MECHANICS OF MATERIALS
7th Edition
ISBN: 9781260471076
Author: BEER
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 2.13, Problem 111P
Two tempered-steel bars, each
Fig. P2.111
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Rigid bar ABC is supported by bronze rod (1) and aluminum rod (2), as shown. A concentrated load P is applied to the free end of aluminum rod (3). Bronze rod (1) has an elastic modulus of E1 = 15,000 ksi and a diameter of d1 = 0.40 in. Aluminum rod (2) has an elastic modulus of E2 = 10,000 ksi and a diameter of d2 = 0.70in. Aluminum rod (3) has a diameter of d3 = 1.00in. The yield strength of the bronze is 48 ksi and the yield strength of the aluminum is 40 ksi. Assume a = 2.5 ft, b = 1.5 ft, L1 = 6 ft, L2 = 8 ft, and L3 = 3 ft.
Two tempered-steel bars, each 316316 in. thick, are bonded to a 1212 -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 to 103 kips and then decreased back to zero. The residual stress in the tempered steel bars is
A 10-mm diameter steel bolt is surrounded by bronze sleeve. The outer diameter of the bronze sleeve is 20 mm and its inner diameter is 10-mm. Given that the yield stress for the steel is 640 MPa and the yield stress for the bronze is 520 MPa, determine the magnitude of the maximum allowable total load that can be applied to this assembly. (Assume full bond between the steel and the bronze sleeve) Esteel = 200 GPa, Ebronze = 100 GPa, Factor of safety = 1.5
Chapter 2 Solutions
MECHANICS OF MATERIALS
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
- A copper bar consists from three sections: sections 1 is of 25 mm diameter and 60 mm long, section 2 is of 15 mm diameter and 50 mm long and section 3 is 20 mm square and 40 mm long. The bar is subjected to an axial tensile load which induces a stress of 20 MN/m2 on the smallest cross section. Determine the total Increase in the length of the bar when the load is applied. For copper E=100 GN/m2.arrow_forwardA solid aluminum [E = 64 GPa] rod (1) is connected to a solid bronze [E = 114 GPa] rod (2) at flange B, as shown. Aluminum rod (1) has an outside diameter of 36 mm and bronze rod (2) has an outside diameter of 17 mm. The normal stress in the aluminum rod must be limited to 124 MPa, and the normal stress in the bronze rod must be limited to 92 MPa. Assume L1 = 168 mm and L2 = 399 mm. Determine: (a) the maximum downward load P that may be applied at flange B. (Answer: P = 146kN)(b) the deflection vB (downward is positive) of flange B at the load determined in part(a). (Answer: vB = .322 mm)arrow_forwardA steel rod of 30 mm diameter is enclosed centrally in a hollow copper tube of external diameter 40 mm and 5 mm thick. The composite bar is then subjected to an axial pull of 45 kN. If the length of the compound rod is 150 mm , and the elasticity moduli are Est = 200 GPa and Ecu = 100 GPa , determine: 1.2.2 The load carried by the rod and that carried by the tubearrow_forward
- THe bracket shown is made of cold drawn steel with Sy=400MPa and Su=480 MPa, and is fastened to a beam made of the same material by five rivets that are made of a steel with Sy=300 MPa and Sut=365 MPa. The thickness of the bracket and the beam are 12 mm and 16 mm respectively.Diameters of the rivets are 20 mm. What safe load F(steady) can be supported by the riveted joint for a factor of safety of 2. Use distortion energy theory of failure.arrow_forwardA timber column, 8in. by 8in. in cross section is reinforced on all four sides by steel plates, each plate being 8in. wide and "t"in. thick. Determine the smallest value of "t" for which the column can support an axial load of 300 kips if the working stresses are 1200psi for timber and 20ksi for steel. The moduli of elasticity are 1.5x10^6psi for timber and 29x10^6psi foe steel -Draw and label the diagram correctly, No diagram in the solution will be marked wrong. -Shortcut solution will be marked wrong.- Direction of the assumption of the equilibrium equation must be shown, no direction will be marked wrong.arrow_forwardA steel [E=200 GPa] rod with a circular cross section is 10 m long. Determine the minimum diameter required if the rod must transmit a tensile force of 260 kN without exceeding an allowable stress of 240 MPa or stretching more than 10 mm.arrow_forward
- A timber column, 8 in. by 8 in. in cross section, is reinforced on all four sides by steel plates, each plate being 8 in. wide and t in. thick. Determine the smallest value of tfor which the column can support an axial load of 300 kips if the working stresses are 1200 psi for timber and 20 ksi for steel. The moduli of elasticity are 1.5 x106psi for timber and 29 x 106psi for steel.arrow_forwardThe five-bolt connection shown must support an applied load of P = 330 kN. If the average shear stress in the bolts must be limited to 295 MPa, determine the minimum bolt diameter that may be used in the connection.arrow_forwardAn axial load of 100 kN is applied to a flat bar 20 mm thick, tapering in width from 120 mm to 40 mm in a length 0f 10 m. Assuming E=200 GPa, determine the total elongation of the bar.arrow_forward
- 1. A lever ABC is pinned at C and attached to a 12-mm diameter control cable AD. a. If the allowable tensile stress in the control cable is 140 MPa, what is the maximum safe value of the load P applied as shown in the diagram? b. What is then the shearing stress developed in the 20-mm diameter pin support at C? c. What is the bearing stress between the pin and the 25-mm thick support plates at C?arrow_forwardA steel rod is subjected to a gradually applied load (F) which gave a rise to a maximum stress of 200 MPa. The rod is 250 mm long and one part of its length is square and the remainder is circular with a diameter of 25 mm. If the total strain energy in the rod and modulus elasticity of the material is 1.3 J and 200 GPa, determine the following:1.The applied load F2.The total extension of the bar3.The length of the square portion of the bar4.The suddenly applied load that will induce the same amount of energy 5.The load that falls from a height of 8 mm induces 1,3 J in the bar.arrow_forwardA 75 mm diameter compound bar is constructed by shrinking a circularbrass bush onto the outside of a 45 mm diameter solid steel rod. If thecompound bar is then subjected to an axial compressive load of 170 kN,determine the load carried by the steel rod. The modulus of elasticity for steel,Es = 200 GN/m2 , and brass, Eb = 100 GN/m2arrow_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 PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering 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 on Axial Loading Normal Stress in 10 MINUTES - Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=jQ-fNqZWrNg;License: Standard YouTube License, CC-BY