A solid compound bar (which is made of an aluminum segment and a bronze segment) is fixed to a rigid wall, as shown in the figure. There is a 0.02 in. gap between the left end of the bar and the wall when temperature is 200°F. If the temperature is increased to 300°F, determine: (1) the normal stress developed in the aluminum segment, and (2) the length of the bronze segment. 0.02 in. L=10 in. L=20 in. Bronze Aluminum Bronze Aluminum Note: length (L), cross sectional area (4) and Young's modulus (E) and linear coefficient of thermal expansion (a) of the two segments are given in the figure, respectively. A = 4 in? E = 25x10 psi a = 10x106 /°F A = 6 in? E = 15x10° psi a = 20x10 /°F %3D
A solid compound bar (which is made of an aluminum segment and a bronze segment) is fixed to a rigid wall, as shown in the figure. There is a 0.02 in. gap between the left end of the bar and the wall when temperature is 200°F. If the temperature is increased to 300°F, determine: (1) the normal stress developed in the aluminum segment, and (2) the length of the bronze segment. 0.02 in. L=10 in. L=20 in. Bronze Aluminum Bronze Aluminum Note: length (L), cross sectional area (4) and Young's modulus (E) and linear coefficient of thermal expansion (a) of the two segments are given in the figure, respectively. A = 4 in? E = 25x10 psi a = 10x106 /°F A = 6 in? E = 15x10° psi a = 20x10 /°F %3D
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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Transcribed Image Text:### Educational Resource: Thermal Expansion and Stress in a Compound Bar
#### Problem Statement
A solid compound bar, consisting of an aluminum segment and a bronze segment, is fixed to a rigid wall. As depicted in the figure, there is a 0.02 in. gap between the left end of the bar and the wall when the temperature is 200°F. If the temperature is increased to 300°F, determine:
1. The normal stress developed in the aluminum segment.
2. The length of the bronze segment.
#### Material Properties and Dimensions
- **Bronze Segment:**
- Cross-sectional area (A): 4 in²
- Young's modulus (E): 25×10⁶ psi
- Linear coefficient of thermal expansion (α): 10×10⁻⁶ /°F
- Original length (L): 10 in.
- **Aluminum Segment:**
- Cross-sectional area (A): 6 in²
- Young's modulus (E): 15×10⁶ psi
- Linear coefficient of thermal expansion (α): 20×10⁻⁶ /°F
- Original length (L): 20 in.
#### Diagram Explanation
The diagram displays a compound bar with two segments: bronze and aluminum. The bronze segment is on the left, fixed to a rigid wall with a visually marked 0.02 in. gap indicating thermal expansion accommodation. The aluminum segment is adjacent to the bronze and extends further to the right. The total length of the bronze segment is 10 in., and the aluminum segment is 20 in.
#### Additional Notes
The calculations of normal stress and changes in length require considering both the thermal expansion properties and the elastic modulus of the materials.
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