Someone had a great catch (see comment below) - while the final answer is correct, I had a unit error. When I solved for w, I said it was lbs/in divided by lbs/in which is incorrect. The allowable from Table 6 is 11,200*w lbs/in and our actual was 3,756 lbs/in. So setting them equal and then solve for w would yield 11,200*w lbs/in = 3,756 lbs/in -> w = 3,756 lbs/in /11,200 lbs/in/in… so I had lost an inch unit in the denominator when I wrote it out.
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Great question and great catch. It’s really not lb/in divided by lb/in. The reason being, f_allowable = 0.707*w*stress_allowable. Then you set f_actual equal to f_allowable, then you solve for w. So when I solved for w and pulled it out of the f_allowable term, f_allowable went from units lb/in to lb/in^2 since w is units in. (I mistakenly left it as lb/in when I solved). If you look at Table 6 where I grabbed the f_allowable, it is 11,200*w lb/in (which is 15,800psi allowable stress * 0.707 * w), so if we set our f_actual of 3,756 lb/in equal to f_allowable of 11,200*w lb/in and then that’s when we solve for w. So in short, the units I wrote out is wrong (i.e 11,200*w is lbs/in, but 11,200*w divided by w is lbs/in/in) but the process is correct. Hard to write in words but hopefully this helps clear that up - probably would be easier if I made another video
