Explanation Given information: The torque in the pulley A ( T A ) is 2 kip ⋅ in . . The angle in the pulley D ( φ ) is 7.5 ° . The modulus of rigidity of the steel ( G ) is 11.2 × 10 6 psi . The allowable shearing stress ( τ a l l ) is 12 ksi . The radius of the gear B ( r B ) is 2 in . The radius of the gear C ( r C ) is 5 in . Assume that clockwise direction is negative and anticlockwise direction is positive. Calculation: Gear B : Show the free body diagram of the gear B as in Figure 1. Calculate the force F produced in the gear B by taking moment about gear B . ∑ M B = 0 ( F × r B ) − T B = 0 F = T B r B Here, T B is the torque produced at B and r B is the radius of the gear B . Gear C : Show the free body diagram of the gear C as in Figure 2. Calculate the torque in the pulley D ( T D ) by taking moment about gear C . ∑ M C = 0 ( F × r C ) − T D = 0 T D = F × r C Here, r C is the radius of the gear C . Substitute T B r B for F . T D = ( T B r B ) × r C = r C r B T B = n T B Where, n is referred as r C r B . Calculate the value of n using the relation: n = r C r B Substitute 5in . for r C and 2in . for r B . n = 5 2 = 2.5 Torque in the shafts: In shaft AB , T A B = T A = T B . In shaft CD , T C D = T C = T D . Here, T C is the torque produced at gear C . Substitute n T B for T D . T C D = T C = n T B Substitute T A for T B . T C D = T C = n T A Deformations in the shafts: In shaft CD , φ C / D = T C D L G J Here, L is the length of the shaft CD and J is the polar moment of inertia of the shaft CD . Substitute n T A for T C / D . φ C / D = n T A L G J In shaft AB , φ A / B = T A B L G J Substitute T A for T A / B . φ A / B = T A L G J Since no rotation produced in the pulley D that is φ D is 0. Calculate the rotation in the gear C using the relation: φ C / D = φ C + φ D Substitute 0 for φ D and n T A L G J for φ C / D . n T A L G J = φ C + 0 φ C = n T A L G J Calculate the rotation in the gear B using the relation: r B φ B = − r C φ C φ B = − r C r B φ C Substitute n T A L G J for φ C and n for − r C r B . φ B = n ( n T A L G J ) = n 2 T A L G J Calculate the rotation in the pulley A using the relation: φ A = φ B + φ A / B Substitute n 2 T A L G J for φ B and T A L G J for φ A / B

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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 3, Problem 155RP

To determine

Find the required diameter of the shafts (d).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 154RP

Chapter 3, Problem 156RP

Students have asked these similar questions

Calculate the forces in members BC, BG & FG of the truss shown using the Method of Sections. For your answer, provide atruss diagram of the calculated member forces and indicate whether the member is in Tension (+) or Compression (-)

Select the speed, feed and depth of the cut to turn wrought, low carbon steel (hardness of 200 BHN) on lathe with AISI tool material of HSS M2 or M3. (Hint: refer to Chapter 21 for recommended parameters).

Only question 1&2

Chapter 3 Solutions

Mechanics of Materials, 7th Edition

Ch. 3.1 - Determine the torque T that causes a maximum...Ch. 3.1 - For the cylindrical shaft shown, determine the...Ch. 3.1 - (a) Determine the torque T that causes a maximum...Ch. 3.1 - (a) Determine the maximum shearing stress caused...Ch. 3.1 - (a) For the 3-in.-diameter solid cylinder and...Ch. 3.1 - Fig. P3.6 3.6 A torque T=3 kN m is applied to the...Ch. 3.1 - The solid spindle AB is made of a steel with an...Ch. 3.1 - The solid spindle AB has a diameter ds = 1.5 in....Ch. 3.1 - Fig. P3.9 and P3.10 3.10 The shafts of the pulley...Ch. 3.1 - Knowing that each of the shafts AB, BC, and CD...

Ch. 3.1 - Fig. P3.11 and P3.12 3.12 Knowing that an...Ch. 3.1 - Under normal operating conditions, the electric...Ch. 3.1 - In order to reduce the total mass of the assembly...Ch. 3.1 - The allowable shearing stress is 15 ksi in the...Ch. 3.1 - The allowable shearing stress is 15 ksi in the...Ch. 3.1 - The solid shaft shown is formed of a brass for...Ch. 3.1 - Solve Prob. 3.17 assuming that the direction of Tc...Ch. 3.1 - The solid rod AB has a diameter dAB= 60 mm and is...Ch. 3.1 - Fig. P3.19 and P3.20 3.20 The solid rod AB has a...Ch. 3.1 - A torque of magnitude T = 1000 N m is applied at D...Ch. 3.1 - Fig. P3.21 and P3.22 3.22 A torque of magnitude T...Ch. 3.1 - Under normal operating conditions a motor exerts a...Ch. 3.1 - Fig P3.23 and P3.24 3.24 Under normal operating...Ch. 3.1 - Prob. 25P Ch. 3.1 - Fig. P3.25 and P3.26 3.26 The two solid shafts are...Ch. 3.1 - For the gear train shown, the diameters of the...Ch. 3.1 - Fig. P3.27 and P3.28 3.28 A torque T = 900 N m is...Ch. 3.1 - Fig. P3.29 3.29 While the exact distribution of...Ch. 3.1 - Fig. P3.30 3.30 (a) For a given allowable shearing...Ch. 3.3 - Determine the largest allowable diameter of a...Ch. 3.3 - The ship at A has just started to drill for oil on...Ch. 3.3 - (a) For the solid steel shaft shown, determine the...Ch. 3.3 - (a) For the aluminum pipe shown (G = 27 GPa),...Ch. 3.3 - The electric motor exerts a 500 N m-torque on the...Ch. 3.3 - The torques shown are exerted on pulleys and B....Ch. 3.3 - The aluminum rod BC (G = 26 GPa) is bonded to the...Ch. 3.3 - The aluminum rod AB (G = 27 GPa) is bonded to the...Ch. 3.3 - The solid spindle AB has a diameter ds = 1.75 in....Ch. 3.3 - Fig. p3.39 and p3.40 3.40 The solid spindle AB has...Ch. 3.3 - Two shafts, each of 78in. diameter, are connected...Ch. 3.3 - Two solid steel shafts each of 30-mm diameter, are...Ch. 3.3 - A coder F, used to record in digital form the...Ch. 3.3 - Fig. p3.43 3.44 For the gear train described in...Ch. 3.3 - The design specifications of a 1.2-m-long solid...Ch. 3.3 - 3.46 and 3.47 The solid cylindrical rod BC of...Ch. 3.3 - 3.46 and 3.47 The solid cylindrical rod BC of...Ch. 3.3 - The design of the gear-and-shaft system shown...Ch. 3.3 - The electric motor exerts a torque of 900 Nm on...Ch. 3.3 - A hole is punched at A in a plastic sheet by...Ch. 3.3 - The solid cylinders AB and BC are bonded together...Ch. 3.3 - Solve Prob. 3.51, assuming that cylinder AB is...Ch. 3.3 - The composite shaft shown consists of a...Ch. 3.3 - Fig. p3.53 and p3.54 3.54 The composite shaft...Ch. 3.3 - Two solid steel shafts (G = 77.2 GPa) are...Ch. 3.3 - Solve Prob. 3.55, assuming that the shaft AB is...Ch. 3.3 - 3.57 and 3.58 Two solid steel shafts are fitted...Ch. 3.3 - 3.57 and 3.58 Two solid steel shafts are fitted...Ch. 3.3 - The steel jacket CD has been attached to the...Ch. 3.3 - A torque T is applied as shown to a solid tapered...Ch. 3.3 - Prob. 61P Ch. 3.3 - A solid shaft and a hollow shaft are made of the...Ch. 3.3 - An annular plate of thickness t and modulus G is...Ch. 3.5 - Determine the maximum shearing stress in a solid...Ch. 3.5 - Determine the maximum shearing stress in a solid...Ch. 3.5 - Using an allowable shearing stress of 4.5 ksi,...Ch. 3.5 - Using an allowable shearing stress of 50 MPa,...Ch. 3.5 - While a steel shaft of the cross section shown...Ch. 3.5 - Determine the required thickness of the 50-mm...Ch. 3.5 - A steel drive shaft is 6 ft long and its outer and...Ch. 3.5 - The hollow steel shaft shown (G = 77.2 GPa, all =...Ch. 3.5 - A steel pipe of 3.5-in. outer diameter is to be...Ch. 3.5 - 3.73 The design of a machine element calls for a...Ch. 3.5 - Three shafts and four gears are used to form a...Ch. 3.5 - Three shafts and four gears are used to form a...Ch. 3.5 - The two solid shafts and gears shown are used to...Ch. 3.5 - Fig. P3.76 and P3.77 3.77 The two solid shafts and...Ch. 3.5 - The shaft-disk-belt arrangement shown is used to...Ch. 3.5 - A 5-ft-long solid steel shaft of 0.875-in....Ch. 