Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Question
What will be the result shear flow of the object?
a. 207,967.94 N/m
b. 208,968.98 N/m
c. 209,978.96 N/m
d. 209,979.00 N/m
![### Educational Website Transcription
**Image Description**
The provided image is a handwritten set of calculations related to stress analysis in a mechanical component. Below is a detailed transcription and explanation of the content, including a diagram and mathematical equations.
---
**Diagram**
A diagram of a mechanical component is shown. It is a rectangular bar with a semi-circular end. The dimensions and details in the diagram are as follows:
- Height (H): 20 mm
- Length (L): 12 cm (120 mm)
- Radius (R) of the semi-circular end: 20 mm
- A line is labeled "Q" intersecting vertically in the middle of the semi-circular portion.
**Problem Details**
- **Force Applied (T):** 408 N
- **Twisting Moment (M):** 12 Nm
- **Shear Modulus (G):** 28 GPa
---
**Step-by-Step Calculation**
1. **Calculation of the Cross-Sectional Area (A)**
\[
A = H \cdot L + \pi \cdot \left(\frac{D}{2}\right)^2
\]
Given:
\[
H = 20 \, \text{mm}, \quad L = 120 \, \text{mm}, \quad \text{and} \quad D = 40 \, \text{mm}
\]
Substitution:
\[
A = (20 \times 120) + \pi \left( \frac{40}{2} \right)^2
\]
\[
A = 2400 + \pi (20)^2
\]
\[
A = 2400 + 1256.64 \approx \boxed{3657.08 \, \text{mm}^2}
\]
2. **Calculation of the Median Line Length (S)**
\[
S = 2L + \frac{\pi D}{2}
\]
Given:
\[
L = 120 \, \text{mm}, \quad \text{and} \quad D = 40 \, \text{mm}
\]
Substitution:
\[
S = 2(120) + \frac{\pi \cdot 40}{2}
\]
\[
S =](https://content.bartleby.com/qna-images/question/0ef7dced-e510-451b-b91a-a720e02ad23a/3f1a683c-e9bf-415a-a489-b69189bcf926/a7qf5la_processed.png)
Transcribed Image Text:### Educational Website Transcription
**Image Description**
The provided image is a handwritten set of calculations related to stress analysis in a mechanical component. Below is a detailed transcription and explanation of the content, including a diagram and mathematical equations.
---
**Diagram**
A diagram of a mechanical component is shown. It is a rectangular bar with a semi-circular end. The dimensions and details in the diagram are as follows:
- Height (H): 20 mm
- Length (L): 12 cm (120 mm)
- Radius (R) of the semi-circular end: 20 mm
- A line is labeled "Q" intersecting vertically in the middle of the semi-circular portion.
**Problem Details**
- **Force Applied (T):** 408 N
- **Twisting Moment (M):** 12 Nm
- **Shear Modulus (G):** 28 GPa
---
**Step-by-Step Calculation**
1. **Calculation of the Cross-Sectional Area (A)**
\[
A = H \cdot L + \pi \cdot \left(\frac{D}{2}\right)^2
\]
Given:
\[
H = 20 \, \text{mm}, \quad L = 120 \, \text{mm}, \quad \text{and} \quad D = 40 \, \text{mm}
\]
Substitution:
\[
A = (20 \times 120) + \pi \left( \frac{40}{2} \right)^2
\]
\[
A = 2400 + \pi (20)^2
\]
\[
A = 2400 + 1256.64 \approx \boxed{3657.08 \, \text{mm}^2}
\]
2. **Calculation of the Median Line Length (S)**
\[
S = 2L + \frac{\pi D}{2}
\]
Given:
\[
L = 120 \, \text{mm}, \quad \text{and} \quad D = 40 \, \text{mm}
\]
Substitution:
\[
S = 2(120) + \frac{\pi \cdot 40}{2}
\]
\[
S =
Transcribed Image Text:This diagram depicts a geometric shape consisting of a rectangle with a semicircular end. The measurements provided are as follows:
- The rectangular part has a length of 40 mm and a height of 20 mm.
- The semicircular end has a radius of 10 mm.
- Additionally, there are dotted lines indicating the internal boundary of the shape which is uniformly offset from the outer boundary.
Key measurements:
- The total horizontal length from one end of the rectangle to the curved edge of the semicircle is 80 mm.
- The internal offset from the outer boundary is 2 mm.
This diagram can be utilized to understand geometric shapes, properties of combined shapes (rectangles and semicircles), and methods to calculate areas or perimeters of such composite figures.
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