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Not an engineer, but I think you should be looking at this:
https://www.engineersedge.com/calculators/flat-plate-deflection.htm
The dimensions should be 700 x 550mm
HDPE has a tensile modulus of about 1200 and a poisson ratio of 0.46.You'll probably want it to survive a sizable child standing on one foot in the center of a gap. Let's say a child's foot has a contact patch with a radius of roughly 30mm and at 50kg that would give (500N/(pi*30mm^2) 0.2N/mm2.
A sheet of 15mm thick would then give you a displacement of ~4mm, which sounds acceptable. But that sheet would weigh about 30kg, which is a bit much. If you reduce that weight to 20kg by making the weight 10mm you'd get a displacement of 15mm, not sure if it'll survive that and don't know how to tell. Perhaps tell your children not to climb on the trailer, you'd get away with a far thinner sheet.
These are static loads though, riding over rough roads will introduce all sorts of vibrations but I had switched to the design faculty by then so I don't have a clue.
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Tijmen
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Thanks, I'll throw some numbers into that for the various materials. It'll only be carrying bikes, no humans, and each 10-15kg bike will be upside down spreading its weight over 3 points.
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Given this datasheet: https://www.aiplastics.com/media/amari/datasheets/Nylon-6%20Datasheet.pdf
Is there enough information to get the Modulus of Elasticity and Poisson ratio? There is a tensile modulus of elasticity, but the unit is MPa. and there's no mention of Poisson.
edit: google says 1 MPa = 1 N/mm^2... and typical poisson ratio for Nylon 6 is 0.42
I'm assuming that calculator is for a plate just supported at the edges, whereas my sheet will be bolted down to a rigid frame, so different calc needed? Taking advantage of the tensile strength to compensate for a lack of rigidity?
Emyr
I've built my partner a rather large trailer and now need to add a surface.
The surface needs to carry a multitude of kids bike and an adult bike, in all weathers. The frame is made of 30mm wide aluminium profiles with 8mm slots and I have nuts with M6 threads.
The overall dimensions of the surface need to be 2040 x 1000mm and I'll cut out where the wheels go. In the photo below, I've mounted the axles on the wrong side of the frame, but now I've corrected that and the crosswise supports are level with the side rails. The width between the inner rails (inboard of the wheels) is 680mm, so 710mm between mounts, and along the length of the trailer the longest gap is 550mm.
I'm thinking a sheet of HDPE, Nylon 6 or 66 or polypropylene would work, but I don't know how to calculate how thick a sheet of each material would need to be to support about 120kg of unevenly distributed bicycles, without adding an extra 5pk just for the surface. I've run out of bolts, so can order button-head screws if the sheet is too thin to countersink.
There is a supplier about 20 miles away so it'll cost be about £5 to fuel my van to collect from https://www.visionplastics.co.uk/
Any engineers feeling curious and helpful?