Non-Circular Vessels, Apx 13

[SnTMan]

Hey Folks, my question is related to language in Sec VIII, Div 1, Apx 13, 13-4(k). This para speaks of moments of inertia calculated on a unit-width basis: I = b*t^3 / 12, with b = 1.0. The direction of dimension b is not formally defined in sketches or nomenclature so far as I know.

Given that the MOI is used to calculate bending stress in the side plates, I have always reasoned that b is in the vessel length direction, or looking at, say, Fig 13-2(a)(1) for example, normal to the plane of the figure.

I have recently had cause to explain my interpretation but I have no real confirmation. I’m asking myself “How do you know that?”

What say you?

TIA

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[DriveMeNuts]

I guess you have to go back to the fundamentals of the bending equations in Appendix 13. I1 (short side) and I2 (long side) only work if 'b' is in the length direction.

I = b*t^3 / 12, with b = 1.0 also does not define 't'. You have to make the leap of judgement and assume that 't' is substituted for t1 and t2 in the App 13 equations. As there is no bending in the stay plates, 't' can't equal t3.

 

[SnTMan]

Yes, "t" is obviously defined by t1, t2, etc, etc. I feel b can only be in length direction if bending is in the plane of the figure, but just wondered if formally shown or defined somewhere...

Thx

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[LearningENG-]

Hi SnTMan,

This seems to be a very interesting question - I myself have been wondering about the answer when designing my chamber these days. However, I might have a different opinion from you. It makes more sense to me if b is along the direction of h (for long plate) or H (for short plate). Think of an extreme case when b is not a unit length but the length of the plate. if b is along the vessel length Lv, then the moment of inertia I would be Lv*t^3/12, which is greater than when b is h (or H) direction, where I = h*t^3/12. This results in the bending stress Mc/I not being the greatest on the plate.

Regards,
XS

 

[DriveMeNuts]

Go back to basics.

To calculate the second moment of area I for any S = My/I application, 'b' is always in line with the axis of the acting moment, and orthogonal to the direction of the resulting bending stress.

Setting 'b' to be in the direction of the resulting bending stress makes no sense.

 

[LearningENG-]

Yes I agree with your statement of how the direction of b is relative to the bending stress. However from where do we know the bending stress is in the direction of h not Lv?

Regards,
XS

 

[r6155]

SnTMan
Please see Roark 7th ed.
TABLE 11.4 Formulas for flat plates with straight boundaries and constant thickness
Case 1 Rectangular plate; all edges simply supported

I hope I've helped.
Regards

 

[LearningENG-]

Hi r6155,

This does help a lot, Table 11.4 is exactly what is needed. Except that, I think the case that applies is case 8, all edges fixed.

Regards,
XS

 

[r6155]

LearningENG-
You are correct.
Similar concept is factor "Z" in ASME VIII Div 1 UG-34.

Regards

 

[SnTMan]

r6155 I was aware of Roark of course. It is similar, but not as definitive from a Code standpoint as I had hoped to find.

Thanks all the same

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[DriveMeNuts]

If you can't quickly work out what 'b' is from intuition and fundamentals....you're possibly in the wrong career.

ASME BPVC is not a how-to guide.

 

[SnTMan]

DriveMeNuts, if you don't know that it is formally defined it Code somewhere, it's OK, just say so

The problem with sloppy work is that the supply FAR EXCEEDS the demand