I am working to reduce the deflection in a cantilever/ dive board at work.$300 mm(L) \times 30mm(B) \times 2 mm(H)$, i.e. it's a rectangular cross section currently.
I can't change the material, or length.
I started playing with cross sections to reduce the deflection. So I stacked 7 semi circular beams of 4mm Dia. next to each other(thus not changing the height from rectangular beam) assuming it would increase my "I" by 7 X I of single semi circular beam, thus making it stiffer than the current beam but IT DID NOT. Any idea why?
I(Rectangular cross section): $bh^3/12= 20 mm^4$
I (single Semicircular Beam of Dia 4)= $\pi \cdot r^4/8= 6.28 mm^4$
Again, I assumed stacking up next to each other would make the total area moment of inertia(I) = $7 \cdot 6.28 = 43.96 mm^4.$
And Using Deflection = $FL^3/48EI$, I thought it would decrease my deflection by more than half.IT DIDN'T WORK. FEA results showed increase in deflection.
Any idea why? Sorry if it's a dumb question