At a temperature of 60°F, a 0.05-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v=0.32; a = 12.5 x 106/°F] bar with a width of 2.7 in. and a thickness of 0.65 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 9.6 x 10-6/°F] bar with a width of 1.6 in. and a thickness of 0.65 in. The supports at A and Care rigid. Assume h₂=2.7 in., h₂=1.6 in., L₁=26 in., L₂=40 in., and A = 0.05 in. Determine (a) the lowest temperature at which the two bars contact each other. (b) the normal stress in the two bars at a temperature of 225°F. (c) the normal strain in the two bars at 225°F. (d) the change in width of the aluminum bar at a temperature of 225°F. L₁ h₂ BO Answer: Tcontact = h₂ Determine the lowest temperature, Tcontact at which the two bars contact each other. eTextbook and Media L₂ °F

At a temperature of 60°F, a 0.05-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v=0.32; a = 12.5 x 106/°F] bar with a width of 2.7 in. and a thickness of 0.65 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 9.6 x 10-6/°F] bar with a width of 1.6 in. and a thickness of 0.65 in. The supports at A and Care rigid. Assume h₂=2.7 in., h₂=1.6 in., L₁=26 in., L₂=40 in., and A = 0.05 in. Determine (a) the lowest temperature at which the two bars contact each other. (b) the normal stress in the two bars at a temperature of 225°F. (c) the normal strain in the two bars at 225°F. (d) the change in width of the aluminum bar at a temperature of 225°F. L₁ h₂ BO Answer: Tcontact = h₂ Determine the lowest temperature, Tcontact at which the two bars contact each other. eTextbook and Media L₂ °F

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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At a temperature of 60°F, a 0.05-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; α=α=12.5 x 10-6/°F] bar with a width of 2.9 in. and a thickness of 0.80 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; α=α=9.6 x 10-6/°F] bar with a width of 1.9 in. and a thickness of 0.80 in. The supports at A and C are rigid. Assume h1=2.9 in., h2=1.9 in., L1=28 in., L2=42 in., and Δ=Δ= 0.05 in. Determine(a) the lowest temperature at which the two bars contact each other.(b) the normal stress in the two bars at a temperature of 255°F.(c) the normal strain in the two bars at 255°F.(d) the change in width of the aluminum bar at a temperature of 255°F. Determine the lowest temperature, Tcontact, at which the two bars contact each other.
At a temperature of 60°F, a 0.03-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; α=α=12.5 x 10-6/°F] bar with a width of 3.0 in. and a thickness of 0.70 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; α=α=9.6 x 10-6/°F] bar with a width of 1.9 in. and a thickness of 0.70 in. The supports at A and C are rigid. Assume h1=3.0 in., h2=1.9 in., L1=27 in., L2=47 in., and Δ=Δ= 0.03 in. Determine(a) the lowest temperature at which the two bars contact each other.(b) the normal stress in the two bars at a temperature of 260°F.(c) the normal strain in the two bars at 260°F.(d) the change in width of the aluminum bar at a temperature of 260°F.
At a temperature of 60°F, a 0.03-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; α=α=12.5 x 10-6/°F] bar with a width of 3.0 in. and a thickness of 0.70 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; α=α=9.6 x 10-6/°F] bar with a width of 1.9 in. and a thickness of 0.70 in. The supports at A and C are rigid. Assume h1=3.0 in., h2=1.9 in., L1=27 in., L2=47 in., and Δ=Δ= 0.03 in. Determine:
At a temperature of "T" °F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; a = 13.9 x 10/°F] bar with a width of 3 inches and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; a = 8.4 x 10 /°F) bar with a width of 2 inches and a thickness of 0.75 in. The supports at A and C are rigid. Determine the lowest temperature at which the two bars contact each other. Answer in °F rounded-off to 2 decimal places. A (1) L T = 62 °F a = 34 inches b = 49 inches a 3 in. B 2 in. b 0.04-in. gap acer
A 16-mm-diameter steel [E= 200 GPa] rod (2) is connected to a 50-mm-wide by 8-mm-thick rectangular aluminum [E= 70 GPa] bar (1). Determine the force Prequired to stretch the assembly 3.00 mm.
