How to calculate dead/live load on this 2x4 structure
Updated: I see a lot of questions referring to spans, strengths etc. Here is a very useful link for calculators regarding all things mentioned. 
http://www.awc.org/codes-standards/calculators-software

Edit: Based on your diagram now showing.

I do not what type of finish look you are going for but as mentioned by others, the chance of hitting studs where you need them and lack of support are problematic. Either rethink your material or consider either metal bracing for a rustic look or a cable system if you want something that doesn't stand out.





Since your diagram is not showing up and you have a shelving tag, I will give it a go. 

For a shelf you can use a sagulator calculator to give you the info you need. Which can be found here. http://woodbin.com/calcs/sagulator.htm

Strength values for lag bolts into 2x4s.


A 3/8" lag bolt 2" deep has a pull force of 1900lbs.
At 1/2" at 3.5" deep and you have a pull force of 3500lbs.


If you are looking for a box frame dead load, let me know.