1. QUIZ
7. What are the min number of pieces you will have to consider for determining the centroid of the area?
1 B) C) D) 4
8. For determining the centroid, what is the min number of pieces you can use?
A) Two B) Three
C) Four D) Five
3cm
1 cm

2. QUIZ
10. For determining the centroid of the area, what are the coordinates (x, y ) of the centroid of square DEFG?
A) (1, 1) m B) (1.25, 1.25) m
C) (0.5, 0.5 ) m D) (1.5, 1.5) m A 1m y E F G C B x D

3. Moments of Inertia

4. Chapter Objectives
Method for determining the moment of inertia for an area

5. Chapter Outline Definitions of Moments of Inertia for Areas
Parallel-Axis Theorem for an Area
Moments of Inertia for Composite Areas

6. 10.1 Definition of Moments of Inertia for Areas
Measures the beam ability to resist bending.
The larger the M.I the less the beam will bend.
M.I is a geometrical property of a beam and depends on a reference axis.
The smallest M.I about any axis passes through the centroid.

7. Moments of Inertia for Composite Areas
Composite area consist of a series of connected simpler parts or shapes
Moment of inertia of the composite area = algebraic sum of the moments of inertia of all its parts
Procedure for Analysis
Composite Parts
Divide area into its composite parts and indicate the centroid of each part to the reference axis
Parallel Axis Theorem
Moment of inertia of each part is determined about its centroidal axis

8. Moments of Inertia for Composite Areas
Procedure for Analysis
Parallel Axis Theorem
When centroidal axis does not coincide with the reference axis, the parallel axis theorem is used
Summation
Moment of inertia of the entire area about the reference axis is determined by summing the results of its composite parts

10. Example 1
Compute the moment of inertia of the composite area about the x axis.

11. Solution
Composite Parts Composite area obtained by subtracting the circle form the rectangle. Centroid of each area is located in the figure below.

12. Solution

13. Example 2
Compute the moment of inertia of the composite area about the x axis & y-axia.

14. Solution

15. Example 3
Compute the moment of inertia of the composite area about the y-axis.

16. Solution

17. Example 4
Compute the moment of inertia of the composite area about the x/-axia.

18. Solution

19. Example 5
Determine the moment of inertia of the beam’s cross-sectional area about the x axis.

20. Solution

21. Example 6
Determine the moment of inertia of the composite area about the x axis.

22. Solution

23. Example 7
Determine the moment of inertia of the composite area about the x &y-axes.
7.5 mm

24. Solution

25. Determine the H-beam,s moment of inertia about the x &y-axes.
Example 8
Determine the H-beam,s moment of inertia about the x &y-axes.

26. Solution

27. Assignment 6( due date 03/05/2011)
1)For the T-section below , determine the moment of inertia about centroidal axes.

28. Assignment
2) Determine the moment of Inertia about x/ & y-axis

29. Assignment
3) Determine the moment of Inertia about y-axis