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Unformatted text preview: Sec_3.8.qxd 9/27/08 310 1:13 PM Page 310 CHAPTER 3 Torsion Solution 3.8-10 Bar enclosed in a tube
TORQUES IN THE BAR (1) AND TUBE (2)
FROM EQS. (3-44A AND B)
Bar: T1 Ta IP1
IP1 + IP2 Ta Tube: T2 100.2783 N # m IP2
IP1 + IP2 299.7217 N # m (a) MAXIMUM SHEAR STRESSES
d1 25.0 mm G d2 30.0 mm d3 37.5 mm POLAR MOMENTS OF INERTIA
Tube: IP2 p
32 3 38.3495 * 10
IP2 4 m 114.6229 * 10 T1L
GIP1 T 2L
GIP2 1.03° f 9 32.7 MPa
49.0 MPa ;
; (b) ANGLE OF ROTATION OF END PLATE 80 GPa p4
32 1 T1(d1/2)
IP1 ; 0.017977 rad (c) TORSIONAL STIFFNESS
9 m4 kT T
f Problem 3.8-11 A solid steel bar of diameter d1 1.50 in. is enclosed
by a steel tube of outer diameter d3 2.25 in. and inner diameter
d2 1.75 in. (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 length L 30.0 in., is twisted by a torque T 5000 lb-in.
acting on the end plate.
(a) Determine the maximum shear stresses 1 and 2 in the bar and
(b) Determine the angle of rotation (in degrees) of the end plate,
assuming that the shear modulus of the steel is G 11.6 106 psi.
(c) Determine the torsional stiffness kT of the composite bar. (Hint: Use
Eqs. 3-44a and b to find the torques in the bar and tube.) 22.3 kN # m ; Tube
T Bar End
plate L d1
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.
- Fall '11