Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 4.6, Problem 4.75P
The 40-ft-long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap δ so that the rails just touch one another when the temperature is increased from T1 = −20°F to T2 = 90°F. Using this gap, what would be the axial force in the rails if the temperature rises to T3 = 110°F? The cross-sectional area of each rail is 5.10 in2.
Prob. 4−75
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The 40-ft-long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap d so that the rails just touch one another when the temperature is increased from T1 = -20F to T2 = 90F. Using this gap, what would be the axial force in the rails if the temperature rises to T3 = 110F? The cross-sectional area of each rail is 5.10 in2.
The center rod CD of the assembly is heated from T₁ = 30 °C to T₂ = 165
°C using electrical resistance heating. At the lower temperature T₁ the gap
between C and the rigid bar is 0.7 mm. Rods AB and EF are made of
steel, and each has a cross-sectional area of 125 mm². CD is made of
aluminum and has a cross-sectional area of 375 mm². Est = 200 GPa,
Eal = 70 GPa, and cal = 23 (10-) /°C.
(Figure 1)
Figure
0.7 mm
240 mm
300 mm
Determine the force in the rod AB caused by the increase in temperature.
Express your answer to three significant figures and include the appropriate units.
FAB =
Submit
Part B
FEF=
_O
Submit
μA
Value
Request Answer
Determine the force in the rod EF caused by the increase in temperature.
Express your answer to three significant figures and include the appropriate units.
|μA
Value
Units
Request Answer
?
Units
?
The aluminum cube (600x600x600 mm) is put inside a hole of a rigid boundary as
shown below. Initially, there is a gap of 0.2 mm between the cube and the rigid
boundary. Determine the new dimensions of the cube if a stress of 100 MPa is applied
on the top face of the cube and the temperature of the cube increased by 35°C.
For aluminum: Ea=73 GPa, va-0.35, aai = 23*10C
y.
o=100 MPa
Rigid boundary
Rigid boundary
Aluminum
cube
600 mm-
0.2 mm
Chapter 4 Solutions
Mechanics of Materials (10th Edition)
Ch. 4.2 - In each case, determine the internal normal force...Ch. 4.2 - Determine the internal normal force between...Ch. 4.2 - The post weighs 8kN/m. Determine the internal...Ch. 4.2 - The rod is subjected to an external axial force of...Ch. 4.2 - The rigid beam supports the load of 60 kN....Ch. 4.2 - The 20-mm-diameter A-36 steel rod is subjected to...Ch. 4.2 - Segments AB and CD of the assembly are solid...Ch. 4.2 - The 30-mm-diameter A992 steel rod is subjected to...Ch. 4.2 - If the 20-mm-diameter rod is made of A-36 steel...Ch. 4.2 - The 20-mm-diameter 2014-T6 aluminum rod is...
Ch. 4.2 - The 20-mm-diameter 2014-T6 aluminum rod is...Ch. 4.2 - The A992 steel rod is subjected to the loading...Ch. 4.2 - The copper shaft is subjected to the axial loads...Ch. 4.2 - The composite shaft, consisting of aluminum,...Ch. 4.2 - The composite shaft, consisting of aluminum,...Ch. 4.2 - The 2014-T6 aluminium rod has a diameter of 30 mm...Ch. 4.2 - The A-36 steel drill shaft of an oil well extends...Ch. 4.2 - The truss is made of three A-36 steel members,...Ch. 4.2 - The truss is made of three A-36 steel members,...Ch. 4.2 - The assembly consists of two 10-mm diameter red...Ch. 4.2 - The assembly consists of two 10-mm diameter red...Ch. 4.2 - The load is supported by the four 304 stainless...Ch. 4.2 - The load is supported by the four 304 stainless...Ch. 4.2 - The rigid bar is supported by the pin-connected...Ch. 4.2 - The post is made of Douglas fir and has a diameter...Ch. 4.2 - The post is made of Douglas fir and has a diameter...Ch. 4.2 - The coupling rod is subjected to a force of 5 kip....Ch. 4.2 - The pipe is stuck in the ground so that when it is...Ch. 4.2 - The is made of three pin-connected A992 steel...Ch. 4.2 - The linkage is made