# How to compute flexure and failure loads of acrylic sheets

1. Apr 29, 2010

### bootstrap

I am designing a 25-meter long by ~10-meter wide by 2~4 meter deep swimming pool from transparent acrylic or polycarbonate sheets, and need to determine what thickness the plastic sheets must be to not break... as well as how much the center of each sheet will deflect under the load. I am not sure how to calculate this, and appreciate any help or pointers to places that describe how a semi-dummy like me can compute this.

The following is a description of the known characteristics:

The entire structure (all sides and bottom surface) is composed of 96" x 72" x ???" sheets of transparent acrylic or polycarbonate sheet. All four edges of each sheet will be attached to aluminum structural material (like square tubes or I-Beams or U-Beams) with some kind of thin surgical-rubber-like material between the metal support structure and plastic sheets (to prevent water leaks and protect the plastic from the harshness of the metal surfaces, and to assure even support along the edge). Presumably somewhere between 1" and 3" of the edge of the sheet will be supported by the aluminum structural material.

Understand that the BOTTOM of the pool will be 7 to 8 feet ABOVE the floor, and people will be able to walk around beneath the pool and watch people swim races above them (and vice versa). People on the next floor up can walk beside the pool and watch people swim along next to them (and vice versa). Presumably super strong vertical concrete-filled steel columns will be situated at all corners of every sheet (~6-feet apart in one direction, and ~8-feet apart in the other direction assuming the largest standard sheets available at the thickness I intuitively suspect will be required (8mm ~ 16mm == 0.3125" ~ 0.6250")).

Presumably the plastic sheets on the bottom surface must be strongest and thickest, and presumably the plastic sheets on the sides could be somewhat thinner. For various reasons, all plastic sheets on the bottom must be the same thickness, and all plastic sheets on the sides must be the same thickness, even though sheets near the surface suffer less water-pressure forces, and could be made thinner if not for other considerations.

Thus, one or two computations are necessary, I suspect.

The first is the computation for a sheet on the bottom of the pool supporting the 2-meters or 4-meters of water above it. Thus approximately 10 to 20 cubic meters of water is supported by each plastic sheet on the bottom of the pool, which is 10,000 to 20,000 liters, which is 10,000kg to 20,000kg spread across the surface of each plastic sheet (assuming I have these numbers correct). If I knew how to compute this, I'd probably start by taking my intuitive guess of appropriate thickness (12mm or 1/2"), compute the deflection in the center of the plastic sheet given this evenly distributed load, then somehow determine whether this would rupture the acrylic or polycarbonate material. Given the result, thinner or thicker plastic sheets could be tried in the same computation to arrive at the appropriate stock thickness.

And yes, on general principles I intend to overdesign by about 2x (if that seems sufficient to prudent folks for a situation like this). If anyone knows how to perform vastly more complex computations, the next obvious question is "what if someone walks along below the bottom sheet with a metal spike and scratches a nasty gouge in one of the sheets. Would this substantially weaken the plastic sheet by providing a failure point (somehow I imagine it would if the material was glass, but I'm not so sure for more flexible materials like acrylic or polycarbonate). If this might be a problem, then I might be inclined to add a thin sheet of glass between the metal frames and the plastic sheets to protect against "malicious jerks".

The other computation would be to compute the same information for a plastic sheet on the side of the pool at the greatest depth (2-meters or 4-meters). I have no idea how to compute the horizontal force the contained water would generate, but once that is known, probably the rest of the computation could be the same as the first computation to generate a conservative result (though again, that's just my intuitive inference).

One final question. I imagine there are two ways to design and fabricate this structure. One method leaves the edges of the plastic sheets supported on one surface (against the metal framework), but otherwise (its edge and opposite side) unconstrained. The other method would "pinch" the edge of the plastic between two pieces of structural metal by tightening bolts through the two pieces of metal to squeeze the plastic sheet. I intuitively suspect the second configuration is slightly stronger, and slightly reduces the flexure suffered by the plastic sheets. It also seems to provide more than twice the protection against leakage around the edges. So I tend to prefer the second configuration, though it makes me worry a bit about differential thermal expansion between the aluminum frame and the plastic sheets. However, saying this just now makes me realize that differential thermal expansion will only be a problem if the pool is located outdoors AND the water temperature is allowed to vary significantly. My assumption is the water will be always kept at about 30C, which tends to mitigate this concern. Nonetheless, nothing "terrible" should be allowed to happen if for some unexpected reason the temperature does cycle between 1C and 35C.

