Question

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

Answer 1

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).