of three pin connected A992...Ch. 4.2 - The assembly consists of three titanium...Ch. 4.2 - The rigid beam is supported at its ends by two...Ch. 4.2 - The rigid beam is supported at its ends by two...Ch. 4.2 - The steel bar has the original dimensions shown in...Ch. 4.2 - Determine the relative displacement of one end of...Ch. 4.2 - The assembly consists of two rigid bars that are...Ch. 4.2 - The truss consists of three members, each made...Ch. 4.2 - Solve Prob. 426 when the load P acts vertically...Ch. 4.2 - The observation cage C has a weight of 250 kip and...Ch. 4.2 - The steel bar has the original dimensions shown in...Ch. 4.2 - The ball is truncated at its ends and is used to...Ch. 4.5 - The column is constructed from high-strength...Ch. 4.5 - The column is constructed from high-strength...Ch. 4.5 - The A-36 steel pipe has a 6061-T6 aluminum core....Ch. 4.5 - If column AB is made from high strength precast...Ch. 4.5 - If column AB is made from high strength precast...Ch. 4.5 - Determine the support reactions at the rigid...Ch. 4.5 - If the supports at A and C are flexible and have a...Ch. 4.5 - The load of 2000 lb is to be supported by the two...Ch. 4.5 - The load of 2000 lb is to be supported by the two...Ch. 4.5 - The A-36 steel pipe has an outer radius of 20 mm...Ch. 4.5 - The 10-mm-diameter steel bolt is surrounded by a...Ch. 4.5 - The 10-mm-diameter steel bolt is surrounded by a...Ch. 4.5 - The assembly consists of two red brass C83400...Ch. 4.5 - The rigid beam is supported by the three suspender...Ch. 4.5 - The bolt AB has a diameter of 20 mm and passes...Ch. 4.5 - If the gap between C and the rigid wall at D is...Ch. 4.5 - The support consists of a solid red brass C83400...Ch. 4.5 - If there are n fibers, each having a...Ch. 4.5 - The rigid bar is pinned at A and supported by two...Ch. 4.5 - The rigid bar is pinned at A and supported by two...Ch. 4.5 - The rigid bar is pinned at A and supported by two...Ch. 4.5 - The rigid bar is pinned at A and supported by two...Ch. 4.5 - The 2014-T6 aluminum rod AC is reinforced with the...Ch. 4.5 - The 2014-T6 aluminum rod AC is reinforced with the...Ch. 4.5 - The three suspender bars are made of A992 steel...Ch. 4.5 - The three A-36 steel wires each have a diameter of...Ch. 4.5 - The A-36 steel wires AB and AD each have a...Ch. 4.5 - The post is made from 6061-T6 aluminum and has a...Ch. 4.5 - The post is made from 6061-T6 aluminum and has a...Ch. 4.5 - The bracket is held to the wall using three A-36...Ch. 4.5 - The bracket is held to the wall using three A-36...Ch. 4.5 - If each of the posts has an unloaded length of 1 m...Ch. 4.5 - The rigid bar is supported by the two short white...Ch. 4.5 - The assembly consists of two posts AB and CD each...Ch. 4.5 - The assembly consists of two posts AB and CD each...Ch. 4.5 - The assembly consists of two posts AB and CD each...Ch. 4.5 - The wheel is subjected to a force of 18 kN from...Ch. 4.6 - The C83400-red-brass rod AB and 2014-T6- aluminum...Ch. 4.6 - The assembly has the diameters and material...Ch. 4.6 - The rod is made of A992 steel and has a diameter...Ch. 4.6 - The two cylindrical rod segments are fixed to the...Ch. 4.6 - The two cylindrical rod segments are fixed to the...Ch. 4.6 - The pipe is made of A992 steel and is connected to...Ch. 4.6 - The bronze C86100 pipe has an inner radius of 0.5...Ch. 4.6 - The 40-ft-long A-36 steel rails on a train track...Ch. 4.6 - The device is used to measure a change in...Ch. 4.6 - The bar has a cross-sectional area A, length L,...Ch. 4.6 - When the temperature is at 30C, the A-36 steel...Ch. 4.6 - When the temperature is at 30C, the A-36 steel...Ch. 4.6 - When the temperature is at 30C, the A-36 steel...Ch. 4.6 - The 50-mm-diameter cylinder is made from Am...Ch. 4.6 - The 50-mm-diameter cylinder is made from Am...Ch. 4.6 - The wires AB and AC are made of steel, and wire AD...Ch. 