4. A load P is applied concentrically to the bar shown. If the allowable normal stress is 76 ksi, determine the maximum allowable load P. P 3.5 in. 0.5 in. dia. hole 0.4 in. rad. 2.5 in. P
4. A load P is applied concentrically to the bar shown. If the allowable normal stress is 76 ksi, determine the maximum allowable load P. P 3.5 in. 0.5 in. dia. hole 0.4 in. rad. 2.5 in. 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 Maximum Allowable Load on a Bar with Applied Load P
#### Problem Statement:
A load \( P \) is applied concentrically to the bar shown. If the allowable normal stress is 76 ksi, determine the maximum allowable load \( P \).
#### Diagram Description:
The provided diagram displays a vertically oriented bar that is subject to a load \( P \) applied concentrically on both ends, represented by red arrows pointing towards the bar.
Key dimensions and features highlighted in the diagram include:
- The bar has an overall length, which includes specific sections of 3.5 inches and 2.5 inches.
- There is a reduction area in the bar with dimensions involving a radius of 0.4 inches at a specific spot.
- A circular hole with a diameter of 0.5 inches is present in the section labeled 3.5 inches.
The geometry involves a middle section curving inward (with the specified radius), creating a region of decreased cross-sectional area where the load is concentrated.
#### Calculations:
To determine the maximum allowable load \( P \), follow these steps:
1. **Identify the Critical Cross-Sectional Area**:
- The critical area is typically where the nominal stress will likely be the highest, often at the location where the bar has the smallest cross-section, which in this case is around the 0.5-inch diameter hole.
2. **Calculate the Cross-Sectional Area**:
- **Width Before and After Hole**: Assume the bar has a consistent width 'w'.
- **Net Cross-Sectional Area** (area after accounting for the hole):
\[
A = w \times t - (\text{Area of the hole}) \ =\ w \times t - \left( \frac{\pi \times (d/2)^2}{4} \right)
\]
where \( w \) is the width of the bar, \( t \) is the thickness, and \( d \) is the diameter of the hole (0.5 inches).
3. **Allowable Stress**:
- The normal stress \( \sigma \) is \( 76 \) ksi. Using the stress formula:
\[
\sigma = \frac{P}{A}
\]
where \( P \) is the load and \( A \) is the cross-sectional area.
4. **Determine Maximum Load \( P](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf5aa2e5-f0b0-4839-a4ef-6f98d6dc8551%2F53614186-f60e-41ce-a133-842c676ff7ec%2Fojht79ca_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Maximum Allowable Load on a Bar with Applied Load P
#### Problem Statement:
A load \( P \) is applied concentrically to the bar shown. If the allowable normal stress is 76 ksi, determine the maximum allowable load \( P \).
#### Diagram Description:
The provided diagram displays a vertically oriented bar that is subject to a load \( P \) applied concentrically on both ends, represented by red arrows pointing towards the bar.
Key dimensions and features highlighted in the diagram include:
- The bar has an overall length, which includes specific sections of 3.5 inches and 2.5 inches.
- There is a reduction area in the bar with dimensions involving a radius of 0.4 inches at a specific spot.
- A circular hole with a diameter of 0.5 inches is present in the section labeled 3.5 inches.
The geometry involves a middle section curving inward (with the specified radius), creating a region of decreased cross-sectional area where the load is concentrated.
#### Calculations:
To determine the maximum allowable load \( P \), follow these steps:
1. **Identify the Critical Cross-Sectional Area**:
- The critical area is typically where the nominal stress will likely be the highest, often at the location where the bar has the smallest cross-section, which in this case is around the 0.5-inch diameter hole.
2. **Calculate the Cross-Sectional Area**:
- **Width Before and After Hole**: Assume the bar has a consistent width 'w'.
- **Net Cross-Sectional Area** (area after accounting for the hole):
\[
A = w \times t - (\text{Area of the hole}) \ =\ w \times t - \left( \frac{\pi \times (d/2)^2}{4} \right)
\]
where \( w \) is the width of the bar, \( t \) is the thickness, and \( d \) is the diameter of the hole (0.5 inches).
3. **Allowable Stress**:
- The normal stress \( \sigma \) is \( 76 \) ksi. Using the stress formula:
\[
\sigma = \frac{P}{A}
\]
where \( P \) is the load and \( A \) is the cross-sectional area.
4. **Determine Maximum Load \( P
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