Installing additional joists in garage

Hello,



I am hoping to install insulation in my attached garage, my garage has 4 out of a possible 16 ceiling joists installed.



I made up some drawings of the garage in sketchup, I've also made a short video that may help in showing the present state of things and what I hope to do.



Garagefa.skp

This file is the original garage.

Garagefb.skp

This file is the garage with the support for the ceiling joists.



As I mentioned, these are files for sketchup, I have no idea if they would work in any other programs, but they should give an excellent view on where and what everything is. Sketchup is free to download and install 3D for Everyone | SketchUp



To make things a little more simple, here are some picture links that might help.

http://ift.tt/1FzF89G

http://ift.tt/1Fzpiqp



This is a video I took of the garage that should help illustrate things a bit as well. http://ift.tt/1FzF89J



My plan is to install the other 12 ceiling joists using 3 seperate 2x6 boards, joining two in the middle with the third using screws. I am hopeful the illustrations show how I plan to support the boards in the middle using a temporary, floor supported set of 2x8s that span across the garage.



By how far should the board joining the middle of each ceiling joist overlap? I am currently planning on using 4 feet in each direction for all of the joists that I can.



Is 2x6 strong enough?



There are three boards that tie the 4 existing joists to the rafters, I was thinking of either copying this system or just using 2 boards. I don't have any plans for hanging anything from the ceiling beyond drywall with some sort of insulation.



I also plan to install an attic door access access through the ceiling, between joists 2 and 4 (counting from the joists closest to the attic door).



Does anyone see any obvious mistakes in this plan or have any advice?



Thanks for reading!

Installing additional joists in garage