Problem 9.51 In (Figure 1), Tzy = 55.3 MPa. Figure 80 MPa 1 of 1 > Part A Determine the principal stresses. Specify the orientation of the element. Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval (-90°; 90°]. —| ΑΣΦ11 | vec ? 01, 02, 0p1 = MPa, MPa, ° Submit Request Answer Part B Determine the maximum in-plane shear stress and average normal stress. Specify the orientation of the element. Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval (-90°; 90°]. Π| ΑΣΦ ↓↑ vec ? Tmax=, davg=, 0s = in-plane MPa, MPa, ° Submit Request Answer 6 of 13 <) Review
Problem 9.51 In (Figure 1), Tzy = 55.3 MPa. Figure 80 MPa 1 of 1 > Part A Determine the principal stresses. Specify the orientation of the element. Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval (-90°; 90°]. —| ΑΣΦ11 | vec ? 01, 02, 0p1 = MPa, MPa, ° Submit Request Answer Part B Determine the maximum in-plane shear stress and average normal stress. Specify the orientation of the element. Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval (-90°; 90°]. Π| ΑΣΦ ↓↑ vec ? Tmax=, davg=, 0s = in-plane MPa, MPa, ° Submit Request Answer 6 of 13 <) Review
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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![### Problem 9.51
#### In (Figure 1), \(\tau_{xy} = 55.3 \, \text{MPa}\).
---
### Figure:
**Description:**
The figure depicts a square element subjected to various stresses. The following stresses are labeled:
- A vertical tensile stress of \( 80 \, \text{MPa} \) acting normally on the top face of the element.
- Directions of the stresses are indicated with arrows.
---
### Part A:
**Objective:**
Determine the principal stresses. Specify the orientation of the element.
**Instructions:**
Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval \([-90^\circ, 90^\circ]\).
**Input Format:**
\[
\sigma_1, \, \sigma_2, \, \theta_{p1} = \, \text{MPa}, \, \text{MPa}, \, ^\circ
\]
---
### Part B:
**Objective:**
Determine the maximum in-plane shear stress and average normal stress. Specify the orientation of the element.
**Instructions:**
Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval \([-90^\circ, 90^\circ]\).
**Input Format:**
\[
\tau_{\text{max in-plane}}, \, \sigma_{\text{avg}}, \, \theta_s = \, \text{MPa}, \, \text{MPa}, \, ^\circ
\]
---
### Notes:
To solve Part A and Part B:
1. **Principal Stresses and Orientation (Part A):**
- Use the given stress values, including \(\tau_{xy}\) and normal stress, to calculate \(\sigma_1\) and \(\sigma_2\) using the appropriate formulas.
- Determine the angle \(\theta_{p1}\) at which these stresses occur.
2. **Maximum In-plane Shear Stress and Average Normal Stress (Part B):**
- Use the stresses to find the maximum shear stress \(\tau_{\text{max in-plane}}\).
- Calculate the average normal stress \(\sigma_{\text{avg}}\).
- Determine the angle \(\theta_s\) for the maximum shear stress orientation.
Submit your calculations in the provided space and ensure accuracy to three](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12c0a0e9-4d98-45bb-8c42-bb6fd08d9097%2Fdcd163f6-b3c0-4b10-b805-cc3dff78b0f2%2Fyulzmks_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 9.51
#### In (Figure 1), \(\tau_{xy} = 55.3 \, \text{MPa}\).
---
### Figure:
**Description:**
The figure depicts a square element subjected to various stresses. The following stresses are labeled:
- A vertical tensile stress of \( 80 \, \text{MPa} \) acting normally on the top face of the element.
- Directions of the stresses are indicated with arrows.
---
### Part A:
**Objective:**
Determine the principal stresses. Specify the orientation of the element.
**Instructions:**
Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval \([-90^\circ, 90^\circ]\).
**Input Format:**
\[
\sigma_1, \, \sigma_2, \, \theta_{p1} = \, \text{MPa}, \, \text{MPa}, \, ^\circ
\]
---
### Part B:
**Objective:**
Determine the maximum in-plane shear stress and average normal stress. Specify the orientation of the element.
**Instructions:**
Express your answers, separated by commas, to three significant figures. Choose the angle from the half-interval \([-90^\circ, 90^\circ]\).
**Input Format:**
\[
\tau_{\text{max in-plane}}, \, \sigma_{\text{avg}}, \, \theta_s = \, \text{MPa}, \, \text{MPa}, \, ^\circ
\]
---
### Notes:
To solve Part A and Part B:
1. **Principal Stresses and Orientation (Part A):**
- Use the given stress values, including \(\tau_{xy}\) and normal stress, to calculate \(\sigma_1\) and \(\sigma_2\) using the appropriate formulas.
- Determine the angle \(\theta_{p1}\) at which these stresses occur.
2. **Maximum In-plane Shear Stress and Average Normal Stress (Part B):**
- Use the stresses to find the maximum shear stress \(\tau_{\text{max in-plane}}\).
- Calculate the average normal stress \(\sigma_{\text{avg}}\).
- Determine the angle \(\theta_s\) for the maximum shear stress orientation.
Submit your calculations in the provided space and ensure accuracy to three
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