03-02ChapGere.0028

03-02ChapGere.0028 - 1 5 25.0 mm d 2 5 30.0 mm d 3 5 37.5...

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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 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 t 2 in the bar and tube, respectively. (b) Determine the angle of rotation f (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.) Solution 3.8-10 Bar enclosed in a tube SECTION 3.8 Statically Indeterminate Torsional Members 231 A Tube T End plate B Bar L d 3 d 2 d 1 d
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Unformatted text preview: 1 5 25.0 mm d 2 5 30.0 mm d 3 5 37.5 mm G 5 80 GPa P OLAR MOMENTS OF INERTIA Tube: I P 2 5 p 32 d 3 4 2 d 2 4 5 114.6229 3 10 2 9 m 4 Bar: I P 1 5 p 32 d 1 4 5 38.3495 3 10 2 9 m 4 T ORQUES IN THE BAR (1) AND TUBE (2) FROM E QS . (3-44 A AND B ) (a) M AXIMUM SHEAR STRESSES (b) A NGLE OF ROTATION OF END PLATE (c) T ORSIONAL STIFFNESS k T 5 T f 5 22.3 kN # m f 5 1.03 8 f 5 T 1 L GI P 1 5 T 2 L GI P 2 5 0.017977 rad Tube: t 2 5 T 2 ( d 3 / 2) I P 2 5 49.0 MPa Bar: t 1 5 T 1 ( d 1 @ 2) I P 1 5 32.7 MPa Tube: T 2 5 T I P 2 I P 1 1 I P 2 5 299.7217 N # m Bar: T 1 5 T I P 1 I P 1 1 I P 2 5 100.2783 N # m A Tube (2) T = 400 N . m End plate B Bar (1) L = 550 mm d 3 d 2 d 1 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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