L10_TwistAngle-fall 10

L10_TwistAngle-fall 10 - EAS 209-Fall 2010 Instructors...

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Unformatted text preview: EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 1 Lecture 10- Angle of Twist Lecture 10 Angle of Twist and Statically Indeterminate Shafts In the previous lecture, we saw that the maximum shear stress and shear strain on a shaft subjected to torsion occurs on the surface ( ρ =c ): max L c φ γ = , max Tc J τ = Today’s Objectives: • Calculate the magnitude of the angle of twist • Analyze statically indeterminate torsion problems Today’s Homework: Where φ is the angle of twist in radians EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 2 Lecture 10- Angle of Twist Angle of Twist In the elastic range, shear stresses and strains are related by: τ =G γ Substituting for maximum shear stress and shear strain L c G J Tc φ = and rearranging TL JG φ = EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 3 Lecture 10- Angle of Twist Analogy: Axial - Torsion Prismatic axially loaded member Circular bar in torsion Axial force N Torque T Deformation AE PL = δ (elongation) Deformation TL JG φ = (angle of twist) Young’s Modulus E Determined from axial...
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L10_TwistAngle-fall 10 - EAS 209-Fall 2010 Instructors...

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