Torsion of Circular Shaft

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ME2113-2 TORSION OF CIRCULAR SHAFTS (EA-02-21) SEMESTER 3 2012/2013 DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE CONTENTS NOMENCLATURE (i) INTRODUCTION 1 THEORY 1 APPARATUS 2 PROCEDURE 2 REFERENCES 3 Table 1 Experimental Data for solid and hollow shafts Table 2 Strength and stiffness of hollow and solid shafts having the same outer diameter Table 3 Strength and stiffness of hollow and solid shafts having the same volume NOMENCLATURE Dh outer diameter of hollow shaft Ds diameter of solid shaft dh inner diameter of hollow shaft G shear modulus of the shaft material Ip polar second moment of area about the shaft axis K torsional stiffness L length of the shaft T applied torque ( total angle of twist of the shaft over L ( induced shear stress at any point on the shaft and ( radial distance of that point on the shaft at which the shear stress is measured INTRODUCTION Purpose The purpose of this manual is to provide guidelines/instruction to enable students to carry out experiment with an apparatus to study the torsion of solid and hollow circular shafts. Scope The manual deals with a brief theory of pure torsion of circular shafts. It also contains a list of apparatus used and the experimental procedure to evaluate the torsional stiffness and strengths of circular shafts. THEORY Whether the shaft is solid or hollow, its response to an applied torque may be expressed mathematically by the well known torsional formula [pic] (1) For a hollow shaft having Dh and dh as the outer and inner diameters respectively, its polar second moment of area is [pic] (2) For a solid shaft of diameter Ds , its polar second moment of area is given by [pic] (3) Equation (1) also shows that the shear stress

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