Could you put your door on an end wall? Then you wouldn't have the roof to contend with and could go taller. You could also look at using a steel beam for a header, that will give you less depth with the same strength. Perhaps put a dormer over where the door is going so that you can raise your framing up into that space.
I'm thinking you shouldn't loose 2' for your door though in any case. how wide of a door are you putting in and how deep is your garage? You can get a 12' door with a 2x12 header depending upon depth of your building. That would only give you a loss of a little over a foot....if you are even looking at a door that wide. A LVL will give you more span(or less height).
Tad
1946 Chevy OS 1.5ton, 1955 GMC 3100, along with other various IH,Ford,Nash,MGB,.....
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