3/16" fillet weld, minimum required weld filler ultimate Shear strength is 7.5 ksi.
7018 welding rods meet that. Welding rod diameter doesn't really matter on the weld strength calculation, you can use 3/16" or 1/8" or 5/32" 7018 rods to make a 3/16" fillet weld.
Although that page has the engineering calculations, it is NOT the way to call out a weld on a fabrication drawing.
You're in Florida, and this is important enough that you have a structural engineer stamping a plan/drawing and an inspector (building inspector or welding inspector?) involved.
AWS D1.1 is the usual structural steel welding code. Hopefully you haven't been backed into a corner by building code requirements that the welding has to meet D1.1 requirements, because then you would have to get certified to D1.1 and everything would have to be inspected (before, during, and after) by a CWI.
And a 3/16" fillet weld does not meet the minimum allowable structural steel fillet weld size in D1.1. The minimum allowable fillet weld size in D1.1 is generally a 1/4" fillet weld.
And before using an FCAW-S wire electrode, double check that said wire electrode meets all of the requirements for not just Shear and tensile strength but also possible CVN building code weld requirements. Most FCAW-S Wires that can be used with a 180 amp class small Welder do NOT meet any CVN requirements.
7018 rods do have CVN properties and can meet most structural steel welding code requirements.
