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1、Chapter 3 Torsion Mechanics of Materials3.9 Thin-Walled Tubes Thin-Walled Tubes Thin-walled tubular members with noncircular closed cross sectionslightweight structures,such as aircraft and spacecraftThin-Walled Tubes Shear Stresses and Shear FlowThe stresses act parallel to the boundaries of the cr
2、oss section and“flow”around the cross section.Thin-Walled Tubes Shear Stresses and Shear FlowStresses acting on the longitudinal faces ab and cd produce forcesThin-Walled Tubes Shear Stresses and Shear FlowFrom the equilibrium of the element in the longitudinal directionThe shear force per unit dist
3、ance along the cross section.Shear Flow Thin-Walled Tubes Torsion Formula for Thin-Walled TubesLm the length of the median lineAm the area enclosed by the median line of the cross sectionThin-Walled Tubes Torsion Formula for Thin-Walled Tubesr the radius of the median lineconstant around the cross s
4、ectionThin-walled circular tubeThin-walled rectangular tubeThin-Walled Tubes Strain Energy and Torsion ConstantThe total strain energy of the elementThe total strain energy of the tubeThin-Walled Tubes Strain Energy and Torsion ConstantThe total strain energy of the tubeTorsion ConstantFor constant
5、thickness tThin-Walled Tubes Angle of TwistThe total strain energy of the tubeGJTorsional RigidityThe work W done by the applied torque TFrom the principle of conservation of energyThin-Walled Tubes ExampleComparison of circular and square tubes.Both tubes have the same length,same wall thickness,and same cross-sectional area.Solution:Circular tube:Square tube:Thin-Walled Tubes ExampleSolution:The circular tube not only has 21%lower shear stress than does the square tube but it also has a greater stiffness against rotation.End