This document contains 6 problems related to determining centroids of geometric shapes and composite sections: 1. Determine the centroid of a triangle. 2. Determine the centroid of a shaded area. 3. Find the centroidal distance of a composite section shown. 4. Calculate the centroidal distance of a composite section with three parts. 5. Calculate the distance to the centroid of a cross-section. 6. Practice problem to find the centroidal distance of another cross-section.

1. VDB 1023
Engineering Mechanics
Tutorial 7
Centre of Gravity

2. Problem 1

4. Determine the centroid of the triangle shown below:
Problem 2
Similar to Problem 1, Solve it at Tutorial

5. Determine the centroid of the shaded area shown below:
Problem 3

7. Find the centroidal distance, 𝑦 of the composite section
shown below
Problem 4

8. Segment A (mm2) y (mm) yA (mm3)
1 50*200 100 1000000
2 50*400 225 4500000
3 50*200 100 1000000
Sum 40000 6500000
𝑦 =
𝑦𝐴
𝐴
=
6500000
40000
= 162.5 mm

9. Problem 5

10. Solution

11. y
y
x
C
xʹ
50
35
10
50
3520 20
10
10 10
Calculate the distance y to the centroid, C of the
cross-section.
Problem 6
Do it Yourself
Ans: 10.17mm