EAS209 L11_TwistAngle-spring 11

EAS209 L11_TwistAngle-spring 11 - EAS 209-Spring 2011...

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EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 1 Lecture 11- Angle of Twist Lecture 11 Angle of Twist and Design of Transmission 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 where =c max L c , max Tc J Today’s Objectives: Calculate the magnitude of the angle of twist Design transmission shafts Today’s Homework: here is the angle of twist in radians EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 2 Lecture 11- Angle of Twist Angle of Twist In the elastic range, shear stresses and strains are related by: =G Substituting for maximum shear stress and maximum shear strain L c G J Tc and rearranging TL JG
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EAS 209-Spring 2011 Instructors: Christine Human 1/18/2011 3 Lecture 11- Angle of Twist Analogy: Axial - Torsion Prismatic axially loaded member Circular bar in torsion Axial force N Torque T Deformation AE PL (elongation) Deformation TL JG (angle of twist) Young’s Modulus E Determined from axial stress and strain Shear Modulus G Determined from shear stress and strain Cross Sectional Area, A (function of r 2 ) Polar moment of inertia J (function of r 4 ) small change in r has large effect on twist on J and hence Axial flexibility L EA Torsional flexibility L GJ Axial stiffness EA L
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