A tubesheet is drilled with a pitch of holes along each row, and a plugsheet has plug holes in line with them. The holes remove material in the same section that carries the membrane force and the bending moment. App 13-6 gives two efficiencies for a row with holes of several diameters through the thickness: one for membrane, one for bending. They multiply the allowable, or equivalently divide the stress.
The row is described by the pitch p along the row and a list of segments from the inside face outward, each with a diameter dk and a length Tk. The segment lengths must add up to the plate thickness. The plugsheet of a header often has a counterbore on the outside face, which is why the inside-first order matters.
From efficiencies to stresses (13-4(g))
E is the joint efficiency that would apply at the row with no holes. The engine reads the row as follows.
- em and eb both below E: net stresses Sm/em and Sb/eb are compared with the allowables using E = 1.0 (13-4(g)(1)).
- em and eb both at or above E: gross stresses with E (13-4(g)(2)).
- One below, one not: the code is silent. Default policy ligamentMixedRule = worst evaluates both readings and keeps the larger ratio.
- Away from the rows on a perforated plate (corners, other points), default policy divides the membrane stress by the smallest em of the plate and leaves the bending gross. This reproduces PTB-4 E4.12.1 and COMPRESS. The literal reading of 13-4(g) would divide the bending by eb everywhere; that is a selectable policy, off by default.
COMPRESS 50183 tubesheet, corroded, p = 2.625 in (vector V-C1)
| Segments inside first (d, T) in | (1.264, 0.1875) (1.2952, 0.125) (1.264, 0.25) (1.2952, 0.125) (1.264, 0.25) |
| t = ΣT | 0.9375 |
| DE_m = Σd·T / t | 1.27232, em = (2.625 − 1.27232)/2.625 = 0.51531 |
| X̄ from the inside face, c | 0.46894, 0.46894 |
| I (in⁴ per row pitch) | 0.093160 |
| eb = 6·I / (p·t²·c) | 0.51664 |
| Sm gross = P·h/(2·t1) | 150 · 9.625 / 1.875 = 770.0 psi |
| Sm net = Sm/em | 770.0 / 0.51531 = 1494.3 psi |
| (Sb)N gross at midspan | 5180.6 psi |
| (Sb)N net = Sb/eb | 5180.6 / 0.51664 = 10027.3 psi |
| ST at N inner | 1494.3 + 10027.3 = 11521.6 psi, allowable 27150 psi |
The fixture holds em 0.515306667, eb 0.516644102 and ST 11521.575 psi. Its X̄ (0.46856) is measured from the other face; X̄ depends on the datum, but em, eb, c and I do not. The plugsheet gives em 0.47144 and eb 0.45825 on the same method, with a counterbore 0.0312 in deep on the outside face.
Corrosion allowance is taken from the inside segments (CA_in) and from the outside segments (CA_out) before the formulas run, and a segment worn away completely is dropped. The pressure test uses the uncorroded segments.
[UNVERIFIED] The engine does not compute an equivalent solid plate thickness for a hole row. I searched box-engine/src for it and found none. The weakening enters only as em and eb dividing the stresses. Any equivalent-thickness statement, such as t·√eb for bending alone, is outside what the code does.
Limits. One HoleRow describes the plane of hole centres at a distance dj from the plate midspan. 13-6 is applied to each row separately (results are keyed by plate and row). Rows on a corner arc are refused, rows on the reinforced plates of sketch (4) are refused (13-6 gives no rule for a composite section), and a row that sits on a stay is warned. Openings and nozzles are not checked (13-4(j)); only the holes entered as rows are.