It's actually even better than that. Stiffness is proportional to the thickness cubed (a.k.a. to the third power).
Great cab!
Are you sure? Correct me if I'm wrong, but I believe you are talking about ordinary Beam Theory, which is a little different than Sandwich Beam Theory.
I posted most of this back on
page 22 but I'll go through it again for my own benefit.
From what I've read, ordinary beam theory stiffness (D) is the product of the modulus of elasticity (E) and the second moment of inertia (I). In sandwich beam, D is the sum of the flexural rigidities of the different parts about the centroidal axis of the entire section.
So for ordinary beam theory, you are correct. D = E * [(b*t
3)/6]. Here the stiffness does indeed very with the cube of the thickness of the beam. Where b = width of beam cross section and t = thickness of beam cross section.
With a sandwich beam your stiffness equation is the sum of the parts of the beam. You've got to consider the local stiffness of the facings, then the stiffness of the facings about the centroidal axis of the entire cross section, then finally the stiffness of the core. The equation looks like this:
Where:
E
f = Elastic Modulus of the Facings (Skins)
E
c = Elastic Modulus of the Core
b = Width of the Beam
d = Distance Between Facing Centroids
t = Thickness of a Facing
c = Core Thickness
In most cases the first and third terms of that equation can be neglected. More specifically, when d/t > 5.77, the first term amounts to less than 1% of the second. When (E
f/E
c)*(td
2/c
3) > 16.7, the third term amounts to less than 1% of the second term.
I plain(er) english, this means that if you have facings (fiberglass skins) that are significantly thinner than the core and the modulus of elasticity of the facings is higher than the core, your stiffness boils down to: D = E
f * (btd
2)/2
Therefore, I would say that the stiffness of the composite panels I'm using is proportional to the square of the thickness and not the cube.
Here's where I got most of this info: [Invalid or Expired Link Removed],
BoatDesign.net article
Please let me know if I'm wrong here. I'm still trying to figure all this stuff out, and am a total novice.