Need Clarification Regarding API 650 Variable Design Point Method 4

[Soln]

Can anyone clarify the difference, in design approach in API 650 Appendix K- Example #2, between the second course, and the second course as upper course design procedures? Why two different approaches? There's a note on API 650 p. 5-16 stating that when "the ratio" (I'm assuming (h/rt^0.5)) is >= 2.625 shell plate with lower allowable stress than course one may be used in the calculation of the second course as the upper course- I suppose this is understandable enough, but why refer to it as the "upper course" thickness?

 

[JStephen]

Refer to Timoshenko’s “Theory of Plates and Shells” for a full discussion of analysis of cylindrical shells.

The attached sketch tries to illustrate what is going on.

The natural tendency of a cylinder filled with liquid is to deflect in proportion to the pressure, so deflection varies from zero at the top to maximum at the bottom. If the ends are free, the deflected shape will be a straight line, although sloped.

If two shell courses of different thicknesses are stacked atop each other, the thinner one would naturally deflect more than the thicker at the junction. Since they are connected, there must be some bending where they connect. The maximum stress in the upper course in that case actually occurs some distance above the junction, at point A, rather than at the bottom of the course, and it is this point that the variable design point method is supposed to be locating.

If a shell course is long enough, it can be treated as “infinitely” long, and bending at the top of the course is not affected by bending at the bottom. In that case, it is necessary only to treat the junction between two courses, rather than trying to find the entire deflected shell shape. This is the assumption made for “upper” shell courses in the method.

The bottom shell course is a special case. It is treated as radially constrained at the bottom with a plastic moment connection. The point of maximum deflection, shown at point B, may be some distance up the course.

The distinction you’re asking about is this: If that bulge at “B” is down at the bottom of the first course, then the top of the first course will have a similar deflected shape to the other shell courses above, and the same approach can be used.

However, if that bulge in B extends up into the second course, then the stress distribution in the second course must be calculated differently. In fact, there are not very many tanks that fall into this category, as playing with the numbers will show.

 

[IFRs]

Now that was one hell of an explanation!

 

[Soln]

Thanks JStephen! That was a great explanation. I'll look into Timoshenko's Theory of Plates and Shells. In the meantime, are you hiring? A young tank/vessel engineer would really benefit from your exposure.

 

[lganga]

Sir
that was a professional answer.
We use the rules but forgot the analysis where they came from.
Thanks very much