FEXLA

How long should the shell be around a nozzle

A drinks can, two programs and one rule: model the shell out to the real heads and rings, or 50√(R·t) each side when they are not known.

FEXLA engineering · · 6 min read

Shell model of a padded nozzle on a cylinder, the deformed shape drawn exaggerated with the cylinder's open end pulled oval
Fig. 1 · Shell model of a padded nozzle on a cylinder, the deformed shape drawn exaggerated with the cylinder's open end pulled oval

Long enough for the shell to go oval as it does in the real vessel: out to the real heads, rings or cone junctions, or 50√(R·t) each side of the nozzle when they are not known. A model cut short and held round at its cut is too stiff, so it reads the stresses from a radial force and a circumferential moment low and those from a longitudinal moment high.

Pressure alone hardly cares. This post explains why with a drinks can, shows the numbers from our solver and from CalculiX, and says what the tool now asks for.

The drinks can

Take an empty drinks can and press your thumb on its side. The can does not only dent under your thumb. The whole section squashes into an oval, and the oval spreads a long way along the can.

Now slide two tight rings onto the can, one close to each side of your thumb, and press again. The can feels much stiffer, because the oval cannot spread past the rings.

The drinks can: a short model and a long modelTwo cans lying on their side, each pressed by a thumb at mid-length, the dent drawn exaggerated with the original top edge dashed. Top: two tight rings sit close either side of the thumb, so the dent stops at them and the can feels stiff. Bottom: the rings sit near the ends, so the dent spreads a long way along the can, as it does in a long shell.Short model: rings close to the thumbthumbThe dent stops at the rings: stiffer, so the stress reads lowLong model: rings far awaythumbThe dent spreads along the can: the true answerring
Figure 2. A short model is the can with the rings pushed up to the thumb. A long model lets the oval spread as it does in the vessel.

A shell model of a nozzle is a piece of the vessel cut out around it. The model has to be held somewhere, and where it is held, at a cut end, it holds the shell round. A cut close to the nozzle is a ring pushed up to the thumb.

Quadrilateral shell mesh of a nozzle on a cylinder, finer near the junction
Figure 3. The shell mesh of a nozzle model: small elements at the junction where the stress changes fast, larger ones away from it.

Why the short model reads wrong

A nozzle load reaches along the shell in two ways. Bending of the wall right at the weld dies out within about 2.5√(R·t), and that is what short models were sized for. A push on the nozzle or a sideways bend also turns the shell into an oval, and the oval travels much further, roughly R·√(R/t).

wall bending: about 2.5·√(R·t) ovalisation: about R·√(R/t) = (R/t)·√(R·t)

Held round too close, the shell cannot oval freely, so it carries a radial force P and a circumferential moment MC with less bending than it really does. Those stresses read low, on the unsafe side. The longitudinal moment ML loads the shell more locally, and the short model reads it a little high, on the safe side.

Short against long, in two programs

We took the three nozzles where the effect was largest and modelled each one twice: short, by the former rule of about 5 to 7√(R·t) each side, and long, 50√(R·t) each side, with 10 kN or 10 kN·m on the nozzle. The same meshes with the same holds at the cut ends were then solved in CalculiX, a second, independent program.

LoadVessel D/t, nozzle d/DShort, MPaLong, MPaChange, FEXLAChange, CalculiX
P100, 0.54.38.1−47 %−47 %
P100, 0.37.312.3−41 %−41 %
P50, 0.51.42.3−38 %−38 %
MC100, 0.518.424.0−23 %−23 %
MC100, 0.344.248.8−9 %−9 %
MC50, 0.55.66.6−16 %−16 %
ML100, 0.57.06.5+8 %+8 %
ML100, 0.318.317.8+3 %+3 %
ML50, 0.52.42.2+6 %+6 %
Largest shell stress at the weld, bending plus membrane. Minus means the short model reads low (unsafe); plus means it reads high (safe side).
Short model against long model, in two programsBars of the change in the largest shell stress at the weld when the model is cut short (about 5 to 7 √(R·t) each side) instead of long (50 √(R·t)), for three nozzles under a radial force P, a circumferential moment MC and a longitudinal moment ML. Each nozzle has two bars, FEXLA and CalculiX, and each pair is the same length: P about minus 38 to minus 47 percent, MC minus 9 to minus 23 percent, ML plus 3 to plus 8 percent.FEXLACalculiXsame mesh, same endsRadial force PD/t 100, d/D 0.5−47 %D/t 100, d/D 0.3−41 %D/t 50, d/D 0.5−38 %Circumferential moment MCD/t 100, d/D 0.5−23 %D/t 100, d/D 0.3−9 %D/t 50, d/D 0.5−16 %Longitudinal moment MLD/t 100, d/D 0.5+8 %D/t 100, d/D 0.3+3 %D/t 50, d/D 0.5+6 %−40 %−20 %0← short model reads lowreads high →
Figure 4. Each pair of bars is one nozzle. Our solver and CalculiX agree on every change to within one percentage point.

