Is my estimate for the bending of a plastic plate reasonable?

[Lion_Engineer]

Salutations!

Recently I decided to run some hand calculations to test and see if the thickness of plastic sheet / material selection for the sheet are reasonable for being bent by hand. The sheet is 0.5m x 0.461m and 3mm thick, however the actual part has cutouts for access. Ideally the sheet should be somewhat rigid, but bend to allow the part to be installed by hand.

Since it'll be made from laser-cut plastic, I went and used the flexural modulus of the plastics to estimate the kind of force I would expect to bend the sheet about 0.25m, however the results are a bit confounding.

If the material were acrylic, it would only take about 50lbs to bend fully, but if it were polycarbonate, 1,000lbs.

Are these kinds of results reasonable? Or have I made some oversight that's given me a useless result?

 

[MintJulep]

You've done something wrong.

Possibly units.

 

[Lion_Engineer]

MintJulep:
That was my first instinct so I switched over into m*kg*s with all units and double checked to make sure I wasn't missing something obvious.

Attached is the spreadsheet I used to run the numbers, only thing I can think of that would be off is either the moment of inertia or the material modulus, which are direct from the source so I'm back at square one.

 

[GregLocock]

E for acrylic is around 3e9 Pa, you have 1e8

Cheers

Greg Locock


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[Lion_Engineer]

Greg:

You're totally right, looks like it was a misconversion on my end . Although it only brings the force up in line with the rest of the values, at 500lbs instead of 50.

 

[Orange_kun]

You changed the stiffness by a factor of 30 and the force only dropped by half? Something else is up.

Also, the magnitude of your desired bending is huge compared to the part in question. You should be well within plastic deformation, at which point I would not trust that particular equation. For deformations around 0.025m, sure.

Also, there are 4.4N per lbf, not the other way around. I suggest you draw this out and think about the magnitude of the deformations, as well as doing a dimensional analysis on your equation.

 

[Lion_Engineer]

Orange_kun:

Yeah, you've got a point. I was afraid that the beam bending wouldn't apply and the more looking I do the less confident I am that simple hand calculations will work.
Right now I'm between finding equations for plate bending (Don't apply for large deformations) and the Föppl–von Kármán equations, which every source on has plastered warnings to the effect that "They're coupled, fourth-order, nonlinear equations" = a huge pain in the posterior to solve.

Surely there's some rule of thumb plastic workers have gone with for determining the flex in varyingly thick sheets of plastics I can use? After all, I only really need to know if bending this much will take excessive force or not.

 

[Compositepro]

Plastics are bent while hot, almost molten.

 

[MintJulep]

For the cost of your time doing calculations you could do a whole bunch of tests.

Small pieces of common plastic sheet are pretty cheap.

 

[Lion_Engineer]

MintJulep

You're probably right, I'd need to test them anyway to make sure they don't damage what they're supposed to be contacting.

The original idea was to design a kind of cover from the plastic, one which is installed via flexing - similar to many consumer phone cases only much larger.