Crippling Strength in bending and Plastic Bending Theory 3

[kilbchoi]

Hi,

Regarding the compressive failure mode in the bending member such as circular tube, rectangular tube, or hat section,

What is the relationship between the plastic bending theory and the crippling strength ?

If I consider the crippling stregnth as the compressive strength (Fcc < Fcy), it's fine and conservative. If Fcc> Fcy, the plastic bending theory can be fully applicable. it's my basic understanding.

However right now I'm checking the tested structure which has hat section stiffeners and was failed in the compressive side in the bending. The theoretical crippling strength on the outermost flange (two clapmed ends for the crippling) is slightly lower than its Fcy. If the failure load is calculated with Fcc in the elastic range, it is too conservative and the difference from the tested failure load is too big. My partner in OEM calculated allowable bending moment with the plastic bending theory by their own program and it is well matched to the tested failure load.

How do you explain it ? The crippling in the outermost flange in bending is not critical ?

Thanks,

kilb

 

[edbgtr]

Kilb

The bending compressive stress in the outermost flange is definitely a limiting factor in the plastic bending capacity of the section.

Remember, when the flange cripples in compression, it is assumed to &quot;hold&quot; that load (stress). This equates to an equivalent strain taken off the Hill stress-strain curve. The strain distribution through the depth of the section is linear, so the associated tensile strain at the opposite outer fibre can be determined.

The hat section is usually unsymmetrical because of the hat's bent flanges which are in turn fastened to a skin, web or base plate of the hat. Drawing the linear strain distribution through the section provides you with the starting point for determining the plastic Cozzone moments carried by the upper and lower portion of the section. I refer you to Bruhn section C3.7 for methods to calculate the plastic moment carried by unsymmetrical crippled sections.

Determining the fo and fm Cozzone stresses, can be achieved by reading the values off the published Cozzone curves, or using the Ramberg-Osgood (Hill) definition of the stress-strain curve combined with the Cozzone definition of the &quot;equivalent&quot; plastic stress distribution through a rectangular section, and calculating the fo value by equating the section moments.

Determine the k-factor for each of the upper and lower portions of the hat section, and calculate the &quot;equivalent&quot; rupture stress (Fb) from Fb=fm+fo(k-1). Fb times the section modulus (I/c)yields the maximum plastic bending moment carried by the section.

Even if the outer fibre stress is equal to Fcy, there is still an fo component (Fcy is beyond the proportional limit of the material (at 0.2% set), and is effectively in the plastic range already) and thus the yield Cozzone rupture stress is Fby>Fcy.

If you still have difficulty calculating or calibrating your test results with the theory, provide us with an e-mail address where you can receive moderately large attachments, and I will provide you with the math models of the stress-strain curve and fo formula, which can be derived from just 4 parameters, i.e. Ftu, Fty, E, and eu.

Hope this helps.

Ed.

 

[kilbchoi]

Hi Ed,

Thank you for your help.

Could you please send it to my email address,
Gilbert.Choi@eurocopter.ca

Thanks,

Kilb

 

[jediknight]

Hi Ed

Please could you send a copy to me as well, at
besant.bhakta@dunlop-aerospace.com

Thanks

Besant

jedi-knight@fsmail.net
&quot;Keep Concorde Flying&quot;

 

[royalra]

Ed:

I would be interested in seeing your math models also.

r.royal@aeromec.com

Thanks

Russ

 

[Aeromark]

Ed,

If you could send them to me I sure would love to take a look at your models!

Regards,
Mark

 

[Aeromark]

Oops -

somehow the email address didn't stick.

aeromark@bigfoot.com

 

[LeRoiV]

Hi Ed

Please could you send a copy to me as well, at
viorel_ene@tiscalinet.it

Thank You

 

[MigrantFirmWorker]

The NASA Structures Manual (TM X-73305) presents a good method for bending crippling (section B4.4).
Your choice of cutoff stress (Fcy, 1.1Fcy, etc) will determine how conservative your answer is. Using Fcy as a cutoff is safe, but not always accurate. The only truly accurate method is test (which, fortunately you have).

http://www-glast.slac.stanford.edu/...ferences/NASA/NASA Design Manual/asm-A000.htm