03-01ChapGere.0006

03-01ChapGere.0006 - 186 A-PDF Torsion CHAPTER 3 Split DEMO...

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Problem 3.3-4 An aluminum bar of solid circular cross section is twisted by torques T acting at the ends (see figure). The dimensions and shear modulus of elasticity are as follows: L 5 1.2 m, d 5 30 mm, and G 5 28 GPa. (a) Determine the torsional stiffness of the bar. (b) If the angle of twist of the bar is 4°, what is the maximum shear stress? What is the maximum shear strain (in radians)? Solution 3.3-4 Aluminum bar in torsion 186 CHAPTER 3 Torsion L d TT L 5 1.2 m d 5 30 mm G 5 28 GPa f5 4 8 (a) T ORSIONAL STIFFNESS (b) M AXIMUM SHEAR STRESS From Eq. (3-15): f 5 TL GI P Ê T 5 GI P f L f 5 4 85 (4 8 )( p / 180) rad 5 0.069813 rad k T 5 1860 N . m k T 5 GI P L 5 G p d 4 32 L 5 (28 GPa)( p )(30 mm) 4 32(1.2 m) From Eq. (3-11): M AXIMUM SHEAR STRAIN Hooke’s Law: g max 5 873 3 10 2 6 rad g max 5 t max G 5 24.43 MPa 28 GPa t max 5 24.4
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