1. MECHANICS OF MATERIALS Third Edition Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf CHAPTER © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 7 Transformations of Stress and Strain

2. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.1

3. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.2

4. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.3

5. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.4

6. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.5

7. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.6

8. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.8

9. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.9

10. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.10

11. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.11

12. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.12

13. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.13

14. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.14

15. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.15

16. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.16

17. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.18

18. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.19

19. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.20

20. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.21

21. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.22

22. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.23

23. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.24

24. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.25

25. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.26

26. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.27

27. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.28

28. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.29

29. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.30

30. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.31

31. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.32

32. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.33

33. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.34

34. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.35

35. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.36

36. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.37

37. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.38

38. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.39

39. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.40

40. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.41

41. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.42

42. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.43

43. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.44

44. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.45

45. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.46

46. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.47

47. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.48

48. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.49

49. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.51

50. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.52

51. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.53

52. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.54

53. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.55

54. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.56

55. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.57

56. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.58

57. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.59

58. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.60

59. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.61

60. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.62

61. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.63

62. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.64

63. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.66

64. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.67

65. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.68

66. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.69

67. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.70

68. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.71

69. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.72

70. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.73

71. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.74

72. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.75

73. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.76

74. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.77

75. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.78

76. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.79

77. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. MECHANICS OF MATERIALS ThirdEdition Beer Johnston DeWolf Fig. 7.80