6. The 160 mm diameter steel (G = 80 GPa) shaft ABCD shown in Figure Q6 has a 100 mm diameter bronze (G = 40 GPa) core inserted in 3 m of the right end, BCD and securely bonded to the steel. Determine: a) the maximum shearing stress in each of the materials, b) the angle of twist of the free end, D of the shaft. Steel 200 kNm 2 m 120kNm B. 1.5 m 1.5 m Bronze D Figure Q6 [Ans: a) Tmax,st = 162 MPa (at section BC), tmax,br = 51 MPa (at section BC); b) -0.00684 radl

6. The 160 mm diameter steel (G = 80 GPa) shaft ABCD shown in Figure Q6 has a 100 mm diameter bronze (G = 40 GPa) core inserted in 3 m of the right end, BCD and securely bonded to the steel. Determine: a) the maximum shearing stress in each of the materials, b) the angle of twist of the free end, D of the shaft. Steel 200 kNm 2 m 120kNm B. 1.5 m 1.5 m Bronze D Figure Q6 [Ans: a) Tmax,st = 162 MPa (at section BC), tmax,br = 51 MPa (at section BC); b) -0.00684 radl

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 3.4.11P: A tapered bar AB with a solid circular cross section is twisted by torques T = 36,000 lb-in. (sec...

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A propeller shaft for a small yacht is made of a solid steel bar 104 mm in diameter. The allowable stress in shear is 48 MPa, and the allowable rate of twist is 2.0° in 3.5 meters. (a) Assuming that the shear modulus of elasticity is G = 80 GPa, determine the maximum torque that can be applied to the shaft. (b) Repeat part (a) if the shaft is now hollow with an inner diameter of 5d18. Compare values to corresponding values from part (a).
A hollow tube ABCDE constructed of monel metal is subjected to five torques acting in the directions shown in the figure. The magnitudes of the torques are T1= 1000 lb-in., T2= T4= 500 lb-in., and T3= T5= 800 lb-in. The tube has an outside diameter of d2= 1.0 in. The allowable shear stress is 12,000 psi and the allowable rate of twist is 2.0°/ft. Determine the maximum permissible inside diameter d1, of the tube.
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A solid brass bar of diameter d = 1.25 in. is subjected to torques T1as shown in part a of the figure. The allowable shear stress in the brass is 12 ksi. What is the maximum permissible value of the torques T1? If a hole of diameter 0.625 in. is drilled longitudinally through the bar, as shown in part b of the figure, what is the maximum permissible value of the torques T2? What is the percent decrease in torque and the percent decrease in weight due to the hole?
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A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and T2acting in opposite directions, as shown in the figure. The larger segment of the shaft has a diameter of dv- 2.25 in. and a length Lt= 30 in.; the smaller segment has a diameter d2— 1.75 in. and a length L, = 20 in. The torques are T, = 21,000 lb-in. and fz=10.000 lb-in. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: x = L1/2 and x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams (FBDs).
A circular aluminum tube subjected to pure torsion by torques T(sec figure) has an outer radius r2equal to 1.5 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 400 × 10-6 rad, what is the shear strain y1at the inner surface? (b) If the maximum a1lo-abk rate of twist is 0.125 °/m and the maximum shear strain is to be kept at 400 × 10-6 rad by adjusting the torque T, that is the minimum required outer radius ( r2)Min?
A solid copper bar of circular cross section has length L = 1.25 m and shear modulus of elasticity G = 45 GPa. The bar is designed to carry a 250 N · m torque acting at the ends. If the allowable shear stress is 30 M Pa and the allowable angle of twist between the ends is 2.5°, what is the minimum required diameter?
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