EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 9780100257061
Author: BEER
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3.8, Problem 105P
A solid circular rod is made of a material that is assumed to be elastoplastic. Denoting by TY and ϕY, respectively, the torque and the angle of twist at the onset of yield, determine the angle of twist if the torque is increased to (a) T = 1.1 TY, (b) T = 1.25 TY, (c) T= 1.3 TY.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The solid circular drill rod AB is made of a
steel that is assumed to be elastoplastic
with TY = 22 ksi and G = 11.2 x 106 psi.
Knowing that a torque T = 73 kip-in. is
applied to the rod and then removed,
determine the permanent angle of twist of
the rod. The permanent angle of twist of
the rod is
5) A brass rod 8mm diameter and 400mm long fits centrally inside aluminum tube of the same
length having an external diameter of 16mm and a wall thickness of
3mm. The rod and tube are rigidly connected at their ends so that they twist together when a
torque of 20 Nm is applied. Galuminum = 30GPA; Gbrass = 40GPA.
Determine:
%3D
a) The values of the torsional stiffness for the rod and the tube
b) The torque transmitted by each
c) The maximum shear stress in each
d) The angle of twist
01. : A rod of 400-mm-long, 18-mm-diameter is made of homogenous, isotropic steel material. The rod is
subjected to an axial load of 16 kN. It is observed that the rod is to increase in length by a ratio
0.008 mm/kN of the applied load, and to decrease in diameter by 0.0017 mm. Determine the modulus of
elasticity and Poisson's ratio of the material.
(20 Marks)
L= 400 mm
8,= 0.008 mm / kN
16 kN
d = 18 mm
0.0017 mm
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...
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.Similar questions
- A cylindrical bar of steel 10.4 mm (0.4094 in.) in diameter is to be deformed elastically by application of a force along the bar axis. Determine the force that will produce an elastic reduction of 2.8 x 103 mm (1.102 x 104 in.) in the diameter. For steel, values for the elastic modulus (E) and Poisson's ratio (v) are, respectively, 207 GPa and 0.30. i pu Narrow_forwardDetermine the torque needed to twist a short 2-mm-diameter steel wire through several revolutions if it is made from steel assumed to be elastic perfectly plastic and having a yield stress of tY = 50 MPa. Assume that the material becomes fully plastic.arrow_forwardForces is appliedarrow_forward
- A solid brass [E = 93 GPa] axial member is loaded and supported as shown. Segments (1) and (2) each have a diameter of 23 mm and segment (3) has a diameter of 12 mm. Assume L₁ = 1.9 m, L₂= 1.3 m, L3 = 1.7 m, R = 36 kN, Q = 12 kN, and P = 24 kN. Determine: (a) the deformation of segment (2). (b) the deflection of joint D with respect to the fixed support at A. (c) the maximum normal stress in the entire axial member. (1) A L₁ R (2) L2 L3 (3) D P B Carrow_forwardA solid brass [E = 99 GPa] axial member is loaded and supported as shown. Segments (1) and (2) each have a diameter of 20 mm and segment (3) has a diameter of 11 mm. Assume L₁ = 1.6 m, L₂=1.0 m, L3= 1.6 m, R = 36 kN, Q = 14 kN, and P = 28 kN. Determine: (a) the deformation of segment (2). (b) the deflection of joint D with respect to the fixed support at A. (c) the maximum normal stress in the entire axial member. L₁ L2 L3 (3) Answer: F₂ = (1) D B C (a) Determine the axial force in section (2) in kN. kN.arrow_forwardA cylindrical bar of steel 10.4 mm (0.4094 in.) in diameter is to be deformed elastically by application of a force along the bar axis. Determine the force that will produce an elastic reduction of 3.3 x103 mm (1.299 x104 in.) in the diameter. For steel, values for the elastic modulus (E) and Poisson's ratio (v) are, respectively, 207 GPa and 0.30. iarrow_forward
- Need correctly. Thank youarrow_forwardDo not round intermediate answers. Give your final answer(s) to three decimal places. Check your units. A 24-mm-diameter rod made of an experimental plastic is subjected to a tensile force of magnitude P=9 kN. Knowing that an elongation of 17 mm and a decrease in diameter of 0.57 mm are observed in a 300-mm length, determine: (a) the modulus of elasticity, (b) the modulus of rigidity, and (c) Poisson's ratio for the material. E = G = nu = MPa MPaarrow_forward1.11 (a) A test piece is cut from a brass bar and subjected to a tensile test. With a load of 6.4 kN the test piece, of diameter 11.28 mm, extends by 0.04 mm over a gauge length of 50 mm. Determine: (i) the stress, (ii) the strain, (iii) the modulus of elasticity, (b) A spacer is turned from the same bar. The spacer has a diameter of 28 mm and a length of 250 mm, both measurements being made at 20°C. The temperature of the spacer is then increased to 100°C, the natural expansion being entirely prevented. Taking the coefficient of linear expansion to be 18 x 10-6°C determine: (i) the stress in the spacer, (ii) the compressive load on the spacer. [C.G.] [64 MN/m², 0.0008, 80 GN/m², 115.2 MN/m², 71 kN.]arrow_forward
- Using Tall = 8.7 ksi and knowing that G= 5.6 × 106 psi, determine for each of the cold-rolled yellow brass bars shown the largest torque T that can be applied and the corresponding angle of twist at end B. Refer to Table 3.1. B 2 in.- T 2 in. B 2.8 in. 1.4 in. 16 in. The torque for the brass bar (a) is The angle of twist for the brass bar (a) is The torque for the brass bar (b) is The angle of twist for the brass bar (b) is kip-in. kip-in. 0arrow_forwardWith FBD please, thanks.arrow_forwardA standard tension test is used to determine the properties of an experi-mental plastic. The test specimen is a 58-in.-diameter rod and it is subjected to an 800-lb tensile force. Knowing that an elongation of 0.45 in. and a decrease in diameter of 0.025 in. are observed in a 5-in. gage length, determine the modulus of elasticity, the modulus of rigidity, and Poisson’s ratio for the materialarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Understanding Torsion; Author: The Efficient Engineer;https://www.youtube.com/watch?v=1YTKedLQOa0;License: Standard YouTube License, CC-BY