Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2.13, Problem 120P
For the composite bar in Prob. 2.111, determine the residual stresses in the tempered-steel bars if P is gradually increased from zero until the deformation of the bar reaches a maximum value δm = 0.04 in. and is then decreased back to zero.
2.111 Two tempered-steel bars, each
Fig. P2.111
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Que 1.23. A steel rod of 3 cm diameter is enclosed centrally in a
hollow copper tube of external diameter 5 cm and internal diameter
4 cm. The composite bar is then subjected to an axial pull of 45000 N.
If the length of each bar is equal to 15 cm.
Determine :
i.
The stresses in the rod and the tube.
ii. Load carried by each rod.
E for steel = 200 GPa and for Copper = 100 GPa.
4. A steel rod of 3 cm diameter is enclosed centrally in a hollow
copper tube of external diameter 5 cm and internal diameter of 4
cm. The composite bar is then subjected to an axial pull of 45 000
N. If the length of each bar is equal to 150 mm. Determine
(i) The stress in the rod and tube
(ii) Load carried by each bar
Question 1
Not yet answered
Marked out of 2.00
P Flag question
the bar shown is subjected to uniform tensile stresses along the x and y axes of a
magnitude 676 MPa.
if the length a =
45 mm and the length b = 34 mm
if the modulus of elasticity E = 120 GP, and the Poisson's ratio is 0.3
then, its new length b is
mm
a
a. 34.1915
b. 34.0575
C. 168.0733
d. 34.1341
Chapter 2 Solutions
Mechanics of Materials, 7th Edition
Ch. 2.1 - A nylon thread is subjected to a 8.5-N tension...Ch. 2.1 - A 4.8-ft-long steel wire of 14 -in.-diameter is...Ch. 2.1 - An 18-m-long steel wire of 5-mm diameter is to be...Ch. 2.1 - Two gage marks are placed exactly 250 mm apart on...Ch. 2.1 - An aluminum pipe must not stretch more than 0.05...Ch. 2.1 - A control rod made of yellow brass must not...Ch. 2.1 - A steel control rod is 5.5 ft long and must not...Ch. 2.1 - A cast-iron tube is used to support a compressive...Ch. 2.1 - A 4-m-long steel rod must not stretch more than 3...Ch. 2.1 - A nylon thread is to be subjected to a 10-N...
Ch. 2.1 - A block of 10-in. length and 1.8 1.6-in. cross...Ch. 2.1 - A square yellow-brass bar must not stretch more...Ch. 2.1 - Rod BD is made of steel (E = 29 106 psi) and is...Ch. 2.1 - The 4-mm-diameter cable BC is made of a steel with...Ch. 2.1 - A single axial load of magnitude P = 15 kips is...Ch. 2.1 - A 250-mm-long aluminum tube (E = 70 GPa) of 36-mm...Ch. 2.1 - The specimen shown has been cut from a...Ch. 2.1 - The brass tube AB (E = 105 GPa) has a...Ch. 2.1 - Both portions of the rod ABC are made of an...Ch. 2.1 - The rod ABC is made of an aluminum for which E =...Ch. 2.1 - For the steel truss (E = 200 GPa) and loading...Ch. 2.1 - For the steel truss (E = 29 106 psi) and loading...Ch. 2.1 - Members AB and BC are made of steel (E = 29 106...Ch. 2.1 - The steel frame (E = 200 GPa) shown has a diagonal...Ch. 2.1 - Link BD is made of brass (E = 105 GPa) and has a...Ch. 2.1 - Members ABC and DEF are joined with steel links (E...Ch. 2.1 - Each of the links AB and CD is made of aluminum (E...Ch. 2.1 - The length of the 332-in.-diameter steel wire CD...Ch. 2.1 - A homogenous cable of length L and uniform cross...Ch. 2.1 - The vertical load P is applied at the center A of...Ch. 2.1 - Denoting by the "engineering strain'' in a...Ch. 2.1 - The volume of a tensile specimen is essentially...Ch. 2.3 - An axial centric force of magnitude P = 450 kN is...Ch. 2.3 - An axial centric force of magnitude P = 450 kN is...Ch. 2.3 - The 4.5-ft concrete post is reinforced with six...Ch. 2.3 - The 4.5-ft concrete post is reinforced with six...Ch. 2.3 - An axial force of 200 kW is applied to the...Ch. 2.3 - The length of the assembly shown decreases by 0.40...Ch. 2.3 - A polystyrene rod consisting of two cylindrical...Ch. 2.3 - Three steel rods (E = 29 106 psi) support an...Ch. 2.3 - Fig. P2.41 2.41 Two cylindrical rods, one of steel...Ch. 2.3 - Solve Prob. 2.41, assuming that rod AC is made of...Ch. 2.3 - Each of the rods BD and CE is made of brass (E =...Ch. 2.3 - The rigid bar AD is supported by two steel wires...Ch. 2.3 - The rigid bar ABC is suspended from three wines of...Ch. 2.3 - The rigid bar AD is supported by two steel wires...Ch. 2.3 - The aluminum shell