Jiangyu Li, University of Washington

Lecture 10Torsion

Mechanical Behavior of Materials Section 4.9.3-4.9.4

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Mechanics of Materials Lab

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Fig. 3-3 Deformations of a circular bar in pure torsion.

Angle of Twist

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

©2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Jiangyu Li, University of Washington

©2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Fig. 3-5 Shear strains in a circular tube.

Shear Strain

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Shear Stress

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©2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

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

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©2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Torque

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Fig. 3-10 Circular tube in torsion.

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Fig. 3-20 Stresses acting on a stress element cut from a bar in torsion (pure shear).

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©2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

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

Principal Stress

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Fig. 3-25 Strains in pure shear: (a) shear distortion of an element oriented at θ = 0, and (b) distortion of an element oriented at θ = 45°.

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Torsion Test

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

Jiangyu Li, University of Washington

Jiangyu Li, University of Washington

©2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Fig. 3-34 Prismatic bar in pure torsion.

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Strain Energy

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Torsion of Thin Tube

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Assignment• 3.5-1 A hollow aluminum shaft has outside diameter d2=4.0 in,

and inside diameter d1=2.0 in. When twisted by torque T, the shaft has an angle of twist per unit distance equal to 0.62o/ft. The shear modulus of the aluminum is G=4.0x106 psi. (a) what is the maximum tensile stress in the shaft? (b) what is the magnitude of the applied torque T?

• 3.5-4 A solid circular bar of diameter d=50 mm is twisted in a testing machine until the applied torque reaches T=1300 T.m . At this value of torque, a strain gage oriented at 45o to the axis of the bar gives a reading ε=331x10-6. What is the shear modulus?