Question

3) Calculate the centroid location (7 and moment of inertia (1y) about the y-axis for the following shape: 3 in. 6 in. 3 in. 6 in. 18 in.

Answer 1

It requires PARALLEL AXIS THEOREM to calculate moment of inertia when several blocks are there together.

a in. * 3 in. Gin. 1 Bin Gin. 18in. 个 X AL = bxd = 18x6 = 108 in? ; &, = b = 12 - 9 in. =hi A2 = {xbxh = *63 = 9in?; 2, = 9+3 +4** 6) = 14 in. = ha A3 = 1TY = TT (3) - 7.069in?; 13 = 8+3- 4x3 = 10.72 7ina ha az AIX+ A222 +A3x3 = (108*9)+(9x14) +(7-069X10,727) 4 24 - 3XTI AltAzt A3 108 + 9 + 7.069, [x = 9.461 in Iy = BD 34 A, nr + BH3 + A2b² + gr. 1 t + Az hez? Iy = (1800*7 (68X49 16X9*+(00474 fixe 14 +67.009/10.127)] 36 36 L12 Jy - 9841.5 4 1768.5 + 829.324, = 12439.324 in 4,

Which states that M.I about any other axis is equal to M.I about its centroidal axis plus a product of its area and square of a distance between both axes.

And some regular formulas were involved. Though quarter circle is rare and it's M.I is π×r^4/(16). About centroids axis.