Question

30mm 150mm 47 SO -somme 300m 10oma 300 mn

Find the centroid of given composite area

Answer 1

If you look over the composite area, it is symmetrical about an axis along y which cuts it into two exact identical pieces thus the centroid lies on this line only.

Now centroid can be given as $\sum$ A_iC_i/$\sum$A_i; where A_i are the areas of the components making up the composite and C_i are the corresponding centroids of those compoenents.

Assuming the x-y axes to be like-

150mm 50mm -somne |300mm 100M Olomn X

Now dividing the whole structure into three parts upper rectangle, middle rectangle and then lower rectangle.

Upper rectangle; centroid will be in the geometric center

C_u,y = 400mm + 25mm = 425mm

C_u,x = 0

A_u = 150mm x 50mm = 7500mm²

Middle rectangle; centroid will be in the geo centre;

C_m,y = 100mm + 150 mm = 250mm

C_m,x = 0

A_m = 300mm x 50mm = 15000 mm²

Lower rectangle; centroid will be in geo centre;

C_L,x = 0

C_L,y = 50mm

A_L = 100mm x 300mm = 30000 mm²

Now from the centroid formula;

C_y = (425mm x 7500mm² + 250mm x15000 mm² + 50mm x 30000 mm²)/(7500 + 15000 + 30000mm²)

=> C_y = 160.7143 mm

C_x = 0

So the centroid will be at central line and at a height of C_y from the base.