Never worked with steel beams before so I'll assume your math is right. I'm sure someone out there will be sure to correct you if your wrong. So how do you attach the wood to the beam? Does it just sit on top or does it need to be anchored someway, I'll assume you can't drill through the beam as that would weaken it.
Typically there is a sill-plate bolted to the top of the i-beam. For example, if the beam top flange is 6" wide, you would use a 2x6 laid down on it and bolted down.
The minimal effect of "weakening" the beam with the holes is more than bade up for by the strength of that 2x6 being attached:thumbsup:
Then simply toe-nail the joists on the sill, or use some of those special simpson connectors, like hurrican ties, or whatever they are called:confused2:
A couple of suggestions if this is the route you take. These are only suggestions and my personal preference, but check your local codes if they apply.
First, I like to over-lap the joists a bit, OR use a full length 20' that rests on top of the beam. If you dont use the 20' length one, use 2 12'ers (I know I am contradicting my previous post) and overlap them. OR you can butt them end to end and use a 2 or 3 foot peice to tie them together.
Second, you need to make sure the floor joists stay vertical. There natural tendancy is to want to lay (flop) over on their side when a load is applied. There are two ways you can do this.
1. use those metal X connectors that go from the top of one joist to the bottom of the other. (If your house has a basement, you will probabally see these). or 2. use a block of wood nailed in that is the spacing of the joist and the same size. For example, If you use 2x6 joists on 16" centers, you will cut a block of 2x6 that is just under the 16" (to fit snug up in between the joists) and nail it in place. This prevents the joists from "twisting" or flopping over.:thumbsup:
And wether you use steel or something else, I would reccomend this.