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Lag Bolts into Narrow Face of a Stud

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I have a condition where I’m using a 1.75” engineered lumber ledger for roof framing in a building with a flat roof.

 

I want to balloon frame the studs to the parapet above, continuous from the mudsill to the underside of the parapet double top plate.

 

The load from the rafters is too big for nails, so I need to use lag bolts. I am concerned about splitting the 2x studs and wondering if someone has some guidelines they use….

 

What is the maximum size lag bolt diameter would you use for a 2x stud: 3/8” dia? ½” dia?

 

Same question for 3x’s: ½” dia? 5/8” dia? ¾”dia?

 

I may end up needing 3x studs anyway once I check the combined loads w/ wind. The studs are going to be either

2x8’s or 3x8’s (hoping to avoid 3x’s obviously because it’s less common/more expensive).

 

TIA,

-gm