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. Graphically present (sketch) the general form of variation of each of these stresses across the cylinder wall, clearly indicating the calculated values at the cylinder bore and at 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, and are (also) the Principal stresses. (Please refer to Stress Transformation). Graphically present (sketch) the general form of the maximum shear stress variation across the cylinder wall clearly indicating the values at the cylinder bore and the outer surface.
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. Graphically present (sketch) the general form of variation of each of these stresses across the cylinder wall, clearly indicating the calculated values at the cylinder bore and at 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, and are (also) the Principal stresses. (Please refer to Stress Transformation). Graphically present (sketch) the general form of the maximum shear stress variation across the cylinder wall clearly indicating the values at the cylinder bore and the outer surface.
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
Related questions
Question
![TASK
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.
Graphically present (sketch) the general form of variation of each of these
stresses across the cylinder wall, clearly indicating the calculated values at
the cylinder bore and at 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 are
(also) the Principal stresses. (Please refer to Stress Transformation).
Graphically present (sketch) the general form of the maximum shear
stress variation across the cylinder wall clearly indicating the values at the
cylinder bore and the outer surface.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a85682f-9639-4a87-a262-c17a635aa035%2F08abbf40-cf7d-454b-9c17-1fc03b3fc76c%2Fprc0knb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:TASK
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.
Graphically present (sketch) the general form of variation of each of these
stresses across the cylinder wall, clearly indicating the calculated values at
the cylinder bore and at 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 are
(also) the Principal stresses. (Please refer to Stress Transformation).
Graphically present (sketch) the general form of the maximum shear
stress variation across the cylinder wall clearly indicating the values at the
cylinder bore and the outer surface.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Can i have this written up by hand, as viewing like this is confusing to me.
Solution
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Control Systems Engineering](https://www.bartleby.com/isbn_cover_images/9781118170519/9781118170519_smallCoverImage.gif)
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
![Mechanics of Materials (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337093347/9781337093347_smallCoverImage.gif)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
![Engineering Mechanics: Statics](https://www.bartleby.com/isbn_cover_images/9781118807330/9781118807330_smallCoverImage.gif)
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY