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What would be the compressive stress in MPa developed in the silica glass furnace tube constrained in the way illustrated in the figure if it were heated to 1000C?

What would be the compressive stress in MPa developed in the silica glass furnace tube constrained in the way illustrated in the figure if it were heated to 1000C?

Elements Of Electromagnetics
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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What would be the compressive stress in MPa developed in the silica glass furnace tube constrained in the way illustrated in the figure if it were heated to 1000C?
**Diagram Explanation:** The image consists of three vertical columns representing a process involving thermal expansion and compression: 1. **First Column:** - Labeled \( T_1 \). - Shows a vertical rod seated on a base. - Represents the initial state of the rod at temperature \( T_1 \). 2. **Second Column:** - Labeled \( T_2 \gg T_1 \). - Shows the rod expanded due to a significant increase in temperature. - Represents the free expansion phase where temperature \( T_2 \) is much greater than \( T_1 \). 3. **Third Column:** - Labeled \( T_2 \). - Shows the rod under compression, indicated by an arrow pointing downward marked with \( \sigma \). - There is a visual representation of stress or damage on the rod, depicted by a zigzag line. - Represents the compression phase following the free expansion. **Text:** - On the left side, it states: "free expansion followed by compression." This process visually demonstrates how thermal expansion occurs when temperature increases significantly and the subsequent effects of applying compressive stress.
Transcribed Image Text:**Diagram Explanation:** The image consists of three vertical columns representing a process involving thermal expansion and compression: 1. **First Column:** - Labeled \( T_1 \). - Shows a vertical rod seated on a base. - Represents the initial state of the rod at temperature \( T_1 \). 2. **Second Column:** - Labeled \( T_2 \gg T_1 \). - Shows the rod expanded due to a significant increase in temperature. - Represents the free expansion phase where temperature \( T_2 \) is much greater than \( T_1 \). 3. **Third Column:** - Labeled \( T_2 \). - Shows the rod under compression, indicated by an arrow pointing downward marked with \( \sigma \). - There is a visual representation of stress or damage on the rod, depicted by a zigzag line. - Represents the compression phase following the free expansion. **Text:** - On the left side, it states: "free expansion followed by compression." This process visually demonstrates how thermal expansion occurs when temperature increases significantly and the subsequent effects of applying compressive stress.
The image depicts a concept related to thermal expansion and the resultant mechanical stress in materials. On the left side of the diagram: - **Illustration Description:** A vertical gray bar is constrained at both ends by brown horizontal blocks. - **Label:** "Constraint of thermal expansion" - **Temperature Notation:** \( T_1 \) On the right side of the diagram: - **Illustration Description:** A similar vertical gray bar, again constrained by brown horizontal blocks, now shows a fracture indicated by a jagged red line in the middle of the bar. - **Label:** "Fracture due to excessive compressive stress (\( \sigma \))" - **Temperature Notation:** \( T_2 \gg T_1 \) **Explanation of the Diagram:** - Initially, the material is at a temperature \( T_1 \) with constraints that prevent its expansion. - As the temperature increases significantly to \( T_2 \), the material tends to expand. - Due to the constraints, the expansion leads to excessive compressive stress, denoted by \( \sigma \), resulting in a fracture within the material. This diagram explains how materials can fail under thermal expansion when they are constrained, leading to a buildup of stress and potential structural failure.
Transcribed Image Text:The image depicts a concept related to thermal expansion and the resultant mechanical stress in materials. On the left side of the diagram: - **Illustration Description:** A vertical gray bar is constrained at both ends by brown horizontal blocks. - **Label:** "Constraint of thermal expansion" - **Temperature Notation:** \( T_1 \) On the right side of the diagram: - **Illustration Description:** A similar vertical gray bar, again constrained by brown horizontal blocks, now shows a fracture indicated by a jagged red line in the middle of the bar. - **Label:** "Fracture due to excessive compressive stress (\( \sigma \))" - **Temperature Notation:** \( T_2 \gg T_1 \) **Explanation of the Diagram:** - Initially, the material is at a temperature \( T_1 \) with constraints that prevent its expansion. - As the temperature increases significantly to \( T_2 \), the material tends to expand. - Due to the constraints, the expansion leads to excessive compressive stress, denoted by \( \sigma \), resulting in a fracture within the material. This diagram explains how materials can fail under thermal expansion when they are constrained, leading to a buildup of stress and potential structural failure.
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