Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 4.6, Problem 4.77P
The bar has a cross-sectional area A, length L, modulus of elasticity E, and coefficient of thermal expansion α. The temperature of the bar changes uniformly along its length from TA at A to TB at B so that at any point x along the 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
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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.
The central bar CD of the assembly is heated from 30 ° C to 180 ° C by means of an electrical resistance. Also the two bars AB and EF are heated from 30 ° C to 50 ° C. At the lower temperature of 30 ° C, the space between C and the rigid bar is 0.7 mm.
Determine the force in bars AB and EF caused by the increase in temperature. Bars AB and EF are made of steel and each has a cross-sectional area of 125 mm ^ 2; CD is aluminum with a cross-sectional area of 375 mm ^ 2. Steel = 200GP; Ealuminum = 70 GPa; alpha steel = 12 X10 ^ -6 (1 / ºC); alpha aluminum = 23 X10 ^ -6 (1 / ° C).
The wires AB and AC are made of steel, and wire AD is made of aluminum. Before the
300 kN force is applied, AB and AC are each 150 mm. long and AD is 100 mm. long. If the
temperature is increased by 30°C, determine the force in each wire needed to support the load.
Take Est =
200 GPa, Eal
= 70 GPa, st =
12 (10") / °C, aal = 23 (10") / °C. Each wire has a
cross-sectional area of 0.02 mm².
B
100 mm
45° 45°
150 mm
150 mm
A
300 kN
Chapter 4 Solutions
Mechanics of Materials
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 - Prob. 4.1PCh. 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 - 4-5. The assembly consists of a steel rod CB and...Ch. 4.2 - 4-6. The bar has a cross-sectional area of 3 in2,...Ch. 4.2 - 4–7. If P1 = 50 kip and P2 = 150 kip, determine...Ch. 4.2 - *4-8. If the vertical displacements of end A of...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 - Prob. 4.14PCh. 4.2 - Prob. 4.15PCh. 4.2 - *4-16. The hanger consists of three 2014-T6...Ch. 4.2 - 4-17. The hanger consists of three 2014-T6...Ch. 4.2 - Prob. 4.18PCh. 4.2 - Prob. 4.19PCh. 4.2 - The assembly consists of three titanium...Ch. 4.2 - Prob. 4.21PCh. 4.2 - Prob. 4.22PCh. 4.2 - Prob. 4.23PCh. 4.2 - Determine the relative displacement of one end of...Ch. 4.2 - Prob. 4.25PCh. 4.2 - Prob. 4.26PCh. 4.2 - 4-27. The circular bar has a variable radius of r...Ch. 4.2 - Prob. 4.28PCh. 4.2 - Prob. 4.29PCh. 4.2 - Prob. 4.30PCh. 4.5 - 4-31. The concrete column is reinforced using four...Ch. 4.5 - Prob. 4.32PCh. 4.5 - 4-33. The steel pipe is filled with concrete and...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 - Prob. 4.38PCh. 4.5 - Prob. 4.39PCh. 4.5 - Prob. 4.40PCh. 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 assembly consists of two red brass C83400...Ch. 4.5 - *4-44. The assembly consists of two red brass...Ch. 4.5 - Prob. 4.45PCh. 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 - Prob. 4.49PCh. 4.5 - Prob. 4.50PCh. 4.5 - Prob. 4.51PCh. 4.5 - Prob. 4.52PCh. 4.5 - 4-53. Each of the three A-36 steel wires has the...Ch. 4.5 - 4-54. The 200-kg load is suspended from three A-36...Ch. 4.5 - The three suspender bars are made of A992 steel...Ch. 4.5 - Prob. 4.56PCh. 4.5 - 4-57. The rigid bar is originally horizontal and...Ch. 4.5 - Prob. 4.58PCh. 4.5 - 4-59. Two identical rods AB and CD each have a...Ch. 4.5 - *4-60. The assembly consists of two posts AD and...Ch. 4.5 - Prob. 4.61PCh. 4.5 - Prob. 4.62PCh. 4.5 - Prob. 4.63PCh. 4.5 - Prob. 4.64PCh. 4.5 - 4-65. Initially the A-36 bolt shank fits snugly...Ch. 4.5 - Prob. 4.66PCh. 4.5 - Prob. 4.67PCh. 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 - Prob. 4.71PCh. 4.6 - Prob. 4.72PCh. 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 - 4-90. Determine the maximum axial force P that can...