3.5 - A 2.5-m-long steel shaft of 30-mm diameter rotates...Ch. 3.5 - The design specifications of a 1.2-m-long solid...Ch. 3.5 - A 1.5-m-long tubular steel shaft (G = 77.2 GPa) of...Ch. 3.5 - Fig. P3.82 and P3.83 3.83 A 1.5-m-long tubular...Ch. 3.5 - The stepped shaft shown must transmit 40 kW at a...Ch. 3.5 - The stepped shaft shown rotates at 450 rpm....Ch. 3.5 - Knowing that the stepped shaft shown transmits a...Ch. 3.5 - The stepped shaft shown must rotate at a frequency...Ch. 3.5 - Fig. P3.87 and P3.88 3.88 The stepped shaft shown...Ch. 3.5 - A torque of magnitude T = 200 lbin. is applied to...Ch. 3.5 - Fig. P3.89, P3.90 and P3.91 3.90 In the stepped...Ch. 3.5 - In the stepped shaft shown, which has a full...Ch. 3.8 - The solid circular shaft shown is made of a steel...Ch. 3.8 - Prob. 93P Ch. 3.8 - Prob. 94P Ch. 3.8 - Prob. 95P Ch. 3.8 - Fig. P3.95 and P3.96 3.96 The solid shaft shown is...Ch. 3.8 - It is observed that a straightened paper clip can...Ch. 3.8 - The solid shaft shown is made of a mild steel that...Ch. 3.8 - Prob. 99P Ch. 3.8 - Prob. 100P Ch. 3.8 - Prob. 101P Ch. 3.8 - Prob. 102P Ch. 3.8 - Prob. 103P Ch. 3.8 - Prob. 104P Ch. 3.8 - A solid circular rod is made of a material that is...Ch. 3.8 - Prob. 106P Ch. 3.8 - Prob. 107P Ch. 3.8 - Prob. 108P Ch. 3.8 - Prob. 109P Ch. 3.8 - Prob. 110P Ch. 3.8 - Prob. 111P Ch. 3.8 - A 50-mm diameter cylinder is made of a brass for...Ch. 3.8 - Prob. 113P Ch. 3.8 - The solid circular drill rod AB is made of a steel...Ch. 3.8 - Prob. 115P Ch. 3.8 - Prob. 116P Ch. 3.8 - After the solid shaft of Prob. 3.116 has been...Ch. 3.8 - The hollow shaft shown is made of a steel that is...Ch. 3.8 - Prob. 119P Ch. 3.8 - Prob. 120P Ch. 3.10 - Determine the smallest allowable square cross...Ch. 3.10 - Prob. 122P Ch. 3.10 - Using all = 70 MPa and G = 27 GPa, determine for...Ch. 3.10 - Prob. 124P Ch. 3.10 - Determine the largest torque T that can be applied...Ch. 3.10 - Each of the two brass bars shown is subjected to a...Ch. 3.10 - Prob. 127P Ch. 3.10 - Prob. 128P Ch. 3.10 - Prob. 129P Ch. 3.10 - Shafts A and B are made of the same material and...Ch. 3.10 - Prob. 131P Ch. 3.10 - Shafts A and B are made of the same material and...Ch. 3.10 - Prob. 133P Ch. 3.10 - Prob. 134P Ch. 3.10 - Prob. 135P Ch. 3.10 - A 36-kipin. torque is applied to a 10-ft-long...Ch. 3.10 - A 4-m-long steel member has a W310 60 cross...Ch. 3.10 - Prob. 138P Ch. 3.10 - A 5-kipft torque is applied to a hollow aluminum...Ch. 3.10 - A torque T = 750 kNm is applied to the hollow...Ch. 3.10 - A 750-Nm torque is applied to a hollow shaft...Ch. 3.10 - 3.142 and 3.143 A hollow member having the cross...Ch. 3.10 - A hollow member having the cross section shown is...Ch. 3.10 - A 90-Nm torque is applied to a hollow shaft having...Ch. 3.10 - 3.145 and 3.146 A hollow member having the cross...Ch. 3.10 - 3.145 and 3.146 A hollow member having the cross...Ch. 3.10 - A cooling tube having the cross section shown is...Ch. 3.10 - A hollow cylindrical shaft was designed to have a...Ch. 3.10 - Equal torques are applied to thin-walled tubes of...Ch. 3.10 - A hollow cylindrical shaft of length L, mean...Ch. 3 - A steel pipe of 12-in. outer diameter is...Ch. 3 - A torque of magnitude T = 120 Nm is applied to...Ch. 3 - Fig. P3.152 3.153 Two solid shafts are connected...Ch. 3 - Prob. 154RP Ch. 3 - Prob. 155RP Ch. 3 - A torque of magnitude T = 4 kNm is applied at end...Ch. 3 - Ends A and D of the two solid steel shafts AB and...Ch. 3 - As the hollow steel shaft shown rotates at 180...Ch. 3 - Prob. 159RP Ch. 3 - Prob. 160RP Ch. 3 - Prob. 161RP Ch. 3 - The shaft AB is made of a material that is...

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.

Find the required diameter of the shafts ( d ).

Solution Summary: The author shows the free body diagram of the gear B as in Figure 1. Calculate the torque in the pulley A (T_A) is 2kip

Concept explainers

Find the required diameter of the shafts (d).

Want to see the full answer?

Chapter 3 Solutions