Find out the centroid of the shaded area, Mechanical Engineering

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Find out the centroid of the shaded area:

Find out the centroid of the shaded area illustrated in Figure (a).

Solution

1343_Find out the centroid of the shaded area1.png

The shaded area A may be considered as the algebraic sum of three areas - A1, A2 and A3 as illustrated in Figure b).

          A =  A1 +  A2  -  A3

Taking the origin of axes at H we may write:

A1 = 200 × 200 = 40,000 mm2 with centroid at (100, 100),

A2  = π× 100 2 /2 = 15, 708 mm2 with centroid at (242.4, 100), and

A3  = - π × 602/2    =  - 5655 mm2 with centroid at (100, 25.44).

Table

1826_Find out the centroid of the shaded area2.png

∴ x¯ = 724/5.0053         = 144.65 mm                           ∴ y¯ = 543/5.0053       = 108.50 mm .


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