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Please work out c and d

Please work out c and d

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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Please work out c and d

### Clockwise Rotation of a Stress Element with No Shear Stress The state of stress at a point in a material is illustrated on a rectangular stress element in **Figure 6**. In this figure, the magnitudes of the stresses are given as: - \(\sigma_x = 13 \, \text{ksi}\) - \(\sigma_y = 12 \, \text{ksi}\) The task is to determine the state of stress on an element that is rotated such that the new \(+x'\) axis is \(60^\circ\) below the original \(+x\) axis. **Express your answers**, separated by commas, to three significant figures. Field for input: - \(\sigma' = \sigma' = \tau'_{xy}\) Submit your answer and click on the "Submit" button. #### Diagram Explanation The figure shows a square element with two orthogonal stress components: - \(\sigma_x\) acting left to right. - \(\sigma_y\) acting vertically (upwards and downwards). This visual representation aids in understanding how the rotational transformation affects the stress components on an inclined plane. It is crucial to apply the rotation transformation equations correctly to find the new stress components \(\sigma'_x\), \(\sigma'_y\), and \(\tau'_{xy}\). To aid in your calculations, hints and formulas are available for reference by expanding the "View Available Hint(s)" section. ### Return to Assignment You can provide feedback or return to the main assignment to review additional details.
Transcribed Image Text:### Clockwise Rotation of a Stress Element with No Shear Stress The state of stress at a point in a material is illustrated on a rectangular stress element in **Figure 6**. In this figure, the magnitudes of the stresses are given as: - \(\sigma_x = 13 \, \text{ksi}\) - \(\sigma_y = 12 \, \text{ksi}\) The task is to determine the state of stress on an element that is rotated such that the new \(+x'\) axis is \(60^\circ\) below the original \(+x\) axis. **Express your answers**, separated by commas, to three significant figures. Field for input: - \(\sigma' = \sigma' = \tau'_{xy}\) Submit your answer and click on the "Submit" button. #### Diagram Explanation The figure shows a square element with two orthogonal stress components: - \(\sigma_x\) acting left to right. - \(\sigma_y\) acting vertically (upwards and downwards). This visual representation aids in understanding how the rotational transformation affects the stress components on an inclined plane. It is crucial to apply the rotation transformation equations correctly to find the new stress components \(\sigma'_x\), \(\sigma'_y\), and \(\tau'_{xy}\). To aid in your calculations, hints and formulas are available for reference by expanding the "View Available Hint(s)" section. ### Return to Assignment You can provide feedback or return to the main assignment to review additional details.
## Part C - Counterclockwise Rotation of a Stress Element The state of stress at a point in a member is shown on the rectangular stress element in Figure 5, where the magnitudes of the stresses are: - \(\sigma_x = 16 \, \text{ksi}\) - \(\sigma_y = 29 \, \text{ksi}\) - \(\tau_{xy} = 8 \, \text{ksi}\) Determine the state of stress on an element rotated \(50^\circ\) counterclockwise from the element shown. **Express your answers**, separated by commas, to three significant figures. [View Available Hint(s)] **Input:** The input box is provided for entering the calculated values for the rotated stresses in ksi (kips per square inch). ## Part D - Clockwise Rotation of a Stress Element with No Shear Stress The state of stress at a point in a member is shown on the rectangular stress element in Figure 6, where the magnitudes of the stresses are: - \(\sigma_x = 13 \, \text{ksi}\) - \(\sigma_y = 12 \, \text{ksi}\) ### Figure Explanation The figure depicts a rectangular element under stress with labeled arrows indicating the directions and magnitudes of normal stresses (\(\sigma_x\) and \(\sigma_y\)) and shear stress (\(\tau_{xy}\)). The arrows point in conventional directions to represent tension and shear. For more detailed calculations and transformations, use appropriate stress transformation equations to find the stresses at the specified angle of rotation.
Transcribed Image Text:## Part C - Counterclockwise Rotation of a Stress Element The state of stress at a point in a member is shown on the rectangular stress element in Figure 5, where the magnitudes of the stresses are: - \(\sigma_x = 16 \, \text{ksi}\) - \(\sigma_y = 29 \, \text{ksi}\) - \(\tau_{xy} = 8 \, \text{ksi}\) Determine the state of stress on an element rotated \(50^\circ\) counterclockwise from the element shown. **Express your answers**, separated by commas, to three significant figures. [View Available Hint(s)] **Input:** The input box is provided for entering the calculated values for the rotated stresses in ksi (kips per square inch). ## Part D - Clockwise Rotation of a Stress Element with No Shear Stress The state of stress at a point in a member is shown on the rectangular stress element in Figure 6, where the magnitudes of the stresses are: - \(\sigma_x = 13 \, \text{ksi}\) - \(\sigma_y = 12 \, \text{ksi}\) ### Figure Explanation The figure depicts a rectangular element under stress with labeled arrows indicating the directions and magnitudes of normal stresses (\(\sigma_x\) and \(\sigma_y\)) and shear stress (\(\tau_{xy}\)). The arrows point in conventional directions to represent tension and shear. For more detailed calculations and transformations, use appropriate stress transformation equations to find the stresses at the specified angle of rotation.
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