Domed plates

[nuche1973]

I am working on a panel that will withstand 27" of water (1psig). The client wants to use 304L stainless steel, the panel itself will be of varying dimensions and also a circular version, both of various thicknesses. I have a spreadsheet set up to evaluate the panels vs thickness at 1 psig. My problem is that the thicknesses I have do not hold up to the pressure. I have two choices add stiffening elements or change the section to a dome/arch. The flat plate withstiffeners, I can analyze,I am having trouble evaluating the domed section. I am using Roark's Formulas for Stress and Strain, 7th edition. I am a new hire and the only resources at my disposal are pen, paper and MS Excel. Any suggestions will be greatly appreciated. Thanks.

There are days when I wake up feeling like the dumbest man on the planet, then there are days when I confirm it.

 

[rb1957]

i suspect you're analyzing the plate as a plate, ie stiff in bending. these formulas are good for deflection < 1/2 thickness. they assume zero stress on the neutral axis, ie allthe loa is reacted by bending stresses.

larger deflections show that the plate is working like a membrane (ie hoop stress). the trick then is to show the loadpath for the in-plane tension stresses, ie how does the rest-of-the-world get to react the hoop tension stress ?

don't worry about thinking you're the dumbest person on the planet ...
1) the dumbest person doesn't think that they are, therfore you're better off; and
2) she's probably blonde

 

[racookpe1978]

27 inches of standing water can be held in a 0.045 thick plastic garbage can.

What thickness steel are you evaluating?

 

[kingnero]

Is the domed section domed "into" the water, or otherwise?

If the dome is positioned against the pressure (i.e. top of the dome = highest point), I can't help you... haven't done that before.
You may want to ask in the structural forum, as this has several similarities with some rooftops + snow load.

If otherwise (think of a bowl of water), you can analyse it as a membrane (only tensile stresses), which is explained in Roark's.


PS why the 304L instead of 304?

 

[nuche1973]

Sorry: I should have been clearer. I am evaluating several plates (12-22ga) to withstand 27" of water column (1psig) over several spans (12x18,18x36,24x24,36x36 etc). These are for an explosion vent, so weight is a factor: the lighter the better. I am looking at two options: flat plate with stiffeners or domed plate. I know how to evaluate the flat plate. I need help or direction on the domed analysis. I have a copy of Roark's 7 edition and Advanced Strength and Applied Elasticity, by Ugural and Fenster. The pressure is negative pressure and will be applied uniformly to the exterior (convex) side of the dome.

There are days when I wake up feeling like the dumbest man on the planet, then there are days when I confirm it.

 

[rb1957]

i'm not so sure that weight is key ... strength is 'cause you want the disc to fail at close to the specified stress.

but you have several failure modes and details about how the disc is supported (i imagine that it is efectively built-in, and that under load it is bending about a "sharp" edge. how quickly is the pressure applied ?? presumably you'll test your design ??

often these "structural fuses" have stress concentrations deliberately added to ensure failure when needed, and adequate life at the working load ... not an easy thing to design.

 

[nuche1973]

Weight becomes a factor because I have a 9psf limit on my panel.

Someone asked why 304L in lieu of 304: 304L, source dependant, is weaker than 304. However, I received test results that state they are interchangeable...to a point. And 304L is what was specified.

There are days when I wake up feeling like the dumbest man on the planet, then there are days when I confirm it.

 

[hendersdc]

You might look at case 3a, section 13.8, pg 597 in Roark's. This case is for a uniform external pressure on a partial spherical pressure vessel.