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Calculate Pb (bending stress) linearization

Calculate Pb (bending stress) linearization

Calculate Pb (bending stress) linearization

(OP)
thread292-95338: Correct Interpretation of Stress Linearization Ansys/Sec VIII

Hi, I need some help. I have to calculate the stress bending tensor in a SCL (stress classification line), I have the stress tensor at the SCL but now I have to apply this:

σib=(∫σi(x-t/2)dx)/(t2/6)

How can I do this?.

I have 6 σi, the distance between Node 1 and Node 2 is the same for all the nodes (0.0018). So, I don't know what is t and x terms at the formule.

RE: Calculate Pb (bending stress) linearization

t is the thickness

x is the distance along the SCL from the surface

These terms are defined in 5-A.7 Nomenclature

Make sure that you are compliant with 5-A.4.1.2 Step 2(a).

RE: Calculate Pb (bending stress) linearization

(OP)
Thanks for your response TGS4, but I don't understand how to integrate that values, If the thickness is 0.02 and the SCL measures the same, but the distance between nodes is 0.018, then t=0.02 and X=0.018?

RE: Calculate Pb (bending stress) linearization

How many nodes do you have in the through-thickness direction?

RE: Calculate Pb (bending stress) linearization

You can't have t=0.02 AND dx=0.018 (constant through thickness) as the two do not have a common integer divisor.
Say you have n+1 nodes along the SCL, number them from 0 to n: then you have x[n]-x[0]=t, x[i+1]-x[i]=dx. Now you know the stress components at the nodes σc[i] for c=1..6 and i=0..n. The integral will be (with dx not necessarily constant):
σcb=(t2/6)*Σ1n(σc[i]+σc[i-1])/2*(x[i]+x[i-1]-t)/2*(x[i]-x[i-1])

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: Calculate Pb (bending stress) linearization

(OP)
Hi, Prex and TGS4, Thanks for your responses.

I had a mistake. t=0.02 and dx=0.0018, I have 11 nodes. My values are:

NOEUD SIXX SIYY SIZZ SIXY SIXZ SIYZ
N1 -9.35135774870612E+03 1.44904368707696E+04 5.46195550842431E+04 2.13903010629624E+02 0 0
N2 -3.10130407542474E+02 3.04631426573855E+04 4.84247495421045E+04 2.16978847517025E+02 0 0
N79 -8.23328643101347E+02 2.90061817701311E+04 4.89417817923215E+04 4.55949913709594E+02 0 0
N80 -1.67184364329331E+03 2.74089218443930E+04 4.93754457437592E+04 8.28238349733271E+02 0 0
N81 -2.55136744117160E+03 2.57907213966972E+04 4.98431076755923E+04 1.09774457590994E+03 0 0
N82 -3.46687351487052E+03 2.41560638632808E+04 5.03478864434795E+04 1.26430654050799E+03 0 0
N83 -4.42341779551139E+03 2.25091570337280E+04 5.08931682065791E+04 1.32688783439494E+03 0 0
N84 -5.42627403378603E+03 2.08541301217865E+04 5.14826599584353E+04 1.28355094035272E+03 0 0
N85 -6.48112800108697E+03 1.91951719304120E+04 5.21204195948152E+04 1.13142101197749E+03 0 0
N86 -7.59424380238696E+03 1.75367178623852E+04 5.28109169112810E+04 8.66619176866407E+02 0 0
N87 -8.77262292509850E+03 1.58836565594585E+04 5.35591124447636E+04 4.84249463335018E+02ç 0 0

for each node I need the stress bending tensor (6 component). SIXZ and SIYZ are 0 because it is an axysimetric model.

Can you show me how can I do the integral?. Remember I need the bending stress for each component of each node. It is not 1 per node. I need 6.

Thank you so much.

RE: Calculate Pb (bending stress) linearization

You have pretty much reached the limit of what you can get for free over the anonymous internet (at least from me). You are free to contact me off-line and pay me to assist you. Maybe someone else will do this for free, but remember that you get what you pay for.

RE: Calculate Pb (bending stress) linearization

(OP)
Oh, TGS4 sorry I didn't mean that I wanted you to solve the problem. I just wanna know that I want to get is possible. And I put my values to give you an idea.

