Maximizing I Beam Strength
Maximizing I Beam Strength
(OP)
I am working with what is essentially a cast I beam. What I would like to do is to maximize strength and minimize weight for a given load. I only have general limitations on the dimensions. I started trying to solve the derivative of my moment of inertia equation, but it's been a bit too long. My reference books are not too much help either.
My question: does someone have an equation that I can use for this (and possible future projects) situation? Like I said, all dimensions can vary for my purpose.
My question: does someone have an equation that I can use for this (and possible future projects) situation? Like I said, all dimensions can vary for my purpose.






RE: Maximizing I Beam Strength
The University of Nebraska developed a new kind of precast prestressed I bridge girder using studies to maximize the efficiency of the beam during initial release, construction loads, and design loads. Its called the NU girder.
Here's a link: NU Girder
RE: Maximizing I Beam Strength
RE: Maximizing I Beam Strength
Now that I consider my specific problem a little more, I can only change the webbing. However, I am still interested in maximizing I and minimizing weight for future designs.
Thanks for the link, that was a great read.
RE: Maximizing I Beam Strength
If you apply a fairly rigid set of rules (say, a structural steel design code) to a beam section, you can then optimize the dimensions on a spreadsheet. Even this approach would get fairly involved, as you have to allow for the reductions for thin sections, allow for fillet radii, etc. But in the case of something like a jack stand, where it may have a ratchet mechanism on it, etc., you could only apply a steel code in an approximate sort of way, so I don't know that it would be worth the bother.
If you only look at section modulus and moment of inertia, without regard to buckling issues, then the optimum shape is to make the cross section enormous with paper-thin elements, which is obviously not a realistic design. If you hold the outside dimensions and disregard buckling issues, the optimum design is to make the web paper thin and put all the material into the flanges, which is once again an unrealistic design.
RE: Maximizing I Beam Strength
RE: Maximizing I Beam Strength
RE: Maximizing I Beam Strength
The "i-beam" in a typical jackstand is a column with eccentric loading, not a beam.
Mike Halloran
Pembroke Pines, FL, USA
RE: Maximizing I Beam Strength
Mike, I think you're right. Actually, in addition to material yielding, our stands must not deform in such a way to cause a 0.125" height change. I've found the equation for column displacement with an eccentric load, but that gives me horizontal displacement. What I need is the vertical displacement at the point of the load. I'll keep looking, I'll probably have to check out a structural engineering book I imagine.
Would it be reasonable to think I can get a good estimate for vertical displacement based on the before-and-after geometry calculated from the horizontal displacement?
RE: Maximizing I Beam Strength
RE: Maximizing I Beam Strength
Thanks for the input, it's never to late! Well, the other answers pretty much helped me get what I needed to, but more info isn't a bad thing.