Both programs show the same change in the same direction, and on the same model they gave the same stress to within 0.6 %. So the effect is not a quirk of one solver. It comes from where the model holds the shell round.

When it matters, and when it does not

  • It matters most for large nozzles, d/D of about 0.3 and above.
  • It matters more on thinner shells: the higher the D/t, the further the oval reaches.
  • It matters for the nozzle loads P, MC and ML, the radial force most of all.
  • It hardly matters for a small nozzle, which makes only a small oval.
  • It hardly matters for pressure alone: the change stayed under about 3 % in our study.

What holds a shell round

In a real vessel the shell is held round by something stiff all the way round it: the heads, stiffening rings, tray-support rings and cone junctions. These are its lines of support. A few lugs, legs or clips do not count. They touch the shell at a few points and do not stop it going oval.

What holds a vertical vessel round, and what does notA vertical vessel in elevation: a top and a bottom head, a narrower upper shell joined to the main shell by a cone, a stiffening ring, a tray-support ring inside, a lifting lug near the top and legs at the bottom. Yellow dots mark the parts that hold the shell round all the way round: the heads, the cone junctions, the stiffening ring and the tray-support ring. Open circles mark the lug and the legs, which touch the shell at a few points and do not.HeadCone junctionTray-support ringStiffening ringHeadLifting lugLegsElevation
Figure 5. Full rings, cone junctions and heads hold the section round. A lug or a set of legs touches it only at points.

Other attachments nearby matter in three ways. A small nozzle or clip close by has little effect on the oval and can be left out. A large nozzle or a pad close by stiffens the shell: model it with the first one. A ring or a head close by is a line of support: model the shell out to it.

Vertical and horizontal vessels, and heads

On a vertical column the heads, tray-support rings and stiffening rings are usually close together, so the real lines of support are often nearer than 50√(R·t). Model to them. The bending of the whole column under wind or earthquake is a separate, global check. The local model takes the nozzle's own loads and the pressure.

A horizontal drum is the opposite. Its heads are far apart and it seldom has rings between them, so the oval can run a long way: use the real tangent-to-tangent length. The weight of the liquid also ovals the shell near the supports, and saddle supports are outside the scope of this tool.

A nozzle on a head needs some cylinder below the head in the model. Take at least 2.5√(R·t) of attached shell so the junction bending is complete, and more for a large nozzle or one near the knuckle. The tool models 4√(R·t) below the head unless you enter another length.

What the tool does now

  • It asks for the real vessel along the axis: the tangent-to-tangent length and the nozzle's place on it, or the distance to the nearest head, ring or cone junction each side. The model runs out to those lines and holds the shell round there.
  • When they are not given, it uses a long model: each cut the largest of 50√(R·t), one nozzle diameter and one shell radius beyond the nozzle.
  • On a thin shell, where R·√(R/t) is longer still, it says so plainly and asks for the real vessel.
  • When a typed length cuts the shell closer than 50√(R·t), it warns that the radial-force and circumferential-moment stresses may read low, unless that end really is a head or a ring.
  • Far from the nozzle the elements grow longer along the axis, so a long model costs fewer of them.

These changes are in the workbench release now being prepared. Shell model results are early access and under verification.

Where it stops

  1. 01The check covered three radial nozzles without pads on one shell size, each load alone. Pads, offset nozzles and groups were not measured.
  2. 02Above a D/t of about 100 no fixed length is right: only the real distance to the heads or rings settles the answer.
  3. 03Saddle supports and the global bending of the vessel are outside this local model.
  4. 04Shell model results are early access and under verification. Until that is finished they are not a source of design values.
B-31

Try it in FEXLA

The Nozzles and clips card runs WRC 537 and builds the shell model of the same nozzle; give it the real vessel and it models the shell out to the heads and rings.

Open the card

References

  • ASME Section VIII Division 2, Part 5, Design by Analysis: the PL+Pb+Q value read at the junction.
  • Thin-shell theory: the decay length √(R·t) used throughout the method notes.

Method notes this draws on

Next post: Corrosion allowance in a local model: inside, outside, pads and clips

Educational article. It explains principles and is not design guidance; follow your governing code and edition.