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Problem 2: Consider the two gears mounted on the shaft, as shown. Distances are L; = 100 mm, L; = 250 mm, and Ly = 175 mm. Diameter of shaft AB is 15 mm, diameter of shaft BC is 20 mm, and diameter of shaft CD is 17.5 mm. Young's modulus for each portion is 200 GPa. Determine the displacement of point D with reference to point A. Also, determine the displacement of point A relative to C. b. Determine the axial strain at any point in shaft segments AB, BC and CD, respectively. If Poisson's ratio for the material of the shafts is v = 0.2, determine the lateral strain in each of the shaft segments. "p Based on your answers to part (a), do the gears move towards each other, or do they separate from each other? Note that in real gearboxes, movement of gears towards or away from each other is prevented by using thrust bearings. 10 kN 4 kN 5 kN 7 kN 10 kN 4 kN

Problem 2: Consider the two gears mounted on the shaft, as shown. Distances are L; = 100 mm, L; = 250 mm, and Ly = 175 mm. Diameter of shaft AB is 15 mm, diameter of shaft BC is 20 mm, and diameter of shaft CD is 17.5 mm. Young's modulus for each portion is 200 GPa. Determine the displacement of point D with reference to point A. Also, determine the displacement of point A relative to C. b. Determine the axial strain at any point in shaft segments AB, BC and CD, respectively. If Poisson's ratio for the material of the shafts is v = 0.2, determine the lateral strain in each of the shaft segments. "p Based on your answers to part (a), do the gears move towards each other, or do they separate from each other? Note that in real gearboxes, movement of gears towards or away from each other is prevented by using thrust bearings. 10 kN 4 kN 5 kN 7 kN 10 kN 4 kN

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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**Problem 2:** Consider the two gears mounted on the shaft, as shown. - Distance \(L_1 = 300 \, \text{mm}, \, L_2 = 250 \, \text{mm}, \, L_3 = 175 \, \text{mm}\). - Diameter of shaft AB is \(20 \, \text{mm}\), and diameter of shaft CD is \(15 \, \text{mm}\). - Young's modulus for each portion is \(200 \, \text{GPa}\). **Tasks:** a. Determine the displacement of point A relative to point B and also determine the displacement of point A relative to C. b. Determine the axial strain at any point in shaft segments AB, BC, and CD respectively. c. Determine the lateral strain in each of the shaft segments. d. Poisson's ratio for the material of the shaft is \(\nu = 0.2\). The axial forces acting on the shaft are: - At point A: \(5 \, \text{kN}\) upwards - At point B: \(10 \, \text{kN}\) downwards - At point C: \(4 \, \text{kN}\) upwards - At point D: \(7 \, \text{kN}\) upwards These forces are distributed along the segments of the shaft with different diameters. Note that the axial movement of gears towards or away from each other is prevented by using thrust bearings. **Diagram Explanation:** The diagram shows a vertical shaft with forces acting along different segments. - **Segment AB**: The topmost section with forces acting upward at A and downward at B. - **Segment BC**: Middle section connected by gears. - **Segment CD**: Bottom section with a force acting upward at D. This setup is a typical problem in mechanical engineering to find displacements and strains in shaft segments under given forces.
Transcribed Image Text:**Problem 2:** Consider the two gears mounted on the shaft, as shown. - Distance \(L_1 = 300 \, \text{mm}, \, L_2 = 250 \, \text{mm}, \, L_3 = 175 \, \text{mm}\). - Diameter of shaft AB is \(20 \, \text{mm}\), and diameter of shaft CD is \(15 \, \text{mm}\). - Young's modulus for each portion is \(200 \, \text{GPa}\). **Tasks:** a. Determine the displacement of point A relative to point B and also determine the displacement of point A relative to C. b. Determine the axial strain at any point in shaft segments AB, BC, and CD respectively. c. Determine the lateral strain in each of the shaft segments. d. Poisson's ratio for the material of the shaft is \(\nu = 0.2\). The axial forces acting on the shaft are: - At point A: \(5 \, \text{kN}\) upwards - At point B: \(10 \, \text{kN}\) downwards - At point C: \(4 \, \text{kN}\) upwards - At point D: \(7 \, \text{kN}\) upwards These forces are distributed along the segments of the shaft with different diameters. Note that the axial movement of gears towards or away from each other is prevented by using thrust bearings. **Diagram Explanation:** The diagram shows a vertical shaft with forces acting along different segments. - **Segment AB**: The topmost section with forces acting upward at A and downward at B. - **Segment BC**: Middle section connected by gears. - **Segment CD**: Bottom section with a force acting upward at D. This setup is a typical problem in mechanical engineering to find displacements and strains in shaft segments under given forces.
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