Need a pair of forumlas to help me build a lifting platform

[zyberwoof]

I'm planning on building a platform for Olympic weightlifting. I'm trying to minimize the weight, so I'd like to be able to properly estimate the sturdiness.

The first one is for a piece of wood sitting on beams of some sort. I know that as the beams move father and farther apart, the board can support less and less weight inbetween the beams.

What is the formula for estimating the strength difference for the board for different spacings of the beams? I.e. If the board has a limit of 10 lbs with the beams x inches apart, what is the weight limit with the beams y inches apart?


The second question has to do with relating the strength to the thickness of a board. For a scenario like above, imagine that the distance of the beams are fixed, but the thickness of the board is not.

Ex: If a board 1/2" thick can support 10 lbs, how much weight can a board 3/4" thick support?


In case you can't tell, I'm hoping to have a board sitting on beams, and I'm trying to estimate how thick to make the board and how far apart to have the beams. The thinner/farther apart, the lighter it will be.

 

[LightHero]

The formula for estimating the strength difference in this case is related to the modulus of elasticity. The modulus of elasticity is a measure of how much a material will stretch or bend under a given load. The formula for calculating the strength difference between two different thicknesses of the same material is: Strength Difference = (Thickness1/Thickness2)^3 * Modulus of Elasticity For example, if the board is 1/2" thick and can support 10 lbs, and you want to know how much weight a 3/4" board can support, you would plug those numbers into the equation: Strength Difference = (0.5/0.75)^3 * Modulus of Elasticity This will give you an estimate of the amount of additional weight the thicker board can support.