Whenever the weld sits in a load path with real consequences: mezzanines, building frames and modifications, commercial stairs and guardrails, lifting points, and anything a city will plan-review. The engineer specifies members and connections; AWS D1.1 governs the welding itself. Ornamental work does not need a stamp.
More detail
The engineering line follows consequence, not complexity. On one side: ornamental and functional work (yard art, gates, handrails on a private porch, brackets holding nothing critical) where good workmanship is the whole standard. On the other: welds whose failure injures someone or drops a structure, and that side gets an engineer. Concrete cases in this corridor: a mezzanine added inside a shop or warehouse (a floor over people's heads is the definition of a life-safety load path), modifications to a pre-engineered metal building's frame (those frames are optimized to their original design, and cutting a new opening or hanging a new load from a rafter without the manufacturer's or an engineer's blessing can compromise the building), commercial stairs, guardrails, and platforms (which cities plan-review against the IBC), lifting lugs and spreader hardware, and any repair to a structural member of a building. What the engineer contributes is the design: member sizes, connection details, weld type and size, and in Texas that work carries a TBPELS-licensed seal where jurisdictions require it. What the welding code contributes is the execution: AWS D1.1 governs procedures, fit-up, and workmanship on structural steel, and it is the standard the field and shop work here follows on load-bearing jobs. The practical rule for an owner: if the piece holds up people, a building, or a suspended load, budget for the engineer, and treat any bid that shrugs at that as the flag it is.