ASME VIII - Appendix 13 - Sketch 6 Spreadsheet issue 3

[Crompto29]

Hi there,

I have converted all of Appendix 13 (Non-Circular Vessels) into a spreadsheet.

I am having a problem ironing out the errors in the more complex Sketch 6. Is anyone an expert on this?

I am prepared to give all my Appendix 13 spreadsheets if someone wants to work with me on this. Is there a Spreadsheet forum that anyone knows of?

In Particular, ThetaM is supposed to measure the angle on the long-side radiused bend where the bending stress is the greatest. It comes up with angles over 70°. However the bend in my example is only 45° in total. I get similar results for other examples. How can a stress be at 70° when the bend is only 45°. Below is the equation which makes no sense. It is close to the beginning of the calcs so I can't see an error.

Theta1 = arctan(-K5*S1/(2R²-R*S1-L3*t1))

where
K5 = L2 + L21
S1 = 2*R + t1 (This dimension makes no sense.)

Also betaM = arctan(CM/(L3-E*Theta1)) is strange

Surely it should be betaM = arctan(CM/(L3-EM))
But ASME has no errors? Right?

I have attached a drawing of the example if it helps.

I have used CodeCalc to check it. It gives a similar crazy angle but I found that CodeCalc has a few errors in its App13 calcs so can't trust it to much.

Any help would be appreiciated.

 

[bradsr0138]

I am a near expert in spreadsheets and have Appendix 13 readily available to me. I am sure I can help. lets see what you have thus far.

 

[Crompto29]

That would be Great,

Attached is the problemed spreadsheet.

Two cells are my greatest problem. If you can campare betaM and ThetaM that would be good.

I suspect there may still be an error or two in the final stress calcs. So it would be good if you have the time to pdf a few examples of your own. If you have the time.



Thanks,

 

[torsani]

Hi, Crompto29

The Theta1 equation is Theta1 = arctan(L4/L3).
The equation that you show is ThetaM equation.
I think that you should use E*Theta1 at BetaM equation. You are using EM, that I think is wrong. There are a variable E(subscribe)theta1 that I think shouldn't used here.

 

[Crompto29]

Thank you torsani,

I have already made all your thoughts a few times over. And I agree that Appendix 13 says what you are saying.

However these equations are simple geometry equations. If drawn in AutoCAD ThetaM and BetaM don't line up with the geometric drawing.

betaM = arctan(CM/(L3-E*Theta1)) has no geometric meaning.

What is the Youngs modulus or weld efficiency doing in a geometric equation.

betaM = arctan(CM/(L3-EM)) works perfectly in the geometry.


And then there is Theta1 = arctan(-K5*S1/(2R²-R*S1-L3*t1)) which is supposed to find the angle at which the greatest stress occurs in a bend, however returns an angle greater then the total angle of the bend. You can't calculate a stress in thin air.

These two equations are at the beginning of the spreadsheet and are quite simple. It doesn't add up.

 

[doct9960]

Crompto29,

betaM = arctan(CM/(L3-E*Theta1)) has no geometric meaning.

What is the Youngs modulus or weld efficiency doing in a geometric equation.

E*Theta1 is a typo in ASME 2007. Theta1 should be a subscript. The formula should be...
[β]_M = tan^-1 [C_M / (L₃ - E_[θ]1)]
where E_[θ]1 = R(1.0 - cos [θ]₁)

 

[torsani]

Hi,

Crompto29 is right about the use of E_M instead of E_theta1 in the equation of Beta_M. I think that ASME is wrong. But the equation of Theta1 is still a mystery ...

 

[doct9960]

Crompto29,

You could write the ASME B&PVC committee and request for an interpretation.

With regards to [θ]_M being greater than [θ]₁, my guess is that if [θ]_M > [θ]₁, then [θ]_M = [θ]₁. I think that's what ASME did in their example on Appendix 13-17(j). The example showed the result for the membrane stress at the corner segment, (S_m)_M. Try to calculate for (S_m)_M and see if you get the same result as ASME.

 

[Crompto29]

Excellent doct9960,

That worked. The example isn't referenced in the beginning of the Appendix. Somehow I didn't find it.

It appears that much of the design geometry for this type of rectangular vessel is not exact however is adequate for Appendix 13 purposes.

So,

?M = tan-1 [CM / (L3 - E?1)] is a typo and should be

?M = tan-1 [CM / (L3 - EM)]

and

?M should be calculated as per the code but have a maximum value of ?1.

(How do you do make letters subscript in your posts?)

 

[doct9960]

http://www.tipmaster.com/includes/tgmlinfo.cfm?w=450&h=450