ogeth le of 25° with the horizontal. Knowing that the allowable str 0 kPa and t = 600 kPa, determine the largest axial load P
ogeth le of 25° with the horizontal. Knowing that the allowable str 0 kPa and t = 600 kPa, determine the largest axial load P
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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![## Determining the Largest Axial Load for Glued Joint
**Problem Statement:**
Two members of uniform cross-section, 50 mm by 80 mm, are glued together along a plane \( a - a \), which forms an angle of 25° with the horizontal. Knowing that the allowable stresses for the glued joint are \( \sigma = 800 \text{ kPa} \) and \( \tau = 600 \text{ kPa} \), determine the largest axial load \( P \) that can be applied.
### Diagram Description:
The diagram provided is a side view of two rectangular members that are glued together along a plane \( a - a \), which is represented by a red line. The plane is tilted at an angle of \( 25° \) with the horizontal axis. A labelled vertical arrow indicates the direction of the applied axial load \( P \). Additionally, dimensions are noted as follows:
- The height of the members is 50 mm.
### Solution Steps:
To solve for the largest allowable axial load \( P \):
1. **Identify the given data:**
- Cross-section of the members: \( 50 mm \times 80 mm \)
- Angle of the glued plane with the horizontal: \( 25° \)
- Allowable normal stress: \( \sigma = 800 \text{ kPa} \)
- Allowable shear stress: \( \tau = 600 \text{ kPa} \)
2. **Calculate the area of the glued joint:**
The area \( A \) of the cross-section is:
\[
A = 50 mm \times 80 mm = 4000 mm^2
\]
3. **Determine the components of the stresses on the glued plane:**
- **Normal Stress Component:**
\[
\sigma_n = \frac{P \cos(25°)}{A}
\]
- **Shear Stress Component:**
\[
\tau_s = \frac{P \sin(25°)}{A}
\]
4. **Apply the allowable stress conditions:**
- For normal stress:
\[
\sigma_n \leq 800 \text{ kPa}
\]
- For shear stress:
\[
\tau_s \leq 600 \text{ kPa}
\]
5. **](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ffdf15f-05e2-48b7-8b52-eedbb16e260c%2F34ad8ee4-e4cd-44f0-84d7-a42fe897c3d8%2Fnp86e3m_processed.png&w=3840&q=75)
Transcribed Image Text:## Determining the Largest Axial Load for Glued Joint
**Problem Statement:**
Two members of uniform cross-section, 50 mm by 80 mm, are glued together along a plane \( a - a \), which forms an angle of 25° with the horizontal. Knowing that the allowable stresses for the glued joint are \( \sigma = 800 \text{ kPa} \) and \( \tau = 600 \text{ kPa} \), determine the largest axial load \( P \) that can be applied.
### Diagram Description:
The diagram provided is a side view of two rectangular members that are glued together along a plane \( a - a \), which is represented by a red line. The plane is tilted at an angle of \( 25° \) with the horizontal axis. A labelled vertical arrow indicates the direction of the applied axial load \( P \). Additionally, dimensions are noted as follows:
- The height of the members is 50 mm.
### Solution Steps:
To solve for the largest allowable axial load \( P \):
1. **Identify the given data:**
- Cross-section of the members: \( 50 mm \times 80 mm \)
- Angle of the glued plane with the horizontal: \( 25° \)
- Allowable normal stress: \( \sigma = 800 \text{ kPa} \)
- Allowable shear stress: \( \tau = 600 \text{ kPa} \)
2. **Calculate the area of the glued joint:**
The area \( A \) of the cross-section is:
\[
A = 50 mm \times 80 mm = 4000 mm^2
\]
3. **Determine the components of the stresses on the glued plane:**
- **Normal Stress Component:**
\[
\sigma_n = \frac{P \cos(25°)}{A}
\]
- **Shear Stress Component:**
\[
\tau_s = \frac{P \sin(25°)}{A}
\]
4. **Apply the allowable stress conditions:**
- For normal stress:
\[
\sigma_n \leq 800 \text{ kPa}
\]
- For shear stress:
\[
\tau_s \leq 600 \text{ kPa}
\]
5. **
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