(1.6.4)--3.3材料力学材料力学.ppt

Chapter 3 Torsion Mechanics of Materials3.3 Torsional Deformations of a Circular BarTorsional Deformations of a Circular BarPure TorsionSince every cross section of the bar is identical,and since every cross section is subjected to the same internal torque T,the bar is in pure torsion.uIf the angle of rotation between one end of the bar and the other is small,neither the length of the bar nor its radius will change.uAll cross sections remain plane and circular,and all radii remain straight.Torsional Deformations of a Circular BarAngle of TwistUnder the action of the torque T,the right-hand end will rotate(with respect to the left-hand end)through a small angle,known as the angle of twist(or angle of rotation).The angle of twist varies along the axis of the bar at intermediate cross section denoted by(x).Torsional Deformations of a Circular BarShear Strains at the Outer SurfaceAngle of twist per unit length(Rate of twist)Torsional Deformations of a Circular BarShear Strains within the BarRadii in the cross sections of a bar remain straight and undistorted during twistingThis equation shows that the vary linearly the radial distance from the center.Torsional Deformations of a Circular BarCircular TubesTortional moment diagramLimitationsAll of the preceding equations for the strains in a circular bar are valid for any material,whether it behaves elastically or inelastically,linearly or nonlinearly.However,the equations are limited to bars having small angles of twist and small strains.End