Re: [PSUBS-MAILIST] ASME - say what??

["Sean T. Stevenson" <cast55@telus.net>]

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


On April 8, 2010 08:22:36 you wrote:
> Hi Sean,
> 
> Thanks for the information.  I have PVHO-1-2007 which appears to be
> setup a bit different since I don't see the references you mentioned on
> Page 36, however I know which illustration you are describing and it is
> on page 56 of the 2007 document.  While the math is easy enough, I'm not
> sure what the value represents when I arrive at an answer.  Using the
> K350 as a known example, I've got a 1/4inch stiffened shell for the
> hull.  The viewport dimensions are Do = 8, Df = 6, t=1.25.
> Additionally, lets assume maximum external pressure of 350psi giving me
> a bit of an operational safety factor.  I know that the K350 viewport
> seat has 1/2inch thick sides and 3/4 inch thick seat.
> 
> For shear loading:
> Viewport circumference = 8 * pi = 25.132
> Viewport area = 50.265
> k = ?    How do I calculate minimum thickness for k?  Is this just the
> same thickness used for the hull (.25)?
> Shear area = 25.132 * .25 = 6.283
> Shear area = 25.132 * .75 = 18.849 (known thickness of viewport seat for
> K350)
> Total load = 350 * 50.265 = 17592.75
> Shear stress for .25 thick seat (k) = 17529.75 / 6.283 = 2747.05
> Shear stress for .75 thick seat (k) = 17529.75 / 18.849 = 930.00
> 
> So what exactly do the numbers 2747.05 and 930 indicate?  Is it the psi
> carried by seat (k) material?
> 
> Jon
> 
> Sean T. Stevenson wrote:
> > Jon - assuming you have PVHO-1-2002, look at figure 2-2.20 (c), on
> > page 36.  This gives you basic dimensional constraints on the seat
> > cavity geometry.  I am assuming that you have already designed the
> > window itself (i.e. required diameter and thickness), as this will
> > dictate the cavity geometry.  D_o is the outer diameter of your
> > acrylic window.  D_s is set by section 2-2.12.9, D_f is constrained by
> > the relation in the figure (1.250 <= D_o/D_f).  You will note in that
> > figure that the dimension "K" in that figure is selected on the basis
> > of structural analysis - this must be so, as there is no way for the
> > standard to anticipate the shell loads that must be accommodated by
> > the viewport seat in the absence of the shell material in the hole
> > (since the acrylic viewport is specifically prohibited from bearing
> > loads in this manner).
> >
> > The necessary analysis is not that difficult.  Perhaps the simplest
> > one to start with is the direct shear, as the shear area will be
> > simply the circumference of the viewport (pi multiplied by D_o in the
> > figure) multiplied by the minimum thickness K.  Calculate the total
> > load (pressure x area of the viewport) and then divide by the shear
> > area above to arrive at the shear stress, and then adjust K to get
> > your desired safety factor.
> >
> > Next, examine the bending stress.  Simplify the problem by analyzing
> > it as a beam in 2D, just as it is presented (in section view) in the
> > figure.  To put that another way, imagine cutting the ring radially at
> > one location, and then straightening it so you end up with a bar with
> > a ledge on it - i.e. nothing more than a cantilevered rectangular
> > beam, with width (conservatively assuming the smallest diameter) b =
> > pi * D_f, height K, and section modulus Z = (b*K^2)/6.  Conservatively
> > assuming that the entire load will occur at the inner diameter of the
> > cavity (D_f), the maximum bending stress at the corner will be the
> > load W (pressure * window area), multiplied by the length of the beam
> > l ((D_s - D_f)/2), divided by the section modulus.  Obviously, the
> > fact that it is not a beam but a circular object will change the
> > assumed geometry, and the fact that the load is distributed and not a
> > point load will change the actual stress, but since all of the
> > assumptions made above are in the direction of increased conservatism,
> > that gives the worst-case scenario.  Again, check this stress against
> > the material maximum, and if not sufficient, adjust K to obtain your
> > desired safety factor.
> >
> > Torsional stress doesn't really need to be considered in this case,
> > since there is no torsional loading.  The only other stresses
> > experienced by the viewport cavity are those imposed upon it from the
> > shell.  If you have not already included reinforcement in the adjacent
> > shell, then the viewport cavity insert could be considered as the
> > necessary reinforcement as long as it meets the requirement for
> > sufficient material replaced.  I would suggest incorporating this seat
> > into the shell in a manner which avoids abrupt geometry changes (i.e.
> > taper the outer diameter of the seat into the shell through some
> > combination of machining and/or weld deposition), just as with any
> > transition between plates of differing thickness.
> >
> > -Sean



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