olid steel bar of diameter di = 1.4 in. is enclosed by a steel tube of outer diameter dz = 2.25 in. and inner diameter d2 = 1.9 in. (see the figure). Both bar and tube are held rigidly by a oport at end A and joined securely to a rigid plate at end B. The composite bar, which has length L = 26 in., is twisted by a torque T = 5,100 lb-in. acting on the end plate. Tube End plate Determine the maximum shear stresses T and T2 in the bar and tube, respectively. Round your answers to the nearest whole number. psi psi Determine the angle of rotation (in degrees) of the end plate, assuming that the shear modulus of the steel is G = 11.5 × 10° psi. Round your answer to three decimal places. Determine the torsional stiffness kT of the composite bar. Round your answer to the nearest whole. [Hint: Use equations below to find the torques in the bar and tube.] GIp, = T G¡Ip, + G2IP, k-in.

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter3: Torsion
Section: Chapter Questions
Problem 3.8.13P: A solid steel bar of diameter d1= 1.50 in. is enclosed by a steel tube of outer diameter d3= 2.25...
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A solid steel bar of diameter di = 1.4 in. is enclosed by a steel tube of outer diameter d3 = 2.25 in. and inner diameter d2 = 1.9 in. (see the 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 = 26 in., is twisted by a torque T = 5,100 lb-in. acting on the end plate.
Tube
A
Bar
End
plate
(a) Determine the maximum shear stresses T1 and T2 in the bar and tube, respectively. Round your answers to the nearest whole number.
T1 =
psi
T2 =
psi
(b) Determine the angle of rotation (in degrees) of the end plate, assuming that the shear modulus of the steel is G = 11.5 × 10° psi. Round your answer to three decimal places.
(c) Determine the torsional stiffness kT of the composite bar. Round your answer to the nearest whole. [Hint: Use equations below to find the torques in the bar and tube.]
T = T
GIp, + G2IP,
kT =
k-in.
Transcribed Image Text:A solid steel bar of diameter di = 1.4 in. is enclosed by a steel tube of outer diameter d3 = 2.25 in. and inner diameter d2 = 1.9 in. (see the 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 = 26 in., is twisted by a torque T = 5,100 lb-in. acting on the end plate. Tube A Bar End plate (a) Determine the maximum shear stresses T1 and T2 in the bar and tube, respectively. Round your answers to the nearest whole number. T1 = psi T2 = psi (b) Determine the angle of rotation (in degrees) of the end plate, assuming that the shear modulus of the steel is G = 11.5 × 10° psi. Round your answer to three decimal places. (c) Determine the torsional stiffness kT of the composite bar. Round your answer to the nearest whole. [Hint: Use equations below to find the torques in the bar and tube.] T = T GIp, + G2IP, kT = k-in.
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