1. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIGURES FOR CHAPTER 12 REVIEW OF CENTROIDS AND MOMENTS OF INERTIA Click the mouse or use the arrow keys to move to the next page. Use the ESC key to exit this chapter.

2. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-1 Plane area of arbitrary shape with centroid C

3. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-2 Area with one axis of symmetry

4. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-3 Area with two axes of symmetry

5. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-4 Area that is symmetric about a point

6. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-5 Example 12-1. Centroid of a parabolic semisegment

7. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-6 Centroid of a composite area consisting of two parts

8. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-7 Composite areas with a cutout and a hole

9. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-8 Example 12-2. Centroid of a composite area

10. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-9 Plane area of arbitrary shape

11. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-10 Moments of inertia of a rectangle

12. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-11 Composite areas

13. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-12 Example 12-3. Moments of inertia of a parabolic semisegment

14. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-13 Derivation of parallel-axis theorem

15. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-14 Plane area with two parallel noncentroidal axes (axes 1-1 and 2-2)

16. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-15 Example 12-4. Parallel-axis theorem

17. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-16 Example 12-5. Moment of inertia of a composite area

18. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-17 Plane area of arbitrary shape

19. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-18 Polar moment of inertia of a circle

20. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-19 Plane area of arbitrary shape

21. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-20 The product of inertia equals zero when one axis is an axis of symmetry

22. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-21 Plane area of arbitrary shape

23. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-22 Parallel- axis theorem for products of inertia

24. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-23 Example 12-6. Product of inertia of a Z-section

25. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-24 Rotation of axes

26. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-25 Rectangle for which every axis (in the plane of the area) through point O is a principal axis

27. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-26 Examples of areas for which every centroidal axis is a principal axis and the centroid C is a principal point

28. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-27 Geometric representation of Eq. (12-30)

29. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 12-28 Example 12-7. Principal axes and principal moments of inertia for a Z-section

30. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROBS. 12.3-2 and 12.5-2

31. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROBS. 12.3-3, 12.3-4, and 12.5-3

32. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROBS. 12.3-5 and 12.5-5

33. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROBS. 12.3-6, 12.5-6, and 12.7-6

34. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROBS. 12.3-7, 12.4-7, 12.5-7, and 12.7-7

35. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.3-8

36. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.4-6

37. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.4-8

38. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.5-4

39. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.5-8

40. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.7-3

41. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.7-4

42. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.8-1

43. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.8-2

44. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROBS. 12.8-4 and 12.9-4

45. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROBS. 12.8-5, 12.8-6, 12.9-5, and 12.9-6

46. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.9-1

47. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.9-2

48. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.9-3

49. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROB. 12.9-7

50. Copyright 2005 by Nelson, a division of Thomson Canada Limited PROBS. 12.9-8 and 12.9-9