--at)skilling.com>
• Date: Thu, 12 Aug 1999 13:18:48 -0700
• Comments: Authenticated sender is <mtv(--nospam--at)linux.skilling.com>
• Priority: normal

```James:

You wrote:
> maximum deflection or failure. If as a minimum columns must be able
> to be removed how would a push over analysis help. Educate me.

I use SAP2000 for both dynamic nonlinear and static nonlinear
analysis.  I'll outline the concept you might use as the basis for
your analysis and another important consideration.

First, remember that SAP2000 and XLinea are general purpose
analysis programs.  Don't be discouraged if the manual or tutorials
ignore your class of problem.  My most interesting and rewarding
analyses have involved figuring out how to get the program to do what
I want.

The simplest approach is to simply design the system (statically) for
each possible missing column condition.  However, the resulting
design might not be economical and certainly wouldn't indicate what
happens when the element goes away.  Saying this method is not an
option...

The basic approach to the removal of an element (using a program like
SAP, that doesn't directly support element removal) is as follows:
With the element in the model, apply the static loads that simulate
the initial condition.  Find out the internal loads in the element in
question.  Modify the model by removing the element and introducing
noted.  Now you should be able to run a static analysis with the
before.  The analysis proceeds by ramping the "internal" loads to
zero, which simulates loss of the element.  The idea is to remove the
element and watch what fun things happen as a result.

If you are performing a dynamic analysis, the rate of load removal
(element death) can be significant; you will need to play with this
parameter.  Because the analysis is nonlinear dynamic, it is
important that the mass, stiffness, damping, and strength
characteristics of the system (and elements) are appropriate.  Simply
run time history analysis where the load ramps to zero and stays at
zero for a suitable length of time (for instance, until the resulting
motion damps out).

If you are performing a nonlinear static analysis, the rate of load
removal is not as significant since the analysis consists of a series
of static analyses; inertia and damping do not come into play.  The
strength and stiffness of the system (and elements) are the important
parameters.  Using SAP2000, a pushover analysis can be either force
or displacement controlled.  The controlling parameter can be in the
vertical direction (although that's certainly not how most pushover
analyses are performed).

The important consideration I alluded to involves the decision of
whether to use dynamic or static analysis.  If the response of the
system is expected to be dynamic (dependent on inertia and damping),
you really should not use nonlinear static analysis.  I've had a lot
of discussion with the folks at CSI and with the developer of XLinea
on this topic.  We all agree that one of the two biggest weaknesses
of the pushover method is the fact that it misses dynamic response.
Even when the final results aren't dependent on dynamic interaction,
the presence of inertia and damping in the dynamic solution method
significantly improves convergence.  In the static method there are
several key decisions that must be made by the software developer and
user that affect load redistribution, etc.  I can provide a little
more detail offline if you're interested.

> Correct me if I am wrong but SAP and Xlinea both do a pushover
> analysis. SAP does 3-D and Xlinea only 2-D. SAP does not do shear
> walls while Xlinea does.

XLinea is still based on the DRAIN-2Dx elements, input file,
and solution engine.  The DRAIN panel element is limited to elastic
behavior, just as the SAP2000 shell elements are.  SAP2000 can do 3D
pushover analysis.  However, I would caution that it becomes much
more difficult to understand what's happening as the structure
becomes more complex.  Under most circumstances 2D pushover analysis
offers improved understanding without being so difficult to
understand.  (Of course, there are times when you may really need 3D
interaction; make sure your fee is large.)

-Mike

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Michael Valley                                   E-mail: mtv(--nospam--at)skilling.com
Skilling Ward Magnusson Barkshire Inc.                  Tel:(206)292-1200
1301 Fifth Ave, #3200,  Seattle  WA 98101-2699          Fax:        -1201

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