EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220102804487
Author: BEER
Publisher: YUZU
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Chapter 3.10, Problem 126P
Each of the two brass bars shown is subjected to a torque of magnitude T = 12.5 kip·in. Knowing that G = 5.6 × 106 psi, determine for each bar the maximum shearing stress and the angle of twist at B.
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3) The electric motor exerts a torque of 600 N.m on
the steel shaft ABCD when it is rotating at a
constant speed. Design specifications require that
the diameter of the shaft be uniform from A to D
and that the angle of twist between A and D not
exceed 1.5°. Knowing that t max < 65 MPa and G =
77 GPa, determine the minimum diameter the shaft
that can be used.
200 N.m
400 N.m
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The aluminum rod AB (G= 27 GPa) is bonded to the brass rod BD (G= 39 GPa). Knowing that portion CD of the brass rod is hollow and
has an inner diameter of 40 mm, determine the angle of twist at A if TB = 1300 N-m.
Тв
36 mm
TA-800 N-m
400 mm
60 mm
250 mm
375 mm
The angle of twist at A is
3.46 The electric motor exerts a torque of 800 N · m on the steel shaft
ABCD when it is rotating at a constant speed. Design specifications
require that the diameter of the shaft be uniform from A to D and
that the angle of twist between A and D not exceed 1.5°. Knowing
that Tmas s 60 MPa and G = 77 GPa, determine the minimum
diameter shaft that can be used.
300 N- m
500 N- m
04 m
0.6 m
0.3 m
Fig. P3.46
Chapter 3 Solutions
EBK MECHANICS OF MATERIALS
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. 25PCh. 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. 61PCh. 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. 93PCh. 3.8 - Prob. 94PCh. 3.8 - Prob. 95PCh. 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. 99PCh. 3.8 - Prob. 100PCh. 3.8 - Prob. 101PCh. 3.8 - Prob. 102PCh. 3.8 - Prob. 103PCh. 3.8 - Prob. 104PCh. 3.8 - A solid circular rod is made of a material that is...Ch. 3.8 - Prob. 106PCh. 3.8 - Prob. 107PCh. 3.8 - Prob. 108PCh. 3.8 - Prob. 109PCh. 3.8 - Prob. 110PCh. 3.8 - Prob. 111PCh. 3.8 - A 50-mm diameter cylinder is made of a brass for...Ch. 3.8 - Prob. 113PCh. 3.8 - The solid circular drill rod AB is made of a steel...Ch. 3.8 - Prob. 115PCh. 3.8 - Prob. 116PCh. 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. 119PCh. 3.8 - Prob. 120PCh. 3.10 - Determine the smallest allowable square cross...Ch. 3.10 - Prob. 122PCh. 3.10 - Using all = 70 MPa and G = 27 GPa, determine for...Ch. 3.10 - Prob. 124PCh. 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. 127PCh. 3.10 - Prob. 128PCh. 3.10 - Prob. 129PCh. 3.10 - Shafts A and B are made of the same material and...Ch. 3.10 - Prob. 131PCh. 3.10 - Shafts A and B are made of the same material and...Ch. 3.10 - Prob. 133PCh. 3.10 - Prob. 134PCh. 3.10 - Prob. 135PCh. 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. 138PCh. 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. 154RPCh. 3 - Prob. 155RPCh. 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. 159RPCh. 3 - Prob. 160RPCh. 3 - Prob. 161RPCh. 3 - The shaft AB is made of a material that is...
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- Solve correctlyarrow_forward2.1arrow_forwardThe aluminum rod AB (G= 27 GPa) is bonded to the brass rod BD (G= 39 GPa). Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A if TR= 1540 N-m. 60 mm 36 mm T.- S00 N m 250 mm 375 mm 400 mm The angle of twist at A isarrow_forward
- The aluminum rod AB (G= 27 GPa) is bonded to the brass rod BD(G= 39 GPa). Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A.arrow_forwardThe aluminum rod AB (G = 27 GPa) is bonded to the brass rod BD (G = 39 GPa). Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A. 60 mm TB = 1600 N-m 36 mm TA = 800 N-m 400 mm B 375 mm 250 mm Then, determine the maximum and minimum shearing stress in shaft CD.arrow_forwardEXERCISE 2 The electric motor exerts a 500-N m torque on the aluminum shaft ABCD when it is rotating at a constant speed. Given that 300 N-m. the G = 27 GPa.Knowing that and that the torques exerted on 200 N.m pulleys B and C are as shown, determine the angle of twist 45mm between 0.9 m 1.2 m (a) B and C 40 Ans: B/c 1.384° (b) B and D Ans: 9 B/D= 3.22°arrow_forward
- A flanged bolt coupling consists of ten steel ½-in.-diameter bolts spaced evenly around a bolt circle 14 in. in diameter. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is 6000 psi.arrow_forwardThe electric motor below, exerts a torque of 800 N.m on the steel shaft ABCD when it rotates at constant speed. Design specifications require that the shaft diameter be uniform from A to D and that the angle of twist between A and D not exceed 1.5°. Knowing that tmax < 60 MPa e G = 77.2 GPa, determine the minimum shaft diameter that can be used. 300 N-m 500 N-m B D 0.4 m 0.6 m 0.3 marrow_forwardThe aluminum rod AB (G = 27 GPa) is bonded to the brass rod BD (G = 39 GPa). Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A if TB = 1540 N·m.arrow_forward
- 3.36 The torques shown are exerted on pulleys B, C, and D. Knowing that the entire shaft is made of aluminum (G = 27 GPa), deter- mine the angle of twist between (a) C and B, (b) D and B. 30 mm 30 mm 400 N- m GG 36 mm 900 N- m 36 mm 500 N. m B "0.6 m E. 0.5 m D m 0.5 Fig. P3.36arrow_forwardQ2/ The torques shown, in Fig. 2, are exerted on pulleys A and B. Knowing that the shafts are solid and made of steel (G=77 GPa), determine the maximum shear stress (t) of shaft BC, and then find the total angle of twist (0) between A and C. Fig. 2 TA Ta 300 N-m 30 mm 400 N-m 46 mm 0.9 m 0.75 m c!arrow_forwardThe allowable shearing stress is 15 ksi in the 1.5-in.-diameter steel rod ABand 8 ksi in the 1.8-in.-diameter rod BC. Neglecting the effect of stress concentrations, determine the largest torque that can be applied at Aarrow_forward
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