FIGURES FOR CHAPTER 3

Copyright 2005 by Nelson, a division of Thomson Canada Limited

FIGURES FOR

CHAPTER 3

TORSION

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FIG. 3-1

Torsion of a screwdriver due to a torque T applied to the handle


FIG. 3-2 Circular bar subjected to torsion by torques T1 and T2


FIG 3-3 Deformations of a circular bar in pure torsion


FIG. 3-4 Deformation of an element of length dx cut from a bar in torsion


FIG. 3-5

Shear strains in a circular tube


FIG. 3-6 Shear stresses in a circular bar in torsion


FIG. 3-7 Longitudinal and transverse shear stresses in a circular bar subjected to torsion


FIG. 3-8 Tensile and compressive stresses acting on a stress element oriented at 45° to the longitudinal axis


FIG. 3-9 Determination of the resultant of the shear stresses acting on a cross section


FIG. 3-10 Circular tube in torsion


FIG. 3-11 Example 3-1. Bar in pure torsion


FIG. 3-12

Example 3-2. Torsion of a steel shaft


FIG. 3-13 Example 3-3. Comparison of hollow and solid shafts


FIG. 3-14

Bar in nonuniform torsion (Case 1)


FIG. 3-15 Bar in nonuniform torsion (Case 2)


FIG. 3-16 Bar in nonuniform torsion (Case 3)


FIG. 3-17 Example 3-4. Steel shaft in torsion


FIG. 3-18

Free-body diagrams for Example 3-4


FIG. 3-19 Example 3-5. Tapered bar in torsion


FIG. 3-20

Stresses acting on a stress element cut from a bar in torsion (pure shear)


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)


FIG. 3-22 Graph of normal stresses and shear stresses versus angle of the inclined plane


FIG. 3-23 Stress elements oriented at = 0 and = 45° for pure shear


FIG. 3-24 Torsion failure of a brittle material by tension cracking along a 45° helical surface


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°


FIG. 3-26 Example 3-6. Circular tube in torsion


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


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


FIG. 3-28 Geometry of deformed element in pure shear


FIG. 3-29 Shaft transmitting a constant torque T at an angular speed


FIG. 3-32

Statically indeterminate bar in torsion


FIG. 3-33

Example 3-9. Statically indeterminate bar in torsion


FIG. 3-34 Prismatic bar in pure torsion


FIG. 3-35 Torque-rotation diagram for a bar in torsion (linearly elastic material)


FIG. 3-36

Element in pure shear


FIG. 3-37

Example 3-10. Strain energy produced by two loads


FIG. 3-38 Example 3-11. Strain energy produced by a distributed torque


FIG. 3-39 Example 3-12. Tapered bar in torsion


FIG. 3-40 Thin-walled tube of arbitrary cross-sectional shape


FIG. 3-41 Cross section of thin-walled tube


FIG. 3-42

Thin-walled circular tube


FIG. 3-43

Thin-walled rectangular tube


FIG. 3-44 Angle of twist for a thin-walled tube


FIG. 3-45

Example 3-13. Comparison of approximate and exact theories of torsion


FIG. 3-46 Example 3-14. Comparison of circular and square tubes


FIG. 3-47 Stepped shaft in torsion


FIG. 3-48 Stress-concentration factor K for a stepped shaft in torsion. (The dashed line is for a full quarter-circular fillet.)


PROBS. 3.2-1 and 3.2-2


PROBS. 3.2-3, 3.2-4, and 3.2-5


PROB. 3.3-1


PROB. 3.3-2


PROB. 3.3-3


PROB. 3.3-4


PROB. 3.3-5


PROB. 3.3-6


PROB. 3.3-7


PROB. 3.3-9


PROB. 3.3-10


PROBS. 3.3-11 and 3.3-12


PROBS. 3.3-13 and 3.3-14


PROB. 3.3-15


PROB. 3.3-16


PROB. 3.3-17


PROB. 3.4-1


PROB. 3.4-2


PROB. 3.4-3


PROB. 3.4-4


PROB. 3.4-5


PROB. 3.4-6


PROB. 3.4-7


PROBS. 3.4-8, 3.4-9, and 3.4-10


PROB. 3.4-11


PROB. 3.4-12


PROB. 3.4-13


PROB. 3.4-14


PROBS. 3.5-1, 3.5-2, and 3.5-3


PROB. 3.5-4


PROB. 3.5-7


PROB. 3.5-9


PROB. 3.5-10


PROB. 3.7-1


PROB. 3.7-2


PROB. 3.7-3


PROB. 3.7-4


PROB. 3.7-7


PROBS. 3.7-9 and 3.7-10


PROB. 3.8-1


PROB. 3.8-2


PROB. 3.8-3


PROB. 3.8-4


PROB. 3.8-5


PROB. 3.8-6


PROB. 3.8-7


PROB. 3.8-8


PROB. 3.8-9


PROBS. 3.8-10 and 3.8-11


PROBS. 3.8-12 and 3.8-13


PROB. 3.8-14


PROBS. 3.9-1 and 3.9-2


PROBS. 3.9-3 and 3.9-4


PROB. 3.9-5


PROB. 3.9-6


PROB. 3.9-7


PROB. 3.9-8


PROB. 3.9-9


PROB. 3.9-10


PROB. 3.9-11


PROB. 3.10-1


PROB. 3.10-2


PROBS. 3.10-3 and 3.10-4


PROB. 3.10-5


PROB. 3.10-6


PROB. 3.10-7


PROB. 3.10-8


PROB. 3.10-9


PROB. 3.10-10


PROB. 3.10-11


PROB. 3.10-12


PROB. 3.10-13


PROBS. 3.11-1 through 3.11-5

FIGURES FOR CHAPTER 3

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