(1.6.7)--3.6材料力学材料力学.ppt

Chapter 3 Torsion Mechanics of Materials3.6 Stresses and Strains in Pure ShearStresses and Strains in Pure ShearStresses on Inclined Planes are positive in tension,are positive when they tend to produce counterclockwise rotation of the material.Pure shearStresses and Strains in Pure ShearStresses on Inclined PlanesA0 is the area of the vertical face.yxStresses and Strains in Pure ShearStresses on Inclined Planesmax=min=-Stress elements orientedStresses and Strains in Pure ShearTorsion FailureDuctile materialThe plane of maximum shear stressA plane perpendicular to the shaft axisStresses and Strains in Pure ShearTorsion FailureBrittle materialA 45 helical surfaceThe plane of maximum tensile stressStresses and Strains in Pure ShearStrains in Pure ShearRectangular ParallelepipedOblique ParallelepipedShear DistortionFor a linearly elastic materialG-the shear modulus of elasticityStresses and Strains in Pure ShearStrains in Pure ShearRectangular ParallelepipedRectangular ParallelepipedNo Shear DistortionFor a linearly elastic materialStresses and Strains in Pure ShearRelationship Between Moduli of Elasticity E and GUsing the Law of Cosinessmall strainsStresses and Strains in Pure ShearRelationship Between Moduli of Elasticity E and GFor a linearly elastic materialStresses and Strains in Pure ShearExampleAluminum tube with G=27GPa(a)Determine the maximum shear,tensile,and compressive stresses in the tube;(b)Determine the corresponding maximum strains in the tube;(c)What is the maximum permissible torque Tmax if the allowable normal strain is a=0.910-3？Circular Bars of Linearly Elastic MaterialsSolution:Part a:Circular Bars of Linearly Elastic MaterialsSolution:Part b:Circular Bars of Linearly Elastic MaterialsSolution:Part c:End