Please work out c and d ### Clockwise Rotation of a Stress Element with No Shear StressThe 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 ExplanationThe 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 AssignmentYou can provide feedback or return to the main assignment to review additional details. ## Part C - Counterclockwise Rotation of a Stress ElementThe 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 StressThe 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 ExplanationThe 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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Answered: Please work out c and d

Engineering

Mechanical Engineering

Please work out c and d

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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Concept explainers

Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

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.

## 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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