A copper [E = 102 GPa, a = 17.1x10-6/°C] rod (2) is placed within a steel [E = 204 GPa, a = 11.6x10-6/°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 = 63 mm, and its cross-sectional area is A₁ = 2965 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 copper [E = 102 GPa, a = 17.1x10-6/°C] rod (2) is placed within a steel [E = 204 GPa, a = 11.6x10-6/°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 = 63 mm, and its cross-sectional area is A₁ = 2965 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)

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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Q1: 30-mm-diameter steel bar is to be used as a torsion spring. If the torsional stress in the bar is not to exceed 110 MPa when one end is twisted through an angle of 30°, what must be the length of the bar in m? modulus of rigidity=80 GPa . (close to two decimal)
A load P is supported by a structure consisting of rigid bar ABC, two identical solid bronze [E = 12600 ksi] rods, and a solid steel [E = 32100 ksi] rod, as shown. The bronze rods (1) each have a diameter of 0.61 in. and they are symmetrically positioned relative to the center rod (2) and the applied load P. Steel rod (2) has a diameter of 0.42 in. Assume L₁-53 in and L₂=73 in. If all bars are unstressed before the load P is applied, determine the normal stresses in bronze rods (1) and steel rod (2) after a load of P = 21 kips is applied. Answers: 0₁ = i 02 = i L₂ (2) B ksi. ksi.
Rigid bar ABCD is loaded and supported. Bars (1) and (2) are unstressed before the load P is applied. Bar (1) is made of bronze [E= 100 GPa] and has a cross-sectional area of 400 mm2. Bar (2) is made of aluminum [E= 70 GPa] and has a cross-sectional area of 600 mm2. After the load P is applied, the force in bar (1) is found to be 60 kN (in compression). Determine: (a) the stresses in bars (1) and (2).(b) the vertical deflection of point A.(c) the load P.
QUESTION 01 320 mm 470 mm 42 mm 54 mm B T= 2.2 kN.m Aluminium Steel Figure Q1/ Rajah S1 The solid aluminium cylinder AB and solid steel cylinder BC are bonded (welded) together at B and are attached to fixed supports at A and C as shown in Figure Q1. The assemble is subjected to torque, T = 2.2 kN.m at B. Knowing that the modulus of rigidity of aluminium and steel are 24 GPa and 80 GPa respectively, determine: (a) Is this problem statically determinate or statically indeterminate? Justify your answer. (b) The internal torque develops in the aluminium cylinder AB and steel cylinder BC. (c) The maximum shear stress for cylinder AB and BC (d) The angle of twist at B Fixed Support Fixed Support
A load P is supported by a structure consisting of rigid bar ABC, two identical solid bronze [E = 17200 ksi] rods, and a solid steel [E = 31400 ksi] rod, as shown. The bronze rods (1) each have a diameter of 0.69 in. and they are symmetrically positioned relative to the center rod (2) and the applied load P. Steel rod (2) has a diameter of 0.53 in. Assume L₁=45 in and L₂=67 in. If all bars are unstressed before the load P is applied, determine the normal stresses in bronze rods (1) and steel rod (2) after a load of P = 16 kips is applied. (1) Answers: 01 02 = i i L2 (2) Save for Later B P eTextbook and Media (1) ksi. ksi. L₁ Attempts: 0 of 5 used Submit Answer
Rigid bar ABC is supported by two aluminum alloy (E = 10,000 ksi) rods as shown below. The horizontal distance between rods (1) and (2) is a = 150 in. Rod (1) has a length of L₁ = 99 in. and a cross-sectional area of A₁ = 0.55 in.². Rod (2) has a length of L₂ = 96 in. and a cross-sectional area of A₂ = 0.95 in.². Rigid bar ABC is to remain horizontal under a load of P = 35 kips. Determine the distance x from joint A to the location of load P so that bar ABC remains horizontal. L Answer: X= i (1) eTextbook and Media Save for Later x in. B (2) L2 Attempts: 0 of 5 used Submit Answer
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 an aluminum 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 the figure) 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 the temperature reaches -11°F. A Answers: (a) T= (b) σ₁ = 0₂ = L₁ tel i L2 °F ksi ksi
A load P is supported by a structure consisting of rigid bar ABC, two identical solid bronze [E = 14100 ksi] rods, and a solid steel [E = 28000 ksi] rod, as shown. The bronze rods (1) each have a diameter of 0.61 in. and they are symmetrically positioned relative to the center rod (2) and the applied load P. Steel rod (2) has a diameter of 0.47 in. Assume L₁-39 in and L2-72 in. If all bars are unstressed before the load P is applied, determine the normal stresses in bronze rods (1) and steel rod (2) after a load of P = 29 kips is applied. O (1) A Answers: 0₁ = i 0₂ = i L2 (2) B P ksi. ksi. L