4.6 - The cylinder CD of the assembly is heated from T1...Ch. 4.6 - The cylinder CD of the assembly is heated from T1=...Ch. 4.6 - The metal strap has a thickness t and width w and...Ch. 4.9 - Determine the maximum normal stress developed in...Ch. 4.9 - If the allowable normal stress for the bar is...Ch. 4.9 - The steel bar has the dimensions shown. Determine...Ch. 4.9 - The A-36 steel plate has a thickness of 12 mm. If...Ch. 4.9 - Determine the maximum axial force P that can be...Ch. 4.9 - Determine the maximum normal stress developed in...Ch. 4.9 - The member is to be made from a steel plate that...Ch. 4.9 - The resulting stress distribution along section AB...Ch. 4.9 - The resulting stress distribution along section AB...Ch. 4.9 - Prob. 4.96PCh. 4.9 - The weight is suspended from steel and aluminum...Ch. 4.9 - The bar has a cross-sectional area of 0.5 in2 and...Ch. 4.9 - The distributed loading is applied to the rigid...Ch. 4.9 - The distributed loading is applied to the rigid...Ch. 4.9 - The rigid lever arm is supported by two A-36 steel...Ch. 4.9 - The rigid lever arm is supported by two A-36 steel...Ch. 4.9 - The 300-kip weight is slowly set on the top of a...Ch. 4.9 - The rigid beam is supported by three 25-mm...Ch. 4.9 - The rigid beam is supported by three 25-mm...Ch. 4.9 - The rigid beam is supported by the three posts A,...Ch. 4.9 - The rigid beam is supported by the three posts A,...Ch. 4.9 - The bar having a diameter of 2 in. is fixed...Ch. 4.9 - Determine the elongation of the bar in Prob.4108...Ch. 4.9 - The rigid beam is supported by three A-36 steel...Ch. 4 - The assembly consists of two A992 steel bolts AB...Ch. 4 - The assembly shown consists of two A992 steel...Ch. 4 - The rods each have the same 25-mm diameter and...Ch. 4 - Two A992 steel pipes, each having a...Ch. 4 - The force P is applied to the bar, which is made...Ch. 4 - The 2014-T6 aluminum rod has a diameter of 0.5 in....Ch. 4 - The 2014-T6 aluminum rod has a diameter of 0.5 in....Ch. 4 - The rigid link is supported by a pin at A and two...Ch. 4 - The joint is made from three A992 steel plates...
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
- Two rods are horizontally fixed to the rigid walls so that there is a gap of 0.008 inch between them when the temperature is 60°F. The following are the properties of the rods: Property Rod 1 Rod 2 Diameter 1.25 inches 1.25 in Length 3.5 inches 7.5 inches Thermal Coefficient of 9.4 x10-6 /OF 13 x10-6 /°F Expansion Modulus of Elasticity 10 x 103 ksi 18 x 103 ksi a. What is the average stress in the rods if the temperature is increased to 240°F. b. What is the total deformation of the first rod?arrow_forwardA thermo gate consist of an aluminum plate AB and a magnesium plate CD, each having a width of 15.2mm and fixed supported at their ends as shown in Figure Q2. If the gap between them is 1.5 mm when temperature is T1=25.3C (a) Determine the temperature, T2 required to just close the gap. (b) Determine the axial force in each plate when the temperature T2 becomes 100°C. 10 mm 10 mm в с D 600 mm 400 mmarrow_forward3. Three bars each made of different materials are connected together and placed between two walls when the temperature is T₁ = 12 degrees Celsius. Determine the force exerted on the rigid supports when the temperature becomes T₂ = 70 degrees Celsius. The material properties and cross-sections are given in the figure. Steel Est = 200 GPa Cst = 12(10-6)/°C Ast = 200 mm2 300 mm Brass Ebr = 100 GPa abr=21(106)/°C Abr = 450 mm² Copper Ecu = 120 GPa acu = 17(10-6)/°C 515 mm² Acu 200 mm- 100 mmarrow_forward
