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FIGURES FORCHAPTER 3

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FIG. 3-1Torsion 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. 3-5Shear 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. 3-12Example 3-2. Torsion of a steel shaft

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

FIG. 3-14Bar 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. 3-18Free-body diagrams for Example 3-4

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

FIG. 3-20Stresses 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 sq and shear stresses tq versus angle q of the inclined plane

FIG. 3-23 Stress elements oriented at q = 0 and q = 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 q = 0, and (b) distortion of an element oriented at q = 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 w

FIG. 3-30 Example 3-7. Steel shaft in torsion

FIG. 3-31 Example 3-8. Steel shaft in torsion

FIG. 3-32Statically indeterminate bar in torsion

FIG. 3-33Example 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. 3-36Element in pure shear

FIG. 3-37Example 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. 3-42Thin-walled circular tube

FIG. 3-43Thin-walled rectangular tube

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

FIG. 3-45Example 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.)

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