1. A steel rod that is 5.5 feet long, stretches 0.04 inches while under a 2-kip tensile load. a. Determine the smallest diameter rod that should be used b. Find the normal stress caused by the load
1. A steel rod that is 5.5 feet long, stretches 0.04 inches while under a 2-kip tensile load. a. Determine the smallest diameter rod that should be used b. Find the normal stress caused by the load
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
![### Problem Statement
1. A steel rod that is 5.5 feet long stretches 0.04 inches while under a 2-kip tensile load.
a. Determine the smallest diameter rod that should be used
b. Find the normal stress caused by the load
### Solution Approach
To solve these problems, we'll apply concepts from material mechanics, specifically focusing on the relationships between stress, strain, and the modulus of elasticity.
#### Definitions
- **Tensile Load**: The pulling force applied to the rod.
- **Normal Stress**: The force per unit area within materials resulting from externally applied forces.
#### Steps for Calculation
**a. Determine the smallest diameter rod that should be used:**
1. **Calculate the Strain**: Strain (ε) is defined as the change in length per unit length.
\[
\text{Strain} (\epsilon) = \frac{\Delta L}{L}
\]
Where \(\Delta L = 0.04 \text{ inches}\) and \(L = 5.5 \times 12 \text{ inches}\).
2. **Use Modulus of Elasticity**: Assuming the modulus of elasticity (E) for steel is given or known from literature.
3. **Calculate Stress**: Stress (σ) is given by Hooke's Law for elastic materials.
\[
\sigma = E \times \epsilon
\]
4. **Diameter Calculation**: From the relation of stress = force/area, rearrange to find the area and hence the diameter:
\[
A = \frac{F}{\sigma}
\]
\[
A = \pi \left(\frac{d}{2}\right)^2
\]
**b. Find the normal stress caused by the load:**
1. **Apply the formula for stress**:
\[
\sigma = \frac{P}{A}
\]
Where P is the load (2 kips converted to pounds).
2. **Calculate using previously found area**.
Through these steps, you can determine both the smallest diameter needed and the normal stress experienced by the steel rod.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57f707f5-6291-45f6-815f-d5d5911b5c88%2Fb604b5b3-4bee-4689-99e3-0dfefa086b7a%2Fgatgq5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
1. A steel rod that is 5.5 feet long stretches 0.04 inches while under a 2-kip tensile load.
a. Determine the smallest diameter rod that should be used
b. Find the normal stress caused by the load
### Solution Approach
To solve these problems, we'll apply concepts from material mechanics, specifically focusing on the relationships between stress, strain, and the modulus of elasticity.
#### Definitions
- **Tensile Load**: The pulling force applied to the rod.
- **Normal Stress**: The force per unit area within materials resulting from externally applied forces.
#### Steps for Calculation
**a. Determine the smallest diameter rod that should be used:**
1. **Calculate the Strain**: Strain (ε) is defined as the change in length per unit length.
\[
\text{Strain} (\epsilon) = \frac{\Delta L}{L}
\]
Where \(\Delta L = 0.04 \text{ inches}\) and \(L = 5.5 \times 12 \text{ inches}\).
2. **Use Modulus of Elasticity**: Assuming the modulus of elasticity (E) for steel is given or known from literature.
3. **Calculate Stress**: Stress (σ) is given by Hooke's Law for elastic materials.
\[
\sigma = E \times \epsilon
\]
4. **Diameter Calculation**: From the relation of stress = force/area, rearrange to find the area and hence the diameter:
\[
A = \frac{F}{\sigma}
\]
\[
A = \pi \left(\frac{d}{2}\right)^2
\]
**b. Find the normal stress caused by the load:**
1. **Apply the formula for stress**:
\[
\sigma = \frac{P}{A}
\]
Where P is the load (2 kips converted to pounds).
2. **Calculate using previously found area**.
Through these steps, you can determine both the smallest diameter needed and the normal stress experienced by the steel rod.
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