Quiz 5 Wed - A and joined securely to a rigid plate at end...

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SECTION 3.8 Statically Indeterminate Torsional Members 309 Solution 3.8-9 Bar with a hole L 5 50 in. L /2 5 25 in. d 2 5 outer diameter 5 3.0 in. d 1 5 diameter of hole 5 2.4 in. T 0 5 Torque applied at distance x Find x so that T A 5 T B E QUILIBRIUM T A 1 T B 5 T 0 (1) R EMOVE THE SUPPORT AT END B T A 5 T B 5 T 0 2 I PA 5 Polar moment of inertia at left-hand end I PB 5 Polar moment of inertia at right-hand end (2) Substitute Eq. (1) into Eq. (2) and simplify: C OMPATIBILITY f B 5 0 so LVE FOR x : S UBSTITUTE NUMERICAL VALUES : ; x 5 50 in. 4 c 2 + a 2.4 in. 3.0 in. b 4 d 5 30.12 in. ; x 5 L 4 c 2 + a d 1 d 2 b 4 d I PB I PA 5 d 2 4 2 d 1 4 d 2 4 5 1 2 a d 1 d 2 b 4 x 5 L 4 a 3 2 I PB I PA b x I PB 5 3 L 4 I PB 2 L 4 I PA f B 5 T 0 G c L 4 I PB + L 4 I PA 2 x I PB + L 2 I PB 2 L 2 I PA d 2 T 0 ( L /2) GI PA f B 5 T B ( L /2) GI PB + T B ( L /2) GI PA 2 T 0 ( x 2 L /2) GI PB B 5 Angle of twist at B Problem 3.8-10 A solid steel bar of diameter d 1 5 25.0 mm is enclosed by a steel tube of outer diameter d 3 5 37.5 mm and inner diameter d 2 5 30.0 mm (see figure). Both bar and tube are held rigidly by a support at end
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Unformatted text preview: A and joined securely to a rigid plate at end B . The composite bar, which has a length L 5 550 mm, is twisted by a torque T 5 400 N ? m acting on the end plate. (a) Determine the maximum shear stresses t 1 and 2 in the bar and tube, respectively. (b) Determine the angle of rotation (in degrees) of the end plate, assuming that the shear modulus of the steel is G 5 80 GPa. (c) Determine the torsional stiffness k T of the composite bar. ( Hint : Use Eqs. 3-44a and b to find the torques in the bar and tube.) A Tube T End plate B Bar L d 3 d 2 d 1 Sec_3.8.qxd 9/27/08 1:13 PM Page 309...
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This note was uploaded on 03/06/2011 for the course EM 319 taught by Professor Kennethm.liechti during the Spring '08 term at University of Texas at Austin.

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