Specific Weld Design

[Rocks1]

I was asked by a reviewer to analyze and determine the minimum weld length X of a 5/16 weld of a column reinforcement in the attached pdf.
The column reinforcement is an existing jib-crane plate doubling as a cover plate and an added channel cover that overlaps.
Does anyone know how to go about determining the length X in the attached?
All of the Code checks pass for the sections A-A, B-B, and C-C.

 

[ProgrammingPE]

I would design the weld where the plate and channel overlap so that it can transfer the full yield stress of the smaller of the plate and the channel, so:

X = Φ*Fy*Ag,min/(Φ*0.6*Fexx*2*0.707*w)​

(Φ in numerator is 0.9, Φ in denominator is 0.75, Ag,min = MIN(Ag,plate, Ag,channel))​

(The calculation above does not consider fatigue, so be sure to adjust accordingly if it applies.)

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