L9_Torsion- fall10

# L9_Torsion- fall10 - EAS 209-Fall 2010 Instructors...

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Unformatted text preview: EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 1 Lecture 9-Torsion Lecture 9 Chapter 3 – TORSION In addition to axial loading, we are interested in stresses and strains of circular shafts subjected to twisting couples or torques • Turbine exerts torque T on the shaft • Shaft transmits the torque to the generator • Generator creates an equal and opposite torque T ’ Today’s Objective: Derive elastic torsion formulae: used to calculate magnitude and distribution of shear stresses in circular shafts due to torsion Today’s Homework EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 2 Lecture 9-Torsion Units of Torque, T (force x distance) N.m (SI) or lb.in, lb-ft (US) Notation Direction (or sense) of the arrow is given by the right-hand rule ; fingers curl in the direction of the moment, thumb points in the direction of the vector. The moment of a couple can be represented by a vector in the form of a double-headed arrow Arrow is perpendicular to the plane containing the couple EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 3 Lecture 9-Torsion Shear Stresses in a Shaft How is torque transferred through shaft? A section perpendicular to the member axis will have pure shear stresses. Element dA has shear force dF For equilibrium, Σ M=0 gives ∫ = T dF ρ where ρ is the distance from the force dF to the axis of the shaft since dA dF τ = ( ) T dA dF = = ∫ ∫ τ ρ ρ This condition must be...
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L9_Torsion- fall10 - EAS 209-Fall 2010 Instructors...

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