timber shelf - how much support needed?

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I'm putting a shelf in the study above the desk. Plan is for the shelf to go from wall to wall, so it will be 3.5m wide (long?), 300mm deep.

Question is: will it be enough to support the shelf on 3 sides (along the back, and 300mm on each side wall)? Do I need something in the middle? If so, what? Will the ends be strong enough if they're just sitting on some supports.

I was planning to use some architrave timber (16mm deep?) to match the doorways as the supports and will be screwing the whole lot into studs. I've had an extra stud added in each side wall (200mm from the corner) when the room was built so the side supports will go into studs.

Shelf will hold books, and other junk.. heavy-ish I guess, but not overloaded.. Shelf is a solid plank of Jarrah :) (heavy!)

See attached plan.
http://www.renovateforum.com/attachments/f85/96443-timber-shelf-how-much-support-needed-shelf.jpg

Thanks !
Attached Thumbnails http://www.renovateforum.com/attachments/f85/96443d1364644368t-timber-shelf-how-much-support-needed-shelf.jpg (http://www.renovateforum.com/attachments/f85/96443d1364644368-timber-shelf-how-much-support-needed-shelf.jpg)



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