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# Generalizing Zick's Formulas for Horizontal Pressure Vessels

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 jyspowers (Aerospace) 3 Sep 12 19:45
 All, I've been tasked with the analysis of a large pressure vessel resting horizontally on two supports. Initially, this sounds like a perfect application for Zick's formulas, but several complicating factors challenge the assumptions made by Zick. The complicating factors are: 1. The locations of the saddle supports are not symmetrically located about the midspan of the vessel. 2. The geometry of one head is ellipsoidal, and the other head is toriconical. I am attempting to generalize Zick's formulas, but I don't understand where some parts of his equations come from. Specifically, I don't understand 1. how Zick obtains the equivalent length of the vessel to be L + (4H/3) and 2. how Zick obtains the force couple correcting factor he uses to replace the shear force at the head-cylinder junction. I would appreciate any clarification or mathematical justification for the values he obtains. Finally, for context, I'm sure some of you may wonder why build such a complicated pressure vessel. Unfortunately, the reasons are proprietary, and I cannot disclose them. The simple fact is the tank exists and the supports must be designed around it. Thank you in advance, JP
 jtseng123 (Mechanical) 4 Sep 12 0:30
 Here you go: zick is to simply engineer's daily task without resorting to FEA in the old time. Even for the modern age,time is money and in highly competative world, we have to do thing quick to save manhour, and with good engineering judgement and an "approximate" approach that won't "fail" is good enough in lieu of FEA. So, Zickis is formally mentioned in the code. It is based on shear and moment diagram, with maximum 0.2L saddle location. All the coefficents and factors in the formula is to calculate the shear, moment and stress at the specific saddle location not exceeding 0.2L. You can analyze the formula, but probably won't get much from it unless you ask Zick. Understanding the background, it is how you apply this simple approach and twist some factors if you like, not challenge what assumptions made by Zick. I have done many unsymetric saddles, unequal weight and many huge drums. If you can tell the diameter, shell length, saddle locations, and CG location, I shall be able to help. Do know that you still have FEA option since Zick is only approximate method.
 LSThill (Mechanical) 4 Sep 12 3:30
 jtseng123 (Mechanical) Question: Have you used Paulin Research Group Saddle Wizard part of Nozzle Pro Software? "http://paulin.com/Products.html"
 jyspowers (Aerospace) 4 Sep 12 10:39
 LSThill: The short answer is no. Paulin's software has been mentioned in several other Zick related threads, but I consider FEA to be a detail design step. Presently, I'm in a more preliminary design phase, and I hope to generate a simple spreadsheet that calculates Zick's formulas so I can quickly change a few parameters without setting up a new FEA simulation. Additionally, my company doesn't work regularly with pressure vessels this large, and it's unlikely we'll invest in such a specialized package. We do, however, have Solidworks. jtseng123: The diameter is 10ft, the shell length is 27.25ft, the first saddle is 4.7ft from the left end, the second saddle is 23.8ft from the left end, the CG is approximately 17ft from the left end. I'd prefer if you can share your calculations, not because I don't trust you, but because I want to understand them. =D Thanks again, JP
 jtseng123 (Mechanical) 4 Sep 12 13:01
 JStephen (Mechanical) 4 Sep 12 21:21
 I don't have the Zick paper in front of me, but will point out some issues. First, Zick assumed hemispherical heads for the moment distribution. It may be that you have to neglect metal weight to make the numbers exactly match his. Secondly, if you take a cross section through the tank and analyze moments about that cross section, there is a fairly large moment due to the pressure variation down through the depth of the liquid. If you neglect that effect, it will throw things off. Next, there are various additions and modifications to the method, and it is helpful to read the different PV handbooks on the issue. For example, the normal assumption is that the top flange is part of the saddle, other designers deduce that the top flange can be omitted altogether, or treated as a wear pad, etc. Lastly, if pressures are low (say, 25 or 50 psi), it can be difficult to make the saddle calcs work due to the thin shell. If pressures are high (200 psi), saddle design won't be so critical.

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