Von Misers criterion or Principle stress?
Von Misers criterion or Principle stress?
(OP)
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
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






RE: Von Misers criterion or Principle stress?
Anyone have a good explanation?
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RE: Von Misers criterion or Principle stress?
RE: Von Misers criterion or Principle stress?
I feel that this is generally neglected in wide flange members because different portions of the beam do the majority of the work in resisting bending and stress stress, respectively. In other words, the flanges resist most of the bending, and the web resists most of the shear.
RE: Von Misers criterion or Principle stress?
Example: simple supported beam 5m long, udl 10Kn/m, Z=100e3mm3. Mmid = 31.25kNm. Say steel yield stress is Gr 450Mpa.
stress and midspan = M/Z = 312.5Mpa > 0.66Fy( which is the principle stress code limit and appears to be no good). But when using the VM criteria 312.5Mpa < Fy/1.1 (VM criteria with FOS of 1.1 on yield and appears to be OK!)
RE: Von Misers criterion or Principle stress?
Besides, you are generally required to evaluate under the more stringent criterion.
RE: Von Misers criterion or Principle stress?
If using principal stress limits you would check the location of maximum bending against 0.66Fy and maximum shear against 0.4Fy.
If you are using von Mises then I think you would be obligated to examine all locations on the beam. Even if neither the bending or the shear is at a maximum the combined effect could be. Since you have done a somewhat more detailed analysis you could reasonably use a smaller factor of safety.
RE: Von Misers criterion or Principle stress?
AS to what the applicable code requirement is I don't know....
Ed.R.
RE: Von Misers criterion or Principle stress?
RE: Von Misers criterion or Principle stress?
So the Von mises criterion is one of the YIELDING criteria, not Shearing stress criterion.
(Remember that for materials subjected to uniaxial stress conditions, material yeilds at a simple known Yeild stress.
However, for materials subjected to Bi-axial or Tri-axial stress conditions, material yeilds at a complicated range of stress. This complicated range of stress is defined and approximated by certain yeild criteria, which includes Von Mises.)
Now coming back to the question:
The case of the allowable stress comes from the fact that it is the result of the conservative approximation of
Plastic Section Modulus (abt x-axis)-> Zx , and Elastic Section Modulus (abt x-axis) -> Sx
i.e. Zx / Sx = 1.1....recall the allowable bending stress formula = 0.6*Mn/Sx = 0.6*(Mp)/Sx = 0.6*(Fy*Zx)/Sx
where, Mp = Plastic moment (due to full yeilding of the crossection)
Hence, you get allow. bend. stress= 0.6*Fy(1.1)= 0.66Fy
So the moral of the story is the codes are conservative to a reasonable degree (and they have to be!) and you gott to follow them.
RE: Von Misers criterion or Principle stress?
I gather from your comments that the principle stress needs to be less than 0.66Fy, AND ALSO when substituted into VM equation the stress needs to satisfy <=Fy/1.1 (obviously with s2 being 0). That is both criteria need to be satisfied!
RE: Von Misers criterion or Principle stress?
The other thing is...in your example, you just dont have only bending stress,you also have shear stresses acting too.
RE: Von Misers criterion or Principle stress?
I see your point and yes, satisfying 0.66Fy automatically satisfies VM..
BTW, in my example, it was a simplistic case looking at midspan, where shear is 0. Just to emphasis my case with the longitudinal bending stress
Thanks again for your input and help!!
RE: Von Misers criterion or Principle stress?
reread carefully the standard you are using. It is simply impossible that a structural standard would limit an actual (equivalent) stress to Fy/1.1 .
And whether the equivalent stress is calculated with VM or Tresca doesn't change much, as correctly noted above by omairzali.
The criterion Fy/1.1 is likely used by your standard (that I don't know of) for factored loads in the ultimate state of stress, in that case you would be mixing up oranges and apples.
prex
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RE: Von Misers criterion or Principle stress?
Even for the case of a beam continuous over a support where there is max moment and shear at the same section, the parts of the beam that take the respective forces are different. I don't imagine that an extremely localized yielding (at some arbitrary location between the neutral axis and the extreme fiber) is detrimental to the beam. That is the reason that shear yielding has a reduction factor of 1.0 in LRFD, right?
RE: Von Misers criterion or Principle stress?
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BA
RE: Von Misers criterion or Principle stress?
The issue is not so much the equations, or what the euqations reduce to. It;s really about the factors of safety. s1<0.66Fy(for Principle stresses) versus s1<Fy/1.1(for VM criteria) as a code requirement.
Thanks to all who answered this query - Big Help!!!
RE: Von Misers criterion or Principle stress?
I'm still questioning the applicability of the VM stress. Does your code require you to check that? AISC doesn't (at least as far as I know). The max longitudinal stress is always as a location where there is 0 shear stress, and the max shear stress is always at a location where there is 0 longitudinal stress (for a beam element). Because of this, VM stresses really only apply at a location where the shear/longitudinal stresses are not a maximum. How can you possibly check these locations efficiently?
RE: Von Misers criterion or Principle stress?
Can you give an AS code reference on the stress limits you quote? I couldn't find it in AS4100 or AS3990.
If you have to satisfy both requirements then obviously the principal stress limit will govern for a SS beam, as noted above.
I see the real value of the VM limit check being for combined flexural, compression, shear and/or torsion stresses, as determined by FEA.
RE: Von Misers criterion or Principle stress?
Sure. AS1250 is the working stress code. I think it is clause 5 that stipulates the principle stress limit. However, the VM yield limit is referred to in the Source book for the AS1250. The Source book is a commentary on the 1250.
RE: Von Misers criterion or Principle stress?
RE: Von Misers criterion or Principle stress?
Please, george69, carefully reread that part of the standard.
prex
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RE: Von Misers criterion or Principle stress?
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.
RE: Von Misers criterion or Principle stress?
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!
RE: Von Misers criterion or Principle stress?
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 Fy/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
RE: Von Misers criterion or Principle stress?
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).
RE: Von Misers criterion or Principle stress?
That is the "trump" card I was looking for!!!