Beam Design

What sort of beam? Structural? Steel?

http://webstructural.com/how-to/steel-beam/

Nice link to a tutorial with engineering teck words. The only thing I didn't see for the OP, is that you want to select the deepest lightest weight per foot beam.

The OP want's to put this in some sort of table, I assume for automatic calculation. That can be fun.

σ=M*c/I = stress, don't allow this to exceed max for the material the beam is made of.

There is an equation for him.

The OP really needs to learn the basics, such as taking a "Statics and Strength of Materials" course, say at the local Community College.

A little information for the uninformed is a dangerous weapon.....

Design a beam is based on a number of factors, such as span, end condition type (simply supported, fixed, pinned, roller, propped, continuous etc), or cantilever etc etc etc, load patterns, and load magnitudes. That's just the statics end of it.

Then you have the materials portion to consider. You need to know the sectional properties such as: cross-sectional area, Section Modulus, Moment of Inertia, Radius of Gyration, beam material and material strengths.

Just dropping all of that into a computer program or Ap is dangerous w/o having any knowledge base behind you when you cannot analyze the output correctly to ascertain it's accuracy.

IMO, GARBAGE IN = GARBAGE OUT.

I understand the OP most likely does not have a clue. So the max stress equation I referenced most likely would be no help without knowing what M is or how to compute it, as well c and I. I did have to convince my local building folks I knew what I was doing even though I'm not a PE. It's interesting that building inspectors (in this county of IA) with no engineering training will use their program to run numbers for wood framing, and without a PE license, make structural rulings, but won't let a degree'd engineer, not doing it for hire, and clearly over designing (on residential out building), doing the same.

It was a bit ago, but that was one of the more useful courses from the civil engr department. My job I just retired from yesterday, didn't need me to have a PE, and as I did not take the EIT, I really didn't have any drive to get this. But it would have been useful to tell the local building department where to go.