This is the boss. No calculator — the pressures, bores and wall thicknesses are chosen so that every line falls out in your head, the way a good inspector actually works on a plant floor. One vessel, one long problem, and every answer feeds the next: pressure and geometry give the hoop stress, the hoop gives the longitudinal, the pair give the peak shear in the wall, the hoop gives the factor of safety, and the factor of safety gives the signature. Write each line down — one early slip rolls all the way to the verdict.

And the verdict is the point. Every number above it is a means to an end, and the end is a decision a real person signs their name under: certified for another year, or condemned. The code minimum is stated in the scenario, not remembered from a rule of thumb, because that is how margins actually work.

A bonus mark closes the shift, and it is a re-rate dealt one of two ways. Either the cylindrical shell is checked on pd/2t, or the hemispherical heads are checked on pr/2t with r equal to half the bore. The heads need half the metal the shell does, because a sphere curves both ways. 5★ under par here is the chapter crown. Clock in.