The six nozzle load components P, VC, VL, MC, ML, MT and their signs

The calculator's frame sits at the junction, on the nozzle axis. One axis runs along the vessel (longitudinal), one round it (circumferential), and one along the nozzle into the shell (radial). A and B are the two points on the nozzle edge on the longitudinal line, C and D the two on the circumferential line. Each is checked on the outer and the inner surface, eight points in all.

The radial load pushes or pulls the shell wall under the whole nozzle, so it stresses all four points. A positive, inward P gives compressive membrane stress at A, B, C and D; the bending part has one sign on the outer surface and the other on the inner. A and B see the same stress from P, and so do C and D.

This is the sign that matters most. Reversing P changes the membrane stress at every point at once, and pressure adds tension there, so a P that pulls outward can govern when one that pushes does not. A connected line that pushes the nozzle into the vessel gives a positive P here.

A moment rocks the nozzle. ML rocks it along the vessel and stresses A and B only: a positive ML puts compression at A and the same magnitude of tension at B, in membrane and in bending. MC rocks it round the vessel and does the same at C and D, compression at C and tension at D.

Because A and B see the same stress from P, reversing ML only swaps the two points, and both are checked; the worst normal stress is the same either way. The same holds for MC at C and D. What the sign can change is the shear stress that goes with each point, below.

The shears and the torsion give shear stress in the shell round the nozzle, not membrane or bending stress. On a round nozzle:

• VC, the circumferential shear, gives its shear stress at A and B, with one sign at A and the other at B.
• VL, the longitudinal shear, does the same at C and D.
• MT gives the same shear stress at all eight points.

So at one of each pair the shear from VC or VL adds to the torsion, and at the other it subtracts. On a rectangular clip WRC 537 gives no stress for torsion, and the calculator records MT there without using it.

WRC 537 defines the loads at the junction. If the table gives them at the flange face instead, the calculator carries them down the nozzle: a shear at the end adds a moment at the junction equal to the shear times the length. With the senses above, that is:

P, MT and the shears do not change. On a formed head the calculator names the loads P, V1, V2, M1, M2 and MT; M2 pairs with V1 the way ML pairs with VL, and M1 with V2 the way MC pairs with VC.

Loads from a line stress analysis may come in global axes. The shell model in FEXLA can take them that way, or in its own frame: an axis out along the nozzle, the vessel axis made square to it, and the third by the right-hand rule. In the shell model P is positive pulling the nozzle away from the shell, the opposite of the WRC 537 calculator, and loads are in kN and kN·m. The two tools do not yet share one convention, so a load set moved between them must be converted by hand, starting with the sign of P.