How to calculate the center of gravity of a T -section?/ Calculating centroid of a T- section.

Let us consider a T- section as shown below.

Given data:

Width of flange = 120mm.

Depth of flange = 25mm.

Depth of T - section = 150mm.

Web width = 25mm.

Calculation:

The given T- section is symmetrical to Y-axis 

What does that mean?

Let us observe the below drawing.

When we divide the T-section into two equal halves by drawing  Y-axis,  two parts on either side are identical having the same mass. The same is not true for the X-axis.

Therefore the center of gravity lies on the Y-axis.

Let us split the T-section into two rectangles ABCD & EFGH having the line XX as the reference axis.

The Axis of reference is the lowest line that we take on the drawing. As CG lies on Y-axis, in this case, line XX becomes the reference axis.

Area of rectangle ABCD 

A1= [width × depth]

    = [120mm. × 25mm.]

 A1= 3000 mm2

Co-ordinate Y1 (observe above drawing)

  = [ depth of T - section - (rectangle ABCD depth ÷ 2)]

 = [ 150mm. - ( 25mm. ÷ 2)]

Y1 = 137.5mm.

Area of rectangle EFGH 

A2 = [width × depth]

    = [25mm. ×  (150mm. - 25mm.)]

A2= 3125 mm2

Co-ordinate Y2

= [ depth of rectangle EFGH  ÷ 2)]

= [ (150mm - 25mm )  ÷ 2)]

Y2= 62.5mm.

Now, the center of gravity of given T-section

Ӯ = [(A1×Y1 + A2 ×Y2 ) ÷ ( A1 + A2)]

    = [(3000× 137.5 + 3125 ×62.5 ) ÷ ( 3000 +3125)]

   = [6,07,812.50  ÷ 6125 ]

 Ӯ   = 99.23mm.

Note: 

1. Distance of Y1, Y2, & center of gravity Ӯ, is measured from the reference axis - XX.

Also, go through 👇

👀. How to find the center of gravity of an L-section?

Thank you for going through these calculation steps❤. Have a good day 😄.

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