Sec VIII Div 2... para 4.5 nozzle calculations formula derivation 7

[Minamtungekar]

Hi all,
I usually tend to understand the principle behind the calculations done by software which brings me back to the code time and again.
So while understanding nozzle area calculations in para 4.5 of division 2, I came across formula 4.5.119 and 4.5.120 in which there is an equation showing 0.78 Times Square root Rn times to where Rn is nozzle radius and tn is the nozzle thickness.
HOW IS THIS DERIVED??
Please help me as it's eating me
Also this equation is used at many places in both the divisions!!

Thank you

 

[TGS4]

Have you looked in PTB-1?

[edit]ASME PTB-1 doesn't have the derivation of these equations. It just refers to WRC 529. You will need to obtain WRC 529 in order to obtain the derivation.[/edit]

 

[JStephen]

Never bothered to research it.
Where I assume it comes from-
If you take an infinitely long cylinder, and apply a radial force distributed around it, and calculate the deflection from that force;
And do the same for a circular ring;
And then set the deflections equal and find the circular ring area that gives the same deflection, it would give you that result.
The formulas for radial deflection in the cylinder would be in Timoshenko's Theory of Plates and Shells, and also in Roark's Formulas for Stress and Strain.

 

[TomBarsh]

The derivation of the methods and formulas of Div 2 Part 4.5 nozzle analysis are presented in the WRC bulletin 529 "Development of Design Rules for Nozzles in Pressure Vessels for the ASME B&PV Code, Section VIII, Division 2".

The particular term 0.78*sqrt(Rt) relates to the theory of beams on elastic foundations (which is used in many analysis situations for pressure vessels). Essentially, the "local" stresses at a structural discontinuity will dissipate down to the "general" stress level over some distance related to the sqrt(Rt). See, for example, "Theory and Design of Modern Pressure Vessels" by John Harvey (Chapter 4), or similar textbooks (not certain if Bednar, etc, cover this).

 

[Minamtungekar]

@TSG4,TonBarsh and JStephen
Thank you so much for the replies. I did not get the derivation but by TomBarsh's answer I got an idea of the use of Rt. I am still searching for a copy of WRC 529.

 

[TomBarsh]

Welding Research Council bulletin 529 is available directly from the WRC at

https://forengineers.org/bulletin/wrc-529

 

[MrPDes]

ASME PTB-1 suggests that 0.78 factor is applied to compensate for the ASME VIII Div 2 reinforcement method not calculating bending stresses.

I assume the WRC 529 derivation includes the effects of bending in the Shell-Neck junction and ASME VIII Div 2 is a simplified method.

 

[Minamtungekar]

This is what I have found out..
bending stresses due to concentrated external loads, are of high intensity only in close proximity to the area where the load is applied. The attenuation or the decay length, the distance from the load where the stresses are significantly reduced, is limited and quite short for example in a cylinder it is sqrt Rt

Pressure vessels design handbook - bednar

 

[Minamtungekar]

Regarding the factor of 0.78, I do not know about it. But as said by MrPDes.. 0.78 is used to compensate for not taking into account bending stresses? How is tha possible ?? If bending stresses are not considered, then should the factor be more that 1 ?

 

[MrPDes]

Minamtungekar,

sqrt(Rt) is the maximum length along the nozzle neck that "actually" contributes to reinforcement.......at least approximately.

ASME VIII Div 1 reduces this length and therefore reinforcement area to 0.78 in the reinforcement calculation. This means that more reinforcement area needs to be added.

 

[Minamtungekar]

Yup got it now ! Thank you
Still why 0.78 only is a mystery. Will let you guys know if I get to know the reason for 0.78

 

[JohnGP]

In the Les M. Bildy paper "A Proposed Method for Finding Stress and Allowable Pressure in Cylinders with Radial Nozzles"

https://www.codeware.com/company/docs/PVP-399-Les-Bildy.pdf

, the Background discussion more or less reiterates TomBarsh's explanation by stating "...the discontinuity stress attenuates with increasing distance and is assumed to be insignificant at a distance of (RT)^1/2/1.285". Note that 1/1.285 = 0.78. I don't know what the basis of the "assumption" is though.

 

[NRP99]

Dear all,

Please refer "2.6.3-Die-out effects" in book-Pressure vessel design:Concepts and Principles edited by Spencer and Tooth for derivation of the equation.

 

[MrPDes]

"Pressure vessel design: Concepts and Principles" has the following equation for calculating "die out distance":

Die out distance along nozzle neck = nR/β = 0.78×sqrt(Rt) where there is a complex derivation saying β^4 = 3(1-v)²×(R/t)² and n = 1 and v = 0.3.

There is a figure with different stress graphs showing that n equals a different number for finding die out distance for membrane, bending, shear, rotation etc.

It looks like the selection of n=1 which results in 0.78 is arbitrarily selected off of shell theory stress graphs depending on how conservative you want to be, for instance ASME VIII uses 0.78 for all nozzle neck geometries however the bildy paper that developed the method allows a special case of 2*0.78 for larger Rn/Rs ratios. PD5500 uses 1.00 instead of 0.78. EN13445 uses sqrt(2) instead of 0.78.

My assumption in earlier posts about ASME VIII Div 2 using 0.78 to compensate for not including bending in the design method is probably wrong.

 

[Minamtungekar]

@MrPDes Thank you. that was very helpful. I believe understanding the principal behind how the formulas are derived gives one a better understanding of the effects of different parameters.