sjs derivation of aisc tbl 10-2

huangyhg

s&j's derivation of aisc tbl 10-2
i am reviewing the derivation of asic table 10-2.
equation 13.2.8 (see p. 806 of 4th ed. or p. 672 of 5th ed.) of s&j seems to derive the equation used in the table.
my question is on eq. 13.2.5, they seem to take moment equilibrium about some point.  however, i do not understand why they ignore the stress in the "l/6" portion of the angle (see fig. 13.2.5-b). i also do not understand the moment arm they use, the "2/3 l".  
any help would be much appreciated.

can you post the equations you are looking at? i only have the 3rd edition of s&j.
i believe a review of blodgett's "design of welded structures" section 5.4 will provide a derivation of the equations used for the aisc table 10-2.
yes you are correct blodgett's fbd is much clearer.
thanks
here's another one, in table 10-2, and 10-3 what is the purpose of the small return weld? does it have something to do with the torsion at the connection?
according to the commentary to article 8.8.6 of aws structural welding code, tests on header angles show that "the end returns tend to delay the initial tearing of welds under ultimate failure conditions."  nothing is said about torsion at the connection.