## Stress Linearization 2nd thread

## Stress Linearization 2nd thread

(OP)

Hello Prex/TGS4,

I red your previous posts you wrote regarding ASME SECTION VIII, DIVISION 2 ANNEX 5.A.

I am still not 100% sure how to calculate it

The first two steps of ANNEX 5.A are clear. I am confused how to calculate Bending Stress and Membrane + Bending Stress:

My questions refer to the forum and the following sources:

http://www.eng-tips.com/viewthread.cfm?qid=412084

http://fsefea.com/stress-linearization-asme-sec-vi...

https://pveng.com/home/fea-stress-analysis/lineari...

Sm= VonMisesStress of (Snm, Stm, Shm, Tntm, Tnhm, Tthm) = PmV =sigma_ eqvm

All right, all three sources are calculating Membrane Stress with the same formula.

In a post here in the forum user Soave posted on Mar 17 calculated the Bending Stress with the formula:

Sb = VonMisesStress (Sbxx, Sbyy, Sbzz, Sbxy, Sbxz, Sbyz)

At pveng.com

PbV = VonMisesStress(Snb, 0, Shb, 0, Tnhb, 0)

Suave used sxx at node 1 and subtracted it with the formula that fits to the formula of Annex 5.A. In example min= sxx(0)-(Smxx+Sbxx).

At pveng.com the total Vmises Stress is used.

Suave calculated the Bending Stress with the formula:

Sm+b = VonMisesStress of (Smxx+Sbxx,Smyy+ Sbyy, Smyy+Sbzz, Smxy+Sbxy, Smxz+ Sbxz,Smyz+ Sbyz)

At pveng.com and fsefea.com it is done by:

- Membrane + Bending Stress - end i (+ bending) [->sigma_ eqvmb0]

PmbVi = VonMisesStress of (Snm + Snb, Stm, Shm + Shb, Tntm, Tnhm + Tnhb, Tthm)

- Membrane + Bending Stress - end j (- bending) [ ->sigma_ eqvmbt]

PmbVj = VonMisesStress of (Snm - Snb, Stm, Shm - Shb, Tntm, Tnhm - Tnhb, Tthm)

Here the maximum of one of these two values is the value for Membrane + Bending Stress. I guess this difference is also related to the hoop and meridional component issue.

If I want to visualize Membrane + Bending Stress I draw a line from PmbVi to the Point L=half thickness/height membrane stress and from this point to PmbVj?

Any help would be greatly appreciated. I am a Student from Germany and tried my best to explain. I know my English is not perfect, but I hope anyone can understand.

Best regards

I red your previous posts you wrote regarding ASME SECTION VIII, DIVISION 2 ANNEX 5.A.

I am still not 100% sure how to calculate it

The first two steps of ANNEX 5.A are clear. I am confused how to calculate Bending Stress and Membrane + Bending Stress:

My questions refer to the forum and the following sources:

http://www.eng-tips.com/viewthread.cfm?qid=412084

http://fsefea.com/stress-linearization-asme-sec-vi...

https://pveng.com/home/fea-stress-analysis/lineari...

*Membrane Stress*Sm= VonMisesStress of (Snm, Stm, Shm, Tntm, Tnhm, Tthm) = PmV =sigma_ eqvm

All right, all three sources are calculating Membrane Stress with the same formula.

*Bending Stress:*In a post here in the forum user Soave posted on Mar 17 calculated the Bending Stress with the formula:

Sb = VonMisesStress (Sbxx, Sbyy, Sbzz, Sbxy, Sbxz, Sbyz)

At pveng.com

PbV = VonMisesStress(Snb, 0, Shb, 0, Tnhb, 0)

**First question:**According ANNEX 5.A bending stresses should be calculated only for the local hoop and meridional (normal) component Stresses, therefore I think pveng.com used the right formula?*Membrane + Bending Peak Stress:*Suave used sxx at node 1 and subtracted it with the formula that fits to the formula of Annex 5.A. In example min= sxx(0)-(Smxx+Sbxx).

