Hello!

Let's say we have a square, horizontal surface resting on stable joists spaced 50 cm apart in both directions. The surface consists of a board screwed and glued to the joists.

In the middle of the square "hole" between the joists, we now place a weight of 100 kg with a base area of 10x10 cm. Where the board is weakest between the joists, it's subjected to a load of 100 kg/dm2.

If the board is, for example, plywood, how thick does it need to be to avoid breaking? Is there a general measure for this that hardware stores specify, so one can know in advance whether a board of a certain thickness and material will hold up or not?

Thanks in advance for the help!
 
It corresponds to a heavy man standing on one leg. A 3 mm plywood sheet would probably hold without breaking, but it will naturally bend significantly. If it needs to be bend-free, I guess you would need to go up to about 20 mm.
 
I believe that the type of strength on composite boards is obtained through empirical data. Even for the manufacturer. They probably use a standardized test case/load case. The likelihood that this load case matches yours is small. So I think the best thing you can do is test it yourself.

For example, nail together a frame/square (50x50cm) using stable battens. Glue-screw a board on. 4-20mm thick plywood. Place the test piece on a flat and very stable surface. Measure the height of the battens. Take a piece of clay (borrow from the kids) and make a 2-3 cm thick rod that is placed right under the plywood down to the surface. Take a 10x10cm wood block and load with 200kg. Measure the height of the clay rod and see how much the plywood has bent. Repeat for a few different thicknesses of plywood until you find the threshold between two thicknesses where the thinner one breaks but the thicker one holds.

This gives you a 2x margin of strength for the minimum thickness that does not break.

This test proposal is by no means perfect, but it is good enough for the purpose, I believe. It is simply designed to be doable at home. There may also be other variants that might be faster/easier to execute.

Edit: I now realize that the clay and height measurement are not necessary.
 
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