The Parallel Axis Theorem (example continued)

Sum these terms to obtain the total moment of inertia, I_zzcg, for the composite area about

its centroid.

I_zzcg = I_{zzcg1 +} I_{zzcg2 +} I_zzcg3

I_zzcg = 2[ (1/12)bh³ + (bh)d² ] + (1/12)hb³ + (bh)e²

I_zzcg = [ (1/6)bh³ + 2(bh)d² ] + (1/12)hb³ + (bh)e² (result)

where d = c - h/2 = (5h + b)/6 - h/2 = h/3 + b/6

and e = h + b/2 - c = h + b/2 - (5h + b)/6 = h/6 + b/3

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