Though the viewport penetrations in the cylinder wall are, strictly speaking,

fully three dimensional, nonsymmetric problems, and should be treated

accordingly, an approximate method can be employed that renders conservative

results. This method is possible because of the small ratio of the

penetration diameter, d, to the mean diameter of the cylinder D, in this case

1:12.3. This method involves the use of an axisymmetric shell analysis which

includes a Fourier series loading capability. Specifically, a flat circular

annular plate of thickness equal to the cylinder wall thickness, with the

inner radius equal to the penetration radius and reinforced as actually

reinforced, with an outer radius of at least 10 times the inner radius, is

subjected to an in-plane edge load, P([theta]) of

3

1

P([theta]) = - (ST) - - (ST) cos 2 [theta]

4

4

S = the hoop stress found in an unpenetrated cylinder, away from

any stress riser, psi

T = thickness of shell, away from reinforcement, inches

[theta] = angle from longitundinal plane.

To include the effect of the resultant pressure from the viewport itself, the

penetration reinforcement as actually developed is modeled into the center of

a hemispherical shell with twice the inner radius of the cylinder. The

resultant pressure of the viewport is then applied as a pressure band over

the actual area of contact. This three component model is shown in Figure

2-32. Fourier loading was used to analyze this approximate model. The hoop

stresses in the vicinity of the penetration, for both the circumferential and

longitudinal sections, [theta] = 90 and [theta] = 0 degrees are shown plotted

in Figure 2-33. As can be seen, the stresses developed around the

penetration decay quite rapidly along the shell.

The axial stress distribution was also developed but not plotted.

The

maximum stress condition is shown in this figure.

(5) Categorization of Stress. At this point the stresses should

be broken into the stress categories, as fully defined in the previous

example.

(6) Stress Intensities. As in the previous example, the stresses

are now converted into stress intensities. We will consider only one point

in the vessel (all other stress intensities are satisfactory). Examining

Figures 2-29 and 2-30 we note that the maximum stress intensity in the

tori-spheroidal head, on the inner surface is

Smax = 34,800 - (-9,800) = 44,600 psi.

Now in the knuckle (torus) of a tori-spheroidal head the stress must be

categorized as a primary local membrane plus a secondary bending stress.

Thus the stress intensity limit for this configuration is (see Figure 2-7)

PL + Pb + Q

/ = 3 Sm = 69,600 psi

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