- The bar has a cross-sectional area A, length L, modulus of elasticity E, and coefficient of thermal expansion a. The temperature of the bar changes uniformly along its length from TA at A to TB at B so that at any point x alongthe bar T = TA + x(TB - TA)>L. Determine the force the bar exerts on the rigid walls. Initially, no axial force is in the bar and the bar has a temperature of TA.arrow_forwardThe steel bar AB has a x-in.square cross section and is held by pins that are a fixed distance apart and are located at a distance e = 0.034 in. from the geometric axis of the bar. Determine the required distance d for which the bar will just make contact with point C when the temperature increases by 120°F. Use E= 29 × 106 psi and a coefficient of thermal expansion a = 6.5 × 10-6/°F. Use a simple approximation by ignoring the eccentricity during the thermal part of your calculation. (Round the final answer to four decimal places.) in.- B The distance dis 4 in. 4 in. in.arrow_forwardA steel rod 3 ft long with a cross-sectional area of 0.3 in2 is stretched between two fixed points. The tensile force in the rod is 1200 lb at 40°F. Using α = 6.5 x 10-6/°F and E = 29 x 106 psi, calculate the temperature (in °F) at which the stress in the rod will be zero.arrow_forward
- The 58-mm-diameter cylinder is made from Am 1004-T61 magnesium and is placed the clamp when the temperature is T₁ = 20°C. (Figure 1) Figure 100 mm 150 mm Part A If the 304-stainless-steel carriage bolts of the clamp each have a diameter of 9 mm, and they hold the cylinder snug with negligible force against the rigid jaws, determine the force in the cylinder when the temperature rises to T₂ = 130°C. Express your answer to three significant figures and include the appropriate units. F = 2.37 Submit μÀ ^ Provide Feedback KN WX Previous Answers Request Answer ? X Incorrect; Try Again; 3 attempts remaining Next >arrow_forwardThe steel rails of a railroad track are laid in the winter at a temperature of 15 degrees fahrenheit with gaps of 0.01 feet between the ends of the rails. Each rail is 33 feet long. At what temperature will the rails touch end to end? What stress will result in the rails if the temperature rises to 110 degrees fahrenheit? Answer: 9,434.1 psi. I'm not sure how to come up with this answer. Could you help me work this problem out step by step please?arrow_forwardThe wires AB and AC are made of steel, and wire AD is made of copper. Before the 150-lb force is applied, AB and AC are each 60 in. long and AD is 40 in. long. If the temperature is increased by 80F, determine the force in each wire needed to support the load. Each wire has a cross-sectionalarea of 0.0123 in2. Take Est = 29(10 3) ksi, Ecu = 17(10 3) ksi, fast = 8(10 6)>F, acu = 9.60(10 -6)>F.arrow_forward
- At room temperature (20°C), a 0.5-mm gap exists between the ends of the rods shown. The temperature eventually reaches a value of 140°C. Determine the normal stress in the aluminum rod. Determine the change in length of the aluminum rod.arrow_forwardThe three rods are made of A-36 steel and form a pin-connected truss as shown. The assembly is stress- free at 50 °F. Determine the force in each bar when the temperature of the assembly is increased to 110 °F. The cross-sectional area of each bar is 2.5 in². 5 ft 4 ft D 5 ft 3 ft 3ftarrow_forwardThe assembly shown constructed from a steel bolt with a diameter of 8 mm and fits and a magnesium sleeve with an inner diameter of 10 mm and an outer diameter of 12 mm. The length of the sleeve is 150 mm. The assembly is originally at a temperature of T1 = 20°C and then the temperature is raised to a final value of T2 = 120°C. If there is gap of 0.1 mm between sleeve and the rigid washer at end B before the heating, determine the average normal stress in the bolt and the sleeve. Est = 200 GPa, Emg = 44.7 GPa, ɑst = 14(106)/°C, ɑmg = 26(106)/°C. Rigid washers A B 150 mm 0,1 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 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
Understanding Conduction and the Heat Equation; Author: The Efficient Engineer;https://www.youtube.com/watch?v=6jQsLAqrZGQ;License: Standard youtube license