The four gears are attached to a steel shaft that is rotating at 2 Hz. Gear B supplies 70 kW of power to the shaft. Of that power, 20 kW are used by gear A, 20 kW by gear C, and 30 kW by gear D. (a) Find the uniform shaft diameter if the shear stress in the shaft is not to exceed 60 MPa. (b) If a uniform shaft diameter of 100 mm is specified, determine the angle by which one end of the shaft lags behind the other end. Use G = 83 GPa for steel.

The four gears are attached to a steel shaft that is rotating at 2 Hz. Gear B supplies 70 kW of power to the shaft. Of that power, 20 kW are used by gear A, 20 kW by gear C, and 30 kW by gear D. (a) Find the uniform shaft diameter if the shear stress in the shaft is not to exceed 60 MPa. (b) If a uniform shaft diameter of 100 mm is specified, determine the angle by which one end of the shaft lags behind the other end. Use G = 83 GPa for steel.

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 3.7.8P: A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The...

See similar textbooks

Similar questions

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?
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 motor driving a solid circular steel shaft with diameter d = 1.5 in, transmits 50 hp to a gear at B, The allowable shear stress in the steel is 6000 psi. Calculate the required speed of rotation (number of revolutions per minute) so that the shear stress in the shaft does not exceed the allowable limit.
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).
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 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 short stub shaft, made of SAE 1035, as rolled, receivers 30 hp at 300 rpm via a 12-in. spur gear, the power being delivered to another shaft through a flexible coupling. The gear is keyed (profile keyway) midway between the bearings. The pressure angle of the gear teeth   20o, N = 1.5 based on the octahedral shear stress theory with varying stresses. (a) Neglecting the radial component R of the tooth load W , determine the shaft diameter. (b) Considering both the tangential and the radial components, compute the shaft diameters. (c) Is the difference in the results of the parts (a) and (b) enough to change your choice of the shaft size?
Bearing stress 4. Please provide proper discussion and illustration also complete solution and clear solution please thank you Determine the length of a square key to be used for a 3.73 kW, 1800 rpm electric motor if the motor shaft diameter is 35 mm and the width of the key is approximately one-fourth of the shaft diameter. The allowable shearing stress on the key is 2.45 MPa
A motor is used to drive a gear assembly at 200 rpm. The main gear is in the center of a 1 m long (0.5 m to the left and right of the gear) 50 mm diameter solid circular shaft, and power is taken from the two shaft ends. 25 kW is taken on the left end and an unknown amount of power is taken at the right end. the torque to the left side of the gear is? maximum shear stress to left of gear? If the maximum shear stress on the shaft to the right of the gear is 125 MPa, approximately how much power is being drawn off from the right side of the shaft? The shaft can be made from 6061-T6 aluminum. It has adequate strength to withstand the loading conditions in the scenario, including the loading on the right side of the shaft. true or false?
Steel shaft can be produced as solid body or circular tube with circular tube. The shaft must bear a torque of 1200 Nm. Since the shear strength for the shaft material is 40 MPa, the maximum allowable unit torsion angle of the bar is 0.75 ^ 0 / m and the shear modulus of steel is G = 78 GPa;a) Find the required diameter d0 for a solid circle shaft.b) Find the required outside diameter d2 for a ring-section shaft whose thickness is one tenth of the outer diameter.c) Find the diameter ratio (d2 / d0 ratio) and weight ratio for ring cross section and solid section shafts
A 7/8 in. diameter shaft made out of ductile material is used to transmit power frommotor. The maximum allowable shear stress, τallow = 14.5 ksi is used for this shaft, andthe shaft rotates at 200 rpm. a. Find out the polar moment of inertia of the shaft. b. Find out the maximum Torque, T is being applied to the shaft. c. What would be the power of the motor? d. What are the general state of stresses for this application? Is it plane stress? Pleaseshow the general stress information, choosing any point in the shaft and zoomingin that point. e. If the shaft fails, how will it fail? Show it by a free hand sketch. f. What will be the maximum in-Plane shear stress, and its associated average normalstress? Please use the analytical equations. ONLY D, E, & F PLEASE
Bearing stress 5. Please provide proper discussion and illustration also complete solution and clear solution please thank you A solid shaft is designed to transmit 50kN @ 1800 rpm to a gear by means of 156 mm long key with square cross-section. The shaft diameter is 35.6mm. What should the cross-section be in mm2 to resist shearing, if the allowable shear stress on the key is 20 MPa?