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A rectangular brass bar of 120 mm length with a cross sectional area of 200 mm² is rigidly bonded along a side face to a similar steel bar of the same length and cross-sectional area of 100 mm? to form a compounded bar of length 120 mm. This bar is then subjected to an axial compressive load of P kN whereupon the temperature is changed by an amount t °C until the brass bar carries no load. If the overall change in length of the compound bar is 0.22 mm, calculate the temperature change t and the magnitude of P (EsT = 200 GPa; Egr = 80 GPa; asr = 12 × 10-6 /°C; aBr = 18 × 10-6 /°C)

A rectangular brass bar of 120 mm length with a cross sectional area of 200 mm² is rigidly bonded along a side face to a similar steel bar of the same length and cross-sectional area of 100 mm? to form a compounded bar of length 120 mm. This bar is then subjected to an axial compressive load of P kN whereupon the temperature is changed by an amount t °C until the brass bar carries no load. If the overall change in length of the compound bar is 0.22 mm, calculate the temperature change t and the magnitude of P (EsT = 200 GPa; Egr = 80 GPa; asr = 12 × 10-6 /°C; aBr = 18 × 10-6 /°C)

Elements Of Electromagnetics
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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52% 17:50 Question 1 A rectangular brass bar of 120 mm length with a cross sectional area of 200 mm? is rigidly bonded along a side face to a similar steel bar of the same length and cross-sectional area of 100 mm? to form a compounded bar of length 120 mm. This bar is then subjected to an axial compressive load of P kN whereupon the temperature is changed by an amount t °C until the brass bar carries no load. the overall change in length of the compound bar is 0.22 mm, calculate the temperature change t and the magnitude of P (EST = 200 GPa; EBr = 80 GPa; asT = 12 x 10-6 /°C; aBR = 18 x 10-6 /°C) [10] Question 2 A round steel bar, 20 mm in diameter and 400 mm long, is placed concentrically within a brass tube which has an outside diameter of 30 mm and thickness 4 mm, also 400 mm long. The upper end of the vertically placed compound bar is rigidly fixed and a collar is fitted to the bottom end. The application of a load P results in the compound rod storing a total of 5 J of energy. Calculate a. The gradually applied load b. The suddenly applied load c. The impact load that falls 100 mm and induces 5 J of energy d. The instantaneous stresses in both materials (5) (5) (5) (5) e. The instantaneous elongation of the compound rod. (5) (EST = 200 GPa; EgR = 100 GPa) [25] Question 3 The built-up beam of box section shown in Figure 1 is simply supported over a span of 3 m and carries a point load of 15 kN at 1m from the end. The plate is attached to the channel sections by rivets pitched at 100 mm intervals. If the shear stress in the rivets must not exceed 50 MPa, determine a suitable rivet diameter. All dimensions are in mm. 150 [25] 10 150 10 I10 130 Figure 1 16 SOM3601/101/0/2021 Question 4 Two 127 mm x 64 mm steel channel sections are placed back with their backs a distance of 2d apart. If two 200 mm x 15 mm steel plates are welded to the flanges of the channels as shown in Figure 2, calculate the value of d if ly = ly, for the built-up section, as well Iy. 2d 200
Transcribed Image Text:52% 17:50 Question 1 A rectangular brass bar of 120 mm length with a cross sectional area of 200 mm? is rigidly bonded along a side face to a similar steel bar of the same length and cross-sectional area of 100 mm? to form a compounded bar of length 120 mm. This bar is then subjected to an axial compressive load of P kN whereupon the temperature is changed by an amount t °C until the brass bar carries no load. the overall change in length of the compound bar is 0.22 mm, calculate the temperature change t and the magnitude of P (EST = 200 GPa; EBr = 80 GPa; asT = 12 x 10-6 /°C; aBR = 18 x 10-6 /°C) [10] Question 2 A round steel bar, 20 mm in diameter and 400 mm long, is placed concentrically within a brass tube which has an outside diameter of 30 mm and thickness 4 mm, also 400 mm long. The upper end of the vertically placed compound bar is rigidly fixed and a collar is fitted to the bottom end. The application of a load P results in the compound rod storing a total of 5 J of energy. Calculate a. The gradually applied load b. The suddenly applied load c. The impact load that falls 100 mm and induces 5 J of energy d. The instantaneous stresses in both materials (5) (5) (5) (5) e. The instantaneous elongation of the compound rod. (5) (EST = 200 GPa; EgR = 100 GPa) [25] Question 3 The built-up beam of box section shown in Figure 1 is simply supported over a span of 3 m and carries a point load of 15 kN at 1m from the end. The plate is attached to the channel sections by rivets pitched at 100 mm intervals. If the shear stress in the rivets must not exceed 50 MPa, determine a suitable rivet diameter. All dimensions are in mm. 150 [25] 10 150 10 I10 130 Figure 1 16 SOM3601/101/0/2021 Question 4 Two 127 mm x 64 mm steel channel sections are placed back with their backs a distance of 2d apart. If two 200 mm x 15 mm steel plates are welded to the flanges of the channels as shown in Figure 2, calculate the value of d if ly = ly, for the built-up section, as well Iy. 2d 200
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