A steel [E = 30,300 ksi; a = 6.7 x 106/°F] pipe column (1) with a cross-sectional area of A₁ = 5.70 in.² is connected at flange B to analuminum alloy [E = 10,100 ksi; a = 12.7 x 10-6/°F] pipe (2) with a cross-sectional area of A₂ = 4.30 in.². The assembly (shown in thefigure) is connected to rigid supports at A and C. It is initially unstressed at a temperature of 90°F. Assume L₁ = 126 in., L₂ = 156 in., P =34 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 thetemperature reaches -11°F.AAnswers:(a) T=(b) σ₁ =0₂ =L₁teliL2°Fksiksi

Answered: Image /qna-images/answer/f1d9bb61-9406-4e97-a189-dead3af4a7ea.jpg

Answered: A steel [E = 30,300ksi; a = 6.7 x…

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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A steel [E = 29,200 ksi; a = 6.5 x 10-6/°F] pipe column (1) with a cross-sectional area of A₁ = 5.20 in.² is connected at flange B to an aluminum alloy [E = 10,600 ksi; a = 13.0 × 106/°F] pipe (2) with a cross-sectional area of A2 = 4.20 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 91°F. Assume L₁ = 101 in., L₂ = 114 in., P = 23 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 -18°F. A Answers: (a) T= (b) 01 = (1) L₁ i i B P L2 °F ksi
A steel [E = 30,100 ksi; a = 6.3 x 10-6/°F] pipe column (1) with a cross-sectional area of A₁ = 5.80 in.² is connected at flange B to an aluminum alloy [E = 10,700 ksi; a = 13.1 x 10-6/°F] pipe (2) with a cross-sectional area of A₂ = 3.50 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 92°F. Assume L₁ = 115 in., L₂ = 149 in., P = 22 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 -11°F. A (1) L₁ B P P L2 с
An aluminum alloy [E = 8400 ksi] pipe with a cross-sectional area of A₁ = 4.20 in.² is connected at flange B to a steel [E = 23800 ksi] pipe with a cross-sectional area of A₂ = 2.96 in.². The assembly is connected to rigid supports at A and C. Assume L₁= 154 in., L₂= 200 in., and P = 56 kips. For the loading shown, determine: (a) the normal stresses in aluminum pipe (1) and steel pipe (2) (₁, ₂ use positive if tensile, negative if compressive). (b) the deflection ug (use positive if it moves to the right and negative if it moves to the left) of flange B. Answers: (a) 6₁ (b) ug = (1) L₁ Save for Later B eTextbook and Media L2 ksi, 0₂ = i in. ksi, Attempts: 0 of 5 used Submit Answer
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)
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
An aluminum alloy [E = 10,000 ksi; oy= 40 ksi] pipe (1) is connected to a bronze [E = 16,000 ksi; Oy= 45 ksi] pipe at flange B. The pipes are attached to rigid supports at A and C. Pipe (1) has an outside diameter of 2.475 in., a wall thickness of 0.19 in., and a length of L1 = 10 ft. Pipe (2) has an outside diameter of 4.60 in., a wall thickness of 0.18 in., and a length of L2 = 17 ft. If a minimum factor of safety of 1.8 is required for each pipe, determine: (a) the maximum load P that may be applied at flange B. (b) the deflection of flange Bat the load determined in part (a). Deflection to the right is positive. (1) B L2 Answer: (a) P = i 34.1 kips (b) uB = i .319 in.
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)
An aluminum alloy [E = 10,000 ksi; oy = 40 ksi] pipe (1) is connected to a bronze [E = 16,000 ksi; ay = 45 ksi] pipe at flange B. The pipes are attached to rigid supports at A and C. Pipe (1) has an outside diameter of 2.425 in., a wall thickness of 0.21 in., and a length of L₁ = 8 ft. Pipe (2) has an outside diameter of 5.00 in., a wall thickness of 0.20 in., and a length of L₂ = 14 ft. If a minimum factor of safety of 2.1 is required for each pipe, determine: (a) the maximum load P that may be applied at flange B. (b) the deflection of flange B at the load determined in part (a). Deflection to the right is positive. (2) (1) C Answer: (a) P = i (b) Ug = i P< L₁ B L₂ ! kips in.
Rigid bar ABC is supported by two identical solid bronze [σy=331 MPa; E = 105GPa; α= 22.0 x 10-6/ °C] rods and a single solid steel [σy=250 MPa; E=200GPa; α=11.7x10-6/°C] rod. Bronze rods (1) each have diameter d1=25 mm and L1=3.0 m. Steel rod (2) had lenght L2=4.0 m. a) Calculate the Diameter d2 required for steel rod (2) so that the deflection of joint B is zero for any change in temperature. b) Using the value of d2 determined in part (a), determine temperatur decrease that is allowable for this assembly if a factor of sfety of 2.0 is specified for the normal stress in each rod.
An aluminum alloy [E = 10,000 ksi; ay = 40 ksi] pipe (1) is connected to a bronze [E = 16,000 ksi; oy = 45 ksi] pipe at flange B. The pipes are attached to rigid supports at A and C. Pipe (1) has an outside diameter of 2.550 in., a wall thickness of 0.22 in., and a length of L₁ = 6 ft. Pipe (2) has an outside diameter of 4.35 in., a wall thickness of 0.24 in., and a length of L₂ = 10 ft. If a minimum factor of safety of 1.9 is required for each pipe, determine: (a) the maximum load P that may be applied at flange B. (b) the deflection of flange B at the load determined in part (a). Deflection to the right is positive. (1) (2) C Answer: (a) P= i (b) Ug = i P L₁ B L2 kips in.
The axial assembly consists of a solid 1-in.-diameter aluminum alloy [E = 11000 ksi, v = 0.26, α= 10.5 × 10−6/°F] rod (1) and a solid 1.49-in.-diameter bronze [E = 15300 ksi, v = 0.15, α= 7.6 × 10–6/°F] rod (2). Assume L1=11 in., L2=22 in. If the supports at A and C are rigid and the assembly is stress free at 16°F, determine:(a) the normal stresses σ1, σ2 in both rods at 213°F (positive if tensile, negative if compressive).(b) the displacement uB of flange B (positive if to the right, negative to the left).(c) the change in diameter Δd1 of the aluminum rod.
A copper [E = 96 GPa, a = 17.5x10-6/°C] rod (2) is placed within a steel [E = 192 GPa, a = 11.5×10- 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 = 92 mm, its inside diameter is d₁ = 77 mm, and its cross- sectional area is A₁ = 1991 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 48°C. Pin Steel Tube (1) Pin Copper Rod (2)

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