A stepped steel shaft, shown below, is used in a spur gear reducer. The shaft is subjected to a constant axial stress (A=40 MPa), a constant bending stress due to loads by bearings and gears (M=60 MPa), and a steady torque (T-80 MPa) during shaft rotation. Neglect the stress concentration factors (we will cover this next week) that result from the stepped shaft geometry. The shaft is made of steel with Su=1006 MPa, Sy=648 MPa, and HB-229. The size of the shaft results in a gradient factor of CG=0.9. The shaft has a fine-ground finish. A 95% reliability is required. Calculate the safety factor relative to infinite life (10 cycles). If the safety factor is less than one (i.e., shaft fails), find the number of cycles to failure.

A stepped steel shaft, shown below, is used in a spur gear reducer. The shaft is subjected to a constant axial stress (A=40 MPa), a constant bending stress due to loads by bearings and gears (M=60 MPa), and a steady torque (T-80 MPa) during shaft rotation. Neglect the stress concentration factors (we will cover this next week) that result from the stepped shaft geometry. The shaft is made of steel with Su=1006 MPa, Sy=648 MPa, and HB-229. The size of the shaft results in a gradient factor of CG=0.9. The shaft has a fine-ground finish. A 95% reliability is required. Calculate the safety factor relative to infinite life (10 cycles). If the safety factor is less than one (i.e., shaft fails), find the number of cycles to failure.

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 3.7.5P: The propeller shaft of a large ship has an outside diameter 18 in. and inside diameter 12 in,, as...

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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 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 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 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?
The propeller shaft of a large ship has an outside diameter 18 in. and inside diameter 12 in,, as shown in the figure. The shaft is rated for a maximum shear stress of 4500 psi. If the shaft is turning at 100 rpm, what is the maximum horsepower that can be transmitted without exceeding the allowable stress? If the rotational speed of the shaft is doubled but the power requirements remain unchanged, what happens to the shear stress in the shaft?
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 solid circular bar A BCD with fixed supports at ends A and D is acted upon by two equal and oppositely directed torques T0, as shown in the figure. The torques arc applied at points B and C each of which is located at distance x from one end of the bar. (The distance x may vary from zero to L/2.) For what distance x will the angle of twist at points B and C be a maximum? What is the corresponding angle of twist 0max?
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.
When drilling a hole in a table leg, a furniture maker uses a hand-operated drill (see figure) with a bit of diameter d = 4.0 mm. If the resisting torque supplied by the table leg is equal to 0.3 N · m, what is the maximum shear stress in the drill bit? If the allowable shear stress in the drill bit is 32 MPa, what is the maximum resisting torque before the drill binds up? If the shear modulus of elasticity of the steel is G = 75 GPa, what is the rate of twist of the drill bit (degrees per meter)?
A heavy flywheel rotating at n revolutions per minute is rigidly attached to the end of a shaft of diameter d (see figure). If the bearing at A suddenly freezes, what will be the maximum angle of twist <£of the shaft? What is the corresponding maximum shear stress in the shaft? (Let L = length of the shaft, G = shear modulus of elasticity, and / = mass moment of inertia of the flywheel about the axis of the shaft. Also, disregard friction in the bearings at Sand Cand disregard the mass of the shaft.) Hint: Equate the kinetic energy of the rotating flywheel to the strain energy of the shaft.
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.]