week3-2 - Torsion TorsionofCircularShafts Aftertwisting

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rsion of Circular Shafts Torsion of Circular Shafts After twisting Plane sections remain planar Radial line on cross section remains straight
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rsional ear Strain Torsional Shear Strain After applying torque (T) Longitudinal lines twist into helixes Free end of shaft rotates through an angle φ Shaft length remains constant Angle of twist φ varies linearly with length
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rsional ear Strain Torsional Shear Strain For torsional strain ρ γ max = R
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ress Distribution Stress Distribution For torsional stress ρ τ R max =
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ist and Strain Twist and Strain γ ρ L φ=
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ist and Stress Twist and Stress ρ γ φ L = τ G = and So, in terms of shear stress L L max RG G
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elationship of shear stress with T Relationship of shear stress with T TR = max τ Elastic torsion rmula p I formula max earranged p I R T Rearranged
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rque ist relationship Torque twist relationship I TL = φ p GI r shafts that are For shafts that are • homogeneous (constant G) • uniform cross section (constant I p ) • constant internal torque T
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olar Moment of Inertia Polar Moment of Inertia ssesses the ability of a member to resist torsion. Assesses the ability of a member to resist torsion. The larger it is, the less a member will twist. Units are mm or in Solid circular shaft 4 4 32 2 D R I p π = = Hollow circular shaft [ ] [ ] 4 4 4 4 32 2 d D r R I p = =
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rque ist relationship Torque twist relationship Twist increases with TL • higher torque • greater length p GI = φ Twist decreases with • higher modulus •greater polar moment of inertia
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This note was uploaded on 12/01/2009 for the course CIVE 207 taught by Professor Shao during the Winter '09 term at McGill.

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week3-2 - Torsion TorsionofCircularShafts Aftertwisting

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