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The Parallel Axis Theorem (example continued)

(Strategy continued)

Calculate the centroid of the composite section, y_cg :

Σ A_i y_cg = ΣA_iy_i (3bh) y_cg = (bh)(h/2) + (bh)(h/2) + (bh)(h + b/2)

y_cg = c = [h + h + (h+b/2)] / 3 = (5h + b)/6

Locate the distances of the centroid of the three rectangular areas from the centroid of

the composite section. i.e. d and e

Calculate the moment of inertia of each rectangular area about its own centroidal axis.

Moment of inertias: I_zz1 = I_zz2 = (1/12)bh³ I_zz3 = (1/12) hb³

Use the parallel axis theorem to obtain the moment of inertia of the composite section

about its centroidal axis.

I_zzcg1 = I_zz1 + (bh)d² = I_zzcg2 and I_zzcg3 = I_zz3 + (bh)e²

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

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