gm9_10notes - M9 Shafts Torsion of Circular Shafts Reading...

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M9 Shafts: Torsion of Circular Shafts Reading: Crandall, Dahl and Lardner 6.2, 6.3 A shaft is a structural member which is long and slender and subject to a torque (moment) acting about its long axis. We will only consider circular cross-section shafts in Unified. These have direct relevance to circular cross-section shafts such as drive shafts for gas turbine engines, propeller driven aircraft and helicopters (rotorcraft). However, the basic principles are more general and will provide you with a basis for understanding how structures with arbitrary cross-sections carry torsional moments. Torsional stiffness, and the shear stresses that arise from torsional loading are important for the design of aerodynamic surfaces such as wings, helicopter rotor blades and turbine fan blades. Modelling assumptions (a) Geometry (as for beam). Long slender, L >> r (b,h) Note: For the time being we will work in tensor notation since this is all about shear stresses and tensor notation will make the analysis more straightforward. Remember we can choose the system of notation, coordinates to make life easy for ourselves! (b) Loading Torque about x 1 axis, T (units of Force x length). We may also want to consider the possibility of distributed torques (Force x length/unit length) (distributed aerodynamic moment along a wing, torques due to individual stages of a gas turbine) No axial loads (forces) applied to boundaries (on curved surfaces with radial normal, or on x 1 face) = 11 22 = 33 = 0
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(c) Deformation -Cross sections rotate as rigid bodies through twist angle , varies with x 1 (cf. beams – plane sections remain plane and perpendicular) - No bending or extensional deformations in x 1 direction Cross-section:
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gm9_10notes - M9 Shafts Torsion of Circular Shafts Reading...

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