2. A composite shaft is subjected to two torques as shown below. Shaft AB is a solid aluminum (G = 25 GPa) shaft and is welded to brass (G = 37 GPa) shaft BCD. Segment BC of the brass shaft is solid and the segment CD is hollow with inner diameter of 40 mm. Determine the maximum shear stresses in the aluminum and brass shafts, and the angle of twist of end A. 60 mm T = 1600 N - m 36 mm T- S00 N- m 250 mm 375 mm 400 mm

2. A composite shaft is subjected to two torques as shown below. Shaft AB is a solid aluminum (G = 25 GPa) shaft and is welded to brass (G = 37 GPa) shaft BCD. Segment BC of the brass shaft is solid and the segment CD is hollow with inner diameter of 40 mm. Determine the maximum shear stresses in the aluminum and brass shafts, and the angle of twist of end A. 60 mm T = 1600 N - m 36 mm T- S00 N- m 250 mm 375 mm 400 mm

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 3.8.14P: The composite shaft shown in the figure is manufactured by shrink-Fitting a steel sleeve over a...

See similar textbooks

Similar questions

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 solid circular shaft AB of diameter d is fixed against rotation at both ends (sec figure), A circular disk is attached to the shaft at the location shown. What is the largest permissible angle of rotation 0max of the disk if the allowable shear stress in the shaft is Tallow? [Assume that a >b. Also, use Eqs. (3-50a and b) of Example 3-9 to obtain the reactive torques.]
What is the maximum power that can be delivered by a hollow propeller shaft (outside diameter 50 mm, inside diameter 40 mm, and shear modulus of elasticity 80 GPa) turning at 600 rpm if the allowable shear stress is 100 MPa and the allowable rate of twist is 3.0°/m?
The steel axle of a large winch on an ocean liner is subjected to a torque of 1.65 kN · m (see figure). What is the minimum required diameter dminif the allowable shear stress is 48 M Pa and the allowable rate of twist is 0.75º/m? (Assume that the shear modulus of elasticity is 80 G Pa.) Repeat part (a) if the shaft is now hollow with an inner diameter of 5d/8, Compare dminvalues 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.
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 thin-walled rectangular tube has uniform thickness t and dimensions a x b to the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio = a/b if the total length Lmof the median line of the cross section and the torque T remain constant? From your results, show that the shear stress is smallest when the tube is square (ß = 1).
A stepped shaft ACB having solid circular cross sections with two different diameters is held against rotation at the ends (sec figure). If the allowable shear stress in the shaft is 6000 psi, what is the maximum torque (T0) that may be applied at section C? Find (T0)max if the maximum angle of twist is limited to 0.55º. Let G = 10,600 ksi.
A thin tubular shaft with a circular cross section (see figure) and with inside diameter 100 mm is subjected to a torque of 5000 N · m. If the allowable shear stress is 42 MPa, determine the required wall thickness t by using (a) the approximate theory for a thin-walled tube and (b) the exact torsion theory for a circular bar.
The composite shaft shown in the figure is manufactured by shrink-Fitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion. The outer diameters of the two parts are dY= 40 mm for the brass core and d2= 50 mm for the steel sleeve. The shear moduli of elasticity are Gb= 36 GPa for the brass and Gs= 80 GPa for the steel. (a) Assuming that the allowable shear stresses in the brass and steel are rb= 48 MPa and ts= 80 MPa, respectively, determine the maximum permissible torque Tmax that may be applied to the shaft. (b) If the applied torque T = 2500 kN · m, find the required diameter d2so that allowable shear stress t3is reached in the steel.
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?
A steel punch consists of two shafts: upper shaft and lower shaft. Assume that the upper shaft has a diameter d1= 24 mm and the bottom shaft has a diameter d2= 16 mm. The punch is used to insert a hole in a 4 mm plate, as shown in the figure. If a force P - 70 kN is required to create the hole, what is the average shear stress in the plate and the average compressive stress in the upper and lower shaft of the punch?