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# Reliability / Probability in Structural Design

## Reliability / Probability in Structural Design

(OP)
I've been reading a few papers on reliability and probability in structural design.  They have all seemed pretty theoretical so far. I'm wondering if anyone is incorporating these methods in their design work and if you could suggest PRACTICAL books on the topic.

If you are using these ideas, where do you get information regarding the statistical parameters to use?

### RE: Reliability / Probability in Structural Design

I'm not sure many consulting engineers use reliability directly in their daily work.  Most of the reliability work is done at the universities and testing labs where lab tests of structural elements are studied in terms of their variability.  Also, the actual tested strength is studied as to how sensitive the strength is to variations in parameters that go into estimating the strength.

For instance, a concrete beam's flexural strength is affected by flange width, B; web width b; depth to reinforcing, d; concrete strength, f'c; reinforcing yield, fy, etc.  Each of these has larger and smaller direct effects on strength....f'c not affecting the flexural strength as much as d does.  So each parameter has a level of influence on predicted strength, and each parameter has a degree of variability in the field vs. estimated. (i.e. - d can be strictly calculated but in the field, it varies based on how accurate were the chairs, did they sit tight to the forms, were the forms cut/sized correctly, etc.)

One of the most prolific writers on reliability in structural engineerins is a professor named Bruce Ellingwood.  Don't know where he currently works but an internet search could bring him up.

On paper I wrote some time ago for a graduate class dealt with taking a large number of tests of composite metal deck/concrete slabs and developing a phi factor (strength reduction factor) for the shear bond mode of failure.  Again, lots of variables in the predictive equation for shear that had different amounts of influence on the shear strength (the weight of the variable) and different amounts of variability.  These combined into a sort of statistical weighted average to develop a probability of failure for various phi factors (0.65, 0.75, 0.85) and these in turn were compared to other probabilities of failure of shear mode failures (i.e. concrete beam shear failure).

So the reliability that I'm aware of is focused on studying the statistical character of an estimate of strength and ends up being eventually published in a code somewhere.

### RE: Reliability / Probability in Structural Design

(OP)
JAE,

Thanks for the note, you have obviously been reading some on this topic too and you hit upon my real question.  How can we make use of these ideas in the real world for better design; a safer or a more rational design.

One of the papers I read had a practical example where pile groups under a building footing/pile cap were analized.  The author showed how a small reduction (about 8%) in the allowable pile stress resulted in an increase in footing reliabilty (about 100%).  This was based on the fact that the probabilty of failure/pile decreased as the number of piles under a footing increased. I suppose this should be known intuitively because you can't install partial piles, but the author showed a relatively straight forward, practical format for calculating the relative magnitude of the increase.

I thought that there might be more practical examples out in cyberland.  Some of these research papers can be hard to apply to everyday design work, so we tend to do things the same familiar way.

### RE: Reliability / Probability in Structural Design

jheidt2543:

Where did you find the article on pile groups?  I missed it -

Please see FAQ731-376  by VPL for tips on how to make the best use of Eng-Tips Fora.

### RE: Reliability / Probability in Structural Design

(OP)
The Paper is: Safety and the Probabilty of Structural Failure, by Alfred M. Freudenthal, ASCE Transactions, Vol. 121, 1956, pages 1337-1397 with discussions.  One of the discussers, Jose M. Corrso, includes the pile example in his discussion of the paper.

It is an old paper but, not having read it before, it is new to me.  If you can't find a copy, I can try to scan it or fax a copy to you.  Let me know at jheidt2543@aol.com

### RE: Reliability / Probability in Structural Design

I have the cite - thanks for offering to send it.

Those guys with Jackson & Moreland sure dominated the discussion...all five from the same firm?!  I assume they were all Freudenthal's former students -

Jose Corso's discussion was quite good.  It was actually quite readable while Freudenthal's really wasn't.  An interesting read - thanks.

Please see FAQ731-376  by VPL for tips on how to make the best use of Eng-Tips Fora.

### RE: Reliability / Probability in Structural Design

(OP)
Focht3,

I don't know how you found it and read it so fast, unless it was already in your library.  I feel vindicated!  I have now read 5 or 6 of Frudenthal's papers and while he is obviously a very smart man, he can't write in an understandable way for ....  and I don't mean the math.  Some of his sentences are longer than a paragraph, 8-9 lines!  He must never have learned what a period was.

