Finished garage ceiling for storage: 2 x 6 spanning 11' 6" - 16 on center?

You're residential so your storage loads should be 40 psf to match the interior floor live load. For the dead load, lets assume 5 psf and 11' 6" true span from inside of wall to inside of wall with floor joists bearing on top.

Yes, the tables are correct, you would need a 2x8 at 16" oc. This is for Hem-fir #2 graded lumber.

The good news - You have other options

You can change any combination of the materials, spacing, and joist counts

1. Double 2x6, DF (Doug-fir) #2 or HF #1, @ 16" oc
2. Double 2x6, HF #2 @ 12" oc

The Code requires a live load of 20 lbs. per square foot for limited attic storage and 30 lbs. per square foot for attic storage with fixed stairs. (See IRC Table 301.5)

Limited storage is defined as an attic space that has trusses. (See Table 301.5, footnote “g”.) I doubt that is your condition. Therefore, you need to design to 30 lbs. per square foot, unless you’re going to store stacks of books or other heavy objects.

A No. 2 Doug-Fir 2x6 spanning 11’-6” can support the following:

1) At 12” oc = 50 psf 2) At 16” oc = 37 psf

You’ll have a dead load of:

1) 3/8” plywood floor = 1.2 psf 2) 2x6’s at 16” oc = 2.0 psf 3) 1/2” plywood ceiling = 1.5 psf ———————————————- Total Dead Load = 4.7 psf

Therefore, your 2x6’s at 16” oc can support a live load of: 37-4.7 = 32.3 psf

I’d use 2x6’s at 16” on center.

The Code allows you to notch the end of the joist at the bearing wall a maximum of 1/4 the height of the joist. (See IRC Figure R502.8) Therefore, you can notch 1.37” from the top of your 2x6 joists.

That is probably not enough in your situation. I’d talk to the Building Official and explain that you only need 1.5” of bearing, so you’d like to notch 1.37” at the 1.5” bearing point. Therefore, the remainder of the 2x6’s could be notched more without violating Figure R502.8. I’d guess he’d agree.