Stresses in wall of vacuum chamber 2

[jeg]

Consider one wall of a rectangular vacuum chamber(approx 1m x 1m). The wall is thin steel plate welded to the rectangular steel frame(box section).
The pressure applied to the plate is maximum one atmosphere = 101.3 kN/m2
The pressure will produce shear and tensile stresses in the plate.
The shear stresses will define the thickness of the plate.
The tensile stresses will define the stiffness of the frame box sections and the welds between plate and frame.
Any assistance with calculating the shear and tensile stresses will be greatly appreciated.

 

[Ron]

jeg...I know you've been a member for quite a while, but this sounds like a homework problem. Is it or is there a real application for this?

In any case, FEA is the way to analyze such. Obviously it can be done by hand, but to do so accurately is a bit tedious.

Rectangular is an odd shape for a pressure vessel (or vacuum chamber). The stress distributions can get a bit whacky at corners...that's one reason they're usually cylindrical.

 

[corus]

As a rectnngular vessel each face can be assumed to be pinned at its edges as a worst case for stresses at the centre of the plate. Use Roark for a uniform pressure on a rectangular plate to calculate the stresses.

corus

 

[rb1957]

"The shear stresses will define the thickness of the plate."

why ?

be careful about the thickness of the plate ... if it is a true thick plate then the deflection under pressure shold be less than 1/2 thickness (somewhat arbitrary). if the plate is this thick then the edges are probably supported (tho' maybe only partially). if the deflections are large, then the plate is going to develop in-plane membrane loads (as well as plate bending) to carry the pressure; in the limit plate bending becomes less significant compared with membrane loads.

 

[jeg]

Thank you Ron for supporting my Peter Pan daydreams; unfortunately my homework days are 35 years in the distant past! Shape of cabinet is defined by the client, who also requires a full wall to open as a door.

corus and rb1957 , Initial calculations with fixed perimeter (welded to steel frame) indicate that plate bending will require a heavy plate greater than 12mm. I agree that membrane effect will be essential to procure the most economic solution. Any suggestions where I can find guidance on this topic?

 

[rb1957]

if you want to investigate the membrane effects i think you're into FE (and non-linear FE at that).

i'd stick to Roark in this case, even tho' the displacements look a little large (close to the thickness) ... i used Roark 7th ed table 11.4 case 1a
15psi, 40" square, steel, 1/2" thick (guess which continent i'm on) ... stress = 25ksi, deflection < 0.5".

in your case i think the end moments from each side (at a corner) combine on the corner piece. it's not my area but i wouldn't weld two faces together (directly), i'd support the corner with an angle extrusion.

btw, consider the faces as 1" wide doubly cantilevered beam (Roark table 8.8, case 24) gives conservative stresses (and unconservative deflections ... interesting

 

[jeg]

Thank you all.
membrane action saves the day with plate thickness down to approx 5mm - still to be refined and checked. There are some great interactive formulae on

http://www.xcalcs.com

(rectangular membranes:4 supported and fully held sides: uniform load) that proved very useful and saved me having to pursue the FEA route (not my forte)
JEG

 

[prex]

jeg,
in the site below you'll find calculation sheets for rectangular plates in large deformations (under Plates -> Large defo -> Rectangular.
You can choose among a simply supported plate, a plate supported and held in a in plane direction normal to each side and a supported and held in both directions normal and tangent to each side (the clamped condition is not very useful as a thin plate will behave almost the same as simply supported).
I don't think you can use one of the held conditions, as your frame (that I understand is along all sides of the cube) will also deflect more or less in the direction of diagonals, so that the distance of two opposite sides of each face will not remain unchanged (this is the meaning for them to be held). And I'm not considering the door, that for sure is not held.
So you are left with the simply supported condition that will behave a bit worse than the actual condition, so that you are on the safe side.
However you'll have to accept really LARGE deflections (centimeters). You should also check the frame under the side reactions applied by the faces, and don't forget of course to check each side of the frame for buckling.
My gut feeling is that a 12 mm thickness for such a beast would be VERY thin, unless you go for stiffening also the faces with cros beams or you use stays (not very interesting because they'll be in compression, but it is a possibility, except for the face with the door and the opposite one).
Really an odd object: will you keep us informed on how you'll proceed?

prex

http://www.xcalcs.com

Online tools for structural design

 

[jeg]

Thank you Prex.
I shall be using a cuboid, external, structural frame, not yet defined, but probably rectangular hollow section with plate steel sheeting (approx 5mm but hoping to refine to 4mm) operating as a membrane to form the sides.
Stresses in the membrane calculated from

http://www.xcalcs.com

(rectangular membranes:4 supported and fully held sides: uniform load.
Currently, I am considering the difficulty proposed by rb1957 regarding welding long corner joints and the need for angle reinforcement.
JEG

 

[prex]

Can't figure out the arrangement of your cuboid.
However be careful with membranes with fully held sides: the held condition requires a practically infinite stiffness of the supporting frame, I don't think it is realistic.
In the graph of the sheet on

http://www.xcalcs.com

you can show s_a and s_b (undocumented feature ). These are the horizontal pulls at the sides: you should check your frame with these.
You must have very good reasons to go for a so small thickness: what's the use of your gadget?

prex

http://www.xcalcs.com

Online tools for structural design

 

[JStephen]

If the vacuum will be repeatedly applied and released, you'd want to be much more careful about how you handle the bending stresses at the corners.

I'd recommend stiffeners across the area, rather than just thick plate or large deflections.

 

[jeg]

Thank you Prex and JStephen.
The vacuum chamber will be used for mixing and moulding polymers in a gas free environment.
Yes it will cycle on and off approximately every hour.
Your comments are all very helpful and informing my development process.
All further comments will be very gratefully received.