Elastic Modulus of the bar?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![**Text:**
A 6 in long steel bar has a rectangular cross section that measures 0.2 in. x 3.2 in. This bar is pulled in tension with a load of 20,000 lbf and experiences an elongation of 6.0 × 10⁻³ in. Based on this information, what is the Elastic Modulus of the bar?
**Explanation:**
This problem involves calculating the Elastic Modulus (Young's Modulus) of a steel bar subjected to tensile stress. The Elastic Modulus is a constant that measures a material's ability to resist deformation under load. The bar in question has specific dimensions and is subjected to a given tensile force, resulting in a measurable elongation.
**Given Data:**
- Length of the bar: 6 in
- Cross-sectional dimensions: 0.2 in x 3.2 in
- Force applied (tensile): 20,000 lbf
- Elongation: 6.0 × 10⁻³ in
The formula to calculate the Elastic Modulus (E) is:
\[ E = \frac{\text{Stress}}{\text{Strain}} \]
Where:
- Stress \( (\sigma) \) = \( \frac{\text{Force}}{\text{Area}} \)
- Strain \( (\epsilon) \) = \( \frac{\text{Change in Length}}{\text{Original Length}} \)
You would use these equations to input the given values and solve for the Elastic Modulus.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9203a303-d0a7-4a72-8bbd-2a7378a7da0a%2F983c1af5-ef3b-4d5b-9ddb-17fb85d7c2c9%2Fwr9a8i5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Text:**
A 6 in long steel bar has a rectangular cross section that measures 0.2 in. x 3.2 in. This bar is pulled in tension with a load of 20,000 lbf and experiences an elongation of 6.0 × 10⁻³ in. Based on this information, what is the Elastic Modulus of the bar?
**Explanation:**
This problem involves calculating the Elastic Modulus (Young's Modulus) of a steel bar subjected to tensile stress. The Elastic Modulus is a constant that measures a material's ability to resist deformation under load. The bar in question has specific dimensions and is subjected to a given tensile force, resulting in a measurable elongation.
**Given Data:**
- Length of the bar: 6 in
- Cross-sectional dimensions: 0.2 in x 3.2 in
- Force applied (tensile): 20,000 lbf
- Elongation: 6.0 × 10⁻³ in
The formula to calculate the Elastic Modulus (E) is:
\[ E = \frac{\text{Stress}}{\text{Strain}} \]
Where:
- Stress \( (\sigma) \) = \( \frac{\text{Force}}{\text{Area}} \)
- Strain \( (\epsilon) \) = \( \frac{\text{Change in Length}}{\text{Original Length}} \)
You would use these equations to input the given values and solve for the Elastic Modulus.
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