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.(adsbygoogle = window.adsbygoogle || []).push({});

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).

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# How to compute flexure and failure loads of acrylic sheets

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