I've a completed table top for a light-duty work bench, and now I'm ready to design the base. The thought occurred to me that, because the amount of deflection of the bench top will increase in proportion to the third power of the span between the base supports, I may be able to minimize sagging by reducing the span and allowing the ends of the top to overhang the base on the ends. However, I'm guessing that the cantilevered ends would deflect at an even greater rate than the middle part.

I realize that in practice, the deflection of the table top will depend on how the load is distributed both between the base supports and along the cantilever. However, the thing I'm mainly concerned with is how this type of a table-and base-combo will handle the hypothetical worst-case situation, a load that rests completely on the line defined by edge of the table top. Anyone know the formula to calculate the deflection of the cantilever under those conditions?

I realize I may be splitting hairs here, but I find this type of stuff fun to think about, and besides, it may matter for real in a future project.

Thanks in advance.