what's needed to hold up a roof with some soil on it?

I am curious about living roofs.  I will be putting up the posts and rafters next week for my cob green house, and would like to know how much understructure is needed to hold up a roof with 2-3 inches of soil.

Current plans are:  spanning a 13 foot space, 4 redwood 4x4 posts set in the ground.  Above the posts a 4x6 beam, which also overlaps a wood frame structure by 8 feet, and is supported at the other end by the cob wall.

Onto the 4x6 beam I have planned 2x6 rafters which span a horizontal distance of 10 feet.  The slope is an inch or two less than 40 inches in the 120, but I could adjust this to be flatter.

I was planning to use blocking to keep the rafters straight and true.

Yesterday, after I read a post about living roofs, I started thinking about things like putting a second supporting beam across (takes out 6 inches of head room)  doubling up the 2x6 rafters, (planned at 16 inch centers).  Or putting the 2x6 on 12 inch centers, then I began to wonder what would hold up the weight of the extra lumber....

On the rafters, decking, a combination of the thinnest OSB (which was used as packing on a delivery I received)  and similar thickness pallet wood.  Then 15 # tar paper, then corrugated metal, the old kind, from a garage disassembled on this property before I bought it 24 years ago.

I would love to throw some soil up there.  Have thought I could make less of a load by putting in a layer of aluminum soda cans, and shoveling loose dirt and straw over the cans.  But, though I will not sleep in this building (it is a green house)  I have gone to a lot of trouble so far, and do not want to do something stupid like putting more weight up than the roof can hold.

I would appreciate any help anyone can give me.

Thanks
Thekla

Difficult to make any suggestion without being able to see what you're doing.  My guess based on what I think you're trying to say... is that you're going to put too much load on that 4x6. 

Your best bet is to get a local contractor to look at it.  Free advice on the internet is worth even less than you pay for it.

Hi Dirt!

Thanks for your comment.  I want to be sure I understand you.  Are you saying that without any dirt on top of the metal I may be overloading the 4x6 beam?

Is there some kind of table somewhere that tells what load a 4x6 can carry?  or what a 4x4 post can support?  The guy at the lumber yard (more free advice) thought 3 4x4 posts would be adequate, to carry the beam across the 13 foot span, in addition to the beam being supported on each end.

Does decreasing the slope decrease the overall weight significantly?  Seems like since you have fewer square feet of roof, you have fewer pounds of everything.

If I can't get any real numbers, then I'm not putting anything else up there.

Anyway, thanks again for taking the time to post

Thekla

There's a decent amount to this, actually. What you want are span tables. Here is more info on them and how to properly use them.
http://bct.eco.umass.edu/publications/by-title/understanding-loads-and-using-span-tables/

If you have any doubts whatsoever, hire an engineer.

Are you saying that you will be putting soil onto a functioning metal roof?