03-02ChapGere.0007

03-02ChapGere.0007 - 210 A-PDF Torsion CHAPTER 3 Split DEMO...

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Problem 3.5-2 A hollow steel bar ( G 5 80 GPa) is twisted by torques T (see figure). The twisting of the bar produces a maximum shear strain g max 5 640 3 10 2 6 rad. The bar has outside and inside diameters of 150 mm and 120 mm, respectively. (a) Determine the maximum tensile strain in the bar. (b) Determine the maximum tensile stress in the bar. (c) What is the magnitude of the applied torques T ? Solution 3.5-2 Hollow steel bar 210 CHAPTER 3 Torsion G 5 80 GPa g max 5 640 3 10 2 6 rad d 2 5 150 mm d 1 5 120 mm 5 29.343 3 10 6 mm 4 (a) M AXIMUM TENSILE STRAIN e max 5 g max 2 5 320 3 10 2 6 5 p 32 [(150 mm) 4 2 (120 mm) 4 ] I P 5 p 32 ( d 2 4 2 d 1 4 ) (b) M AXIMUM TENSILE STRESS t max 5 G g max 5 (80 GPa)(640 3 10 2 6 ) 5 51.2 MPa (c) A PPLIED TORQUES Torsion formula: 5 20,030 N ? m 5 20.0 kN # m T 5 2 I P t max d 2 5 2(29.343 3 10 6 mm 4 )(51.2 MPa) 150 mm t max 5 Tr I P 5 Td 2 2
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