Shell courses and thickness steps with UW-9(c) tapers

When sections joined by a butt weld differ in thickness by more than a quarter of the thinner one, or 3 mm (1/8 in), whichever is less, the thicker one is tapered at least three times the offset between the surfaces. The rule also covers a thickness reduction within a course. Below the trigger no taper is needed.

Under pressure the thin course grows more than the thick one, and the two are held together at the seam. That mismatch gives a discontinuity moment and shear at the joint, as at a head-to-shell junction. If the mid-surfaces do not line up, the axial membrane force N also acts with an offset e, and adds a moment N·e.

On a 2000 mm diameter shell at 1 MPa, the axial membrane force is P·R/2 = 500 N per mm of circumference. A 1 mm offset between mid-surfaces, the case of a 12 to 10 mm step flush on the inside, gives N·e = 500 N·mm per mm. That moment dies away over a few decay lengths √(R·t). Far from any attachment it is small. Inside an attachment's zone it adds to the local membrane plus bending stress.

• Courses are entered from the bottom seam up, each with its thickness. The alignment is inside flush (the default), outside flush or centred.
• One node surface is used: the mid-surface of the course that holds the first attachment. Every other plate carries a section offset from it, so the real eccentricity is in the model.
• Past the UW-9(c) trigger the thicker plate gets a 3:1 taper beside the seam, built as two to eight rows of elements of stepped thickness and offset.
• Below the trigger the step is square. Its offset is modelled within 2.5·√(R·t) of an attachment's footprint and ignored elsewhere, with a note in the report.
• Every seam and taper edge is a grid line. A nozzle's refined block stops at the nearest seam beyond its footprint, and a seam on a footprint is refused with the clearance needed.
• The shell below a head can take its own thickness instead of the head's.

The stepped cylinder was checked against the hand discontinuity solution for two courses under pressure: the radial growth within 1 % of the free-growth jump, and the peak axial moment within 3 % at the default mesh size and closer on a finer mesh.

The report lists the courses, each seam with its UW-9(c) reading, taper or plain step, and the note on any step whose offset was left out far from the attachment.

The seam and the attachment each disturb a zone a few decay lengths wide. When the zones overlap, the two bendings add, and the report reads them together. The seam rows also appear as their own weld lines, so a stress at the taper or the step is reported where it occurs, not smeared into the attachment's zone.

WRC 537 takes one shell thickness and treats the attachment as alone on the shell. A seam within the attachment's decay zone is outside its assumptions, and the shell model is the way to see it.