Small scale application of structural cross sections

[Manta173]

I am working on fixing a heavy walnut cedar chest lid that has bowed convexly from the chest. It is about 1/4" high in the center of a 24" deep lid. The lid is ~2' x 5'. It is made from 3/4" walnut with 3/4" x 3" ribbing on the top.

I thought that adding in some C-channel or square tubing would be the easiest way to straighten the depth of the lid. Unfortunately I am a chemical engineer and do not have the references to calculate which material and which cross section would be the most resistant to mild flexing. I also have a thickness restriction of 3/8" (1/2" is the absolute limit) in order to properly hide the material underneath wooden decoration. The width can be as wide as 1.5". but I was thinking that 2 -3/4" pieces may provide more bend resistance.

I have found various sites supplying different configurations of cross section but the small height and the short length (24") have restricted my options. I think a 2000 or 7000 grade of aluminum would be a good fit, but they only seem to exist in bar form and not a structural cross section. Would stainless steel or 6061 aluminum be strong enough? or should I go for the bars?

 

[Dr.D]

What is needed for stiffness is to maximize the EI product, the product of Young's modulus and area moment of inertia. Thus, steel will be a better choice than aluminum because of a much higher Young's modulus.

Your height constraints make it very difficult to get much improvement in I which is usually done by going to taller sections. So, bars look like your best bet. Use the thickest bars that will fit.