Calculate Pb (bending stress) linearization

[olgamsp]

thread292-95338

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.

 

[TGS4]

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).

 

[olgamsp]

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?

 

[TGS4]

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

 

[prex]

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=dx. Now you know the stress components at the nodes σ_c for c=1..6 and i=0..n. The integral will be (with dx not necessarily constant):
σ_cb=(t²/6)*Σ₁ⁿ(σ_c+σ_c[i-1])/2*(x+x[i-1]-t)/2*(x-x[i-1])

prex
[URL unfurl="true"]http://www.xcalcs.com[/url] : Online engineering calculations
[URL unfurl="true"]http://www.megamag.it[/url] : Magnetic brakes and launchers for fun rides
[URL unfurl="true"]http://www.levitans.com[/url] : Air bearing pads

 

[olgamsp]

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.

 

[TGS4]

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.

 

[olgamsp]

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.

 

[TGS4]

Can you show me how can I do the integral?

Did you mean to ask a different question, then?

 

[prex]

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
[URL unfurl="true"]http://www.xcalcs.com[/url] : Online engineering calculations
[URL unfurl="true"]http://www.megamag.it[/url] : Magnetic brakes and launchers for fun rides
[URL unfurl="true"]http://www.levitans.com[/url] : Air bearing pads

 

[olgamsp]

Ok thanks a lot !

Regards

 

[TGS4]

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).

 

[olgamsp]

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

 

[TGS4]

Yes

 

[olgamsp]

Hi, I have use the σcb=(t2/6)*Σ1n(σc+σc[i-1])/2*(x+x[i-1]-t)/2*(x-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.

 

[prex]

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
[URL unfurl="true"]http://www.xcalcs.com[/url] : Online engineering calculations
[URL unfurl="true"]http://www.megamag.it[/url] : Magnetic brakes and launchers for fun rides
[URL unfurl="true"]http://www.levitans.com[/url] : Air bearing pads

 

[TGS4]

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.

 

[olgamsp]

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-classification-lines-scl/

Thanks for your help.

 

[TGS4]

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.

 

[olgamsp]

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.