is fully bonded to the brass...Ch. 2.3 - The aluminum shell is fully bonded to the brass...Ch. 2.3 - The brass shell (b = 11.6 10-6/F) is fully bonded...Ch. 2.3 - The concrete post (Ec = 3.6 106) psi and c = 5.5 ...Ch. 2.3 - A rod consisting of two cylindrical portions AB...Ch. 2.3 - A rod consisting of two cylindrical portions AB...Ch. 2.3 - Fig. P2.52 2.52 A rod consisting of two...Ch. 2.3 - The steel rails of a railroad (rack (Es = 200GPa,...Ch. 2.3 - Two steel bars (Es = 200 GPa and s = 11.7 10-6/C)...Ch. 2.3 - Determine the maximum load P that can be applied...Ch. 2.3 - An aluminum rod (Ea = 70 GPa, a = 23.6 10-6/C)...Ch. 2.3 - Knowing that a 0.02-in. gap exists when the...Ch. 2.3 - Determine (a) the compressive force in the bars...Ch. 2.3 - At room temperature (20C) a 0.5-mm gap exists...Ch. 2.9 - A standard tension test is used to determine the...Ch. 2.9 - A 2-m length of an aluminum pipe of 240-nun outer...Ch. 2.9 - A line of slope 4:10 has been scribed on a...Ch. 2.9 - A 2.75-kN tensile load is applied to a test coupon...Ch. 2.9 - Fig. P2.65 2.65 In a standard tensile test a steel...Ch. 2.9 - The change in diameter of a large steel bolt is...Ch. 2.9 - The brass rod AD is fitted with a jacket that is...Ch. 2.9 - A fabric used in air-inflated structures is...Ch. 2.9 - A 1-in. square was scribed on the side of a large...Ch. 2.9 - The block shown is made of a magnesium alloy for...Ch. 2.9 - The homogeneous plate ABCD is subjected to a...Ch. 2.9 - For a member under axial loading, express the...Ch. 2.9 - In many situations it is known that the normal...Ch. 2.9 - In many situations physical constraints prevent...Ch. 2.9 - The plastic block shown is bonded to a rigid...Ch. 2.9 - The plastic block shown is bonded to a rigid...Ch. 2.9 - Two blocks of rubber with a modulus of rigidity G...Ch. 2.9 - Fig. P2.77 and P2.78 2.78 Two blocks of rubber...Ch. 2.9 - An elastomeric bearing (G = 130 psi) is used to...Ch. 2.9 - 2.80 For the elastomeric bearing In Prob. 2.79...Ch. 2.9 - A vibration isolation unit consists of two blocks...Ch. 2.9 - Prob. 82PCh. 2.9 - Prob. 83PCh. 2.9 - Prob. 84PCh. 2.9 - Prob. 85PCh. 2.9 - A 2.75-kN tensile load is applied to a test coupon...Ch. 2.9 - A vibration isolation support consists of a rod A...Ch. 2.9 - Prob. 88PCh. 2.9 - Prob. 89PCh. 2.9 - Show that for any given material, the ratio G/E of...Ch. 2.9 - Prob. 91PCh. 2.9 - Prob. 92PCh. 2.13 - Knowing that, for the plate shown, the allowable...Ch. 2.13 - Knowing that P = 38 kN, determine the maximum...Ch. 2.13 - A hole is to be drilled in the plate at A. The...Ch. 2.13 - Fig. P2.95 and P2.96 2.96 (a) For P = 13 kips and...Ch. 2.13 - 2.97 Knowing that the hole has a diameter of 9 mm,...Ch. 2.13 - For P = 100 kN, determine the minimum plate...Ch. 2.13 - Prob. 99PCh. 2.13 - A centric axial force is applied to the steel bar...Ch. 2.13 - The cylindrical rod AB has a length L = 5 ft and a...Ch. 2.13 - Fig. P2.101 and P.102 2.102 The cylindrical rod AB...Ch. 2.13 - Rod AB is made of a mild steel that is assumed to...Ch. 2.13 - Prob. 104PCh. 2.13 - Rod ABC consists of two cylindrical portions and...Ch. 2.13 - Prob. 106PCh. 2.13 - Prob. 107PCh. 2.13 - Prob. 108PCh. 2.13 - Each cable has a cross-sectional area of 100 mm2...Ch. 2.13 - Prob. 110PCh. 2.13 - Two tempered-steel bars, each 316 in. thick, are...Ch. 2.13 - Prob. 112PCh. 2.13 - Prob. 113PCh. 2.13 - Prob. 114PCh. 2.13 - Prob. 115PCh. 2.13 - Prob. 116PCh. 2.13 - Prob. 117PCh. 2.13 - Prob. 118PCh. 2.13 - Prob. 119PCh. 2.13 - For the composite bar in Prob. 2.111, determine...Ch. 2.13 - Prob. 121PCh. 2.13 - Bar AB has a cross-sectional area of 1200 mm2 and...Ch. 2.13 - Bar AB has a cross-sectional area of 1200 mm2 and...Ch. 2 - The uniform wire ABC, of unstretched length 2l, is...Ch. 2 - The aluminum rod ABC (E = 10.1 106 psi), which...Ch. 2 - Two solid cylindrical rods are joined at B and...Ch. 2 - Prob. 127RPCh. 2 - Prob. 128RPCh. 2 - Prob. 129RPCh. 2 - A 4-ft concrete post is reinforced with four steel...Ch. 2 - The steel rods BE and CD each have a 16-mm...Ch. 2 - Prob. 132RPCh. 2 - Prob. 133RPCh. 2 - The aluminum test specimen shown is subjected to...Ch. 2 - Prob. 135RP
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
