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RE: Progressive Collapse Design

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James:

You wrote:
> The pushover analysis gradually increases the load to a specified
> 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 
loads that are equal and opposite of the internal loads previously 
noted.  Now you should be able to run a static analysis with the 
applied loads and the new "internal" loads and get the same answer as 
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

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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