Question

The centroid a t-section 100 mm x 150 mm x 50 mm from its bottom is

Answer 1

a1 = 100*50 = 5000; a2 = 50*100 =5000;

y1 = 50; y2=125;

cg = (a1*y1+a2*y2)/(a1+a2). 

150 = 87.5.

Answer 2

Given

A centroid of section 100 mm x 150 mm x 50 mm

To find

Center of gravity

Solution

We can solve this mathematical problem using the following method

let A₁ & A₂ be individual areas & y₁ & y₂ be centroid of each from x-axis reference

$y_{2}$ = (A₁ y₁ +A₂ y₂)/ (A₁ + A₂) where y is the combined centroid from the x-axis.

A₁ = 150*50 = 7 500 & y₁ = 100.25 & A₂ = 100*50 = 5 000 & y₂ = 50.

$y_{2}$ = (7 500*100.25 + 5 000*50)/ (7 500 + 5 000)

$y_{2}$ = (751 875 + 250 000)/ 12 500

$y_{2}$ = 1 001 875/12 500

$y_{2}$ = 80.15 from the x-axis as reference point

Therefore from the top is 150-80.15 = 69.85mm Answer