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 - Prob. 4.93PCh. 4.9 - 4-94. The resulting stress distribution along...Ch. 4.9 - Prob. 4.95PCh. 4.9 - *4-96. The 10-mm-diameter shank of the steel bolt...Ch. 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 - Prob. 4.99PCh. 4.9 - *4-100. The rigid beam is supported by a pin at A...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 - Prob. 4.103PCh. 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 - Prob. 4.106PCh. 4.9 - Prob. 4.107PCh. 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 - Prob. 4.110PCh. 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 - Prob. 4.113PCh. 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
- 4-69. Three bars each made of different materials are connected together and placed between two walls when the temperature is T₁ = 12°C. Determine the force exerted on the (rigid) supports when the temperature becomes T₂ = 18°C. The material properties and cross-sectional area of each bar are given in the figure. Steel Brass dEst = 200 GPa Ebr = 100 GPa bast=12(10-6)/°C abr 21(106)/C α = = Aut= 200 mm² Abr = 450 mm² pha2kn 300 mm- 4kn -200 mm- Prob. 4-69 Copper Ecu = 120 GPa-44 17(10-6)/°C Acu = 515 mm² 100 mmarrow_forwardThe metal strap has a thickness t and width w and is subjected to a temperature gradient T1 to T2 (T1 6 T2). This causes the modulus of elasticity for the material to vary linearly from E1 at the top to a smaller amount E2 at the bottom. As a result, for any vertical position y, measured from the top surface, E = [(E2 - E1)>w]y + E1. Determine the position d where the axial force P must be applied so that the bar stretches uniformly over its cross-section. warrow_forwardThe rod is made of A-36 steel and has a diameter of 0.25in. If the rod is 4ft long when the springs are compressed 0.5in and the temperature of the rod is T=40°F, determine the force in the rod when its temperature is T=160°F. k= 1000 lb/in. ww 4 ft k = 1000 lb/in. WWarrow_forward
- A steel bar 300 mm long, 50 mm wide and 40 mm thick is subjected to a pull of 300 kN in the direction of length. Determine the change in volume. Take E = 2x105 N/mm2and μ= 0.25.arrow_forwardThe 50-mm-diameter piston of the shown pneumatic cylinder retracts 130 mm from its present position (p1 = 2 bars gage, V1 = 300 cm3) due to the external load on the rod. If the port at the blank end of the cylinders is blocked, find the new pressure, assuming the temperature does not change.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 80 F, 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
- 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 ?arrow_forwardThe 40ft long A-36 steel rails on a train track are laid with a small gap between them to allow for the thermal expansion. Determine the required gap & 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 were to rise to T3=110°F? The cross-sectional area of each rail is 5.10 in²arrow_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
- 3. The rigid bar ABC and EFG are supported by pins at A and G. The vertical rods are made of steel (rod DC and rod BE). Determine the vertical displacement at C if the change in temperature is 50°C. Use a = 0.0000117/°C and E = 200 GPa. Neglect the weight of the members. A=125 sq. mm L= 2 m A 2 m B 2 m A=135 sq. mm L = 3 m E G 2 m F 3 m 50 kNarrow_forwardThere is a gap c = 1mm between the rods in the picture, the temperature changes evenly quantitatively ΔT = 1.9°C. Calculate the normal force on the cross section of the rods. E1 = 200 GPa, L = 1.0 m, E2 = 80 GPa, A1 = 5000 mm2, A2 = 2000 mm2, α1 = 12*10-61/°C, α2 = 8*10-61/°Carrow_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_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 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