I have a staggered 2x4 wall on a 2x6 sill plate as illustrated below (16" on center on each side = 8" on center each stud). The wall is loaded from both sides by floor joists, so I would consider it to be loaded in the center of the axis of the "5.5" inch wall. My problem is that this causes an eccentricity of 1 inch with regards to the 2x4 studs centre line. Should I consider this to be equivalent to a 2x4 wall with studs @ 8" on center with a 1" eccentricity? Can the studs buckle in opposite directions?
I am not an SE, but I would think that with a significantly ridging top and bottom plate, your wall would be equivalently strong as a non-eccentric 2x4 wall with equivalent spacing. Calculating the whole wall with 1" eccentricity like you mentioned would ensure some safety factor.
Eccentricity occurs when you have a moment. If your top wall plate was thin plywood you would have to certainly figure eccentricity for each. Since your top plate has 1 or 2 laminated ridged 2x6 boards it will transfer majority of the moment between left and right members. To know how much you will probably have to figure in the geometry of your floor joists. It would be a good fea project, but at the end of the day you are likely going to have to follow code anyways so I would contact someone with code experience in your area and ask their thoughts. Looks like you are building a standard sound isolation wall; its likely someone may have already calculated and published an equivalent loading factor for this.
Just ignore it. Wood is resilient and will redistribute load. Also, there are large safety factors involved.
I'm going to guess that you're a newer engineer. I used to think and do this too, it was hard for me to let go of thinking about these type of small details. If you doing this, it's a good, it means that you're a good engineer in my book, as you think of and understand the details, more than most. After a while you're start to see how and when to be concerned about these things and when to know that it's not an issue
BTW, the inside faces of the studs are not braced and you do need to consider that for F'c