[MNsawyergp]

Here is my suggestion. Use lag screws and washers through the bottom of the first shelf into the first uprights. Then, countersink for lag screws through the second shelf and into the first uprights. Then, make holes for dowel pegs into the second shelf so the dowels stick up and receive the next uprights. Once you slide the uprights onto the dowels, add the next shelf and again countersink and attach lags into the uprights. Keep doing this until you get to the top.

As an addition, I would attach a piece of 2" x 1/8" iron bar stock to the back of each upright stack for additional holding power. There is a remote possibility that the whole thing could rock due to no diagonal support, but I think it would be minimal.

 

[MNsawyergp]

I did a google search for a reference for you. Here is a picture and description on Amazon.

STEELWORKS BOLTMASTER 11662 FLAT STEEL BAR 1/8"x2"x36" - Amazon.com

If you have a farm supply store near you, they should carry it. A welding shop or metal supply company should also carry it. Lumber stores like Menards and Home Depot have some sizes, but I don't remember if they have this. You could go with a narrower or 2 shorter pieces. You will have to use a 3/16" drill bit to drill pilot holes in the bar stock, then make countersink indents with a 5/16" or 3/8" bit for the screws to go into.

Here is one more link to give you a range of metal stock you can get.

http://www.metalsdepot.com/products/hrsteel2.phtml?page=expanded

Oh, as for shimming under the uprights to keep the stack going straight....the simplest shims are from cereal boxes, tag board, vinyl flooring scraps, thin plywood, and real shims. When I did finish carpentry I had a tote box with dividers to hold all of these materials.