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week3-2 - Torsion Aftertwisting Torsional Torsional...

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Torsion of Circular Shafts After twisting Plane sections remain planar Radial line on cross section remains straight
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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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Torsional Shear Strain For torsional strain ρ γ γ ρ R max =
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Stress Distribution l τ For torsional stress ρ τ ρ R max =
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Twist and Strain γ φ ρ L = ρ
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Twist and Stress γ L ρ φ ρ = γ τ G = and So, in terms of shear stress L L max τ τ φ ρ = = RG G ρ
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Relationship of shear stress with T I TR = max τ Elastic torsion formula p I T max τ = Rearranged p R
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Torque twist relationship Torque twist relationship GI TL = φ p For shafts that are • homogeneous (constant G) • uniform cross section (constant I p ) • constant internal torque T
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