# How to determine minimal wall thickness for a rectangular pressure vessel?

I know this is a basic question but google only gives formulas for more "rounded" shapes. How to calculate the minimal thickness for a flat wall knowing tensile strength of the material and the maximum pressure difference between two sides?

• What is your intended max pressure? Dec 1, 2019 at 11:57
• This is good example of a situation where if you have to ask the question you shouldn't be doing it. Pressure vessels can be very dangerous if you are storing gasses. You should not use high strength materials as they tend toward brittle fracture vs. ductile fracture. Dec 30, 2019 at 21:45
• Why can't we consider a problem based on it's technical problem solving merits instead of calling out the chicken little safety cops? You don't learn anything by hid ing behind mom's safety apron and assuming all problems must be risk free. Oct 6, 2022 at 17:16

The reason that you can't find anything on Google is that it is a bad idea to make a rectangular pressure vessel. You get stress concentrations at the corners which makes the vessel much weaker. This is bad because when pressure vessels fail, they release a huge amount of energy very suddenly. It only takes a little googling to find examples of fatalities due to pressure vessel failures. Pressure vessel design should not be attempted by inexperienced people. Hire a professional or just buy one off the shelf.

• If I could up vote this more than once I would. Dec 30, 2019 at 21:42

There are two ways to deal with this question and both have to do with the deflection of plates (sides and top and bottom of the container) under the pressure load. The first alternative is to demand small deflection,1/2t, the second is allowing for large deflections say up to 20t to save on the material.

In your case, the supports are the corners of the container and the can be approximated as a simple support.

These have discussion and formulas among other references in Roark’s Formulas for Stress and Strain WARREN C. YOUNG RICHARD G. BUDYNAS Seventh Edition McGraw-Hill pp 451 through 473. 11.10 Bending of Uniform-Thickness Plates with Straight Boundaries.

I quote the intro into the rectangular plates, but you got to search through the text to find your case.

In Ref. 35 experimentally determined deflections are given and compared with those predicted by theory. In Ref. 74 a numerical solution for uniformly loaded rectangular plates with simply supported edges is discussed, and the results for a square plate are compared with previous approximate solutions. Graphs are presented to show how stresses and deflections vary across a square plate. Chia in Ref. 91 includes a chapter on moderately large deflections of isotropic rectangular plates. Not only are the derivations presented but the results of most cases are presented in the form of graphs usable for engineering calculations. Cases of initially deflected plates are included, and the comprehensive list of references is useful. Aalami and Williams in Ref. 92 present 42 tables of large-deflection reduction coefficients over a range of length ratios a=b and for a variety—three bending and four membrane—of symmetric and nonsymmetric boundary conditions. Loadings include overall uniform and linearly varying pressures as well as pressures over limited areas centered on the plates.

• While this is a reasonable approach for the deflection in the center of the plate, it does not address the stress at the corners, which is going to be the hardest location to analyze and the most likely point of failure. Dec 1, 2019 at 0:53
• @DanielK, stress on the corners depends on the material and manufacturing method. If the container is plastic the corners do not have any residual stress from rolling or welding and the stresses are less than membrane and plane moment at the center of each face. unless the containers are banged around. the same book has guidelines for handling those and faces with holes, etc. and also FEM software can analyze the stresses. I have used 3' by 3' cubic containers of water, sand, or other construction materials. Some with protective wire mesh cage some without. they are convenient for Jobsite. Dec 1, 2019 at 2:36
• Well that's fine for a box of sand but the OP asked about a *pressure vessel *. A box of sand won't hurt anyone if it fails but a pressure vessel might take out an eye or even kill someone if it fails. You have to hold those things to a very high standard. Dec 1, 2019 at 13:09