I asked the same Q on levers... I think thin as you dare , just take 'em down a whisker at a time and quit at the first sign of flex (or go back a tad )
I went for a slightly triangular section, wider on the back, slightly concave sides, narrow on the belly...
Del
This is correct. the idea is to reduce weight while not having them bend excessively, or be laterally unstable. A triangle, Gothic arch, or diamond cross section is my usual result, but round or square is fine, too.
I don't remember the exact numbers, but once on another site I asked a Q? and got a great answer. Imagine a bar or board 2 cm square. It will have "x" stiffness, and strength. A round cross section of a 2" diameter will be something like 96% as stiff and strong. A round, hollow section, like a tube will be 92% as strong and stiff. A triangle cross section of the same length of side will be 87% as strong, etc...........angle iron will be blah blah, blah, channel iron will be...... I don't have the correct numbers handy, but as you can see, the triangle section will be like 38% lighter, but will only 13% weaker...