Jon - I am very busy in the real world right now, so I don't have a lot of
time to look at this stuff. I saw your discussion on shell reinforcement, but
I need to find time to sit down and read the applicable documents before I feel
I can comment. Perhaps in a week or two.
That said, stress, as you surmised, is expressed in units of pressure (psi or
MPa), since it is force acting over an area. The thickness K is not the shell
thickness - it will be the minimum thickness necessary to achieve your desired
safety factor on the part you are analyzing, based on the yield strength of
that material. So, for example, using a steel with a yield strength of 70,000
psi and a desired safety factor of 2, you would adjust K so that the resultant
stress was 35,000 psi. Do this for both shear and bending. As you calculated,
the direct shear stress for your 3/4" seat is 930 psi - far from yield, but
then direct shear is not going to be your mode of failure. (The acrylic will
fail in shear before the seat anyway).
Bending is more of an issue - if you follow my procedure for the bending
stress, with your K=0.75" you end up with 9960 psi in bending, or a safety
factor of 7 on a 70 ksi steel:
sigma=(W*l)/Z
=(W)[(D_o-D_f)/2]/[(D_f*pi)(K^2)/6]
=(350)(pi*4^2)*1/[(18.85)(0.75^2)/6]
=9955 psi
That aside, the real reason your window seat needs to be so beefy is because
it needs to carry the shell stresses that would otherwise be carried in the
shell material which is cut away, so the cross-sectional area of the seat
needs to be at least equivalent to the cross-sectional area of the removed
material, and because the hole acts as an overall stress concentrator, you
should probably double that value. For a 10" hole in your 1/4" shell, the
section area at center is 2.5 in^2. Doubling that for safety, the section
area of the seat has to be 5 in^2, or 2.5 in^2 on one side. Distribution of
this material in the seat cavity is a tradeoff between the strength of the lip
in bending, the effect that the lip thickness has on visibility, and the
strength of the surround since that must accommodate the retaining ring
bolting arrangement, and area lost due to tapped holes must be accounted for.
-Sean