Errors in Roark Stress & Strain 7th Edition?! 2

[sajk14]

Hello All,

Looking in Roark 7th Edition on page 449 for 'Circular plates under distributed load producing large deflections'....

Case no 3 for fixed and held shows a value K4 = 1.73 ( at edge ). However in previous 5th and 6th editions of Roarks stress and strain the value of K4 = 0.476?

Why is there such a big difference in the values or is this an error in the 7th edition? Does anyone have a copy of Roark 8th edition to compare this K4 value?

Any thoughts/comments on the matter would be greatly appreciated.

Skn4

 

[JedClampett]

I've only got the 5th Edition and as the page numbers have changed, I can't find the case you're looking at. But Roark is chock full of typos and misleading formulations. If you need accuracy go to the source documents.

 

[sajk14]

The same case no can be found on page 407 in Roark 5th edition and page 478 in Roark 6th edition. Both these editions show the K4 value as 0.476 but for some reason in Roark 7th Edition this has been increased to 1.73!?

It would be interesting to see what the value is in the latest Roark 8th edition to see if it is an error.

 

[BAretired]

Maybe it would be better to compare it to the value found in "Plates and Shells" by Timoshenko and Woinowsky-Krieger.

BA

 

[JedClampett]

And how do you know which edition is in error? Majority rules? Three editions vs. one edition?

 

[IRstuff]

I have the Mathcad version of v6, and there are TWO K4 values, one for the center = 0.976 and one for the edge = 0.476.

There are two reference cited for Case 3:

Ref. 15. Timoshenko, S.: "Vibration Problems in Engineering," p. 319, D. Van Nostrand Company, Inc., 1928.

Ref. 16. Way, S.: Bending of Circular Plates with Large Deflection, Trans. ASME, vol. 56, no. 8, 1934. (See also discussion by E. O. Waters)

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

 

[RFreund]

I would think that it was an error that was noticed and then updated. Or there is some study that showed new values. Either way I would think the most recent version would be correct as they would have changed it for a reason.

EIT

http://www.HowToEngineer.com

 

[frv]

Tend to side with RFreund. You could always simply take the more conservative result.

I remember reading about some error in the AISC manual (on the conservative side) which made it through the last 5 or 6 editions, until someone caught it.

 

[izax1]

In my 8. edition the value for K4 is 1.73

 

[sajk14]

Thanks for all your comments people.

so it seems that the value to be used shall be taken as K4= 1.73 as per the newer 7th and 8th Editions.

This obviously opens the question of what about any design calcs that have been done in previous years with the lower value of K4=0.476 as a higher value of 1.73 may mean that stresses are now too high in previous calcs!?

 

[izax1]

This is the danger of using text books (or any calculation methods) without a thourough look at what is behind the numbers. It is a good rule to always try to understand why? In Roark reference is made to Timoshenko "Vibration Problems in Engineering" (A good and easily available text) and ASME Transaction from 1934 (Probably not so available)

 

[PEinc]

http://www.linkedin.com/pub/richard-budynas/12/5b5/8a0

It might be worth it to contact one of the 8th edition authors in order to ask about the ddiffering K4 values. The above LinkedIn link should be one of the authors.

http://www.PeirceEngineering.com

 

[JStephen]

"Maybe it would be better to compare it to the value found in "Plates and Shells" by Timoshenko and Woinowsky-Krieger."

That appears to be 0.476, factor alpha-r in Table 82, P. 410 of my copy. I haven't taken time to compare the usage in detail.

 

[BAretired]

I would be surprised if Timoshenko was that far off, but I suppose anything is possible.

BA

 

[IDS]

I've had a look at this, comparing the Roark formulas with Pilkey (Formulas for Stress, Strain, and Structural Matrices, 2nd Edition), and a simple axisymmetric FE analysis. My results are:

Pilkey gives three results:
- 1. Simply supported outer edge with in-plane force
- 2. Simply supported outer edge without in-plane force
- 3. Fixed at outer edge with in-plane force

Roark does not consider Pilkey's case 1
Roark Case 1 is the same as Pilkey Case 2, and the formulas agree
Roark Case 2 is "Fixed but not held", which I take to mean a rotational restraint at the edge, but no radial restraint. The formulas are the same as Pilkey case 3. Since the formula for stress at the edge does not include the component due to axial stress (K4 = 0) it seems likely that the Roark description is the correct one.
Roark Case 3 is "Fixed and held". Pilkey does not cover this case, assuming that Pilkey Case 3 should be fixed with no in-plane force.

Results of a finite element analysis, using 10 8-noded axisymmetric plate elements in Strand7, are shown in the attached spreadsheet file. The deflection results are reasonably close to the Roark values for all three cases, but the stress results are very different for large deflections for Case 1 and 2. The radial stress at the edge for Case 3, which uses the K4 value of 1.73, is the only stress result matching the FEA results reasonably closely.

So my conclusions are:
- Pilkey's description for his Case 3 seems to be wrong. Pilkey Cases 2 and 3 are equivalent to Roark Cases 1 and 2.
- Roark Cases 1 to 3 match the FEA results reasonably closely for maximum deflections.
- Roark Cases 1 and 2 give very different stress results to the FEA results.
- Roark Case 3, with a K4 factor of 1.73, matches the FEA stress results reasonably closely.
- A computer analysis is the quickest and most reliable way of checking standard formulas.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IDS]

Spreadsheet file attached.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/