Chapter 4-torsion - CHAPTER 4 TORSION Torsion refers to the...

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Unformatted text preview: CHAPTER 4 TORSION Torsion refers to the twisting of a structural member when it is loaded by moments/torques that produce rotation about the longitudinal axis of the member The problem of transmitting a torque or rotary motion from one plane to another is frequently encountered in machine design. Normally circular bars are used for such transmissions chiefly because, in these bars, a plane section before twisting remains plane after twisting. 110 TORSION TORSION Assumption to determining the relationship of the shearing stress in circular shaft subjected to torsions: the material of the shaft is homogeneous the maximum shearing stress in the shaft is within the elastic limit the twist remains uniform along the whole length of the shaft the normal cross-section of the shaft which are plane and circular before the twist remain same after the twist the straight radial line of any cross section of the shaft remain straight. the distance between any two cross section of the shaft remain the same torques are applied on planes that are perpendicular to the axis of the shaft 111 Torsional Deformation of Circular Bars Torsional Deformation of Circular Bars Consider a bar of circular cross-section twisted by couples T at the ends. Because the bar is subjected to torsion only, it is said to be in pure torsion. Assuming that the end B is fixed, then the torque will cause end A to rotate through a small angle , known as the angle of twist . Thus the longitudinal line AB on the surface of the bar will rotate through a small angle to position A'B 112 Since the ends of the element remain planar, the shear strain is equal to angle of twist, . It follows that According to Hookes law, for linear elastic materials, shear stresses are proportional to shear strains and the constant of proportionality is the modulus of rigidity, G. Hence L r r L ' BB = = = or 113 L Gr L r G G = = = L G r = G = Torsion Formula: Relationship between Torsion Formula: Relationship between T and T and To determine the relationship between the applied torque T and the stresses it produces, we consider equilibrium of the internal forces and the externally applied torque, T. Considering an elemental area dA dA within an elemental ring of thickness dr dr situated at radius r from the centre: dF= x dA dF= x 2 x.dx 114 = = = = = dx x 2 r M dx x 2 r dx x 2 x r x xdF dM dx x 2 x r dF 3 3 x r r x x x = =...
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This note was uploaded on 02/11/2010 for the course SDF DDT taught by Professor Mdnorihan during the Spring '10 term at University of Winnipeg.

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Chapter 4-torsion - CHAPTER 4 TORSION Torsion refers to the...

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