Originally Posted by ronny31
Sweet. Then you could theoretically do the math for us. Or make an excel sheet so that we can do it ourselves. Is there a formula which tells us how much I-beams strengthen a sheet material given different dimensions and spacing of the I-beams?
Well, yes and no. The equation for stiffness of a beam of a certain cross section is straightforward, and could certainly be put in excel form if not already done and floating on the web. And the displacements involved are rather small, so you don't have to worry about anything more complicated like flange or web buckling. And you can probably ignore any stress related questions.
And that can be compared to the equivalent stiffness of a stanchion to get a grasp on what we're trying to say here. It's been a decade since I put any of this into practice, and am not inclined to go look up the MOI equations and calculate deflection myself, but I would suggest this would be a good exercise for anyone interested. Take the equation for a constrained end beam of a pretty damned rigid stiffener for the sizes we are talking about, like 2x4 dimensional lumber turned on side to produce a blade stiffener of a panel, say 2 feet long. Calculate the deflection with a load applied in the midspan of the beam, say 100 pounds to make it easy. Now do the math for how much compression you get in that same 2x4 turned on end, pretending it is an internal brace spanning to the opposite panel 2 feet away. With that same 100 pound load, the percent of compression will be a fraction of the deflection midspan if used as a stiffener on the panel... same volume of wood. Now find the minimum size of internal brace spanning to opposite panel that will have the same deflection under a 100 pound load as your 2x4 panel beam stiffener. You will find it to be quite small.
That's the simple math, and good enough to prove the point. There are closed form solutions for plate/panel stiffening, but the math is horrendously complex (I hated the advanced applied mechanics courses in grad school) and the solutions depend on the boundary conditions at plate edges (how stiff are the corner joints?) and types/number of stiffeners, and the more complex they get the more unwieldy the math is.
Any sane engineer just whips up the proposed plate/stiffener combo in his FEA software of choice and lets the magic happen. Hell, it would be easier to solve the FE equations by hand than to attempt the closed form solutions! But that doesn't lend itself to something as simple as an excel spreadsheet equivalent. Not an easy way to give you a tool that produces real results for real life practical designs, apart from the FEA software itself.