Prob. 2.2-6. The three-part axially loaded member in Fig. P2.2-6 consists of a tubular segment (1) with outer diameter (d.), = 1.25 in. and inner diameter (d), = 0.875 in., a solid circular rod segment (2) with diameter d₂ = 1.25 in., and another solid circular rod segment (3) with diameter dy = 0.875 in. The line of action of each of the three applied loads is along the centroidal axis of the member. Determine the axial stresses 0₁, 02, and o, in each of the three respective seg- ments. 1.25 in. 0.875 in. (2) 2 kips 0.875 in 3 kips 4 kips P2.2-6 (3)
Prob. 2.2-6. The three-part axially loaded member in Fig. P2.2-6 consists of a tubular segment (1) with outer diameter (d.), = 1.25 in. and inner diameter (d), = 0.875 in., a solid circular rod segment (2) with diameter d₂ = 1.25 in., and another solid circular rod segment (3) with diameter dy = 0.875 in. The line of action of each of the three applied loads is along the centroidal axis of the member. Determine the axial stresses 0₁, 02, and o, in each of the three respective seg- ments. 1.25 in. 0.875 in. (2) 2 kips 0.875 in 3 kips 4 kips P2.2-6 (3)
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 2.2-6
The three-part axially loaded member in Figure P2.2-6 consists of:
1. A tubular segment (1) with outer diameter \( (d_o)_1 = 1.25 \) inches and inner diameter \( (d_i)_1 = 0.875 \) inches.
2. A solid circular rod segment (2) with diameter \( d_2 = 1.25 \) inches.
3. Another solid circular rod segment (3) with diameter \( d_3 = 0.875 \) inches.
The line of action of each of the three applied loads is along the centroidal axis of the member. Determine the axial stresses \( \sigma_1 \), \( \sigma_2 \), and \( \sigma_3 \) in each of the three respective segments.
#### Explanation of Diagram:
- The diagram shows a three-segment axially-loaded member.
- Segment (1) is a tubular section with the inner diameter of 0.875 inches and outer diameter of 1.25 inches.
- Segment (2) is a solid circular rod with a diameter of 1.25 inches.
- Segment (3) is also a solid circular rod but with a diameter of 0.875 inches.
- The member is subjected to axial loads along its length:
- 3 kips (3,000 pounds-force) applied in the direction towards the right end of segment (1).
- 4 kips (4,000 pounds-force) applied in the direction towards the left end in segment (2).
- 2 kips (2,000 pounds-force) applied in the direction towards the right end in segment (3)
#### Calculation of Axial Stresses:
1. **For Segment (1):**
\[
\sigma_1 = \frac{P_1}{A_1} = \frac{3 \text{kips}}{\pi \left[\left(\frac{(d_o)_1}{2}\right)^2 - \left(\frac{(d_i)_1}{2}\right)^2\right]}
\]
2. **For Segment (2):**
\[
\sigma_2 = \frac{P_2}{A_2} = \frac{4 \text{kips}}{\pi \left(\frac{d_2}{2}\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93c89597-7ce2-4451-bd61-6716aa1c2201%2Fa4e35db9-662c-4240-9df5-1a544c167eda%2Fho77c6au_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 2.2-6
The three-part axially loaded member in Figure P2.2-6 consists of:
1. A tubular segment (1) with outer diameter \( (d_o)_1 = 1.25 \) inches and inner diameter \( (d_i)_1 = 0.875 \) inches.
2. A solid circular rod segment (2) with diameter \( d_2 = 1.25 \) inches.
3. Another solid circular rod segment (3) with diameter \( d_3 = 0.875 \) inches.
The line of action of each of the three applied loads is along the centroidal axis of the member. Determine the axial stresses \( \sigma_1 \), \( \sigma_2 \), and \( \sigma_3 \) in each of the three respective segments.
#### Explanation of Diagram:
- The diagram shows a three-segment axially-loaded member.
- Segment (1) is a tubular section with the inner diameter of 0.875 inches and outer diameter of 1.25 inches.
- Segment (2) is a solid circular rod with a diameter of 1.25 inches.
- Segment (3) is also a solid circular rod but with a diameter of 0.875 inches.
- The member is subjected to axial loads along its length:
- 3 kips (3,000 pounds-force) applied in the direction towards the right end of segment (1).
- 4 kips (4,000 pounds-force) applied in the direction towards the left end in segment (2).
- 2 kips (2,000 pounds-force) applied in the direction towards the right end in segment (3)
#### Calculation of Axial Stresses:
1. **For Segment (1):**
\[
\sigma_1 = \frac{P_1}{A_1} = \frac{3 \text{kips}}{\pi \left[\left(\frac{(d_o)_1}{2}\right)^2 - \left(\frac{(d_i)_1}{2}\right)^2\right]}
\]
2. **For Segment (2):**
\[
\sigma_2 = \frac{P_2}{A_2} = \frac{4 \text{kips}}{\pi \left(\frac{d_2}{2}\
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