Explanation Given information: The motor produces torque of 20 N ⋅ m . The inner and outer diameter of the shaft is 30 mm and 50 mm. Calculation: Sketch the free body diagram of the gears as shown in Figure 1. Refer Figure 1. Here, F is force and T ′ is torque. For 30 mm radius of the gear, F ( 0.03 m ) = 20 N ⋅ m F = 666.67 N For 100 mm radius of the gear, T ' = F ( 0.1 m ) (1) Substitute 666.67 N for F in Equation (1). T ' = ( 666.67 N ) ( 0.1 m ) = 66.67 N ⋅ m The shaft is fixed at C , so the torque exists only in the region EF of the shaft. Find the angle of twist of F with respect to E ( ϕ F / E ) using the relation. ϕ F / E = T L J G (2) Here, the torque applied in the shaft is T , the length of the shaft is L , the polar moment of inertia is J , and the shear modulus of elasticity of the material is G . Length of shaft from F to E is 0.6 m. The polar moment of inertia for a hollow shaft of outer radius ( r 0 ) and inner radius ( r i ) is π 2 ( r 0 4 − r i 4 ) . Substitute π 2 ( r 0 4 − r i 4 ) for J in Equation (2). ϕ F / E = T L ( π 2 ( r 0 4 − r i 4 ) ) G = 2 T L ( π ( r 0 4 − r i 4 ) ) G (3) The value of outer radius ( r 0 ) and inner radius ( r i ) of the hollow shaft is 25 mm and 15 mm. Refer the properties of L 2 steel: The value of shear modulus of elasticity of L 2 steel is 75 GPa. Substitute 66.67 N ⋅ m for T , 0.6 m for L , 25 mm for r 0 , 15 mm for r i , and 75 GPa for G in Equation (3). ϕ F / E = 2 T L ( π ( r 0 4 − r i 4 ) ) G = 2 ( 66.67 N ⋅ m ) ( 0.6 m ) ( π ( ( 25 mm ) 4 − ( 15 mm ) 4 ) ) ( 75 GPa ) = 2 ( 66.67 N ⋅ m ) ( 0.6 m ) ( π ( ( 25 mm × 10 − 3 m 1 mm ) 4 − ( 15 mm × 10 − 3 m 1 mm ) 4 ) ) ( 75 GPa × 10 9 N m 2 1 GPa ) = 0

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Design of Shafts and Shaft Components

The shaft is basically defined as the machine element that rotates, is in circular cross-section, it is majorly used to transfer the power from one part of the system to another, or from a power generating machine to a power absorbing machine. The shaft …

Question

Chapter 5.4, Problem 5.73P

To determine

The angle of twist of F with respect to E

The angle of twist of F with respect to D

The absolute maximum shear stress in the shaft

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.4, Problem 5.72P

Chapter 5.4, Problem 5.74P

Students have asked these similar questions

The two shafts are made of steel (G=11x106 lb/in2). Each has a diameter of 1 in. , and they are supported by bearings at A, B and C, which allow free rotation. If the support at D is fixed, determine the angle of twist of end A when the torques are applied to the assembly as shown. Torque applied at H of 80 ft lbs, and at G of 40 ft lbs in opposing directions as seen in the figure

(1) The shaft has an outer diameter of 1.5 in. and an inner diameter of 0.8 in. If it is subjected to the applied torques as shown, determine the shear stress distribution on the cross-section within region EA. The smooth bearings at A and B do not resist torque

The compound shaft made from the same material consisting of two segments AC and CB is firmly attached to rigid supports. The allowable shear stress in the shaft is limited to 5500 psi. Determine the maximum torque TO that may be applied at C. Calculate also the angular rotation incurred by segment BC. Use G= 12 x 106 psi. (Please provide detailed solution, thank you with FBD) To = ? lb-in ϴBC = ? degree

Chapter 5 Solutions

Mechanics of Materials (10th Edition)

Ch. 5.3 - Determine the internal torque at each section and...Ch. 5.3 - Determine the. internal torque at each section and...Ch. 5.3 - The solid and hollow shafts are each subjected to...Ch. 5.3 - The motor delivers 10 hp to the shaft. If it...Ch. 5.3 - The solid circular shaft is subjected to an...Ch. 5.3 - The hollow circular shaft is subjected to an...Ch. 5.3 - The shaft is hollow from A to B and solid from B...Ch. 5.3 - Determine the maximum shear stress in the...Ch. 5.3 - Determine the maximum shear stress in the shaft at...Ch. 5.3 - Determine the shear stress a: point A on the...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The angle of twist of F with respect to E The angle of twist of F with respect to D The absolute maximum shear stress in the shaft

Concept explainers

The angle of twist of F with respect to E The angle of twist of F with respect to D The absolute maximum shear stress in the shaft

Want to see the full answer?

Chapter 5 Solutions

The angle of twist of F with respect to E

The angle of twist of F with respect to D

The absolute maximum shear stress in the shaft