Thanks in advance to anyone who can provide (or point to) simple algebraic equations to solve this problem. PS: www.wikipedia.com gives fairly complete material information for polycarbonate (but not acrylic/plexiglass)... but I suspect acrylic is not dramatically wimpier than polycarbonate (my intuitive guess is 10% to 25%... similar to the price differential).

2. Apr 29, 2010

### Studiot

Since you will be inviting members of the public to walk around underneath this structural design I think you should employ a professional.

3. May 1, 2010

### bootstrap

Where did I say "the people" would be "the public" and where did I say they would be "invited"?

Also, where did I say I would not have professionals review the design before anything is built? Presumably you understand reviews cost vastly less than complete design and engineering work. Also, where did I say test rigs would not be constructed to confirm failure-mode calculations before the full-size device is constructed? And who says I'm not a professional, for that matter?

If I'm not mistaken, I asked this question in a physics forum, not a legal forum. I will much appreciate a physics answer, or pointers to easy-to-follow methods --- if anyone has any.

If not, I'll figure this out myself [possibly from first or fundamental principles], as I usually do, but at much greater effort. If you want to offer ideas or suggestions, but somehow imagine you could somehow bear some kind of blame, consider the questions speculative or educational, and also understand any completed design will be reviewed by at least two other parties (per my general practice), and you are hereby held harmless.

My thanks in advance to anyone interested and knowledgable in physics and/or mechanics who is willing to discuss topics as controversial as swimming pools and materials as dangerous as water. BTW, the pool will contain only sub-micron filtered, concentrated-solar-purified-and-heated, UV-and-oxygenation-treated water with zero chlorine or other gross chemicals.

4. May 2, 2010

### Studiot

You owe a duty of care to anyone who walks under your structure or swims in it, they are all 'members of the public' in that respect.

The practice of Structural Engineering requires significant safety factors to be incorporated in any structural design. These are enshrined in building codes in most countries. As a result any legal design will be considerably stronger than one derived from 'first principles'.

However the problem you face is not one of strength - it would not be difficult to obtain a sheet of said plastic and test load it with bags of sand.

The problem is one of the long term response of the material to load - this is known as creep. Plastics materials suffer greatly from this so the design difficulties that present are twofold. One is the design of the fixings to spread the load so that there are no stress concentrations to initiate catastrophic failure. The other is to establish a suitable inspection regime to monitor any incipient long term failure by creep mechanisms, either in watertightness or structurally.

You did not mention any of these matters either.

5. May 3, 2010

### bootstrap

Thanks for including some mechanics tips along with legal warnings everyone seems compelled to offer. Yes, I understand safety factors and that many fatigue and failure modes apply to real-world designs. I have been often criticized in the past for posting "vastly too long and detailed" messages, so my original message purposely limited itself to information relevant to the specific question I asked. I guess I just can't win, huh?

Yes, the load must be supported evenly everywhere there is contact. That's why the mating portions of the metal surfaces will be machined flat, and a sufficiently thick material with a consistency like surgical rubber or inner-tube rubber will additionally assure even loading and limit or eliminate leakage. I did mention this briefly in my original message.

But I did not mention long term creep. While I suspect overdesigning by 2x to 10x (depending on what thickness this requires) will render these other issues mute. Of course, I am not certain of that, and must verify this too (depending on expected lifetime). Alternately, and extra support across the diagonals of the bottom sheets may be appropriate if the thickness require to assure sufficient conservatism is too extreme. Likely the sheets on the side will be less problematic.

If the bottom sheets need to be thicker than practical from an availability or cost point of view, then the entire structure will sit on the ground, and we will only be able to walk along the sides and ends. Let's hope not, but we'll see. We could also bond long bars of the plastic against the outside of the sheets to reduce sag and further strenthen them, at modest cost in optical distortion along those sections. Many ways exist to design around limitations of the plastic material, but first I want to figure out whether the clean and simple configuration works. And yes, if those strengthening bars are bonded on the inside of the pool, given the modest difference of index of refraction between the plastic and water, they would be much less visible than external pieces, but then a swimmer could catch on them or bang into them too easily, even if they're only a couple inches thick.

Right now I just want "plate equations for distributed loads and edge support" to determine whether my intuitive guess of required thickness from experience is "in the ballpark". Then I can spend significantly more time reviewing the details of the many considerations this design presents. If someone hadn't stolen my two favorite physics/mechanics handbooks, or I was near a populated area, I could solve this myself in short order. However, I'm much too dumb to remember these equations since I last needed them (~3 years ago), and I don't have easy access to anything from my remote location (I'm ~100km from the nearest human, over 200km from "town", and don't need supplies for another 2~3 months). It would have been nice if someone here could have helped. I guess not. I'll figure out something.