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# ASME 2021 edition Section VIII Div.2 part 5 | Local failure criteria - elastic analysis

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## ASME 2021 edition Section VIII Div.2 part 5 | Local failure criteria - elastic analysis

(OP)
Hi,

Instead of evaluating the algebraic sum of 3 linearized principal stresses to be less than 4S, if the algebraic sum of 3 principal stresses (not linearized)is calculated using a user defined formula in ANSYS WB i.e. s1+s2+s3 - and found to be less than 4S, is it safe to say that the linearized sum will be less than this user defined formula value and that the local failure criteria is satisfied?

Thanks,
Shiraz

Shiraz
Sr. Engineer

### RE: ASME 2021 edition Section VIII Div.2 part 5 | Local failure criteria - elastic analysis

That’s your judgement call as an engineer to make. The Code neither permits nor prohibits this.

Is there any reason why you can’t linearize?

### RE: ASME 2021 edition Section VIII Div.2 part 5 | Local failure criteria - elastic analysis

(OP)
Hi TGS4,

I was being lazy to calculate at several points the linearized principal stresses. Hence I thought just giving a user defined formulae will suffice.

Another point, When I see the user defined formula and plot the stress using this function (s1+s2+s3) I get a plot with minimum value and maximum value of the plot and minimum value (negative value) is greater than the 4S limit. So I have to linearize to prove that the sum of linearized principal stresses is less than the limit.

Another point is that when I linearize the principal stresses (maximum, middle and minimum), ANSYS shows the linearized membrane, membrane plus bending, peak, total. So for the sum of linearized principal stresses, do I have to take the membrane plus bending or total to sum the maximums and minimums? Attach is a picture of 3 plots representing linearized principal stresses and a plot of user defined formula (bottom right)

Sum of linearized principal stresses (considering membrane + bending (outside)) = 172.03 + - 0.48+ (-71.4) = 100.15 MPa
User defined formula = -1288.6 MPa (not at the same location as the linearized stress path)

So it seems user defined formula is conservative but if it is greater than the allowable limit then go with sum of linearized principal stresses.

Shiraz
Sr. Engineer

### RE: ASME 2021 edition Section VIII Div.2 part 5 | Local failure criteria - elastic analysis

Section 5.3.2 does specify "algebraic sum of the three 'linearized' primary principal stresses". At least in the 2021 code, it does.

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