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
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
< / = 23,200 psi
< / = 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.