The compound shaft is attached to a rigid wall at each end and is subjected to the torque T = 6 kN.m applied at point B. For the bronze segment AB, the diameter is dį = 71 mm and Gbr = 35 GPa. For the steel segment BC, the diameter is d2 = 49 mm and Gst = 83 GPa. Given that a = 2.4 m and b = 1.6 m, what is the torque reaction TA developed at end A? d2 Bronze Steel C

The compound shaft is attached to a rigid wall at each end and is subjected to the torque T = 6 kN.m applied at point B. For the bronze segment AB, the diameter is dį = 71 mm and Gbr = 35 GPa. For the steel segment BC, the diameter is d2 = 49 mm and Gst = 83 GPa. Given that a = 2.4 m and b = 1.6 m, what is the torque reaction TA developed at end A? d2 Bronze Steel C

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.3.17P: A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and...

See similar textbooks

Similar questions

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.]
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 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 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).
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?
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 long, thin-walled tapered tube AB with a circular cross section (see figure) is subjected to a torque T. The tube has length L and constant wall thickness t. The diameter to the median lines of the cross sections at the ends A and B are dAand dB, respectively. Derive the following formula for the angle of twist of the tube: Hint: If the angle of taper is small, you may obtain approximate results by applying the formulas for a thin-walled prismatic tube to a differential element of the tapered tube and then integrating along the axis of the tube.
A solid steel shaft ABCDE turns freely in bearings at points A and E. The shaft is driven by the gear at C,which applies a torque T2 = 325lb−ft. Gears at B and D are driven by the shaft and have resisting torquesT1 = 200lb − ft and T3 = 125lb − ft, respectively. Segments BC and CD have lengths LBC = 20 in. andLCD = 15 in. and the shear modulus G = 11, 600ksi. Determine the minimum required diameter (d) ofthe shaft if the allowable shear stress τa = 6ksi. Also calculate the angle of twist between gears B and D.
A propeller shaft for a small yacht is made ofa solid steel bar 104 mm in diameter. The allowablestress in shear is 48 MPa, and the allowable rate oftwist is 2.08 in 3.5 meters.(a) Assuming that the shear modulus of elasticityis G = 80 GPa, determine the maximum torqueTmax that can be applied to the shaft.(b) Repeat part (a) if the shaft is now hollow withan inner diameter of 5d/8. Compare Tmax valuesto corresponding values from part (a).
A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It is further subjected to a torque of 10 kN-m. The maximum principal stress experienced on the shaft is closest to a) 41 MPA b) 82 MPA c) 164 MPA d ) 204 Mpa