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Unformatted text preview: Chapter 3 Torsion Introduction Analyzing the stresses and strains in machine parts which are subjected to torque T Circular Crosssection Noncircular Irregular shapes Material (1) Elastic (2) Elastoplastic Shaft (1) Solid (2) Hollow 3.1 Introduction • T is a vector • Two ways of expression Applications: a. Transmission of torque in shafts, e.g. in automobiles Assumptions in Torque Analysis: a. Every cross section remains plane and undistorted. b. Shearing strain varies linearly along the axis of the shaft. 3.2 Preliminary Discussion of the Stresses in a Shaft ( ) ρ τ = ∫ dA T dF T ρ = ∫ Freebody Diagram Where ρ = distance (torque arm) Since dF = τ dA The stress distribution is Statically Indeterminate. Must rely on “deformation” to solve the problem. Analyzing a small element: 3.3 Deformations in a Circular Shaft φ = φ (T, L) the angle of twist (deformation) Rectangular cross section warps under torsion » ¼ ' ' = CD C D ∴ A circular plane remains circular plane L ρφ γ = (in radians) Determination of Shear Strain γ The shear strain γ ∝ ρ max c L φ γ = max ρ γ γ = c max γ φ ∴ = L c ρ = c = radius of the shaft L ρφ γ = Since γ...
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This note was uploaded on 12/03/2011 for the course EMA 3702 taught by Professor Wu during the Fall '11 term at FIU.
 Fall '11
 Wu

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