I wish I could find more examples like Jose Corso's discussion, I thought it was very practical and usable.  Thanks for looking it up and the comments.

### RE: Reliability / Probability in Structural Design

I attended a weeklong lecture at University of Wisconsin-Madison were Dr. Bruce Ellingwood presented an excellent lecture on loads, probabilities and reliability. He gave a handout during his lecture. I cherish it and refer to it when I debate loads with colleagues. At the time, Dr. Ellingwood used to teach at Johns Hopkins. I hear he is at Georgia Tech these days (another fine school).

I am sure he might be gracious to pass a copy of his loads notes.

Good luck.

### RE: Reliability / Probability in Structural Design

Just bring to mind some comments I read form a past ACI director. He was saying that people meeting to modify the standing codes, when facing something they didn't find the real reason why it was in the code, were sometimes retiring such specific wording. He said, and I agree, that whilst the cause of the thing not being entirely discovered, such wording should be retained, for in other case one would be forfeiting what were solutions to problems discovered in the past, the reasons for which remain somewhat unclear.

Well, I have a recent instance of it. Now LRFD says follow ASCE 7 for combinations. OK, as long as the ASCE are those of the date, as mandated, and "if equal" to those that were consistent or better than safety by ASD, as was touted was made for LRFD, OK. But really any change in the combinations of course affects overall safety, and its statistical forecast of safety as wanted to remain consistent with standing safety. Hence, I don't think remitting the combinations to ASCE was at all wise.

### RE: Reliability / Probability in Structural Design

jheidt2543:

Second bookshelf, top row, 5th book - right in front of me.  While I can speed read, I didn't read them in detail.  In fact, I found most of the work too tedious to study.  I hate those run-on sentences that are two paragraphs long - especially when they have partial differential equations and probability theory in them as well.  Can you say, "My brain hurts!"?

I suspect that Freudenthal's ideas might have been widely accepted and adopted at the time if he had done a better job of communicating those ideas.

Please see FAQ731-376  by VPL for tips on how to make the best use of Eng-Tips Fora.

### RE: Reliability / Probability in Structural Design

(OP)
Lutfi,

I see quite a few citations of Ellingwood's papers.  Could you tell us when the seminar was and who sponsored it?  Perhaps the lecture notes might still be available through the organization?  I have been to Ellingwood's webpage and looked at his list of publications, very impressive!

Sorry, I'd rather be a Badger. Good school, sometimes good sports, always a good marching band!  GO BADGERS!

### RE: Reliability / Probability in Structural Design

The lecture was titled "Design Loads for Structures" and was given back on October 1996.Dr. Ellingwood lectured on probability based loads and load combinations. The second lecture was Live Loads. He handed out excellent papers covering both topics.

Although I am not a badger, I think it is a darn good school.

### RE: Reliability / Probability in Structural Design

I might suggest the following references - as well.

D'Appolonia, 24th Karl Terzaghi Lecture.  "Monitored Decisions" Journal of Geotechnical Engineering , Vol 116, No. 1, January 1990.

Whitman, 17th Karl Terzaghi Lecture.  "Evaluating Calculated Risk in Geotechnical Engineering" Journal of Geotechnical Engineering , VOl 110, No. 2, February 1984.

Peck, 9th Rankine Lecture.  "Advantages and Limitations of the Observational Method in Applied Soil Mechanics", Geotechnique 19, No. 2, 1969.

Also I have a chapter in a book (compiled in India) as per:

Muir Wood, Control of Uncertainty in Geotechnical Engineering

I will get the proper citation of Muir Wood's chapter tomorrow and post it then.  These references might contain some provoking thought for some.

### RE: Reliability / Probability in Structural Design

Muir Wood's chapter:  Saxena, K.R. (editor)   Geotechnical Engineering Emerging Trends in Design and Practice Oxford and IBH Publishing Co. Pvt. Ltd. New Delhi.  It's a nice presentation.

### RE: Reliability / Probability in Structural Design

(OP)
BigH,

Thanks, I'll do some more research...

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