At pveng.com the total Vmises Stress is used.

**Second question:**If I compare Step 3 of ANNEX 5.A I would say I have to calculate it with the formulas 5.A.3 and 5.A.4. Here Suave is right?*Membrane + Bending Stress:*Suave calculated the Bending Stress with the formula:

Sm+b = VonMisesStress of (Smxx+Sbxx,Smyy+ Sbyy, Smyy+Sbzz, Smxy+Sbxy, Smxz+ Sbxz,Smyz+ Sbyz)

At pveng.com and fsefea.com it is done by:

- Membrane + Bending Stress - end i (+ bending) [->sigma_ eqvmb0]

PmbVi = VonMisesStress of (Snm + Snb, Stm, Shm + Shb, Tntm, Tnhm + Tnhb, Tthm)

- Membrane + Bending Stress - end j (- bending) [ ->sigma_ eqvmbt]

PmbVj = VonMisesStress of (Snm - Snb, Stm, Shm - Shb, Tntm, Tnhm - Tnhb, Tthm)

Here the maximum of one of these two values is the value for Membrane + Bending Stress. I guess this difference is also related to the hoop and meridional component issue.

**Last Questions:**TGS4 wrote on 2 Aug 16 a tensor, where I can not find + Tnhb. I do have to include Tnhb right?If I want to visualize Membrane + Bending Stress I draw a line from PmbVi to the Point L=half thickness/height membrane stress and from this point to PmbVj?

Any help would be greatly appreciated. I am a Student from Germany and tried my best to explain. I know my English is not perfect, but I hope anyone can understand.

Best regards

## RE: Stress Linearization 2nd thread

This is the wrong way.

These are from my training class (hence the reference to "slides").

## RE: Stress Linearization 2nd thread

TGS4,What is the motive for not including the bending effects of the through thickness stresses?I know this is the procedure as provided by the code but I do not know what the reason is. My guess is the following:

For the through thickness shear stresses since they have a distribution like a parabola the moment around the mid-point is very close to zero.

For the through thickness normal stress I do not have any idea why bending effects are neglected.

How much does that neglecting change the results by the way?

## RE: Stress Linearization 2nd thread

TGS4, there is also 5.A.4.1.2.b.2, and as 'needs to be considered only' to me implies 'but may be considered in all cases', I would say that, to promote standardization of procedures (and also because I don't know how to check whether a stress distribution results in torsion...), it would be simpler to include in your first table the σ_{yz,b}component. This is what pveng.com does, as reported byRobse(I didn't personally check) and I think it is a correct procedure in all cases.Robse, concerning the peak stress, only the tensor is defined (at wall surfaces) in STEP 3. If you refer to Step 6 in pveng site, then that's not the same; they define the peak stress as the highest stress resultant on the SCL, whilst STEP 3 in App.5.A defines the single components of the peak stress as theincrementof the total stress components at wall surface with respect to the previously calculated m+b stress components (where some b components are zero).Concerning your second question, I don't see your point: STEP 3 refers exclusively to the peak stress tensor (and not to a 'Membrane + Bending Peak Stress', as you say; such a quantity is not defined in the code).

Your last question is already answered above. But you don't need to visualize the m+b stress along the SCL, as the code only requires to determine the stress resultants (VonMises here)

at wall surfaces, the rest doesn't matter.prex

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## RE: Stress Linearization 2nd thread

I will calculate the Bending stress with VonMisesStress(Snb, 0, Shb, 0, Tnhb, 0)

Thank you also for clarifying peak stress and Membrane + Bending Peak Stress! I completely overlook the difference.

## RE: Stress Linearization 2nd thread

paulettea- the explanation in WRC429 (and mostly repeated in PTB-1) is thorough.

## RE: Stress Linearization 2nd thread

prex

http://www.xcalcs.com : Online engineering calculations

https://www.megamag.it : Magnetic brakes and launchers for fun rides

https://www.levitans.com : Air bearing pads

## RE: Stress Linearization 2nd thread