EAS209 L10_Torsion- spring 11

# EAS209 L10_Torsion- spring 11 - EAS 209-Spring 2011...

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EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 1 Lecture 10-Torsion Lecture 10 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 formula: formula used to calculate magnitude and distribution of shear stresses in circular shafts due to torsion Today’s Homework EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 2 Lecture 10-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 couple can be represented by a vector in the form of a double-headed arrow Arrow is perpendicular to the plane containing the couple

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EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 3 Lecture 10-Torsion Shear Stresses in a Shaft How is torque transferred through shaft? A section perpendicular to the member axis will be in pure shear. Element dA distance from the center of the shaft has shear force dF For equilibrium, M=0 gives T dF since dA dF   T dA dF This condition must be satisfied by the shear stresses. Unfortunately, we cannot determine the shear stress
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EAS209 L10_Torsion- spring 11 - EAS 209-Spring 2011...

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