An aluminum [E = 10,000 ksi] control rod with a circular cross section must not stretch more than 0.37 in. when the tension in the rod is 2000 lb. If the diameter of the rod is 0.372 in., determine the maximum length of the rod. 239.0 in. 127.7 in. O 144.5 in. O 188.9 in. O 201.1 in.
A copper [E = 104 GPa. a = 17.1x10-6/°C] rod (2) is placed within a steel [E = 208 GPa, a = 11.3x10-6/°C] tube (1) of the same length. The two components are connected at each end by pins that pass through both the tube and the rod. The outside diameter of the steel tube is D₁ = 88 mm, its inside diameter is d₁ = 69 mm, and its cross-sectional area is A₁ = 2343 mm². The diameter of the solid copper rod is d₂ = 45 mm, and its cross-sectional area is A₂ = 1591 mm². Calculate the normal stress in the copper rod if the temperature of the entire assembly is raised by 40°C. Pin Answer: 02- i Steel Tube (1) Pin MPa Copper Rod (2)
1.1 A 25 mm square cross-section bar of length 300 mm carries an axial compressive load of 50 kN. Determine the stress set up in the bar and its change of length when the load is applied. For the bar material E = 200 GN/m². [80 MN/m2; 0.12 mm] minn on axial
A steel [E = 30,100 ksi; a = 6.6 x 10-6/°F] pipe column (1) with a cross-sectional area of A₁ - 5.10 in.² is connected at flange B to an aluminum alloy [E - 10,900 ksi; a = 12.6 x 106/°F] pipe (2) with a cross-sectional area of Az -3.70 in.². The assembly (shown in the figure) is connected to rigid supports at A and C. It is initially unstressed at a temperature of 93°F. Assume L₁ - 104 in., L₂-132 in., P- 35 kips. (a) At what temperature will the normal stress in steel pipe (1) be reduced to zero? (b) Determine the normal stresses (positive if tensile, negative if compressive) in steel pipe (1) and aluminum pipe (2) when the temperature reaches -10°F. A Answers: (a) T- (b) G₁ = 0₂ = L₁ i i i B P L2 °F ksi ksi
X Your answer is incorrect. The axial assembly consists of a solid 1.01-in-diameter aluminum alloy [E - 8900 ksi, v- 0.33, a = 12.4x 10-6/°F] rod (1) and a solid 1.63-in-diameter bronze [E - 15400 ksi, v- 0.17,a = 7.3 x 10-6/°F] rod (2). Assume L;-15 in., L2-29 in. If the supports at A and Care rigid and the assembly is stress free at 6°F, determine: (a) the normal stresses o1,02 in both rods at 167°F (positive if tensile, negative if compressive). (b) the displacement ug of flange B (positive if to the right, negative to the left). (c) the change in diameter Ad, of the aluminum rod. B (1) L L2 Answers: (a) o 26.591 ksi, o2 = 10.209 ksi (b) ug - i 0.0418 in. (c) Adi in. 0.0003288
A copper [E = 102 GPa, a = 16.8x10-6/°C] rod (2) is placed within a steel [E = 204 GPa, a = 11.3x10-6/°C] tube (1) of the same length. The two components are connected at each end by pins that pass through both the tube and the rod. The outside diameter of the steel tube is D₁ = 101 mm, its inside diameter is d₁ = 78 mm, and its cross-sectional area is A₁ = 3234 mm². The diameter of the solid copper rod is d₂ = 55 mm, and its cross-sectional area is A₂ = 2376 mm². Calculate the normal stress in the copper rod if the temperature of the entire assembly is raised by 44°C. Pin Steel Tube (1) Pin Copper Rod (2)
A polymer cylinder (2) is clamped between rigid heads by two steel bolts (1). The steel [E - 29,000 ksi; a - 6.5x10-6/°F] bolts have a diameter of 0.45 in. The polymer [E - 370 ksi; a - 39.9x 10-6/°F] cylinder has an outside diameter of 6.2 in. and awall thickness of 0.35 in. Assume a - 27 in. and b - 35 in. If the temperature of this assembly changes by AT - 145°F, determine: (2) the normal stress in the polymer cylinder. (b) the normal strain in the polymer cylinder. (c) the normal strain in the steel bolts. (1) (2) (1) Answer: (a) 02 - psi. (b) E2 - (c) E1 - με