1:A stepped shaft ACB having a solid circular cross sections with two different diameters and two different materials joined and attached at their ends, in the fisrt section AC of aluminum has a diameter of 20mm lenght of 225mm and G= 28x109 N/m2 and in the second section CB of steel has a diameter of 25mm leght 450mm and G=83x109N/m2. The torque appied is of 1000N.m and applied in the joint of the pieces. Determine the shear stress in both the aluminium and the steel. II. A stepped shaft ACB having a solid circular cross sections with two different diameters and two differentmaterials joined and attached at their ends, in the first section AC of aluminum has a diameter of 20 mm,length of 225 mm and G = 28x10° and in the second section CB of steel has a diameter of 25 mm,Nlength of 450 mm and G = 83x10°m2"The torque applied is of 1000 N m and applied in the joint ofthe pieces. Determine the shear stress in both the aluminum and the steel.20 mm25 mmTo225 mm-450 mmFigure 2

Given LA= 225 mm ; diameter of circular cross section A (dA)= 20 mm ;And LB= 450 mm ; diameter of…

II. A stepped shaft ACB having a solid circular cross sections with two different diameters and two different materials joined and attached at their ends, in the first section AC of aluminum has a diameter of 20 mm, length of 225 mm and G = 28x10° and in the second section CB of steel has a diameter of 25 mm, length of 450 mm and G = 83x10° The torque applied is of 1000 N m and applied in the joint of the pieces. Determine the shear stress in both the aluminum and the steel. 20 mm 25 mm To - 225 mm- - 450 mm-

II. A stepped shaft ACB having a solid circular cross sections with two different diameters and two different materials joined and attached at their ends, in the first section AC of aluminum has a diameter of 20 mm, length of 225 mm and G = 28x10° and in the second section CB of steel has a diameter of 25 mm, length of 450 mm and G = 83x10° The torque applied is of 1000 N m and applied in the joint of the pieces. Determine the shear stress in both the aluminum and the steel. 20 mm 25 mm To - 225 mm- - 450 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 3.8.5P: A stepped shaft ACB having solid circular cross sections with two different diameters is held...

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).
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?
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?
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.
Two sections of steel drill pipe, joined by bolted flange plates at B, arc subjected to a concentrated torque 4000 kip-in. at x = 3 ft, and a uniformly distributed torque t0= 50 kip-ft/ft is applied on pipe BC. Let G = 11,800 ksi and assume that pipes AB and BC have the same inner diameter, d = 12 in. Pipe AB has a thickness tAB= 3/4 in., and pipe BC has a thickness tBC= 5/8 in. Find the reactive torques at A and C and the maximum shear stresses in each segment.
The stepped shaft shown in the figure is required to transmit 600 kW of power at 400 rpm. The shaft has a full quarter-circular fillet, and the smaller diameter D1= 100 mm. If the allowable shear stress at the stress concentration is 100 MPa, at what diameter will this stress be reached? Is this diameter an upper or a lower limit on the value of D2?
A full quarter-circular fillet is used at the shoulder of a stepped shaft having diameter D2= 1.0 in. (see figure), A torque T = 500 lb-in. acts on the shaft. Determine the shear stress at the stress concentration for values as follows: D1= 0.7,0.8, and 0.9 in. Plot a graph showing versus D?
A tapered bar AB with a solid circular cross section is twisted by torques T = 36,000 lb-in. (sec figure). The diameter of the bar varies linearly from dAat the left-hand end to dBat the right-hand end. The bar has length L = 4,0 ft and is made of an aluminum alloy having shear modulus of elasticity G = 3.9 × 106 psi. The allowable shear stress in the bar is 15,000 psi and the allowable angle of twist is 3.0°. If the diameter at end B is 1.5 times the diameter at end A, what is the minimum required diameter dAat end A?
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)
Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.
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.
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.