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L12_ ElastoplasticMaterial- fall10

# L12_ ElastoplasticMaterial- fall10 - EAS 209-Fall 2010...

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EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 1 Lecture 12 Lecture 12 Circular Shafts Made of Elastoplastic Material In deriving the equations for stress distribution and angle of twist, we assumed that Hooke’s Law applied throughout the material. These equations are therefore not valid if: the yield strength is exceeded in some portion of the shaft Today’s Objectives: Understand the behavior of an ideal elastoplastic material subjected to torsion. Today’s Homework: EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 2 Lecture 12 Calculation of Torque We can determine the torque from the shear stress distribution. Consider an annular element of radius ρ , and thickness d ρ . dA dF dF T c τ ρ = = 0 Since the area of this element is: ρ πρ d dA 2 = = = c c d T d T 0 2 0 2 ) 2 ( ρ τ ρ π ρ ρ πρ τ ρ d ρ Equation holds for any distribution of shear stress

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EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 3 Lecture 12 Elastoplastic Material in Torsion
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