Chapter 3 Torsion

Chapter 3 Torsion - Chapter 3 Torsion Introduction--...

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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-- Cross-section Non-circular Irregular shapes-- Material (1) Elastic (2) Elasto-plastic-- 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 ( ) = dA T dF T = Free-body Diagram Where = distance (torque arm) Since dF = 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 = (T, L)-- the angle of twist (deformation) Rectangular cross section warps under torsion ' ' = CD C D A circular plane remains circular plane L = (in radians) Determination of Shear Strain The shear strain max c L = max = c max = L c = c = radius of the shaft L = Since...
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Chapter 3 Torsion - Chapter 3 Torsion Introduction--...

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