RE: Calculate Pb (bending stress) linearization

Quote (olgamsp)

Can you show me how can I do the integral?
Did you mean to ask a different question, then?

RE: Calculate Pb (bending stress) linearization

0.0018*11=0.0198, not 0.02.
How to do the integral is in my previous post and in the first post by TGS4. You need to be more confident with mathematical symbols if you need to make a numerical integration, otherwise you won't know what you get.

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: Calculate Pb (bending stress) linearization

(OP)
Ok thanks a lot !

Regards

RE: Calculate Pb (bending stress) linearization

Don't forget that you are computing the membrane-plus-bending at the component level (each of your SIXX, SIYY, SIZZ, and SIXY will have a membrane-plus-bending).

Then yo combine them into an invariant as described by 5-A.4.1.2 Step 2(a).

RE: Calculate Pb (bending stress) linearization

(OP)
Hi again, I forgot explain that my model was axysimetric, The form to calculate membrane and bending stress is the same?

RE: Calculate Pb (bending stress) linearization

Yes

RE: Calculate Pb (bending stress) linearization

(OP)
Hi, I have use the σcb=(t2/6)*Σ1n(σc[i]+σc[i-1])/2*(x[i]+x[i-1]-t)/2*(x[i]-x[i-1]) but that is for the final result, I need the bending stress for each node, and for node 1 the bending stress is 0 using that formule because X(i) is 0.

I think I have to use the trapezoidal method but I don't know how to.

RE: Calculate Pb (bending stress) linearization

You can't have a local bending stress at single points through thickness, this is nonsense: the only local stresses you can define are the components of the stress tensor, 3 normal stresses and 3 shear stresses.

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: Calculate Pb (bending stress) linearization

As prex says - the calculated quantities of membrane stress and bending stress are for the entire section, depending on the stress distribution through the section. They have no meaning at-a-point.

RE: Calculate Pb (bending stress) linearization

(OP)
ok, I am confuse then...

Because, the engineers of PVENG make graphics showing the SCL line at the x axis and for the y axis they show the Pm+Pb stress, for each node of the line, like this image.



So, what means Pm+Pb in the graphic if there is just one Pb.

http://pveng.com/fea-stress-analysis/notes/stress-...

Thanks for your help.

RE: Calculate Pb (bending stress) linearization

That is a graphical representation of a straight line. If you read the text of the article, you will see that there is only one value for Pb.

RE: Calculate Pb (bending stress) linearization

(OP)
Yes, they say there is only one value for Pb, but there is one value for Pm too. So, how can I get the graphic where Pb+Pm is not constant, like the image.

RE: Calculate Pb (bending stress) linearization

As the word linearization implies, you calculate a linear stress distribution that has the same bending moment as the actual stress distribution. The result is a bending stress value Pb that, in your graph above, equals some 60 (MPa?). You have that value at one wall face, minus the same value at the other face and zero at mid thickness. It is hence irrelevant the local value of this (idealized) linear distribution, only the single bending stress Pb at the face has an interest.
My advice is to deepen your knowledge of the theory of the linearization procedure by reading some related texts.

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: Calculate Pb (bending stress) linearization

(OP)
Hi again, I used the formule σcb=(t2/6)*Σ1n(σc[i]+σc[i-1])/2*(x[i]+x[i-1]-t)/2*(x[i]-x[i-1]), but what equation I should used for the node 0 and the node n?

RE: Calculate Pb (bending stress) linearization

(OP)
Hi, I made the model in ANSYS and the linearization bending results are not the same. I think this is because Ansys doesn't with the ASME Code Linearization. But Do you know what code ansys uses?

RE: Calculate Pb (bending stress) linearization

See 5-A.4.1.2, Step 2 c)

RE: Calculate Pb (bending stress) linearization

(OP)
Yes, I am doing exactly what the code says, because I am doing an excel tool to linearized stresses, But I compared the results of bending stress using ansys with the integral at the code, and are very different.

Also I saw a post from you TGS4:

"When I said that ANSYS linearization doesn't follow the Code methodology, I mean that it does not follow the procedure in 5.A.4.1.2., which is a mandatory part of the new 2007 Edition of Division 2"

So I wish know what is the difference.

thanks

RE: Calculate Pb (bending stress) linearization

Without further details, I'm not sure what I can do to assist. You need to upload whatever calculations you are doing.

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