Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
(OP)
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
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





RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
[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]
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
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.
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
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).
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
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.
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
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.
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
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
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
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.
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
Still why 0.78 only is a mystery. Will let you guys know if I get to know the reason for 0.78
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
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.
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation
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.
RE: Sec VIII Div 2... para 4.5 nozzle calculations formula derivation