This procedure is not as cumbersome as it seems, but it does take a little

getting used to. Most computer programs will calculate the total stresses at

any point. All the terms in each of the quantity brackets, (), above are

actually the same as those shown as the inner and outer stresses in the

computer printout.

EXCEPTION:

There is the one exception to this where one of the brackets

contains the F component which was calculated separately.

This is the exact procedure you would follow if you were doing

your discontinuity stress calculations by hand as shown by the

example in Article 4-7, Paragraph 4-730 of Section VIII,

Division 2. The maximum stress intensities occurring in each

part of the three models were calculated and are shown in

Tables 2-3, 2-4, and 2-5.

To be very conservative, stress concentration factors of kPHI, k[theta] =

2.0 were assumed to act at all welds where there occurred a thickness change.

This is a highly conservative assumption and is only made here for example's

sake. For good full penetration welds, particularly butt welds, that are

ground smooth and flush and all imperfections removed there really should be

no noncalculable stress concentration at all. This is only true, of course,

if the stresses that you have calculated are based on a model geometry that

truly mathematically modeled the weld geometry.

(6) Stress Intensity Limits.

The stress intensity limits for this

vessel were determined as

Pm

< / = 23,200 psi

PL

< / = 34,800 psi

Pm (or PL) + Pb

< / = 34,800 psi

PL + Pb Q

< / = 69,600 psi

PL + Pb + Q + F

< / = 74,000 psi

Examining the values listed in Tables 2-3 through 2-5, it is noted that, even

with the very conservative assumptions of high stress concentration factors

at all the welds where a change of thickness takes place, the maximum stress

intensities shown are quite acceptable with but two exceptions. These occur

in Parts 8 and 11 in Model No. 2, listed in Table 2-5. The stress

concentration of 3.0 used here is a realistic one, These parts are the

portions of the flanges inwards from the bolt circle or clamp contact ring.

Geometrically, the flanges are flat annular plates. The high stresses occur

at the bolt circle position and are almost wholly bending stresses. If bolt

holes are present and the diameter of these holes are smaller than the

thickness of the flange, as is the usual case, then the stress concentration

at the hole would be greater than 2.2* and would approach 3.0 as the holes

got smaller as compared to the plate

* Note: See Reference 25, Peterson, Stress Concentration Design Factors,

Figure 85, page 101, 1966.

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