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For the composite lamina shown in Figure 5, determine the coordinates of its centroid. - Engineering Mechanics

Answer in Brief

For the composite lamina shown in the figure, determine the coordinates of its centroid.

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Solution

Area of the shaded region = Rectangle ABFG + Rectangle OCDF + Quarter Circle OCB – Triangle AEG

Figure Area x coordinate y coordinate Aixi Aiyi
Rectangle
ABFG
90 x 60
= 5400 mm2
`(-60)/2 = - 30` `50-90/2 =5` -162000 27000
Rectangle
OCDF
40 x 50
= 2000 mm2
`50/2 = 25` `-40/2`=-20` 50000 -40000
Quarter Circle
OCB
`1/4 xx pi xx 50^2= 1963.495 mm^2` 21.22 21.22 41665.3639 41665.3639
Triangle
AEG
`-1/2 xx 75 xx 90 = 3375 mm ^2` -35 -10 118125

33750

 

ΣAi = 5400 + 2000 + 1963.495 – 3375 = 5988.495
ΣAixi = -162000 + 50000 + 41665.3639 + 118125 = 47790.3639
ΣAiyi = 27000 - 40000 + 41665.3639 + 33750 = 62415.3639

`overlineX = (ΣAix i)/(ΣAi) =(3790.3639)/5988.495  = 7.98m`

`overlineY = = (ΣAix i)/(ΣAi) = 10.423m`

Coordinates of centroid are (7.98,10.423).

Concept: Centroid for Plane Laminas
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