ASME VIII-1 Par. UG-47: Theory Behind

[Ganfoss2]

I have tried to understand which is the safety criteria behind this roule, but there is something that do not work fine (I'm in the classical situation in which a flat surface pass or not pass in function of the value of the factor C. Staybolts: Tubes of OD=120 mm x WT=8mm; Flat Circular Plate: OD = 1600 mm x WT = 15 mm; P= 11 bar.g @ 250°C SA-516/70).

I know the SAFETY criteria: the MIM thickness of a flat stayed surface is the thickness of a circular plate which diameter is the MAXIMUM diameter that may be inscribed inside the path array of the stay bolts (The CODE "semplify" considering the Max Diam. as the MAX Pitch in the Center of the Staybolt Array Pattern, in all possible directions).

I know that the formula reported in UG-47 is the formula to design flat circular cover and that the value of C should reflect the edge constraints (Simply Supported or Fixed Circular Plates).

UG-47 Formula: tr = Pitch x SQRT( P / S / C)

From Theory (Annaratone, "Pressure Vessel Design" Ed. Springer - Page 220 Chapter)

- For Fixed Edge: SQRT( 1 / C) = 0.285
by which, C = 12.31

- For Simply Supported Edge: SQRT( 1 / C) = 0.454
by which, C = 4.85

But, if I assume:

1 / C = 0.285 -> C = 3.5

or

1 / C = 0.454 -> C = 2.2

I get (quite) the same figures stated inside ASME Par. UG-47(a)).

May I suppose that my discussion is right and that ASME has forgot to implement the SQRT operation?

Somebody can explain me which is a possible fault in the above reported discussion?

Many thanks to all.

 

[prex]

Not sure to see your point.
For a circular plate with supported edge the center stress is
S=(3(3+[ν])/32)Pd²/t²
and rearranging this to calculate t:
t=d[√](P/CS)
with C=32/3/(3+[ν])=3.2
Therefore the coefficients in UG-47 are safer even for a supported plate, as they are lower. An additional factor of safety comes from the fact that the allowable stress in bending should be 1.5S (but this is a different matter).
Note that UG-34 uses a similar approach, except that the C is inverted there. The value for a supported plate is 0.33 (m=1), whose inverse is close to 3.2, whilst the value for a perfectly fixed plate is 0.2 with the inverse being theoretically 5.33 (again quite close). Here again no account is made for a higher allowable in bending: the code possibly worries about excessive deflection with a higher allowable.

prex

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[Ding123]

Regidity has to be provided for liquid/gas tight as well.

 

[Ganfoss2]

Many Thanks! Now I have understood!

In short:

t = d x SQRT ( P / S / C)

With:

S = Sm = Allowable MEMBRANE Stress in lieu
of the typical value of 1.5 x Sm
for primary bending stresses.

and for:

SIMPLY SUPPORTED CIRCULAR PLATE (@ centerline):
C = 32 / (3 (3 + Nu))
for Nu = 0.3, C = 3.23 close to 3.2

CLAMPED/FIXED CIRCULAR PLATE (@ centerline):
C = 32 / (3 (1 + Nu))
for Nu = 0.3, C = 8.21

CLAMPED/FIXED CIRCULAR PLATE (@ fixed/clamped edge):
C = 16 / 3 = 5.33

Therefore the factor of C = 3.2 stated in UG-47 consider a "circular plate" of Diameter equal to the MAX Pitch of the stay-bolt array pattern, assumed simply supported at its peripherical circular edge.

The figures of C = 2.1 and C = 2.2 are more or less the 67% of C = 3.2 (NOTE: 67% = 1 / 1.50), but this is to be assumed as a SAFETY FACTOR and not as a factor depending on the use of 1.5 x Sm or Sm as allowable stress in the UG-47 formula or if the "equivalent circular plate" is campled/fixed or simply supported at its peripherical edge.

For UG-34 the formula consider 1/C in lieu of C and the factor changes: SIMPLY SUPPORTED C' = 1 / C = 1 / 3.21 = 0.31 close to figure of 0.30 stated in the Code and for CLAMPED/FIXED EDGE C' = 1 / C = 1 / 5.33 = 0.19 close to 0.20 stated in the Code.

NOTE: now I understand why with EN-13445 Section 3 or VSR (Italian Code), thickness of stayed flat plates are lower respect to an ASME design.