Bending in weak axis: multiple thin plates stronger than one thick plate ??? S(thin) = 4x S(thick) 1

[TpaRAF2]

Here's an odd puzzle I've encountered. I must be missing something, as the calcs do not match 'common sense' (IMO).

I am reviewing bending of a flat steel bar about the weak axis. Very straight forward to determine I, y and then S.

If I compare using multiple, thin flat bars (same width that add up to the same thickness), the value for the composite I and S are 4 times _greater_ than the single thick bar. This was computed using parallel axis theorem [I= Σ(Io + A·d²]. The thin plates are adequately connected to resist sliding or separating.

A bit of surfing the web results in a lot of composite material topics, and CLPT (classical laminated plate theory). Therein, examples and discussions seem to point to reduced deflection for laminated plates being about 25% of the equivalent sold plate. This matches my calcs suggesting a 4x increase in mom't of inertia.

The underlying assumption for this case, in CLPT and in PAT is the layers don't slip past each other. The proposed stack is stitch fastened, so layers don't slip.

This increase in section modulus is just not logical to me. The stacked bars should be weaker than the equivalent solid bar. If not, we'd be making durn near every thick flange steel beam out of stacks of thinner plates.

Thanks for your help and guidance on this puzzling observation.

 

[BridgeSmith]

"...the assumption of equal load distribution between the layers is at best a very rough approximation."

I definitely agree. Depending on how the load is applied and the faying surface condition, the friction between the plates could be significant, which could change the stress distribution substantially.