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Using a modulus of rigidity of G=3.704 × 10° ksi and a modulus of elasticity of E = 10.1 × 10° psi, determine the value of Poisson's ratio for the aluminum alloy.

Using a modulus of rigidity of G=3.704 × 10° ksi and a modulus of elasticity of E = 10.1 × 10° psi, determine the value of Poisson's ratio for the aluminum alloy.

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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### Learning Goal: To determine the modulus of rigidity of a material from its shear stress-strain diagram, Poisson’s ratio, and the expanded diameter of a cylindrical shaft made of the material that is loaded under compression. The cylindrical shaft shown below is made of an aluminum alloy with a lower yield limit of 20 ksi in shear. The initial length of the specimen is given by \( L_0 = 50 \) in and the initial diameter is given by \( d_0 = 3.00 \) in. The specimen is then compressed between the two flat metal plates until it reaches a new compacted length of \( L_f = 49.95 \) in. ![Cylindrical Shaft Diagram](attachment:image.png) #### Diagram Description: The diagram shows a cylindrical shaft compressed between two flat metal plates. The shaft’s initial length \( (L_0) \), initial diameter \( (d_0) \), and compacted length \( (L_f) \) are annotated on the diagram: - \( L_0 = 50 \) in - \( d_0 = 3.00 \) in - \( L_f = 49.95 \) in This setup illustrates the physical conditions under which the material properties such as modulus of rigidity and Poisson's ratio can be experimentally determined.
Transcribed Image Text:### Learning Goal: To determine the modulus of rigidity of a material from its shear stress-strain diagram, Poisson’s ratio, and the expanded diameter of a cylindrical shaft made of the material that is loaded under compression. The cylindrical shaft shown below is made of an aluminum alloy with a lower yield limit of 20 ksi in shear. The initial length of the specimen is given by \( L_0 = 50 \) in and the initial diameter is given by \( d_0 = 3.00 \) in. The specimen is then compressed between the two flat metal plates until it reaches a new compacted length of \( L_f = 49.95 \) in. ![Cylindrical Shaft Diagram](attachment:image.png) #### Diagram Description: The diagram shows a cylindrical shaft compressed between two flat metal plates. The shaft’s initial length \( (L_0) \), initial diameter \( (d_0) \), and compacted length \( (L_f) \) are annotated on the diagram: - \( L_0 = 50 \) in - \( d_0 = 3.00 \) in - \( L_f = 49.95 \) in This setup illustrates the physical conditions under which the material properties such as modulus of rigidity and Poisson's ratio can be experimentally determined.
### Educational Exercise: Determining Poisson’s Ratio and Lateral Expansion --- #### Problem Statement Using a modulus of rigidity of \( G = 3.704 \times 10^3 \; \text{ksi} \) and a modulus of elasticity of \( E = 10.1 \times 10^6 \; \text{psi} \), determine the value of Poisson’s ratio for the aluminum alloy. ##### Instructions: - Express your answer to four significant figures. - Click "View Available Hint(s)" if you need help. ##### Input Section: ```plaintext ν = . (note .3888 was attempted but marked incorrect with 5 attempts remaining) ``` <button>Submit</button> <a href="#">Previous Answers</a> --- #### Feedback You have attempted an incorrect answer: - Current Attempt: \( \nu = 0.3888 \) - Status: Incorrect; Try Again; 5 attempts remaining --- #### Part C - Lateral Expansion of the Cylindrical Shaft due to the Axially Applied Force **Scenario Description:** The cylindrical shaft experienced a lateral expansion due to the compressive force applied to it. Determine this lateral expansion, \( \delta' \), of the radius of the cylindrical shaft. ##### Instructions: - Express your answer to three significant figures and include appropriate units. --- By following these guidelines and accurately calculating the required values, you will gain a deeper understanding of material properties such as Poisson’s ratio and how they influence structural deformations.
Transcribed Image Text:### Educational Exercise: Determining Poisson’s Ratio and Lateral Expansion --- #### Problem Statement Using a modulus of rigidity of \( G = 3.704 \times 10^3 \; \text{ksi} \) and a modulus of elasticity of \( E = 10.1 \times 10^6 \; \text{psi} \), determine the value of Poisson’s ratio for the aluminum alloy. ##### Instructions: - Express your answer to four significant figures. - Click "View Available Hint(s)" if you need help. ##### Input Section: ```plaintext ν = . (note .3888 was attempted but marked incorrect with 5 attempts remaining) ``` <button>Submit</button> <a href="#">Previous Answers</a> --- #### Feedback You have attempted an incorrect answer: - Current Attempt: \( \nu = 0.3888 \) - Status: Incorrect; Try Again; 5 attempts remaining --- #### Part C - Lateral Expansion of the Cylindrical Shaft due to the Axially Applied Force **Scenario Description:** The cylindrical shaft experienced a lateral expansion due to the compressive force applied to it. Determine this lateral expansion, \( \delta' \), of the radius of the cylindrical shaft. ##### Instructions: - Express your answer to three significant figures and include appropriate units. --- By following these guidelines and accurately calculating the required values, you will gain a deeper understanding of material properties such as Poisson’s ratio and how they influence structural deformations.
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