FEXLA

Skirt access openings and buckling

Why the wall beside a skirt opening is the weak point, the two hand checks, and the buckling check of the model.

FEXLA engineering · · 4 min read

Shell model of a tombstone access opening in a skirt
Fig. 1 · Shell model of a tombstone access opening in a skirt

A skirt carries the vessel's weight and the wind or seismic overturning moment as axial compression, and an access opening cuts a piece out of that load path. The wall beside the hole takes the load the hole removed, its corners concentrate it, and on the compression side the weakened wall buckles earlier.

The skirt card checks this three ways: the skirt wall thickness for axial compression, the opening's reinforcement under axial compression by ASME Section VIII Division 2, 4.5.17.3, and a shell model with an eigenvalue buckling analysis.

Loads at the base

The inputs are a foundation load summary: weight W, base shear V, base moment M, and optionally a vertical seismic part and an eccentric-weight moment. The tool turns them so that the opening side is in compression whatever the opening's angle, and checks wind or seismic from the other side too. Above the opening the stress follows beam theory:

σ(z) = −W/A ∓ M(z)·R/I, M(z) = M − V·zA and I of the thin ring of mean radius R; z height above the base

A test confirms that the shell model reproduces this stress above the opening within 5 %.

Shell model of a skirt with a tombstone access opening and its sleeve
Figure 2. A skirt with a tombstone access opening and its sleeve, as a shell model: the opening is where the skirt is weakest under weight and wind.

Hand check 1: the skirt wall

t_r = W/(π·Dm·Sc) + 4·|M|/(π·Dm²·Sc)Dm mean diameter, Sc allowable compressive stress

Sc is entered by the engineer, as factor B from the external-pressure chart in Section II Part D; the tool reports A = 0.125/(Ro/t) to read it. The check runs at the base and at the opening's centre height. The loads carry the factor of their basis: 0.6 for wind, 0.7 for earthquake, 1 when already at allowable level.

Hand check 2: the opening under axial compression

Division 2, 4.5.17.3 asks for an area of reinforcement Ar that depends on the opening size against √(R·t):

γn = d/(2√(R·t)); Ar = 0 if d ≤ 0.4√(R·t); Ar = 0.5·d·t_r if γn ≤ ((R/t)/291 + 0.22)²; Ar = d·t_r otherwiseeqs. 4.5.222 to 4.5.225; d clear width across the load path

The area available is the shell beyond what it needs within 0.75√(R·t) each side, the sleeve outside and inside, the fillet welds and any pad. The check passes when it is at least Ar. Openings wider than 25 % of the diameter, the limit of 4.5.17.1, are flagged.

The shell model

The model spans the whole skirt, from the bottom of the base ring to the skirt-to-head joint, both held as lines of support. The opening is tombstone, obround or round, with its sleeve, inside and outside projections, an optional pad and vertical stiffener bars either side. The mesh follows the decay length √(R·t), refined in rings to the exact sleeve-to-shell intersection. Pressure, temperature and cycles are off.

From a static run to a buckling checkA flow chart. A static run at the applied load gives the stresses; the stresses give the stress stiffness; solving gives the multipliers λ and their mode shapes. Two routes follow: a linear check, λ1 times a reduction factor divided by a design margin must be at least 1; or a nonlinear check that uses mode 1 as an imperfection and lets the metal yield.1. Static run at theapplied load2. Stress stiffnessfrom those stresses3. Solve for λ andthe mode shapesLinear checkλ1 × reduction factor÷ design margin ≥ 1Nonlinear checkmode 1 as a dent,metal allowed to yield
Figure 3. From a static run to a buckling check: the static state gives the membrane forces, the eigenvalue run gives the load factor, and the code's factors turn it into a pass or fail.

Buckling: from a load factor to a pass

Compression adds a negative term to the shell's stiffness. The eigenvalue analysis finds the factor λ on the load at which the total stiffness goes singular, for each combination of Table 5.15. A linear, perfect shell overstates the real buckling load, so Division 2, 5.4.2 Method A reduces it by a capacity reduction factor βcr at the critical element: for a cylinder in axial compression βcr = 338/(389 + Do/t), or 0.207 when Do/t is 1247 or more.

σcrit = βcr·λ·σm; Sc = min(σcrit, 0.55·Sy)/2; pass if σm ≤ Sceq. 5.13; σm membrane equivalent stress at the critical element

Read another way, the check needs βcr·λ ≥ 2. For the skirt above, Do/t = 189.5 gives βcr = 0.584, so the smallest load factor that passes is about 3.4. An opening on the compression side buckles at a lower factor than the same opening in tension; a test checks that ordering.

Where it stops

  1. 01The base ring, anchor bolt chairs, gussets and the skirt-to-head weld are not modelled; the ring and the head joint are lines of support.
  2. 02Sc is entered; the external-pressure charts are not in the tool.
  3. 03Buckling is linear and perfect, with all the knock-down in βcr. Method B (5.4.3, elastic-plastic with imperfections) is not available.
  4. 044.5.17.1 also limits the opening against the ring spacing; only the 25 % diameter limit is checked.
  5. 05The skirt opening job is early access and under verification against hand checks and an independent solver.
B-10

Try it in FEXLA

The Skirt access opening card builds the skirt with its opening, runs the two hand checks beside the model, and checks buckling under weight and wind or seismic.

Open the card

References

  • ASME Section VIII Division 2: 4.5.17.1 and 4.5.17.3 (openings under axial compression, eqs. 4.5.222 to 4.5.225), 5.4.2 Method A (eqs. 5.13 to 5.17), Table 5.15.
  • ASME Section VIII Division 1, UG-23(b) (factor B).

Method notes this draws on

Next post: Limit load (VIII-2 5.2.3) when the elastic check fails

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