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Problem 3.8-14 A steel shaft ( G s 5 80 GPa) of total length L 5 4.0 m is encased for one-half of its length by a brass sleeve ( G b 5 40 GPa) that is securely bonded to the steel (see figure). The outer diameters of the shaft and sleeve are d 1 5 70 mm and d 2 5 90 mm, respectively. (a) Determine the allowable torque T 1 that may be applied to the ends of the shaft if the angle of twist f between the ends is limited to 8.0°. (b) Determine the allowable torque T 2 if the shear stress in the brass is limited to t b 5 70 MPa. (c) Determine the allowable torque T 3 if the shear stress in the steel is limited to t s 5 110 MPa. (d) What is the maximum allowable torque T max if all three of the preceding conditions must be satisfied? SECTION 3.8 Statically Indeterminate Torsional Members 235 T A BC T = 2.0 m Steel shaft Brass sleeve = 2.0 m d 2 = 90 mm d 1 = 70 mm L 2 L 2 T A T = 2.0 m Steel shaft Brass sleeve = 2.0 m d 2 = 90 mm d 1 = 70 mm L 2 L 2 P ROPERTIES OF THE STEEL SHAFT (s) G S 5 80 GPa d 1 5 70 mm Allowable shear stress: t S 5 110 MPa G S I PS 5 188.574 3 10 3
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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