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A hydraulic cylinder with a bore radius of 100 mm and an outer radius of 200 mm has been designed to withstand a maximum internal pressure of 200 MPa in service. During operation, the pressure within the cylinder is retained by a freely sliding piston. The steel used in the manufacture has Young's modulus of 210 GNm-². Note: There is no axial stress generated in the cylinder wall in this application. 1. Elastic Stress Distributions in a Single Cylinder a) At an operating pressure of 200 MPa, calculate using Lame's equations the radial and circumferential stresses at the cylinder bore and the outer surface. b) For the same operating pressure, calculate the maximum shear stress values at the cylinder bore and the outer surface. Hint: For axisymmetric problems, there are no shear stresses generated on the faces of a radial element in the cylinder wall. Therefore, der, and az are (also) the Principal stresses. (Please refer to Stress Transformation). c) Verify the values of the maximum shear stress calculated in 1(b) at the cylinder bore and the outer surface by drawing to a suitable scale (using computer-aided graphical construction) the Mohr's circle representations of the stresses acting on a 2-D element at each of these two locations. (You may take radial direction as the x direction)

A hydraulic cylinder with a bore radius of 100 mm and an outer radius of 200 mm has been designed to withstand a maximum internal pressure of 200 MPa in service. During operation, the pressure within the cylinder is retained by a freely sliding piston. The steel used in the manufacture has Young's modulus of 210 GNm-². Note: There is no axial stress generated in the cylinder wall in this application. 1. Elastic Stress Distributions in a Single Cylinder a) At an operating pressure of 200 MPa, calculate using Lame's equations the radial and circumferential stresses at the cylinder bore and the outer surface. b) For the same operating pressure, calculate the maximum shear stress values at the cylinder bore and the outer surface. Hint: For axisymmetric problems, there are no shear stresses generated on the faces of a radial element in the cylinder wall. Therefore, der, and az are (also) the Principal stresses. (Please refer to Stress Transformation). c) Verify the values of the maximum shear stress calculated in 1(b) at the cylinder bore and the outer surface by drawing to a suitable scale (using computer-aided graphical construction) the Mohr's circle representations of the stresses acting on a 2-D element at each of these two locations. (You may take radial direction as the x direction)

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
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A hydraulic cylinder with a bore radius of 100 mm and an outer radius of 200 mm has been designed to withstand a maximum internal pressure of 200 MPa in service. During operation, the pressure within the cylinder is retained by a freely sliding piston. The steel used in the manufacture has Young's modulus of 210 GNm-². Note: There is no axial stress generated in the cylinder wall in this application. 1. Elastic Stress Distributions in a Single Cylinder a) At an operating pressure of 200 MPa, calculate using Lame's equations the radial and circumferential stresses at the cylinder bore and the outer surface. b) For the same operating pressure, calculate the maximum shear stress values at the cylinder bore and the outer surface. Hint: For axisymmetric problems, there are no shear stresses generated on the faces of a radial element in the cylinder wall. Therefore, der, and oz are (also) the Principal stresses. (Please refer to Stress Transformation). c) Verify the values of the maximum shear stress calculated in 1(b) at the cylinder bore and the outer surface by drawing to a suitable scale (using computer-aided graphical construction) the Mohr's circle representations of the stresses acting on a 2-D element at each of these two locations. (You may take radial direction as the x direction)
Transcribed Image Text:A hydraulic cylinder with a bore radius of 100 mm and an outer radius of 200 mm has been designed to withstand a maximum internal pressure of 200 MPa in service. During operation, the pressure within the cylinder is retained by a freely sliding piston. The steel used in the manufacture has Young's modulus of 210 GNm-². Note: There is no axial stress generated in the cylinder wall in this application. 1. Elastic Stress Distributions in a Single Cylinder a) At an operating pressure of 200 MPa, calculate using Lame's equations the radial and circumferential stresses at the cylinder bore and the outer surface. b) For the same operating pressure, calculate the maximum shear stress values at the cylinder bore and the outer surface. Hint: For axisymmetric problems, there are no shear stresses generated on the faces of a radial element in the cylinder wall. Therefore, der, and oz are (also) the Principal stresses. (Please refer to Stress Transformation). c) Verify the values of the maximum shear stress calculated in 1(b) at the cylinder bore and the outer surface by drawing to a suitable scale (using computer-aided graphical construction) the Mohr's circle representations of the stresses acting on a 2-D element at each of these two locations. (You may take radial direction as the x direction)
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