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Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 145 MPa, Sy = 120 MPa, and Sxy = 75 MPa. Assume ß = 65°. Sxy Construct Mohr's circle for this state of stress on paper and use the results to answer the questions in the subsequent parts of this GO exercise. For this Mohr's circle, point x, which represents the state of stress on the x face of the stress element, should appear:

Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 145 MPa, Sy = 120 MPa, and Sxy = 75 MPa. Assume ß = 65°. Sxy Construct Mohr's circle for this state of stress on paper and use the results to answer the questions in the subsequent parts of this GO exercise. For this Mohr's circle, point x, which represents the state of stress on the x face of the stress element, should appear:

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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**Part 9** Use the center of the circle \( C \), the circle radius \( R \), and the angle \( \beta \) determined in Part 8 to compute: (a) the normal stress \( \sigma_n \). Give the stress value including sign if any. (b) the shear stress \( \tau_{nt} \). Give the stress value including sign if any. **Answers:** (a) \( \sigma_n = \) [Input Box] MPa (b) \( \tau_{nt} = \) [Input Box] MPa [Button: eTextbook and Media] [Button: Save for Later] Attempts: 0 of 6 used [Button: Submit Answer] --- **Part 10** Calculate the absolute maximum shear stress magnitude. **Answer:** \( \tau_{\text{abs max}} = \) [Input Box] MPa [Button: eTextbook and Media] [Button: Save for Later] Attempts: 0 of 6 used [Button: Submit Answer]
Transcribed Image Text:**Part 9** Use the center of the circle \( C \), the circle radius \( R \), and the angle \( \beta \) determined in Part 8 to compute: (a) the normal stress \( \sigma_n \). Give the stress value including sign if any. (b) the shear stress \( \tau_{nt} \). Give the stress value including sign if any. **Answers:** (a) \( \sigma_n = \) [Input Box] MPa (b) \( \tau_{nt} = \) [Input Box] MPa [Button: eTextbook and Media] [Button: Save for Later] Attempts: 0 of 6 used [Button: Submit Answer] --- **Part 10** Calculate the absolute maximum shear stress magnitude. **Answer:** \( \tau_{\text{abs max}} = \) [Input Box] MPa [Button: eTextbook and Media] [Button: Save for Later] Attempts: 0 of 6 used [Button: Submit Answer]
### Plane Stress and Mohr's Circle Consider a point in a structural member subjected to plane stress. At this point, the normal and shear stress magnitudes acting on the horizontal and vertical planes are as follows: - \( S_x = 145 \, \text{MPa} \) - \( S_y = 120 \, \text{MPa} \) - \( S_{xy} = 75 \, \text{MPa} \) Assume \( \beta = 65^\circ \). #### Diagram Explanation The image illustrates a stress element with: - \( S_x \): Horizontal normal stress acting rightward on the element. - \( S_y \): Vertical normal stress acting downward on the element. - \( S_{xy} \): Shear stress acting on the element, demonstrated with arrows in the tangential directions. The angle \( \beta \) (65°) represents the orientation of the plane in question relative to a reference plane. #### Instruction Construct Mohr's circle for this state of stress on paper. Use the circle to solve the questions in the subsequent parts of this exercise. For Mohr's circle, point \( x \) represents the stress state on the \( x \) face of the stress element and should be plotted accordingly. --- This exercise is designed to help understand the graphical representation of the stress state using Mohr's circle, a vital tool in analyzing stress transformations in materials.
Transcribed Image Text:### Plane Stress and Mohr's Circle Consider a point in a structural member subjected to plane stress. At this point, the normal and shear stress magnitudes acting on the horizontal and vertical planes are as follows: - \( S_x = 145 \, \text{MPa} \) - \( S_y = 120 \, \text{MPa} \) - \( S_{xy} = 75 \, \text{MPa} \) Assume \( \beta = 65^\circ \). #### Diagram Explanation The image illustrates a stress element with: - \( S_x \): Horizontal normal stress acting rightward on the element. - \( S_y \): Vertical normal stress acting downward on the element. - \( S_{xy} \): Shear stress acting on the element, demonstrated with arrows in the tangential directions. The angle \( \beta \) (65°) represents the orientation of the plane in question relative to a reference plane. #### Instruction Construct Mohr's circle for this state of stress on paper. Use the circle to solve the questions in the subsequent parts of this exercise. For Mohr's circle, point \( x \) represents the stress state on the \( x \) face of the stress element and should be plotted accordingly. --- This exercise is designed to help understand the graphical representation of the stress state using Mohr's circle, a vital tool in analyzing stress transformations in materials.
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