1. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIGURES FOR CHAPTER 3 TORSION 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. 3-1 Torsion of a screwdriver due to a torque T applied to the handle

3. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-2 Circular bar subjected to torsion by torques T 1 and T 2

4. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG 3-3 Deformations of a circular bar in pure torsion

5. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-4 Deformation of an element of length dx cut from a bar in torsion

6. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-5 Shear strains in a circular tube

7. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-6 Shear stresses in a circular bar in torsion

8. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-7 Longitudinal and transverse shear stresses in a circular bar subjected to torsion

9. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-8 Tensile and compressive stresses acting on a stress element oriented at 45° to the longitudinal axis

10. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-9 Determination of the resultant of the shear stresses acting on a cross section

11. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-10 Circular tube in torsion

12. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-11 Example 3-1. Bar in pure torsion

13. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-12 Example 3-2. Torsion of a steel shaft

14. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-13 Example 3-3. Comparison of hollow and solid shafts

15. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-14 Bar in nonuniform torsion (Case 1)

16. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-15 Bar in nonuniform torsion (Case 2)

17. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-16 Bar in nonuniform torsion (Case 3)

18. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-17 Example 3-4. Steel shaft in torsion

19. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-18 Free-body diagrams for Example 3-4

20. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-19 Example 3-5. Tapered bar in torsion

21. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-20 Stresses acting on a stress element cut from a bar in torsion (pure shear)

22. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-21 Analysis of stresses on inclined planes: (a) element in pure shear, (b) stresses acting on a triangular stress element, and (c) forces acting on the triangular stress element (free- body diagram)

23. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-22 Graph of normal stresses   and shear stresses   versus angle  of the inclined plane

24. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-23 Stress elements oriented at  = 0 and  = 45° for pure shear

25. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-24 Torsion failure of a brittle material by tension cracking along a 45° helical surface

26. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-25 Strains in pure shear: (a) shear distortion of an element oriented at  = 0, and (b) distortion of an element oriented at  = 45°

27. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-26 Example 3-6. Circular tube in torsion

28. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-27a Stress and strain elements for the tube of Example 3-6: (a) maximum shear stresses, and (b) maximum tensile and compressive stresses

29. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-27b Stress and strain elements for the tube of Example 3-6: (c) maximum shear strains, and (d) maximum tensile and compressive strains

30. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-28 Geometry of deformed element in pure shear

31. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-29 Shaft transmitting a constant torque T at an angular speed 

32. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-30 Example 3-7. Steel shaft in torsion

33. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-31 Example 3-8. Steel shaft in torsion

34. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-32 Statically indeterminate bar in torsion

35. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-33 Example 3-9. Statically indeterminate bar in torsion

36. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-34 Prismatic bar in pure torsion

37. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-35 Torque-rotation diagram for a bar in torsion (linearly elastic material)

38. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-36 Element in pure shear

39. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-37 Example 3-10. Strain energy produced by two loads

40. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-38 Example 3-11. Strain energy produced by a distributed torque

41. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-39 Example 3-12. Tapered bar in torsion

42. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-40 Thin-walled tube of arbitrary cross-sectional shape

43. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-41 Cross section of thin-walled tube

44. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-42 Thin-walled circular tube

45. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-43 Thin-walled rectangular tube

46. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-44 Angle of twist  for a thin-walled tube

47. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-45 Example 3-13. Comparison of approximate and exact theories of torsion

48. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-46 Example 3-14. Comparison of circular and square tubes

49. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-47 Stepped shaft in torsion

50. Copyright 2005 by Nelson, a division of Thomson Canada Limited FIG. 3-48 Stress-concentration factor K for a stepped shaft in torsion. (The dashed line is for a full quarter-circular fillet.)

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