using r instead of j to determine angle of twist in steel be
 

using r instead of j to determine angle of twist in steel be
i am a new bridge engineer, fresh out of college and 2 weeks on the job. my boss uses r, torsional resistance, instead of j, polar moment of inertia, to determine the angle of twist in an i-beam. the reference he showed me only refers to a section with equal plates for the web and flanges. is it correct to always use r to determine the angle of twist, and if so is it always more accurate.
i have attached the page sumitted as a reference in all his calculations.
thank you,
a rookie
when considering torsion of non-circular cross-sections plane sections do not remain plane and as such the polar moment of inertia is not applicable. the notation that i am familiar with for this general cross sectional property is the torsional constant, j (i believe that this is what your boss is calling torsional resistance, r) which is in general different from the polar moment of inertia ip=ix+iy (for which your boss uses j). ...check out roark's stress and strain, but note that they use k for what i'm calling j, and for what i believe your boss is calling r.
when you have a circular cross section then plane sections remain plane and the torsional constant is equal to the polar moment of inertia--but this is true only for circular cross sections.

j really only actually applies to circular shafts or circular tubes. j doesn't readily apply to non-circular and open sections. r = torsional resistance factor is more appropriate.
see blodgett, "design of welded structures" or ,"design of weldments". both are books i keep on the bookshelf right next to my desk, alongside roarks, aisc, etc...
in blodgett's texts he compares the use of j and r in "angle of twist" calculations with physical testing results. for instance, a channel:
conventional j: .006 degrees
torsional resistance r: 9.7 degrees
actual testing results: 9.5 degrees
after writing all of this i looked at the attachment you provided in your post - that page is from "design of welded structures"...
your boss is probably using blodgett's "design of welded structures." his method is extremely easy and comes withing 5% (usually less) than experimentally tested values. i recommend using this because the calculation is simple, accurate and tested. the read is only like 3 pages. or you could use the aisc design guide on torsion for wide flange sections. i believe it is like 200 pages. each calculation takes pages. blodgett is great. everyone uses it. aisc is a case of professors gone mad.