College Physics
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ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Example Shear Modulus Problem for Educational Context**
A material has a shear modulus of \( 5.0 \times 10^9 \, \text{N/m}^2 \). A shear stress of \( 1.7 \times 10^7 \, \text{N/m}^2 \) is applied to a piece of the material. What is the resulting shear strain?
In this example, the problem involves the following concepts:
- **Shear Modulus (\(G\))**: A property that describes a material's ability to resist shear deformation. It is usually denoted in Newtons per square meter (N/m²).
- **Shear Stress (\( \tau \))**: This is the force per unit area causing the deformation, also measured in Newtons per square meter (N/m²).
- **Shear Strain (\( \gamma \))**: The dimensionless measure of deformation representing the angle of deformation.
To find the resulting shear strain, use the relationship:
\[ \gamma = \frac{\tau}{G} \]
Given:
\[ G = 5.0 \times 10^9 \, \text{N/m}^2 \]
\[ \tau = 1.7 \times 10^7 \, \text{N/m}^2 \]
Solution:
\[ \gamma = \frac{1.7 \times 10^7 \, \text{N/m}^2}{5.0 \times 10^9 \, \text{N/m}^2} \]
\[ \gamma = 3.4 \times 10^{-3} \]
Thus, the shear strain \( \gamma \) is \( 3.4 \times 10^{-3} \).
This means the material experiences a shear strain of 0.0034 when subjected to the given shear stress.](https://content.bartleby.com/qna-images/question/70495d9e-d834-4a3c-919e-f23d4c42494e/79c9ff56-6f16-427a-94be-b41bea826167/3635ch_processed.png)
Transcribed Image Text:**Example Shear Modulus Problem for Educational Context**
A material has a shear modulus of \( 5.0 \times 10^9 \, \text{N/m}^2 \). A shear stress of \( 1.7 \times 10^7 \, \text{N/m}^2 \) is applied to a piece of the material. What is the resulting shear strain?
In this example, the problem involves the following concepts:
- **Shear Modulus (\(G\))**: A property that describes a material's ability to resist shear deformation. It is usually denoted in Newtons per square meter (N/m²).
- **Shear Stress (\( \tau \))**: This is the force per unit area causing the deformation, also measured in Newtons per square meter (N/m²).
- **Shear Strain (\( \gamma \))**: The dimensionless measure of deformation representing the angle of deformation.
To find the resulting shear strain, use the relationship:
\[ \gamma = \frac{\tau}{G} \]
Given:
\[ G = 5.0 \times 10^9 \, \text{N/m}^2 \]
\[ \tau = 1.7 \times 10^7 \, \text{N/m}^2 \]
Solution:
\[ \gamma = \frac{1.7 \times 10^7 \, \text{N/m}^2}{5.0 \times 10^9 \, \text{N/m}^2} \]
\[ \gamma = 3.4 \times 10^{-3} \]
Thus, the shear strain \( \gamma \) is \( 3.4 \times 10^{-3} \).
This means the material experiences a shear strain of 0.0034 when subjected to the given shear stress.
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