At room temperature (20°C), a 0.5-mm gap exists between the ends of the rods shown. The temperature eventually reaches a value of 139°C.Determine the normal stress in the aluminum rod. **Overview of Materials and Thermal Expansion**This diagram illustrates two different materials joined together with a gap of 0.5 mm between them. **Material Segments:**1. **Aluminum Segment (A)** - Length: 300 mm - Cross-Sectional Area (A): 2000 mm² - Elastic Modulus (E): 75 GPa - Coefficient of Thermal Expansion (α): \(23 \times 10^{-6}/°C\)2. **Stainless Steel Segment (B)** - Length: 250 mm - Cross-Sectional Area (A): 800 mm² - Elastic Modulus (E): 190 GPa - Coefficient of Thermal Expansion (α): \(17.3 \times 10^{-6}/°C\)**Key Points:**- **Expansion Gap:** The two segments are separated by a 0.5 mm gap. This gap allows for thermal expansion of the materials.- **Comparative Properties:** - Aluminum has a higher coefficient of thermal expansion compared to stainless steel, meaning it will expand more when subjected to the same temperature increase. - Stainless steel has a higher elastic modulus, indicating it is stiffer than aluminum.Understanding the differences in properties is crucial for applications where thermal expansion and material strength are factors. Adjusting for these differences ensures structural integrity and functionality in engineering designs.

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Answered: At room temperature (20°C), a 0.5-mm…

At room temperature (20°C), a 0.5-mm gap exists between the ends of the rods shown. The temperature eventually reaches a value of 139°C. Determine the normal stress in the aluminum rod.

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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Question

At room temperature (20°C), a 0.5-mm gap exists between the ends of the rods shown. The temperature eventually reaches a value of 139°C.

Determine the normal stress in the aluminum rod.

**Overview of Materials and Thermal Expansion**

This diagram illustrates two different materials joined together with a gap of 0.5 mm between them.

**Material Segments:**

1. **Aluminum Segment (A)**
- Length: 300 mm
- Cross-Sectional Area (A): 2000 mm²
- Elastic Modulus (E): 75 GPa
- Coefficient of Thermal Expansion (α): \(23 \times 10^{-6}/°C\)

2. **Stainless Steel Segment (B)**
- Length: 250 mm
- Cross-Sectional Area (A): 800 mm²
- Elastic Modulus (E): 190 GPa
- Coefficient of Thermal Expansion (α): \(17.3 \times 10^{-6}/°C\)

**Key Points:**

- **Expansion Gap:** The two segments are separated by a 0.5 mm gap. This gap allows for thermal expansion of the materials.
- **Comparative Properties:**
- Aluminum has a higher coefficient of thermal expansion compared to stainless steel, meaning it will expand more when subjected to the same temperature increase.
- Stainless steel has a higher elastic modulus, indicating it is stiffer than aluminum.

Understanding the differences in properties is crucial for applications where thermal expansion and material strength are factors. Adjusting for these differences ensures structural integrity and functionality in engineering designs.

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