- 1. The normal strains of a solid under a uniaxial stress of 60MPa are and. When the solid is subject to a hydrostatic stress of 100MPa, determine (a) the bulk modulus (b) the dilatation of the solid.arrow_forwardTwo tempered-steel bars, each in. thick, are bonded to a 1/2 -in. mild-steel bar. This composite bar is subjected as shown to a centric axial load of magnitude P. Both steels are elastoplastic with E= 29 × 106 psi and with yield strengths equal to 100 ksi and 50 ksi, respectively, for the tempered and mild steel. Determine the residual stresses in the tempered-steel bars if the load P is gradually increased from zero until the deformation of the bar reaches a maximum value 5m = 0.04 in. and is then decreased back to zero. Take L = 17 in. 2.0 in. in. 33 in. 3 16 in. The residual stress in the tempered-steel bars is ksi.arrow_forwardA 50-kN force is subjected to a lap joint fastened by three 20-mm diameter rivets.(a) the shearing stress in each rivet.(b) the bearing stress in each plate.(c) the maximum average tensile stress in each plate. Assume that the axial load P is distributed equally amongthe three rivets. equally among the three rivets.arrow_forward
- solve i and ii please.arrow_forward2.36 A 250-mm bar of 150 x 30-mm rectangular cross section consists of two aluminum layers, 5 mm thick, brazed to a center brass layer of the same thickness. If it is subjected to centric forces of magni- tude P = 30 kN, and knowing that E, = 70 GPa and E, = 105 GPa, determine the normal stress (a) in the aluminum layers, (b) in the brass layer. P' 250 mm 5 mm 5 mm 5 mm Aluminum Brass Aluminum P 30 mm Fig. P2.36arrow_forward2. A steel wire 30 ft long, hanging vertically, supports a load of 500 lbf. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 20,000 psi and the total elongation is not to exceed 0. in. Assume E = 29 × 106 psi.arrow_forward
- The rigid beam BC is supported by rods (1) and (2). The cross-sectional area of rod (1) is 9 mm². The cross-sectional area of rod (2) is 18 mm². For a uniformly distributed load of w = 4.5 kN/m, determine the length a so that the normal stress is the same in each rod. Assume L = 3.70 m. (1) (2) W a B Answer: a = i L Earrow_forwardProb.6: [2.53] A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion AB is made of brass (Es =105 GPa , ab= 20.9 x 106 /"C) and portion AB is made of aluminum (Ea =72 GPa , a.= 23.9 x 10-6 /C). Knowing that the rod is initially unstressed, determine (a) the normal stresses induced in portions AB and BC by a temperature rise of 42°C, (b) the corresponding deflection of point B. A 60-mm diameter 1.1 m - 40-mm diameter 1.3 m Carrow_forwardA spherical gas tank is fabricated by bolting together two thin-walled hemispherical shells with an inner diameter of 8 m. The gas is pressurized to 2.0 MPa. The shells have an allowable normal stress of 150 MPa, and the 25 mm-diameter bolts have an allowable normal stress of 250 MPa. (a) Determine the minimum thickness of the walls of the tank to the nearest mm. (b) Determine the minimum number of bolts to connect the hemispheres.arrow_forward
- 2.60 At room temperature (20°C) a 0.5-mm gap exists between the ends of the rods shown. At a later time when the temperature has reached 140°C, determine (a) the normal stress in the aluminum rod, (b) the change in length of the aluminum rod. 0.5 mm 300 mm 250 mm B Aluminum Stainless steel A = 2000 mm² E = 75 GPa a = 23 × 16-6/°C Fig. P2.60 A = 800 mm² E = 190 GPa a = 17.3 × 10-6/°Carrow_forwardThe rigid beam BC is supported by rods (1) and (2). The cross-sectional area of rod (1) is 11 mm². The cross-sectional area of rod (2) is 14 mm2. For a uniformly distributed load of w = 4.1 kN/m, determine the length a so that the normal stress is the same in each rod. Assume L = 5.35 m. A (1) (2) a L. Answer: a = i marrow_forward3) An eccentric force P is applied as shown in Fig. 2 to a steel bar of 25 x 90-mm cross section. The strains at A and B have been measured and found to be ƐA = + 400µ and be ЄB = - - 90μ. Knowing that E = 210 GPa, determine (a) the magnitude of force P, (b) the distance d, and (c) neatly draw the stress distribution diagrams of the system. 30 mm 25 mm- 90 mm A B Fig. 2 1 45 mm 15 mmarrow_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
Everything About COMBINED LOADING in 10 Minutes! Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=N-PlI900hSg;License: Standard youtube license