How much load can a (wood) board support, if it is supported only at the ends? has already been asked, but I found the answers unsatisfactory because they focused mostly on the asker's particular setup and barely mentioned anything about the properties of the wood. One answer references PSI which seems completely irrelevant to me. Another answer references the Sagulator, but the Sagulator does not help you determine the breaking weight.
In this answer, @Ecnerwal tells how much weight the asker's particular boards can hold, but doesn't mention how he calculated that or includes references.
This is an important generalize-able question
without a satisfactory answer on this site and without a "layman's" answer on the internet. It has been asked twice on here already and seems like a basic tenant of building anything that's more than decorational.
How do I calculate the force (weight) a board can reasonably withstand across its grain?
The answer should include:
- An algebra-level equation
- A lookup table for the relevant properties of different species of wood
- I should only have to come up with the pounds (lbs) or kilograms(kg) of my force. I do not know how to measure the kPa that my lawn mower exerts.
- Any relevant notes
In @Doresdoom's answer, he includes a link to Mechanical Properties of Wood and says the relevant variable is the Modulus of Elasticity (E) found in Table 4-3a. This PDF could be used to satisfy bullet point 2 of my question or not; I don't know if it is helful, hence why I'm asking this question.
I am not asking about the compression PSI a board can withstand, the force with the grain, the pulling tension, etc. I know this question can get complicated fast, but we're dealing with what's called a simple beam. This should be as simple as possible for all the homeowner/backyard engineers out there.
Example: There is a 10' wide moat. I lay a nominal 2" x 12" x 12' (so 1.5" x 11.5" x 12') across. The board is Shortleaf Pine. It is not fixed to either side, just laying there. My soldiers line up in order of weight and cross one at a time. They tiptoe and move as smoothly as possible so they can be considered a static load (don't go off-topic here). Once in the very middle, the soldier represents a worst case scenario. How much will the soldier weigh that will break the board?
Wood obviously has variations, but so does rope and they somehow come up with strength measurements for that. The key here is to generalize. Obviously, I could get a terrible board so I wouldn't really base someone's life off of these calculations.