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Determine the Position of the Centroid of the Plane Lamina. Shaded Portion is Removed. - Engineering Mechanics

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Short Note

Determine the position of the centroid of the plane lamina. Shaded portion is removed.

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Solution

FIGURE AREA
(mm2)
X co-ordinate Of centroid 
(mm)
Y co-ordinate Of centroid (mm) Ax (mm2) Ay (mm2)
Rectangle 120 x 100 =12000 `120/2=60` `120/2=60` 720000 600000
Triangle `1/2`120 x 60 =3600 `120/3=40` `-60/2=60` 144000 -72000
Semicircle `1/2`𝝅 x 602 =1800 𝝅
=5654.8668
`120/2=60` `100+(4∗60)/(3x)`
=125.4648
339292.01 709486.68
Circle
(Removed)
- 𝝅 x 402
=5026.5482
`120/2=60` 100 -301592.89 -502654.82
Total 16228.32     901699.12 734831.86

`(Σ Ax)/(Σ A)=(901699.12)/(16228.32)= 55.56 mm`
`(Σ Ay)/(Σ A)=(734831.86)/(16228.32)= 45.28 mm`
Centroid is at (55.56,45.28)mm

Concept: Centroid for Plane Laminas
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