Air-cooler plug header ligaments and Appendix 13

A plug header is a rectangular box. Its plates carry pressure as a membrane force from equilibrium and as bending, each plate a beam between corners whose moments come from the frame of Appendix 13. A hole row sits somewhere along a plate, often near midspan, and the stress there is read from the same moment line as the rest of the plate.

A hole is often not one diameter through the plate: a tube hole may have grooves, and a plug hole a counterbore on the plugsheet's outside face. The row is entered as a pitch p and a list of segments from the inside face outward, each a diameter d_k over a length T_k, adding up to the plate thickness. The order matters, because bending depends on where the metal is.

Each row is placed by the distance of its hole centres from the plate's midspan, and 13-6 is applied to each row on its own, so a plate with two rows reports two pairs of efficiencies. The joint efficiency E at the row is that of a butt weld lying there, and 1.0 where there is none, as at a corner joint that is not a butt weld.

For holes of one diameter both reduce to (p − d)/p. For a stepped hole they differ: a groove near one face costs more in bending than in membrane, and moves the neutral axis.

• Both efficiencies below the joint efficiency E: the stresses at the row are divided by e_m and e_b, and compared with the allowables using E = 1.0.
• Both at or above E: the gross stresses are compared with the allowables using E.
• One below and one above: the code is silent. By default the engine evaluates both readings and keeps the worse ratio.
• Away from the rows, on a drilled plate, the default divides the membrane stress by the plate's smallest e_m and leaves the bending gross. That reproduces the published PTB-4 example. The literal reading, dividing bending by e_b everywhere, is a selectable policy.

The allowables are S·E on membrane and 1.5·S·E on membrane plus bending of a plate. With both efficiencies near a half, the row stresses double, which is why a hole row at midspan can govern a plate whose corner looks worse on gross stress.

Corrosion comes off the inside and outside segments before the formulas run, and a segment worn away is dropped. The pressure test uses the uncorroded segments.

Every stress in the frame grows in proportion to the pressure for the plain box sketches, so the maximum allowable pressure follows directly: the design pressure times the allowable over the stress, taken at the worst row, hole rows included, then the lower of that and the end plates. In the published PTB-4 box the governing row is at midspan of the pair B plates, at 397.4 psi.