Von Misers criterion or Principle stress? 3

[george69]

Hi All

My question is in relation to Von Misers Yield stress criterion vs Principle stress limits.

If I have a simply supported beam with a point load in the middle, should the longitudinal bending stresses in the beam be checked to priciple stress limitations or to Von misers criteria.

The reason I ask is that I thought both methods were acceptable but were just differnet ways of looking at stresses. However, when you look at the Australian code provisions, one requirement is to have s1<=0.66Fy when checking priciple stresses, whereas the other requirement is to use VM equation; s1^2-s1s2+s2^2<= (Fy/1.1)^2. Note the 1.1 is the FOS on yield.

Clearly the VM equation will give you a better answer by allowing you to accept higher stresses.( i.e 1/1.1 = 0.9 compared to 0.66) So... why would you not ALWAYS use VM equation( and in my example, with s2 value zero)???

From what I have gathered from others, it seems as though both provisions must always be checked. But at the moment I can not see why. Is there a requirement that BOTH s1 and s2 must be present on an element such that one can use VM equation?


many thanks to all of you

 

[apsix]

Thanks George, I'll chase up the source book.

 

[prex]

So, in this thread, many are silently admitting that a uniaxial state of stress could be limited by (any) code (on earth) to 90% of the yield stress under design conditions?
Please, george69, carefully reread that part of the standard.

prex

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[apsix]

Actually Prex it appears to say 100% of yield.

I'll be interested to read your comments after you read it for yourself (see attached).

Note that the AISC here is the Australian version, not the American.

 

[george69]

Spot on apsix!! Thats the page that I was referring to. Although no code should allow designing to full yield, going to 90% in the VM criteria is close and vastly different to satisfying 0.66Fy for principle stresses.

Personally I think that the code is vague and should be prescriptive on when VM should be used. Perhaps even stating that "both criteria need to be satisfied" even though it may allude to this. The ambiguity is that for single direction stresss, you could argueably used a combined stress equation(ie VM) and.... voila ..comply!

 

[prex]

Difficult to judge from what I can read, apsix.
Some points to be noted:
-this is clearly not a standard, as already noted above, so it doesn't prescribe anything
-the purpose of a sentence like 'if a design formulation is needed it is suggested...' is unclear to me
-also unclear is the sentence 'on the basis of the localised nature of the stresses involved': of which stresses are we speaking about?
And george69 the VonMises criterion is just one of the methods that allow to derive, from a set o 3 (in plane) or 6 (in space) stress components an equivalent uniaxial stress that can be compared to material strength values obtained from uniaxial tests.
The VM criterion is also called the criterion of the maximum octahedral shear stress, Tresca is the criterion of the maximum shear stress and also common is the criterion of the maximum principal stress.
To be noted that all of these criteria must be (and indeed are) applicable to stress states with only a single stress component (uniaxial stress) and that they all give in that situation exactly the same obvious result: the equivalent stress is equal to that single stress component!
What you do with the calculated uniaxial equivalent stress is another matter: for design (or service) conditions and general (not local) stresses calculated with an elastic method the equivalent stress will generally be compared to F[sub]y[/sub]/1.5, but this may slightly vary from one code to another, and also the limit will be different for other methods (plastic, elastoplastic) and other load conditions (e.g. fatigue).

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes and launchers for fun rides

http://www.levitans.com

: Air bearing pads

 

[apsix]

George69 (and other interested parties)

I can close this one out with a reference to a current AS. To those who stated that the Von Mises check should also be limited to about 0.66 of yield, thanks, you were correct.

BS449 and the AS1250 source book are non-conservative and their requirements/recommendations do not comply with today's requirements.

Part of the Crane Code; AS1418.18, equation 5.7.3.3(2) requires the VM 'stress' to not exceed 0.66 of yield (see attached).

 

[george69]

Apsix- great work !!

That is the "trump" card I was looking for!!!