First off, if I were you, I would get a licensed structural/civil
engineer to help you out. You can find one on your state's
Professional Engineers website or in the phonebook.
Having said that, here's how you'd go about calculating the required
I-Beam size FOR PRICING ESTIMATES ONLY.
First, you need to determine the moment in your beams. Assuming 480
lb/ft is the correct load, then your beam moment can be calculated at
M = wl^2/8, where w is your load in lb/ft and l is your beam length in
So, that gives you 480 * 44^2/8 or 116160 ft-lb. This is your bending
moment, abbreviated as "M". Note that this number SHOULD already have
a safety factor built into it (assuming the individual who gave you
the 480 value knew what he was doing).
Next, you need to size your beam to accomodate this bending moment.
The key piece of info here is the Section Modulus, also abbreviated as
"S". This is given in tables. If you know the dimensions of your
I-Beam, you can also calculate this.
Finally, you need to know what type of material you are using. A
steel I-Beam will support much more weight than an engineered wood
I-beam of the same dimensions. The value you are looking for here
(found in the manufacturer's list of properties) is the ALLOWABLE
Your final equation becomes
ALLOWABLE BENDING STRESS > BENDING MOMENT / SECTION MODULUS
As long as this criteria is met, you're OK for stress.
Next, you need to be OK for deflection.
For a roof, deflection needs to be less than L/240, meaning
44ft*12inches/foot/240 = 2.2 inches at midspan
Actual deflection is 5wl^4/384EI
E is Young's Modulus, and is dependent on material properties. It is
roughly 30 x 10^6 psi for steel.
I is your moment of inertia. This can be found in tables of beam properties.
w and l are the same as before.
As long as ACTUAL DEFLECTION < 2.2 inches, you're OK for deflection.
If you're OK for deflection and stress, then your beam size is
appropriate. Pick the smallest beam that meets both criteria.