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Re: LRFD-PBD-USD - Push Over - P-Delta (long)

• To: seaint(--nospam--at)seaint.org
• Subject: Re: LRFD-PBD-USD - Push Over - P-Delta (long)
• From: Charley Hamilton <chamilto(--nospam--at)uci.edu>
• Date: Fri, 28 Jan 2005 05:54:48 -0800

```[Editor's note:  My answers always seem longer than I intended.  I've
marked the short form of each response with SHORT ANSWER so you can skip right
to it.]

Carlos -

> 1. Performance based Design 2. Limit State Design
>
> I have an idea about what they mean independently, but I would like to know
> how they are related, if there is any relation between them, of course.

============
The general concept of limit-state design is that you define a particular
state (plastic hinge formation, first yield, drift < D_allowable, etc) at
which you check the capacity of the structure to resist the applied demands.
```
After all, we can't practically analyze structural response at an infinite number of response states. LRFD is based on limit-state design. PBD is also
```based on limit-state design.  If you are a programmer, think of limit-state
design as a class of design methods, and LRFD and the various PBD
methodologies are all instantiations of that class.

===========
The concept of performance-based design (PBD) is that you define certain
target performance-states in terms of a metric you believe is representative
of important behavior of the structure:

P1) life-safety  (collapse prevention)
P2) major damage (heavy repairs, probable replacement)
P3) minor damage (easily repairable, probable repair)
P4) no damage    (stuff stays on desks, no cracks in gypboard)

These performance-states are then linked to an engineering metric,
such as:
- global or interstory drift limits
- peak in-structure acceleration

You can even combine indicator metrics to obtain a better correlation
between the combined metric and your target performance state.
Chuck Menun and Armen Der Kiureghian have done some recent work on this,
as has Eduardo Miranda, I believe.

For probabilistic PBD, you would compute the likelihood of exceeding target
values of those engineering metrics corresponding to your chosen performance
states, and those are the likelihoods of exceeding your target performance.

You also need a concept of the demands associated with the target likelihoods
```
of exceeding a given performance state. That is, if you want a building to survive with little or no damage, how large an event do you want it to survive? For example, you can characterize demands in terms of their return period/probability of occurrence in the lifespan of the structure:
```
D1) 50% in 50 years
D2) 10% in 50 years
D3) 2% in 50 years

You might pair demand level 1 (50% in 50) with performance state 1 (no damage)
if you want the structure to survive loads reasonably expected to occur
throughout the life span of the structure.  A typical single-family dwelling
might pair D2 with P1 or P2.  An emergency operations center might require
```
achieving P3 or even P4 for D2 level demands in order to provide emergency services after a major earthquake.
```
============
> If I have to design a structure for a certain Limit State (
> Serviciability/Damage control/Survival Limit).  Is there any recommendation
> to select vertical load factors in a LRFD or allowable stresses in a ASD or
> they are simply related with the level of seismic load.

You might review the SEAOC Blue Book (e.g 1999) for some guidance on this.
Appendix I deals with some tentative performance-based guidelines
and implementation recommendations.  However, they're "not quite ready for
prime time" from my brief glance at them.

Also, the ASCE 4 committee was working on some performance-based guidelines
for structures in the nuke arena a couple of years ago.  I'm not sure what
the status of that document is.

```
The PEER Center (headquartered at http://peer.berkeley.edu) has several reports dealing with their methodologies for executing performance-based assessment. These included what was sometimes referred to as "the Dreaded PEER Loss Integral" [caps added for dramatic effect] in some of the meetings I attended.
```
There are nearly as many ideas for how to conduct PBSD as there
are engineers who are thinking about it.  And each of them has features
and bugs to consider.  That's what you get when you throw a bunch of smart
folks at an interesting problem.

> On the other hand, is Push Over Analysis related with Material Nonlinearity
> and P-Delta Analysis related with Geometrical Nonlinearity.

Yes to both questions, but pushover analysis should also address geometric
nonlinearity as a typical collapse limit state can be generated due to
P-Delta effects as the structure reaches large drifts.

```
Anyway, there's lots of good literature out there on these topics, although not a lot of it is aimed directly at implementation just now.
```
```
Hmm.... Long answer to a seemingly simple question. I appear to be competing for the Dennis Wish Longest Post Award. ;-)
```
Charley Hamilton

--
Charles Hamilton, PhD EIT               Faculty Fellow
Department of Civil and                 Phone: 949.824.3752
Environmental Engineering           FAX:   949.824.2117
University of California, Irvine        Email: chamilto(--nospam--at)uci.edu

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