First, where are you located?
The link you provide goes to a chart for Doug Fir joists. Most people use #2 and better Hem-Fir because it has a better cost/performance ratio and is widely available.
Based on a LL of 50 and a DL of 10 and deflection limit of L=1/240 and 2x6 joists at 16"o.c. spacing you can span 8'-11".
The beams would need to support #240/LF.
Using L=1/360 and Hem-Fir.
For the 12' span, 2-2x10's would suffice.
For the 8' spans use single 2x10's.
Use joist hangers.
Properly support the beams.
Total uniformly supported live load capacity would be 4800#.
To size a joist you need to know the desired uniform live load, dead load and the span.
Then you decide on the allowable deflection, pick the species of lumber and based on the spacing you find the allowable span.
http://www.awc.org/calculators/span/calc/timbercalcstyle.asp?species=Hem-Fir&size=2x6&grade=No.+2&member=Floor+Joists&deflectionlimit=L%2F240&spacing=16&wet=No&incised=No&liveload=50&snowload=-1&deadload=10&submit=Calculate+Maximum+Horizontal+Span#answer
For the beam(s), you take the contributing area which is half the span times the total load per SF, which gives you the load per lineal foot on the beam. Go to the beam tables and find a beam or pair of beams that supports that weight for each span with the Fb for the species (1.3 for hem-fir). Note the deflection limits for the table.
http://www.awc.org/pdf/wsdd/c2b.pdf
The point of the above exercise is to show that just picking a bigger piece of lumber doesn't always do it.
Yes, beams support more than joists....substantially more. And need to be deeper and/or doubled.
You can go to a stronger material, like Douglas Fir, to get more capacity in the same size, but at a premium cost.
You need to know the species and grade of wood to do calculations.
In the real world, there are no uniform loads, so everything is over-engineered to account for point loads.
To know what your structure will support, you need to do calculations and read tables. To do that, you need to input all the variables.
You can adjust any of the variables to allow for other ones to be what they need to be.
In this case, I took the 2x6's you chose, but in a less expensive species, and found they would support a higher load than you calculated. Based on this, the beams were undersized.
Or, you could use the loads you specified, 30#LL and 10#DL, for the beams. This give a contributing load of 160#/LF for the beams. You could use 2x8's for the 8' spans and 2-2x8's for the 12' span. The 2x6 joists would be oversized, so you could either leave them that way, or go to 24"o/c/ spacing. You would need to check the deck material to make sure it would span this.
Fun...huh?
Bill
