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1 Eaxial Ehoop 91 92

1 Eaxial Ehoop 91 92

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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The image depicts a cylindrical object with a close-up view highlighting axial and hoop strains. ### Description: - The main feature is a cylinder, representing a pressure vessel or similar structure. - A zoomed-in section on the side of the cylinder shows two strain gauges. ### Detailed Explanation: - **Strain Gauges (`g1` and `g2`):** - `g1`: Arranged vertically, aligned with the axial direction of the cylinder (ε_axial). This gauge measures the strain along the length of the cylinder. - `g2`: Arranged horizontally, aligned with the hoop direction of the cylinder (ε_hoop). This gauge measures the strain around the circumference of the cylinder. - **Directional Arrows:** - **Axial Strain (ε_axial):** Indicated by an upward arrow, showing the direction along the length of the cylinder. - **Hoop Strain (ε_hoop):** Indicated by a rightward arrow, showing the circumferential direction. The diagram illustrates the setup for measuring the material deformation in two key directions, which is crucial for evaluating the mechanical behavior under pressure.
Transcribed Image Text:The image depicts a cylindrical object with a close-up view highlighting axial and hoop strains. ### Description: - The main feature is a cylinder, representing a pressure vessel or similar structure. - A zoomed-in section on the side of the cylinder shows two strain gauges. ### Detailed Explanation: - **Strain Gauges (`g1` and `g2`):** - `g1`: Arranged vertically, aligned with the axial direction of the cylinder (ε_axial). This gauge measures the strain along the length of the cylinder. - `g2`: Arranged horizontally, aligned with the hoop direction of the cylinder (ε_hoop). This gauge measures the strain around the circumference of the cylinder. - **Directional Arrows:** - **Axial Strain (ε_axial):** Indicated by an upward arrow, showing the direction along the length of the cylinder. - **Hoop Strain (ε_hoop):** Indicated by a rightward arrow, showing the circumferential direction. The diagram illustrates the setup for measuring the material deformation in two key directions, which is crucial for evaluating the mechanical behavior under pressure.
The pressure vessel shown has a diameter of 7.4 inches and a thickness of 0.176 inches. It is made of steel with a modulus of elasticity of 29 Mpsi. Two gauges are mounted on it, with one aligned with the axis of the vessel. A measurement of 340 microstrain is taken from the axial gauge. Use the formula for hoop stress given below for a thin-walled vessel to calculate the internal pressure of the vessel. \[ \sigma_{\text{hoop}} = \frac{P d}{2 t} \] Note: This equation relates hoop stress (\(\sigma_{\text{hoop}}\)) in the vessel wall to the internal pressure (P), diameter (d), and wall thickness (t).
Transcribed Image Text:The pressure vessel shown has a diameter of 7.4 inches and a thickness of 0.176 inches. It is made of steel with a modulus of elasticity of 29 Mpsi. Two gauges are mounted on it, with one aligned with the axis of the vessel. A measurement of 340 microstrain is taken from the axial gauge. Use the formula for hoop stress given below for a thin-walled vessel to calculate the internal pressure of the vessel. \[ \sigma_{\text{hoop}} = \frac{P d}{2 t} \] Note: This equation relates hoop stress (\(\sigma_{\text{hoop}}\)) in the vessel wall to the internal pressure (P), diameter (d), and wall thickness (t).
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