torsion1 - Ömer ATAŞ 23/12/2009 Oğuzhan DEDE TORSION 1-...

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Unformatted text preview: Ömer ATAŞ 23/12/2009 Oğuzhan DEDE TORSION 1- Mechanics of Materials Approach 2- Prandtl Stress Function Approach -more sufficient for axial cylinder problem Sufficient insufficient sufficient 1-) Mechanics of Material Approach to Torsion of Circular Bars Assumptions: 1-) All plane sections perpendicular to torsion axis z remain perpendicular. 2-) Cross sections are undistorted in their individuals planes -Shearing strain Ɣ varies linearly from at the center to a maximum at the outer surface 3-) Material is homogenous T= 𝜏 . ?𝑑𝐴 T= ? ? ? . 𝜏 𝑚𝑎¡ . ?𝑑𝐴 = 𝜏 𝑚𝑎¡ ? . ? 2 𝑑𝐴 Where ? 2 𝑑𝐴 is polar moment of inertia J= ? 2 𝑑𝐴 and τ max = 𝑇 . ? 𝐽 τ(ρ)= 𝑇 . ? 𝐽 Note: Polar moment of inertia for circle of radius r ; J= ¢ . ? 4 2 Angle of Twist Φ : Φ .r = Ɣ max .L Ɣ max = 𝜏 𝑚𝑎¡ £ ( Hooke’s law) so, Ɣ max = 𝑇 . ?...
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This note was uploaded on 02/28/2011 for the course AEE 361 taught by Professor Daglas during the Spring '11 term at College of E&ME, NUST.

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torsion1 - Ömer ATAŞ 23/12/2009 Oğuzhan DEDE TORSION 1-...

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